Characteristics of large particles and their effects on the submarine light field

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Characteristics of large particles and their effects on the submarine light field

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Title:
Characteristics of large particles and their effects on the submarine light field
Creator:
Hou, Weilin
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Tampa, Florida
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University of South Florida
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English
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xiii, 149 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Particles -- Optical properties ( lcsh )
Ocean -- Water -- Optical properties ( lcsh )
Light -- Scattering ( lcsh )
Dissertations, Academic -- Marine Science -- Doctoral -- USF ( FTS )

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General Note:
Includes vita. Thesis (Ph. D.)--University of South Florida, 1997. Includes bibliographical references (leaves 120-128).

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University of South Florida
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University of South Florida
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All applicable rights reserved by the source institution and holding location.
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024208028 ( ALEPH )
38233015 ( OCLC )
F51-00203 ( USFLDC DOI )
f51.203 ( USFLDC Handle )

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CHARACTERISTICS OF LARGE PARTICLES AND THEIR EFFECTS ON THE SUBMARINE LIGHT FIELD by WEILINHOU A dissertation submitted in partial fulfillment of the requirement for the degree of Doctor of Philosophy Department of Marine Science University of South Florida August 1997 Major Professor: Kendall L. Carder, Ph.D.

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Gradu a te School University of South Florida Tampa, Florida CERTIFICATE OF APPROVAL Ph.D Dis sert ation This is to certify that the Ph.D. Dis se rtation of WEILINHOU with a major in Marine Science has been approved by the Examining Committee on Apri l 25, 1997 as satisfactory for the dissertation requirement for the Doctor of Philosophy degree Examinin g Committe e Major Professor: Kendall L. Carder, Ph .D. Member: Thomas L. Hopkins, Ph.D. M e mber: Mark E. Luther Ph.D Member: Gabriel A. Vargo, Ph.D. Member: John J. Wal s h, Ph. D

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I dedicate this dissertation to my dear parents Xu Zhenyi and Hou Dongyuan for their love and support.

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ACKNOWLEDGEMENTS This dissertation has culminated, due to many people's help and support, in data, equations, figures, tables, and results. I would like to express my thanks here to those who have greatly helped me to finish this dissertation These include members of my committee ( Drs. Thomas L. Hopkins, Mark E. Luther, Gabriel A. Vargo, and John J. Walsh) who guided me ; my colleagues (Robert Steward, Feng-I Chen, and especially David Costello) who helped me with data, methodology, and concepts, Dr. Alice Alldredge of University of California at Santa Barbara for her invaluable suggestions and data, and Dr. Yu-lin Xu of University of Florida for his help in calculations of scattering by an aggregation of small marine particles I am grateful to Joan Hesler for all of her administrative help. My special thanks goes to my advisor, Dr. Kendall L. Carder, who not only provided me with invaluable guidance and suggestions, but also a top notch research environment.

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TABLE OF CONTENTS LIST OF TABLES ......... . ...... ......................... ... . .................. ... ....... ...... ....... ..... .... . .. . .iii LIST OF FIGURES ... . ...... ...... . . .... ... ... ........ ........ ... ..... ......... ................. ....... ..... . ..... iv LIST OF SYMBOLS ... ....... .... . ............... ... ...... ..... .... . ........ . .... .... .... .... ................ . ..... vii ABSTRACT ..................... .... .... ................ . ...... ... . ........ .............. .... .... ......... ..... ..... . xi Chapter 1 rnTRODUCTION ... ..... ............ ..... .... ............ ... .... .......... ........... .... ...... ... ... 1 1 1 Background .... .... . ........ ..... . ............ ... ...... ... ........ .... .............. .............. . ... . ... ... 1 1 2 Current Study ......... . ....... ........................ . . .......... .......... .................................... 10 Chapter 2 THE AUTOMATIC SIZrnG AND CLASSIFYING OF LARGE PARTICLES USrnG MULTI VIDEO METHODS ...................... ...... ... .... 1 2 2. 1 B ackg round ..................... . .... . .......... ................ ... ........................ ...................... 12 2.2 Measurement and Analysis Sy ste m : MAPPER/ICE ........... .... .... .... .... . ... ........... 18 2.2. 1 MAPPER .. ...... ...... ...................................................... .... .... .............. ........ ... 19 2.2 .2 ICE .. ........... ............... . ... .......... ... .............. . .......... .... ............ ......................... 21 2.3 Particle Size Distributi o n Mea s ured by MAPPER/ICE ....... .... .... .... . .... ......... ....... 24 2 3.1 Measurement Setup ................... .......... ..... ...... ...... .... ............ .... ... ............. . 24 2.3.2 Me as urement Re s ults ..... .......... ....... .... ..... .............. ... ...... ............................ 27 2 4 Discus s ion . ..... ...... ...... ........ ... ... ...... . ... ........ .......... . ................ .... ......... ..... ...... 38 2.4 1 Slope vs. Concentr a tion Con s tant s ... .................... .... ...... .... .... ..................... . 38 2.4.2 P ar ticle Size vs. Po ros ity ........ ..... ... ...... ........................ .... . . ............... ......... .45 2.5 Summary .... .... .... ....... .... . .... ... . .... . ... . .... ........... ... .... .... ... .......... . .... .... ..... ........ 47 Chapter 3 SOME MARrnE OPTICAL PROPERTIES AFFECTED BY PARTICLE SIZE DISTRIBUTIONS . ....... .................... . .... .................... 49 3. 1 B ackg round ................ ... ..... . ........ . ........ . ............................. .... .... .... . ... ....... . 49 3 .2 Large-particle Total Scattering Contribution ...... ... ......... . .... ............ .... . ... ...... . 52 3.3 Bea m-c Correction Using Measured PSD Slope . ...... .... ......................... ... . ... ....... 58 3.4 Estimating the PSD for Small e r Particle s from Beam-c and MAPPER PSD ......... 64 3 5 Slope vs. Beama ttenu a tion Ratios .... ........ ....... .... ....... . ...... ....... . ....... .... ............ 70 3.6 Summary ..... ............ .... .... .......... ...................... ............... ............... ...... ...... .... ... 73

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Chapter 4 LARGE-PARTICLE PHASE FUNCTIONS MEASURED BY MAPPER AND ICE .... ................ .......... ......... ... ........................ . .............. 75 4.1 Backg round .... .... ............ ........... ..... ..... ........................... . .. ......... . .... . .... . ... ... ... 75 4.2 Setup and ICE Measu rement ......... ..... . ..................... .... .... ..... ... . ...... ..... .... .... ... ... 79 4.3 Res ults ... ..... .......... .. ...... . .......... ... ...... ..... .... ............................. ................ ... . ... ... 83 4.4 Calculating Large-particle Phase Function by Monte Carlo Simulation s ............... 88 4.5 Discu ssio n ................ ............... ........................... .......... ........................................ 93 4 .6 Summary ................. ... ... .... . ..................... ............... ... .... ... ..... ...... . ....... ....... ...... 95 Chapter 5 PARTICLE CLASSIFICATION .... ..... .......... ........................................... . 96 5.1 Moment-invari ants a nd Identification of Large Particles . .... ............... . ............ ... 96 5.1 1 Background .................. .......... . .. ....... . ... ...... . .... .................................. ......... 96 5.1.2 Moment-invariant and Zemike Notation ... .... ..... ..... ..... ................. . ...... ..... . lOl 5 1 3 Calculating the Complete Zemike Moment-invariant Set for Large Particles ........ . .... ... . .......... . ... .. ..... .......... ............................. ..... ....... 102 5.1.4 Characteristics of Some Special Particles in the Ocean .. . ...... .... .... . ............. 107 5.2 Optical Scatterin g Characteristics of Large Particles ...... .... ......... .... ................ . 111 5 3 Summary ...... ......... .......... .... ........... ...... ... ... .... .... ........................... .................. 115 Chapter 6 SUMMARY .......... ... .... ............ ... .... . . ... ... . ...... .......... ..... .... .... ...... ......... 117 6.1 Conclusion ........................... ......... .... ....... ..... ....... .... ...... ...... . ........... ..... ............. 117 6.2 Future Work .... ................. . .......... ..... . ................ ... ...... .... . .... ...... ..... .... ...... ..... 119 REFERENCES .... . ....................... ............. ............. ......... . .. ... ...... ......... . ....... ... .... .... . 120 APPENDICES ... .............. .......... ............. ... ..... ... ......................... ... .. ...... .... . ... ........ 129 Appendix A Single-particl e-scattering G eome try .......... ...... .... ........... ... ........... ... .... 130 Appendix B General Theory of Moments .................. ... ... ...................................... ..... 133 Appendix C Effect of Unit Change on x0 ........ ........................................ .................... 137 Appendix D Pattern Recognition .... . .... .... .... ... ... ....... ............. ........... .... ............... 139 Appendix E Multi-sphere Mie Scattering . ..... ......... . ..... .... ......... . .......... . .... ............. 143 E nd P age ..... ......... ........ ........... .......... ............................................................ ............... 150 ii

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LIST OFT ABLES Table 1 Data used from Friday Harbor SIGMA cruise at East Sound WA during April14-21, 1994 ... ...... ... ...... ... . ............ ......... .... .... .... ................. ... 25 Table 2. Particle size bins for the 3 MAPPER fields .... . ........ . .... ... .... ... ..... ...... . ... ...... 28 Table 3 Hyperbolic Particle size distribution parameters and scattering contributions measu r ed at East Sound, W A . .... .. . .. .... . .. . . ...... ... ..... . . ..... ..... 31 Table 4 Regression between log (A) and k for different MAPPER downcasts .... ... ... . 39 Table 5. Percentage contribution of scattering in size group for n.-=1.05 . ............ ...... ...... 55 Table 6. Percentage contribution of scattering in size group for n.= 1.15 ...... . ........ . ....... 56 Table 7 Percentage contribution of s cattering in size group for n,= 1.05 ... . ..... .... .. . . ... 57 Table 8 Estimation of small particle distribution by MAPPER PSD and c p for data measured at East Sound, W A .............. . .... .... .... ....... ... ... .............. 68 Table 9. Attenuation ratios compared with PSD slopes measured in-situ by MAPPER at different depth ( is the averaged value over two depth bins) ... ..... ... .... ..... .... . . . .................. .................... ...... ............. ...... ..... 71 Table 10. Beardsley-Zaneveld scattering phase function parameters obtained by fitting MAPPER single particle scattering results . .... . ... ....... . .... 87 Table 11. Particles types identified by ICE using imaging pattern recognition ...... . ...... 110 Table 12. Individual particle optical propert i es used in identification .... . .... . ... . ...... ... 112 Table 13. Particles identified by ICE using scattering properties ......... .... ......... ........... 113 111

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LIST OF FIGURES Figure 1. Particles from small field cameras of MAPPER (a) (b) (d) are loosely connected marine snow aggregates; (e) (f) are copepods From East Sound W A ..... ........ ....... ........ ...... ... .... ........... ................................ 3 Figure 2. Sketch of MAPPER in 3-D view ...... ... ... .......... ..... ... ........... .......... ...... ..... ... 19 Figure 3. Flow chart of a automatic video processing system: Image Control and Examinination (ICE) System .......... ... .... ....... ..... ........ ....................... . ...... 22 Figure 4. Study site at East Sound WA during April 14-21 1994 ................................... 24 Figure 5. Parlicle Size Distribution For Each of 3 MAPPER Fields Measured at East Sound, WA on April21, 1994 Midnight (4/21A) .............. ...... ..... ........ 29 Figure 6. Combined PSD from 3 MAPPER fields (from Figure 5) .... ... ......... ........... ... . 30 Figure 7. Measured in-situ profiles of hyperbolic PSD Slopes (-)and hearn-e (--)at East Sound, W A during 4114-4119/94 .......... ......... ..... .............................. 32 Figure 8. Measured in-situ profiles of hyperbolic PSD slopes k and hearn-e at East Sound, W A during 4/20 4/21194 .. ......................... ...... ... ........ ................ 33 Figure 9. PSD measured by a Coulter Counter and MAPPER. ... ...................... ...... . ..... 34 Figure 10. Combined PSD from MAPPER and Coulter Counter (see Figure 9) ....... .... 35 Figure 11. Measured PSD slopes in surface waters for small (Coulter Counter) versus large particles (MAPPER) ...................................... ... .............. ... .... ... 37 Figure 12. PSD slopes (k) vs. concentration constants log(A) measured at East Sound, W A .............. .......... ......... ... ... ..... .................................. .... ................... 39 Figure 13. Sketch of k vs. log(A) in 6 situations .............. ..... . .... .................................. .40 IV

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Figure 14. Variation s of s ituations in Figure 13 expressed in PSD plots ........... .... . ... .. .41 Figure 15. Particle size v s 2 dimensional fill factors F2 (the dash line indicates a linear regression) ..... ... ... . . . .... . .... ...... .......... .... .... ... ... ... . . .... .... ..... ...... 46 Figure 16. Mirror view of percentage scattering contribution by different size groups due to changes in the hyperbolic slope paramete r k . . . ......... ......... .... 54 Figure 17. Sketch of a beam attenuation meter and error caused by forward s cattering into the s mall acceptance angle (no absorption sho w n) . . ............ . 59 Figure 18. Per c enta ge e rror s underes timated by c-meter with a 0 9 acceptance angle different PSDs and relative indices of refra c tion . .... .... . ............. ..... .... 62 Figure 19. E s timated total particle attenuation cp (estimated small particle c ontribution s plu s larger ones using MAPPER measurement s ) vs measured cp ( corrected for forward scatting) for Eas t Sound W A ......... ......... 67 Figure 2 0 Geometry of single particle scattering within HMM of MAPPER that is used for 3 D s c a ttering calculation s (see Appendix A) .. ...... .... .... .... ... 80 Figure 2 1 Measured s ingle particle scattering fitted to Bea rd s ley (BZ) and Heyney-Gree n s t e in ( HG) phase functions (normaliz e d by 90 s catterin g for c omp ar i s on) (data taken from 4/21194 mid-night downcast in depths 0-10 meter ) . . . .... . . . . .... .... . .... .... .... ...... . . .......... .... . ... 85 F i gure 22 Sin g le part i cle scatte r ing mea s ured from MAPPER downcast at night of April 20 1994 at Ea s t S o und, WA at: ( a) 0-1 Om; (b ) 10-20m ; ( c) 20-24m .... .... . .......... . ... ..... . ...... .... ... ...... .. . .. . .... . .... . ..... ..... ..... 86 Figure 23. Geometry for multiple s cattering in Monte C ar lo s imulation s ..... . . .... ...... . . 91 Figure 24. Comparison of dif f erent sc a ttering phase functions (BZ Beardsley and Zane veld phase function-; Petzold . . ; Multiple scattering using Monte Carlo---; MAPPER aggreg a te scattering o) . . ........ . ..... .... . ... 92 Figure 25 Sample particle ima g e s with reduced resolution tak e n from MAPPER s mall field c a mer a of April 20 night downca s t at Eas t Sound WA . ... . ... . . 103 Figure 26. Eff ect of differen t re s olutions on Zernike moment-invariants for a sample large particle t a ken from Ea s t Sound WA ..... .... ... .... ....... . ... ...... 104 Fi g ure 27 Effect of reduced re s olution on size mea s urement using different description method s ( unit in number of pixel s) ..... .... . . . . . .... . ... . ..... . ... . I 05 v

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Figure 28. The effect of different threshold on calculations of moment invariants (upper line: traditional pixel selection method; lower line: using all pixels in region) ............ ... .......... ................... ....... . . ..... ...... 106 Figure 29. Zemike moment-invariants for sample particles taken from MAPPER small field image Upper: copepods; lower : aggregates . ... ... ..... ..... ....... ... . l09 Figure 30. Sketch of minimum mean distance classification in k-space . ... ... ... ........... 141 Figure 31. Sketch of multi-sphere aggregate scattering calculation ...... ............ .... . . . ... l49 Vl

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LIST OF SYMBOLS Symbols unit Descriptio n a m-1 Total absorption coefficient b m-1 Total scattering coefficient bb m-1 Total backscattering coefficient c m 1 Total beam atten u ation, c = a+b Cp m-1 Total particle beam attenuation c mgm-3 Concentration of phytopla n k t on pigme n ts p lu s phaeo-pigments m-1 s(1 Volume scattering function p m 1 s(1 Scattering phase func t ion Paz -1 -1 m sr Beards l eyZ a n eveld scattering phase functio n A (em) Concentration constant for the particle size distri b u ti on k (em) Expo nent of the particle size dist r ib u tion, or the s l o p e of the particle size distribu t ion in log-log space N Cumu l ative partic le size distri b ution function f em 4 Differen ti al particle size d istrib u tio n fu n ctio n D em Part icle size measured in diamete r of a sphe r e or eq u ivalent lOP Inherent optica l property Vll

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AOP v w I L W -2 -1 m sr E R p nm 8 radian radian sr Apparent optical property Volume Radiant flux Radiant intensity Radiance Water-leaving radiance Irradiance Irradiance reflectance Remote sensing reflectance Refractive index of sea water Relative index of refraction to sea water Diffuse attenuation coefficient of downwelling, upwelling irrdiance, respectively extinction efficiency factor scattering efficiency factor absorption efficiency factor optical phase shift Wavelength of light Scattering angle Azimuth angle in 3 dimensional spherical coordinate Solid angle Constant for Beardsley-Zaneveld phase function (backward scattering) Vlll

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Er l o p no f-l pq M; ESD ESP TEP MAPPER ICE SIGMA ADCP MAPS OPC TBC LF I m -I m Constant for Beardsley Zaneveld phase funct ion (forward scattering) Mean free path Probability density function Radius of gyration 2-dimensional porosity Average number of collisions of a photon with scattering centers General (p,q) order moment (p,q = 0,1 ,2 ... ) General (p,q) order central moment Zernike moment-invariant Element of scattering matrix Equivalent spherical diameter Equiva lent spherical projection Tra nsparent exopolymer particle Marine Aggregated Profiling and Enumerating Rover Image contro l & examination Significant interactions governing marine aggregation Acoustic Doppler current profiler Multi-fr e quency Acoustic Profiling System Optic a l plankton counter Time ba s e corrector Large field ix

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MF Medium field SF Small field FG Frame grabber HMM Hyper-stereo mirror module SLS Structured light sheet PSD Particle size distribution X

