Speleogenesis

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Speleogenesis

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Speleogenesis
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Speleogenesis
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Klimchouk, Alexander B. (Aleksandr Borisovich)
Ukrainian Institute of Speleology and Karstology
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No. 3 (2003)

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Speleogenesis and Evolution of Karst Aquifers The Virtual Scientific Journal www.speleogenesis.info Karst processes from the beginning to the end: How can they be dated? Pavel Bosk Institute of Geology, Academy of Sciences of the Czech Republic, Rozvojov 135, 165 02 Praha 6, Czech Republic E-mail : bosak@gli.cas.cz Re-published by permission from: Gabrovšek, F. (Ed.). 2002. Evolution of karst: from prekarst to cessation. Postojna-Ljubljana, Zalozba ZRC, 155-190. Abstract Determining the beginning and the end of the life of a karst system is a substantial problem. In contrast to most of living sys tems development of a karst system can be „fro zen“ and then rejuvenated several times (pol ycyclic and polygenetic nature). The princ ipal problems may include precise definition of the beginning of karstification (e.g. incepti on in speleogenesis) and the manner of preservation of the products of karstifica tion. Karst evolution is particularly de pendent upon the time available for process e volution and on the geographical and geological conditions of the exposure of the rock. The longer the time, the higher the hydraulic gr adient and the larger the amount of solvent water entering the karst syst em, the more evolved is the ka rst. In general, stratigraphic discontinuities, i.e. intervals of nondepos ition (disconformities and unconformities), directly influence the intensity and ext ent of karstification. The higher the order of di scontinuity under study, the greater will be the problems of dating processes and eve nts. The order of unconformities influences the stratigraphy of the kars t through the amount of time available for subaerial processes t o operate. The end of karstification can also be viewed from various perspectives. The final end occurs at the moment when the ho st rock together with its karst phe nomena is completely eroded/denuded. In such cas es, nothing remains to be dated. Karst forms of individual evolution stages (cycles) can also be destroyed by erosion, denudation and abrasion without the necessity of the destruction of the whole sequence of karst rocks. Temporary and/ or final interruption of the karstification process can be caus ed by the fossilisation of karst due to loss of its hydrological functi on. Such fossilisation can be caused by metamorphism, mineral isation, marine transgressions, burial by continental deposits or volcanic products, tectonic movements, clim atic change etc. Known kars t records for the 1st and 2nd orders of stratigraphic discontinuity cover only fro m 5 to 60 % of geological time. The shorter the time available for karstification, the greater is the likelihood that karst phenomena will be preserved in the stratigraphic record. While products of short-lived karstification on shallow carbonate plat forms can be preserved by deposition during the immediately succeeding sea-level rise, products of more pronounced karstifica tion can be destroyed by a number of different geomorphic processes. The longer the duration of subaerial exposur e, the more complex are those geomorphic agents. Owing to the fact that unmetamorphosed or only slightly metamo rphosed karst rocks containing karst and caves have occurred since Archean, we can apply a wide range of geochronologic methods Most established dating methods can be utilised for direct and/or indirect dating of karst and paleoka rst. The karst/paleokarst fills are very va ried in composition, including a wide ran ge of clastic and chemogenic sediments, products of surface and subsu rface volcanism (lava, volcaniclastic materials, tephra), and de epseated processes (hydrothermal activity, etc). Stages of evolu tion can also be based on dating correlated sediments that do not fill karst voids directly. The application of individual dating met hods depends on their time ranges: the older the subject of study the more limited is the choice of method. Karst and cave fills are re latively special kinds of geologic materials. The karst enviro nment favours both the preservation of paleontological remains and their destruction. On one hand, karst is well known for its richne ss of paleontological sites, on the other hand most cave fills are comple te sterile, which is true especially for the inner-cave faci es. Another problematic feature of karst records is the reactivation of pro cesses, which can degrade a record by mixing karst fills of diff erent ages. Keywords: karst, speleogenesi s, dating methods, geochronology Principle:The time scal e for the development of karst features cannot be longer than that of the rocks on which they form. (White 1988, p. 302) 1. Introduction The beginning and the end of the life of living organisms (plants, animals) are really clear thresholds (insemination/pollination death) that can be precisely determined and described. On the other hand, to establish the beginning and the end of the life of a karst system is a substantial problem. In contrast to most of living systems, the development of karst systems can be „frozen“ (halted) and then rejuvenated, often for several times. Fossilisation and rejuvenation of karst can be viewed according to thermodynamic principles

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.2 (Eraso 1989): when the external dissipation function of the system, which represents the velocity of entropy production, reaches a minimum, the system is in a stationary state – water circulation and its chemical potential for rock dissolution has ceased – and the karstification is interrupted. The introduction of new energy (hydraulic head) to the system may cause reactivation of karstification. Polycyclicity of karst formation is a typical feature (e.g., Panoš 1964; Ford and Williams 1989). The polygenetic nature of many karsts that evolved in several different steps should be stressed, too (Ford and Williams 1989), e.g., overprint of cold karst processes on earlier deep-seated/hydrothermal products, which themselves followed meteoric early diagenesis (e.g., Bosk 1997). The dating of karst evolution poses philosophical problems, principally (1) the precise definition of the beginning of karstification, and (2) modes of preservation of any karstification products, recognising that karst rocks are more easily soluble than other rock types under specific conditions that differ with the individual lithologies (limestones, dolomites, gypsum, anhydrite, rock salt, quartzite). The role of preservation is very important because karstlands function as traps or preservers of the geologic and environmental past, especially of terrestrial (continental) history where correlative sediments are mostly missing, but also of evidences in the marine records (Hor ek and Bosk 1989). Karstification of the host rocks may start during their formation phases – diagenesis – changing the soft sediment to a consolidated rock shortly after deposition itself. Such karstification is a consequence of the emergence of part of a depocenter (sedimentary basin) and the introduction of meteoric water to the diagenetic system. The formation of a freshwater lens and a halocline zone related to the surface relief and sea-level changes is the result. The early stages of origin of dissolutional (karst) porosity by meteoric diagenesis in carbonate rocks have been described in numerous sedimentological and paleokarst studies (e.g., Longman 1980; James and Choquette 1984; Tucker and Wright 1990; James and Choquette, Eds. 1988; Wright, Esteban and Smart, Eds. 1991; Moore 1989, 2001). Some authors suppose karst to be merely the facies of meteoric diagenesis (Esteban and Klappa 1983). The evolution of a karst depends especially on the time available for processes to operate and on the geographical and geological conditions of rock exposures. The longer the time available, the higher the hydraulic gradient and the larger the quantity of solvent water entering the system, the more evolved will be the karst in all its modes of occurrences (exoand endokarst). In general, we can state that the kind of stratigraphic discontinuities, i.e. intervals of nondeposition (disconformities and unconformities; see Esteban 1991), directly influences the intensity and extent of karstification. The higher the order of discontinuity under study, the bigger are the problems to be expected when dating the processes and events. The end of karstification can also be viewed from various perspectives. An undisputed end of karstification occurs at the moment when host rock together with its karst phenomena is completely eroded/denuded, i.e. at the end of the karst cycle sensu Grund (1914; see also Cviji 1918). In such a case, nothing is left to be dated. Karst forms of individual stages of evolution (cycles) can also be destroyed by other, non-karst processes of erosion or by the complete filling of epikarst and burial of karst surfaces by impermeable sediments, without the necessity of destroying an entire sequence of karst rocks (the cycle of erosion of Davis 1899; see also Sawicki 1908, 1909). Temporary and/or final interruption of karstification can be caused by fossilisation due to the loss of the hydrological function of the karst (Bosk 1989, p. 583). The fossilisation can be caused by metamorphism, mineralisation, marine transgressions, burial by continental deposits or volcanic products, tectonic movements, climatic change etc. (see Bosk 1989). The principal question in this paper is: Can we date karst processes at all? The answer is given at the end. The paper deals mostly with karst in carbonate rocks, although the geochronologic methods and some of approaches reviewed are universal. Unconformities: the time frame The beginning and the end of karst is clearly associated with conformities, unconformities and disconformities. Esteban (1991) in an excellent review following the sequence stratigraphic approach outlined the role of nondepositional events (stratigraphic discontinuities) in karst evolution. Different ranks of stratigraphic discontinuity represent the differing time gaps in deposition that have been available for dissolution (karstification; see also Moore 1991, pp. 247-264). The stratigraphic discontinuity (gap, lacuna) represents the chronostratigraphic interval(s) missing through nondeposition (hiatus) and/or lithostratigraphic interval(s) missing through erosional truncation. Excluding conformities, Esteban (1991) proposed classification of

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.3 unconformities into (1) single (SUK) and (2) composite (CUK), both with measurable stratigraphic gaps. Conformities have no measurable stratigraphic gap and correspond to bedding planes or parasequence boundaries. The single unconformity represents a stratigraphic gap equivalent to a sequence boundary and the composite one is formed by the stacking or superposition of single unconformities (Esteban 1991, p. 92). A hierarchy of stratigraphic discontinuities was proposed, too (Fig. 1). Most (paleo)karsts are composite unconformities, representing long timespans without deposition. Stratigraphy of karst The order of unconformities influences the stratigraphy of the karst due to the time involved in subaerial processes (Table 1). There are two general systems of the karst stratigraphy based on: (1) the carbonate sedimentological/sequence stratigraphic approach (Choquette and James 1988), and (2) general karst models (Bosk, Ford and G azek 1989). Choquette and James (1988) distinguished: (1) depositional karst (2) local karst and (3) interregional karst They noted, that to distinguish the products of local and in terregional karsts may be difficult in some cases. Esteban (1991) stressed that the depositional karst of Choquette and James (1988), which is associated with parasequence boundaries (single unconformities) reflects a Caribbean model of karst development, while interregional karst resulting from complex evolution producing composite unconformities represents the general (non-Caribbean) model of karst. The Caribbean model (Esteban 1991, p. 93) is characterised by brief exposure time, unstable carbonate mineralogy, shallow burial, minor tectonics, minor deep (freshwater) phreatic zone, with primary and fabric-selective porosities predominant, restriction to tropical to semi-arid environments, diffuse recharge-diffuse flow only, affected by mixing marine zone processes but not by hydrothermal mixing. However, geothermal-driven convection of groundwater has been detected in some Caribbean-type of settings (e.g., Rougerie and Wauthy 1993). The General model (Esteban 1991, p. 93) is characterised by longer exposure time, stable mineralogy, deep burial, one or several tectonic events, an important deep phreatic zone, secondary and fracture porosities predominant, a wider range of climatic environments, conf luent recharge, pipe and confined flow, absence of mixing marine zone effects and presence of hydrothermal mixing. Local karst forms when part of a carbonate shelf is exposed, usually because of tectonism, drops in sea level or synsedimentary block tilting. Depending on the length of time involved, the effects of exposure can vary from minor to extensive with the development of exoa nd endokarst (Choquette and James 1988, pp. 16-17). Fig. 1. Hierarchy of stratigraphic discontinuities (modified after Esteban 1991).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.4 TABLE 1 Stratigraphic discontinuities, time gaps (modified after Esteban 1991) and stratigraphy of karst TIME GAP SCALE STRATIGRAPHY OF KARST STRATIGRAPHIC DISCONTINUITIES ORDER Ma Chronostratigraphy CORRESPONDING STRATIGRAPHIC UNITS James & Choquette, Eds. 1988 Bosk et al., Eds. 1989 E. UNCONFORMITY MEGAUNCONFORMITY SUPERUNCONFORMITY SET SUPERUNCONFORMITY 1 2 200 >60 30 4-12 ERATHEM SYSTEM SERIES STAGE MEGASEQUENCE SUPERSEQUENCE SET SUPERSEQUENCE INTER-REGIONAL KARST KARST PERIOD UNCONFORMITIES SINGLE COMPOSITE REGIONAL UNCONFORMITIES (sequence boundaries) 3 ~1 BIOZONE DEPOSITIONAL SEQUENCE SYNTECTONIC UNCONFORMITIES 3-4 0.0X-1 Variable LOCAL KARST BOUNDARY OF SHOLAING CYCLES 4 0.0X PARASEQUENCE CONFORMITIES BEDDING PLANE 5 0.00X Not recognisable BED DEPOSITIONAL KARST KARST PHASE Interregional karst is much more widespread, is related to major eustatic-tectonic events, and results in karst terranes that may exhibit profound erosion, a wide variety of karst features, and deep, pervasive dissolution (Choquette and James 1988, p. 17). Depositional karst forms as a natural consequence of sediment accretion at and around sea level. It is to be expected within the sed iment packages that typify carbonate platforms. It is most commonly associated with meter-scale depositional cycles (Choquette and James 1988, p. 16). Bosk, Ford and G azek (1989) distinguished between: (1) the karst phase and (2) the karst period The connection to individual types of unconformities clearly proves the temporal relationships between all types of the karst, which may be mutually correlated (Table 1). Karst period defines long-lasting times of groundwater circulation and continental weathering, which were terminated by an ensuing marine transgression. They are recognised by higher order unconformities or disconformities (= interregional karst of Choquette and James (1988). Their karst features can usually be divided into several generations ( karst phases). G azek (1989a) defined the tectonic conditions for karst periods as being induced by orogenies. Those lengthy periods are caused by the post-collisional uplift of orogens and their fringes. The periods are marked by unconformities and disconformities over broad areas and need not to be confined to individual modern continents. These long periods display diachronicity and many lesser phases. They are longest in duration and most complex at former mountain crests and become gradually shorter on the former mountain slopes and their broad fringes along adjacent continents. These periods result from major changes of plate motion patterns and they divided structural complexes corresponding to orogenic cycles (G azek 1973). A karst phase is caused by a geodynamic or major climatic change, e.g., uplift or downwarping, sealevel change, a phase of permafreezing, etc. (Bosk, Ford and G azek 1989). From the tectonic point of view, G azek (1989a) distinguished two kinds of karst phases: (1) represented as unconformities within the limited areas of one past shallow marine platform and its continental fringes, or of one continent created by the collision of two plates (= local karst of Choquette and James 1988); and (2) disconformable or paraconformable surfaces resulting from glacial-eustatic fluctuations of sea level or from local tectonic events (= depositional karst of Choquette and James 1988). Interregional (paleo)karst and products of karst periods can be linked with composite unconformities of the 1st and 2nd orders sensu Esteban (1991). Such products can be correlate d over extensive regions, e.g., post-Kaskadia and post-Variscan karstifications in North America and Europe, respectively (G azek 1989a). Local (paleo)karst and products of type 1 of karst phases ( sensu G azek 1989a) are common products during single unconformities and syntectonic unconformities, i.e. of the 3rd order.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.5 Karst forms created during the 4th and 5th order unconformities (conformities) correspond to depositional (paleo)karst and to Type 2 karst phases. Karst record The principal differences between the Caribbean karst model and the general karst model are concerned with exposure time. The former is associated with brief exposures to subaerial agents, i.e. with stratigraphic discontinuities of 3rd to 5th order with durations of 0.00X to about 1 Ma, the latter with lengthy exposures corresponding to stratigraphic discontinuities of 2nd and 1st order; i.e. with times of X00 to X02 Ma (Table 1). The karst record of 1st and 2nd order stratigraphic discontinuities on the Eastern European Platform and epi-Variscan Central European Platform in Poland was identified by G azek, D browski and Gradzi ski (1972) and G azek (1973, 1989a). It encompasses a maximum of 50 to 60 % of the geological time elapsed since deposition of the rocks (Fig. 2). Analysis of the Bohemian Massif (epi-Variscan Platform; Bosk 1987, 1997; Table. 2, Fig. 3) showed that 12 to 45 % of geological time since the regression of Paleozoic seas in the Upper Devonian/Lower Carboniferous is in such records and 55 to 88 % of time is not recorded in the preserved marine or continental sequences (Bosk 1987). These two examples of platform areas differ in the time recorded in the subsequent cover sediments. The Bohemian Massif is a relatively young body resulted from amalgamation of individual terranes during the Variscan Orogeny. Since that time uplift has prevailed over subsidence as a consequence of the tectonic stress caused by the Alpine Orogeny in its foreland. Platform sediments are rather rare there (Upper Jurassic and Upper Cretaceous regional transgressions, several minor Oligocene and Miocene transgressions covering only margins of the massif; see Fig. 3). The Polish territory is composed of slightly older elements in a different geotectonic setting, and the geologic structure is little affected by younger orogenies. Platform cover is developed more continuously and individual stratigraphic discontinuities are shorter. Therefore, there is a significant difference in the preserved record of time in the two regions, i.e. 12-45 % vs. 50-60 %. Some old cratonic units can be nearly completely without any platform cover (e.g., Scandinavian Shield), partly as a consequence of glacial isostasy. In such terranes, the time recorded can represent less than 10 %. On some recent and fossil carbonate platforms, time recorded in sediments represents only 5 to less than 10 % (Great Bahama Bank, Devonian carbonate platform on Moravia; Bosk et al. in print). It can be readily asserted that the shorter the time available for karstification, the greater is the probability of preservation of the karst phenomena in the stratigraphic record. While products of shortlived karstification on shallow carbonate platforms can be preserved by deposition during the sea-level rise following immediately after, products of more pronounced karstification may be destroyed by a variety of geomorphic processes. The longer is the duration of subaerial exposure, the more complex are those geomorphic agents. Further, individual long periods of subaerial exposure (stratigraphic discontinuities of the 1st and 2nd orders – karst periods) may coalesce, being separated only by a short interruption (e.g., marine transgression/ ingression). TABLE 2 Review of temporal data for the evolution of the B ohemian Massif since the Paleozoic regression (after Bosk 1987, 1997) Regional geological unit Duration since regression (Ma) Record preserved (Ma) Record in continental deposits (Ma) Record (%) Gap without record (%) Moldanubicum Bohemicum Saxothuringicum Brunovistulicum a. in outcrops b. covered by Carpathian Foredeep 375 375 420 320 320 45 48 52 75 100-145 45 36 40 36 2 12 13 12 23 31-45 88 87 88 77 69-55

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.6 Fig. 2. Time distribution of paleokarst phenomena and sediments in Poland (from G azek 1989b; with permission). Metamorphosed basement: 1 – silicate rocks, 2 – marble lenses ; Sedimentary rocks: 3psammites and psephites, 4 – silts, clays, marls, 5 – carbonates, 6 – deep -sea carbonate-silicate, 7 – sulphates, 8 – salts, 9 – unknown deposits (eroded), 10 – subaerial degradation; Boundaries: 11 – unconformable cove r, 12 – synsedimentary faults, 13 – synsedimentary overthrusts, 14 – supposed limits of deposition, 15 – subrosion depressions with fills (a. brown coal, b. drift deposits), 16 – poljes, 17 – sinkholes, 18 – shafts, 19 – caves, 20 – minor solution forms, 21 – syngenetic caves, 22 – karst corrosion surfaces, 23 – maximal extent of Pleistocene glaci ers, I to IV – periods of karstification.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.7 Fig. 3. Distribution of paleokarst and sediments in selected sec tions of the Bohemian Massif (simplified and schematized; modified after Bosk 1997). L ithology: 1 – conglomerates, 2 – sandstones, 3 – lithologically variable siliciclastics (redbeds, alternation of sandstones, siltstones, sandstone, etc.), 4 – shales 5 – carbonate rocks, 6 – volcanics and volcanoclastic rocks; Karst forms: 7 – caves, 8 – dolines, 9 – geological organs, 10 – karst c ones, 11 – karst inselbergs, 12 – collapse shafts, 13 – canyons, 14 – V-shaped valleys, 15 – Ushaped valleys, 16 – poljes and large karst depressions, 17 – corrosional surfaces, 18 – karren and minor solution forms, 19 – neptunian dykes, 20 – mete oric diagenetical vugs, 21 – hydrothermal karst, 22 – volcanic activity black Bohemian Massif, circle Ou ter Western Carpathi ans adjacent to the Bohemian Massif, circle diametre approximate ly covers the time-span of volcanic activity. Products of paleokarst evolution are best preserved directly beneath a cover of marine or continental sediments, i.e. under the deposits, which terminate the periods or phases of karstification. The longer the duration of the stratigraphic gap the more problematic is the precise dating of the paleokarst, unless it can be chronostratigraphically proven. Therefore, the ages of particular paleokarsts have been assigned mostly to times shortly before the termination of the stratigraphic gap (Bosk 1997). This fact can be easily illustrated in the Bohemian Massif for pre-Cenomanian age paleokarst, for pre-Callovian in the Moravian Karst or for Westphalian/Stephanian in central Bohemia (see Fig. 3). An identical situation occurs in Poland (G azek 1989b; see Fig. 2) Some processes can destroy karst features in relatively short time, leaving planated surfaces with little or no traces of previous karstification, e.g., the effect of marine transgressions. This can be illustrated from recent karst in the coastal zone of Palawan Island (Philippines) and the Lower Devonian of the Kon prusy area, Czech Republic. On Palawan, Longman and Brownlee (1980) described wave and surf action destroying or undercutting recent shore cliffs up to 30 m high that were composed of highly karstified limestones with dense networks of pinnacle karren, leaving only a flat abrasion platform with only rare relics of truncated solution fissures and sinkholes in their place. An identical situation is detected at the boundary between Kon prusy Limestones (Pragian) and Suchomasty Limestones (Dalejan, Lower Devonian) at Kon prusy. The truncation plane, which is nicely exposed in Kon prusy Caves, is smoothed by marine abrasion and shows no trace of

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.8 karst, although the limestones contain distinct traces of meteoric diagenesis and the formation of neptunian dykes correlated with the hiatus, which lasted about 5-6 Ma. Minimum time for speleogenesis The evolution of a conduit is rather complicated set of events facing numerous critical thresholds (for summary see White 1988 and Ford Williams 1989). At the present time, two phases of speleogenesis are generally accepted: (1) initiation – initial enlargement of a fracture to a critical size, and (2) enlargement – growth of a protoconduit to full conduit size (White 1988, p. 287). The initial fracture permeability and/or rock porosity has connected apertures on the order of 50 -500 m and the diameter of a dissolutional proto-conduit reaches 5-15 mm (White 1988; Ford and Williams 1989). At diameters of 0.5 to 5 cm there is a kinetic breakthrough (Dreybrodt and Gabrovšek 2000) and flow may change from laminar to turbulent (White 1988, p. 291; Ford and Williams 1989). The duration of a typical initiation phase was calculated to be about 3-5 ka (White 1988) based on experiments of Howard and Howard (1967) and calculations of Palmer (1981). They stated that the maximum dissolution rate is 0.14 m.a-1. Palmer (1991) calculated the initiation phase to minimum of 10 ka under favourable c onditions. Dreybrodt and Gabrovšek (2000) estimated the duration of the initiation (gestation) phase for realistic cases from 1 ka to 10 Ma. The time depends critically on the length and the initial width of the fracture. The enlargement phase i.e. the time in which protoconduit enlarges into full size (of 1-10 m or more) is expected to be 5 20 ka up to 100 ka in many geologic settings (White 1988). Ford and Williams (1989, p. 166) suggested that conduits can expand to diameters of 1-10 m in a few thousands of years (see also Palmer 1991), or even in a few hundreds years in high relief, wet terrains. Palmer (1991) calculated the maximum wall retreat to 0.010.1 cm/a in a typical meteoric groundwater cave. For hydrothermal caves, times on the order of 105 to 106 years are required to produce caves of traversable size (Palmer 1991, p 18). Data of Ford (1980) and Palmer (1984) suggest that an extension time of 10 to 100 ka per kilometre of the conduit may have prevailed in a majority of karst settings. White (1984) obtained an extensi on rate of 3-5 ka per kilometre. Dreybrodt and Gabrovšek (2000) estimated the velocity of enlargement of a conduit under phreatic conditions to about 200 mm/ka, so a phreatic passage of 30 m diameter can be developed within 100 ka. Of course, all those estimates are only illustrative as the velocity of speleogenesis is affected by numerous thresholds (see e.g., White 1988) and agents including geologic conditions (lithology, primary and secondary porosity), climatic conditions (temperature, precipitation, water volumes), hydrochemical conditions (concentration and kind of solvent agents), etc. Theoretical assumptions have been proven by field observations. Mylroie and Carew (1986, 1987) dated the origin of Lighthouse Cave (San Salvador Island, Bahamas) between 85 ka (cementation of eolianite host rock) and 49 ka (U-series datum from a stalagmite), i.e. 36 ka available for the cave formation along the halocline. Numerous data from North America or Ireland indicate the post-glacial origin of caves perfectly adjusted to recently deranged surface landscapes and hydrologic regimes, i.e. caves developed during the last 8-15 ka (e.g., Mylroie and Carew 1986, 1987; White 1988; Ford and Williams 1989). Determining the age of a cave is a problem because the dating is based on cave deposits (both clastic and chemogenic). In most cases we are able to date only the last few events of cave filling. Cases where the original syngenetic cave fill is preserved are rare, e.g., phreatic clays and silts, hydrothermal speleothems quasi-synchronous with phreatic speleogenesis. The dynamic character of karst results in repeating infilling and excavation of cave fills, under differing specific conditions. For example, in the Czech Karst only young Middle and Late Pleistocene deposits are preserved in the caves, with older Quaternary and pre-Quaternary fills found in some vertical corroded fissures as result of sequences of cave fills and exhumations (Loek and Sk ivnek 1965). In the Moravian Karst (Czech Republic), the situation is very similar (Kadlec et al. 2001), although the principal caves in both karst regions are at least of Early Miocene age. Complex watertable caves with pronounced flood histories offer only the age of the last cave fill episode. In Slovenia, Trhlovca and Divaška Caves (Classical Karst) contain sedimentary fill about 0.7 to 1.1 Ma old (Brunhes/Matuyama boundary and Jaramillo subchron; Bosk et al. 2000; Pruner and Bosk 2001), representing the last flood-derived fills. The system of Domica-Baradla Cave (SlovakiaHungary), although pre-Pliocene in age, is filled only by the Late Pleistocene sediments (magnetostratigraphy and U-series dating; Pruner and Bosk 2001 and yet unpublished data of Bosk/Pruner and D.C.Ford teams). So the age of the cave itself (void within the rock) is very far from obtained dates.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.9 Inception: The start of a cave? The preceding discussion has summarised the characteristic time scale for the development of a conduit. The same scale (i.e. 10 to 100 ka) is demanded for the development of a surface landform (White 1988, p. 304). Nevertheless, for caves concepts of legacy karst (V.P.Wright 1991; Wright and Smart 1994) or inception (Lowe 1999) have also been proposed that suggest that there exist prerequisities guiding at least some speleogenesis. Legacy karst according to V.P. Wright (1991) and Wright and Smart (1994) refers to dissolution occurring at the present or in the past whose distribution is controlled by an earlier (paleo)karst system. Inception according to Lowe (1999, 2000) is limited to a minor subset of all stratigraphic partings, those which dominate initially, imprinting incipient guidance for the later cave development. The weaknesses are imprinted within carbonate sequences during or soon after diagenesis, and certainly pre-tectonically. According to Waltham (2000) the inception horizon is a feature within the limestone structure that is a favourable site for the critical first phase of cave enlargement. The feature may be physical or chemical – a fracture, a mineralised fault, a shale bed containing pyrite, or a contrast in limestone chemistry. It is the initial inception stage and not the subsequent development stages, that provides the key to understanding where caves lie. The inception is a part of the initiation phase of cave formation (Lowe and Gunn 1997). It can be commented, that long ago, Ford (1971) stated that some planes or contacts are preferred locii of initiation in some caves. In that view the concept of inception, which states the same, seems to be rather complicated. Taking these concepts into account, reflecting the polycyclic and polygenetic nature of much karst, we are facing a serious problem: how to define the age of origin of caves (protoconduits)? We have two possibilities of approach: (1) to accept all previous paleokarst features as the beginning of speleogenesis (even meteoric diagenesis), or (2) to accept only the result of the last speleogenetic phase (where it is the phase that created the known cave), ignoring all previous events. The second option seems to offer some problems in specific settings. For example, the origin of the Lighthouse Cave (San Salvador Island, Bahamas; Mylroie and Carew 1986, 1987) was as a single event piece of speleogenesis in upper Pleistocene rocks (~125,000 years in age) without any legacy karst; there is no problem to place the beginning of speleogenesis after that age. On the other hand, speleogenesis in the Kon prusy region (Czech Republic; Bosk 1996, 1997, 1998) identified by the analysis of hundreds of cored boreholes in Lower Devonian limestones indicate that each succeeding phase of karstification utilised previously karstified („prepared“) space, starting with Lower/Middle Devonian diagenetic (mostly meteoric) vuggy porosity and neptunian dykes, followed by late Variscan hydrothermal karst (Carboniferous/Permian), Lower/Middle Cretaceous karstification and finally by a complex set of confined hydrothermal/c old karstification during Paleogene/Miocene time = the complex and prolonged history of polycyc lic and polygenetic karst with many interruptions in formation and many changes of geologic and climatic conditions. Where is the beginning of speleogenesis to be dated? Geochronologic methods Owing to the fact that unmetamorphosed or only slightly metamorphosed karst rocks have existed since the Proterozoic, we are facing the wide range of application of geochronologic methods. The oldest karst forms with caves and cave deposits are known from Early Proterozoic of Transvaal, South Africa (2.2 Ga; Martini 1981). Karst breccias of Archean age are known in the Canadian Shield (D.C. Ford, pers. comm. 2002). Somewhat younger are paleokarst surfaces in Canada (Belcher Island – 1.7 Ga, Ontario and Quebec – 1.4 Ga; Ford 1989). Upper Proterozic karst is also known from several locations on old cratons and platforms, e.g., in China (Zhang Shouyue 1989), Russia (Tsykin 1989) or Australia (Rowlands et al. 1980). Most of the methods outlined below can be utilised for direct and/or indirect dating of karst and paleokarst processes. Karst/paleokarst fills are highly variable in origin and composition, including a wide range of clastic and chemogenic sediments, products of surface and subsurface volcanism (lava, volcaniclastic materials, tephra), and deep-seated processes (hydrothermal activity, etc). During burial, paleokarst forms can be cut or penetrated by products of younger deep-seated processes (volcanic or hydrothermal – ore – veins). Evolutionary karst stages can be based also on dating of correlative sediments, which do not fill karst voids directly, i.e. glacial deposits, river terraces, eolian and lacustrine sediments, marine deposits and fossils. Certain dating methods cannot be used for karst events at all, especially those requiring magmatic and/or metamorphic lithologies as suitable materials. Colman and Pierce (2000) reviewed the range of geochronologic methods for the Quaternary period. Their conclusions can be adapted also for older chronologic units. The methods are grouped into six