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CHARACTERISTICS OF LARGE PARTICLES AND THEIR EFFECTS ON THE SUBMARINE LIGHT FIELD by WEILINHOU An Abstract Of a dissertation submitted in partial fulfillment of the requirement for the degree of Doctor of Philosophy Department of Marine Science University of South Florida August 1997 Major Professor: Kendall L. Carder, Ph.D XI

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Large particles play important roles in the ocean by modifying the underwater light field and effecting material transfer. The particle size distribution of large particles has been measured in-situ with multiple-camera video microscopy and the automated particle sizing and recognition software developed Results show that there are more large particles in coastal waters than previously thought, based upon by a hyperbolic size distribution curve with a (log-log) slope parameter of close to 3 instead of 4 for the particles larger than 1 OOJ..Lm diameter. Larger slopes are more typical for particles in the open ocean. This slope permits estimation of the distribution into the small-particle size range for use in correcting the beam-attenuation measurements for near-forward scattering. The l arge-particle slope and c-meter were used to estimate the small-particle size distributions which nearly matched those measured with a Coulter Counter (3 05%). There is also a fair correlation (/=0.729) between the slope of the distribution and it s concentration parameters Scattering by large particles is influenced by not only the concentrations of these particles but also the s cattering phase functions This first in-situ measurement of large particle scattering with multiple angles reveals that they scatter more in the backward direction than was previously believed, and the enhanced backscattering can be explained in part by multiple scattering of aggregated particles. Proper identification of these large particles can be of great help in understanding the status of the ecosystem. By extracting particle features using high-resolution video images via moment-invariant functions and applying this information to lower-resolution images, we increase the effective sample volume without severely degrading classification efficiency. Traditional pattern recognition algorithms of images classified Xll

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zooplankton with results within 24% of zooplankton collected using bottle samples. A faster particle recognition scheme using optical scattering is introduced and test results are satisfactory with an average error of 32%. This method promises given that the signalto-noise ratio of the observations can be improved. Abstract Approved:-----------------Major Professor: Kendall L. Carder Ph.D. Professor, Department of Marine Science Date Approved : 6 0 17+ Xlll

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CHAPTER 1 INTRODUCTION 1.1 Background Unlike the snow falling on earth, on and off with seasonal variation and the movement of the weather sys tems, it seems that the "snow falling onto the bottom of the world ocean never stops. ".. when I think of the floor of the deep sea, the single overwhelming fact that possesses my imagination is the accumulation of sediments. I see always the steady, unremitting, downward drift of materials from above, flake upon flake, layer upon layer -a drift that has continued for hundreds of millions of years, that will go on as long as there are seas and continents .. For the sediments are the materials of the most stupendous snowfall the earth has ever seen ... (Rachael Car son, 1951 ). These large particle s, often fluffy and easily seen by our naked eyes, are termed marine snow (Suzuki and Kato, 1953) typically having a longest dimension larger than 500Jlm ( Alldredge and Silver, 1988 ; Wells and Shanks 1987). These large particles could be formed by various processes. Smaller particles ( -lJlm) collide via Brownian motion and stay attached to form larger particles (Mc Cave, 1984; Jackson, 1990). Turbulent shear stress also bring particles together to form aggregates, while excessive shear also break them up (Krone, 1976 ) Another physical process that aids aggregate formation is differential settling. When a particle sett les

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through water column by the force of gravity at a velocity differing with those of its neighboring particles, it encounters particles along its pathway, scavenging (at various probabilities) small particles and trace metals in its path (Stolzenbach, 1993; Fowler and Knauer, 1986) or colliding with other particles of similar size to form aggregates (McCave, 1984; Jackson, 1990; Alldredge and Cotschalk, 1989; Alldredge and Silver, 1988; Fowler and Knauer, 1986; Alldredge and McGillivary, 1991). It has also been demonstrated in lab experiments that in stratified fluids a falling particle can create a less viscous flow path in its wake, enha ncin g the settling speeds of trailing particles until collisions occur. This forms vertically enlonged aggregates, especially at a density interface (Carder and Steward, 1986 ). These various physical processes can occur throughout the water column, and can be g reatly enhanced in regions of upwelling, and in convergent flows ("slick zone") in the upper layer caused by internal waves fronts, and jets (Mann and Lazier 1991). The aggregation process i s as much a biological as a physical process, when considering that it is the surface "stickiness" or the effectiveness of "biological glues" (Alldredge and Silver, 1 988) of the encountering particles that mostly determines the attachment probability (Jackson, 1990; McCave, 1984 ; Stolzenbach, 1993; Hill and Nowell, 1990), and this "st i ckiness" is related to the biological state (age) of the components. Aggregates can also result from biological activities, such as the residual food from ineffic ient grazers, abandoned larvacean hous es, appendicularians houses, and mucus, feeding webs from pteropods. Fecal pellets are also an important component of aggregates (Alldredge and Silver, 198 8). Because of their size, zooplankton are a small, but important component of snow-sized particles. 2

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Figure 1. Particles from small field cameras of MAPPER, (a) (b) (d) are loosely connected marine snow aggregates; (e) (f) are copepods. From East Sound, WA Because of the diverse origin of large particles, it is understandable to observe great variation in both the morphology and constituents of the particles. Alldredge and Silver ( 1988) depict various shapes of marine snow particles from loosely connected, porous particle agglomerates (Figure 1, a, b, and d) to highly compact structures produced by zooplankters( Figure 1, c, e f, and g). Enhanced biological activity has been observed within such aggregates: chlorophyll-a concentrations can be enriched 3 to 750 fold compared to that in the s urrounding sea water, accounting for 0.1-34% of total bulk primary production The density of bacteria can be 2 to 5 orders of magnitude higher within snow particles (Alldredge and Silver, 1988). These elevated values clearly indicate that marine snow particles serve as micro-environment centers in the water, and that 3

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Goldman's "spinning wheel hypothesis (1984) could be correct; i.e. bacteria, phytoplankton, and protozoa living on aggregates create a small microbial loop, rapidly recycling nutrients to maintain a high turnover rate of biomass. The measured oxygen distribution within and around aggregates also shows indications of photosynthesis and respiration within the aggregate boundary layer (Alldredge and Cohen, 1987), which i s believed to help to maintain high nutrient concentrations within the aggregate and po ss ible high phytoplankton tum-over rates ( Mann and Lazier, 1991 ). These phenomena could also be explained by mutualism between phytoplankton and bacteria (Azam and Smith, 1991). These recent findings greatly enhanced our knowledge on this subject and show how important a role marine snow-type particles can play when they are abundant in the water column. However determinin g the abundance of these particles has proven to be difficult mainly due to their fragile nature, which makes sampling very difficult (Alldredge and Silver, 1988) Traditional sample collection with hydro bottles can easily break these aggregates. They can also si nk within minutes below the spigot of the collection bottle (Ca lv ert and McCariney, 1979 ), or eventually break up when passing through the spigot (Gibbs and Konwar, 1983) Even sample storage and transportation can result in their disruption (Alldredge and Silver, 1988), and common water-filtration syste m s typically destroy aggregates. Desp ite all of the problems researchers have historically been trying to assess the abundance of these particles in order to understand their overall impact on the oceanic sys tem, since it is known that they are responsible for the majority of material flux and sedimentation (Fowler and Knauer, 1986; Stolzenbach, 1993 ), and trace -e lement and 4

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metal transport (Fowler and Knauer 1986) out of the euphotic zone and to depth. They also contribute to enhanced production in the water column especially under bloom conditions (Alldredge and Silver 1988). They are also an important food source for fish and large animals (Alldredge, 1972, 1976; Hopkins et al., 1994). Additionally, accurate abundance and distribution information within the water column is important information for modeling production, aggregation processes (Hill, 1992; Jackson, 1990), sediment flux ( Walsh and Gardner, 1992), and optical properties (Mobley, 1994; Carder and Costello, 1994) Methods that have been traditionally u se d include visual observation (Alldredge et al., 1986) underwater photography (Wells and Shanks, 1987), remote cameras (Honjo et al., 1984; Johnson and Wangersky, 1985; Costello et al., 1991 1995), in-situ large volume pumps ( Bishop et al., 1977) holographic imaging (Costello et al., 1988 ), and sedi ment traps ( Walsh and Gardner, 1992; Bishop et al., 1986) Results show high variation in the concentration of aggregates, generally from a few up to 500 per liter in surface waters, while only a few per liter at most are found in deeper waters (Alldredge and Silver 1988). It has become obvious that the optimal way to quantify the abundance of these large particles is through non-contact methods. At the same time, observing large volumes of water is required in order to achieve a statistically representative number of particles (Carder & Costello, 1994 ). Both acoustical and optical methods could fit these requirement s, but becau se of the relatively weak return of acoustic signals fro m marine s now type particles (Napp et al., 1993), acoustic instruments such as MAPS ( Multi frequency Acoustic Profiling Sy s tem, Napp, et al., 1993), and a modified ADCP (acoustic 5

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Doppler current profiler Flagg and Smith, 1989, 1992) have been used primarily to quantify zooplankton biomass for sizes ranging in diameter from 25J.lm to the millimeter for MAPS and from 250f..Lm to the centimeter size range for the ADCP. The Optical Plankton Counter (OPC, Herman, 1992; Herman et al., 1993) is also designed and used to measure zooplankton from 250f..Lm to 2cm by optically observing a water stream through a narrow ( 4mm by 20 mm) optical chamber. The reduction of collimated light reaching a photodiode indicates the presence and size of a particle (interpreted as if it were a zooplankter). OPC results are typically 30% of those found in net counts (varying from 10% to 200%), and do in fact, show the possible presence of marine snow particles when their transparency factor exceeds 0.7 (Herman et al 1993). The system can be operated at near-real time and observes large volumes of water. None of these systems however, has exhibited the ability to discern particle shapes and type other than correlating the abundance and size with those from net samples. Optical imaging, via either photography or video, seems to be the optimal solution if the burden of data processing can be tolerated. There are additional benefits to using an optical system for quantifying particle abundance. Although these large particles are "rare" in the ocean, there are questions about how they might affect the underwater light field (Carder and Costello, 1994). In understanding the propagation of light in the ocean, the most basic optical properties, such as absorption, attenuation and scattering, are those of the medium (sea water and its components). These are termed inherent optical properties (lOP), and they do not vary with the position of the light source (Preisendorfer, 1961 ). lOPs are measured routinely to predict or model quantities such as remote sensing reflectance, Rrs water-leaving

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radiance Lu and diffuse-irradiance attenuation, Kd which do vary with the location of the light source, and are termed apparent optical properties (AOP). This procedure, usually called model closure i s successful if the derived AOPs match the measured AOPs based upon knowledge of the lOPs and light source(s). Problems arise here if the lOP measurements sample so small a volume of water that observations of large particles are extremely rare lOP measurements from a beam attenuation meter (c-meter) or sca ttering meter typically involve water samples of no more than a few cubic centimeters, and they are less likely than the volumes observed using AOPs to include large ra re", marines now types of particles which on average appear a few times per liter (Alldredge and Silver 1988; McCave, 1984). The measured quantity is therefore "mote-less" (Carder and Costello, 1994 ). On the other hand AOP measurements s uch as water -l eaving radiance, Lu, involve back -scatte red signals from tens of c ubic meters of water and would definitely include the effect of marine s now particle s or "mo tes It has been estimated that 1 ,000 samples need to be taken, in the open ocean, for a 25cm pathlength c-meter to include one 1 mm particle, assuming a flat particle -vo lume di s tribution (t hat the total particle volumes ar e e qual between logarithmic size bins, an d that volume conservation holds), or a cumulative hyperbolic distribution of particl e diamet ers havin g a slope of 3 (Carder and Costello, 1994 ). For a marine ecosystem, due to growth and mortality, on top of advection and sedimentation such volume conservation might not hold. Aggregated particles probably manifest optical properties which differ significantly from the s um of the particles which contribute to the aggregate. The amount of biological activity involved within the particle for example might affect the growth 7

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rate or photosynthetic rate due to shading and light penetrating the water column could be absorbed at these particles at a different rate compared to those in the water column The fact that a good portion of free-living bacteria was found, in fact, attached to a group of transparent exopolymer particles (TEP, Alldredge et al., 1993) suggests that, even in oligotrophic waters, aggregates of these small but closely positioned cells could affect scattering characteristics via multiple scattering Abundant large particles with possible enhanced scattering characteristics (Carder and Costello 1994; Mobley, 1994 ), may play an important role in the underwater light field, affecting image transmission (Mobley 1994) and interpretations of remotely sensed data. The widely used beam attenuation measurements need to be corrected significantly, due the forward scattered light being accepted rather than rejected by the receiver (Bartz, Zaneveld and Pak, 1978) u s ing measured in-situ particle size distributions Since variou ssized particles scatter differently, and generally larger particles scattering more strongly in the forward direction (Mobley, 1994; Mie, 1908), such an effect will affect the beam attenuation measurement significantly. These discrepancies could pose a significant problem if indeed these large particles exist in abundance. It is therefore necessary to either include the effect of large particl e s in lOP measurement or correct for their effect on AOP measurements if model closure is to be achieved. The choice is self-evident. Since it is impractical to simply scale up instruments that measure many of the lOPs (Carder and Costello, 1994), new instrumentation is desired for the measurement of the optical properties of large particles. To fulfill the needs for a non-contact optical sampling system, a multi-camera system was developed at the Marine Science Department, University of South Florida for 8

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the purpose of measuring large-particle abundance, distribution, and optical properties (Costello et al., 1991 ). The free-falling device, Marine Aggregated Particle Profiling & Enumerating Rover (MAPPER), is equipped with video cameras having different magnifications with the intent of covering a wide size range while maintaining reasonably high resolution and sampling a large water volume. A hyper stereo mirror module (HMM) consisting of two tilted mirrors within the full view of the lowest magnification camera system is mounted on MAPPER to provide images of particles at different viewing angles (see Chapter 2 and 3 for detail). The difficulties associated with post proce s sing of photographic images has been noted (Alldredge and Silver, 1988; Napp et al., 1993) with inefficient use of man power even with only a few dozens of photographic images Our requirements called for analysis of tens of thousands of images generated by the MAPPER cameras. A PC-based automated image control and examination (ICE) system has been implemented to accomplish this task (Hou et al., 1994). The system is capable of automatic image capture, digitization, measurement and classification of particles, based on pattern recognition strategies as well as optical characteristics ( See Chapter 2 and 4 for details). With the MAPPER-ICE system, continuous spatial particle-size distributions can be obtained to better assess the role of large particles in the aquatic system The diverse morphology of large marine particles, and the inherent differences in the systems which attempt to measure them, makes it difficult to present a transportable quantification of the "measured size ". Instead of using the traditional equivalent spherical diameter (ESD), it has been shown that a different measure the equivalent spherical projection (ESP), based on the radius of gyration of the particle image is more suitable. 9

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Additionally the "electronic overshoot" of the image system has to be carefully corrected for proper sizing (Costello, Hou and Carder, 1994 ). 1 2 Current Study To address some of the issues raised above, we use data results from the SIGMA (Significant Interactions Gov ern ing Marine Aggregation) project East Sound experiment at Orcas Island, W A., in combination with particle-optic theory (Mie scattering calculations), to test the following hypotheses: (1) A new system that i s based on optical imaging of large particles ( d> 100 ,urn) can be u sed to continuously and accurately measure in-situ size di stribut ions (2) Since particle size distributions exhibit the shape of a hyperbolic curve in a relatively stea dy marine ecosystem, it is hypoth esize d that the same distributions for lar ge particle s can be extended into the smal ler particle range u s ing hyperbo lic curves. (3) We hypothesize that in-situ MAPPER measurements can be used for beam attenuation corrections du e to forward scattering. (4) Since beam tran smmisso meter readings are affected by both small and lar ge particle s, if s t atis tically representative numb ers of all sizes are sampled, the sampling volume of optical instrument s can be adjusted (by integrating or averaging multiple s mall volumes) in order that at le as t one particle (1 mm or larger) i s included in the samp le vo lum e. (5) We hypoth esize that s mall -part icl e size distributions can be estimated u si n g mea s ur ed l arge particle size distributions and beam attenuation measurements. 10

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(6) The scattering characteristics of aggregates are different from those of the ensemble of individuals that form them; more sideand back-scattering is hypothesized for aggregates and less near-forward scattering. (7) It is possible to characterize major groups of zooplankton particles as differing from aggregates, based on digital image processing and image analysis. (8) It is possible to use optical signatures of large particles to identify animals from aggregates, due largely to increased scattering per unit area as a result of increased refractive indices and internal structure. (9) We hypothesis large particles have a significant impact on remotely sensed signals, because of their abundance in surface waters and enhanced back-scattering. If the above hypotheses are confirmed, there will be little doubt that when found in abundance, these large particles play a significant role in biogeochemical cycles and the properties of the underwater light field. The particle size distribution extended to the range of traditionally "large" particles (e.g. longest dimension greater than is required to enable more insight into the role that large aggregates play in the marine biogeochemistry. 11

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CHAPTER 2 THE AUTOMATIC SIZING AND CLASSIFYING OF LARGE PARTICLES USING MULTI-VIDEO METHODS 2 1 Background A particle size distribution (PSD) describes the abundance of particles of certain sizes per unit volume in the environment. Generally there are two types of distributions that are used: the cumulative and differential distributions. The cumulative particle size distribution, describing the number of particles larger than a certain size in a unit sample volume is expressed as ( 2 .1) N(d >D) N(D)= dV where D is the particle size expressed as diameter or other size measure (Bader et al., 1970; Carder et al. 1971; Costello et al., 1995 Jackson et al., 1997), dV is the s ample volume, and N is the total number of particles larger than D. We also use the differential particle size distribution, or particle size spectrum, which is the total number of particles within certain size range (size bin), per unit volume, per bin width (Lerman, Carder and Betzer 1977) (2 2) dN(D) dN f(D) = dD = dDdV We c a n easily see that 12

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(2.3) .. .. dN N(D) = f f(D)dD = f dDdV dD D D Further references to the particle size distribution, unless noted will refer to the differential particle size distribution. Many studies have been reported regarding particle size distributions, especially in the atmospheric and meteorological scie nces The famous Junge type distribution was named after Junge (1963), for example, who showed that the cumulative size di strib ution of aerosol particles could be described in general by a hyperbolic distribution, as can the differential PSD, or particle size spectrum: (2.4) d 2 N =A* v-k dD *dV k>O, where D is the diameter of the particle k is the slope of the particle distribution in loglog coordinate space and A is a concentration constant associated with the distribution In our case where em is used as the base unit this value corresponds to the concentration of particles at 1 em diameter per em bin width per cm3 sample volume. Note that many investigations define A at 1 micron diameter, but for particle volume concentrations and mass concentrations (e.g g!m\ the unit centimeter is more convenient. The measurement of particle size could be performed by visible micro scopy, covering particles sized from a few wavelengths and up, or by electron microscopy which can measure particles as small as few nanometers (10-9m). However, these techniques are ext rem ely tedio us and depend heavily on human decisions Thus, they are not practical for large field studies where automated fast and continuous measurements are preferred. 13

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The Coulter Cou nter which utilizes electrical resistance to measure particle s ize (resistance for dielectric particles proportional to particle volume), can measure particle s (from about 0.3 to 200J1m) concentration automatically (Bader, 1970; Sheldon, 1972; Carder et al., 1 972). Other methods involve laser light diffraction (Bale and Morris 1987), laser hol ography (Costello et al., 1988), and flow cytometry (to obtain size distribution information for particles ranging 1-10 Jlm, Ackleson and Spinrad, 1988 ) In oceanic studies the PSD has mainly been measured at the small-size end, in th e 1 to 10 micrometer range, by particle-resistance methods Most of the published data s how hyperbolic type distributions (Sheldon, et al., 1972; McCave,1984; Wells, 1992 ; Hou et al., 1994, Jackson et al., 1997). Some researchers, however, have shown differen t distributional shapes such as the 3-parameter generalized Gamma functions to fit measured curves (Risovic 1993) or, the Weibull distribution (Carder et al., 1971), and the log-normal distribution, which all allow a "fall-off' instead of a continuous rise in the number of particles at the small end (Lambert et al., 1981; Wellershaus et al., 1973 ; Wells, 1992 ), useful for aerosoles, phytoplankton, and other particles limited to large r sizes (e.g phytoplankton are typically larger than about 0.4,um). Others have used multiple log-normal distributions for "small" and "large" aerosols (Gregg and Carder 1990) In some cases, measurements with more sensitivity in similar and smaller size ranges showed that re s ults like those of Lambert could be caused by limits of instrument resolution. Harri s ( 1977 ). for example, showed a distribution with a cumulative slope of k = 2 .6 2 down to 0.1 J.Un, and Wellershaus ( 1973) also suspected that the "fall-off of hi s data could be an arti fac t Since chemists do not agree on an exact size separating particles 14

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from liquids (e g colloids) we limit our interest to particles larger than O l,um diameter as be i ng o f optical interest due to their scattering efficiencies ( details see Chapter 3 ) Notice that a cumulative slope of 3 or a different i al size distribution slope of 4 indicate a "flat" or uniform volume distribution (McCave 1984), which means that the tot a l volume between log size bins are equals : ( 2 5) 3 fv(D)f( D )dD = f--" D A D _dD_ = 7r log(-D_ 2 ) 6 6 D1 In other words, if there are 1,000 particles larger than then there will be only one particle larger than I mm per unit volume under the assumption of spherical particles Unless specified otherwise all logarithms used here are natural logarithms The PSD is important in de s cribing the abundance of particles in the natural environment. With knowledge of spatial and temporal variations in the distribution, it is possible to predict the rate of aggregation and de-aggregation ( McCave, 1984; Jackson, 1990 ; Hill 1992) assess the role of particles in the underwater light field (Stramski and Kiefer, 1991; Mobley 1994) a s well as understand material transfer. Even though small particle s are numerically dominant in the ocean, they contribute les s flux to the deep ocean than large particles, which sink faster. Thus, mass flux is more of a function of the number of rare large particles than smaller ones as was previously perceived (McCave 1975). A s a matter of fact, it was the intere s t in the flux of materials that brought about the reexamination of marine s now or large-particle size distributions (McCave 1984 ) It has been po s tulated that the size distribution can be used to estimate flux (Walsh and Gardner, 1992 ) though no affirmative relationship has been found for their LPC (Large Particle Camera) s y s tem. 15

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There are considerably more measurements done regarding small sub-micron particle size distributions (Wells, 1992), but due to the difficulties associated with measuring large particles such information was unavailable until recently. No systematic assessment has been carried out to monitor spatial and temporal variations of large particles. Studies also show that the PSD is one of the most important parameters in optics. This is not surprising since optical parameters in natural waters involve various sized particle suites and the particle size distribution is needed for integration over the entire or a segment of the size range. This is the case in calculating all bulk optical properties (Mobley 1994). It has been found, for example, that the backscattering ratio is more dependent on the particle size distribution than on other factors (Ulloa et al., 1994). Additionally the beam attenuation spectrum will follow A_J-k where k is the differential particle size distribution slope (Kitchen et al., 1982) Then the index of refraction of particles can be obtained once particle size distributions and volume scattering functions are known (Brown and Gordon, 1974; Spinrad and Brown, 1986). Gregg and Carder (1990) related the Angstrom exponent to Junge slope k of aerosols ; it also pertains to hydrosols. One of the difficulties similar to those encountered in measuring particle distributions lies in characterizing them especially at the large particle end. Here determination of the size of fluffy and porous aggregated particles is challenging. The most widely used approach, the spherical equivalent diameter (ESD), can significantly underestimate the actual size of the particle (Costello, Hou and Carder, 1994). This is one of the reasons why measured particle settling velocities do not always follow the Stokes 16

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equation (McCave, 1984 ), implying that either the particle has a different density than assumed or they just settle at a different speed than Stokes equation would predict, perhaps due to porosity (Jackson et al., I 997). Note that when the ESD is used to describe the particle size, you "squeeze" the particles into smaller, physically compact spheres while in nature they are porous with holes, resulting in a much lower, effective density and more drag. The equivalent spherical projection (ESP) or radius of gyration of the particle seems to be a reasonable choice (Costeiio, Hou and Carder, I 994 ) If we have an image which is defined as f(x,y and limited to a finite region R, we can define the p1\q1h order moment as (2.6) mp. q = fJ f(x,y)xPyqdxdy R p,q = 0,1,2, ... and we define (2.7) f.lp.q = fJ f(x,y)(x-x)P(yy)qdxdy p,q = O,I,2, .. R as the general moments calculated when the coordinate system originates at the image centroid. These are called central moments. The image can be described to the first order by an ellipse, with parameters (2.8) (2.9) b 2 = f.1.w + f.lo2 ((f12o f.io2 / + 4fit 1 2 )112 f.1oo I 2 and the radius of gyration (rg ) or ESP (equivalent spherical parameter) is (2.10) r = ESP = .J;b. g 17

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To describe the 2-dimentional porosity, a fill-factor", F2 can be defined as the fraction of the particle optical cross-section to the area of the ellipse that "covers" the particle (2.11) The moment representation theorem states that the infinite set of moments uniquely determine the image and vice-versa, and the proof can be obtained by expanding the equations (Equations 2.6 and 2.7) into a power series and interchange the integration order after Fourier transform (Jain, 1989). We will omit the derivation here. As there are vast numbers of particles in the ocean involved in the global carbon cycle for 2/3 of the planet surface area, a well understood particle size distribution especially for those larger particles which contributed significantly to the material flux, would no doubt enrich our ability to monitor and understand many important processes a ffecting carbon sequestration, the green house effect, and global warming 2.2 Measurement and Analy s is System: MAPPERJICE In order to measure the abundance of large particles in the ocean without destroying them, a non-contact, optical measurement is suggested. One such system is a free-falling device, MAPPER (Marine Aggregated Particle Profiling and Enumerating Rover Figure 2) which records underwater large-particle images in-situ onto SuperVHS (SVHS) format video at 3 different camera resolutions (currently 17.5J.lm 90J.Lm and 280J.Lm per pixel at 640x480 digitization). It also provides auxiliary data such as the beam attenuation coefficient, water depth, conductivity and temperature To process the large 18

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number of images involved in the measurement process, we developed the ICE (Image Control & Examination) system an automated PC-based video image-processing system It automatically retrieve large-particle characteristics such as size shape, porosity and reflectivity from video images digitized frame by frame from video tapes. c-meter Figure 2. Sketch of MAPPER in 3-D view. The instrument is deployed with circular frame plane parallel to sea surface (HMM: hyper-stereo mirror module) 2.2 1 MAPPER To address the sampling difficulties associated with the study of marine aggregates and to acquire the optical properties of large, marine-particles MAPPER was developed at the Marine Science Department of University of South Florida (Costello et al., 1991,Costello et al. in prep). This free-fall device is equipped with three video 19

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cameras and recorders plus auxiliary sensors to measure temperature depth, and beam attenuation (Figure 2). To provide a controlled sample volume MAPPER employs 4, 20 mW, 685nm diode lasers, one mounted at each comer of a square with 25-cm sides They each have line-generator optics to produce a thin (I mm), structured-light sheet (SLS) This is the equivalent of optically" filtering the water column with three coincident video cameras at digitized pixel resolutions of 17 .5J..Lm (small field, SF), 90J..Lm (medium field, MF) and 280J..Lm (large field LF), respectively. The equivalent s ample volumes for above cameras are 0 094 liters (SF), 2.4 liters (MF) and 8.03 liters ( LF). A hyper-stereo mirro r module (HMM, Figure 2, also Figure 20) was also mounted on the MAPPER in order to obtain 3-dimensional particle information to compare with the SLS imagery. The large-field camera will image the HMM at a pixel resolution of 280 J..Lm. The HMM uses 2 mirrors to divide the video image into 3 segment s, a left mirror view a central view and a right mirror view. This configuration allows 3-D studies of a ggregates inside the HMM volume. Size shape, and (in a quiescent environment) settling velocity of aggregate s can be determined by comparing these views Scattering characteristics of aggregates can also be retrieved by averaging over time at certain angles since left, central and right views of the image correspond to forward/backward ne a r 90, and backward/forward scattering respectively (for each diode laser) Turning on only one laser diode at a time provides forward side and back scattering measurements of each particle with the HMM. The other two cameras with finer re s olutions (17 5 and 90 J..Lm pixel resolution) will image particles with better accuracy in a fixed region within the central view of the 20

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HMM. Depth and temperature data are encoded and written in the vertical blanking interval of the video record A Seatech transrnissometer with 25 em pathlength is also onboard to allow comparison with the video data from MAPPER. The system is nearly neutrally buoyant and has been trimmed for descent velocities as slow as I em/sec. Ultra high molecular weight polyethylene (UHMW -PE) is used for the crash frame and drag flaps, which produce hydrodynamic resistance during MAPPER deployment and retract during retrieval 2.2 2 ICE It has been noted that one of the biggest obstacles in measuring particle sizes via imaging (video or photographic) methods is the amount of work involved in retrieving information using image-processing software (Alldredge and Silver, 1988, McCave, 1984) The usual pathway involves underwater filming/recording, development of film, digitization via image capture and measurement using an image-processing package or visual measurement through a microscope. The retrieval of a statistically significant PSD involves an enormous amount of work The same applies to the data MAPPER generates. Note that, in order to obtain a continuous PSD for large particles, the 3 video cameras recording in real time onboard MAPPER. During a typical 3-rninute downcast, it generates 3x60x30x3= 16 200 images which need to be processed (compared to the total 96 photographs Wells and Shanks used to obtain their marine snow distribution in 1987). This is equivalent to 4.86 GB (gigabytes ) of data und e r digitization to 640 by 480 pixels per frame. Processing such an immense data stream is time con s uming and makes these optical methods almost 21

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unusable (Alldredge and Silver 1988). An automated, PC-based data-reduction system called Image Control and Examination (ICE) has been developed to retrieve the quantitative information from the MAPPER video imagery. 1---0_u_od_-_bo_x __ ----41 __________ --+ EE Switcher Monitor D DISPLAY CLASSIFY DISP/SAVE AUX DATA NETWORK Figure 3. Flow chart of a automatic video processing system: Image Control and Examinination (ICE) System The system (Figure 3) consists of a set of VTRs (Video Tape Recorders), a Quadbox Switcher to choose any video source, a TBC (Time Base Corrector) to provide external sync and digital freeze a programmable frame grabber (FG, from Data Translation Inc ., model DT2867) to digitize video images auxiliary data inputs from BE 22

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(Blue Earth) and PISCES recording depth, temperature, and beam attenuation (transmissometer). An IBM-compatible PC (486) is the main control module. It controls the advance of each video frame triggers the TBC to freeze the images, and invokes the FG to digitize the images and store them in the host system memory. Once an image is digitized and captured by the FG, the image measurement (IM) routine will examine the image, search and size particles using a line segmentation algorithm (Jain, 1989), extract shape information using Zernike moment-invariants (Hu, 1962, Teague, 1980), then save individual particle information such as area diameter, brightness, shape, porosity and high order Zernike moment-invariants (details see Section 4.1.3 and Appendix B). Analysis of scattering by single, large particles in the HMM yields unique data: the forward (near 50 to 60), side (near 90), and backward (near 130) scattering for large particles (details in Chapter 4) from the sum of each of the four lasers, or from a single laser in the "phase function" operational mode. A particle that appears in each of the small, medium and large-field-camera images provides data to better understand the transformation of particle sizing with different resolution systems, and the use of moment-invariants (Section 4 1.2) shows that particle sizing and identification can often be accomplished across a wide range of sizes. When combined with other data (depth, beam attenuation), the program yields particle size spectra in high spatial resolution (as high as 40mm horizontal and 1 mm vertical, depending on the distribution and the concentration), large-particle optical properties (attenuation, particle reflectance and scattering phase function), and particle characteristics such as individual particle size shape, porosity and 3-D position in space. 23

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2.3 Particle Size Distribution Measured by MAPPER/ICE 2.3. I Measurement Setup Data presented here are from the SIGMA project experiment carried out at East Sound, Orcas I sland ( 48 40.04'N, 122.72'W) Washington (Figure 4) from April 14 to April 21, 1994. Oate s and times when the down casts were carried out are listed in Table I. The date codes (s uch a5 4 I 9A) are used throughout this paper to indicate the corresponding time in 24 hour format in an abbreviated form. Also in the table are the sampling depths, the downcast used (from multiple downcasts), and its duration time. 114 5 124 123.5 llJ. 1225 122 121.5 Figure 4. Study site at East Sound, W A during April14-21, 1994 East S o und is an enclo ed fjord type of embayment with the opening at the SSE e nd Acou s tic Dopp le r Current Profiler (ADCP) current velocity measurements show that 24

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the dominant cu rrent is M2 tidal (Jackson and Kimsey 1995) Surface velocities are generally incre a sed by tidal current s with about twice as much kinetic energy in the top 15 meter s as in the bottom waters. Current s measured as high as 1 rnls at the surf ac e, while the bottom velocity was gener a lly less than 0 5rn!s except for April 14, which measured about 1rnls (Jacks on and Kimsey 1995) Date Code Depth Time Code Downcast Duration (m) (clock) # (s) 4/14 1 9.4 14:11: 36 2 110 4/15 2 2 3 09 :10: 52 1 116 4/16 21. 1 17:2 1 : 56 1 114 4/17 20 9 17: 30 : 42 1 100 4118A 22 8 19:16 :18 2 106 4118B 23 1 20:49 :15 1 114 4/19A 19. 9 09 : 38 : 08 1 103 4/19B 21.7 09 : 56 : 38 2 106 4/19C 2 4.4 20 : 04 : 47 1 104 4/19D 23 6 20 :18: 57 1 99 4/20A 24.4 00 :01: 07 1 116 4/20B 23 6 00 :21: 23 2 146 4/20C 23 5 06 : 31:40 1 104 4/20D 23.9 06 : 46 : 39 1 121 4/20E 21.2 12:32 : 04 1 125 4/20F 23. 9 12: 52 : 25 2 119 4/20G 25 .2 2 0 : 02 :21 1 106 4/20H 25 0 20 : 19 : 37 1 127 4/2 1A 23. 3 23:58:18 1 122 4/21B 24 9 00 : 13:58 1 106 4/21C 24 1 00 : 05 : 03 2 117 4/21D 26 2 06 : 04:42 2 145 4/21E 25.4 12: 36 :16 1 135 4/21F 25 2 12: 58 : 05 2 130 Table 1. Data used from Friday Harbor SIGMA cruise at East Sound, W A during April14-21, 1994 The images from the 3 video camera s were recorded using the SVHS format which s upport s above 400 lines of re s olution. The images were then captured on a video chip 25

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with 640 by 480, square-pixel digitized at 8 bits resolution, using a Data Translation DT2867 image processing board and default settings (Costello, Hou and Carder, 1994 ) Playback of the videos was carried out on a VTR (model JVC-BRS605UB), under RS232 control from the PC unit. To provide a stable image a pause is inserted before each image frame to ensure proper positioning of the drum head of the VTR, and then the frame is buffered by an infinite-window TBC in the freeze mode. The FG inside the host PC grabs the image, digitizing and mapping it into system-memory space. A line-segmentation algorithm is used to detect individual particles within the frame (Jaine, 1989). The algorithm involves registering the beginning and the end of a video line segment falling above a threshold value for a particle image, comparing the positions to the previous and the next image lines in the nearby neighborhood of the segment and deciding whether or not these segments belong to the same particle A closing tolerance is assigned based on visual examination of randomly sampled images It is essentially the maximum separation distance that we allow for scattered segments to be considered as part of the same particle, from the edge of one segment to another (e.g consider segments on either side of a hole in an aggregate). An adaptive grey-scale threshold is used to delimit particles based on the number of counts required above average intens i ty of the entire frame in order for a pixel to be considered part of a particle Such a threshold is obtained by averaging different sections of a digitized image with an 8x8 pixel grid with the maximum grey-scale value of these grids set as the threshold value It has been noted that high grey-scale thresholds affect the direct sizing of particles (e g sum of continuous areas exceeding the threshold value). However, the application of 26