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.10 categories: (1) sidereal (calendar or annual) methods, which determine calendar dates or count annual events; (2) isotopic methods, which measure changes in isotopic composition due to radioactive decay and/or growth; (3) radiogenic methods, which measure cumulative effects of radioactive decay, such as crystal damage and electron energy traps; (4) chemical and biological methods, which measure the results of time-dependent chemical or biological processes; (5) geomorphic methods, which measure the cumulative results of complex, interrelated, physical, chemical, and biologic processes on the landscape; and (6) correlation methods, which establish age equivalence using time-independent properties. Results of dating can be classified into four groups as follows: numerical-age calibratedage relative-age and correlated-age (Colman and Pierce 2000, p. 3). They also proposed to abandon the term absolute date in favour of numerical date The application of individual dating methods depends on their timespans. In general, we can state that the older is the subject of our study, the more limited are the methods of dating available. The nature of geologic materials to be dated represents another threshold. Not all geologic materials are suitable for numerical dating. On the other hand, most of materials are suitable to attempt correlatedage. Karst and cave fills are relatively special kinds of geologic materials. The karst environment favours both the preservation of paleontological remains and their destruction. On one hand, karst is well known for its wealth of paleontological sites (see e.g., Hor ek and Kordos 1989), on the other hand most cave fills are completely sterile, especially for the inner-cave facies. Another problematic feature of karst records is that there may be reactivation of processes, which degrades the record into an unreadable form, often mixing karst fill of different ages (collapses, redepositions, etc., e.g., Hor ek and Bosk 1989; Fig. 4). Fig. 4. A sketch of common types of karst infills and their fossil content. Note the appearance of remains of ancient fills of the inner-cave facies (12) preserved in wall niches, which may lie in the direct contact with much younger deposits (11) or those preserved in different but neighboring cavities (21 vs. 11). Collapse of sedimentary plugs and redeposition may also occur in caves (10), which may also cause serious confusion unless detailed lithological studies are done (see e.g., situation on sites 19 and 10). A – Holocene soils and related deposits, b – loess base of Holocene deposition, c – sequence of Pleistocene and earlier surface deposits, d – former infill of the inner-cave facies, frequently fluvial, e – flowstones, f – carbonate rock, g – ancient residua of strongly weathered surface or subsurf ace sediments, mosty non-calcareous (from Kordos and Hor ek 1989, with permission).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.11 Evaluation of dating results of karst records depends, as in other geologic records, on uncertainties, which vary with the geologic context, age range, and methods applied (Sowers and Noller 2000, p. 8-9). According to these authors, sources of uncertainty can be found in: (1) analytical error; (2) natural variability in sample quality and suitability; (3) geologic context errors; (4) calibration errors, and (5) violations of assumptions. The best reviews of dating methods are offered by Geyh and Schleicher (1990), Noller, Sowers and Lettis (Eds., 2000), and Bradley (1999); some useful data can be found also in Faure (2001). Numerical-ages Numerical-ages are generally subdivided to isotopic, radiometric and sidereal (Colman and Pierce 2000, p. 3). Geyh and Schleicher (1990) divided only the radiometric methods, recognising those using (1) parent/daughter isotope ratios; (2) dating based on radioactive disequilibrium of the U, Th, and Pa decay series, and (3) age determinations using radiation damage. Me thods (1) and (2) of the Geyh and Schleicher (1990) classification correspond to isotopic methods of Colman and Pierce (2000), and method (3) is the equivalent of radiometric methods. The U-Pb method was recently applied to about 92 Ma old spar fill in paleokarst in Guadelupe Mts., U.S.A. by Lundberg, Ford and Hill (2001). TABLE 3 Review of isotopic dating methods I parent/daughter isotope ratios Dating method Dating range Suitable materials 138La/138Ce Ga Basic rocks, acid rocks, pegmatites 138La/138Ba Ga REE-bearing minerals 207Pb/206Pb Ga igneous, metamorphic rocks, sulfides 176Lu/176Hf 500 Ma REE-bearing minerals 187Re/187Os 200 Ma meteorites, molybdenite, ultrabasic magnatic rocks U/Xesf U-minerals 100 Ma terrestrial rocks 1Ga U-bearing minerals; terrestrial rocks Xesf/Xen 100 Ma U-bearing minerals 40K/40Ca 60 Ma high K content, low Ca content (K/Ca > 50) lepidotite, muscovite, biotite, K-fedspars, salt minerals 147Sm/143Nd ca 50 Ma old, especially basic igneous rocks, high grade metamorphics, whole-rock and mineral samples, great resistance of the system 87Rb/87Sr 10 Ma minerals and whole-rock samples, magmatic and metamorphic rocks, sediments with limitations (authigenic clay minerals) salt minerals problems low temperature of metamorphism Krsf/Krn 10 Ma U-bearing minerals 129Xe/136Xe 5-100 Ma U-bearing minerals Common Lead Method Ma to Ga Pb-bearing minerals with low or no U content, whole-rock (igneous) 238U/206Pb 235U/207Pb 232Th/208Pb 0.1 100 Ma Uand Th-bearing minerals in igneous and metamorphic rocks (esp. zircon and monazite), U-bear ing opal and paleokarst calcite 40K/40Ar 100 ka (K-feldspars) 3-5 Ma (alunite, jarosite) K-bearing minerals from igneous, metamorphic and sedimentary rocks feldspars, mica, amphibole, glauconite, clay minerals, whole-rock materials volcanic rocks, particularly basalts 39Ar/40Ar ka-4.5 Ga K-bearing minerals from igneous and metamorphic rocks with low Ca content (mica, alunite, amphibole), sedimentary rocks suitable sometimes (glauconite, clay minerals), K-bearing sulfides Note: The table was compiled according to data in Geyh and Schleicher (1990); Noller, Sowers and Lettis (Eds. 2000); Faure (2001); White (1988), and Ford and Williams (1989). Some data were kindly provided by H. Hercman (Warsaw, Poland).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.12 Isotopic methods Isotopic methods measure changes in isotopic composition due to radioactive decay and/or growth (Colman and Pierce 2000). The methods of parent/daughter isotope ratios (Table 3) are based on radioactive decay: for each parent atom that decays, a stable daughter isotope is formed, either directly or as the end product of a decay series (Geyh and Schleicher 1990, p. 51). The number of decays depends on the quantity of parent nuclides. The decay of each radionuclide is characterised by (1) the kind(s) of radiation they emit (alpha, beta, spontaneous fission, beta-plus decay and orbital electron capture), (2) the energy(ies), and (3) the half-life (Geyh and Schleicher 1990, p. 25). Various radioactive isotopes have different half-lives ranging from several years (210Pb) to billion of years (187Re). This makes geochronological studies possible over the entire range of possible ages. The methods are based on long-lived radionuclides, therefore the application to Quaternary studies is almost excluded (Geyh and Schleicher 1990, p. 53). The method of dating with cosmogenic radionuclides (Table 4) is based on nuclear reaction of cosmic rays with gas molecules in the stratosphere and troposhere produci ng many radionuclides. Samples must have existed in closed system conditions since the beginning of the aging period, i.e. since the geochronological clock was reset to zero (Geyh and Schleicher 1990, p. 158). Most methods are based on, first, the insolation of the material and then its burial at depths too great for cosmic ray penetration (e.g. in most caves or karst deposits). The methods of radioactive disequilibrium of the U, Th, and Pa decay series are based on radioactive disequilibrium utilising the time-dependence of geochemical disturbances of the radioactive equilibrium between parent and daughter isotopes of the natural radioactive decay series of 238U, 235U and 232Th, whose end members are stable lead isotopes (Ivanovich and Harmon, Eds. 1992; Geyh and Schleicher 1990, p. 213). TABLE 4 Review of isotopic dating methods II cosmogenic radionuclides Dating method Dating range Suitable materials 129I 3-80 Ma buried organic matter and its derivatives 53Mn 1-10 Ma meteorites, ice and pelagic sediments 26Al/10Be 0.1-10 Ma ice, marine and lacustrine sediments, corals, organic matter, manganese nodules 81Kr 0.05-10 Ma groundwater and ice 26Al 0.1 5 Ma ice, pelagic sediments, manganese nodules 36Cl 0.1-3 Ma old groundwater, soils, ice, glacial materials 10Be 0.01-15 Ma carbonate-free pelagic sediments, ice, manganese nodules, quartz pebbles 10Be/36Cl X0-X00 ka ice 41 Ca 20-400 ka bones, secondary carbonates 14C 0.3-30 (55) ka organic matter, peat, humus, bones, tissues, carbonate shells, corals, travertines, speleothems, soils, groundwater, ice 39Ar 0.1-2 ka Ice 32Si 0.1-1.5 ka marine siliceous materials 3H 100 a Groundwater 3H/3He 3He 100 a Ice 22Na 1-30 a shallow groundwater Note: The table was compiled according to data in Geyh Schleicher (1990), and Noller, Sowers Lettis (Eds. 2000). Some data were kindly provi ded by H. Hercman (Warsaw, Poland).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.13 TABLE 5 Review of isotopic dating methods III radioactive disequilibrium of the U, Th, Protactinium decay series Dating method Dating range Suitable materials U/He 30 Ma non-recrystallised aragonite (marine fossils, corals) 234U/238U 50 ka – 1.5 Ma marine molluscs, corals, lacustrine and pelagic sediments, speleothems 230Th/234U 100 a 600 ka fossils, bones, travertines, spel eothems, oolite, manganese nodules, marine phosphorites, marine hydrothermal deposits 230Thexcess/232Th 230Th/238U 300 ka 1 Ma marine carbonates, manganese nodules, glass shards (volcanic ash), fish bones+teeth, lacustrine sediments with clay minerals igneous rocks phosphorite deposits 230Th excess 300 ka deep sea sediments, manganese nodules 231Pa/235U 0.1-200 ka fossils, bones, oolite, manganese nodules, marine phosphorites, less often travertines, speleothems; U-content several ppm 231Pa/230Th 0.1-200 ka U-rich marine carbonate (corals mollusc shells) 226Ra 200 ka marine sediments, ice 231Paexcess/230Thexcess 150 ka pelagic sediments 231Paexcess 150 ka pelagic sediments, corals, manganese nodules 210Pb 150 a lacustrine, fluvial and coastal marine sediments, coral, peat, ice 224Ra 228 Ra 100 a corals, Fe-Mn nodules in lakes 228Th excess/232Th 10 a High rate deposition in lakes, deltas, estuaries, along coast Ra/Rn 30 – 100 days groundwater residence time 234Th excess 100 days short-term reworking and diagenesis Note: The table was compiled according to data in Ge yh and Schleicher (1990); Noller, Sowers and Lettis (Eds. 2000); White (1988), and Ford and Williams (1989) Some data were kindly provided by H.Hercman (Warsaw, Poland). The principle of all isotopic methods is that the system has to be closed after deposition, only under such conditions can radioactive equilibrium be gradually established. It means that any disturbance occurring during the evolution of the equilibrium (starting with the closure of the system) can lead to the stopping or resetting of the radiometric clocks. The nature of the „disturbance“ depends on the sensitivity of the system, which mostly closes during the crystallisation of rock-forming minerals from magmas or solutions. The geochronometer can be stopped by heating, recrystallisation, diagenetic processes such as leaching, or corrosion leading to opening of the system or adjustment to new conditions (e.g., heating/cooling). The review of isotopic methods is given in Tables 3-5 summarising only principal data of each method (dating range and suitable materials). Radiometric methods The methods are based on the interaction of nonconducting solids with ionising alpha, beta, gamma, and cosmic radiation that changes their physical and chemical properties (e.g., deffects in crystal lattice). The changes are known as radiation damage. The age determinations are based on two types of damage: (1) electron shell phenomena, and (2) lattice phenomena (Geyh and Schleicher 1990, p. 253-255). The review of methods is given in Table 6. Fission-track method is a radiogenic method of age estimation based on accumulation of damage trails left by nuclei that are expelled during fission decays of 238U. The method can be applied to minerals with relatively high U content (e.g., apatite, zircon, sphene, volcanic glass). It can be used for direct age determination and for indirect date estimates. Tracks in apatite are partially or entirely erased by increased temperature (110-135 oC), which corresponds to a depth of 3-6 km at normal geothermal gradient. This behaviour has been utilised for dating of unroofing, as lesser heat causes reduction in fission-track ages and reduction of fission tracks (Dumitru 2000).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.14 Thermoluminescence methods are based on lattice defects in common minerals (e.g., quartz, feldspars) formed during crystallisation or from exposure to nuclear radiation. Heating of sediments causes vibration of mineral lattice and eviction of timerstored electrons from traps (Forman, Pierson and Lepper 2000). Geyh and Schleicher (1990, p. 257) cite different age ranges for different materials and there can be numerous errors resulting from different sources for the materials and their exposure (see review in Forman, Pierson and Lepper 2000). Electron spin resonance is based on lift of electrons by ionising radiation from the valence band to a conduction band. Some electrons fall into quasistable traps at “forbidden” energy levels. Traps occupied by a single electron act as paramagnetic centres, whose density can be measured by ESR (Geyh and Schleicher 1990, p.273). Numerical-ages are provided also by numerous other methods, which have been applied especially in Cenozoic geochronology (see in Noller, Sowers and Lettis, Eds. 2000). Dendrochronology is based on variations in annual growth rings of trees. There are records extending back more than 7 ka. Varve dating in laminated sediments is based on annual depositional cycles, especially in lakes. The method can be applied for sediments 18 ka old, i.e. deposited since the last glacial maximum. Sclerochronology is the measurement or estimation of ages or time intervals from the growth patterns or inclusions contained in the mineralised biogenic deposits of animals and plants. The method has been applied on corals, molluscs, fish otolith s. Historical records are useful for dating historical events (e.g., collapses, earthquakes). Calibrated-ages, relative-ages Calibrated-age methods can provide approximate numerical ages. Relative-age methods provide an age sequence and most also provide some indication of the magnitude of age differences between the members in a sequence (Colman and Pierce 2000, p. 4). The methods of this type are specially chemical and biological methods and geomorphic ones. TABLE 6 Review of radiogenic dating methods Dating method Dating range Suitable materials Fission track 20 ka-2.7 Ga Direct age -minerals, obsidian, glass (natural and man-made), tectites, petrified wood, etc.) Indirect age of cooling of some minerals uplift and erosional history Thermoluminescence 500 ka archeological objects, quartz and feldspars, flint tools, shells, bones teeth, polymineral fine-grained samples, lava (plagioclase), tectites, volcanic glas, loess, tr avertine and speleothems, fossil calcite shells Optically simulated luminescence 1-700 ka eolians, fluvial, glacial sediments, quartz, zircon Electron spin resionance (ESR and EPR) 25-50 ka to 1 Ma (?100 Ma) fossils, speleothems, travertine, caliche and vein fillings, pelagic sediments, ceramics, cooling ages of quartz, feldspars, silicates, glass, apaptite etc., crystallization age of gypsum Exo-electron method (TSEE) 100 ka bones and dentin Thermally simulated current (TSC) 1-2 Ma basalts only Alpha-recoil track 100 ka crystallisation of rock-forming minerals (esp. mica), ages of bones and dentin, low U content Note: The table was compiled according to data in Geyh Schleicher (1990); Noller, Sowers Lettis (Eds. 2000); White (1988), and Ford Williams (1989). Some data were ki ndly provided by H. Hercman (Warsaw, Poland).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.15 TABLE 7 Review of chemical and biological methods Dating method Dating range Suitable materials Amino-acid racemization < 500 ka theoretical range < 5 Ma dating fossils matter that contains amino acids:bones, teeth, foraminifera, coprolites, mulluscs, land snails, marine phosphorites, tuffs, carbonate mud and oolite, speleothems, wood Amino-acid degradation up to Miocene molluscs, foraminifers Obsidian hydration 0.01->1 Ma obsidian, ignimbrite, basaltic glass, fused shale, slag, vitrophyre, other natural glasses N and collagen dating bones < 100 ka skeletal materials F and U dating bones up to Pliocene skeletal materials Note: The table was compiled according to data in Geyh Schleicher (1990); Noller, Sowers Lettis (Eds. 2000); White (1988), and Ford Williams (1989). Chemical and biological methods are based on the assumption that certain reaction rates (e.g., diffusion, exchange, oxidation, hydration) are at least nearly constant. The age is estimated from the initial and end concentrations of suitable reactants or products (Geyh and Schleicher 1990, p. 345). The amino-acid racemization method is based on the slow conversion of amino acids after an organism has died. The amino-acid degradation method is based on the natural degradation (mainly dehydration) of the ABA acid (Geyh and Schleicher 1990, p. 355). In the obsidian hydration method glasses adsorb water on the surface, where it becomes chemically bound, forming a hydrated layer. The process is diffusion controlled, so the layer grows very slowly. The diffusion front of the hydrated layer is a sharp boundary (Geyh and Schleicher 1990, p. 362). Dating of bones by the nitrogen and collagen method is based on the rate of protein decomposition, which is influenced by numerous natural factors. The fluorine-chlorine-apatite method in combination with the collagen method was modified by Wyszoca ski-Minkowicz (1969) to relative dating of bones identifying climatic conditions of bone fossilisation. Nevertheless, the recent data indicate that the expectations are very far from the reality and the method does not function. The fluorine or uranium methods utilises the fact that skeletal remains continually take up F and U from groundwater via an irreversible ionic exchange. Both methods are very rough with low precision (Geyh and Schleicher 1990, p. 356-357 and 336-370). There are also other methods, like rock-varnish method, lichenometry, soil chemistry applied in Quaternary geochronology (see in Noller, Sowers and Lettis, Eds. 2000, p. 241-292) or chemical electron-spin-resonance dating, molecular (protein and DNA) clocks, Ca diffusion and cation-ratio methods (see in Geyh and Schleicher 1990, p. 359369). Correlated-ages Correlated-ages are based on the methods of classical geology, geochemistry, geophysics, paleontology and, archeology, e.g., paleontology and stratigraphy, paleomagnetism and magnetostratigraphy, climatic correlations and stable isotope studies, astronomical correlations, tephrochronology, archeology. Principles of these methods are summarised in various textbooks (e.g., for Quaternary in Noller, Sowers and Lettis, Eds. 2000). Combinations of methods have been often applied, e.g., paleontol ogy/stratigraphy with magnetostratigraphy or stable isotope studies or astronomical variations. Particularly useful is the combination of correlated-age methods with numerical-age determination of some marker horizons. The methodology applied to obtain correlated-age results depend on the nature of the geologic material filling the (paleo)karst and on the types of karst. The fills of exokarst landforms such as sinkholes offer more possibilities for the preservation of fossil fauna and flora than do cave interiors. Troglobitic fauna and flora are usually much too small in number and volume to be significant (Ford and Williams 1989, p. 367). Therefore, fossil remains within a cave that come from the surface (carried in by sinking rivers) or from trogloxenes (e.g., bats, some birds, some mammals) are more important. Airborne grains (pollen, volcanic ash) can only be important when favourable air-circulation patterns are developed within a cave.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.16 There are also numerous geomorphic methods applied especially to young – Cenozoic – landscape and coast evolution. Methods are in general summarised in Noller, Sowers and Lettis (Eds., 2000). Stratigraphy The duration of stratigraphic unconformity can be determined by its chronostratigraphic representation (Esteban 1991, p. 92) based on (1) minimum gap (the time interval not represented by the sedimentary record in the area, caused either by complete erosional removal or by nondeposition. The minimum gap corresponds to the difference between the youngest age of the truncated section and the oldest age of the onlapping section), and (2) maximum gap (the maximum time interval absent in the sedimentary record in the area. The maximum gap corresponds to the difference between the age of the truncated section and the age of the youngest bed of the onlapping section; Fig.5). The stratigraphic order in sedimentary sequences is governed by the law of superposition according to which under normal tectonic settings the overlying bed is younger than the underlying one. The law is valid for the majority of sedimentary sequences. However, the karst environment represents one exception. Owing to the dynamic nature of karst, its polycyclic and polygenetic character, karst records can be damaged by the simple process of redeposition. In several places in the Czech Karst (Czech Republic) during the Early Quaternary (Biharian stage), destruction of the roofs of some caves and re-opening of fossilised vertical shafts (drawdown vadose connections) caused the excavation of pre-Quaternary fossil-bearing sediments and their deposition into younger caves. In Kon prusy Caves, such re-deposited fill from a vertical chimney was washed into a block collapse in the form of pseudo-matrix (see Bosk, Hor ek and Panoš 1989). Contamination of younger deposits by re-deposited fossil-bearing sediments has been known elsewhere in caves (e.g., re-deposition of Cretaceous forams in Pleistocene deposits in the Moravian Karst). In Castleguard Cave (Canadian Rocky Mts.) there are Cretaceous pollen in basal varve layers of Wrmian age (D.C. Ford, pers. comm. 2002). Well-known are also sandwich structures, described by Osborne (1998). Younger beds are inserted into voids in older ones. Those processes degrade the record in karst conservers (Hor ek and Bosk 1989). Biostratigraphy Reinforcing the law of superposition are the use of index fossils (a widely distributed fossil that occurs only in one stratigraphic horizon), and the concept of facies (different conditions can at one and the same time create different assemblages at different sites, while almost identical assemblages may derive from different time periods). Biostratigraphy is based on vertical subdivision of geologic time according to fossil fauna and flora, which dominated at the studied time. Biostratigraphic systems may be defined either as a range zone i.e. by means of the first and the last appearance dates of suitable index forms, or as an assemblage zone if based on specific characteristics of community structure. The time interval of individual biozones depends on the general evolution velocities of living organisms, therefore intervals shorter than 0.3 Ma can scarcely be recorded by biozonation and the common resolution is 0.7 Ma (Jindrich Hladil, pers. comm. 2002). A useful correlation is given in Haq, Hardebol and Vail (1988) and Berggren et al. (1995) indicating that the resolution of individual biozones of different kinds of fossils range from more than 6.5 to about 0.3 Ma. For biostratigraphic zonation, the application of fauna/flora evolution differs for marine and terrestrial records: nevertheless the principles of zonation in marine and lacustrine sediments are very similar. Fauna and flora in the terrestrial domain are often facies dependent, influenced especially by climate. In the Cenozoic, mammalian biozones (MQ, MN) differ in duration in different regions as a consequence of migration velocities and routes (see Hor ek and Kordos 1989). There is also known “mixing” of flora of Carboniferous and Permian affinities, e.g., in Czech Upper Paleozoic limnic basins; arid facies contain Permian flora deeply below Carboniferous/Permian boundary. Fig. 5. Chronostratigraphic representation of an unconformity (modified after Esteban 1991).

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.17 Submerged caves may be characterised by peculiar biotopes containing very old elements with close ties to deep-sea fauna (e.g., recently in the Caribbean area). Caves can serve as refuges over very long time-spans, with highly conservative faunal assemblages. Such situations need to be recognised during the biostratigraphic interpretation of marine organisms found in cave facies, especially when studying transgressive tracts on karst surfaces (see also Hor ek and Kordos 1989, p. 610). Paleomagnetism and magnetostratigraphy The method is based on variations in the polar declination, inclination and intensity of the Earths magnetic field. The changes are recorded in rocks by the orientation of magnetic minerals during their deposition or crystallisation. Use of records of ancient variations as a dating tool relies on matching the curves of declination and inclination in a given deposit with established curves (standard timescales) that have been dated by independent methods (e.g., Ford and Williams 1989). The method faces numerous constraints and thresholds, especially where there is no independent dating of deposits by numerical-ages. The complete reversals (excursions) of the field occur at 105-106 years and establish the principal time units (chrons). Nevertheless, there were periods when the polarity was stable for very long times, e.g., in the Cretaceous from about 107 to about 83 Ma (see e.g., Haq, Hardebol and Vail 1988). Most normalor reverse-polarised deposits contain shortlived changes of polarity (subchrons) with durations from 100 to 102 ka. The combination of detailed micropaleontology with dense sampling for paleomagnetic analysis can result in high-resolution scales, e.g., a precision of about 5 ka on the Jurassic/Cretaceous boundary in the Tethyan realm (Houša et al. 1999) or even better for reversals in Pleistocene record combining paleomagnetism and thermoluminescence dating (Zhu and Tschu, Eds. 2001). Fig. 6. Measured magnetostratigraphic profiles in some of Slove nian (A) and Slovak caves (B) and their correlation with the magnetostratigraphic chart of Cande & Kent (1995; after Pruner & Bosk 2001). A. Slovenia: 1 – rni Kalernoti e, 2 – Kozina profile, 3 – Diva a profile, 4 – Divaška Jama, 5 –Trhlovca Cave; B. Slovakia 1-2 – Beliansk Cave, 3-7 – Demnovsk jasky a Slobody, 8-9 – Demnovsk jasky a Mieru, 10-13 – Domica Cave, 14 –Ochtinsk Aragonite Cave.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.18 The application of the method for dating clastic cave sediments has been limited by the complex conditions underground, i.e. it is often necessary to combine it with other methods offering numericalrelativeor correlate-ages. Moreover, the character of cave deposition results in numerous breaks in deposition, in which substantial timespans can be lost (Bosk et al. 2000; Pruner and Bosk 2001). The example of correlation of magnetostratigraphy results from selected caves in Slovakia and Slovenia is presented in Fig. 6. Paleomagnetic and magnetostratigraphic studies have been successfully applied also on calcite speleothems (e.g., Latham, Schwartz and Ford 1979, 1986). The secular variations are quasi-periodic changes in declination and to lesser extent also of inclination. The changes are of smaller magnitude than those described as excursions and appear to be merely regional in extent. They presumably result from changes in the non-dipole component of the magnetic field. If the changes are dated independently, they can be used in chronostratigraphic time scales (Bradley 1999). The study of magnetosusceptibility of different age periods when adjusted to numericalor correlateages represents also a useful tool for correlation or dating. The method can be used in deep-sea sediments, carbonate platforms, loess accumulations, etc. The content of ferroand paramagnetic minerals is studied. Their contents are fixed during deposition and/or early diagenesis. Magnetosusceptibility stratigraphy has been applied to some Devonian carbonate sequences (Crick et al. 1997; Hladil et al. 2002) or for some Quaternary deposits (Kadlec et al. 2001). The changes in magnetosusceptibility are believed to be influenced by climatic conditions (temperature, humidity, winds) and, maybe, by Milankovich cycles. Astronomical correlations Orbital perturbations, known also as Milankovich cycles, reflect the astronomical cycles: the precession of the equinoxes (with a periodicity of 19 and 23 ka), obliquity of the ecliptic (41 ka) and eccentricity of the orbit (100 ka). It is widely believed that the orbital-forcing, Milankovich-rhythm mechanism is responsible for continental icesheet build up and the consequent sealevel changes, which can be recorded e.g., in Caribbean-model shallow marine carbonate sequences as erosional/karst surfaces and meteoric diagenetic changes (e.g., Tucker and Wright 1990). Astronomical cycles are well preserved both in marine and continental deposits, especially in laminated sequences and profiles with cyclic patterns. Most of studies indicate cycles of about 2023 ka, 40-41 ka, 100 ka a nd 400-405 ka, which can be mutually superimposed. The detailed study of cyclicity of sediments, i.e. calibration of sedimentary cycles, or other cyclic variations in the geological record, to computed time series of the quasi-periodic variations of the Earths orbit, can result in cyclostratigraphic sequential scales. When calibrated by numerical dating (e.g., Ar/Ar single grain) they can substantially contribute to the construction of geological time scales (e.g., Neogene astrochronology in the Mediterranean; Krijgsman et al. 2002; Abdul Aziz et al. 2002) and to the improvement of previous models, e.g., the standard geomagnetic polarity timescale of Cande and Kent (1995) for the Cenozoic was age-corrected by astrochronology (Abdul Aziz et al. 2002). Stable isotopic studies Oxygen isotopic studies provide data to understa nd past environmental conditions, especially paleotemperatures. Relative abundance of oxygen 16O and 18O, the 18O/16O ratio, is compared with that in standards (PDB belemnite for solids and standard mean oceanic water – SMOW – for liquids; e.g., J.D. Wright 2000). If variations of marine stable isotope records are compared with numerical-ages and correlated-ages, a chronostratigraphic time scale can be constructed (Emiliani 1955; Shackleton and Opdyke 1973; Hays, Imbrie and Shackleton 1976; Imbrie et al. 1984). The oxygen isotope curve shows temperature changes influenced by glaciations. The time scale for the whole Quaternary has been established by this means. It is composed of 22 stages, with boundaries numerically dated by 14C, K/Ar, Ar/Ar and U series dates and compared with paleomagnetic records and orbital variations. The stable isotope time scale has been often used for karst studies (e.g., Mylroie and Carew 1986; see also Ford and Williams 1989). Correlation of cave levels and river terraces Correlation of cave levels with river terraces has been relatively common in the past. Speleogenetic models of extensive areas were based on such correlation (e.g., the Czech Karst with the Berounka River, Czech Republic; Hromas 1968). Nevertheless, most of these correlations were limited to nearby rivers rather than to entire drainage areas (White 1988, p. 318). Sawicki (1909) defined so-called evolution level i.e. connected with the piezometric surface and oriented towards the base level (see also Bgli 1981). This view allows to determined „cave levels“ even for deep phreatic or bathyphreatic systems, see Hlloch Cave System (Muotatal, Switzerland; Bgli 1966) with three main levels of bathyphreatic caves correlated with principal interglacials of the Alps.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.19 White (1988) mentioned several examples of cave levels (water table sensu Ford 1968 or epiphreatic caves sensu Jennings 1985) correlated with the entrenchment of rivers, especially of the Mammoth Cave System (U.S.A.), where cave sediments showed good agreement between magnetostratigraphy and the model for its TertiaryQuaternary evolution. Detailed analysis of factors influencing the interpretation of cave levels was summarised by Palmer (1984). Sharply defined cave levels with narrow vertical ranges (e.g., Mammoth Cave, Kentucky, USA) appear to have formed in response to intermittent episodes of rapid valley entrenchment, probably by headward erosion, followed by lengthy periods of virtually static base level. Maybe the most conspicuous example of correlation of river terraces and cave levels has been in the Demnov Cave System (Demnovsk Valley, Low Tatras Mts., Slovakia) developed by Droppa (1966) and mentioned in numerous textbooks (e.g., Bgli 1981, p. 116-119; Jennings 1985, p. 243-244). Droppa (1966) recognised 9 cave levels and correlated them to the well-developed terrace system of the Vh River. Recent detailed magnetostratigraphic (Pruner and Bosk 2001) and U-series dating of cave sediments and speleothems (Hercman et al. 1997) in the 4th and 5th cave levels ( sensu Droppa 1966) has shown that the cave fill of these passages is older than the age of correlated terrace of the Vh River. From the combination of results, the 4th cave level was dry already at about 700 ka (the base of speleothem is ca 685 ka), although previous correlation with river terraces assumed the age of speleogenesis to Mindel 2, i.e. to ca 330-500 ka (Droppa 1972). Magnetostratigraphic data from higher cave levels from both Demnovsk and parallel Jnsk Valley indicate that the age of cave fill can be correlated with the age of sediments covering river terraces of the Vh River. Caves formed under phreatic and reworked under vadose conditions are therefore older. From the longitudinal sections of the cave system it is concluded that the evolution of passages followed the four state model of Ford (1968, 1971) and Ford and Ewers (1978). Upper levels represent rather deep phreatic caves with multiple deep loops later modified by vadose entrenchment and bypassing, while the lower cave levels can be correlated with nearly ideal watertable cave with minor shallow phreatic loops. Therefore, the cave levels should be correlated with the positions of respective karst springs rather than with terrace surfaces of the same or similar elevation, which can be lowered by subsequent erosion. Conclusions The precise dating of events during karst initiation, evolution and destruction is a highly risky task. Owing to the fact that karst and caves have been developing since the Archean, nearly all known dating methods can be applied. Paleokarst features can be fossilised by infilling and/or cover with a broad variety of rocks: marine and continental chemical and siliciclastic deposits, mineral deposits produced e.g., by weathering or hydrothermal activity, products of volcanism (lava, volcaniclastics). Recent karst surfaces and accessible caves can be covered/filled by a very similar spectrum of fills. The methods determining the age of fills directly are based on physical, chemical and biological methods, plus methods of classical geology and stratigraphy. There are also indirect means of dating – correlation with correlative sediments not occurring in the karst itself. The range of age data produced by individual groups of methods substantially differs. There are geochronologic methods giving real dates – numerical-ages and ages based on correlation – calibrated (or relative)-age and correlate-age. The principal problem of dating of paleokarst features is in determining the duration of stratigraphic discontinuities. The longer are the discontinuities, the greater is the proportion of time not recorded in any correlated sediments (40 to 90 % of time can be missing in old platforms). Results of paleokarst evolution are best preserved directly beneath a cover of marine or continental sediments, i.e. under sediments, which terminated karstification periods or phases. The longer the stratigraphic gap the more problematic is precise dating of the age of the paleokarst, if it cannot be chronostratigraphically proven. Therefore, ages of paleokarsts have been associated chiefly with periods just or shortly before the termination of the stratigraphic gap. The characteristic time scale for the development of a karst surface landform or a conduit is 10 to 100 ka (White 1988, p. 304). The dating of cave initiation and evolution, i.e. the origin of the void within the bedrock is more problematic. The age of the erosional cave falls between the age of the host rock and that of the oldest dated fill. With the inception theory, the true start of speleogenesis can hardly be estimated. Many caves contain only very young fills, older ones having been excavated during repeating cave exhumations/rejuvenations caused by changes in hydraulic conditions, spring position, climate, etc. The minimum age for the cave initiation phase is estimated to be a minimum of 10 ka and cave