PAGE 44

moment-invariant s is more appropriate method since it is Jes s sensitive to the value of the threshold se lection (see Section 5 1 ). After each particle of a frame has been measured, the VTR will advance one frame under control of the PC and sequentia l measurements will be carried out. The data are stored in files on the hard disk of the PC system and are accessible via a computer network. Due to the large number of calculations and, primarily, the pause time for mechanical syste m stabilization, the ICE proce ss ing speed is currently 180 to 1, that is it takes 180 frame times ( 1130 second for each frame) for one frame to be processed or 6 seco nd s per frame. Le ss than 1 / 3 of this time involves CPU operations with the rest involved with mechanical pau si ng and the TBC freeze. Preliminary tests indicate that ICE could be within a factor of 10 of real-time with a faster CPU (Intel Pentium 90), fewer calculations ( up to 3rd order moment-invariants see Section 4.2) a smaller imaging window (320 by 240) and elimination of the mechanical pausing and the TBC freeze. This is an encouraging sign toward real-time processing. All codings are written in ANSI C ( partial code in C++ and asse mbly language ), compiled u s ing Micro so ft C/C++ compiler executed on an Int e l 80486 PC running MSDOS or Windows NT if network accessing of data files are required. 2.3.2 Measurement Re s ults The particle s ize spectrum i s separated into groups where the center of each bin is doubl e d by its volume ( diam ete rs increase by a factor of 1.26 ) as shown in Table 2. Figure 5 s hows particl e size distributions measurement from all 3 fields (large field, medium field and s mall field) for a midnight downcast on April 21, 1994. All particle 27

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counts in each bin from the 3-camera system are utilized in calcu l ating the s lope of the particle s ize distrib u tion, by using a least-square regression in log-log space. Thi s i s performed after the equivalent-volume and bin-width nonnalization has been applied for the differentia l partic l e size distribution according to Equation 2.4. Small Field Medium Field Large Field (mm) (mm) (mm) 0.063 0 317 1.007 0.079 0.400 1 .269 0.100 0.503 1 .599 0. 1 26 0.635 2.014 0.159 0.799 2.538 0.200 1 007 3.198 0.252 1 .269 4.029 0.317 1.599 5 .076 0.400 2 .014 6.395 0.504 2.538 8.058 0.635 3.198 10 .15 0.799 4 029 12.79 1.007 5 .076 1 6.12 1 .269 6.395 20.31 1.599 8.058 25.57 Table 2. Particle size bin s for the 3 MAPPER fields A twos tep proce ss i s then applied. First, all data points are used for a linear regression in log-log space; then each data point is eval u ated by the distance from the regressed result, and the nearest one is picked when multiple values are avai l able (e.g. Fig.5 at 10 1 em). Secondl y all se l ected data points are u se d again to perfonn the final regression, and the slope is thus detennined. The fir s t 2 bins of each re sol uti on field as well as the l as t ones are discarded since we believed that the dip" in co unt s for the beginning bins is caused by limitation s of the system resolution rather than being real 28

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and the last bins suffer from under-sampling of large particles These assumptions are supported by data measured by other groups (Li and Logan, SIGMA report ill, 1995; X. Li, personal communication). The combined result is shown in Figure 6 The smallest particle size presented for our: data then is 1 OOJ..Lm (Table 2, 3rd bin center), equivalent to a particle with a 32-pixel area, which minimizes errors to below 10% (Costello, Hou and Carder 1994) 10-4 10-3 10-2 10-1 10 Particle ESP (em) Figure 5. Particle Size Distribution For Each of 3 MAPPER Fields Measured at East Sound, WA on Apri121, 1994 Midnight (4/21A) 2 9

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Variations in particle size distributions throughout the water column are shown in Table 3 These were obtained during the SIGMA cruise of April 14 to April 21, 1994 to East Sound. Figure 7 and Figure 8 also feature profiles of the measured beam attenuation due to particulates. They share the same scale under different units All the units used through out thi s dissertation, unless specified, are all in em ..... 0 10-4 10-3 10-2 10-1 10 Particle ESP (em) Figure 6. Combined PSD from 3 MAPPER fields (from Figure 5) 30

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Date Depth (m) A*l03 Scattering % Number Jiter=1 (> IOOJ.lm) (>500J.1m) 4/14 0-IOm 2.36 2.39 90.5 109 4114 10-20 0.76 2.95 69.5 134 4115 22.3 0.17 3.30 26.0 73 4116 21. 1 0.34 3.22 34.1 118 4/17 20.9 0.20 3.30 26.0 85 4/18A 22.8 0.09 3.41 16.6 51 4/19A 19.9 0.23 3.26 29.9 89 4/19C 24.4 0.14 3 38 19.4 74 4/20A 24.4 0.21 3 28 28 0 85 4/20C 23.5 0.19 3.28 28.0 77 4/20G 25.2 0.16 3.31 25.5 70 4/21A 23.3 0.21 3.35 22.0 102 4/21C 24.1 0.23 3.22 34. 1 81 4/21E 25.4 0 29 3.21 35.0 99 average -0.32 3.23 26.5 114 Tabl e 3 Hyperbolic Particle size distribution parameters and scattering contributions measured at East Sound, W A It i s int eresting to note that regions where the number of large particles increases represented by a decrease of k, correspond to regions with high gradients with decreasing beam-c values (4114 8m, 4116 lOrn 4/21c l m 7m etc). This often happens at the thermocline (where th e temperature gradient i s greatest) or pycnocline (where the density gradient is highest). For example, the rapid change with depth in beam c values in midnight of April 21 corresponds to a thermocline cente red at 5m where temperature data drop from I2C to 9C between 3 and 8 meters depth, and the density values increase from 22.75 to 23 5 (cr1 ) (A lldr edge and Gotscha lk 1 995). A minimum in k appears at about 9 meters. A simi l ar case occurred the following morning (4/2lc), where 2 thermoc l ine s (1m and 6m) correspond to changes in the PSD s l ope k and the beamc These observations in measured k seem to indicate that l arge particles are likely to be formed at the pycnocline where densities c han ge g re at ly, and this is supportive to the 3 1

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coagulation process discu ssed earlier (Chapter 1 ), especially the process observed at the den s ity interface by Carder and Stew ard ( 1986) And the fact that the number of large particles do not a l ways covary with beam attenuation seems to indicate that the c-meter may not be measuring some of the effects contributed by large particle s, which MAPPER sees We will further discuss this in Chapter 3 with other topics related to light scattering by particle s. -1 o 1 Cp ; : : : : : : . -20 .. \ : : ....... : .. I : : t : l . ( . :. : . 4/14 4 / 15 0 1 2 3 4 0 2 3 4 -,':} .. .... :,{ .... .S-10 ..... . : ..c: : .. g.-20 ........ \ ...... : . .. . ... : ........ 0 : -10 .. J t: .... : : : . -20 .. .. . ': ....... : .......... ... .. 4 / 16 4 / 17 -30 0 1 2 3 4 0 1 2 3 4 0 1 : 10 I ...... . .... \ -20 . . ... ....... . .--:r; 10 ..... .. .. : ......... ; .. ... : . . I : t : -20 ........ . .. ...... .. .. .. ...... . .. ... 4 / 18 4 / 19 -30 0 1 2 3 4 0 4 1 2 3 Figure 7. Measured in situ profiles of h yperbolic PSD S l o p es (-)and hearn e (--)at East Sound, W A during 4/14 4/19/94 32

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.... : I -10 .,;/ Cp : : -20 .... \ .. : .... JK .. ...... 4/2oa ri,idnight 0 2 3 4 .. -:-' } -.. .S-10 .... ; ......... .. 1-20 .... 4/20g 8pm 0 2 3 4 .. c!: : ; . ; . -10 ..... \ .. : ........ ; .......... : ........ I : . I -20 .. .. ; ............ : ...... : ....... 4/21c 6am : 0 2 3 4 -10 -20 ........ t .. ;' + ....... ; . _, .. . .. .. . . l ..... : .......... : : : 4/20c 6am 0 2 3 4 -10 ....... .. ... I : : J : : -20 ...... ... : .......... : .............. .. : : : 4/21 a midnight : 0 2 3 4 ........ : ........ [ ... ... '. . .,. . . :,. : 1 : -20 ....... ;,-: .......... : ..... . ... .... ... . 4/21 e riO"on : : -10 0 2 3 4 Figure 8. Measured in-situ profiles of hyperbolic PSD slopes k and hearn-e at East Sound, W A during 4/20 4/21/94 Compared to previous studies of the abundance of lar ge marine-snow-type particles in the ocean, such as those summarized by Alldredge and Silver (1988) with typical numbers on the order of 101 per liter, MAPPER measurements show snow particle numbers for surface waters on the order of 102 (Table 3). They increased abundance numbers is consistent with measurements at other nutrient-rich locations such as at Monterey Bay, CA (Hou et al., 1994), The elevated abundance was obtained when there was no major bloom underway, and it appears that the numbers (291-489 lite(1 ) obtained for surface waters nearby Cape Lookout Bight, NC (by Wells and Shanks (1987)) are comparable. They considered that tidal mixing of different water masses likely increased 33

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the formation of aggregates. Strong resuspension from the bottom could be another r eason for high numbers, along with possible measurement errors due to their small sample volume (Wells and Shanks 1987) SIGMA Friday Harbor (4/15/94 @12m) 108 . : : : ;,.: : . . . .. . . .................... .... ......... .. . . .... ...... .............. ........ .. ... ... ... ...... :coulter Couhter : : : : : : : : : : : : : : : : : : : : : : : . . . . . .. . . ... ..... . ... .. . . . . . . . . . ..... . p 10-2 .......... .... .. ....... .. ...... . . . . . . . . 10-2 Particle Size (em) .. ....... ........ . . . ... . ... . .... .. ...... . ... .... ..... .. . . . . . . . . . .. . .... . . . -. ..... . .... -.. -....... -.-. .. ....... -.. .. Figure 9. PSD measured by a Coulter Counter and MAPPER Further, the numbers measured by MAPPER also compared consistently with other instruments such as the photographic system SNOWCAM from UCSB by Alldredge, and particle counters like the Coulter Counter and Elzone particle counter. A comparison between the measured PSD slope derived by a Coulter Counter (kcc. from Dr. B Logan, University of Arizona) and MAPPER (kM) is plotted in Figure 11, for 34

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measurements taken at 12 meters depth in the morning of April 15, 1994 at East Sound W A It i s necessary to mention that MAPPER results were me as ured in-situ while Coulter Counter data are taken f rom Niskin bottles tripped about 15 minutes later. The figure indicates that MAPPER/ICE measurement slopes ranged from 3.1 to 3.4, for p a rticle size s ranging from IOO,um to 2 5mm while Coulter Counter-derived slopes ranged from 2 9 to about 3 5 for particle s from 1 0 to I OO,um diameter. SIGMA Friday Harbor (4 / 15/94 @12m) 108 . . .. . .. . .. ..... .. . ... .... ... ... . . ......... .... .... .............. .. ...... .. ....... .. . . . . . . . . . . . . . . . ...... . . . ... . ... . . ... .... ............. ... . ... . . ... ........ .. .... . . ........ . . .... . ........ ....... ... . . . . . . . . . . . . . . . . . . . . .. . . . .. . . -. . -. -. ..... . .................... -........ .......... . .... . . ..... . ......... -.... . .. -... -.-. . . .. . .. . . . . . . . . . . . . . ... -.. ............ . ... ... . ..... ........................... .. 1 o -4 1 o -3 1 o -2 1 o -1 Particle Size (em) Figure 10. Combined PSD from MAPPER and Coulter Counter (see Figure 9) F rom Figure 9 we c a n s ee that wh e n the size become s s maller than IOO,um, MAPPER data appear to s tart s u f fering from under-sampling though not quite as 35

PAGE 53

drastically as is observed in Figure 5 Similarly, when the size range becomes larger than 70,um, approaching the Coulter Counter upper limit, the data also appear to show signs of underestimation or "drop-off'. We can adjust for this by truncating the Coulter Counter data at 70,um and MAPPER data at I OO,um and simply connect the two segments together (e.g. see Figure 10). The consistency of the results from two different instruments, although they each focus on different particle size ranges, is more obviously displayed in Figure 10, with a regression performed following the same procedure described earlier in this section. The regression is plotted as a dashed line, with a hyperbolic slope of k=3.2 0 and a concentration constant of A=0.434x 103 It is worth mentioning that at the small end of the size spectrum, the slope gets steeper (regression from 2 to 15J..Lm gives a slope of 3.9). This indicates that when the possibilities of artifacts are ruled out, the particle size distribution at the small end will be different from those at the larger end Thus a direct application of the same hyperbolic distribution obtained strictly from large particles can lead to erroneous conclusions. A closer examination of measured particle distributions in the surface water at East Sound, W A for all 7 days support the above argument. Coulter Counter measurements from hydrocast samples at 5 meter depth were plotted against averaged insitu MAPPER results (centered at 5 meter depth, with 4 1-meter bins averaged) in Figure 11. The vertical variation bars are the standard deviations of MAPPER data used in the average, indicating that their values can change rapidly with depth, especially in high gradient regions such as those found on April 19 (Figure 7). There is no error bar associated with Coulter Counter measurements since they are single measurements from 36

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individual samples taken from some region within the 4-m range exhibited for MAPPER data. It a ppears that the hyperbolic slopes measured by MAPPER (kM) average a bit higher than those of the Coulter Counter (kcc), indicating the number of small particles is higher in the smaller range. This is most likely caused by higher phytoplankton growth rates (Alldredge and Gotschalk, 1995), with the aggregation rate lagging slightly behind. 3.5 3.4 ::;: 3.3 0. 0 Ui 0 C/) a... 3 2 3.1 3 2.8 () 2.9 3 C) 3.1 3 2 3.3 3.4 3.5 PSD slope kcc Figure 11. Measured PSD slopes in surface waters for small (Coulter Counter) versus large particles (MAPPER). MAPPER values are 4-meter averages, and the vertical standard deviations of in-situ MAPPER measurements are indicate by the bars to illustrate the effect of vertical gradients on the data 37

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2.4 Discussion 2.4.1 Slope vs. Concentration Constants From our measurements, it can be observed (Figure 7 and Figure 8) that although the PSD seems to be changing throughout the water column, spectral analyses for all of the down casts show no dominant spatial frequency. This indicates that the variations may be caused by random patchiness of large particles, perhaps due to sedimentation transport of large particles from layers found above. However, there seems to exist a definite relationship between the PSD slope constant A and slope k, as shown in Figure 12. When concentration constant A is plotted against PSD slope k for all the depths measured over the 7-day experiment period, a total of 282 value pairs of 1-meter depth bins result, and a significant correlation appears among these data points Since we use a depth bin of 1 meter, therefore the water depth is the indicator of degrees of freedom (minus 2) for each down cast. These were used to obtain the critical correlation coefficients for the corresponding days ForD = 1, we have log(A)=log(f ( D ) ) so that constant A represents the particle concentration at a certain fixed size, depending on the unit used (in our case, em). For each separate down cast, a least square regression was carried out between log(A) and k, and the results are listed in Table 4, in which / is the correlation coefficient between the two values over the water column, critical r2 is the critical value for correlation coefficients at the 95% significance level (Table 25, Statistical Table, F. J. Rohlf and R. R. Sokal, 1981), and the depth column gives the total number of 1-meter depth bins which is used as the degrees of freedom (minus 2) to look up the critical / values. 38

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-3 -4 0 -5 -6 -7 Ol 0 __J -8 -9 -10 -11 -12 -4 -3.5 -3 -2.5 -2 -1.5 hyperbolic PSD S lope Figure 12. PSD slopes (k) vs. concentration constants log(A) measured at East Sound, WA DATE log(A)=a*k+b (k
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-s bll 0 -.. .o .. o o .o .. .. k. 0 -5 (j) .. o .. .. .. ... o f.' o . .. .. .. -4 k -3 Figure 13. Sketch of k vs.Iog(A) in 6 situations To di sc u ss the underlying relationship of the data shown in Figure 12 and Table 4, sec tion s of Figure 12 are labeled and redisplayed in Figure 13, in which the directions of perturbations in the positions of points relative to the line is sketched by arrows labeled as CD, @ ... Note that the dashed lin e corresponding to and is what we observe in Figure 12. Trends can be better understood by cons i dering the PSD description, where the number of particles per size bin per unit volume is plotted aga in st the particle size, as in Fig ur e 14. A l ine in Figure 1 4 is represented by a data point in Figure 12 or Figure 13. Examining the variations along with the perturbation s s u ggest that changes in log(A) and s lop e k have different indications If the data point is moved upward (Figure 13, case CD), 40

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it provides an inc r ease of concentration across the entire size spectrum, indicating a possible advective or perhaps a resuspension event, providing more particles In case with an increase of slope but no concentration change at lcm s ize we see a hinge point at l em size a nd the system losing particles smaller than I em and gaining large particles. This is indicative of an aggregation process. Case @ is a general situation between and with the aggregation point the point where concentration not changing moving toward the smaller particle end ......... C:Uj lcm \ \ \ ell \ .... c::: ::::3 0 u 4....... (xO yO) .......... SIZe Figure 14. Variations of situations in Figure 13 expressed in PSD plots It is interesting to see what det e rmines this "aggregation point" The intercept point for any two lines, line 1 and line 2 ( 2.12) for line I ( 2.13 ) for line 2 could be easily solved as 4I

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(2.14) If, w e have two lines in PSD plot (a1 b1 ) and (a2 b2 ) (Figure 14), each representing a PSD and that each line i s a data point in Figure 12 and Figure 13, (2.15) (2.16) so that we solve (xa.Yo) (2.17) 1:1log(A1 ) Yo= log(A1)-k1 M I Notice that 1:1log(A1 ) is the slope in the log(A) vs k plot (Figure 12). If the regression is Ml significant, i.e., the relationship between log(A) and k exists, we have a unique constant. This corresponds to a particle size at which point the concentration of this size class of particles doe s not change when the slope of the PSD changes. This could be used to describe a characteristic process related to the aggregation. For such a constant with a value of 2, x0 = -2 it indicates that the intercept is occurring at e -2 em which is 1 35 mm, and for a value of -3, the point is at e-3 = 0.498 mm or 498 These values could be regarded as "aggregation points" since the particles smaller would be aggregated" into ones bigger than this point or vise versa while the concentration at this point is not 42

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changing. In another words, we see a Joss in particles smaller than this point and an increase in particles larger than this point. The value y0 seems to be the "critical concentration" of aggregation, at which point the particle concentration does not change, while on either side of this point, changes occur in opposite directions. The fact that these data points line up well seems to indicate that the system is enclosed, i.e., volume is conserved, which may be explained by small circulation cells of mixing in vertical directions. If losses due to settling occurred, the total concentration would decrease The "aggregation point" assumption is further supported by the fact that the down casts with relatively poor fits, such as 4/21A, seem to correspond to times when high zooplankton populations are observed (data regarding zooplankton abundance for continuous sampling are all not available, but an extreme high abundance was observed during the mid-night downcast on April 21; personal communication with A Alldredge; also see Alldredge and Gotschalk, 1995). For the total 282 data points, we have a regression (2.18) log( A)= 2.774 k + 1.067 which means that our "average aggregation size" is e -2 774 em = Note the above relationship was derived using natural logarithms, while for base-10 logarithm, the regressiOn IS (2. I 9) log10(A) = 1.205 k + 0.463 . 10-I 205 624 Al h h It naturally has the same "average aggregatiOn size em = t oug we used em as our length unit, it is easy to see that the above relationship and the average aggregation size" is not related to this choice of units (Appendix C). 43

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Further analysis of data from other SIGMA cruises, such as one in Monterey Bay during July 24-31, 1993, confirms the above observation. The relationship exists between log(A) and k for the two down casts analyzed, the 3rd downcast from July 29 and the 2nd downcast from July 30. All have high correlations (Table 4, bottom 2 rows) (Hou, Carder, Costello in prep.). By checking all the regressed relationship in Table 4, it can be seen that the two downcasts from Monterey Bay fit well with Friday Harbor data. In fact the combined 352 data points (282 from Friday Harbor 70 from Monterey Bay), yield a regression with a correlation coefficient of ? = 0.723 with a slope k = 3 692 and an intercept of 4.09. The aggregation points of different down casts correspond to particle sizes ranging from 280J..Lm to 1.4mm for all the relationship regressed thus far, with an average of 624J..Lm for Friday Harbor data (400J..Lm for Monterey Bay). It is rather interesting that these sizes are in such a narrow range considering the variation of the sampling environment and the size range covered. Also, these value are close to our operational definition of marine-snow particles (d> 500J..Lm), especially for Monterey Bay where many aggregates have been observed (Alldredge and Silver, 1988) These values could be a function of the physical as well as the biological environment. However, if they are rather close to a constant or in a tight range for different sites, one might postulate such a value is a functional constant of the natural environment such as the smallest eddy size. Another significant implication of Figure 12 is that it is possible that only one parameter, such as k, is needed to describe the particle size distribution: (2.20) 44

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Even if this only applies to individual downcasts, it simplifies measurements and brings enormous convenience to other applications. The existence of the relationship between multi-day and multi-down-casts indicates that there might be a single set of constants ( a and b in Equation 2 20) that fit all of our data at Friday Harbor. Thi s could be due to the fact that the system is semi-enclosed in a well-mixed environment, and Langmuir types of vertical circulation cells help bring small particles down and bigger ones up (Mann and Lazier, 1991). 2.4.2 Particle Size vs. Porosity H R is the radius of gyration (for detail s see Section 2 .1) of an aggregate, and r0 is the spherical-equivalent diameter of N small spheres that make up the aggregate we have (2 21) as the two-dimensional porosity of the aggregate Our measurements show a strong correlation between the particle size and its porosity (Figure 15). The correlation coefficient r2 = 0.98 and a least square fit could be obtained for these multi-day downcast measurements as (2.22) F2 = -0.27log(D) + 0.235 Since F2 is directly related to the fractal dimension of the particle (Jackson et al., 1997), and the above relationship indicates that the larger the particle, the more porous it will become, this will affect the average traveling distance (mean-free path) of photons and the scattering properties of these particles. We thus should expect different scattering 45

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behavior from within the aggregate This relationship is used later for calculating mean free path for photons for a Monte Carlo s imulation ( s ee Chapter 4 for more details) 1 2 I I I I I I 1 .... ( .. . .... .. : . ......... . f '-{ j 0.8 r............ ... 0 ... . ':' ..... ................................................ -. 0 . 0 0 0 ', : : 0 . : : 0 : : 0 : s 0 : LLN 0.6 ...... ..... ............... : .... ......... :. @ :' ........... :0 .. .............. . 0 0 : : 0.4 r............ : ............. : .............. : .... ..... 0 ... : ........ ........... o ......... . -. : 0 : @ 0 : 0 0 2 ..... : 1 0 c 0 .. : ...... O ..... ..... 0 : 8 l ______ J_ ______ -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Log (D) (em) Figure 15. Particle size vs 2 dimensional fill factors F2 (the dash line indicates a linear regression) A proper parameter to describe the size of the s e porous particles is necessary To better describe the in-situ particle size, equivalent spherical parameter (ESP) is u s ed to replace equivalent spherical diameter (ESD) which most researchers have been using Thi s parameter is not only a better de s criptor in replicate field truth but also is a necessity 46

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in explaining multi-camera data (Costello, Hou and Carder, 1995). ESP should be used so that different measurement methods can be compared without artificially introducing error (Costello et al., 1994; Jackson et al., 1997). To accurately represent the particle size is very important, especially for applications such as settling velocity of the particle using Stokes Equation, where particle size is one of the most important factors. The same applies for use with aggregation models (Jackson et al., 1997). It is possible that some of the discrepancies observed in particle size distributions, especially those with log-normal types of distributions are errors caused in part by a lack of this treatment. Size distributions in natural environment may be in a state of equilibrium most of the time. If the particle community is in such stage, there should be a constant volume (flat volume) distribution with a PSD slope of 4, when no porosity or fractals involved Any differentiation from that point is an indication of fractal volume, which is demonstrated by Logan and Li (1994, 1995). Such "flat" distributions have the shape of hyperbolic rather than of Gaussian or Gama-type distributions, as these "peak" should be quickly smoothed out by nature except for mono-phytoplankton blooms. 2.5 Summary In this chapter hypotheses #1 and #2 are tested. We see that in order to accurately assess the role of large, marine-snow-type particles in the ocean in-situ measurements such as those carried out using MAPPER and processed by ICE system can be used to obtain accurate results. Hypothesis #1 thus is tested to be true However, the hyperbolic distributions measured by MAPPER for large particles can not be accurately extended into smaller ones size classes. A direct comparison with 47

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measured small particle distributions by Coulter Counter indicates that for surface waters of East Sound, W A, such an extension will lead to a systematic underestimation of small particles, at least in regions with high phytoplankton growth rates. Hypothesis #2 then is tested to be false. A hyperbolic distribution was measured which indicates large particles an order of magnitude higher than previous assumptions in coastal surface waters: a differential particle size distribution slope closer to 3 than 4, which will give added importance to large particle scattering (see next chapter). However, different scattering properties should be expected for these large marine snow type particles (see Chapter 4). 48

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CHAPTER 3 SOME MARINE OPTICAL PROPERTIES AFFECTED BY PARTICLE SIZE DISTRIBUTIONS 3.1 Background When a photon encounter s an obstacle, two things can happen : either it will be absorbed (terminated), or it will be scattered. The basic element in describing the behavior of the scattered photon i s the directionality of its path, the volume scattering function P C8,
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When light interacts with a sphere part of the light will be refracted diffracted, and reflected, and part will be absorbed. The effective area that causes the loss or deviation of photons divided by the geometrical cross-sectional area of the sphere (7! ? where r is the spherical radius) is defined as the extinction efficiency factor, Qexr (van de Hulst, 1957). It consists of two parts the part caused by scattering, Q sc a. and the part caused by absorption Qabs Also Qext = Qabs + Qsc a Note that these values can be greater than 1 since diffraction occurs from photons passing near a particle. This is because a particle in an electromagnetic field, which will not only cast its shadow on the field it physically intercepts but also perturbs the surrounding field In terms of geometrical optics, one can imagine that light can be refracted or reflected when intercepted by the particle and also be diffracted by passing near the edge of the particle. The general solution of Maxwell's Equations for light impinging on spherical particles (Mie scattering) is often presented in scattering-matrix format in which the characteristics of the particle scattering such as polarization and scattering intensity in certain directions are included (see Appendix E). To simplify our case study, we first neglect the effects of particle absorption (absorption coefficient a0) and concentrate on scattering only. This is justified in part for the reason that beam-c measurements ( c =a+ b ) that we will compare to are at a wavelength of 660 nm at where the effect of absorption by most marine particles is small (Mobley, 1994). This is also the case with our single-particle scattering me a surements using only one of the 685 J..Lm lasers of MAPPER. For a non-absorbing spherical particle, the scattering and hence the total attenuation caused by the particle can be obtained by an exact solution to the governing 50

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electromagnetic field equations, Maxwell equations, with proper boundary conditions (van de Hulst, 1957). We omit the lengthy derivation and adopt those simplification provided by van de Hulst under his anomalous diffraction theory for particles with a refractive index near that of the medium. The total scattering efficiency factor is (3.4) 4sin(p) 1-cos(p) Q b(p) = 2-+4 2 p p (3 .5) 2n(n, 1)nw p= D II. nP and n =-is the relative particle index of relative refraction to the medium (water), n w and 'A is the wavelength in vacuum Note that this expression is a suitable approximation for particles with relative indices of refraction up to twice of that of the medium This equation is derived for particles with sizes larger than the wavelength. However, it has been proven also applicable to the situation when the wavelength is comparable to the size of particle (van de Hulst, 1957), which is Rayleigh-Gans situation So Mie theory can be considered the general solution to spherical particle scattering. Deirmendjian (1969) showed that randomly oriented polydisperse, nonspherical particles behave like spheres in their scattering behavior. It is obvious that the scattering properties of a particle depend on its composition, which is described by the index of refraction (it is a complex number if we consider both scattering and absorption, and real if no absorption is involved) and most importantly, its size and shape Mathematically, if the index of refraction is known, the exact scattering phase function of a perfect sphere can be derived (van de Hulst 1957), which is 51

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commonly referred to as Mie scattering. Mie first solved this problem for spheres of all sizes in 1906 (Mie 1908) It is worth mentioning that there is a distinctive difference between small and large-sphere scattering properties; namely the small spheres have a size very much smaller than the wavelength of light, and scatter about equally into forward and backward directions. The larger spheres scatter strongly into the forward angle. As many as half of the photons can be scattered into the forward 0-5 (out of 180 ), while scattering at and beyond 90 is weak 3.2 Large-particle Total Scattering Contribution It has been postulated that large particles could play an important role affecting the underwater light field (Carder and Costello 1994) especially when they have strong back scattering. The scattering contributions made by large particles are now presented, assuming Mie scattering and using measured particle size distribution data. With the particle size distribution measured and the single-particle scattering efficiency calculated, we can use (3. 6) D2 D 2 b = J f(D)Qc(D)n-dD Dl 4 to obtain the total particle scattering for particles in a size range D1 to D2 By i ntegrating over the entire size spectrum we get the total scattering for a given particle suite. By integrating over a particular size range, we get the contribution made by particles in this size range The ratio of these two yields the relative fraction of scattering contributed by particles in a particular size range. If the slope of the total particle size d i stribution is the same across the entire size spectrum range (from 0 1Jlm to 1 Ocm), the relative scattering contributions by large 52

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particles can be estimated using our slope measurements. As measurements from the East Sound SIGMA cruise show, the maximum difference in PSD slope measured for particles down to the micrometer range was less than 15% when compared to measurements of other size ranges (Jackson et al., 1997). For example, on April 15, 1994 at Friday Harbor, Coulter Counter measurements show a slope of k = 3.39 (size range from 2.5 to 200J..Lm) (SIGMA Report ill, 1995, X. Li, and personal communication), while MAPPER data showed k = 3 06 at the depth of 12m, where the maximum difference occurred. Since errors associated with the determination of the slope (ie, size bins to choose from, method of fitting the slope, calibration etc) could easily contribute to the variations of the slope measurement, we will therefore simply use our MAPPER data as the standard to which other results have been compared (Jackson et al., 1997). Furthermore, the author believes that the same slope should be applicable to the entire size spectrum if the system is in equilibrium and could be treated as enclosed. Thus only small variations should occur within the system (see Section 2.4.1) With this assumption, scattering contributed by particles larger than lOOJ..Lm are calculated using the measured PSD and tabulated in Table 3. The size class above lOOJ..Lm is chosen to illustrate the effect of large-particle scattering contributions on scattering (the ESD size is used for scattering since only the cross-sectional area is contributing to scattering), while particles larger than 500J..Lm are used for the snow-particle contribution. We notice that about 26.5% of the total particle scattering was caused by particles larger than IOOJ..Lm, but it could reach as high as 90% for extreme cases such as on April 14. 53

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80 c g 60 :::J .0 ;:: c 8 40 Q) C)
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Figure 16 shows the relative percentage contributions of particle scattering in different particle size ranges related to total s cattering, by assigning particle size from less than 1J..Lm to 10 em in spherical diameter, with PSD slope k varying from 2 5 to 4.5. These calculated results are for a f i xed relative index of refraction (to the sea water) of 1.05, which is suitable for small marine organic particles in the water (Stramski and Kiefer, 1991) This theoretical calculation clearly illustrates that scattering contributions by different size classes is very sensitive to the slope of the PSD (a break-down of results is shown in Table 8 and Table 5). The contribution from particles which are represented by a higher relative index of refraction (1.15 could represent inorganic materials such as quartz in sand) also affects the scattering calculations (Equation 3.5) From Figure 16, we see that when the slope is less than 3 obviously only the large particles contribute to the total scattering This changes when at 3, the size group from 1J..Lm and up provided about equal contributions for each group (Table 8 and Table 5), while subrnicron particles do not contribute significantly As the slope gets steeper (k increases), a smaller contribution comes from the large-particle end ; e.g. when k = 4 only 1 36 % is contributed by particles larger than 1 OOJ..Lm (nr = 1 05). This i s also the case (0.45 % ) when using a different relative index of refraction (nr = 1 15) as in Table 6. This is not surprising since the change in relative index of refraction is equivalent to shifting the optical size (Equation 3 5) Slope 0-1J..Lm 1-lOfJm 10-lOOJ..Lm 0.1-lmm 1-10mrn 1-IOcm 3 0 5 18. 6 21.4 20.7 19.8 18. 9 3 5 4.1 56 9 26.7 8.60 2.72 0 86 4 15.7 70. 3 12.6 1.24 0 12 0 .01 4.5 43.2 52.7 3.9 0 .13 0 004 0.00 Table 5. Percentage contribution of scattering in size group for nr=l.OS 55

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Slope 0-1J,Lm 1-lOJ.Lm 10-100J.Lm 0.1-1mm 1-lOmm 1-lOcm 3 3.72 23.3 19.5 18.7 17.8 17.0 3 5 19.9 57.4 15.6 4.96 1.57 0.496 4 43.4 51.9 4.21 0.406 0 039 0.0037 4.5 70.9 28.3 0.77 0.024 0.001 0.0000 Table 6. Percentage contribution of scattering in size group for nr=l.lS Along with the argument that the scattering by a small number of large particles may be compensated for by a possible elevated back-scattering efficiency (Carder and Costello, 1994; Mobley, 1994; Stramski and Kiefer, 1991 ), Figure 16 Table 8 and Table 5 show that the s lope of the PSD will most likely determine the contribution of total s cattering s ince it implies the presence of more large particles than was previously perceived. These two factors combined will likely bring the total scattering contribution of large particles up nearly being comparable to that of smaller ones. A better understanding of the scattering of these large particles is critical unless their scattering properties do not significantly deviate from Mie theory. We will discuss this in detail in the next chapter. Our particle size distribution has shown that contrary to the common measurement of flat volume PSDs found in the open ocean (McCave 1984, Carder and Costello 1994 Stramski and Kiefer, 1991), the slope of the measured differential particl e size distribution is much less than 4, usually around 3.3 (Table 3) In this case an average scattering contribution of 26 % of total scattering may come from particles for East Sound larger than 1 00!-lm in s pherical-equivalent diameter. This significant contribution of total scattering may be greater for backscattering if the effect of enhanced backscattering (at near 180 ) is taken into account (Latimer 1984, Bourrely Chiappetta and Torresani 1986, Kug a and Ishimaru 1989 Xu, 1995). 56

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The above conclusion was based on the assumption that the particle size distribution is continuous for the entire particle size spectrum, and that the same slope applies to the whole range. Some people argue that the slope is not single-valued and might be larger at the small-particle end. If this were the case, the contribution of particle scattering would be exclusively attributed to small particles of less than 10J..Lm in diameter (Table 7). In this table, the first three size groups ( up to 1 OJ..Lm) are assigned a varie d slope (first column ) and the rest of the size group have a fixed slope of k = 3.5, connecting the concentrations at 10J..Lm. It shows that a 13% contribution comes from 0 to 1J..Lm range when k = 4, and it jumps to 99% when the slope is changed to 5.3. slope* 0-0.1u 0.1-1u 1-10u 10-100u 0.1-1mm 1-10mm 1-10cm 3.5 0.13 4.07 56 9 26.7 8 60 2 72 0.86 4.0 1.31 11.9 61.2 17.6 5.67 1.79 0.57 4 5 14.4 25.6 48 5 7 86 2.53 0.802 0.25 5.0 75.4 14. 0 9 .51 0 797 0.26 0.081 0.026 5.3 94.9 3.69 1.34 0.073 0.02 0.007 0.002 Table 7. Percentage contribution of scattering in size group for n,.=l.OS However, the above s lope for smaller particles is que stionable in reality. A connected slope of -6 will generate 1019 particles per m3 using our slope measurements (Table 3), and even assuming a slope of k = 4, the tot a l number would st ill be 1016 5 again using a slope of k = 3 for the rest of the sizes with the two segments connecting at the 10J..Lm point. Conversely, our average data, A=3.23* 10-4, k = 3.23 (Table 3), provide 1.87 1014 particles per m3 for the O .IJ..Lm size bin (between 0.1 and 0 .2J..Lm to be exact), or 9 54* 1012 particles per m3 between 0.38 to 1J..Lm. This is comparable to measurements of s ub-mi cron particles on the order of 1013 from 0.38 to 1J..Lm (Koike, et al., 1990). 57