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.20 enlargement up to accessible diameters usually takes about 10-100 ka under fa vourable conditions. The end of karstification occurs at the moment when host-karst rock together with its karst phenomena is completely eroded/denuded the end of the karst cycle. In such case, nothing can be dated, all has been denuded. Karst forms of individual evolutionary stages (cycles) can be destroyed by erosion, denudation and abrasion, complete filling of epikarst and covering of karst surface by impermeable sediments, without the necessity of destroying the entire sequence of karst rocks (the cycle of erosion). Temporary and/or final interruption of karstification is caused by the fossilisation of karst due to loss of the hydrological function of the karst. Nevertheless, in contrast to living organisms, the development of the karst system can be „frozen“ and rejuvenated even for a multiplicity of times (polycyclic and polygenetic nature of karst). Further, the dynamic nature of karst can cause redeposition and reworking of classical stratigraphic order, making the karst record unreadable and problematic for interpretation. The final answer to the question posed in the introduction is: according to my long-lasting experience, yes we can date karst processes and events; under extremely favourable conditions we can date the products of some processes very precisely by numerical dating and/or a combination of methods, but in a majority of cases we have to handle a number of unknown factors. To solve the problem we apply complex approaches, including geopoetry, more or less successfully depending on talent of student of the karst. Acknowledgement The compilation of this review was supported by the Grant Agency of the A cademy of Sciences of the Czech Republic (Grant No. A3013201) and the Research Plan of the Institute of Geology of the Czech Republic (No. CEZ Z 03-013-912). The author especially acknowledges the contribution of Derek C. Ford (McMaster University, Canada), who carefully and critically reviewed the manuscript. Helena Hercman (Institute of Geological Sciences, Polish Academy of Sciences, Warsaw) supported special data concerning numerical dating in karst sciences. Jindrich Hladil (Institute of Geology, Academy of Sciences of the Czech Republic, Prague) contributed by some critical comments and data. References Abdul Aziz H., Krijgsman W., Hilgen F.J., Wilson D.S., Langereis C.G. and Calvo J.P. 2002. An astronomical polarity time scale for the Middle Miocene based on continental sequences. Geophysical Research Abstracts, 4 (CD ROM). Berggren W.A., Kent D.V., Swisher C.C.II and Aubry M.-P. 1995. A revised Cenozoic geochronology and chronostratigraphy. In: Geochronology time scales and global stratigraphic correlation, SEPM Special publication 54, 129-212. Bgl, A. 1966. Karstwasserflche und unterirdischer Karstniveaus. Edrkunde 20, 11-19. Bgli A. 1981. Karst hydrology and physical speleology. Berlin: Springer, 284 pp. Bosk P. 1987. Paleokarst – key to paleogeography and stratigraphy of continental periods. 3. Pracovni seminr z paleoekologie. Sbor. Konf., 2-14, Brno (in Czech) Bosk P. 1989. Problems of the origin and fossilization of karst forms. In: Bosk P., Ford D.C., G azek J. and Hor ek I. (Eds.), Paleokarst. A Systematic and Regional Review. Amsterdam-Praha:.Elsevier-Academia, 577-598. Bosk P. 1996. The evolution of karst and caves in the Kon prusy region (Bohemian Karst, Czech Republic) and paleohydrologic model. Acta Carsologica 25, 57-67. Bosk P. 1997. Paleokarst of the Bohemian Massif in the Czech Republic: an overwiev and synthesis. International Journal of Speleology 24 (1-2), 3-40. Bosk P. 1998. The evolution of karst and caves in the Kon prusy region (Bohemian Karst, Czech Republic), part II: hydrothermal paleokarst. Acta Carsologica, 27(23), 41-61. Bosk P., Ford D.C. and G azek J. 1989. Terminology. In: Bosk P., Ford D.C., G azek J. and Hor ek I. (Eds.), Paleokarst. A Systematic and Regional Review. AmsterdamPraha:.Elsevier-Academia, 25-32. Bosk P., Hor ek I. and Panoš V. 1989. Paleokarst of Czechoslovakia. In: Bosk P., Ford D.C., G azek J. and Hor ek I. (Eds.), Paleokarst. A Systematic and Regional Review. AmsterdamPraha:.Elsevier-Academia, 107-135. Bosk P., Mylroie J.E., Hladil J., Carew J.L. and Slavk L., in print. Blow Hole Cave: Unroofed cave on San Salvador Island, the Bahamas, and its importance for detection of paleokarst caves

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.23 Dreybrodt (Eds.), Speleogenesis: Evolution of Karst Aquifers. Huntsville: National Speleological Society, 184-193. Lowe D.J. and Gunn J. 1997. Carbonate speleogenesis: An inception horizon hypothesis. Acta Carsologica 26/2, 38, 457-488. Loek V. and Sk ivnek F. 1965. The significance of fissures and their fills for dating of karst processes. eskoslovensk kras 17, 7-22, Praha. Lundberg J., Ford D.C. and Hill C.A. 2001. A preliminary U-Pb date on cave spar, Big Canyon, Guadalupe Mountains, New Mexico, U.S.A. Journal of Cave and Karst Studies 62(2), 144148. Martini J.E.J. 1981. Early Proterozoic paleokarst of the Transvaal, South Africa. Proceedings 8th International Congress of Speleology, I, 4-5, Huntsville. Moore C.H. 1989. Carbonate Diagenesis and Porosity. Developments in Sedimentology 46, New York: Elsevier, 1-338. Moore C.H. 2001. Carbonate Reservoirs. Porosity Evolution and Diagenesis in a Sequence Stratigraphic Framework. Developments in Sedimentology 55, Amsterdam: Elsevier, 1-444. Mylroie J.E. and Carew J.L. 1986. Minimum duration for speleogenesis. Comunicacions 9o Congreso Internacional de Espeleologia, Vol. I, Barcelona, 249-251. Mylroie J.E. and Carew J.L. 1987. Field evidence of the minimum time for speleogenesis. National Speleological Society Bulletin 49 (2), 67-72. Noller J.S., Sowers J.M. and Lettis W.R. (Eds.). 2000. Quaternary Geochronology. Methods and Applications. Washington: American Geophysical Union, 582 pp. Osborne R.A.L. 1998. Lateral facies changes, unconformities and stratigraphic reversals: their significance for cave sediment stratigraphy. Cave Science 11 (3), 175-184. Palmer A.N. 1981. Hydrochemical controls in the origin of limestone caves. Proceedings of the Eight International Speleological Congress, Bowling Green, 120-122. Palmer A.N. 1984. Geomorphic interpretation of karst features. In: LaFleur G.A. (Ed.), Groundwater as a Geomorphic Agent. London: Allen & Unwin, 173-209. Palmer A.N. 1991. Origin and morphology of limestone caves. Geological Society of America Bulletin 103, 1-21. Panoš V. 1964. Der Urkarst in Ostflgel der Bhmishen Masse. Zeitschrift fr Geomorphologie 8 (2), 105-162. Pruner P. and Bosk P. 2001. Palaeomagnetic and magnetostratigraphic research of cave sediments: theoretical approach, and examples from Slovenia and Slovakia. Proceedings, 13th International Speleological Congress, 4th Speleological Congress of Latin America and the Carribean, 26th Brazilian Congress of Speleology, Brasilia, July 15-22, 2001 (CD ROM). Rougerie F. and Wauthy B. 1993. The endoupwelling concept: from geothermal convection to reef reconstruction. Coral Reefs 12 (1), 19-30, Berlin. Rowlands N.J., Blight P.G., Jarvis D.M. and Von Der Borch C.C. 1980. Sabkha and playa environments in late Proterozoic grabens, Willouran Ranges, Australia. Journal of Geological Society of Australia 27 (1), 55-68. Sawicki L. 1908. Skizze des slowakischen Karstes und der geographische Zyklus im Karst berhaupt. Kosmos 6-7, 395-444, Lww (in Polish). Sawicki L. 1909. Ein Beitrag zum geographischen Zyklus im Karst. Geographisches Zeitschrift 15, 185-204, Wien. Shackleton N.J. and Opdyke N.D. 1973. Oxygen isotope and paleomagne tis stratigraphy of equatorial Pacific V28-238: Oxygen isotope temperatures and ice volumes on a 105 and 106 year scale. Quaternary Research 3, 39-55. Sowers J.M. and Noller J.S. 2000. The essence of Quaternary geochronology. In: Noller J.S., Sowers J.M. and Lettis, W.R. (Eds.), Quaternary Geochronology. Methods and Applications. Washington: American Geophysical Union, 5-10. Tsykin R.A. 1989. Paleokarst of the Union of Soviet Socialist Republics. In: Bosk P., Ford D.C., G azek J. and Hor ek I. (Eds.), Paleokarst. A Systematic and Regional Review. AmsterdamPraha:.Elsevier-Academia, 2253-295. Tucker M.E. and Wright V.P. 1990. Carbonate Sedimentology. Oxford: Blackwell, 482 pp. Waltham T. 2000. Caves is where you find “em”. Caves & Caving, 26-29. White W.B. 1984. Rate processes: Chemical kinetics and karst landforms development. In: LaFleur G.A. (Ed.), Groundwater as a Geomorphic Agent. London: Allen & Unwin, 227-248. White W.B. 1988. Geomorphology and Hydrology of Karst Terrains. New York: Oxford University Press, 464 pp.

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P.Bosk / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.24 Wright J.D. 2000. Global climate change in marine stable isotope records. In: Noller J.S., Sowers J.M. and Lettis, W.R. (Eds.), Quaternary Geochronology. Methods and Applications. Washington: American Geophysical Union, 427433. Wright V.P. 1991. Palaeokarst types, recognition, controls and assocations. In: Wright V.P., Esteban M. and Smart P.L. (Eds.), Palaeokarsts and Palaeokarstic Reservoirs, Reading: P.R.I.S. Occassional Publication Series 2, 56-88. Wright V.P., Esteban M. and Smart P.L. (Eds.). 1991. Palaeokarsts and Pa laeokarstic Reservoirs. Reading: P.R.I.S. Occassional Publication Series 2, 1-158. Wright V.P. and Smart P.L. 1994. Paleokarst (Dissolution Diageneis): Its Occurrence and Hydrocarbon Exploration Significance. In: Wolf K.H. and Chilingarian G.V. (Eds.), Diagenesis, IV, Developments in Sedimentology 51, Amsterdam: Elsevier, 489-502. Wyszocza ski-Minkowicz T. 1969. An attempt at relative age determination of fossil bones by fluorine-chlorine-apatite method. Studia Geologica Polonica, XXVIII, 1-79, Warszawa. Zhang Shouyue 1989. Paleokarst of China. In: Bosk P., Ford D.C., G azek J. and Hor ek I. (Eds.), Paleokarst. A Systematic and Regional Review. Amsterdam-Praha:.Elsevier-Academia, 297-311. Zhu R.X. and Tschu K.K. (Eds.) 2001. Studies in Paleomagnetism and Reve rsals of Geomagnetic Field in China. Beijing: Sciences Press, 168 pp.



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Speleogenesis and Evolution of Karst Aquifers The Virtual Scientific Journal www.speleogenesis.info Karst Landscape Evolution Georg Kaufmann Institute of Geophysics, Un iversity of Gttingen, Herzberger Landstrasse 180,37075 Gttingen, Germany E-mail : gkaufman@uni-geophys.gwdg.de Re-published by permission from: Gabrovšek, F. (Ed.). 2002. Evolution of karst: from prekarst to cessation. Postojna-Ljubljana, Zalozba ZRC, 243-258. Abstract We present results of a numerical study of karst denudati on on limestone plateaux. The la ndscape evolution model used incorporates not only long-range fluvial pro cesses and short-range hill-sl ope processes, but also large-scale chemical dissolut ion of limestone surfaces. The relative efficiencies of fluvial and chem ical processes are of equal importance to the landscape evolut ion of a plateau dropping to sea level along an escarpment. While fluvial pr ocesses have an impact confined to river channels, the kar st denudation process is more uniform, removing material also from the plateau surface. The combined effect of both processes resu lts in a landscape evolution almost twice as effective as th e purely erosional evolution of an insoluble landscape. Keywords: Landscape evolution, disso lution kinetics, denudation, karst Introduction Landscape evolution is governed by a balance of forces; on the one hand, vertical tectonic movements resulting from the interaction between lithospheric plates, and on the other, erosion and deposition controlled by a range of processes whose relative importance depend on local climatic conditions, vegetation, and rock type. During the last decade, numerical models simulating landscape evolution from a large-scale, long-term perspective have become increasingly sophisticated. Most surface process models incorporate the effects of short-range processes such as local hillslope diffusion and longrange processes such as fluvial transport (Willgoose et al. 1991, Beaumont et al. 1992, Chase 1992, Howard et al. 1994, Tucker et al. 1994, Kooi et al. 1994, Braun et al. 1997), and they have been applied to the evolution of rifted margins, regions of continental convergence and mountain building. While these models describe landscape evolution satisfactorily in temperate climates and insoluble geological settings, other surface processes of regional importance have so far been largely neglected. For example, glacial erosion has been regarded as an important process in midto highlatitude active orogenic regions, which have experienced repeated large-scale glaciations during the last two million years. Recently, Braun et al. (1999) have incorporated a first-order parameterization of ice-bedrock interaction into a large-scale fluvial erosion model. They showed how the interplay between the two processes leads to enhanced rates of surface erosion in mountaineous areas affected by periodic climatic fluctuations. In the present paper, another process governing landscape evolution in soluble rocks is considered. As surface runoff enriched in carbon dioxide becomes weakly agressive and is able to remove calcite by chemical dissolution, typical karst landscapes evolve, forming steep-walled valleys, enclosed depressions, and, finally, subsurface drainage through caves (e.g. Jennings 1985). While the evolution of subsurface drainage in a karst landscape had been successfully modeled in the past (e.g. Groves et al. 1994, Howard et al. 1995, Clemens et al. 1997, Siemers et al. 1998, Kaufmann et al. 1999, Kaufmann et al. 2000), no attempt has been made so far to parameterize chemical dissolution on the surface of a karst landscape, which is termed karst denuda tion (e.g. Jennings 1985).

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.2 These two processes, subsurface drainage through evolving cave systems and surficial karst denudation, are coupled in that the surface discharge on a mature karst landscape quickly disappears underground and drainage is dominated by subsurface flow. As a consequence, valleys become dry, streams disappear at sinks and closed depressions, and surface processes driven by surface flow become less efficient. Herein, attention is focussed on the karst denudation process, while the effect of subsurface drainage and chemical enlargement of fractures within the rock is disregarded. Such a simplified model can thus be regarded as a first step in quantifying the evolution of a soluble landscape. A karst landscape is often characterized by steep and prominent gorges, which separate limestone plateaux. Compared to insoluble landscapes, gorges occur more frequently and are more rugged. Examples include the Vico s Gorge in Greece, the Verdon Gorge in southern France, the Strickland Gorge in New Guinea, which are very deep and steep and all formed in relatively young mountain ranges, but also the Geikie, Windjana, and Galeru Gorges in Western Australia and the Tarn, Lot, and Dourbie Gorges in the Grandes Cau sses of southern France, which are prominent features in lower relief landscapes. In all cases, the plateaux dissected by these steep-walled gorges are denudated more evenly. Measurements of long-term denudation rates on soluble landscapes are often based on the height of pedestals above the surrounding limestone surface. These pedestals are remnants of an older surface, protected by erratic boulders from the last glaciation. It is commonly assumed that the height of the pedestals is a measure of surface lowering since the retreat of the ice at the end of the last glaciation. Jennings (1985) has reviewed literature data on pedestals, and reports denudation rates between 15 and 40 mm/kyr. Short-term denudation rates can be measured by micro-erosion meters (Trudgill et al. 1981). Forti (1984) reports denudation rates from the Triestine karst in Italy, ranging from 20 mm/kyr in regions of relatively low (1442 mm/yr) precipitation, to 30 mm/kyr near Mount Canin characterized by a much higher (2800 mm/yr) precipitation rate. Additional short-term de nudation rates reported by Jennings (1985) are around 5-17 mm/kyr on bare rock surfaces. In the present paper, a simple parameterization of solutional processes is developed and incorporated into an existing surface process model (CASCADE). A series of numerical experiments is then performed in which an originally steep escarpment flanking a flat, high-elevation plateau is allowed to evolve through time. In these experiments, the parameters controlling the efficiency of each process (fluvial incision, hillslope diffusion, and chemical dissolution) are varied to investigate their relative influence on the form of the landscape and the rate at which it evolves. TABLE 1 Reference model parameters Parameter Decription Unit Value i! Net precipitation [mm yr-1] 400 D" Diffusion constant [m2 yr-1] 0.2 i R! Erosion constant [m yr-1] 0.01 SL Alluvium length scale [km] 10 BL Bedrock length scale [km] 100 # Calcite density [kg m-3] 2700 CT Temperature [oC] 10 2COp CO2 pressure [atm] 10-3.5/10-2.5 i C! Dissolution constant [m yr-1] 0.007/0.014 Geomorphic model Large-scale landscape evolution on tectonic timescales is controlled by a number of processes. Short-range hillslope processes, such as weathering, slope wash, mass wasting, and soil creep, redistribute mass over short distances, while long-range flow processes, such as fluvial erosion and sedimentation, and karst denudation, control landscape evolution over long distances. Other processes such as glacial erosion and landsliding are not discussed in the present formulation. The mathematical approach for both shortand long-range processes used in model simulations is outlined below.

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.3 Hillslope processes Hillslope processes are modelled by means of linear downslope diffusion (e.g. Kooi et al. 1994, Braun et al. 1997), i D diffusion ih dt dh2$ % & ( ) + (1) which assumes that the rate of change of topographyih at nodeiis proportional to the second spatial derivative ofih, D" is assumed constant and is termed diffusivity. The topography ih is the sum of bedrock height and sediment cover. Following Beaumont et al. (1992), the diffusivity can be expressed as D D Dh u % ", where Dh is the thickness of a regolith layer and Du is the transport velocity of the eroded material. This implies that D" is a function of both the lithology (small D" for resistant bedrock, larger D" for detachable sediments) and climate (increased weathering increases the thickness of the regolith layer). Thus, short-range processes are important on steep landscapes with strong curvature; they reduce the high-frequency content of the topography spectrum. As a consequence, topography is smoothed, slopes decline, drainage divides are eroded and move towards the area of lower slope gradients (Kooi et al. 1994). Fluvial processes Erosion and deposition of sediments and bedrock is modeled as a channel-flow process. The discharge iq (in m3 s-1) at node i is defined as the sum of upstream discharge u iq and local discharge i i l iA q %, i i u i iA q q %, (2) where i i ie p % is the net precipitation (precipitationip minus evapotranspiration ie, in m s-1), Ai is the surface area around node i and u iq is the amount of surface runoff already collected in the upstream catchment of node i The maximum carrying capacity of the channel between node i and lower neighbour j is given as (e.g. Beaumont et al. 1992, Kooi et al. 1994) i i R e iq s Q %, (3) where R" is a dimensionless river erosion constant. Note that the maximum carrying capacity (in m3 s-1) depends both on local slope is and discharge iq, but a river must not necessarily be at maximum carrying capacity. Sediment flux iQ (including suspended sediment and bedload) is calculated as the cumulative sum of sediment transported from the upstream nodes. iQis compared to the maximum carrying capacity, e iQ. In cases where e i iQ Q ., the river deposits sediments; in cases where e i iQ Q /, the river incises. The fluvial erosion rate (in m s-1) is given by ,, e i i e i e i fluvial i e i i i e i i fluvial iQ Q L w Q dt dh Q Q A Q Q dt dh 0 % & ( ) + % & ( ) + (4) In (4), eL is a characteristic length scale for erosion, which is defined differently for erosion in alluvials(s eL L %) or in bedrock (b eL L %), i r iq w w %is the channel width, with 1 0 %rw (in 1 -ms), and il as the channel length. For i el L 00, material is easily eroded, as it is highly detachable. In this situation, the downstream graded river section of the river rapidly propagates upstream towards the headwater of the river, and the ungraded river section rapidly steepens. River profiles are characterized by a short steep upper section and a long low-gradient downstream section. In contrast, i el L 11 characterizes more resistant bedrock and longer erosion timescales. In these situations, grading is inefficient and river profiles are characterized by a more uniform gradient. In summary, long-range fluvial transport processes result in landscapes in which drainage divides are not eroded and remain stationary, while river profiles steepen in the upstream part of the ungraded section, and slope gradients decline in the downstream graded section. Chemical processes On soluble landscapes such as limestone plateaux, the landscape is also altered by chemical dissolution, as surface water enriched in carbon dioxide is weakly aggressive and is able to dissolve the limestone surface. The denudation rate (in m s-1) can be defined as (e.g. Dreybrodt1988) 103 i i C chemical iA q dt dh "-% & ( ) + (5)

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.4 TABLE 2 Karst denudation parameters Parameter Description Unit Value T Absolute temperature [oK] 16 273 ,CT I Ion activity [-] 0.1 A Debye-Hckel coefficient [-] CT x410 074 8 4883 0-, B Debye-Hckel coefficient [-] CT x410 600 1 3241 0-, Ca2 log Activity coefficient [-] I B x I A810 0 5 1 4-, 3logHCO2 Activity coefficient [-] I B x I A810 4 5 1 1-, 1K Mass-balance coefficient [mol l1] 2/ 1684915 log 8339 126 / 37 21834 06091964 0 3094 356 T T T T , 2K Mass-balance coefficient [mol l1] 2/ 9 563713 log 92561 38 / 79 5151 03252849 0 8871 107 T T T T , CK Mass-balance coefficient [mol2 l2] T T T log 595 71 / 319 2839 077993 0 9065 171 , HK Mass-balance coefficient [mol l-1 atm-1] 2/ 669365 log 45154 40 / 53 6919 01985076 0 3865 108 T T T T , where C" is a dimensionless dissolution constant given by ] [ 10 402 3# "eq CCa x,% (6) Here, # is the density of calcite (in kg m-3), and [Ca2+]eq the equilibrium concentration of calcium (in mol l-1), given as (Dreybrodt, 1988, pp. 27) 3 / 1 2 2 1 23 24 ] [ & & ( ) ) + %, HCO Ca H C CO eqK K K K p Ca 2 2 (7) The coefficients CK K K ,2 1, and HK are experimentally derived mass balance coefficients (e.g. Plummer et al. 1982), which depend on temperature (Table 2). The dimensionless ion activities of calcium and bicarbonate, Ca2 and 3HCO2, can be derived from the extended DebyeHckel equation (e.g. Truesdell et al. 1974, Robinson et al. 1955). The carbon dioxide pressure 2COp (in atm) may vary over several orders of magnitude in nature, from 10-3.5 atm over bare rock, 10-2.5 atm in temperate climate soils, to 10-1.5 atm in tropical soils (e.g. White, 1984). Hence, C" depends on climate (temperature), and strongly on lithology (CO2-pressure in atmosphere and soil). Note that (5) depends on discharge only. The factor 40 is necessary to transform [Ca2+]eq from mol l-1 to kg m-3. In Fig. 1, denudation rates as a function of discharge are shown for three different temperatures and carbon dioxide pressures. It is observed that the carbon dioxide pressure is the dominant factor controlling denudation, while changes in temperature are less important. Results All numerical experiments start with identical initial topographies. The model domain is a rectangular area of 100-km side length, discretized into an irregular grid of 2500 nodal points, with an average nodal spacing of 2 km. An initial topography is chosen resembling a high plateau with an average height of 1000 m, and dropping to sea level (0 m) along its southern boundary over a distance of 10

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.5 km. This drop in topography simulates an escarpment created by a recent continental rifting event. The plateau itself rises slightly towards the northern boundary to ensure that initial drainage is towards the south and all surface runoff drains through the escarpment. Both northern and southern boundaries have fixed elevation, but sediment is allowed to exit across these boundaries. Fig 1. Denudation rate as a function of discharge for different partial carbon dioxide pressures (in atm) and water temperatures (in oC). Reference experiments Two reference runs based on fluvial erosion and diffusion alone where initiated to establish reference landforms to which soluble landscapes can be compared. Both the modelled topography after 1 Myr of evolution and a characteristic example of a river profile through time were examined in order to better define differences in morphology between the evolving landscapes. Model parameters are listed in Table 1 for reference run 1 shown in Fig. 2. To characterize each experiment, following Kooi et al. (1994), the ratio of diffusive to fluvial efficiency is given as .1 i R DR " % (8) For run 1, R1 = 20 m; this low value of R1 indicates that long-range fluvial processes dominate the landscape evolution, which can be seen in the modeled topography after 1 Myr (Fig. 2a), dominated by eight steep rivers draining the plateau. All rivers follow fairly linear courses, and the valleys are characterized by steep sidewalls and are relatively narrow. The initial escarpment is left unchanged except where it has been incised by the rivers. A typical river profile is shown in Fig. 2b and is characterized by a convex shape near the escarpment edge and a relatively linear, less steep section near the base. This indicates that diffusive processes control the evolution in the ungraded river section. Fluvial erosion is responsible for the efficient removal of sediments, and the resulting graded river section is less steep and more linear. The escarpment retreats fast along the main rivers, but the headwaters of the rivers on the plateau remain at a constant height. Results of the reference run 2 are shown in Fig. 3. Here, the diffusion constant is increased by a factor of 100 to 20 %D" m2 yr-1 to simulate a wetter climate. With a diffusive to fluvial efficiency ratio of R1=2000 m, diffusion is much more efficient in this run. As a consequence, the simulated topography is much smoother after 1 Myr. The short-range diffusional processes have filtered out the highfrequency components of the topography, especially across the escarpment. Rivers flow in wide valleys with gentle sidewalls. The ungraded river section extends much further downstream, as can be seen in the typical river profiles redrawn (Fig. 3b). The convex shape of the ungraded river section extents halfway down the escarpment, and the shorter graded river section is characterized by a steep gradient. Escarpment retreat is less effective, when compared to reference run 1. Notably, the river erosion on the plateau itself is not very effective for both reference runs, as the erosion rate (4) depends on the product of channel slope and discharge. Hence, the lack of relief on the top of the plateau inhibits erosion. Karst denudation experiments Next, the additional effect on landscape evolution introduced by chemical dissolution of limestone is examined. According to (5), removal of material by chemical dissolution only depends on discharge, not on slope gradient (as for fluvial erosion), nor on curvature (as for hillslope processes). Therefore, karst denudation is also an efficient process on the

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.6 Fig 2. Modeled topography after 1 Myr. The evolution is based of fluvial erosion and diffusion, parameters are given in table 1. The thick line on top of the topography represents the course of the river, whose profile is shown in the top panel as a function of time, for subsequent time steps 0.2, 0.4, 0.6, 0.8, and 1 Ma. Fig 3. Same as Fig. 2, but based on fluvial erosion and increased hillslope diffusion. gently sloping plateau area, where surface runoff increases in downstream direction to the south, and along the base of the escarpment. However, drainage divides cannot be eroded away by fluvial processes, or any process that is dependent on discharge. As a consequence, a different landform evolution is expected on a soluble landscape. A second ratio is introduced, relating diffusive efficiency to the sum of fluvial and chemical efficiency, ) (2 i C R DR " % (9) Results from the first of the two model runs are shown in Fig. 4. A low value of carbon dioxide pressure of PCO2=10-3.5 atm is assumed that is characteristic of barren karst surfaces. All other parameter values are as defined in Tables 1 and 2. For the given parameters, the dissolution constant i C! is comparable to the fluvial constant i R! "; therefore both processes are similarly effective. Hence, the efficiency ratio is reduced to R2=12 m (compared to R1=20 m for the reference run 1). Long-range processes are therefore more effective. This can be seen after 1 Myr of landscape evolution, by which time the plateau is deeply dissected by eight major rivers (Fig. 4b). Most of the rivers have wide flat-bottomed valleys in their downstream graded section, whose sidewalls are generally steeper than in the reference run 1. In parts, the old plateau surface is reduced to na rrow necks between deep river gorges. Major differences in river profile geometry can be observed (Fig. 4a).