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This analysis indicates that the slope is very important in determining the relative contribution by different size groups to the scattering and attenuation coefficients A very steep slope is not likely to exist in nature from both a conservation of volume sense (see aggregate models such as Jackson, 1990; Hill 1992) as well as considerations of particle growth rates when assuming the number of small particles represent naturally grown bacteria and viruses (Stramski and Kiefer, 1991), and our slope measurements together with other SIGMA data (Jackson, 1995 ; Jackson et al., 1997) support the assumption of a continuous PSD over large and small size range. A similar exercise can be applied towards total volume contributions by particles of different size. The result indicates that when the slope of PSD has values of 3 0, 3 5 and 4.0, the total volume contributions by size class larger than lOO,um are 99 86% 95.7% and 41.45% respectively. The flux of material transferred by large particles will be no less than this percentage, as settling velocities increase with particle size (Hawley 1982 ; Alldredge and Gotschalk, 1988). Measurements indicate that settling velocities on the order of 100 meters per day by large particles are attributed to total flux (Nelson et al., 1987; Deuser et al. 1990; Tsunogai and Noriki, 1991 ; Asper et al., 1992) Unfortunately, due to strong horizontal advection (Jackson and Kimsey, 1995), settling velocity was not measured at the study site. 3 3 Beam-c Correction Using Measured PSD Slope The beam transmissometer or c-meter is a widely used in-situ sensor, since it provides a better estimation than the Secchi disc regarding the turbidity of sea water. This in turn relates to other physical and biological phenomena such as particle concentrations 58

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in regions of upwelling thermocline, sediment re-suspension events and sub-surface chlorophyll maxima, to list a few It is also a basic lOP that plays a very important role in radiative transfer in the underwater light field and remote sensing applications. The beam transmissometer measures the attenuation (both scattering and absorption) of a collimated beam. If we have a beam of radiant flux C/J passing through a thin layer with a thickness r as shown by shaded area in Figure 17, the loss after traveling a small incremental distance dr is (3.7) del> -=-cdr c'P r Receiver Source Figure 17 Sketch of a beam attenuation meter and error caused by forward scattering into the small acceptance angle (no absorption shown) The negative sign is necessary since we want c to be positive, and integrating over distance will yield 59

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(3.8) or (3. 9) In(-)= -cr o = 0 -cr where o is a constant, representing the initial flux. This means that the intensity of radiant flux is attenuated exponentially alo ng its path, by the product of the beam attenuation coefficient, c, and the traveling distance Although hearn-e has been extensively measured and utilized in many different applications few have treated it thoroughly. As we can see from the illustration shown in Figure 17, if a photon is scattered in the case labeled as "o", it will not be collected by the receiver. But photon "r" will be captured by the receiver, even though it is also scattered The result is an overestimation of the amount of light that shou ld be received or underestimates the true value of beam attenuation (Equation 3.9). By the optical design of c-meters, the receiver acceptance ang l e, which is the angle that it will "mistakenly" capture scattered photons, can be calculated using the focal length of the receiver, the index of refraction of sea water and the size of the detector along with Snell's Law. For a Sea Tech Inc. 25-cm path-length transmissometer with a focal length of 60mm and detector area of 0.051 cm2 the calculated half angle is 0 91, assuming sea water index of refraction n w = 1.33. Due to the strong forward scattering, this s eemingly small acceptance angle can result in large errors. Since the collimated beam is much larger compared to the detector of the receiver, the photons with scattering angles smaller than the acceptance angle of 60

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the receiver will be intercepted by the receiver. We need to remove this underestimation in the beam attenuation measurements by removing this forward scattering contribution General Mie theory shows that for spherical particles with known size and indices of refraction, the scattering properties can be calculated. For a scattered plane scalar wave (Borhen and Hoffman, 1983; van de Hulst, 1957), we have (3.10) e-iKr+iW u = S(B, rp)-iK_r_ where K = 2n/'A i s the wave number, S(B ,
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(3.13) 0 9 Jmm D2 I S11 (B)sin(B)dB b0.9 = I 0.J,u I S11(B)sin(B)dB 0 % error underestimated by c-meter with a 0.91 o acceptance angle . 50 ....... .. ...... ..................... . ................. . . .... ........ 40 .... 20 ..... ..... / 10 : / / : ; : :m=1.01 / :f / -4.5 -4 -3.5 -3 -2.5 slope of a differential particle size distribution -2 Figure 18. Percentage errors underestimated by c-meter with a 0.9 acceptance angle, different PSDs and relative indices of refraction Note that in Equation 3 13, we directly substitute S11(8) for the volume scattering function since they only differ by a constant which is a function of the particle size and the wavelength and their ratio will not be affected in our calculations. Scattering efficiency factor Q s c a is calculated without approximations. Sn(8) is calculated by Mie 62

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scattering codes from Bohren and Hoffman ( 1983) and the codes are tested against volume scattering function of water as well as Qsca (Equation 3.4, for large particles). To make better use of these calculations, we choose to express the overestimation in fractional ratio between b0 9 to b180 in which case, the result will not be affected by the concentration constant A0 and is only a function of the slope of PSD, the relative index of refraction and the wavelength. The results for a fixed wavelength A.= 660nm, variable relative index of refraction from 1.01 to 1.15, over particle size distributions with slopes 2 to 5, are shown in Figure 18. Although these calculations are carried out primarily to correct our Sea Tech c-meter measurement results, the above formulas and the program are applicable to different wavelengths and indices of refraction. It is shown that the errors can be as high as 60% for this transrnissometer if correction is not carried out. For a coastal marine environment such as East Sound with a average PSD slope of 3.3 and assumed relative index of refraction nr = 1.05, beam-c is underestimated by 16.4%. For a PSD slope of 4, the error drops sharply to around 6%. Again, we see the importance of an accurate assessment of the PSD slope. Some publications also cited different acceptance angles, such as 1.35 (Zane veld et al., 1980) and 1.8 (Bartz et al., 1978), which correspond to much larger errors if not corrected. Calculations show that for 660nm light, relative index of refraction of 1.05 and a PSD slope of 3.3, errors for those angles are 21% and 29% respectively A fit is carried out for the curve in Figure 18 with nr= 1.05, (3.14) 63

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where Cmea is the direct measurement result and Creal is the correct value. The above relationship applies to particles with PSD slope 5 < k < 2 and relative index of refraction of 1.05. 3.4 Estimating the PSD for Smaller Particles from Beam-c and MAPPER PSD The in-situ particle size distribution can help us better assess the role that different size class particles play in the underwater light field especially when the variations in the water column are large, in regions of high gradient such as thermocline It has been shown that MAPPER can measure the distribution of large particles (Jackson et al., 1997; Costello et al., 1995; Hou et al., 1994) Since the beam attenuation coefficients are influenced by particles both small and large it is interesting to see if it is possible to use the beam-c and MAPPER measurements to extrapolate the PSD for smaller particles We will refer to particles being small or large by a separation point at and assume tha t the measurement results from MAPPER can be extended to This is done since the Coulter Counter measurements to which we will compare our results to are accurate for particle sizes ranging from 2 to To estimate the small-particle size distribution, we use the scattering by small particles by removing the portion caused by larger ones from beam-c measurement, and calculating the small-particle PSD needed to match the difference distributions. We first remove the contribution to beam attenuation due to the scattering of large particles (> up to some size, Dmax see below), by integrating the total scattering cross-sectional area of these particles in a 1 cm3 cube multiplied by the scattering efficiency factor, Qsca (detail see Section 2.4.1 and Equation 3.4) This gives us the total 64

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attenuation due to large-particle scattering per em. Enlarging this value by a factor of 100 provides the total scattering (attenuation) per meter due to large particles. By removing this quantity from the total particulate attenuation coefficient, cp, we then have the portion of beam attenuation that was caused by scattering by small particles: (3.15) fom.. 1tD2 CP small =cp-Qsca(D)--JM(D)dD -?OjJm 4 fo.,., 1tDz k =CPQsca(D)--AMD MdD 70jlm 4 Note that this residual value is a function of the relative index of refraction of particles, n, the particle size distribution function JM( D) (measured by MAPPER, slope kM, concentration constant, AM), and the upper limit of the size of the particles in the water that affects the c-meter reading, D,rax. If we assume that we can characterize the smaller ( <70!lm) particle size distribution by a hyperbolic distribution with a slope of k and A as the concentration constants, and an average relative index of refraction, n ,, then (3.16) l70jlm 1tD2 k' cp small= Qsca(D,n,)--AD dD 0 4 and these two distributions will give the same value at 70!lm, which links the two concentration constants (3.17) where D o is the connecting point (0.007cm here). With these values calculated we can estimate the small-particle size distribution by finding a set of n,, D,rax and slopes that will generate the closest fit to Cp. The determination of Dmax involves an estimation using 3 different values for upper limits of 65

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the integration range (500J..Lm, 1 mm, and 5mm) by fixing nr and k at different values (nr from 1.03 to 1.09 with step of 0 2 ; k in the range of kM I with step of 0.1). The result provided overall average mean errors of cp estimation to be 7.9 % 4.9 % and 12.5 % for the above integration range, respectively. As we know, for a hyperbolic distribution such as Equation 2.4, the number of particles in a unit volume decreases with the increase of the particle size. Hence the above result s show that the error decreases when we move the upper si z e limit c meter sees (D,uu:) towards larger particle end (from 500um to lmm), indicating that integration up to only 500J..Lm will underestimate what the c-meter sees. On the other hand if we keep moving up from 1 mm, the errors start increasing, indicating that we are overe s timating the range of particles that affects c-meter or are statistically represented in the volume measured by a c-meter. This can also be explained by simple statistical analyses based on the sample volume of our transmissometer. For a 25-cm pathlength SeaTech transmissometer with a beam diameter of 1.5cm, it is easy to estimate that the total sampling volume for each reading i s 51 cm3 or 0 051 liters. Considering a typical particle size distribution with A = 0 00032 kM = 3.23 (Table 3) we can estimate that the total number of part i cles larger than 500J..Lm, lmm, 2mm and 5mm are 114 24, 5 2 and 0.67 per liter respect i vely. Therefore we have on average 5.7 particles larger than 500J..Lm that will appear in each beam-c reading or 1.2 particles larger than 1 mm or 0.26 particles larger than 2mm, and 0 03 particles larger than 5mm. We conclude that we can use lmm as the upper size limit for detection by our c-meter. 66

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3.5,-----.----..------.------,--------.-----, 0 3 ........ ..... .............. 2.5 (ij .3. 2 . . . . . . . ...... .. .......... oc. 0 1.5 ............. . . ................................. . . ........................... 0 5 '------'-------'-----'--------'-------'-----' 0 .5 1 .5 2 5 3 3.5 Figure 19. Estimated total particle attenuation cp (estimated small particle contributions plus larger ones using MAPPER measurements) vs measured cp (corrected for forward scatting) for East Sound, W A With Dmax set at 1 mm, we now move on to find the best fit using different PSD s lopes k. with relative index of refraction nr = 1.05. In order to limit calculations and obtain reasonable estimates, we limit the range of variations of k', so that lk' -kMI
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Counter k cc, for particle sizes ranging from 2J..Lm to 70J..Lm diameter (courtesy of Dr. B Logan, University of Arizona, with permission). Notice that our calculated distribution is rather close to that measured by the Coulter Counter, with an average fractional error of 0.0507. The slopes for larger (> 70J..Lm) particles measured by MAPPER, denoted by kM and also listed in Table 8, and appear to be smaller than the smaller ones on average Cp kM %k %are are ace areac a area chi. a I M 4/15 5m 0 .91 3 39 3.46 3 56 2.81 5 95 0 14 0 .15 0.08 2 5 12m 0 88 3 30 3 .31 3.46 4 34 4 80 0 .16 0 .17 0.09 1.7 16m 0 77 3 20 3 5 3.55 1.41 3 .18 0 .11 0 .11 0 09 1.9 21m 0 82 3 28 3.42 3 12 9 62 0.49 0.16 0 .16 0.16 1.3 i 4/16 5m .. 3 .25 0.18 1.22 3.30 3.55 8.45 10 .1 0.21 0.08 3.0 8m 0 .83 3 .14 3 .77 3.62 4 .14 15.2 0 .12 0.10 0 .10 2 3 12m 0 .71 3.16 3.53 3.43 2 92 5 65 0 .13 0.12 0 .12 1.6 21m 1.25 3 .27 3 66 3.71 1.35 4.55 0 .11 0.12 0.20 1'4717 5m 1.'39 13 .37 -3.34 3 .72 9.41 20.9 0.14 0 18 0.06 4.4 8m 0.93 3.40 3 .57 3.67 2.72 7.91 0 .10 0.11 0 .10 3.7 12m 0.69 3 .18 3 .65 3.5 4 29 11.8 0 .12 0 .11 0.10 3 2 21m 1.09 3 28 3 64 3.64 0 00 0.00 0.11 0.11 0 .19 2 6 4/18a 5m 1.04 3 .01 3.28 3.43 4.37 3 .71 0 24 0 25 0.06 4 6 8m 1.15 3.42 3 .31 3.51 5.70 7.43 0.20 0.22 0 06 3 3 16m 0.80 3.43 3 .53 3.48 1.44 3.07 0 .19 0.13 0.11 1.7 21m 0.97 3.49 3.48 3 5 L 1.42 2.98 0.14 0.15 0.10 1.9 4/19a 5m 3.28 3 29 3.22 3.67 12.2 18 2 0 27 0.33 0.11 10 9 7m 2.78 3 .51 2.99 3.44 13.1 7.03 0.41 0.39 0 .12 9 ; 8 12m 2.14 3 07 3.44 3.84 10.4 28.3 0.16 0 .22 0 .11 --4/20c6m 1.49 3 .20 2.92 3.27 10.7 19.3 0 59 0 .49 0 .10 8 5 12m 0.75 3.22 3.44 3.49 1.43 2 56 0.13 0.13 0 09 3 8 16m 0 64 3 08 3 .55 3.45 2.90 6 .11 0 .11 0 .11 0.08 --21m 0 72 3 .44 3 .39 3.29 3 04 2 .17 0.19 0 .19 0.08 4.4 4/21c 5m l 1. 5 6 3.79 3.06 3.46 11. 6 0.76 0.33 0.33 0.12 8 5 12m 0 85 3.11 3 .37 3.42 1.46 1.76 0.16 0 .16 0.10 4 0 16m 0.68 3 .2 3 3 60 3.50 2.86 7 .19 0 .11 0 .10 0.09 --21m 0 99 3.13 3.40 3 50 2 86 4 72 0.17 0.18 0.09 3 2 Average 1.16 3 .28 3.41 3.51 5 07 7 64 0.18 0.19 0.11 4.11 Average 0 87 3 26 3.49 3.48 3 05 5 06 0 .14 0.14 0.11 2.73 Table 8. Estimation of small particle distribution by MAPPER PSD and cp for data measured at East Sound, W A. Shaded areas are sampling regions with high gradients. The results excluding their presence are also listed on the last row (denoted with *) 68

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The calculated total attenuation by particles, cp( cal) shown in Figure 19, using an estimated small-particle size distribution and the derived large particle scattering using MAPPER measreuement, fits rather well to the c-meter measurement. The small differences cou ld be the results of the fixed relative index of refraction and correction for beam attenuation It is encouraging to see that our estimated small part icle distributions (Table 8) match the Coulter Counter measurements rather closely with an overall mean difference of 5.07%. Excluding gradient regions with large differences, suc h as 4116 5m, 4117 5m, 4/19 all depths, 4/20 6m and 4/21 5m ( Table 8), where there are differences as high as 13% in the slope estimation, reduces the error to 3.05%. Since Coulter Counter measures the electronic resistance of the particles, which is directly related to the volume of the particle, a comparison in volume differences are also liste d in the table, and it shows that the differences can be as high as 38%. These gradie nt measurements are highlighted in the table with shading for better viewing. By examining a break-down of total area for small particles both measured (areacc) and calculated (are3.ca1), in comparison with large particles measured by MAPPER (areaM), we can see that these differences occur mostly associated with correlating variations in smaller particles A closer examination of the data in Table 8, Figure 7 and Figure 8 reveals that all the large errors occurred at regions of high gradients in beam-c measurements They are mostly associated with high chlorophyll concentrations, which are measured by standard fluorometric methods (Parsons e t al., 1984 ). These were collected at the same sample depths as Coulter Counter measurements (courtesy of Dr. A. Alldredge UCSB). In absence of these sharp gradients such as in the surface waters of April 15 and 18, the 69

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estimations closely match those measured As for April 19, when most of our inconsistency occurs, it appears that high gradients of beam attenuation are extended from the surface throughout the entire water column (Figure 7), which are in accordance to the large differences in our estimates to that of Coulter Counter measurements Since data collected on separate casts at slightly different times suffer most from comparisons made at depths where large gradients are found the most accurate estimates of errors are shown on the bottom row of Table 8 Aside from the treatment of data such as corrections to the beam-c measurement, patchiness in sampling, and the assumption of a single relative index of refraction it is possible that the major variations are caused by sampling in different water masses Since Coulter Counter measurements are used water taken from Niskin bottles it is probable that they are somewhat different from the water masses MAPPER encounters during later cast. This would most likely happen in regions of high gradient and especially for Friday Harbor with its fast-moving waters caused by tidal currents in the surface water (Jackson and Kimsey, 1995). Therefore in-situ PSD measurements such as those from MAPPER can provide continuous and more consistent results, which are vital for applications such as modeling aggregation process and in-situ remote sensing measurements. 3.5 Slope vs Beam-attenuation Ratios It is interesting to explore the possible relationship between our newly measured PSD and other commonly measured quantities such as beam attenuation, which might lead to simpler and faster alternatives to determine the in-situ the slope of PSD. Considering that the change in the slope will affect the number of small particles, which 70