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.7 Fig 4. Same as Fig. 2, but based on karst denudation, fluvial erosion and diffusion. The partial carbon dioxide pressure is 10-3.5 atm. Fig 5. Same as Fig. 2, but based on karst denudation, fluvial erosion and diffusion. The partial carbon dioxide pressure is 10-2.5 atm. In contrast to the reference runs on insoluble landscapes, the ungraded upstream river section now is significantly eroded. Valley incision starts close to the headwaters along the northern end of the plateau. The ungraded river section is characterized by a concave gradient similar to gradients resulting from diffusion processes. Gradients in the downstream graded river sections are low and convex to linear in shape, and thus dominated by fluvial processes. With time, the graded river section is cutting back into the plateau and gradients decline, while the ungraded river section is steepening. However, in contrast to reference run 1, incision is significant also on the plateau itself; thus, the total vertical elevation drop across the escarpment is reduced with time. In the next run (Fig. 5), the carbon dioxide pressure is increased to PCO2=10-2.5 atm, simulating a temperate climate soil cover. Surface runoff now percolates slowly through the soil and is enriched in carbon dioxide, thus becoming more aggressive. Consequently, chemical dissolution is enhanced, as can be seen in the larger value of 037 0 %C" The efficiency ratio is further reduced to R2=8 m; thus, diffusion is even less efficient. Surface morphology after 1 Myr is similar to the previous run, with eight major rivers draining the plateau to the south (Fig. 5a). However, river valleys are much more incised, resulting in deep narrow gorges reaching far upstream. The effect of an increased carbon dioxide pressure can be seen more clearly in the chosen set of river profiles (Fig. 5a). While the general characteristics -concave st eepening gradients in the ungraded section and flat convex to linear gradients in the graded section – are similar to the previous run, valley incision has progressed much more. In fact, after 1 Myr the graded low-gradient river section occupies more than 80 percent of the river,

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.8 leaving only a short but very steep ungraded river section close to the main drainage divide in the north. Hypsometric curves The effect of denudation on landscape evolution can also be seen in a statistical quantity, the hypsometric curve (Fig. 6). This quantity is derived from the topographical elevations of the model domain by summing up the elevations for a particular elevation range and relating it to the total elevation. As it can be seen in Fig. 6a, the initial topography for all models is characterized by a peak in the hypsometric curve around the 1000 m elevation, which represents the initial plateau topography. As the escarpment is fairly steep, the initial hypsometric curve for elevations between sea level and 1000 m is almost uniform and orders of magnitude lower than the peak at 1000 m altitude. At sea level, a second peak in the hypsometric curve represents the outwash plain of the plateau. For the reference models shown in Figs. 2 and 3, the final hypsometric curves are characterized by a uniform increase of elevation between sea level and 1000 m elevation, which represents the incised river sections. The plateau surface itself has been reduced in size, as the peak is slightly smaller, but the elevation has been kept, as no erosion is possible on the plateau. No significant differences between the low and high diffusion landscapes is visible. However, for the two models with karst denudation shown in Figs. 4 and 5, the final hypsometric curves are different: The peaks for the plateaux has moved downward and decreased significantly, as the denudation is able to lower the plateaux height itself. For larger effects of karst denudation (higher partial carbon dioxide pressure), the peak has moved further downwards and the hypsometric curve has become more uniform. Discussion The numerical models presented herein are a first attempt to incorporate chemical processes into landscape models. Thus, only a qualitative comparison with topographical data can be made without statistical testing. Fig 6. Hypsometric curves for the initial (solid line) and the final (grey areas) models.

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G.Kaufman / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.9 The modeled topography of the runs including karst denudation is similar to a low-relief plateau dissected by narrow river gorges such as the Grandes Causses in southern France, where the deep, steeply incised gorges of the Tarn, Lot, and Dourbie contrast with the relatively flat segments of the plateau of the Causses in between (Fig. 7). The evolving river valleys can have a significant sinuosity, and often only small remnants of the original plateau surface separate two gorges as narrow necks. As the karst denudation process is as effective as fluvial river erosion in eroding a landscape, evolution on a limestone plateau will downgrade the landscape surface twice as fast as on a similar sandstone plateau. The major difference in the karst denudation and the fluvial erosion processes are visible on the plateau itself: while fluvial erosion is less effective on the flat plateau, as fluvial erosion rate depends on the product of channel slope and river discharge, karst denudation can effectively remove material on the plateau itself, as denudation rate depends only on river discharge. Hence, karst denudation is an efficient process for surface lowering on plateau landscapes. Fig 7. Topography of the Grandes Causses in southern France, w ith the deep, narrow gorges of the rivers Lot, Tarn and Dourbie, and the Causse de Sauveterre (CS), Causse Mejean (CM), and Causse Noir (CN). Acknowledgements The DEM data have been kindly provided by Francis Lucazeau from Universite de Montpellier II. The figures in this paper are drawn using the GMT graphics package (Wessel et al. 1991, Wessel et al. 1998). References Beaumont C., Fullsack P. and Hamilton J. 1992. Erosional control of active compressional orogens. In: McClay K. R. (Ed.), Thrust Tectonics. New York: Chapman and Hall, 1-18. Braun J. and Sambridge M. 1997. Modelling landscape evolution on geological time scales: a

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.10 new method based on irregular spatial discretisation. Basin Res. 9, 27-52. Braun J., Zwartz D. and Tomkin J. H. 1999. A new surface processes model combining glacial and fluvial erosion. Ann. Glaciol. 28, 282-290. Chase C. G. 1992. Fluvial landsculpturing and the fractal dimension of topography. Geomorphology 5, 39-57. Clemens T., Hckinghaus D., Sauter M., Liedl R. and Teutsch G. 1997. Modelling the genesis of karst aquifer systems using a coupled reactive network model. In: Hard Rock Hydrosciences, Proceedings of Rabat Symp. S2., IAHS Publ., vol. 241, Colorado, 3-10. Dreybrodt W. 1988. Processes in Karst Systems. Berlin: Springer. Forti F. 1984. Messungen des Karstabtrages in der Region Friaul-Julisch-Venetien (Italien). Die Hhle 35, 135-139. Groves C. G. and Howard A. D. 1994. Early development of karst systems 1. Preferential flow path enlargement under laminar flow. Water Resour. Res. 30 (10), 2837-2846. Howard A. D. and Groves C. G. 1995. Early development of karst systems 2. Turbulent flow. Water Resour. Res. 31 (1), 19-26. Howard A. D., Dietrich W. E. and Seidl M. A. 1994. Modeling fluvial erosion on regional continental scales. J. Geophys. Res. 99 (B7), 13971-13986. Jennings J. N. 1985. Karst geomorphology. Oxford: Blackwell. Kaufmann G. and Braun J. 1999. Karst aquifer evolution in fractured rocks. Water Resources Res. 35 (11), 3223-3238. Kaufmann G. and Braun J. 2000. Karst aquifer evolution in fractured, porous rocks. Water Resources Res. 36 (6), 1381-1392. Kooi H. and Beaumont C. 1994. Escarpment evolution on high-elevation rifted margins: Insights derived from a surface processes model that combines diffusion, advection, and reaction. J. Geophys. Res. 99 (B6), 12191-12209. Plummer L. N. and Busenberg E. 1982. The solubilities of calcite, aragonite and vaterite in CO2-H2O solutions between 0 and 90oC, and an evaluation of the aqueous model of the system CaCO3-CO2-H2O. Geochim. Cosmochim. Acta 46, 1011-1040. Robinson R. A. and Stokes R. H. 1955. Electrolyte solutions. London: Butterworths Sci. Publ. Siemers J. and Dreybrodt W. 1998. Early development of karst a quifers on percolation networks of fractures in limestone. Water Resour. Res. 34 (3), 409-419. Trudgill S. T., High C. J. and Hana F. K. 1981. Improvements in the micro-erosion meter. Brit. Cave Res. Group Tech. Bull. 29, 3-17. Truesdell A. H. and Jones B. F. 1974. WATEQ, a computer program for calculating chemical equilibria of natural waters. U.S. Geol. Surv. J. Res. 2 (2), 233-248. Tucker G. E. and Slingerland R. L. 1994. Erosional dynamics, flexural isostasy, and long-lived escarpments: A numerical modeling study. J. Geophys. Res. 99, 12229-12243. Wessel P. and Smith W. H. F. 1991. Free software helps map and display data. EOS 72, 441-446. Wessel P. and Smith W. H. F. 1998. New, improved version of generic mapping tools released. EOS 79, 579. White W. B. 1984. Rate processes: chemical kinetics and karst landform development. In: La Fleur R. G. (Ed.), Groundwater as a geomorphic agent. London, Boston, Sydney: Allen and Unwin, 227-248. Willgoose G., Bras R. L. and Rodriguez-Iturbe I. 1991. A physically based coupled channel network growth and hillsl ope evolution model. 2. Applications. Water Resour. Res. 27 (7), 16711684.



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Speleogenesis and Evolution of Karst Aquifers The Virtual Scientific Journal www.speleogenesis.info Karstification and Groundwater Flow L. Kiraly Centre d'Hydrogologie, University of Neuchtel 11, rue Emile-Argand, CH-2000 Neuchtel (Switzerland) E-mail : Laszlo.Kiraly@unine.ch Re-published by permission from: Gabrovšek, F. (Ed.). 2002. Evolution of karst: from prekarst to cessation. Postojna-Ljubljana, Zalozba ZRC, 155-190. Abstract One of the principal aims of hydrogeology is to propose a reasona bly adequate reconstruction of the groundwater flow field, in space and in time, for a given aquifer. For example, interpre tation of the chemical and isotopic composition of groundwater, understanding of the geothermal conditions (anomalies) or forecas ting the possible effects of i ndustrial waste disposals and of intensive exploitation nearly always would require the knowledge of the regional and/or local groundwater flow systems such as defined by Toth (1963) The problem of estimating the groundw ater flow field in fractured and karstified aquifers is approached within the framework of a conceptual diagram showing the rela tionship between groundwater flow, hydraulic parameters (aquifer properties and boundary conditions), distribu tion of voids and geological factors. Autoregulation between groundwater flow and karst aquifer properties, duality of karst, nested model of geological discontinuities, scale effect on hydraulic pa rameters and use of numerical finite elem ent models to check the interpretation of the global response of karst springs are some of the subjects addre ssed by the author. Inferences on groundwater flow regime with respect to the stage of karst evolution can be made only if the hydraulic parameter fields and the boundary conditions are know n by direct observations, or estimated by indir ect methods for the different types of kars t. Practical considerations on the monitor ing strategies applied for karst aquifers, a nd on the interpretation of the global respons e obtained at karst springs will complete the paper, which throughout reflects the point of view of a hydrogeologist. Keywords: karst hydrogeology, karst aquifers, numer ical modelling of karst flow, spring hydrographs 1. Introductory remarks 1.2. Relation between groundwater flow field, hydraulic parameters and geological factors In hydrogeology we do not study karstification or karst evolution for themselves: we are interested in them only in so far as they exert an influence on the groundwater flow field. The reconstruction of a regional groundwater flow fiel d, which is consistent with a given hydraulic conductivity field and with given boundary conditions, nearly always requires the use of numerical models. Presently we have a wide variety of equations describing the groundwater movement in various domains (see, for example, for saturated/unsaturated flow and groundwater/surface-water interaction Tregarot 2000 ; Ababou et al. 1998 ) and we can solve them quite accurately by numerical models if we know, in the modelled region, the field of the relevant hydraulic parameters (hydraulic conductivity, storage coefficient, efficient porosity, etc., in each point of the aquifer), as well as the initial and the boundary conditions (mainly infiltration and fixed head values, such as altitude of springs, lakes or rivers). With the use of numerical models explicitly appears a very important fact: as groundwater flow depends only on hydraulic parameters and on boundary conditions, the geological, geomorphological and climatic factors will exert their influence on the groundwater movement solely through the hydraulic parameter fields and the boundary conditions. If we could measure, for example, the value of the hydraulic parameters everywhere in the Earth's crust, we ought not to bother about fractures, faults, karst channels, lithologies and other geological factors: we could simulate and predict the behaviour of the groundwater flow systems without geology. In other words, if we will give a hydrogeological meaning to the geological, geomorphological or climatic factors, if we will examine their influence on the groundwater flow field, then we have to "translate" them (if possible, explicitly) into boundary conditions and hydraulic properties of the aquifer.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.2 Evidently enough, geology will influence the hydraulic conductivity and porosity through the distribution of "voids": increase of density opening and connectivity of the voids will increase the hydraulic conductivity and the porosity. If fracture or microfracture families show well defined, preferred orientation the hydraulic conductivity may become anisotropic, thus conducting groundwater better in a direction than in another. At this stage sedimentation, diagenesis and tectonic deformations are the principal processes influencing the void distribution in sedimentary rocks. Complications may appear in carbonate rocks, which are soluble in water: the groundwater in movement may dissolve the limestone around the existing voids, thus increasing their opening and the hydraulic conductivity of the aquifer. The amount of dissolved limestone, the enlargement of fractures depend obviously on the chemical composition of the rock and of the water, but the relative karstification of the various fracture families will depend mainly on the direction and the magnitude of the groundwater flux density vector !"qKgradh #$ !!" given by Darcy's law, where !"K is the hydraulic conductivity tensor and h is the hydraulic head ( Bedinger 1966 ; Kiraly et al. 1971 ). Considering that 1. q depends on the hydraulic conductivity and the hydraulic gradient, 2. the hydraulic conductivity depends on the opening of pores and fractures, 3. the opening of karstified pores and fractures is strongly influenced by the direction and magnitude of q during the previous stages of the groundwater flow field, we arrive in a very important and characteristic feed-back loop of the karstification process. It shows, that in karst aquifers the hydraulic conductivity field and the void distribution result not only from the geological history of the rocks, but also from the whole history, from the whole evolution of the groundwater flow systems: the present state of the groundwater flow field and the hydraulic conductivity field is the result of successive, short-term and long-term autoregulations between the fields q ", !"K, gradh !!" and the boundary conditions (infiltration, altitude of discharge areas, etc.). Indeed, we have to emphasize, that geographical position of the recharge and discharge areas represent boundary conditions for the flow field q and their evolution in time (paleo-geography, geomorphology) could influence karstification and hydraulic conductivity field as much as other geological factors (facies, structure, etc.). All these conceptual relations between groundwater flow systems, hydraulic parameters, void distribution and geological factors are represented as a partly self-regulating system in the diagram of Fig. 1 The feed-back of the flow field on the hydraulic conductivity field will produce it's effect only after a "certain time", thus giving an important role to the "duration", to the "history" in the karstification process. This means, that understanding the karstifica tion in a given aquifer would require the knowledge of the "paleohydraulic" conditions, as it was proposed by Mandel (1966 ) and Kiraly et al. (1971) Fig. 1. Schematic representation of the relations between groundwater flow field, hydraulic properties and geological factors in karst aquifers (after Kiraly 1975 modified).

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.3 1.1 Duality of karst aquifers The partly self-regulating system of Fig. 1 is, in fact, a graphic representation of the karst development according to the ideas of Rhodes and Sinacori (1941) Swinnerton 1949 LeGrand and Stringfield 1966 Mandel 1966 and Bedinger 1966 ). They assume that dissolution starts in non-karstified fractured rocks where the heterogeneity of the permeability field is not very important (1 to 50?). Groundwater flow will enhance the dissolution particularly in fractures which are sub-parallel to the local hydraulic gradient and which are in the vicinity of the free groundwater table ( Bedinger 1966 ). The heterogeneity of the hydraulic conductivity field increases (up to 1 to 1 million!) and the zones with higher permeability will represent discharge regions with respect to the lower permeability volumes. The competition for the drainage between highconductivity zones will lead to the capture of the slower developing branches and will contribute to the unification of the karst channel network and to the "concentration" of the discharge areas: the karst springs will be less in number but more important as far as the discharge is concerned. The hydrograph of the remaining springs becomes more and more "karstic", i.e. the reaction of the springs to input events will become more and more "violent", with rapidly increasing and rapidly decreasing peak-flow. This is a sign that infiltration becomes strongly heterogeneous, too, with an always growing part of concentrated infiltration. Thank to the works of ( Burger 1956 ; Schoeller 1967 ; Berkaloff 1967 ; Forkasiewicz and Paloc 1967 ; Drogue 1967 ; Mangin 1975 ) we may consider the hydrograph of karst springs as one of the most important indirect indicators on the structure of the hydraulic conductivity field and on the heterogeneity of the infiltration in a karst aquifer. In this "mature" karst aquifer we may speak of the "duality of karst" ( Kiraly 1994 ). Indeed, the organized heterogeneity of the hydraulic conductivity field may be schematized by a high permeability, generally unknown channel network with kilometer wide "meshes", which is "immersed" in a low permeability fractured limestone volume, and is well connected to a local discharge area, the karst spring. The duality of karst aquifers is a direct consequence of this structure: %& duality of the infiltration processes ("diffuse" or slow infiltration into the low permeability volumes, "concentrated" or rapid infiltration into the channel network); %& duality of the groundwater flow field (low flow velocities in the fractured volumes, high flow velocities in the channel network); %& duality of the discharge conditions (diffuse seepage from the low permeability volumes, concentrated discharge from the channel network at the karst springs). Note that besides the rivers disappearing in sinkholes, the concentrated infiltrations could be enhanced by the rapid drainage in a high conductivity "skin" at shallow depth: the epikarst ( Mangin 1975 ). The above presented karst development assumes a very simple and favorable hydrogeological setting, i.e. open or denuded karst. For more complicated hydrogeological settings the reader should consult the beautiful book edited by ( Klimchouk et al. 2000 ), particularly the papers between pages 45 and 100. In the following of the present paper we will show the nested structure of the geological discontinuities, their relation to the hydraulic conductivity tensor and a few hydrogeological consequences of the duality of karst aquifers. 2. The nested structure of the geological discontinuities 2.1 Qualitative observations in the field Geological discontinuities exist at all scales: intragranular cracks not longer than a few microns, microfractures of a few millimetres or centimetres, fractures (in the usual sense) of metric or decametric length, faults of a few hectometres, kilometres or tens of kilometres, big fault zones extending over several hundreds of kilometres, or cave systems with length of tens of kilometres. In sedimentary rocks the bedding planes (stratification) represent very persistent, closely spaced (from a few centimetres to a few meters) discontinuities of considerable lateral extent (several kilometres). Geologists have developed a rather complicated genetic terminology of their own to designate rock discontinuities, but this terminology will not be used here. Following the International Society of Rock Mechanics Suggested Methods for Quantitative Description of Discontinuities in Rock Masses ( Barton, 1978 ), we use only the generic term discontinuity and the somewhat more specific term fracture, to designate discontinuities of metric or decametric length.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.4 Fig. 2. Illustration of the nested model concept (after Feuille d'Avis de Neuchtel) In most cases the enumerated discontinuities are not randomly oriented, but form families, even if the orientation of a family may change from place to place. This is quite normal given the fact that the orientation of the discontinuities must somehow be related to the rather complicated, past or present, regional and local stress fields ( Chinnery 1965 ; Gramberg 1965 ). If the lateral extent of the discontinuities is greater than their spacing, it seems reasonable to suppose that families with different orientations will form more or less connected networks of discontinuities, with "meshes" of different magnitudes ( Jamier and Simeoni 1979 ; Rouleau 1985 ). As the networks of different magnitudes coexist in the r eal systems, the fractured and karstified medium should be characterized by its nested structure of discontinuities. Even if the nested structure concept is a qualitative mental picture only, it allows to ask some important questions when we are investigating flow and mass transport in fractured and karstic media: %& Which magnitudes of the discontinuities are of interest for the investigated phenomena and which may be neglected. %& Which magnitudes could be averaged and which not (is it possible to combine the "discrete fracture" approach with the continuum approach). %& How could we quantify the nested structure of the discontinuities (if required). %& How do the presently used quantitative methods respect the existen ce of nested structures in the real systems (in randomly generated fracture or karst channel networks, for example). %& And finally, the most important question: could the nested structure of the geological discontinuities determine a nested structure of the hydraulic conductivity field? Many of these questions will remain unanswered here. In spite of this fact, they deserve attention from a heuristic point of view. 2.2 The scale effect in nested structures There is an abundant scientific literature on scale effect in fractured media. The interested reader will find the more recent references in Bear et al. (1994) or in Lee and Farmer (1993) In most of these papers the scale effect is investigated by applying the percolation theory or the renormalization theory to a schematic representation of the fractured aquifers. As the above theories don't apply to nested structures, all the schematic discontinuities are of the same order of magnitude, even if there is a certain statistical distribution allowed about the mean fracture length, the mean fracture orientation and the mean fracture opening. The obtained scale effect is related to the clustering of the interconnected discontinuities in randomly generated networks. A different kind of scale effect could appear in the above described nested structures. The idea was developed for fractured and karstic limestone aquifers located in the Jura mountains (Switzerland) in the early seventies ( Tripet 1972 ; Kiraly 1973 1975 ), but the principle might well apply for noncarbonate aquifers, too. In these karstic aquifers, besides the common fracture network with "meshes" of a few meters, there must be a high-permeability channel network with wide, kilometric intervals, which is well connected to a discharge area, the karstic spring. Between the channels, the fractured rock mass has a low hydraulic conductivity, about 610$ to 710$ [m/s], values obtained by pumping tests in 300 to 400 m deep boreholes. Regional numerical models showed, that at a basin-wide scale the overall hydraulic conductivity must be 2000 to 5000 times higher than the "local" conductivity values measured in the boreholes (see Fig. 2 ). This important scale effect is due to the very high hydraulic conductivity of the widely spaced karst channel network. As most of the boreholes are located between the karst channels, the locally measured hydraulic conductivity values don't give any information on the existence of this scale effect. Basin-wide water balance studies and the use of regional numerical models are necessary to put forward the phenomenon. In non-carbonate fractured aquifers there is no karstic network. Neverthe less, it could happen that large discontinuities with a wide spacing have a higher hydraulic conductivity than closely spaced

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.5 Fig. 3. Scale effect on the hydraulic conductivity in fractured and karstified limestone aquifers (after Kiraly 1975 modified). smaller ones, and in this case there will be a certain scale effect on the hydraulic conductivity: local values will not be the same as the overall regional values. This kind of scale effect is very different from what we obtain with the percolation or renormalization theory: it is the consequence of the nested structure of the hydraulic conductivity field inferred from the nested structure of the fractured and/or karstified medium. The idea on the nested structure of the hydraulic conductivity suggests to go back to the real systems and check it. Instead of doing statistics on anonymous conductivity values, it would be far more interesting to obtain information about the spacing of the high-permeability zones, about the lateral extent of the high-permeability zones and about the connectivity of the high-permeability zones. Then it would be possible to compare the structure of the hydraulic conductivity field with the structure of the geological discontinuities. Because presently we are not yet able to answer such fundamental questions as how to predict actually water conducting zones from statistical information about geological discontinuities. Although based on qualitative observations and on inferences, the general ideas developed in these first pages will help to critically evaluate the techniques presented without many comments in the next sections. 2.3 Permeability tensor for fractures and intersections of fractures The estimation of the hydraulic conductivity tensor from idealised fracture geometry was proposed by Romm and Pozinenko (1963) Snow (1969) presented a general method for individual fractures and Kiraly (1969) proposed to estimate the permeability tensor for both fractures and intersections of fractures. We have to emphasize that using the hydraulic conductivity tensor transforms the discontinuous real aquifer into an equivalent continuum. Let us define N families of idealized fractures in the delta-neighbourhood of a point. The mean plane of the i-th family is characterized by in = unit normal of the plane; if= average number of fractures in the direction of the normal; id= average aperture of the i-th family. In Darcy's law given by !"qKgradh #$ !!" the hydraulic conductivity tensor !"K may be calculated for the N families of fractures by !" !"3 112N iiii ig KfdInn' (##$)*"" (1) where = density of water; g = acceleration due to gravity; ( = dynamic viscosity; ) is the tensor product and I is the unit matrix. The geometric or intrinsic permeability !"k is easily identified: it depends only on the fracture parameters if, id and in ". Let us idealize the intersections of two families of fractures by a bundle of tubes, which is characterized by im "= unit vector parallel to the i-th bundle; iF = number of tubes per unit surface perpendicular to im "; iD= average diameter of the tubes in the i-th bundle. Making use of the HagenPoiseuille formula we obtain the global hydraulic conductivity tensor for M bundles of intersections by

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.6 !" !"4 1128M iiii ig KFDmm'+ (##)*"" (2) Knowing the fracture parameters for N families of fractures allows to estimate the parameters for the M bundles of intersections: (1) 2 NN M $ # (number of bundles) ij k ijnn m nn # "" "" (orientation of k-th bundle) kijijFffnn #, "" (density of intersections) where is the vector product; ij -; 1(1) iN #$ #. Obviously, the most ticklish problem is to estimate kD when ijdd .. The idealized representation of the geological discontinuities, which allowed to estimate the permeability tensor, is never totally realized in the real systems. Real fractures are not evenly spaced, their aperture is not constant in the fracture plane, they are not strictly parallel to each other even in the same family, their lateral extent ("length") may vary, in a word: the fractured medium is not only anisotropic, but heterogeneous, too. If the /neighbourhood for which we estimate the permeability tensor is "big" with respect to the local heterogeneities, the [K] tensor will not correctly describe the behaviour of the real system. This simply indicates that one [K] tensor alone cannot describe a whole region and the /-neighbourhood has to be diminished. In this case the heterogeneities will appear clearly in the interior of the region. A last remark: the continuity of the fractures is required only in the /-neighbourhood, not over the entire region. 2.4 The "serial type model" of the void geometry in fractured rocks In three orthogonal and equally developed fracture families, or intersection bundles, the hydraulic conductivity is is otrope and its magnitude depends on the spacing 1/ xf # (or 1/ XF #) and the aperture d (or D). In a diagram log d versus log x (or, for the intersections: log D versus log X) constant permeabilities or constant porosities appear as straight lines (see the diagrams of Figs 3a and 3b ). These diagrams allow to rapidly estimate the permeability value for more or less connected networks of discontinuities, with "meshes" of different magnitudes. The dark zones represent spacing and aperture values which seem reasonable in real fractured or karstic aquifers and show an important scale-effect on the hydraulic conductivities (but not, or less, on the efficient porosities) with progressive karstification. Fig. 4. Hydraulic conductivity and efficient porosity values for various networks of fractures (left) and intersections of fractures or karst channels (right).

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.7 In the Swiss Jura Mountains we have field measurements on the hydraulic conductivity (about 610$ m/s), on the efficient porosity (about 0.4 to 1%) and on the fracture spacing (about 0.6 m). If we represent these values on the diagrams of Fig. 3a and Fig. 3b (see points K and n), we cannot find a unique fracture aperture or channel diameter which could "explain" both the permeability value and the efficient porosity value. In other words, the void geometry which determines the permeability is not the same as the void geometry which determines the efficient porosity. The efficient porosity value requires large openings in the fracture planes (up to 1 mm aperture) but the permeability value shows that these large voids are not well interconnected. Combining the "fracture model" with the "intersection model" may represent a solution to the problem: the permeability is determined by the intersections of fractures (required diameter: about 1 mm) and the efficient porosity is determined by the larger voids in the plane of the fractures (required aperture: about 1 mm). The large openings are well connected to the intersections where the groundwater flows, but are poorly connected to each other. The above described void geometry is schematically represented in Fig. 4 which is not more than the "serial type model" of Scheidegger (1963) adapted to the three-dimensional fractured medium ( Kiraly 1994 ). The idea was taken up later by Hauns, Jeannin and Hermann (1998) who applied it to big karst channels by simulating the changes in width and in depth of the underground rivers. Interestingly enough, the "serial type model" of the void geometry could explain all particularities of the empirical break-through curves observed in fractured and karstic rocks (particularly the "tailing" of the break-through curves), without adsorption and desorption phenomena, and without molecular diffusion into the "immobile water". The above presented example shows that even theoretical and very schematic representations may be useful, provided they are confronted with the observations made in the real system. 3. Interpretation of karst spring hydrographs based on the global methods 3.1 The global response of karst aquifers In the previous chapters we briefly presented the general nested structure of geological discontinuities and the duality of karst aquifers. How do their consequences manifest in the global response of real karst springs? The behavior of the karst spring (hydrograph, water temperature, chemical or isotopic composition, etc.) represents the "global response" of the karst aquifer to input events. As the available data on the three-dimensional distribution of the hydraulic parameters are very limited, the more easily obtained global response is often used to make inferences (sometimes even contradictory inferences) on the infiltration and groundwater flow processes, as well as on the hydraulic parameter fields and the degree of karstification of the aquifer. In most cases, interpretations are based on the analysis of recession hydrographs by using different hydrograph separation methods ( Burger 1956 ; Forkasiewicz and Paloc 1967 ; Drogue 1972 ; Mangin 1975 ; Bonacci 1987 1993), statistical analysis of the whole spring hydrograph ( Mangin 1984 ; Dreiss 1982 ; Labat 2000 ), or analysis of transfer functions between input (infiltration) and output (spring hydrograph) obtained by black-box or grey-box models. A short critical review of these methods is presented by ( Eisenlohr et al. 1997 ) and a more detailed presentation is found in Jeannin and Sauter (1998) In this paper we will only propose a few critical remarks concerning some of the usual interpretations. Fig. 6 represents the hydrograph of a typical karst spring, the Areuse spring in the Jura mountains (Switzerland) for 1979, as well as the registered electric conductivity curve giving an indirect indication on the mineralization of the spring water. The most striking features are the rapid variation of the spring discharge and the generally observed dilution effect of storm or snowmelt events on the spring-water chemistry. They suggest not only a well developed karstificati on of the aquifer, but also, that an important part of the infiltrations should be drained rapidly toward the high permeability karst channel network and the spring. Another important fact is the contrast between the rapidly decreasing recession curve after the peak Fig. 5. "Serial type model" of the void geometry in fractured rocks: large voids in the fracture planes (O), well connected to the intersections or channels (i).