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in tum affect the scattering plus absorption coefficients measured by transsmissometers at different wavelengths, these quantities could have a possible correlation with k, as suggested by Kitchen et al. ( 1982). If we assume the following relationship holds (Gordon and Morel, 1983) for the open ocean (3. 18) b(A.):::: where C is the chlorophyll concentration, 0.30 and 0.62 could be other constants (ap plic ab le to our research site). Since there is little absorption by particles and CDOM at 660nm, we could remove water absorption from c(660) to get bp(660), and bp(450) and/or bp(443) could be derived using the above equation as (3.19) and the same applies to bp(443). The calculated values are in Table 9. Date a0(443) a0(450) c(660) Cp(660)/cp(443) cp(660)/cp( 450) <-k> 4115 5m 0 .103 0.100 1.21 1.62 1.59 3.36 4/15 16m 0.099 0.090 1.13 1.63 1.59 3.10 4115 21m 0.091 0 085 1.11 1.62 1.59 3.30 4/16 5m 0.088 0.083 1.49 1.57 1.54 3.35 4116 12m 0.099 0.092 1.00 1.66 1.62 3.10 4116 21m 0.042 0.040 1.48 1.53 1.50 3.30 4117 5m 0.090 0.084 1.64 1.56 1.53 3.38 4117 8m 0.080 0.076 1.31 1.58 1.55 3.36 4117 21m 0.049 0.046 1.35 1.54 1.52 3.25 4118 5m 0.166 0 154 1.3 1 1.67 1.64 3.15 4118 8m 0.086 0.080 1.39 1.58 1.55 3.30 4118 21m 0.052 0.048 1.26 1.55 1.52 3.45 4119c 4m 0.164 0 156 1.64 1.62 1.59 3.27 4119c 12m 0.167 0 160 1.37 1.66 1.63 3.32 Table 9. Attenuation ratios compared with PSD slopes measured in-situ by MAPPER at different depth ( is the averaged value over two depth bins) 71

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The particulate absorption coefficients in Table 9, ap, are measured using filter pad method following those of Mitchell and Kiefer ( 1988), with the pathlength amplification factor coefficients of Bricaud and Stramski (1990) Spectral readings were taken using a 256-channel spectral radiometer (resolution 2.6nm, half-bandwidth of 7nm, by Spectron Engineering Inc ) The squared correlation coefficient / between cp(450)1cp(650) and <.k> is 0.297 while / for cp(443)/cp(650) is 0.327 Notice for 12 degree of freedom, 95% significant level for r2 is 0 283 (Table 25, Statistical Table, F. J Rohlf and R. R. Sokal, 1981) These ratios show weakly significant correlation to the average slope which is calculated by averaging the values of slope of current meter bin, the one above and the one below Higher correlation, such as r2 = 0 5 for cp(450)1cp(650) and <.k> have been observed by others for small particle ranging from 0 5 to 30Jlm (Kitchen et al., 1992) This could indicate that our PSD slope could not be extended into smaller size range, even though data from other groups have shown that extension is possible at least to the micrometer range. Another more likely possibility is that the application of Equations 3.18 and 3.19 might not be appropriate in our enclosed near-shore coastal waters. Also, if we subtract 0.85 instead of 0.4 for cw(660), a much higher correlation could be obtained (r2 = 0.479), indicating possible contamination in c-meter measurements (recall some values are extremely high, c4 m-1 for 4/21 noon) or different algorithms should be applied. In any event, future exercises to test if there exists some relationship might prove to be useful, when multiple absorption and attenuation channels are measured (nine-channel absorption and attenuation meter, ac-9; four-channel backscattering and attenuation 72

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meter, BBC 4) along with PSD slope. If such a relationship holds, this could be a fast and co nvenient way of eFitimating in situ particle size distributions. 3.6 Summury From discussions in this chapter, we see that the particle size distribution does influence the role of that large particles play in the underwater light field. It is seen that with the measurements that MAPPER obtained at East Sound, W A, large particles contribute on average 26.5% to the total scattering and as much as 90%. This confirms in part that hypothesis #9 is true, since total scattering is directly related to remotely sensed signals, although it is the backscattering that eventually determines the intensity of returned signals. The widely used beam transmissometer requires corrections due to acceptance of forward scattered photon s. Few researchers have met these requirements, since the knowledge of in situ particle size distribution are difficult to obtain. With MAPPER data, such a correction can be performed and with an average of 15% error being removed. This confirms our hypothesi s #3 to be true Further we estimated that the typical Sea Tech transmissometer with a 25-cm pathlength will represent the effect of particle scattering of both small and large particles up to the size of 1 mm in diameter in coastal environments such as those found in East Sound, W A. Hypothesi s #4 thu s, is true. Lastly. small-particle s ize distributions are estimated, using c-meter measurements and MAPPER data The outcome is encouraging for all the depths compared, considering the degree of nntuml var iation involved in the gradient regions. However, uncertainties 73

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can be large in gradient regions for the slope (13.1%) or area (28.3%) estimates. Considering that these large differences were all in the regions of high gradients of beam attenuation, it is possible that slightly different water masses are involved without synoptic sampling. Without such regions, the averaged differences between estimates and actual measurements made by Coulter Counter are small (3.05% for hyperbolic slopes, or 7.64% for areas). Hypothesis #5 is tested true for this location. Note that not only the number of particles will affect the total scattering and thus remotely sensed signals, but more importantly, the scattering characteristics of each particle type. Particles that back-scatter or "reflect significant fractions of incident photons appears brighter than those which scatter few photons in the backward direction for collection by remote sensors. To better assess the role of large particles, we need to examine individual particle scattering functions. 74

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CHAPTER 4 LARGE-PARTICLE PHASE FUNCTIONS MEASURED BY MAPPER AND ICE Scattering properties by large particles are mostly unknown either in theory or by measurement mostly due to the significant variations of large-particle characteristics in the natural environment and the inability to sample them without disruption. 4 1 Background It is not an easy tas k to generalize the effect of scattering by an arbitrary particle in an electromagnetic field. So far only scattering and absorption by particles of a few specialized shapes can be derived exactly The list includes scattering by homogeneous spheres of arbitrary size and index of refraction, first determined by Mie and Lorenz (Van de Hulst, 1957) ; an infinitely long, circular cylinder as first calculated by Lord Rayleigh (1897); spheroids (Asano 1979 ; Latimer, 1980 ; Xing and Greenberg, 1994) ; cylinders (Bird 1972; Cohen and Alpert 1979; Cohen, 1980 ; Xing and Greenberg, 1994) ; and some variation s and combinations of the above such as consideration of holes in particle s (Latimer, 1984), touching spheres (Mishchenko e t al., 1995) and large rough particles (J Perrin and P. L. Lamy, 1983; Perrin and Chiappetta, 1985; Bourrely et al. 1986). Finally, Xu ( 1995) has extended Mie theory to aggregates of spheres 75

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These scattering functions show significant scattering differences compared to spheres. A new factor, the orientation, adds extra difficulties which affects the scattering when the individual particle could not be treated as homogenous in all directions Generally, these effects are reflected in the scattering phase functions; they are more complex and scattering changes rapidly from angle to angle with several oscillations, especially for angles greater than 90 When the scatterers are not densely distributed, independent scattering can be assumed, where the total scattering contribution equals the sum of individual ones (van de Hulst 1957) These scattering functions can be used directly to obtain fairly good results in explaining many naturally occurring phenomena Similarly, when the density of a particle is low such as in the case of a loosely formed aggregate, for photons traveling within the particle, we may assume the same so that a coherent scattering phase can be ignored and a scattering phase function obtained for these large aggregate particles. Unfortunately, for marine aggregates with clusters of particles attached to each other or in close vicinity these functions will no longer adequately describe the scattering characteri s tics Theoretical calculations have demonstrated that with a particle-to-solution rat i o (VIV) of 5 % or greater, the independent scattering assumption will no longer be valid (Zurk et al 1994; Kuga and Ishimaru 1984) Theoretical studies regarding aggregates are currently underway using different approaches such as a direct analytical solution to general multi-sphere system (Xu, 1995), cluster of cylinders or, spheroids (Asano, S, M. Sato, 1980 ; Mishchenko et al 1995) large rough particles (J Perrin and P L. Lamy, 1983), and Monte Carlo simulations for dense multi-sphere solutions (Zurk et al., 1994; Bergougnoux et al., 1996) One of the interesting features shown from these 76

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calculations is the increased scattering in the backward (>90) directions (Latimer, 1985 ; Kuga and Ishimaru, 1989 ; Mandt and Tsang, 1992; Zurk et al., 1994; Xu, 1995). However, these are mostly simulations for non-marine environments The difficulties in these theoretical calculations pale compared to those associated with measurements of the scattering phase function. One characteristic of the scattering of spherical particles with sizes bigger than a few wavelengths of light, is the strong forward scattering into small angles ( <1 ), which is typically 4 or 5 orders of magnitude higher than scattering into larger angles (>90 ) even if we do not consider stronger forward scattering caused by small-scale density fluctuations and ions in the sea water (Mobley, 1994). These phase functions can be measured in the lab with commercially available instruments for every 5 from 20 to 160 (Mobley, 1994), such as the one Petzold described 25 years ago for measurements at large angles (10 to 170). Other setup can give more precise measurements towards smaller angles and near 180 (Fry, 1990 ; Kuga and Ishimaru, 1989). However, the luxury of using an optical workbench is gone for field measurements, and optical alignment can be knocked out easily on research vessels out at sea For larger, aggregated, marine-snow types of particles discussed in this contribution, measurements involve more difficu l ties, severely hampering any attempts to bring the sample into the field lab, as handling could break up the particle or deform it. Further, the conventional small sampling volume obviously will not satisfy statistical requirements of sampling a large enough volume to observe large particles Spatial variation can be a big problem since we often assume homogeneity of the water column based upon a few samples. The measured lOPs will be always different than those in the 77

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real world if under-sampling of large particles is involved. This poses a significant problem for model closure. To overcome such problems, measurements have to be done in -situ, with large scale sampling ability. The HMM onboard MAPPER is designed for this purpose. This first attempt to try to measure the scattering phase function for single large particles provides a first-order estimate of this complicated issue. The measurement is done via examination of large-field images obtained with the hyper-stereo mirror module (HMM) in the near-60, near-90 and near 120 viewing angles, which provides the scattering information for large particles ICE enables fast and accurate processing of each individual video frame to extract information. These calculations are then fitted to an analytica l form of phase function that was u sed by Beardsley and Zanaveld (1968), for multiple locations and sampling sequences, in the hope of quantifying changes in the environment, and to see separately the contributions to the forward and the backward scattering. For particles with any shape diverging from the sphere, the difficulties associated with estimating the scattering increase significantly, as we see in cases of the slabs, spheroids, and cylinders discussed above. The complexity of the origins of marine aggregates and their shapes makes any exact analytical solution impossible at this stage With the help of analyt ic al solutions to a cluster of small particles with the index of refraction typical of marine particles, simulations are generated here by using Monte Carlo methods. The goal is to try to provide the shape of the scattering phase function by approximation, assess the relative contributions of large particles or a cluster of small 78

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ones within an aggregate to the different scattering angles, and use that information to characterize different groups of large particles and their scattering properties. A well defined particle-scattering phase function could give us a better set of lOPs, and model closure could be achieved with increased accuracy. Recent calculations show that different choices of the phase function could result in remote-sensing reflectance values varying as much as 4-fold (Cattrall, 1996). Therefore, in-situ measurements of the large-particle scattering phase function and their abundance could provide valuable information. 4.2 Setup and ICE Measurement With diode lasers mounted on each corner of a square frame and the two mirrors of HMM, the forward, backward and side scattering of an irradiated particle could be measured at the same time. The light sheet was 25cm long on each side with the HMM mirrors angled at 71 up from the plane formed by laser diodes, as shown in Figure 20. When only one laser is turned on, the scattering from the particle into both mirrors and directly into the cameras provide scattering properties of the same particle at different angles. From Figure 20, we see that the "image" of a particle ("I") within the SLS will appear 3 times in the large field (LF) camera, that correspond to forward, side and back scattering. When the particle is at different positions within the SLS, these images correspond to slightly different scattering angles. With multiple single particles found in different locations within the structured light sheet (SLS) it is possible to obtain an averaged large-particle scattering phase function from 50 to 130 continuously 79

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PARTICL DIODE MIRROR (P1) L D CAMERA IN M IRROR CAMERA IN MIRROR "VIRTUAL [QJ R 0 CAMERA Figure 20. Geometry of single particle scattering within HMM of MAPPER that is used for 3-D scattering calculations (see Appendix A) Figure 20 depicts the hyper-stereo module and the instrument in which configuration single scattering of large particles is measured The camera (denoted by letter "0") is looking at the 3 sections of the large field, namely the left mirror (PI), the central direct view and the right mirror (P2). Notice that both mirrors are at 71 to the SLS plane. Only one diode laser (labeled by letter "a") is turned on, and the particle enters the SLS at position "1 ". The dashed lines from the particle indicate the path of scattered photons reaching the camera Using principles of geometric optics, we can imagine that the camera is at location L (for mirror PI) for backward scattering and at 80

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location R (for mirror P2) for forward scattering to achieve calculation results for comparison to the measurements Since all of these camera coordinates and that of the laser diode are fixed in space we choose Cartesian coordinates with the origin at the center of the array of 4 laser diode s as shown in the figure. The exact scattering angles of these 3 scattering path s can be determined mathematically, given a particle location within the SLS After correcting f o r path attenuation and the power spread of the fan beam from the laser diode, the sing l e particle sc a ttering at different angles centered around 50 (forward) 90 (side) and 13
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(3) read in attenuation (c-meter) (4) calculate particle position in the 3-d coordinate rectangle (5) calculate scattering angles, scattering path length (6) measure the scattering intensity for each of 3 views (7) apply geometric and path attenuation factors to get the final result Since the system is calibrated with standard 5% and 10% Spectralon reflectors (from Lab Sphere Inc.), the above procedure involves a conversion from recorded analog video signal to digital values. The images of the standards are digitized to which particle measurements are compared. The background noise and dark current are removed, choosing scene sections adjacent to the standards or particles, using several sections to get an average value. At times mechanical pausing of the VTR causes un-evenly distributed noise across regions of the scene However, even with all the noise and the dark current completely removed, the system still can not always measure all of the scattered light. The reason is that our digitization level is limited to 256 grey scales by our imaging board DT-2867 (achieves 256 counts), when we choose a sensor gain to saturate the signal at 5% (a very good choice since saturation is unusual except for large zooplankters once every 2 downcasts on average), the minimum level of detection for the large field camera is about 0.02% reflectance. That is to say, the system could not measure anything scattering more weakly than that. Another limitation of the system is also associated with the spatial digitization, or resolution. For the large field of MAPPER, we have a pixel (the smallest picture element 82

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in the digital form) resolution of 280 J.l.m. Since sub-pixel contributions are recorded into the entire pixel, an edge pixel with a view consisting of Y2 particle and Y2 background will have roughly Y2 of the brightness of the particle. Pixels of particle edges and of small subpixel particles will both reduce the apparent particle contrast against the background and exaggerate the particle size To be statistically accurate, we choose to measure fixed window positions with HMM and average their values over the water depth With measured particle concentration at about 100 per liter for large particles (500 J.l.m), any average over a 5meter range should provide good statistics, since each window will represent a volume of 0 35 liters for each data point. Each data point is corrected for its attenuation along photon pathways: namely from the laser to the scattering center to the forward, side and backward directions Final plots are those of the normalization to the 90 scattering, which is easier to compare with other functions. 4.3 Results Following the procedures described above, the single-particle scattering from multiple-day downcasts are obtained by the ICE system as shown in Figure 21, Figure 22 and Table 10 To describe the general features of these scattering measurements, scattering data are fit to an analytical phase-function form that was used by Beardsley and Zaneveld ( 1969), (4 .1) 1 f38z = (1&1 cos 8)4 (1 + &b cos 8)4 83

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Notice that this is not a phase function normalized to the total scattering coefficient, b, but normalized to This is a proper form for presentation here, since normalization to 90 makes measurements comparable from different depths profiles It also reduces possible systematic errors during measurements. Even though this function does not well describe forward scattering (Mobely, 1995), it fits our needs, and the two parameters actively describe the relative contributions from the forward and backward directions. This enables us to better understand the enhancement of backscattering caused by large particles It can be easily observed that for Beardsley and Zaneveld phase function, when 0< Eb,Er each constant controls the level of backward (>90, Eb) or forward ( <90 Er ) scattering almost independently It can also be used as a descriptive measure of the degree of scattering in those general directions The fit of the BZ function to measured data was performed via a least-squares fit of their logarithm values due to the scattering data We see in Figure 21 that the BZ function nicely fit (labeled 'BZ') our measured results (dashed circles), from an April 21 midnight downcast through the top 10 meters, with a strong backscattering (Eb=0 .63). Notice that the fit is not better because the worsened signal-to-noise ratio near 90 provides significant data-point scatter. Note that the ability of certain other phase functions chosen are far worse, as we can see when the data are poorly fit using a Heyney-Greenstein phase function (labeled as "HG", see Mobley, 1994) While HG fits most ocean scattering data points well albeit for small, single particles, it can not describe an elevated backscattering (Figure 21). However, it is interesting to notice our measurements show strong back-scattering in this large-particle 84

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category throughout the entire water column over various days and time (Table 1 0). The minimum scattering seems to be located near 105, similar to the 100 found by Petzold for Sargasso and Southern California Bight data. . . . . . .... . .. .. ............ .. ....... . ... . .. ... . .. . ..... ....... . . .. .......... . . . . . . . . . . .... .... z fit . . ;,. .. ; ...... : ..... ;, . . ; .. , ; .. .. .. . . ...... ........ : eb=0 63 : .. :. : : : : : . :: ... : : : ...... : : : . .... ::.:::.: l::::.: . : _d)::: : ... :::.: :::::::::: :::: : r :::::: L::::: . ::: . . . . Scattering angle Figure 21. Measured single particle scattering fitted to Beardsley (BZ) and Heyney Greenstein (HG) phase functions (normalized by 90 scattering for comparison) (data taken from 4/21 mid-night downcast in depths 0-10 meter) Particles seem to scatter differently at various depths of the water column (Figure 22). It changed from strong forward scattering (Figure 22c) to overall weak scattering (Figure 22b) within a few meters, while back-scattering could be weak at certain depths (Figure 22a), although it was pretty strong otherwise 85