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.8 Fig. 7. Possible effects of the duality of recharge, storag e and flow on the hydrogra ph of karst springs (from Hobbs and Smart 1986 ; in Jeannin and Sauter 1998 ).flow, and the very slowly decreasing recession curve in the domain of feeble discharges. The interpretation seems intuitively evident: the two parts of the recession curve represent the rapid emptying of the high-permeability karst channels and the slow emptying of the low-permeability fractured volumes. All these observations seem more or less evident in the light of the duality of karst aquifers and we can guess, at least qualitatively, how the karst springs could react with increasing karstification. This is attempted in Fig. 7 proposed by Hobbs and Smart (1986) where the relations between input and output are represented very schematically as depending on the duality of infiltration, storage and groundwater flow. 3.2 Analysis of recession hydrographs The recession curve is that part of the spring hydrograph which extends from a peak to the start of the next rise. The first aim of analysing the recession hydrograph was to estimate the volume of Fig. 6. Hydrograph and electric conductivity registered for Areuse spring (Jura mountains, Switzerland) in 1979.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.9 groundwater which could be drained by the karst spring in case of drought. As the last part of the slow recession curve can nearly always be approximated by an exponential, it is easy to integrate the approximated discharge from an arbitrary time 0t till "infinity" and get a number for the groundwater volume which could flow out at the spring. The method says naturally nothing about the groundwater volume which is below the spring level, but all the same, it allowed a kind of quantitative comparisons between karst aquifers ( Forkasiewicz and Paloc 1967 ) proposed that the total recession curve be represented as the sum of two, three or more exponential functions: 0 1()iN t i iQtQe0$ ##* where N is the number of exponentials, t is the time, 0 iQare the discharges at t=0 and i0are the recession coefficients for each exponential (see Figs 8 and 9 ). In the interpretation, each exponential is thought to represent the depletion of a reservoir, the hydraulic conductivity of the reservoir being proportional to the recession coefficients i0. Fig. 8. Foux de la Vis spring (south of France): observed hydrograph during spring and summer of 1953. The last part of the slow recession curve is approximated by an exponential (after Forkasiewicz and Paloc 1967 ) Fig. 9. Illustration of the hydrograph separation method of ( Forkasiewicz and Paloc 1967 ) as applied to the hydrograph of Fig. 8

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.10 Fig. 10. Separation of a theoretical hydrograph simulated by finite element model. There are only two classes of hydraulic conductivity in the model, yet the separation gives three exponentials (after Kiraly and Morel 1976b ). According to this interpretation, the exponential with the highest recession coefficient (10 in Fig. 9 ) would represent the rapid depletion of the high permeability karst channels and the exponential with the lowest recession coefficient (30in Fig. 9 ) would correspond to the base-flow, i.e. to the slow depletion of the low hydraulic conductivity fracture network. Intermediate exponentials (see 20in Fig. 9 ) are thought to represent the emptying of aquifer volumes with intermediate values of hydraulic conductivity. If the interpretation of the first and last exponential seems reasonable, the interpretation of the intermediate exponential is not necessarily true, as it was shown by ( Kiraly and Morel 1976b ). Fig. 10 shows the separation of a theoretical hydrograph simulated by an oversimplified 2-D finite element model. There are only two classes of hydraulic conductivity in the model, i.e. there is no aquifer volume with an intermediate hydraulic conductivity, the depletion of which causes the appearance of an intermediate exponential, yet the separation gives three exponentials. The intermediate exponential could simply be the result of transient phenomena in the vicinity of the high hydraulic conductivity channel network as we proposed it in Kiraly and Morel (1976b) Fig. 12. Two finite element models with the same geometry and the same hydraulic conduc tivities, but with different channel network densities. Fig. 11 shows that depletion and "base-flow" are very different for the two "aquifers". Fig. 11. Two nearly exponential recession hydrographs simulated by 2-D finite element models (see Fig. 12). The same geometry and the same hydraulic conductivities are used for the two models, only the channel network is more dense in model K3.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.11 The models show that the last exponential represents the depletion of the low hydraulic conductivity fractured volumes, exactly as assumed in the generally accepted interpretation. It is, however, not true that the last recession coefficient 0of the base-flow depends on the hydraulic properties of the only low permeability volumes. In fact, it depends greatly on the geometry, the hydraulic conductivity and the density of the high permeability channel network. Fig. 11 shows two nearly exponential recession hydrographs simulated by 2-D finite element models (see Fig. 12 ). The same geometry and the same hydraulic conductivities are used for the two models, only the channel network is more dense in model K3. The recession coefficient is greater for K3, although the low permeabilities are the same for K1 and K3. It should be understood that the recession coefficient 0is a global parameter and will depend on the global configuration of the karst aquifers (even on their form and their extension). Using it to compute the hydraulic properties of the low permeability volumes could end up with very misleading conclusions. 3.3 Critical remarks on the chemical or isotopic hydrograph separation methods Fig. 6 showed the generally observed dilution effect of storm or snowmelt events on the springwater chemistry. This suggests that an important part of the infiltrated "fresh-water" should be drained rapidly toward the high permeability karst channel network and the spring. Fig. 13 and 14 show the dilution phenomenon in detail in the case of a single peak flow of the Areuse spring. Careful sampling of the spring water before, during and after the peak flow allowed to visualize the variation of the calcium content, represented in Fig. 14 It shows that during the slow depletion of the low permeability volumes the karst channels are filled up with highly mineralised water characterizing the base-flow. Concentrated infiltration of fresh water determines the dilution effect during the peak flow, by mixing "old" water and "new" wate r in the karst channels. The "diluted" water is evacuated from the karst channels during the rapid recession and is progressively replaced by the "old" water of the base-flow (samples 100 to 104 in Fig. 14 ). These observations do not contradict the general ideas on the duality of karst and careful sampling (rising and falling limbs of peak hydrographs) and chemical analysis of spring water during input events appear as very important auxiliary methods for the understanding groundwater flow. The idea of taking advantage of the quite general dilution effect by separating the whole hydrograph of a river or a karst spring into a "new-water" component and an "old-water" component was popularised in the mid 1970s and remained more or less widely used for the last 25 years ( Martinec et al. 1974 1979 1982 ; Fritz et al. 1976 ; Dreiss 1989 ; Harum and Fank 1992 ; Gu 1992 ). The principle is simple, but many underlying hypotheses remain implicit, never clearly stated. Let us define Q= spring discharge, C= concentration of a "substance" in the spring water, oldQ= old water component, oldC= old water concentration, newQ= new water component, newC= new water concentration. Most authors start from a very simplified mass balance: oldoldnewnewQCQCQC #1 with oldnewQQQ #1(3) expressing oldQ we have () ()new old oldnewCC QQ CC $ # $ witholdnewCC Fig. 13. Single discharge peak of the Areuse spring and dilution effect shown by the electric conductivity curve. Small black, numbered circles represent spring-water samples for chemical analysis (after Kiraly and Muller 1979 ).

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.12 This is a classical end member mixing analysis (EMMA) with oldC and newC as end members. In most cases oldC is chosen to be the concentration of the base-flow and newC is the concentration of the storm or snowmelt water. When applied to real cases, the method gives nearly always a very important old water component: up to 60% or 70% of the peak flow. As long as the chemical or isotopic hydrograph separation is restricted to the "old water" and "new water" concept, there is nothing to say about these definitions. What should be however severely criticized, is the commonly accepted hydrologic and hydrogeologic interpretation of the components. As oldC was taken to be the tracer concentration of the base-flow ( Martinec et al. 1974 1979 1982 ; Fritz et al. 1976 ) and many others do not hes itate to equate the old water component oldQ with the hydrodynamic baseflow BQ, i.e. with the groundwater discharge into the rivers or with the discharge of the low-permeability fractured volumes into the karstic network. The old water component is then compared (and opposed) to the "conventional" base-flow estimate, generally obtained by the backward extrapolation of an exponential recession curve (see, for example, Fig. 9 ). The comparison nearly always shows a high proportion of "old water" in the river or karst spring discharge even during flood events: oldQ may be as important as 60% or 70% of the total discharge Q during peak flow, much more than the "conventional" base-flow estimate. Equating oldQ with the base-flow BQ leads many authors to accept a much higher infiltration rate into the aquifers or into the low-permeability (!!) fractured volumes than the "conventional" estimates, the infiltrations being supposed to increase the hydraulic gradients and to force the older groundwater to rapidly discharge into the rivers or into the high-permeability karstic channels (see, for example, Martinec et al. 1982 ). Unfortunately the authors do not produce any empirical gradient and permeability measurements which would allow, together with the drainage length, for the hydraulic proof of the above mentioned interpretation. As a matter of fact it can be shown very easily, even with an oversimplified double reservoir model, that old water component and base-flow are two concepts totally different. Let us represent a karst aquifer by the simplified two-reservoir model of Fig. 15 The slow reservoir simulates the low permeability fractured volumes and the rapid reservoir represents the karst channels. The variables are defined as follows: Fig. 14. 2Ca1concentration versus discharge for the single peak shown in Fig. 13. Observe the dilution between samples 99 and 100 and the clustering of points located on the slow recession hydrograph (after KiralyandMuller1979 ).

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.13 EBQ= infiltration into slow reservoir; EBC= concentration in EBQ, but it will not be used for the slow reservoir; BV= ground-water volume in the slow reservoir; BQ= base-flow; BC= concentration of the base-flow; ERQ= direct infiltration into the karst channels; ERC= concentration of the direct infiltration; RMV= volume of groundwater which is located above the spring level (it can flow out); RFV= volume of groundwater below the spring level (the volume is fixed); Q= discharge of the spring; C= concentration of the spring-water. It appears clearly that BCis oldC and ERC is newC. Due to the important residence time of the groundwater in the slow reservoir it is assumed that BCis more or less constant. We assume, in addition, an exponential depletion (emptying) for each reservoir and in this case the recession coefficient 0is the ratio between the discharge and the volume of the reservoir: 0=Q/Vand we can pass from Qto Vor from Vto Qeasily. Two differential equations will describe the "flow problem": B EBBEBBBdV QQQV dt0#$#$ (4) RM ERBERBBRMRMdV QQQQVV dt00#1$#1$ (5) A third differential equation will describe the mass balance for the "tracer", where the total mass of tracer in the rapid reservoir is ()RMRFMCVV #1: ()RMRFBBERERdMd CVVQCQCQC dtdt #1#1$or ()RM RMRFdCdV VVC dtdt 111 BBERERQCQCQC #1 (6) Equation 6 will reduced to the dashed box, i.e. to equation 3, if the first two terms are zero. But this would imply that there is no water in the karst channels (RMRFVV 1 is zero! ), and/or the concentration in the spring water is constant. These are unrealistic conditions, thus equation 3 cannot be used to calculate, even approximately, the baseflow Replacing RMdVdtand rearranging the terms we obtain ()() ()()BER BER RMRFRMRFdCCCCC QQ dtVVVV $$ #1 11 (7) Fig. 15. Simplified double reservoir model for karst aquifers Equations 4, 5 and 7 are three simultaneous differential equations which can be solved by the Runge-Kutta method for BQ, Qand C if we give B0, RM0, EBQ, ERQ, ERC and RFV. It must be emphasized that in this simplified model the groundwater volume below the spring level, RFV, does not influence the spring discharge, but it will greatly influence the variation of C, i.e. the dilution effect. For the same base-flow hydrograph or spring hydrograph, for example, very different dilution effects, thus very different "old water" components, could be obtained depending on the volume of RFV. This is the case illustrated in Fig. 16 Fig. 16. Two dilution effects simulated by the double reservoir model of Fig. 15 : only the fixed volume RFV is changed from one variant to another. Observe that baseflow BQ and old water components oldQ are not the same. The concentration is measured in Tritium Units.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.14 The example represented in Fig. 16 aimed to show that the old water component obtained by the usual chemical or isotopic hydrograph separation methods has not much to do with the hydrodynamic base-flow and in its present form rather leads to invalid inferences regarding the groundwater flow processes. In the double reservoir model the ratio between the recession coefficients of the slow reservoir and the rapid reservoir is about 1 to 10, and 50% of the infiltration is "diffuse", into the slow reservoir, and 50% is "concentrated", into the rapid reservoir. Both infiltration functions are triangular: 4 hours for the rising limb and 18 hours for the falling limb. The "tracer" is tritium: the concentration is 80 TU for the old water and 40 TU for the new or storm water. An important parameter for the dilution is RFV, the volume of water in the karst channels located below the spring level. It is probably the principal responsible for the high old water content obtained by the chemical and isotopic hydrograph separation methods and the misinterpretation of the results. The ratio between the volumes RFV used for the two variants was 1 to 4. Increasing the fixed volume diminishes the dilution and increases the old water component (see the C1, C2 curves and the dashed old water curves Cold1, Cold2 in Fig. 16 ), while the baseflow does not change at all. In spite of the many critical remarks presented above, we hope that this important dilution effect could be used, perhaps in the framework of a different paradigm, for a better understanding of karst and karstification. It deserves a better destiny than the only separation into a somewhat arbitrary new water and old water component. 4. Introduction to modeling karst aquifers 4.1. Aims of the modeling Analysing the global response of karst springs stimulates our imagination and incites to make hypotheses about the structure of the aquifer, about the hydraulic parameter fields, about the groundwater flow processes, often about karstification and sometimes about the evolution of karst in the interior of the aquifer. The direct verification of the consequences of our hypotheses by field measurements in the interior of the karstic medium is, obviously, very difficult, if not impossible. The so called "global models", such as the double reservoir model used in the previous chapter, do not help much either, because we have no information on the spatial distribution of the variables and the parameters. An indirect method of verification would consist in introducing the inferred karstic structures into a deterministic numerical model and then simulate the supposed processes and their effect on the "global response" of the aquifer (for example, the spring hydrograph), on the groundwater flow field, on the hydraulic head distribution, etc. The simulated behavior of the theoretical aquifer could then be compared to the usually accepted ideas on the groundwater flow processes in karst aquifers. This is the way followed by the research team of CHYN (Centre d'Hydrogologie de l'Universit de Neuchtel) for years. The aim of this chapter is to present the effect of the karst channel network and the epikarst zone on groundwater flow processes, as obtained by numerical finite element models simulating a few "theoretical" and oversimp lified karst aquifers. The results, although "theoretical", have important practical consequences on the monitoring strategies applied for karst aquifers, on the interpretation of the global responses obtained at karst springs and on the estimation of the recharge of the low conductivity "capacitive" volumes. They suggest to ask such fundamental questions as: what is the meaning of "groundwater level" observations in boreholes when separated from hydraulic conductivity measurements; what is the meaning of the "groundwater table" represented by isolines (equipotentials) in karst aquifers; what is the hydraulic meaning of the "components" obtained by chemical or isotopic hydrograph separation methods; etc. 4.2. Model and reality The reconstruction of a regional groundwater flow field, which is consistent with a given hydraulic conductivity field and with given boundary conditions, nearly always requires the use of numerical models. A model is not the reality, it is only the realization of a schematic and symbolic representation of the real system. The relations between "real system", "abstract scheme" and "numerical model" are represented in Fig. 17 which also shows the principal problems in modeling groundwater flow. Starting from incomplete information on the aquifer to be modeled, a schematic representation of the real system has to be worked out first. Generally, the flow of the groundwater is represented by differential equations, wh ich may change depending on the type of problem to solve (saturatedunsaturated flow, constant or variable density flow, multiphase flow, etc.). The flow equations contain a few parameters depending on the aquifer properties

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.15 Fig. 17. Principal problems in modeling groundwater flow. Observe that experimental methods should be used to check if the real system may be actually considered as a realization of the schematic representation (after Kiraly 1994 modified).(hydraulic conductivity, specific storativity, effective porosity, etc.) and the real medium will be represented by the field of these parameters, i.e. by giving a parameter value to each point of the modeled region, even there where we have never made any observation. As the available data on the hydraulic parameters are very limited, it appears clearly that indirect estimation of the parameters and interpolation or extrapolation of the measured values will be unavoidable when modeling real aquifers (see Fig. 18 ). It must be emphasized that fractured and karstified media may present additional difficulties due to the strong local heterogeneity of the parameter fields. The karst channel network existing in the real system, for example, is never entirely known. Finally, the imposed and initial conditions complete the schematic representation, sometimes also termed the "conceptual model". The second problem is related to the realization of a computer code based on numerical methods which allow to solve the equations defined in the abstract scheme. The problem is far from being simple and in most cases the numerical model is only a more or less imperfect realization of the abstract scheme. The third, very important problem in modelling groundwater flow is the transfer of the simulated results onto the real system Strictly speaking, the simulated results are not "valid" but in the highly simplified scheme or numerical model, and their meaningful transfer onto the real system requires that simplifying assumptions and uncertainties on the data explicitly do appear as uncertainties on the results. This could help to avoid such ridiculous situations as trying to simulate observed piezometric heads to within a few cen timetres, even though the schematised hydraulic conductivity field "ignores" the strong local heterogeneities existing in the real system. As a matter of fact, schematic representation of the real system, numerical modeling and experimental field work should go hand in hand. The numerical models might be used from the very moment where the first hypotheses on geometry, hydraulic parameters a nd boundary conditions are explicitly formulated. Whatever may be the value of these hypotheses, the numerical model will give a "response", which represents the verifiable consequences of our inevitably hypothetical and schematic representation of the real system. Ultimately, it is the observed behaviour of the aquifer which will decide if our hypotheses are acceptable or not.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.16 Fig. 18. Problems related to the reconstruction of hydraulic parameter and flow fields (after Kiraly 1975 modified)Finally it must be emphasized that modeling is not just curve-fitting. As it was pointed out by Klemes (1986) : "For a good mathematical model it is not enough to work well. It must work well for the right reasons It must reflect, even if only in simplified form, the essential features of the physical prototype." This is particularly recommended in modeling karst aquifers. 4.3. Combined discrete channel and continuum approach by using finite element models The nested model concept of the geological discontinuities was presented in the previous chapters. The modelling of this kind of nested structures nearly always requires the combination of the continuum approach with the discrete fracture or discrete channel model. At a regional scale, for example, the discrete fracture (or channel) model alone could not be realized at all, because of the tremendous amount of discontinuities (of different orders of magnitude) which ought to be introduced into the model. On the other hand, the equivalent continuum approach alone would not show the effect of the regional fault zones or the regionally developed karst networks on the groundwater flow systems. So it seems reasonable to model the regional faults or karst networks by 2-D or 1-D "discrete" zones, whereas the volumes between them (which contain only lower order fractures or channels) might be modelled by a 3-D equivalent continuum. As a matter of fact, every discontinuity, which is "big" with respect to the size of the modelled region, should be represented by a discrete zone. Numerical models using the finite element method are excellent for the combined discrete channel (or discrete fracture) and continuum approach, particularly if they allow for the combination of 1-D, 2-D and 3-D finite elements, as it was proposed by Kiraly ( 1979 1985 1988 1994 ) and Helmig (1993) In this case, the high conductivity karst channel network is simulated by 1-D linear or quadratic finite elements, which are "immersed" between 2-D or 3-D linear or quadratic elements representing the low conductivity fractured limestone volumes. The simulations presented in this paper were carried out by the computer codes FEN1 and FEN2. They have been developed at the Centre d'Hydrogologie de Neuchtel and simulate steadystate and transient, one-, twoor three-dimensional saturated groundwater flow by the finite element method. The computer programs allow for the incorporation of one-, twoor three-dimensional linear or quadratic elements within a threedimensional network. The saturated, constant density, transient groundwater flow is represented by equation (8) where

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.17 !"()0sh SdivKgradhQ t 2 1$1# 2 !!" (8) Ss is the specific storage coefficient, [K] is the hydraulic conductivity tensor, h is the hydraulic head and Q represents the general source/sink terms (infiltration, well discharges, etc.). The formulation for the finite elements is based on the Galerkin weighted residual approach and the resulting system of linear equations is solved by the frontal elimination technique of Irons (1970) The time dependent problem is solved in FEN2 by using the robust Crank-Nicholson implicit time-stepping scheme. UFEN1 is a code derived from FEN1 and simulates saturated/unsaturated steady-state groundwater flow. In this paper it is used to simulate the free groundwater table in a theoretical "shallow" karst aquifer. The computer codes allow the modeller to "concatenate" several aquifers into one model and this facility is used to link the epikarst with the mean aquifer. A slightly modified version of FEN2 offers another facility when used to simulate karst aquifers. By giving the identification number of the nodal points located on the karst channels, the program calculates the contribution of each 3-D element (i.e. low conductivity fractured volume) to the karst net. The sum of these contributions is simply the baseflow which can be compared to the total spring hydrograph. Using the linear Darcy's law to simulate the groundwater flow in saturated karst channels represents only a crude approximation of the real system, but our aim was to obtain a rapid and rather "qualitative" indication on the effect of the enormous contrast between the hydraulic conductivities of fractured limestones (10-6 m/s) and karst channels (10 m/s or more). The conclusions presented in this paper will not be changed qualitatively with the simulation of turbulent flow: the effects due to concentrated infiltration into the channel network (inversion of gradients, negative base-flow, etc.), for example, will be only increased. 5. Presentation and discussion of a few results 5.1. The 2-D approach: some early results In the 1970s it was possible to introduce 1-D elements between 2-D finite elements, and thus simulate the karst channel network in 2-D karst aquifers (Kiraly and Morel 1976a 1976b ). These early and very simplified 2-D karst models delivered quite interesting results. %& The simulation of the typical hydrograph of the karst springs (see Fig. 6 ), with the nonexponential rapid recession and the exponential slow recession, nearly always requires the introduction of a high permeability karst channel network in an otherwise low permeability aquifer volume. %& The duality of the hydraulic conductivity field causes an important scale effect in the model: nearly the whole aquifer volume has a very low hydraulic conductivity, however the global structure behaves as a highly transmissive system. Qualitatively it is the right type of structure: we are not very far from karst! We get even closer to karst with the infiltration problem. %& If the chosen spacing of the karst channels allows to simulate correctly the exponential part of the recession curve of springs, the correct simulation of the peak-flow and the rapidly decreasing nonexponential part of the recession curve requires, however, that more than 50% of the infiltration arrive in "concentrated" form, directly into the high conductivity channels. The concentrated infiltration in the model must have a physical counterpart in the real system. A sound hypothesis would be to suppose, that besides small rivers disappearing in sinkholes, an important part of the infiltration is drained rapidly, probably already at shallow depth in a thin high conductivity layer, towards the karst channel network and the kars t spring. This would be the epikarst zone of Mangin (1975) %& The important concentrated infiltration, i.e. the duality of infiltration, has a very important consequence: the temporary inversion of the hydraulic gradients between the channels and the low permeability volumes. %& The temporary inversion of hydraulic gradients has an even more important consequence: the temporary reduction of the base-flow to zero in the vicinity of the peak-flow. And this is not good news for those who equate the old water component of a karst spring with the base-flow. %& At least, we have to mention that the recession coefficient of the last, exponential part of the depletion curve depends as much (if not more) on the conductivity and the density of the karst channels than on the hydraulic properties of the low permeability volumes. Although very simple, these 2-D models were very good from a heuristic point of view. Even if in a very simplified and naive form, they had the most important properties of a karst aquifer (duality of the hydraulic conductivity field, duality of the infiltration processes, duality of the groundwater flow field, concentrated discharge at the karst spring). The problems we met with them were actually relevant to the study of karst aquifers and suggested further investigations on the theoretical level, as well as in the domain of empirical field works.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.18 5.2. The 3-D approach: the Epikarst model Earlier numerical experiments with 2-D Finite Element models showed the necessity to impose a high proportion of concentrated infiltrations in order to generate the typical "karstic" storm hydrographs (Kiraly and Morel 1976a 1976b ). It was supposed, that besides the rivers disappearing in sinkholes, the concentrated infiltrations would result from the rapid drainage in a high permeability "skin" at shallow depth: the epikarst (Mangin 1975) However, the epikarst layer could not be explicitly included in these 2-D models. To indirectly show its role, we explicitly introduced the epikarst layer in a "synthetic" 3-D Finite Element model and varied the proportion of the diffuse infiltrations with respect to the concentrated infiltrations resulting from the rapid drainage in the epikarst zone. As the model is transparent for the modeller, the simulated behaviour of the theoretical karst aquifer will clearly show the effect of epikarst not only on the spring hydrograph, but also on the baseflow component of the spring discharge, on the variation of hydraulic heads and fluxes during recharge and recession periods, as well as on the recharge conditions of the low permeability fractured volumes. The detailed results are presented in (Kiraly et al. 1995) we show here only a few diagrams without many comments. The diagram of Fig. 19a shows the 3-D geometry of a theoretical "half-syncline" drained by a very simplified high-permeability karst channel network. The karst channels are simulated by quadratic 1-D elements introduced "in sandwich" between the quadratic 3-D elements simulating the lowpermeability fractured volumes. The epikarst is simulated by a 2-D finite element layer which will discharge into the channel network of the 3-D syncline, such as represented in Fig. 19a The hydraulic heads are imposed at the base of the epikarst model (where the channels intersect the 2-D layer), and the calculated discharges are injected at each time-step into the channel network of the 3-D model. This will represent the concentrated infiltration function for the mean aquifer. Note that nearly the entire volume of the mean aquifer (including the high permeability channel network) is below the karst spring level, in the saturated zone. Fig. 19b represents a small "shallow" karst aquifer with an important vertical exageration. The aquifers of this type generally develop on plateaus or gently dipping cuestas. In the theoretical aquifer represented in Fig. 19b the karst network is located above the spring level and is everywhere unsaturated. The channels are actually underground rivers and represent seepage surfaces with variable boundary conditions for the low-permeability fractured volumes. The free groundwater table was obtained by simulating the steady-state, saturated/unsaturated flow in the low-permeability volumes. The karst syncline described above and the shallow karst of Fig. 19b represent two extremes and their reaction to important concentrated infiltrations will not be the same. The aim of including the "shallow karst" configurati on in this paper is to remind the reader of the diversity of karst aquifers and to avoid abusive genera lizations of the results obtained by the saturated karst syncline model. The hydraulic parameters are the same for all variants of the epikarst model. The hydraulic conductivities K are realistic: 5 10-6 [m/s] for the low-permeability fractured volumes and 100 [m/s] for the high-permeability karst channels. In the 2-D epikarst layer the transmissivity T is relatively high: about 5 10-2 m2/s. Linear Darcy's law is used throughout the models. Fig. 19a. Representation of the epikar st in the finite element model. Fig. 19b. Shallow karst aquifer model, with unsaturated karst channels.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.19 The specific storage coefficients Ss are kept artificially low in order to "accelerate" the evolution of the simulated hydraulic head and flow field. In the channel network the values of Ss are 400 to 500 times higher than in the low-permeability fractured volumes. Finally it must be emphasized that we use in the model a very simplified karst channel network. In real systems the karst network is hierarchically organized, with lower and higher order branches having lower and higher hydraulic conductivity values. In the above described model all branches of the karst network are of the same order of magnitude and have the same hydraulic conductivity. The volume of the total infiltrations remains the same in each variant, but the proportion of the diffuse and concentrated infiltrations will change from one variant to another. Four cases have been simulated: %& DSYN0: 100% diffuse infiltration 0% drained by the epikarst %& DSYN20: 80% diffuse infiltration 20% drained by the epikarst %& DSYN50: 50% diffuse infiltration 50% drained by the epikarst %& DSYN100: 0% diffuse infiltration 100% drained by the epikarst Fig. 20 represents the intensity of infiltration, as well as the total recharge function of the epikarst and the concentrated recharge function of the karst channels for variant DSYN100. There are three input events ("storms"), of duration of 24 hours each. During the first and second event the infiltrations are distributed over the whole syncline. During the third "storm", infiltration takes place only on a small stripe in the middle part of the model, representing about 30% of the total infiltration area. 5.3. Effect on the shape of the spring hydrograph and on the hydraulic heads Fig. 21 is self-explanatory: it represents the spring hydrographs for different proportions of infiltration drained by the epikarst into the high-permeability channel network. It appears clearly that without some kind of concentrated infiltrations we cannot simulate the typical karstic reactions of the spring. The rise of the groundwater table in the lowpermeability volumes cannot "press" enough water into the karst channels to cause a typical karstic storm hydrograph at the spring. It seems reasonable to admit that in most "open" karst aquifers more than 40% of the infiltrations should be drained rapidly into the karst channels (also see Kiraly and Morel 1976a) The high proportion of "old water" component obtained by the method EMMA (End Member Mixing Analysis) does not represent a serious argument against important concentrated infiltrations into the channel network, because the method is not related to any consistent groundwater flow model. Indeed, in the period preceding the storm event an important quantity of "old water" may be stored not only in the epikarst zone and in the unsaturated zone, but also in the high-permeability karst network itself, at least in the channels located below the spring level. This "old water" flows out rapidly during the peak discharge, even if the low-permeability fractured volumes do not contribute to the peak-flow at all. Fig. 20. Intensity of infiltration (above), as well as total recharge function of the epikarst and concentrated recharge function of the karst channels (below) for variant DSYN100

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.20 Fig. 21. Simulated spring hydrographs for different proporti ons of infiltration drained by the epikarst. Fig. 22a. Variation of the hydraulic head in borehole "B" for DSYN0. Fig. 22b. Variation of the hydraulic head in borehole "B" for DSYN100 Earlier numerical experiments with 2-D finite element models suggested that concentrated infiltrations might cause an inversion of the gradients between karst channels and low-permeability volumes (Kiraly and Morel 1976a 1976b ). These 2D models cannot show, however, the vertical distribution of the hydraulic heads in a borehole. Taking advantage of the 3-D model, we "registered" the simulated heads in an imaginary borehole "B", the location of which is presented in Fig. 23a and 23b. The borehole intersects a karst channel and the hydraulic heads are measured at 7 points between the top and the base of the aquifer. The results are represented for variants DSYN0 (no concentrated infiltrations, see Fig. 22a ) and DSYN100 (100% of the infiltrations are concentrated, see Fig. 22b ). Again, the figures are self-explanatory and need not many comments.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.21 Fig. 23a. Hydraulic head field for DSYN100 in recharge period. Fig. 23b. Hydraulic head field for DSYN100 in recharge period. Location of borehole "B" shown on the figures.During the recharge period there is nearly always an inversion of gradients between the karst channel and the low-permeability volumes located below the channel. The concentrated infiltrations must be really important to produce the same inversion with respect to the low-permeability volumes located above the channel. The bloc-diagrams of Fig. 23a and 23b clearly show the recharge and drainage mechanism with epikarst and concentrated infiltration. The practical consequences of these theoretical results are important: the hydraulic heads should be measured separately in the high-permeability segments and in the low-permeability segments of boreholes or piezometers. If we measure only one "groundwater level" in an otherwise heterogeneous borehole, the results will be rather misleading than helpful. Other practical consequences are related to the determination of the baseflow component, to the recharge mechanism of the low permeability fractured volumes, to the interpretation of the chemical or isotopic composition of the springwater, etc. 5.4. Effect of the epikarst on the "base-flow" component of karst springs In spite of the fact that the inversion of gradients between karst channels and low-permeability volumes is well known by many karst hydrogeologists, most of the graphically obtained base-flow hydrographs don't show the logical consequence, namely the zero (or negative) baseflow value during recharge periods. One of the few exceptions is found in (Tripet 1972) who suppressed the base-flow component of the Areuse spring during the recharge periods. Taking advantage of the possibility to calculate the contribution of the low-permeability 3-D elements to the nodes located on the 1-D karst channels, we computed the baseflow component for each variant. The dramatic effect of the concentrated infiltrations on the base-flow component is presented in Fig. 24 for variants DSYN0, DSYN50 and DSYN100. The appearance of negative base-flow during the recharge period indicates that the karst channels inject more water into the low-permeability volumes than they drain. The volume of this recharge might not be very important, but the fact that the low-permeability volumes may be recharged "from the interior" should not be overlooked. Another consequence of the negative baseflow appears when estimating the "rapid infiltration" from the spring hydrograph. Generally this is done by substracting the graphically determined baseflow component from the total discharge curve. Now, when the baseflow is negative, it should be added to the spring discharge, otherwise the intensity of the rapid or direct infiltration will be systematically underestimated (see Fig. 24b, 24c ).

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.22 Fig. 24. Springflow, baseflow, epiflow and (epiflow+baseflow) for variants DSYN0 (a), DSYN50 (b) and DSYN100 (c). Note that concentrated infiltration (epiflow) may be greater, or even much greater than the spring discharge. The curve (baseflow+epiflow) is not visi ble, because it coincides almost exactly with the springflow.As the model allows for the independent estimation of the baseflow and of the rapid or concentrated infiltration into the karst channel network (which will be called "epiflow", for short, in the following), we can take a critical look at the usually accepted chemical or isotopic hydrograph separation methods. Fig. 24b, 24c show, that the "new water component" obtained by the End Member Mixing Analysis (EMMA) could not be identified with the "rapid recharge to the conduit system after a storm", as it was stated by Dreiss (1989, page 121) Indeed, the "new water component" obtained by EMMA must be always smaller than the spring discharge, but figures 24b and 24c indicate clearly that the rapid recharge into the karst channels, noted as the epiflow, may be greater (or even much greater) than the spring discharge. 5.5. Remarks on the recharge of the low conductivity volumes: the "Faraday cage" effect of epikarst The huge low permeability fractured limestone volumes are often designated as the "capacitive" part of karst aquifers. They might contain important groundwater resources, and their recharge mechanism may have important practical consequences on the groundwater management problems (base-flow of karst springs, exploitation of groundwater by pumping wells or galleries, etc.). Fig. 19a ("deep" karst syncline) and Fig. 19b ("shallow karst") suggest that a well developed epikarst layer enhancing the concentrated infiltration into the high conductivity ka rst channel network will "short-circuit" the low conductivity volumes and will play the role of a "Faraday cage" with respect to the

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.23 main aquifer. Depending on the importance of this "Faraday cage" effect, the recharge of the low conductivity volumes could be much smaller than in the case of pure diffuse infiltration, with the above mentioned important consequences on the groundwater management problems. In the "deep syncline" configuration the inversion of gradients will always contribute to recharging the low conductivity volumes "from the interior", but in the "shallow karst" configuration the "short-circuit" of the low permeability volumes might be almost total. 6. Conclusion and outlook Karst aquifers are 3-D systems and cannot be reduced to 2-D objects without losing important information on the infiltration processes and the distribution of hydraulic heads. Numerical experiments with 2-D and 3-D finite element models using the combined discrete channel and continuum approach, and simulating the infiltration and groundwater flow processes in a highly simplified theoretical karst aquifer, allowed to show the role of the organized karst channel network and the importance of the existence or non-existence of an epikarst zone enhancing concentrated infiltration. The effect of the epikarst on the hydraulic head and the groundwater flow field has practical consequences on the monitoring strategies applied for karst aquifers, on the interpretation of the global responses obtained at the karst springs and on the estimation of the recharge of the low conductivity "capacitive" volumes. Hydraulic head measurements should always be related to zones of known hydraulic conductivity and the "piezometric maps" of karst aquifers should always indicate the hydraulic conductivity at the measurement points (see, for example, Jeannin 1995 ). In a quite general way, it should be examined whether the presently available observations allow to solve the problems which we meet in karst hydrology or not. Indirect estimation of the hydraulic parameter fields, interpolation or extrapolation of the available data are important problems in the practice. A good genetic theory would be, perhaps, the best "interpolation function", but the elaboration of such a theory would require common research between specialists of groundwater flow and specialists of karst evolution. Acknowledgements Some of the computer codes used for the groundwater flow simulation and some of the ideas presented in this paper were developed in the framework of earlier research projects supported by the Swiss National Foundation for Scientific Research. Our most sincere thanks to this Institution. References Ababou R., Trgarot G. and Larabi A. 1998. Partially Saturated Hydrological Flows: Numerical Experiments and Analyses. Proceedings IXth CMWR, Computational Methods in Water Resources, Crete, Greece, June 1998, 8 pp. Barton N. (coordinator). 1978. Suggested methods for the quantitative description of discontinuities in rock masses. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 15(6), 319-368. Bear J., Tsang C.F. and de Marsily G. (Eds.). 1993. Flow and contaminant transport in fractured rock. San Diego: Academic Press Bedinger M.S. 1966. Electric analog study of cave formation. Nat. Speleol. Soc. Bull. 28 (3), 127132. Berkaloff E. 1967. Limite de validit des formules courantes de tarissement de dbit. Chronique d'Hydrogologie 10, 31:41. Bonacci O. 1987. Karst Hydrology. Berlin: Springer Verlag. Bonacci O. 1993. Karst springs hydrographs as indicators of karst aquifers. J. Hydrol. Sciences 38(1-2), 51-62. Bonnet M., Margat J. and Thiery D. 1976. Essai de reprsentation du comportement hydraulique d'un systme karstique par modle dterministe: application la "Fontaine de Vaucluse". Annales scientifiques de l'Universit de Besanon, fasc. 25, 3e srie, 79-95. Deuxime colloque d'hydrologie en pays calcaire. Burger A. 1956. Interprtation mathmatique de la courbe de dcroissance du dbit de l'Areuse, Jura neuchtelois (Suisse). Bull. Soc. Neuch. Sc. Nat. 79, 49-54 Chinnery M.A. 1965. Secondary faulting. 1. Theoretical aspects. Canadian Journ. Earth Sci. 3, 163-174. Dreiss S.J. 1982. Linear kernels for karst aquifers. Water Resour. Res. 18 (4), 865-876. Dreiss S.J. 1989. Regional scale transport in a Karst aquifer: 1. Component separation of spring flow hydrographs. Water Resources Research 25 (1), 117-125.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.24 Drogue C. 1967. Essai de dtermination des composantes de l'coulement des sources karstiques. Chronique d'Hydrogologie 10, 42-47. Drogue C. 1972. Analyse statistique des hydrogrammes de dcrues des sources karstiques. J. Hydrol. 15, 49-68. Eisenlohr L., Kiraly L., Bouzelboudjen, M. and Rossier Y. 1997. Numerical simulation as a tool for checking the interpretation of karst spring hydrographs. J. Hydrol. 193, 306-315. Forkasiewicz J. and Paloc H. 1967. Le rgime de tarissement de la Foux de la Vis. Chronique d'hydrogologie 10, 59:73 Fritz P., Cherry J.A. Weyer K.U. and Sklash M. 1976. Storm runoff analyses using environmental isotopes and major ions. In: "Interpretation of environmental isotope and hydrochemical data in groundwater hydrology", IAEA, p. 111-130. Gramberg J. 1965. The axial cleavage fracture. 1. Axial cleavage fracturing, a significant process in mining and geology. Engineering Geology 1(1), 31-72. Gu W.Z. 1992. Challenge on some rainfall-runoff conceptions traced by environmental isotopes in experimental catchments. In: Hoetzl and Werner (Eds.), Tracer Hydrology. p. 397-403. Harum T. and Fank J. 1992. Hydrograph separation by means of natural tracers. In: Hoetzl and Werner (Eds.), Tracer Hydrology. p. 143-146. Hauns M., Jeannin P.-Y. and Hermann F. 1998. Tracer transport in karst underground rivers: tailing effect from channel geometry. Bull. Centre d'Hydrogol. 16, 123-142. Helmig R. 1993. Theorie und Numerik der Mehrphasenstrmungen in geklftet-porsen Medien. Institut fr Strmungsmechanik und Elektron. Rechnen im Bauwesen der Universitt Hannover, Bericht Nr 34/1993, 186 p. Hobbs S.L. and Smart P.L. 1986. Characterisation of carbonate aquifers: a conceptual base. Proc. 9th Int. Congr. of Speleology, Barcelona. Irons B.M. 1970. A frontal solution program for Finite Element analysis. Int. Journ. Num. Meth. Eng. 2, 5-32. Jeannin P.-Y. and Grasso A. 1995. Recharge respective des volumes de roche peu permable et des conduits karstiques, rle de l'pikarst. Bulletin du Centre d'Hydrogologie 14, 95-111. Jeannin P.-Y. and Marchal J.-C. 1995. Lois de pertes de charge dans les conduits karstiques: base thorique et observations. Bulletin du Centre d'Hydrogologie 14, 149-176. Jeannin P.-Y. 1995. Comportement hydraulique mutuel des volumes de roche peu permable et des conduits karstiques: consquences sur l'tude des aquifres karstiques. Bulletin du Centre d'Hydrogologie 14, 113-148. Jeannin P.Y. and Sauter M. 1998. Analysis of karst hydrodynamic behaviour using global approaches: a review. Bull. Centre d'Hydrogologie 16, 31-48. Jamier D. and Simeoni G. 1979. Etude statistique de la distribution spatiale des lments structuraux dans deux massifs des Alpes helvtiques: consquences pour l'hydrogologie karstique. Bulletin du Centre d'Hydrogologie 3, 1-26. Kiraly L. 1969. Anisotropie et htrognit de la permabilit dans les calcaires fissurs. Eclogae Geol. Helv. 62/2, 613-619. Kiraly L. 1973. Notice explicative de la carte hydrogologique du canton de Neuchtel. Supplment du Bulletin de la Socit neuchteloise des sciences naturelles, Tome 96, 16 p. + carte. Kiraly L. 1975. Rapport sur l'tat actuel des connaissances dans le domaines des caractres physiques des roches karstiques. In: Burger A. and Dubertret L. (Eds), Hydrogeology of karstic terrains, Int. Union of Geol. Sciences, B, 3, 5367. Kiraly L. 1978. La notion d'unit hydrogologique. Bulletin du Centre d'Hydrogologie 2, 83-216. Kiraly L. 1979. Remarques sur la simulation des failles et du rseau karstique par lments finis dans les modles d'coulement. Bulletin du Centre d'Hydrogologie 3, 155-167. Kiraly L. 1984. Rgularisation de l'Areuse (Jura suisse) simule par modle mathmatique. In: Burger A. and Dubertret L. (Eds), Hydrogeology of karstic terrains, Int. Union of Geol. Sciences, B, 3, 94-99. Kiraly L. 1985. FEM301 A three dimensional model for groundwater flow simulation. NAGRA Technical Report 84-49, 96 p. Kiraly L. 1988. Large scale 3-D groundwater flow modelling in highly he terogeneous geologic medium. In: Custodio E. et al. (Eds.), Groundwater flow and quality modelling, NATO ASI series Vol.224, 761-775. Kiraly L. 1994. Groundwater flow in fractures rocks: models and reality. 14. Mintrop Seminar ber Interpretationsstrategien in Exploration und Produktion, Ruhr Universitt Bochum 159/1-21. Kiraly L., Mathey B. and Tripet J.-P. 1971. Fissuration et orientation des cavits souterraines:

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.25 rgion de la Grotte de Milandre (Jura tabulaire).Bull. Soc. Neuchteloise Sc. Nat. 94, 99-114. Kiraly L. and Morel G. 1976a. Etude de rgularisation de l'Areuse par modle mathmatique. Bulletin du Centre d'Hydrogologie 1, 19-36. Kiraly L. and Morel G. 1976b. Remarques sur l'hydrogramme des sources karstiques simul par modles mathmatiques. Bulletin du Centre d'Hydrogologie 1, 37-60. Kiraly L. and Mueller I. 1979. Htrognit de la permabilit et de l'alimentation dans le karst: effet sur la variation du chimisme des sources karstiques. Bulletin du Centre d'Hydrogologie 3, 237–285. Kiraly L., Perrochet P. and Rossier Y. 1995. Effect of the epikarst on the hydrograph of karst springs: a numerical approach. Bulletin du Centre d'Hydrogologie 14, 199-220. Klemes V. 1986. Dilettantism in hydrology: transition or destiny? Water Resources Research 22 (9), 177S-188S. Klimchouk A.B., Ford D.C., Palmer A.N. and Dreybrodt W. (Eds.). 2000. Speleogenesis. Evolution of karst aquifers. Nat. Spel. Soc., Huntsville, Alabama, USA. Labat D. 2000. Nonlinarit et nonstationarit en hydrologie karstique. Ph.D. thesis at Universit de Toulouse, IMFT. Lee C.H. and Farmer I. 1993. Fluid flow in discontinuous rocks. London: Chapman & Hall, 169 p. LeGrand H.E. and Stringfield V.T. 1966. Development of permeability and storage in the Tertiary limestones of the south eastern states, USA. Bull. AIHS 11 (4), 61-73. Mandel S. 1966. A conceptual model of karstic erosion by groundwater. Bull. AIHS XI/1, 5-7. Mangin A. 1975. Contribution l'tude hydrodynamique des aquifres karstiques. Thse, Universit de Dijon, 124 p. Mangin A. 1984. Pour une meilleure connaissance des systmes hydrologiques partir des analyses corrlatoire et spectrale. J. Hydrol. 67, 25-43. Martinec J., Siegenthaler U., Oeschger H. and Tongiorgi E. 1974. New insights into the runoff mechanism by environmental isotopes. In: Isotope techniques in groundwater hydrology, IAEA-SM-182/9, 129-143. Martinec J., Oeschger H., Schotterer U., Siegenthaler U., Nuti S. and Tongiorgi E. 1979. Example of separation of runoff components by environmental isotopes. Rivista Italiana di Geofisica e Scienze Affini 5, 87-89. Martinec J., Oeschger H., Siegenthaler U., Schotterer U., Nuti S. and Tongiorgi E. 1979. Example of a separation of runoff components by environmental isotopes. Rivista italiana di geofisica e scienze affini, vol 5, 87-89. Martinec J., Oeschger H., Schotterer U. and Siegenthaler, U. 1982. Snowmelt and groundwater storage in an Alpine basin. In: Hydrological Aspects of Alpine and High Mountain Areas, IAHS Publ. No 138, 169-175. Mohrlok U. 1996. Parameter-Identifikation in Doppel-Kontinuum-Modellen am Beispiel von Karstaquiferen. Dissertation an der Geowissentschaftlichen Fakultt der Universitt Tbingen, TGA, Reihe C, Nr. 31, 125 p. O.E.C.D. 1988. The International HYDROCOIN Project. Level 1: code verification. OECD Publications, Paris, 198 p. Rhodes R. and Sinacori M.N. 1941. Pattern of ground-water flow and solution. J. of Geology 49 (8), 785-794. Romm E.S. and Pozinenko B.V. 1963. Investigation of seepage in fractured rocks. Trudy VNIGRI, No. 214, Leningrad. (in Russian). Rouleau A. 1985. Statistical characterization and numerical simulation of a fracture system. Application to groundwater flow in the Stripa granite. Ph.D. thesis, University of Waterloo. Scheidegger A.E. 1963. The physics of flow through porous media. University of Toronto Press. Schoeller H. 1967. Hydrodynami que dans le karst. Chronique d'Hydrogologie 10, 7-21. Snow D.T. 1969. Anisotropic permeability of fractured media. Water. Res. Research 5 (6), 1273-1289. Swinnerton A.C. 1949. Hydrology of limestone terrains. In: Meinzer O.E. (Ed.), Hydrology, Physics of the Earth. New York: Dover Publ. Toth J. 1963. A theoretical analysis of groundwater flow in small drainage basins. J. Geophys. Res. 68, 4798-4812. Trgarot G. 2000. Modlisation couple des coulements saturation variable avec htrognits, forages et interfaces hydrologiques Thse de doctorat de l'INP de Toulouse. Institut de Mcanique des Fluides de Toulouse, Mai 2000. Tripet J.-P. 1972. Etude hydrogologique du bassin de la source de l'Areuse. Mat. carte gol. de la Suisse, srie Hydrologie, 21, 183 p.

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L.Kiraly / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.26 Trsch J. and Zurbrgg C. 1995. Turbulent flow in high permeable karst. Bulletin du Centre d'Hydrogologie 14, 235-240. Wollrath J. and Helmig R. 1991. SM-2, Strmungsmodell fr inkompressible Fluide, Theorie und Benutzerhandbuch. Institut fr Strmungsmechanik, Universitt Hannover, Techn. Bericht 1991.



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Speleogenesis and Evolution of Karst Aquifers The Virtual Scientific Journal www.speleogenesis.info Speleogenesis in carbonate rocks Arthur N. Palmer Department of Earth Sciences, State University of New York, Oneonta, NY 13820, USA Re-published by permission from: Gabrovšek, F. (Ed.), Evolution of karst: from prekarst to cessation. Postojna-Ljubljana, Zalozba ZRC, 43-60. Abstract This paper outlines the current views on cav e origin in carbonate rocks, combining id eas from a variety of sources. A typical dissolution cave develops in several stages that grade smoothly from one to the next: (1) Initial openings are slowly enlarged by water that is nearly at solutional equilibri um with the local bedrock. (2) As the early routes enlarge, t hose with the greatest amount of flow grow fastest. (3) These favoured routes eventually become wide enough that groundwater is able to retain most of its solut ional aggressiveness throughout the entire distance to the spring outle ts. This breakthrough time usually requires times on the order of 104 to 105 years and ends the inception phase of spel eogenesis. (4) Discharge along these selected routes increases rapidly, allowing the m to enlarge into cave passages rather uniformly over their entir e length. Maximum enlargement rates are roughly 0.001-0.1 cm/yr, depending on the local water chemistry and lithology. (5) The cave acquires a distinct passage pa ttern that depends on the natu re of groundwater recharge, the geologic setting, and the erosional hist ory of the region. Branchwork patterns dominate in most carbo nate aquifers. Maze caves are produced by any of the following: steep hydraulic gradients (e.g. during floods), short flow paths, un iform recharge to many openings, and mixing of wate rs that contrast in chemistry. (6) Enlargement rate usually decreases as passages become air-filled, owing to loss of aggressiveness as carbon di oxide escapes through openings to the surface. (7) The cave typi cally evolves by diversion of water to new and lower routes as the fluvial base leve l drops. (8) The cave is eventually destroyed by roof collapse and by intersection of passages by surface erosion. At an y given time, different parts of the same cave may be experie ncing different stages in this sequence. Keywords: cave origin in carbonate rocks Introduction Caves are present in all rather pure carbonate rocks that are in geologic settings and climates that allow abundant groundwater recharge. For this reason, it is clear that cave origin requires no special chemical mechanism beyond the circulation of meteoric groundwater. Dissolution caves can form by other processes, but this is the common speleogenetic mode in mo st carbonate aquifers and is the main topic of this paper. Most of the concepts presented here are not new, but, where possible, alternate viewpoints are given in the hope of encouraging further discussion. Cave inception Speleogenesis requires one basic thing: Groundwater must dissolve the bedrock rapidly enough to produce caves before the rock is removed by surface erosion. This requires the through-flow of large amounts of solutionally aggressive water along stable flow paths. The earliest stages At great depth beneath the surface there is very little groundwater flow because openings in the rock are narrow and few, and hydraulic gradients are feeble. But as uplift and erosion expose these rocks near the surface, increasing amounts of groundwater pass through them. Along any given flow path, the solutional enlargement rate is controlled by a simple mass balance. The mass removed from the walls of the growing conduits is equal to that which is carried away in solution. The increase in volume thus depends on how much water passes through the conduit, and how rapidly the water dissolves the rock In other words, the two major controls are discharge and chemical kinetics. Early in the development of a carbonate aquifer, all groundwater becomes nearly saturated with dissolved calcite and/or dolomite before it emerges at the surface. The total amount of rock removed along any flow path is nearly independent of chemical kinetics, because the water has enough time to equilibrate with the rock, regardless of

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.2 dissolution rates. The saturation concentration depends on the minerals present, CO2 concentration, type of system (open vs. closed), temperature, and interactions with other dissolved components. All these show considerable variation, both spatially and temporally, but it is unlikely that there will be major differences between neighboring flow paths within a given aquifer. In contrast, there are great variations in discharge from one flow path to another – and this is the main control over which the early paths are able to grow into caves. Most dissolution takes place at the upstream ends of the flow paths, where aggressive water first enters the carbonate rock. (“Upstream” and “downstream” in the following discussion refer to the up-gradient and down-gradient ends of the system, even where the flow is only laminar seepage.) With time and distance, there is an increase in saturation ratio of the dissolved minerals (actual concentration divided by saturation concentration, C/Cs ). At first the dissolution rate decreases in a roughly linear manner. But as the saturation ratio rises above approximately 60-90% (the exact value depends on temperature and CO2 content), the dissolution rate decreases much more rapidly. The result is that the final approach toward saturation is very slow (see Berner and Morse, 1974; Plummer and Wigley, 1976; Plummer et al., 1978; Dreybrodt, 1990; Palmer, 1991). Dissolution is so rapid in the upstream sections that if the remainder of the dissolution followed the same trend, the water would lose virtually all its aggressiveness after only a short distance of flow. Dissolution would be so slow in the rest of the aquifer that cave development would be almost impossible (Palmer, 1984). Except in the most ideal situations (wide, short fractures with steep hydraulic gradients, e.g. along escarpments), enlargement of the initial openings to cave size would require many millions of years, during which the carbonate rock is likely to be entirely removed by erosion. Interestingly, it would be unlikely for caves to form with either the rapid dissolution at low saturation ratios or the slow dissolution at high saturation ratios. Early slow dissolution along the entire flow path is essential for preparing the way for the rapid dissolution that follows. But the slow dissolution alone cannot enlarge the routes rapidly enough to form caves within a geologically feasible time. Rapid dissolution at low saturation ratios is necessary to achieve this. But, as shown above, the rapid dissolution by itself cannot form caves in most situations. Geological aspects of cave inception The initial width of fissures (e.g. fractures and partings) is perhaps the most uncertain of all field conditions that influence cave inception. By the time a cave is large enough for humans to enter, the evidence has long disappeared. Initial fissure width is a slippery concept, because the widths increase with time even without being dissolved, simply by release of stress as the overlying rocks are eroded away. Field evidence suggests that a minimum initial fissure width of about 0.01 mm is required for cave development (Bcker, 1969). However, this value depends on hy draulic gradient, flow distance, water chemistry, and length of time available, and so the threshold for initial fissure width is not a fixed value, but instead depends on the local setting. To clarify how wide the initial fissures in limestone might be, it is helpful to gather data from relatively insoluble rocks that are approximately as brittle as limestone. Intrusive igneous rocks such as granite should give a close approximation. Water wells in these rocks have fairly small yields, especially at depths of more than 50 m below the surface (Freeze and Cherry, 1979, p. 158). But even with conservative estimates for hydraulic gradient and fissure frequency, the observed well yields require fissures that are roughly 0.1-0.5 mm wide. Surely only a few of the many fissures are this large, but they are important ones, which in soluble rock would grow into caves. Inception horizons were originally defined by Lowe (1992) as beds or stratal interfaces that provide a chemical environment that favours cave development. The presence of pyrite along a geologic contact was cited as a typical example, whereby oxidation of the sulphide to sulphuric acid might give a substantial boost to cave development. One difficulty with this particular example is the deficiency of oxygen in most deep groundwater. Structural and hydraulic factors are also crucial in determining which initial openings are able to develop into caves. The presence of interbedded sulphates within carbonate rocks provides a suitable environment for cave inception. Dissolution of the sulphates can boost porosity, although this process forces calcite to precipitate by the common-ion effect. Because of differences in molar volume, the precipitated calcite usually does not occupy all the porosity generated by dissolution of gypsum or anhydrite. This process is even more potent when limestone, dolomite, and gypsum interact within the same system. As calcite is forced to precipitate, the solubility of gypsum rises to almost 1.5 times more than that of gypsum alone, and the solubility of dolomite rises to several

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.3 times its normal value. Because dolomite dissolves so slowly, the process is drawn out over long distances and times, potentially resulting in long, continuous paths of increased porosity that may pave the way for later cave development. The geochemical process has been validated by field measurements (e.g. Bischoff et al., 1994), but its impact on cave development is still unclear. Breakthrough Eventually the entire length of an incipient cave becomes large enough to allow water to pass all the way through while still retaining most of its aggressiveness. At this time there is a fairly sudden transition (“breakthrough”) to rapid dissolution throughout the entire flow path. From then on, the entire route enlarges rapidly at a roughly uniform rate of about 0.001-0.01 cm/yr, depending on the water chemistry. This rate varies with the amount of turbulence, but only at low saturation ratios (Plummer and Wigley, 1976; White, 1984). At the high saturation ratios of most karst water the effect is minor. In mature caves, abrasion by coarse sediment load can incr ease local rates of cave development (Smith and Newson, 1974). These factors are insignificant compared to the truly great differences in growth rate that distinguish true cave passages with low saturation ratios from narrow flow paths whose water is nearly saturated with dissolved carbonates. Fig. 1 shows the mean enlargement rate in an ideal fissure as a function of discharge and flow length. The steep parts of the curves represent the slow dissolution rates governed by the mass balance, and the horizontal segments at the top represent the rapid dissolution controlled mainly by kinetics (Palmer, 1991). Because the enlargement rates are not uniform throughout the fissure, the rates shown in Fig. 1 cannot be translated directly into the time required for an incipient cave to reach breakthrough. To do this, finite-difference modelling is necessary. The results are shown in Fig. 2. The time required for chemical breakthrough can be considered the “gestation time” through which an incipient cave must pass in order to allow it to grow into a true cave. It is difficult to specify exactly when this time begins. In some ways, it involves the entire age of the carbonate aquifer, if one includes all the effects of early diagenesis, burial, and uplift in order to reach its present state (Klimchouk and Ford, 2000). But before cave growth can truly begin, there must be a substantial hydraulic gradient. Thus it is customary to start the clock when the carbonate rock is first exposed above base level, at the time when both recharge zones and discharge zones are well defined. Computer models can track the growth of idealized fissures of specified initial width, length, hydraulic gradient, and chemical attributes. These show that the breakthrough time is approximately proportional to w-3 ( i / L )-1.4 P-1, where w = initial fissure width, i = mean hydraulic gradient, L = flow distance, and P = initial PCO2 (Palmer, 1988, 1991). Dreybrodt (1996) provided an analytical derivation arriving at nearly the same functional relationships. Fig. 1. Mean enlargement rate of a fissure in limestone, as a function of discharge (Q) and flow length (L). Q = discharge per metre of fissure height (long dimension of fissure cross section). Assumptions include closed conditions, T = 10o C, initial PCO2 = 0.01 atm. (See Palmer, 1991.) Fig. 2. Approximate breakthrough times for cave inception along fissures in limestone. The main part of the graph shows closed conditions at T = 10o C and initial PCO2 = 1%. Variation of breakthrough time with initial fissure width, temperature, and initial PCO2 are shown. The combined variable i/L represents the hydraulic gradient ( h/L) divided by flow distance (L). Modified from Palmer (1991). See also Dreybrodt (1996).

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.4 Laminar discharge through the fissure is proportional to w3 i which is essentially the inverse of two of the most important variables that determine breakthrough time. Thus the paths that develop most rapidly into caves are those with high discharge and short flow distance. High PCO2 is also favourable, as long as CO2 is not lost by degassing. Temperature plays a complex role in determining how long it takes for breakthrough to occur. Higher temperatures speed the chemical reactions, but in long flow systems this can increase the breakthrough time by depleting most of the water’s solutional capacity in the upstream parts, leaving less for the downstream parts. High temperature increases the flow velocity by reducing the viscosity of the water, but it also decreases the amount of limestone or dolomite that can be dissolved. The net result is an increase in breakthrough time with rising temperature. However, another complication is that in warmer climates the CO2 production in the soil is greater, which shortens breakthrough times. As shown in Fig. 2, breakthrough time decreases as much as 5 times if the CO2 consumed by carbonate dissolution is quickly replaced, for example when the water is in close contact with a CO2 source such as soil. This is rare. In general, the early phase of growth takes place in an approximately closed system, where CO2 is used up as dissolution proceeds. In caves with open atmospheres, CO2 is likely to be lost by air exchange with the surface, which more than offsets the apparent advantage of the open system. Fig. 2 shows that initial fissures 0.01-0.1 cm wide would require no more than a few thousand or tens of thousands of years to reach the maximum enlargement rates, from the time aggressive groundwater first begins to flow through the limestone. For example, in a fissure 1 kilometre long, with an initial width of 0.02 cm, hydraulic gradient of 0.02 (20 m/km), PCO2 of 0.05 atm, temperature of 10o C, and closed to further uptake of CO2, the maximum rate of enlargement is reached in about 30,000 years. These conditions are typical, perhaps even conservative. Lab work and computer modelling by Dreybrodt (1990, 1996) suggest even shorter breakthrough times that are probably more valid. Acids can also be generated within passages by oxidation of organic compounds in the water or iron sulphide in the bedrock, diminishing the breakthrough times. Water chemistry and flow vary with the seasons, but their effects average out over the years. Time required for a cave to reach traversable size Beyond the breakthrough time, growth rate of a cave depends chiefly on the nature of its water input. In dense, rather pure limestone, the rate of wall retreat ( S ) can be estimated with the equation S = 11.7 k (1 – C/Cs )n cm/yr where C/Cs is the saturation ratio, k is a reaction coefficient, and n is the reaction order (see Palmer, 1991 for units and further details). Values for k and n vary with PCO2, and k also varies with temperature. For quick applications, some representative averages can be given. At C/Cs < ~0.7, k and n are approximately 0.015 and 1.7 respectively. At C/Cs > ~0.7, k and n are roughly 0.24 and 4 respectively. Because (1C/Cs ) is less than 1, the larger exponent gives a smaller value of S For example, water that collects on insoluble rock and then flows as a sinking stream directly into a limestone cave usually has a PCO2 of about 0.001-0.005 atm. This value is higher than that of the outside atmosphere (0.00036 atm) because even though the stream is open to the atmosphere, it acquires CO2 from seepage that enters the stream through the soil. At ponors, most sinking streams have saturation ratios of about 0.1-0.5. Under these conditions, limestone surfaces in the cave will dissolve as fast as 0.15 cm/yr. Ideally, a water-filled cave can increase its diameter up to 2-3 m in 1000 years. (The diameter increases at twice the rate of wall retreat, S .) Measurements with dial micrometers, repeated over several years, have verified these rates in caves fed by sinking streams (High, 1970; Coward, 1975). In contrast, many caves are fed by water that infiltrates through soil and reaches the caves only after having traveled for a considerable distance along the soil-limestone contact and through narrow fissures in the epik arst. This water has a high PCO2 (about 0.01-0.05 atm) but has a high saturation value, usually about 0.75-0.95 by the time it reaches the caves. The diameter of a waterfilled passage grows no more than about 20 cm per 1000 years under those conditions. Organization of conduits It has been shown that caves in a typical karst aquifer are able to form only along flow paths that increase their discharge with time. This can be achieved in either of two ways:

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.5 !" By increasing the flow efficiency in a system with a fixed head difference. An example is leakage of water from a stream or other body of water that drains to a lower outlet. As the initial fissures widen, the discharge rises dramatically. The upstream head begins to decrease only when the conduit becomes large enough to transmit the entire stream flow. By that time breakthrough has already taken place. !" By increasing the catchment area that feeds an incipient cave passage. At first, water drains into the growing caves as widely dispersed seepage. Dolines form by subsidence into the rapidly growing voids at the soil/bedrock interface. As dolines increase their catchme nt area, their meanannual discharge increases to the caves that they feed. Discharge to th e caves increases in an irregular manner, much less rapidly than in routes fed by leaking streambeds, and hydraulic gradients decrease with time, even during the earliest periods of growth. The difference between these two systems is important. Because the routes fed by surface streams can increase their flow much more rapidly, they are usually the first parts of a cave to form. Passages fed by depressions of limited catchment area require longer times to form, and they usually join the earlier passages as tributaries of a branchwork system. The fi rst passages to form in a cave are usually short and direct, except where short paths are prohibited by the geologic setting. With time, these early p assages serve as low-head targets for passages having more remote recharge sources (Ford and Ewers, 1978; Ford et al., 2000). Less time is required for a cave to grow in small steps (i.e. where new, relatively short upstream passages link to earlier downstream ones) than for a single long passage to form. This is partly due to the non-linear relation between breakthrough time and flow distance. Although the growth of any single passage propagates in the downstream direction, the overall system grows in the upstream direction, away from the springs, by addition of new passages (Ewers, 1982; Ford et al., 2000). A typical sequence is shown in Fig. 3. Assume, for simplicity, that passage segments B-A and C-B have identical lengths and gradients. The breakthrough time for a single passage from C to A would be ( LC-A / LB-A)1.4 longer than the breakthrough time for either of the two segments – i.e. about 2.6 times longer. This is 30% longer than it would take for segments B-A and C-B to reach breakthrough separately, one after the other. Just as importantly, the gradient of C-B would normally be less than that of B-A until the head dropped in B-A (Ford et al, 2000). The tributary from doline (D) has a smaller catchment area and is slower to reach cave dimensions. Fig. 3. Evolution of a typical branchwork cave by successive piracy of sinking streams and development of recharge sources through dolines. Segment B-A forms first because of the short pa th length and steep gradient. Segment C-B links up later, aided by steepening of the gradient as segment B-A develops. (C-B does not necessarily join B-A at point B.) The passage from doline D is last to form b ecause of its limited catchment area. See Ford and Ewers (1978) and Ford et al. (2000) for descriptions of hardware models that illustrate this concept. Since the flow of water through carbonate aquifers is controlled partly by the history of river entrenchment, the vertical arrangement of cave passages also reflects this control. The traditional view is that the largest passages are formed when base level is relatively static (Sweeting, 1950; Davies, 1960). At such times, rivers develop floodplains, and springs are held at fairly constant elevations for lengthy periods of time. Meanwhile the passages that feed the sp rings are able to grow large. In contrast, passages that form during rapid river entrenchment are usually small. The major passages form different levels, which in most cases decrease in age downward. Fluvial aggradation may cause some or all neighboring cave passages to fill with sediment over the vertical range of base-level rise. This conceptual model h as been well validated in Mammoth Cave, Kentucky (Palmer, 1989; Granger et al., 2001). However, in many caves there are several complications that disrupt this simple interpretation. Vadose passages may be perched on insoluble strata and grow to large size above base level. Most phreatic passages contain vertical loops

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.6 that descend far below the local base level. Some phreatic caves follow favourable stratigraphic units such as zones of former su lphates. Even the ideal cave levels controlled by pauses in fluvial entrenchment are not perfectly “level”. For this reason, many people prefer to call them storeys or tiers and either of these terms is preferred in general applications. However, the term cave level is still appropriate where there is a clear relation to fluvial base level. But the critical elevation is not the average elevation of a phreatic passage, but instead where there is a clear transition from vadose to phreatic morphology (for example, a transition from canyon to tube). This transition is not clear in some passages. Fig. 4 is an idealized profile through a multistoreyed cave, as described by Ford (1971). Three main stages of cave development are shown, with decreasing loop amplitudes from the highest storey to the lowest. This is not a characteristic of all multi-storeyed caves, but it is a conceptual ideal. Ford (1971) ascribed the decrease in amplitude to increasing fissure frequency in the host rock with time. Fissures are sparse at first, and passages are constrained to only a few deeply descending loops. As erosional unloading and cave development persist, fissures become more numerous until eventually the passages are able to form more or less along the water table, with minimal phreatic looping. In some caves the greater amplitude of loops in upper passages is instead caused by floodwaters, which superpose ungraded, looping bypass routes around low-flow routes that have more uniform gradients (Palmer, 1972). In the same vein, on the basis of studies in the Alps, Audra (1994) and Huselmann et al. (2001) ascribe an epiphreatic origin to looping passages. Fig. 4. Vertical layout of a typical cave, showing decreasing amplitude of phreatic loops with depth. This trend has been interpreted by Ford (1971) and Ford and Ewers (1978) to be the result of increasing fissure frequency with time. Successive positions of the water table are shown as gray lines. Some researchers consider these lines to represent the upper extent of epiphreatic flow (see text). The earliest passages in a cave system (usually fed by sinking streams) may not show a clear distinction between vadose and phreatic development, because their discharge fluctuates a great deal, and because the initial potentiometric surface is relatively high. As a result, most of these passages are subjected to a variety of flow conditions – phreatic at first, and then vadose and epiphreatic at later times. Still, many of them show a fairly sharp transition from vadose canyons (with continuous downward trends) to phreatic tubes (with low gradients and usually irregular looping profiles). This transition is more sharply defined in secondary passages fed by karst depressions of limited catchment area, because the flow is more uniform with time and the water sources are usually well above the potentiometric surface. Because of their gravitational flow, many vadose passages have a strong down-dip component, especially those in well-bedded rocks. Phreatic passages show no consistent relation to the dip, except where that is the only path to potential outlets, or where prominent fractures also extend in that direction. In well-bedded rocks, the intersection between the dipping beds and lowgradient water table encourage many phreatic passages to develop nearly along the strike of the beds. These relationships tend to be obscure where the geologic structure is complex. Origin of branching systems Branching cave patterns are by far the most common for several reasons: !" As passages enlarge, the local hydraulic head within them decreases. Groundwater flows from surrounding smaller openings, where the potentiometric surface is higher, toward the low heads of the early conduits. !" Vadose passages have no inherent tendency to converge, because they are hydraulically independent. However, the structures that they follow often intersect, forcing independent streams to join as tributaries. Examples include intersecting fractures, and synclinal structures in bedding-plane partings. !" Water from broad recharge areas converges toward outlets of limited extent, generally stream valleys, which causes a natural tendency for conduits to converge simply by competition for space. After two streams have converged, there is little opportunity for them to diverge farther downstream. The exception is in the vicinity of the spring outlet, where local distributary systems may develop because of collapse, backflooding, and widening of fissures by erosional stress release.

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.7 Maze development Besides branchworks, most other caves are mazes in which all the passages form more or less simultaneously. A maze cave can form only if the growth rate is similar along many alternate flow paths. This can happen if all passages evolve simultaneously at the maximum rate shown in Fig. 1. If the ratio of discharge to flow distance ( Q / L ) is large in many alternate flow routes, they will enlarge at roughly the same rate (Palmer, 1991). Specifically, this condition is achieved if Q / rL > 0.001 (cgs units), where r = mean conduit radius. In fissures, this condition is reached if Q / bL > 0.001, where b = long dimension of the fissure cross section, perpendicular to the narrow dimension w Specific settings where this condition is met include: A. High-discharge or high-gradient flow during floods. Water is forced into all fissures in adjacent carbonate rocks under steep gradients, causing them to enlarge at approximately the maximum possible rate (Palmer, 2001). This process is most active in the vicinity of constrictions in the main stream passages, which result fro m collapse, sediment chokes, or poorly soluble strata. B. Short flow paths from where the water first enters the soluble rock. Because of the short flow distances, all fissures ex cept for the narrowest enlarge simultaneously at similar rates. The epikarst is an example. Network mazes are also formed by recharge through a permeable but insoluble material such as quartz sandstone (Palmer, 1975, 2000). C. Uniform recharge to all fissures, regardless of their width. This can be achieved by seepage through porous, insoluble materials, as in B above. D. Sustained high gradients, for example beneath dams. E. Mixing zones, where the groundwater aggressiveness is locally boosted by mixing of waters of contrasting CO2 content or salinity, or by oxidation of sulphide-rich water. Over short flow distances, many alternate routes are enlarged. Mixing of waters of varied CO2 content can decrease breakthrough times, but large differences in CO2 concentration are necessary (Gabrovšek, 2000). The differences in maze types depend partly on geologic structure. Network mazes consist of intersecting fissures, with a pattern resembling city streets. They require many intersecting fractures (joints or faults), which are typical of massive or thick-bedded rock. Most are formed by processes B, C, or E above. Anastomotic mazes have a braided pattern of intersecting tubes, usually arranged two-dimensionally along a single parting or fault. They are nearly all formed by process A above. Spongework mazes form where primary (matrix) porosity is dominant. In pattern they resemble the intersecting holes in a sponge. Most of them form by process E, and less commonly by process A. A two-dimensional variety can form along bedding-plane partings. Ramiform mazes consist of rooms with offshoots extending outward from them at various elevations. They usually include areas of network or spongework maze development and are formed mainly by process E. Many network and anastomotic mazes, and a few spongework mazes, are merely superimposed on a basic branchwork pattern and represent only part of the entire cave development. Fig. 5 provides a summary of typical cave patterns, showing their relation to source of aggressive water and to dominant structural characteristics. Supporting evidence from computer models Finite-difference computer models support and clarify some of these relationships. Conspicuously absent from the list of ways to form maze caves is slow groundwater flow through artesian aquifers. This origin seems logical, and many maze caves are indeed located in aquifers that are partly artesian. However, artesian conditions by themselves do not produce maze caves. Modelling by Palmer (1991) showed that different-sized branches of a loop are least likely to enlarge at the same rate in slowmoving water near saturation. Dreybrodt and Siemers (2000) supported this idea by showing that as breakthrough time increases, passages tend to become unitary and exhibit less complexity. Modelling by Clemens et al. (1997) verified the development of network mazes by uniform seepage through an insoluble caprock, as described in B above. The insoluble cap encourages maze development because it is permeable, rather than a confining unit. Conduit growth and modification At the breakthrough time, when an incipient cave reaches its maximum growth rate, several other changes take place more or less simultaneously (White, 1977). The cave water changes from laminar to turbulent, which increases the solution rate slightly (see earlier discussion). The flow also becomes competent enough to transport detrital sediment. For example, it is able to carry away the soil that subsides into caves through karst depressions, allowing the depressions to grow more rapidly. The sediment load can also help to enlarge

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.8 Fig. 5. Common patterns of solutional caves. Dot sizes show the relative abundance of cave types in each of the listed categories. Single-passage caves are rudimentary or fragmentary versions of those shown here.caves by mechanical abrasion, but, in places, sediment accumulates in thick beds that retard dissolution and erosion. Where sediment accumulates, upward dissolution by paragenesis is a possible consequence, especi ally in caves enlarged by periodic floodwaters. However, water within the sediment is often undersaturated and can still dissolve the underlying rock (Vaughan et al., 1998). When a cave is able to transmit the entire flow from its recharge area, the average flow can increase no further. Instead the head within the passage decreases as the cro ss section continues to enlarge. Much of the upstream part of the cave becomes vadose, and streams may entrench canyons in the passage floors. As caves acquire entrances that allow air exchange with the surface, many free-surface cave streams lose part of their aggressiveness. Inflowing water is fairly rich in soil-derived CO2, and may acquire even more by oxidation of organic materials as it flows through the caves (Bray, 1972). Loss of CO2 through entrances and other openings can drive the stream water to supersaturation with dissolved calcite or dolomite, so that many vadose cave streams are aggressive only during high flow. Some vadose stream channels even acquire a thin coating of calcite in sections of supercritical flow during dry seasons. These deposits are usually removed during the following wet season, but with only a small net amount of solutional entrenchment each year. Measurements in caves of New York State show that the overall entrenchment rate of active stream canyons of this type can be as slow as 10-20 mm per thousand years (Palmer, 1996), despite the continuous flow of water. During six months of continuous monitoring in the largest stream in Mammoth Cave, Meiman and Groves (1997) found that 70% of the passage enlargement took place during the highest 7% of flow. Dating of cave sediments by 26Al/10Be isotope ratios in quartz-rich cave sediment is a powerful tool for interpreting rates of cave development. Usually this sediment is deposited by the most recent active stream flow and gives a minimum age for the passage. At Mammoth Cave, 26Al/10Be dating suggests that the development of each passage level required at least 105 years (Granger et al., 2001). This value is compatible with the range of probable times required for breakthrough (Fig. 2) and for later enlargement to the present diameters of about 5-10 m in the major passages. Headward erosion of resistant beds by cave streams can require a surprisingly long time. For example, sediment on ledges above an entrenched canyon in Mammoth Cave were dated at 1.13 million years, validated by samples at similar elevations elsewhere in the cave (Granger et al., 2001). The passage is floored by a metre-thick sequence of shaly and cherty limestone, which has been breached by a deep canyon that post-dates the sediment. Headward entr enchment has progressed

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Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.9 only 360 m along the passage, and only about half of that has occurred upstream from the sampling site. The entrenching stream is still active today and is quite capable of transporting gravel. The rate of headward entrenchment app ears to be less than half a metre per thousand years. But under favourable conditions, diversion of passages from one level to another can take place rather rapidly. Post-glacial diversion of water in New York State caves h as formed traversable passages up to a metre in diameter and 200 m long since the last glacial retreat about 13,000 years ago (Mylroie, 1977). In many vadose canyons throughout the world, examples can be seen where loops or cutoffs have developed along prominent bedding-plane partings exposed in the canyon floor (Fig. 6). As a result, the floor of the upper level coincides with the ceiling of the lower level. The new passage must develop before the parting is bypassed by deepening of the original canyon. This implies that the breakthrough time for the diversion route is virtually nil, allowing the new narrow path to enlarge competitively with the old wellestablished one. Most such diversions are short. As the land surface becomes dissected by erosion, patterns of groundwater recharge change. The few large initial water sources may be divided into many smaller ones. Vadose water must travel increasingly greater distances to reach the water table, and extensive complexes of vadose canyons and shafts can form. The resulting pattern of active cave streams is much denser than that of the original surface drainage. Growing dolines eventually form a continuous karst surface. Eventually the only surface st reams that retain their flow are the main entrenched rivers and the ephemeral upstream ends of sinking streams. Fig. 6. Stream diversion in an entrenching vadose canyon. The lower loop illustrates nearly zero breakthrough time along the guiding bedding-plane parting, as shown by the minimal entrenchment of segment A below the lower parting. This is a common occurrence, especially in well-bedded carbonates, but it is not a general rule. The final stage As the land erodes, the surface intersects underlying cave passages, segmenting them and eventually destroying them entirely. Evidence for the cave may persist for a while as a canyon-like feature or a rubbly zone of collapsed blocks. This final episode in the life of a cave passage usually occupies tens of thousands or even hundreds of thousands of years. However, newer passages continue to develop where the soluble rock extends to lower elevations. In dipping carbonate rocks, new areas of rock are uncovered by erosion at about the same rate as they are eroded away in the up-dip areas. This process ends when the entire soluble rock in the cave region is eroded away. References Audra P. 1994. Karsts alpins; gense des grands rseaux souterrains. Karstologia Mmoirs 5, 279 p. Berner R.A. and Morse J.W. 1974. Dissolution kinetics of calcium carbonate in sea water; IV: Theory of calcite dissolution. American Journal of Science 274, 108-134. Bischoff J.L., Julia R., Shanks W.C. and Rosenbauer R.J. 1994. Karstification without carbonic acid; bedrock dissolution by gypsumdriven dedolomitization. Geology 22/11, 995998. Bcker T. 1969. Karstic water research in Hungary. International Association of Scientific Hydrology Bulletin 14, 4-12. Bray L.G. 1972. Preliminary oxidation studies on some cave waters from south Wales. Cave Research Group of Great Britain, Transactions 14, 59-66. Clemens T., Hckinghaus D., Sauter M., Liedl R. and Teutsch G. 1997. Simulation of the evolution of maze caves. 12th International Congress of Speleology, and 6th Conference on Limestone Hydrology and Fissured Media, La Chaux-de-Fonds, Switzerland, 2, 65-68. Coward J.M.H. 1975. Paleohydrology and streamflow simulation of three karst basins in southeastern West Virginia. Ph.D. dissertation, McMaster University, Hamilton, Ontario, Canada, 394 p. Davies W.E. 1960. Origin of caves in folded limestone. National Speleological Society Bulletin 22/1, 5-18. Dreybrodt W. 1990. The role of dissolution kinetics in the development of karst aquifers in

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Arthur N. Palmer / Speleogenesis and Evoluti on of Karst Aquifers, 1 (1) January 2003, p.10 limestone: a model simulation of karst evolution. Journal of Geology 98/5, 639-655. Dreybrodt W. 1996. Principles of early development of karst c onduits under natural and man-made conditions revealed by mathematical analysis of numerical models. Water Resources Research 32, 2923-2935. Dreybrodt W. and J. Siemers 2000. Cave evolution on two-dimensional networks of primary fractures in limestone. In: Klimchouk A., Ford D., Palmer A. and Dreybrodt W. (Eds.), Speleogenesis: Evolution of Karst Aquifers. Huntsville, Ala.: National Speleological Society, 201-211. Ewers R.O. 1982. Cavern development in the dimensions of length and breadth. Ph.D. dissertation, McMaster University, Hamilton, Ontario, 398 p. Ford D.C. 1971. Geologic structure and a new explanation of limestone cavern genesis. Transactions of the Cave Research Group of Great Britain 13/2, 81-94. Ford D.C. and Ewers R.O. 1978. The development of limestone cave systems in the dimensions of length and depth. Canadi an Journal of Earth Sciences 15, 1783-1798. Ford D.C., Lauritzen S.-E. and Ewers R.O. 2000. Modeling of initiation and propagation of single conduits and networks. In: Klimchouk A., Ford D., Palmer A. and Dreybrodt W. (Eds.), Speleogenesis: Evolution of Karst Aquifers. Huntsville, Ala., National Speleological Society, 175-183. Freeze, R.A., and J.A. Cherry. 1979: Groundwater. Englewood Cliffs, N.J., Prentice-Hall, 604 p. Gabrovšek F. 2000. Evolution of early karst aquifers: from simple principles to complex models. Postojna, Slovenia, Inštitut za razusjivanje krasa ZRC SAZU, 150 p. Granger D.E., Fabel D. and Palmer A.N. 2001. Pliocene-Pleistocene incision of the Green River, Kentucky, determined from radioactive decay of 26Al and 10Be in Mammoth Cave sediments. Geological Society of America Bulletin 113/7, 825-836. Huselmann P., Jeannin P.-Y. and Monbaron M. 2001. Relation between al pine paleogeography and cave genesis: the case of the cave system of Sieben Hengste (Berne, Switzerland). In Huselmann P. and Monbaron M. (Eds.), Cave genesis in the Alpine belt. Proceedings of 1st Workshop for Alpine Speleogenesis, University of Fribourg, Fribourg, Switzerland, 115-123. High C.J. 1970. Aspects of the solutional erosion of limestone, with special consideration of lithological factors. Ph.D. dissertation, University of Bristol, Bristol, U.K., 228 p. Klimchouk A. and Ford D.C. 2000. Types of karst and evolution of hydrogeologic setting. In: Klimchouk A., Ford D., Palmer A. and Dreybrodt W. (Eds.), Speleogenesis: Evolution of Karst Aquifers. Huntsville, Ala., National Speleological Society, 45-53. Lowe D.J. 1992. The origin of limestone caverns: an inception horizon hypothesis. Ph.D. dissertation, Manchester Polytechnic University, U.K., 512 p. Meiman J. and Groves C. 1997. Magnitude/ frequency analysis of cave passage development in the Central Kentucky Karst. Proceedings of 6th Annual Mammoth Cave National Park Science Conference, 11-13. Mylroie J.E. 1977. Speleogenesis and karst geomorphology of the Helderberg Plateau, Schoharie County, New York. Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, N.Y., 336 p. Palmer A.N. 1972. Dynamics of a sinking stream system, Onesquethaw Cave, New York. National Speleological Society Bulletin 34/3, 89-110. Palmer A.N. 1975. The origin of maze caves. National Speleological Society Bulletin 37, 5676. Palmer A.N. 1984. Recent trends in karst geomorphology. Journal of Geological Education 32, 247-253. Palmer A.N. 1988. Solutional enlargement of openings in the vicinity of hydraulic structures in karst regions. Dublin, Ohio, Proceedings of 2nd Conference on Environmental Problems in Karst Terranes, Association of Ground Water Scientists and Engineers, 3-13. Palmer A.N. 1989. Geomorphic history of the Mammoth Cave System. In W.B. White and E.L. White (eds.), Karst Hydrology: concepts from the Mammoth Cave area. New York, Van Nostrand Reinhold, p. 317-363. Palmer A.N. 1991. Origin and morphology of limestone caves. Geological Society of America Bulletin 103, 1-21. Palmer A.N. 1996. Rates of limestone dissolution and calcite precipitation in cave streams of eastcentral New York State [abstract]: Northeast Section, Geological Society of America 28/3, 89.

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Arthur N. Palmer / Speleogenesis and Evoluti on of Karst Aquifers, 1 (1) January 2003, p.11 Palmer A.N. 2000. Maze origin by diffuse recharge through overlying formations. In: Klimchouk A., Ford D., Palmer A. and Dreybrodt W. (Eds.), Speleogenesis: Evolution of Karst Aquifers. Huntsville, Ala., National Speleological Society, 387-390. Palmer A.N. 2001. Dynamics of cave development by allogenic water. Acta Carsologica 30/2, 1332. Plummer L.N. and Wigley T.M.L. 1976. The dissolution of calcite in CO2-saturated solutions at 25o C and 1 atmosphere total pressure. Geochimica et Cosmochimica Acta 40, 191-202. Plummer L.N., Wigley T.M.L. and Parkhurst D.L. 1978. The kinetics of calcite dissolution in CO2water systems at 5o to 60o C and 0.0 to 1.0 atm CO2. American Journal of Science 278, 179216. Smith D.I. and Newson M.D. 1974. The dynamics of solutional and mechanical erosion in limestone catchments on the Mendip Hills, Somerset. In: Gregory K.J. and Walling D.E. (Eds.), Fluvial processes in instrumented watersheds. Institute of British Geographers, Special Publication 6, 155-167. Sweeting M.M. 1950. Erosion cycles and limestone caverns in the Ingleborough District of Yorkshire. Geographical Journal 124, 63-78. Vaughan K., Groves C. and Meiman J. 1998. Carbonate chemistry of interstitial fluids within cave stream sediments [abstract]. Conference on Carbon Cycling in Karst, International Geological Correlation Program, Western Kentucky University, Bowling Green, Kentucky, 33-34. White W.B. 1977. Role of solution kinetics in the development of karst aquifers. In: Tolson J.S. and Doyle F.L. (Eds.), Karst hydrogeology. International Association of Hydrogeologists, 12th Memoirs, 503-517. White W.B. 1984. Rate processes: chemical kinetics and kast landform development. In: LaFleur R.G. (Ed.), Groundwater as a geomorphic agent. Boston, Allen and Unwin, 227-248.



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Speleogenesis and Evolution of Karst Aquifers The Virtual Scientific Journal www.speleogenesis.info Interaction of Fracture and Conduit Flow in the Evolution of Karst Aquifers Douchko Romanov(1), Wolfgang Dreybrodt(1) and Franci Gabrovsek(2) (1) University of Bremen, Germany. E-mail: dreybrod@physik.uni-bremen.de (2) Karst Research Institute ZRC SA ZU, Postojna, Slovenia. E-mail: gabrovsek@zrc-sazu.si Re-published by permission from: Martin, J. B., Wicks, C. M. and Sasowsky, J. D. (Eds.). 2002. Hydrogeology and Biology of Past Paleozoic Carbonate Aquifers. KWI Special Publ. 7, Charles Town, West Virginia. Abstract Karst aquifers in their initial state consis t of a net of fractures with largely diffe ring aperture widths. As a most simple ex ample we investigate the evolution of a karst aquifer where a wide fractur e with aperture width A0 = 0.03 cm is embedded into a dense ne t of narrow fractures of aperture widths a0 < A0. The aim of this wo rk is to investigate the influence of the hydraulic coupling bet ween these fractures to the evolution of the karst aqui fer. The modelling domain consis ts of a confined aquifer, which is divided into a s quare network consisting of narrow fractures. In its center a straight wide fracture leads from the input at hydraulic head h to the output at head zero. We have computed the breakthrough times of this aquifer as a function of a0. Fo r a0 = 0 the breakthrough time is that of an isolated one-dimensional fracture. As a0 is increased the breakthrough times drop until at about a0 > 0.02 cm they are reduced significantly by almost one order of magnitude. This is caused by the following mechanism. As the central tube gets enlarged in to a funnel like shape from its entrance water from its tip is injected into the fine net of fractures. Therefore more aggressive so lution enters into the central fracture and enhances dissolutional widening there. By this way aquifers with wide fractures embedded into a c ontinuum of fine fractures experience accelerated karstification. Keywords by authors: karst, modelling, evol ution, dual aquifer, limestone dissolution Introduction Karst aquifers due to their complex structure respond in an unexpected way to drawdown of groundwater, rain storms or input of pollutants. In order to facilitate risk assessment with respect to geohazards detailed information on their hydrological properties is of utmost importance. The ultimate aim of karst modeling is to construct a virtual aquifer with properties known in detail such that its reactions to external natural or anthropogenic perturbations can be studied. This work is an attempt into this direction. It deals with the evolution of a simple idealized karst aquifer, which in its initial state consists of a net of narrow fractures into which a wider fracture is embedded. The interaction of flow in this fracture with the continuum has a significant impact on its dissolutional widening and consequently on the evolution of the aquifer. In an earlier study Bauer et al. (2000) reported on a similar scenario, where a tube is embedded into a continuum with known conductivity. This concept, however, is incomplete since dissolutional widening is active only in the tube and the continuum of fractures remains unaffected. This work, which avoids this deficiency, was initiated by workshops of the modeling groups of Bremen, Neuchtel, and Tbingen in spring 2000 and 2001 where differing concepts in karst modeling were discussed. Model structure The idealized model aquifer, depicted in Fig. 1 consists of a limestone bed 1 m in depth, 742.5 m long and 375 m wide. It is dissected by fractures into blocks of 7.5 x 7.5 x 1 m3. The aperture widths of all narrow fractures are equal in scenario A, but log normally distributed in scenario B. They are varied from 10-5 cm to 0.03 cm in different computer runs. Along the center of the aquifer a wider fracture with aperture width of 0.03 cm extends from the left hand boundary with a constant head h to the output at head zero. The upper and lower boundaries are impervious. Flow through the fractures is calculated from mass conservation stating that total inflow and total outflow into each node must balance. For laminar flow, as checked by Reynolds number below 3000, the relation between flow rate Q and hydraulic head h is given by the Hagen-Poiseuille-equation, whereas for turbulent flow the Darcy-Weisbach equation is used. The friction factor in turbulent flow is calculated by employing the Colebrook-White formula ( Dreybrodt, 1988 ). Details of the numerical calculations can be taken from Siemers and Dreybrodt (1998) for laminar flow, and from Clemens et al. (1996) for turbulent flow. The water entering into the fractures at the high head boundary is highly aggressive to calcite. It has low calcium concentration, c = 0, and the capability to dissolve 310 2 mol/l of calcite to attain equilibrium.

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D.Romanov, W.Dreybrodt & F.Gabrovsek / Speleogenesis and Evol ution of Karst Aquifers 1 (3), September 2003, p.2 Fig. 1. Model domain with geometry of continuum fractures. The central fracture is shown by the solid line. The brackets indicate regions as discussed in the text. Dissolutional widening is effective in all fractures of the system by the particular dissolution kinetics of limestone, which is linear for calcium-concentrations below 0.9 ceq and then switches to a nonlinear behaviour of fourth order. Details can be taken from Dreybrodt and Eisenlohr (2000) Rate constants employed here are k1 = 1110 4 and k4 = 810 4 mmol cm-2s-1. The scenario is typical for th e early evolution of karst, when sufficient amounts of water are available to maintain the head. As the fractures widen flow increases and by a positive feedback loop a drama tic increase of flow causes a breakthrough event ( Dreybrodt 1996 Dreybrodt and Gabrovsek, 2000 ). The runs are terminated at a flow rate of 0.5 m3s-1. Thereafter a constant recharge boundary condition must be used. Results In the first set of scenario s A and B the head at the input is chosen as 100 m. This is extremely high and related to situations as they occur on dam sites in karst regions. The model domain then corresponds to a bed of karstifiable rock extending below the dam. Fig. 2 depicts the evolution of flow through the exit of the wide center fracture for various values of the fracture aperture widths in the continuum for scenario A. In all cases flow increases slowly until a dramatic increase occurs which marks breakthrough. Fig. 3 demonstrates these breakthrough times as a function of the fracture aperture widths of the continuum. For very low values the central fracture is isolated because ex change of flow between this fracture and the continuum can be neglected. The breakthrough time therefore is close to that of a single isolated fracture. As the fract ure aperture widths of the continuum increase the central fracture loses flow into the continuum. As a consequence the flow of aggressive solution into its input increases and breakthrough time is reduced. When all fractures have even aperture widths of 0.03 cm flow is directed al ong each fracture and exchange of flow between them is ex cluded. Therefore each fracture behaves like a single isolated fracture and they all have common breakthrough. This explains the behaviour of breakthrough times in Fig. 3 For scenario B breakthrough times are almost identical. Fig. 2. Scenario A: Flow rates through the central conduit as a function of time. The numbers on the breakthrough curves denote the aperture widths of the continuum fractures. The horizontal line separates the regions of laminar and turbulent flow. Fig. 3. Breakthrough times for Fig. 2 as a function of aperture widths of the continuum fractures. scenario A, scenario B. The evolution of the karst aquifer for both a continuum of equal aperture widths a0 = 0.02 cm and for a continuum with log normally distributed widths with average a0 = 0.02 cm and = 0.01 cm is illustrated by Fig. 4 During the first 80 years a conduit propagates downstream along the central channel until br eakthrough occurs after 90 years. From the head distribution one visualizes that flow is concentrated to the central conduit first and then enters into the continuum. This causes fast widening of neighbouring continuum fractures. After 90 years a fan starts to develop propagating uphead into the aquifer. After flow has become turbulent the pressure distribution changes and becomes more evenly distributed with higher gradients at the input. Therefore neighbouring fractures experience fast widening and now a fan of fractures expands downhead. The behaviour of the aquifer with statistically distributed aperture widths is similar but deviates in details. Due to the statistic distributed pathways with wider aver age aperture widths occur.

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D.Romanov, W.Dreybrodt & F.Gabrovsek / Speleogenesis and Evol ution of Karst Aquifers 1 (3), September 2003, p.3 Fig. 4. Evolution of conduits for scenarios A and B. The bar code for fracture widths in centimeters is shown in the second section of scenario A. The head distribution is illustrated by lines of constant head in steps of 5 m.

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D.Romanov, W.Dreybrodt & F.Gabrovsek / Speleogenesis and Evol ution of Karst Aquifers 1 (3), September 2003, p.4 Therefore alternative small channels grow from the input. They cause a redistribution of heads towards the central conduit. This directs the growth of these channels towards the central conduit. Therefore a net of such conduits is integrated in addition. The mechanisms determining the evolution of the aquifer are also reflected by the profiles of flow rate, aperture widths, and concentration along the central conduit. These are shown by Fig. 5 for scenario A at various times. We first discuss the evolution during the first 80 years. The profiles are depicted from 10 to 80 years in steps of 10 years. During this time the conduit propagates downhead and loses flow into the continuum. This can be seen from Fig. 5a showing a significant decrease of flow rates at the not yet widened constriction of the central conduit. The location of this constriction is seen in Fig. 5b which shows the corresponding profiles of the aperture widths. The calcium concentrations illustrated by Fig. 5c increase linearly along the conduit until at its constriction they reach a stable value. This behaviour is in contrast to that of an isolated conduit, where the concentration rises steeply and attains a value close to equilibrium after a very short distance from the input at all times until breakthrough ( Dreybrodt, 1996 ). The reason is that due to the loss of water into the continuum much more aggressive water flows into the central conduit. To show this difference we have performed at each timestep a calculation of the flow through the central channel, when all its connections to the continuum were cut. The full squares on the curves show the much smaller amount of flow. Only one point need to be given since for the central conduit isolated by this way flow remains constant along its length. From 80 to 90 years the profiles are shown in steps of 2 years. During this time the exit opens quickly and a high amount of flow is lost into the continuum, where this attraction of flow with water of comparably low concentration creates the fan of parallel conduits. At 90 years flow becomes turbulent. The concentrations drop to low values along the entire conduit and dissolutional widening becomes even along the conduit. The profiles are shown in steps of ten years. The evolution of the fan which propagates uphead is reflected by the step like profiles which indicate loss of flow into these parallel conduits. At 140 years an increase of flow is observed at the input. It results from the fan propagating downhead. This fan grows quickly and after sufficient time conquers the entire domain. This complex behavior of aquifer evolution occurs, when the aperture widths in the continuum are close to that of the middle fracture. If this is not the case the central fracture evolves as a single conduit. But, because of the low aperture widths in the continuum, dissolution is restricted such that the times cales of the evolution of the parallel fans are much longer than the time needed for the evolution of the central fracture. Shortly after breakthrough the condition of constant head breaks down. Therefore no time is left for the generation of conduits in the continuum. Fig. 5. Profiles of a) flow rate, b) aperture widths and c) concentration along the central conduit at various times. See text. We now turn to the case of low hydraulic head in the order of meters, to model natural karstification. In this case breakthrough times are significantly longer, in the order of ten thousands of years. We have performed runs for a head of 3 m leaving everything else unchanged for both the uniform and the statistical case. A channel propagates downhead and reaches the exit after 45000 years. After this breakthrough event concentration along this channel drops and widening is even and close to the maximal rates. The further time until breakdown of constant head conditions is too short to allow the evolution of a fan of conduits at the exit.

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D.Romanov, W.Dreybrodt & F.Gabrovsek / Speleogenesis and Evol ution of Karst Aquifers 1 (3), September 2003, p.5 Discussion We first consider the evolution of aquifers under extremely high hydraulic heads, e.g. dam sites. In Fig. 6 we have plotted the flow rates at the exit fractures for scenario A from Fig. 4 Curve 0 shows the evolution of flow rates in the central fractur e. Curves 1 to 5 depict the flow which emerges from the segments 1 to 5 as illustrated by Fig. 1 During the first 80 years curves 1 to 5 are identical. This shows that fl ow is evenly distributed at the exits. One may also visu alize this from the head distribution in Fig. 4 Most of this flow originates from flow through the central conduit, which is lost into the continuum (see Fig. 4a ). This solution enters into the continuum with high calcium concentration and is not very effective to widen the fractures there. Enhancement of widening, compared to an isolated channel is effective only in the tube. Therefore one would expect that switching off dissolutional wide ning in the continuum will not change breakthrough time. We have performed such runs and indeed have found no change. We have to consider, however, that in s cenario A all fractures have equal aperture widths. In case B with statistically distributed aperture widths the situation is similar during the first 70 years. Then the exit fan starts to develop due to alternative, more favourable pathways. Nevertheless, our results show that until clos e to breakthrough dissolutional widening in the continuum is not of significant importance in the evolution of the aquifer. Therefore in this time domain models which neglect widening in the continuum ( Bauer et al., 2000 ) are acceptable approximations. After breakthrough flow becomes turbulent and is concentrated to the central conduit and to the fan in section 1. There is only little flow in all the other sections, as illustrated by the steep drop of curves 1 to 5. This flow is laminar everywhere. As one can see from the pressure distribution from 110 to 140 years in Fig. 4 flow in the outer fractures is mainly directed along these and there is little exchange to neighbouring ones. Dissolutional widening is therefore slow in this region. The further behaviour is governed by dissolutional widening of the fractures close to the central region. It is obvious that this cannot be modelled if one neglects widening in the continuum. Now we turn to the case of low hydraulic heads as usual in nature. Under such conditions dissolutional widening is restricted to the central channel. After breakthrough the time needed to create fans is much longer than the time availabl e until the hydraulic head breaks down and further evolution is governed by constant recharge through the central channel. The reason for the different behaviour under high and low hydraulic heads results from the fact that dissolutional widening at the exit of a fracture is proportional to hn/n-1 whereas flow is proportional to h (Dreybrodt, 1996 Dreybrodt and Gabrovsek, 2000 ). With n = 4, as used in our model runs, dissolutional widening at the exits drops by factor of 0.009 when the head changes from 100 m to 3 m. After breakthrough dissolution rates on the central conduit are maximal and even, independent of hydraulic head. By this way the time scales of evolution in the conduit and in the continuum of narrow fractures are similar under high heads but become significantly different when the head drops. In summary we state that modelling of natural karst aquifers containing prominent fractures embedded into a continuum of narrow fractures shows an enhancement of karstification by loss of water from the prominent fractures into the continuum, and evolution of the aquifer proceeds by widening of the pr ominent fractures. In this case dissolutional widening in the continuum has little influence. Under high hydraulic heads and moderate differences between the aperture widths of the prominent fractures and those of the continuum this is no longer the case. Especially when modelling the evolution of karst conduits below dam sites models neglecting dissolution in the continuum ( Bauer et al, 1999 ) may underestimate risks. Fig. 6. Time dependence of flow rates at the exit of the central conduit (curve 0), and of the flow rates exiting from sections 1 to 5 as depicted in Fig. 1 (curves 1 to 5). References Bauer S., Liedl R. and Sauter M. 2000. Modelling of karst development considering conduit matrix exchange flow. In: F.Stauffer, W.Kinzelbach, K.Kovar, and E.Hoehn (Eds.), Calibration and reliability in ground water modelling. IAHS publication 265, 10-15. Bauer S., Birk S., Liedl R. and Sauter M. 1999. Solutionally enhanced leakage rates of dams in Karst regions, In: A.N.Palmer, M.V.Palmer and I.Sasowsky D. (Eds.), Karst Modelling. Karst Water Institute, Special Publication 5. Clemens T., Hckinghaus D., Sauter M., Liedl R. and Teutsch G. 1996. A combined continuum and discrete network reactive transport model for the simulation of karst development. In: Calibration and Reliability in Groundwater Modelling. IAHS Publ, 237, Colorado, pp. 309-318. Dreybrodt W. 1988. Processes in karst systems – Physics, Chemistry and Geology. Springer: Berlin, New York, Heidelberg.

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D.Romanov, W.Dreybrodt & F.Gabrovsek / Speleogenesis and Evol ution of Karst Aquifers 1 (3), September 2003, p.6 Dreybrodt W. 1996. Principles of early development of karst conduits under natural and man-made conditions revealed by mathematical analysis of numerical models. Water Resources Research 32, 2923-2935. Dreybrodt W. and Eisenlohr L. 2000. Limestone dissolution rates in karst environments. In: A.Klimchouk, D.Ford, A.Palmer and W.Dreybrodt (Eds), Speleogenesis: Evol ution of karst aquifers. Huntsville: Natl. Speleol. Soc., 136-148. Dreybrodt W. and Gabrovsek F. 2000. Dynamics of the evolution of a single karst conduit. In: A.Klimchouk, D.Ford, A.Palmer, W.Dreybrodt (Eds), Speleogenesis: Evolution of karst aquifers. Huntsville: Natl. Speleol. Soc., 184-193. Siemers J. and Dreybrodt W. 1998. Early development of karst aquifers in percolati on networks of fractures in limestone. Water Resources Research 34, 409-419.



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Speleogenesis and Evolution of Karst Aquifers The Virtual Scientific Journal www.speleogenesis.info Chemical Weathering of Limestones and Dolomites in A Cave Environment Nadja Zupan Hajna Karst Research Institute ZRC SAZU, Postoj na, Slovenia. E-mail:zupan@zrc-sazu.si Re-published by permission from: Gabrovšek, F. (Ed.). 2002. Evolution of karst: from prekarst to cessation. Postojna-Ljubljana, Zalozba ZRC, 347-356. Abstract The weathered parts of carbonate bedrock on cave walls are a consequence of its incomplete chemical dissolution. The phenomenon is expressed in parts of the caves where walls are in contact with clastic fluvial se diments, wetted by percolation water or wetted by condensation water, and not rinsed by flowing or dripping water. Th e temperature in the cave is not an important parameter of weathered zone fo rmation. Incomplete dissolution is characteristic both of Alpine and of Mediterranean caves. Limestone or dolomite are dissolved by corrosive moisture; the dissolution is distinctly selective and it go as on at intervals depending on inflow of new aggressi ve water. The weathered zone of limestone or dolomite is almost identical to the parent rock s in its chemical and mineral composition yet it is much more porous. During chemical w eathering the amount of Mg, Sr and U is decreased, these components being leached out of limestone and dolomite. The amount of insoluble residue is usually higher in weathered limestones and in some othe r cases in fresh limestones which is not very common but it may occur. Keywords by authors: weathering, limes tone, dolomite, cave, incomplete dissoluti on, selective corrosion, soluble residue Introduction The appearance of thick, soft zones of an unknown white, siltor clay-like substance on the walls of cave passages (Fig. 1), looking very much like moon-milk precipitated on cave walls, was the main interest of this research work. Investigated by speleological, geological and chemical research methods, it was realised that these materials are a "soluble" residue of limestone and dolomite solution. On the cave walls thick zones of weathered limestone or dolomite remain when the solution process ends. This usually happens when there is no more inflow of aggressive water or when flowing water no longer transports the carbonate weathering products. Carbonate rock do not dissolve immediately; and this signifies that they are not carried away completely from their primary place in ionic form, but that the disintegrated particles may remain on the cave passage walls. An incomplete dissolution may just prepare the carbonate rock for the mechanical transport of its particles by the flow of water. Combining the field investigative work with different research methods, I wanted to answer the questions: !" Are we actually witnessing the carbonate rock weathering or just the precipitation of secondary minerals? !" In what way the carbonate rock structure influences dissolution? !" Which factors condition the depth of the weathered zone in carbonate rock? !" In which cases does the weathered rock remain on the channel wall? A few millimeters thick weathered layer may be noticed very often on cave passage walls. It occurs in fissures, as well as on the rock surface where it is reflected in its roughness. Thicker zones of weathered bedrock, however, are much rarer, especially in larger spaces. In the cases I have been investigating, dissolution advances well in depth, but it is, however, an incomplete dissolution. Its operation leaves behind a porous sponge-like weathered zone. The dissolution does not favor only the open cracks but also the various structures present in the rock; it dissolves smaller grains, the borders between grains, etc. The appearance of incomplete dissolution occurs in cave passages, as well as on the earth's surface. Carbonate rock covered by clastic sediments or soil will usually weather under them also. On the surface of a rock covered by alluvium or soil, the so-called subterranean rocky features may get formed due to the flow of water along their contact areas. Their formation as well as the shaping of their surface is, besides the manner of water flow, decided also by the bedrock composition, by the layer graduation

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N.Zupan Hajna / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.2 Fig. 1. Weathered cave walls in Martinska jama, SW of Slovenia. Cave was formed in Cretaceous limestone. structuring and the extent of destruction (Slabe 1999). The processes of chemical reaction between carbonate rock and deposited sediment was described by Renault (1968), who stated that the acid saturated clay in contact with the dolomite absorbs Ca2+ from it and that dolomite thus becomes soft. In the cases I have investigated, the materials which were in contact with each other were carbonate rock and the alluvium of non-carbonate composition and origin. I did not notice any kind of chemical reactions between them (in the sense of data represented by Pezdi et al 1998), at least not on the level of field research as well as when considering their mineral composition. Sometimes, however, we may come across cases when the carbonate rock in contact with clastic sediments does not display visible signs of being weathered (Mihevc 1996). The author describes scallops on the cave wall which are entirely preserved, although they were in the direct contact with the cave clastic sediments. Weathered zones of carbonate bedrock may appear in caves of different geographical position and karst type; in Slovenia for example in Alpine and Dinaric karst caves, where different speleogenesis containing limestone and dolomite of different genesis and ages is presented. Research on weathered limestones and dolomites were done in the caves developed in the Upper Triassic limestone and dolomite, Lower Jurassic dolomite and limestone, in different Cretaceous limestones and dolomites and in Paleocene limestone of different genesis and textures. Case studies were done in caves Pe ina v Borštu, Martinska jama, Krempljak, Jama II na Prevali, Turkova jama, Remergrund II, Spodmol na Ždroclah, Polina pe rnelsko Brezno, ehi II, Renejevo brezno, Velika ledena jama v Paradani and Jama pod Pe no rebrijo (Fig. 2). Let me emphasise that the cases I am describing, Fig. 2. Location of studied caves in Slovenia. Weathered zones of carbonate rocks may appear in caves of different geographical position, karst type and in limestone and dolomite of different origin and age. Legend: 1 Pe ina v Borštu, 2 Martinska jama, 3 Krempljak, 4 Jama II na Prevali, 5 Turkova jama, 6 Remergrund II, 7Spodmol na Ždroclah, 8 Polina pe 9 rnelsko brezno, 10 Cave ehi 2, 11 Renejevo brezno, 12 Velika ledena jama v Paradani, 13 Jama pod Pe no rebrijo.

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N.Zupan Hajna / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.3 are all examples of in situ limestone and dolomite weathering and that phantom rocks with the altered chemical composition were not formed (Vergari and Qinif 1997, Kauffmann et al. 1999), but that what appeared as their residue was a porous and discoloured primary rock skeleton. Research methods and results Different research methods were used to find out what is going on during the weathering of limestone and dolomite in a cave environment. First the field work was done by mapping the passages where weathered cave walls are present. Also the temperature was measured and in one case the in situ pH of weathered limestone (in Pe ina v Borštu cave). Samples were analyzed by chemical methods such as complexometry, EDS analysis on SEM and Ion Beam Analysis, then by x-ray powder diffraction method, in thin-sections, in cross sections of the samples by computer scanner and under the SEM. The weathered zone of limestone and dolomite is soft when it is wet and solid when dry. The surface of a weathered cave wall retains all the structures and textures of carbonate rock, such as different laminations, fossils (Fig. 3), calcite veins; as micrite or sparite grains which seen as micro-roughness of the wall surface. On some weathered walls the beginning of the boxwork (Palmer 1981) formation is noticed. The thickness of the weathered zone varies from less than a millimetre to several centimetres. Weathered cave walls are usually covered by a brown flowstone crust unless there is direct contact with clastic fine-grained sediments where the weathered surface is uncovered. It is quite usual to find the thicker parts of the weathered rock predominantly on walls that have been or still are in contact with clastic fluvial sediments. Thicker zones of the weathered rock may come into existence also in cases where percolation water trickles along the wall. In both cases, that is under clastic sediments and when water trickles along the wall, the water is being pulled into the interior by capillary forces and along the interconnected pores and fissures. The same action takes place with condensed moisture. In cross sections of samples the transition from fresh rock into weathered rock is quite well seen. The dissolution is progressing into the rock along the open fissures (Fig. 4) and along the invisible microporosity; we are unable to view the latter, neither in cross sections nor in thin sections. During weathering, the rock first of all loses some of its colour. Then the fading gradually increases, which leads to a state of complete discoloration, at which point the rock’s residue becomes white. Through the weathering, that is, through dissolution of individual parts of the rock with carbonic acid, the previously solid compact rock becomes more and more porous. And this does not occur, as we may have expected, only along fissures but also in non-fissured parts (Fig. 4). The dissolution advances into the rock's interior along the chosen structures and leaves in its wake ever larger and more interconnected pores. If the dissolution continues, the sponge-like structure may fall apart and the outer part of what was once a solid rock becomes clay-like and completely soft. The collapsing particles are, with regard to the primary rock structure, of the size order of silt or clay. Chemical analysis results demonstrated that the amount of Mg, Sr and U in the weathered zone of carbonate rock consistently decreases with weathering. Thus it became evident that during the weathering they are actually disappearing. Mg is leached from the calcite as well as from the dolomite crystal lattice. To where and in what manner remains unknown to me. Fig. 3. Weathered shells in Upper Cretaceous limestone, from Pe ina v Borštu, SW Slovenia.

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N.Zupan Hajna / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.4 Fig. 4. Progressing of dissolution is faster along open fissures and it is stopped by calcite veins. Paleocene limestone from Jama II na Prevali. Width of the sample is 2,5 cm. The mineral composition of the fresh or weathered parts of carbonate rock does not differ significantly. The amount of insoluble residue is sometimes higher in the weathered and sometimes in the fresh part. The conclusion one may draw from the analyses is that limestones and dolomites in the course of weathering become purer and simultaneously lose their mechanical solidity. By means of mineralogical investigation of the clastic allochthonous sediments I discovered that they do not react chemically with the weathered rock; however they do contribute the moisture required for dissolution. Yet, we do not know whether the deposited sediment might have contained minerals, which would chemically react with the rock on the passage wall and which are not present any more. Discussion According to Dreybrodt (1988) the overall dissolution rate is determined by the dissolution on the crystal's surface, by the transportation of ions through the border layer and by the speed of the conversion CO2 + H2O = H+ + HCO3as well by the lithological parameters of the carbonate rocks. Weathered zones are the result of incomplete carbonate rock dissolution. Thick zones of the weathered bedrock are rare, especially on the larger surfaces. At first sight the most weathered walls appear to be those wetted by percolating water and which are in contact with fluvial sediments, and walls which are subjected to condensation corrosion. During the selective dissolution of individual parts the once compact carbonate rock becomes more and more porous, not only along the cracks, but also along various structures. From analyses of cross sections under SEM, it is quite evident that what is happening is not a case of secondary minerals' precipitation but of dissolving carbonate rock, which increases the porosity of the rock. Field investigations, the analysis of cross sections and the moistening of the weathered limestone have led me to a conclusion that the flow of water is, in the case of thick weathered zones on the passage walls, effected molecular diffusion and capillary action, which proves to be the faster. In the cases I am describing, the rock is not only dissolved on the surface, that is frontally, and it does not leave in its wake the smoothed surfaces of the cave walls, as is the case when it is in contact with flowing water where this contact between water and rock lasts sufficiently long to bring about the chemical reaction. When the inflow or outflow of water stops and the solution which is present in the connected pores gets saturated, or dries up, the rock cease to be dissolved. The weathering of carbonate rocks is usually caused by dissolution, that is, by the transition from rock into solution (Summerfield 1991). The dissolution is distinctly selective. In the first place, smaller grains and the contacts among grains are dissolved. When dealing with clastic sedimentary rocks Skaberne (1980) noted, that they weather chemically and crumble in relation with their structure. I noticed the similar phenomenon also in limestones and dolomites, especially when the dissolution along the edges of mineral granules weakens the mechanical cohesion of the rock. The fact that limestones with sparite and microsparite structure start dissolving along the edges of grains and along the deformities in the crystal surface is already known from the literature (Ford and Williams 1989). During dissolution pores get larger and become more and more interconnected, so that aggressive water advances more easily and deeper into the rock's interior. With the la pse of time even the more

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N.Zupan Hajna / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.5 resistant parts of carbonate rock weather as well. Calcite veins and the shell fragments that jut out from the weathered rock surface become porous and soft. During further dissolution the rock gets more porous and fragile until its structure completely collapses. The flow of water in all these cases is not large and the actual significance may be ascribed to the moisture; this moisture is well capable to cause dissolution. The term corrosive moisture used by Davis and Mosch (1988), when they describe the weathering of the clay pebble surfaces, denotes condensed or vadose (percolation) water. The humidity of weathered walls changed significantly during the course of year. Sometimes the walls were completely wet, at another time entirely dry. The fluctuation of humidity during the year is quite obvious and is related both to the precipitations as well as to the velocity of the trickling along the walls. The penetration of moisture into the weathered part of the wall is very fast. It may stop only at the larger calcite veins, and it may also take some time to cross over open cracks or those partly filled with clay. I attempted to explain the formation of mosaic porosity and the sponge-like rock structure by the model, which is similar to that used by Trudgill (1985), when he tried to determine the formation of porosity in the limestone karst soil (rendzina). Following my own observations, I presume that in cases when the wall dries up, the new moisture penetrates into the rock even faster, because the pores have been emptied. Consequently, I believe that dissolution is going on faster as well, so that water in pores loses its aggressiveness again, the dissolution becomes saturated and pH increases. At every new water wave the water will use the pores and channels which were produced during the previous cycle. It may also widen them a little and the main dissolution front will thus, with each new water wave, move deeper into the rock. Through its contact with carbonate particles in the porous skeleton the aggressive water quickly becomes saturated; so that only a part of its former quantity is still able to interact with the rock. The mechanism is repeated in cycles, so th at the rock becomes ever more porous and does not dissolve entirely at first. This incomplete limestone dissolution is most likely taking place in the vadose zone. The flow of water in the phreatic zone would wash the particles from the wall if not before, then during its retreat, or the silt would crumble away from the wall of its own accord. The water flow may also simultaneously carry away the ions, and the dissolution would progress into the depth slower, for it would act frontally. There may exist a possibility that the incomplete dissolution is, nevertheless, taking place, yet because of the continuous washing away of the particles we are unable to recognize it. Limestone porosity in the given cases increased because calcite grains that were less resistant to dissolution got dissolved. Dissolved primarily were those grains that were smaller and those whose structure was less well ordered due to the presence of Mg ions in their crystal lattice. Mg ions are, owing to their lower ionic potential, more mobile and are the first to leave their places in the crystal lattice thus they further weaken the interior structure and increase the proneness to dissolution. Theoretically, water in porous media in contact with calcite reach equilibrium immediately it becomes saturated or even supersaturated against CaCO3, but it is not necessary that it is also saturated against Mg2+, so the dissolution of the parts containing Mg ion may go on (Bathurst 1975). The decrease of the Mg ion share in the weathered parts of limestones and dolomites has already been observed by several authors. The fact that Mg is being extracted from limestone during dissolution was found out also by Kogovšek and Habi (1981) in their measurements of the magnesium hardness. The reason for this is the greater solubility product of MgCO3 when compared to CaCO3. The leaching of Mg during dolomite weathering was stated also by Burger (1989), yet he did not try to explain it. Slabe (1988) interprets the lower share of Mg on the surface of the cave wall wh ich has already been dissolved by corrosion, as the complete dissolution of impure limestone which contains Mg and as the precipitation of pure calcite crystals from the condensed moisture. Yet, in all the cases, I am describing here, we are actually not witnessing the calcite crystal extraction but the weathering of limestones and dolomites. In cases when the weathered rock is in direct contact with the cave environment, a thin calcite crust is almost always being extracted and deposited on its surface. During the rock's drying, the saturated moisture oozes out of its pores, or it is squeezed towards the weathered rock's surface by the incoming water. However, it still remains somewhat unclear, where do the dissolved ions in these cases actually migrate. Especially when we take into account that the weathered rock which is in contact with the alluvium is not even covered with a flowstone layer and that we have not yet found any minerals containing Mg. The answers to the questions are: !" The zones of carbonate silt or clay and white porous rocks on the cave passage walls are a product of weathering processes and not of secondary minerals precipitation.

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N.Zupan Hajna / Speleogenesis and Evolution of Karst Aquifers 1 (3), September 2003, p.6 !" Dissolution penetrates into the rock along various structures, such as cracks, primary porosity, microstructures, crystal's deformities and primary structures covered by micritization or neomorphism, which may also hinder the expansion of dissolution. !" Selective dissolution forms the coarseness on the surface and the sponge-like structure of the weathered rock, which may reach a depth of several centimetres. My opinion is that the occurrence of the incomplete dissolution of carbonate rocks within speleogenesis may represent an important factor for the formation of initial channels, because carbonate rock porosity increases proportionally with the selective dissolution of calcite and dolomite by carbonic acid and not with dissolution of the more soluble additions (gypsum, anhydrite, etc.). During the weathering, pores in limestone and dolomite augment, they establish connections among them, which leads to increased effective porosity. The enlargement of pores and the expansion of their interconnections consequently leads to the formation of initial channels. Incomplete dissolution accompanied by the simultaneous washing away of the weathered rock also accelerates the growth of passages. By means of th is process the passage's enlargement is faster and more intensive especially during floods or high water splash through the cave channels. References Bathurst R. G. C. 1975. Carbonate Sediments and Their Diagenesis. Second enlarged edition, Amsterdam: Elsevier, 658 pp,. Burger D. 1989. Dolomite weathering and micromorphology of paleosoils in the Franconian Jura. Catena Supplement 15, Cremlingen, 261267,. Davis G. D. and Mosch C. 1988. Pebble indentations: A New Speleogen from a Colorado Cave. National Speleological Society Bulletin 50, 17 – 20. Dreybrodt W. 1988. Processes in Karst Systems. Berlin, Heidelberg: Springer-Verlag, 288 pp. Ford D. C. and Williams P. W. 1989. Karst Geomorphology and Hydrology. London: Unwin Human, 601 pp. Kaufmann O., Bini A., Tognini P. and Quinif Y. 1999. Etude Microscopique d’ une latrite de type fantme de roche. Karst 99: colloque europen: des paysages du karst au gosystme karstique: dynamiques, structures et enregistrement karstiques (Etudes de gographie physique, supplment 28), 129 – 133, Aix-en-Provence. Kogovšek J. and Habi P. 1981. Preu evanje vertikalnega prenikanja vode na primerih Planinske in Postojnske jame. Acta carsologica 9, 129 -148. Mihevc A. 1996. Brezstropa jama pri Povirju. Naše jame 38, 65-75. Palmer A. N. 1981. Geology of Wind Cave. Wind Cave National Park, South Dakota. Hot Springs: Wind Cave Natl. Hist. Assoc., 44 pp. Pezdi J., Šušterši F. and Miši M. 1998. On the role of clay-carbonate reactions in speleoinception; A contribution to the understanding of the earliest stage of karst channel formation. Acta carsologica 27 (1), 187-200. Renault P. 1968. Contribution l’tude des actions mcaniques et sdimentologiques dans la splogense (Troisime partie). Annales de Splologie, Centre National de la Recherche Scientifique 23 (3), 530-596, Moulis. Skaberne D. 1980. Predlog klasifikacije in nomenklature klasti nih sedimentnih kamnin.1.del, Predlog granulometrijske klasifikacije in nomenklature. Rudarsko metalurški zbornik 27 (1), 2146, Ljubljana. Slabe T. 1988. Kondenzna korozija na skalnem obodu Komarjevega rova v Dimnicah. Acta carsologica 17, 79-92. Slabe T. 1999. Subcutaneous rock forms. Acta carsologica, 28 (2), 255-271. Summerfield M.A. 1991. Global geomorphology, an introduction to the study of landforms. New York: John Wiley & Sons, 537 pp. Trudgill S. T. 1985. Limestone Geomorphology. London and New York: Longman, 196 pp. Vergari A. and Quinif Y. 1997. Les paleokarst du Hainaut. Geodinamica Acta 10 (4), 175-187.


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