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a 40 eb=0.02 ef=0 78 20 0-10m : .... .. 0 40 60 80 100 120 140 160 40 eb=0.49 b ef=0 82 10-20m 20 ..... 0 40 60 80 100 120 140 160 40 eb=0 45 c ef=0.94 20-24m 20 0 40 60 80 100 120 140 160 Figure 22. Single particle scattering measured from MAPPER downcast at night of April 20, 1994 at East Sound, WA at: (a) 0-lOm; (b) 10-20m ; (c) 20-24m Measurements taken from other down casts (4119 20:00, or 4119 D ) are presented in Table 10. Notice each value is averaged over a 5-meter continuous measurement (in which each data point is corrected for corresponding path attenuation and individual geometry). Beam attenuation coefficients at 660nm, also listed in the table, are measured by MAPPER, and at this wavelength are almost exclusively caused by scatteri ng The s lope of the differential parti cle size distribution is also pre sented. 86

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Depth (m) Eb Er c (m-1 ) k 4119D 0-5m 0.49 0 .91 6 8 1.79 3 .13 5-10 0 .53 0.93 6.4 1.56 3.21 10-15 0 37 0 82 7.3 1.35 3.16 15-20 0.4 0 .88 8.3 1.14 3.22 4/20B 0-10 0.02 0 78 25 1.83 3.11 10-20 0.49 0.82 4.4 1.27 3 06 20-24 0.45 0.94 9 5 0.99 3.02 4/20D 0-5 0.56 1 8 1 2.45 3 .12 5-10 0.56 0.97 6 9 1.49 3 09 10 -15 0.45 0.74 3.6 1.09 3.02 15-20 0.59 0 78 5.1 0.95 3.06 4/20H 0-5 0.64 1 5.7 2.76 3.04 5-10 0.53 0.95 7.1 1.88 3.16 10-15 0.38 0.81 6.7 1.14 3.24 15-20 0.62 0.98 5.6 1.08 3.19 4/21B 0-5 0.63 0.96 4 8 3 24 3.11 5-10 0.69 0.99 4 3 2.32 3.17 10-15 0.5 0 84 4 .6 1.27 3 .21 15-20 0.51 0 89 5 7 1.14 3.10 Table 10. Beardsley-Zaneveld scattering phase function parameters obtained by fitting MAPPER single particle scattering results It is interesting to see that the minimum va l ue of E r happened when k is also minimum and the c-meter value is low, at 10-15 meter on the evening of April 20. The particle size distribution indicates more larger particles at this depth with less attenuation by small size particles (small c value). This could be an indication of the presence of abundant marine-snow-type particles, as aggregation will reduce the fraction of smaller particles Also the low ratio of also indicates this (see Chapter 4) As a matter of fact large numbers of zooplankters were observed in the upper 10 meter water column on this night (e.g 5600 small copepods and 870 crustacean lavae per m3 while only 2037 and 234 respectively for deeper water were found A. Alldredge, unpublished with permissions), which is a supporting cause for higher aggregate abundance beneath 87

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4.4 Calculating Large-Particle Phase Function by Monte Carlo Simulations Monte Carlo simulations are used when solutions can be provided by calculating randomly occurring events (e.g. photon scattering) through out the system. A simple example is throwing coins in the air and picking the side will face up upon landing. By tracing each individual photon and examining its fate and motion in a medium, we can establish a well defined outcome based upon the probabilities of encountering particles and being scattering in given directions. When the photon leaves the system or an absorption event occurs probabilistically a new photon is launched and followed through the system This approach is summarized in Kirk (1983) and Mobley (1994). As we have discussed previously, marine aggregates appear to have complex structures and wide morphologies due to the various origins. Although many theoretical studies have been carried out on large, rough particles, they mostly deal with astrophysical interests such a star dust and meteoroids or chemical processing. None has been done regarding the marine environment. Since marine aggregates are made up of smaller particles, they may be loosely coupled enough that we might be able to apply multiple, independent scattering We can approximate such overall scattering properties using Monte Carlo simulations. Unfortunately, this may not work well, as we know aggregates are connected, no matter how loosely. However without this assumption the calculation becomes extremely complicated. An alternative is to assume small clusters of connected small particles making up the particle, and only within the small cluster, coherent scattering occurs. In other words, if we know the scattering phase function for a small cluster of small marine 88

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particles, we could assume independent scattering between these clusters and simulate the overall scattering properties. A recent calculation done by Dr. Y. Xu from the University of Florida, based on analytical solutions of small marine particles stacked up in the shape of a 4-particle pyramid (with index refraction 1.04 relative to sea water, size parameter x=7.85, personal communication), provides us with such a scattering phase function. A Monte Carlo simulation of numerous collimated photons entering this system is carried out, to allow multiple scattering (using Xu's phase function) and to choose the future path and fate of each photon until it leaves the system or is absorbed The rate of collisions is determined by mean free path l0 (4.2) which after no collisions the photon will leave the system, which is defined by the diameter of the aggregate R g is the radius of gyration of the aggregate particle, and n o is the average number of collisions for the photon to travel through this particle. If F2 is the area porosity (2-D) for an aggregate with radius of gyration Rg, made up of idealized small particle clusters of radius r (see Section 4 1 .2), then the mean photon path can be expressed as (4.3) where F2 is obtained from Equation 2.16. The probability density function for a photon to travel distance l before encountering a scattering center is 89

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(4.4) 1 l P(l) = -exp(--) lo lo Since this model describes incoherent multiple scattering for the phase function of an aggregate, we could simplify T-matrix methods used by Zurk et al. (1995) and determine the scattering angle after multiple scattering by trigonometry as illustrated in Figure 23. For simplicity of the simulation, we assume that the field is homogenous and the scattering could be described by zenith angle, 8, alone. When a photon encounters a scattering center as shown in Figure 23, it will be scattered into direction 81 which is determined by the sample phase function by a random number weighted by Xu's phase function. Since the scattering phase function is the probability density function for scattering, an integrated probability function, as a function of scattering angles, over increasing angles will give the total probability that a photon will be scattered into this angle. For example, such a function could have values of 0.31, 0.37, 0.41, 0.53 for the scattering angles of 0.1, 0 2, 0.3 and 0.4. When a random number is generated from an uniform distribution between 0 and 1, say 0 38, it is compared to this integrated probability density function for each angle increment of 0 .1 (in our calculations). If the first value of this integrated function is (0.31) smaller than this random number (0.38), then the photon that corresponds to this random number is not scattered into this angle (which is 0 to 0.1 ), and we compare it to the next value until the random number is smaller, at which point the scattering angle is found (in our case here, 0 3). 90

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. . . . . . . . . . . . .. .... .. .. .... . b .... .. .. .. . . ..... 2 ..... 1 : . . . . . .. .. .. .. .. .. .. . . . . . . . Figure 23. Geometry for multiple scattering in Monte Carlo simulations The length of the photon traveling before being scattered again, a is determined by our estimate above. At this point if a is smaller than the size of the particle (as shown by the dotted circle) the second scattering angle is calculated 82 away from the first direction 81 The combined scattering angle would be 8 o =81+82 or 8o=81-82 depending on the direction in which the photon might be scattered A 3rd random number is assigned here to determine the outcome. Again, the traveling length is determined b, and the combined radial distance c, is calculated by (4.5) c = .J a 2 + b 2 -2ab cos (} and will be u sed to determine if the photon is still within the particle. If it has escaped we record the angle of the sca ttering and start with a new photon. Otherwise, the photon will 91

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be treated as with our initial case and the procedure will be repeated until the photon escapes. 104 MA PER 0 20 40 60 80 100 120 140 160 180 scattering angle Figure 24. Comparison of different scattering phase functions (BZ, Beardsley and Zaneveld phase function-;Petzold .... ; Multiple scattering using Monte Carlo---; MAPPER aggregate scattering o) The si mulation was carried out on a DEC Alpha St a tion 200/5000, with 10 million photons, and independent sca tterin g between clusters, was assumed. The re su lt s are s hown in Figure 24 with a 5 smoothing over the angles to depre ss the random oscillations and to brin g out the general features. This shape i s equivalent to the combined scatte ring by a group of Gaussian-distributed spheres ( Bohren and Hoffman 1983) We can see that due to the multiple phase function of Xu (1995), more photon s are 92

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being scattered into larger angles, thus reducing forward scattering and increasing backward scattering. 4.5 Discussion With our digitization of video tapes, and the level of complexity of operations during automated measurement of particles carried out by ICE, it is reasonable to expect errors to occur. The most significant error occurred when the image was not perfectly frozen, causing the 3-D geometrical calculations to be completely thrown out. It can be easily estimated (see Appendix B) that a 5-line (video image) offset in the freeze position (which is typical) could cause about 5 deviations in angular calculations Such distortion will also be carried into path radiance calculations, though the variation here is rather small (less than I% in radiance variation) Another potential problem is related to the concentration of particles in the water. If the concentration is too low and patchiness is high, scattering by large particles can be altered un-evenly by concentration fluctuations in the pathway. On the other hand, if the concentration is too high scattered photons might have a difficult time reaching the detector, especially for larger scattering angles (90 120) where the signals are mostly weaker. This could be partially fixed by bring in automatic gain control and more powerful diode lasers. To improve our measurement information, multiple mirrors could be employed for future MAPPERs to enable more angular distributions to be measured. Higher-power diode lasers are also desirable, to bring in low-scattering targets and increase the signal to-noise ratio. Digital recording or real-time processing can be applied in the near future 93

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for reasonable costs, to eliminate the mechanical noise caused by tape recording and to enhance processing speed. It could also easily widen the saturation range by 4-fold ( 10 bit s ampling) or higher. Our measurements of large-particle (>280J..Lm) scattering indicate that backward scattering is stronger than people previously surmised (Figure 24). This is very clear when our data point s are plotted against the phase function Mobley used (Mobley, 1994) Further, if we could expand our measurements to near 180 we would likely see very significant backscattering perhaps an order of magnitude higher than Mobley's estimate Our simulation seems not to have enough backscattering compared to the measurement s, but more than what Mobley used (Petzold curve). It could be a matter of factors that cause this. First, we did not consider very small scatterers with submicron size. They are extremely abundant in aggregates (Alldredge and Silver, 1988) and have a higher backscattering efficiency (Stramski and Kiefer, 1991 ). The discovery of high abundances of transparent exopolymer particles (TEP) in natural water and in aggregates, with bacteria, previously thought to be free-living, attached to them, seems to indicate that TEP would aggregate small particles such as bacteria and virus together (Alldredge and Ulta 1993) to increase backscattering. Still it is satisfactory to see that our simple simulation better depicts the 60 and backscattering properties of large marine snow type aggregates, considering the degree of variability involved Note that the Petzold curve has extreme f o rward scattering probably caused by large phytoplankters 94

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4.6 Summary A unique set of data is presented in this chapter that provides in-situ, a large particle scattering phase function, by utilizing the HMM of MAPPER and automating the processing via ICE. The scattering functions measured confirm our hypothesis #6. Monte Carlo simulations of small aggregated scattering centers matches the general trend of MAPPER measurements, indicating that coherent scattering within the aggregate might be the key factor that causes increased pathlength and thus scattering. The enhanced backscattering measured by MAPPER seems to indicate that more photons can be scattered into larger angles by this class of large, fluffy particles at the expense of near-forward scattering. Combined with results from Chapter 3 and bearing in mind that the large particles are highly abundant in the surface waters we now fully confirm our hypothesi s #9: that large particles play a significant role in remote sensing applications, which are back-scattering dependant. 95

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CHAPTER 5 PARTICLE CLASSIFICATION The most common method of classifying particles of different origins is by analyzing their chemical content. We present here two approaches that are based on the appearance of the particles: one used pattern recognition, which is commonly used in digital image processing, and the other uses the optical characteristics of the particles. As we will see, each approach has its own advantage, while the optic approach expands a newer dimension. 5.1 Moment-invariants and Identification of Large Particles 5 .1. 1 Background One of the reasons to provide the distribution of large particles in the ocean is that it gives us insight into the rate of generation and degradation of particles and the rate of material flux, which can be proportional to the particle size (Alldredge and Gotschalk, 1988). As we discussed in earlier chapters, there have been some ongoing measurements of the distribution of large particles in the ocean, including efforts using an acoustic approach However, other than by diving with photography, it is difficult to discern the content or origin of these particles. No doubt, the particles being measured in the range 96

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larger than 500)lm diameter include not only the detritus type of particles, like those typical of marine snow aggregates but also those that are alive: e g animals like zooplankters, fish larvae, fish eggs, and even some large phytoplankton cells/chains. The identification and separation of at least these two major types of large particles would not only help to more accurately determine the abundance of aggregated marine-snow types of detrital particles, which would be of great value to the modeling process, it would also provide inf ormation about the distribution of zooplankters versus detrital food sources. The confusion caused by these two groups has been observed especially by optical systems designed to measure zooplankton abundance (Napp et al. 1993; Flagg and Smith, 1989 1992; Herman, 1992 ; Herman et al., 1993). Although there are at least a few up to several hundred marine snow type particles per liter in natural waters (Alldredge and Silver, 1988 ; Hou et al., 1994 ; Jackson 1995), there only a few zooplankter per liter at most (Napp et al., 1993 ; Flagg and Smith, 1989, 1992) Confusion caused by not separating the s e likely re s ults in overestimations of zooplankton abundance much more so than the abundance of large detritus type marine snow particles. An accurately measured distribution of animals and detrital particle s could help us to better understand the status of the ecological system such as the flow of the energy in the system, the distribution pattern of zooplanktons versus their food sources, their rate of mortality, and the rate of growth and consumption of primary producers which in return helps to understand the formation of marine snow particles. Sy s tems like MAPS and modified ADCPs that are used to measure zooplankton biomass distribution are based on the intensity of back-scattered signals Although acoustic scattering models show that the size of the scatterers is related to certain beacon 97

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frequencies and intensities (Napp et al., 1993), it is still at best a correlation between total biomass (volume) and approximate size for zooplankters. Aggregates, being composed of particles that are tiny relative to the acoustic frequencies, are not efficient sound scatterers Besides, the long detection range will inevitably include the influence of particles in the pathways, and although it is noticed that marine snow type particles are less efficient in sound scattering, no results show there are ways to separate them This is understandable when considering the diverse origin of the particles OPC can measure the particle size directly, yet to optically separate these particles using one-dimensional measurements seems difficult, although some characteristics of marine snow type of particles do show up, and are considered "bad" signals to the targeted measurement zooplankton (Herman et al., 1993). Due to the limitations of these systems, little effort has been carried out to amend such errors in measuring either the detrital-marine snow particle distribution or the zookplanton distribution. Direct imaging of the particles and examination by humans has been the only reliable method of accomplishing separation so far, yet it is very time consuming and holding a stick with ruler attached underwater doesn't sound like an easy job (Alldredge and Gotschalk, 1988). Measurement errors could be easily introduced, and the presence of the light needed in the measurements and the turbulence caused by swimmers likely triggers zooplankton escape mechanisms. Examining the images by computer via pattern recognition seems to be a good solution. Digital cameras can bring high-resolution images that allow good particle descriptions to be extracted, while at the same time the target can be easily identified However, continuous storage of these high-resolution images could be a problem in-situ, 98

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and it also requires a more demanding system configuration The video systems used in MAPPER seem to be a good alternative, as they provide continuous cheap storage, with decent resolution provided by multiple video cameras using different magnifications. The initial setup of the MAPPER camera systems was to measure particle abundance at different sizes so we could cover a wider measurement range. The small field camera onboard MAPPER provided descriptions of particles with enough detail to sa ti s fy the needs for use in pattern recognition for marine-snow type particles or larger animals (250 diameter and above range, Costello, Hou and Carder 1995) However since the field of view of this camera is very small, chances to image enough representative large particles are small when one considers that the sample volume is small (0.1 liter per 1 meter depth bin). On the other hand medium and large-field cameras have much larger sampling volumes per meter depth (2.5 and 8 liters respectively) but their resolution is not good enough to provide an accurate description for smaller particles This present a tion recognizes an approach that extracts particle features from the high-resolution, small-field camera that can be applied to lower resolution images like those taken from the MAPPER mediumand large-field cameras which will better enhance the use of MAPPER data. With the advent of computer technology, image processing in the digital domain has been applied in many ways It is now possible to combine various descriptors of certain patterns with those based on artificial intelligence such as expert (knowledge) systems or neuralnetwork systems, to make valid decisions. The first step, however is to find a good pattern descriptor of the target image. General moment theory provides a simple, yet mathematically unique, transformation of the complex image pattern which 99

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could be used to identify different types of targets (Hu 1962; Dudani, 1972; Teague 1980; Costello, et al., 1988) These moments can be presented in ways that are invariant to rotation, scaling, reflection and their combinations, and are excellent to extract image features (Jain, 1989). With MAPPER/ICE system, it becomes possible to identify these feature vectors. However in order to perform pattern recognition operations, many orders of invariants need to be calculated and compared Since calculations of high order and therefore more complete sets of moments have been difficult and slow until recently by traditional iteration methods (Mukundan and Ramakrishnan, 1995), few efforts have been applied to such tasks, especially to large, naturally occurring targets like large marine snow-type particles. We will make such an attempt and calculate high orders of moment-invariants expressed by Zernike polynomials (Teague, 1980). The method to calculate Zernike moments is based on a modified approach from those of Mukundan and Ramakrishnan (1995), with modifications using non-circular transformations to avoid image distortion Their original theory was expressed in circular transformations It is slightly faster since rotational transformations can be expressed internally (for details please refer to Appendix B and related publications) The complete set of moment-invariants follows those of Wallin and Kubler (1995), which is the generalization of those made by Teague (1980), and our feature vectors will be extracted from these invariants. The results also will show that moment-invariants can be used to prove the effectiveness of multiple-camera/multiple resolution systems as well (Section 5 1.3). 100

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5.1.2 Moment-invariant and Zernike Notation Recall that in Section 2.1, we defined general moments (p1\qth order) of an image f(x,y)'2:.0 as (2.6) and (2.7) as central moments. mp.t, = Jf f(x, y)xpyqdxdy R p,q = 0,1,2, . J.ip.q = fJ f(x,y)(x-x)P(yy)qdxdy p q = 0,1,2, .. R Historically, it was Hu (1962) who first used general moment representations to study the pattern recognition problem and introduced the invariants of moments. This is the combination of general moments that have the same quantity under the transformations caused by scaling, reflection and rotation. Later several researchers formalized the theory and applied it to the general pattern recognition problem, using lower orders of moments such as those for aircraft identification (Dudani, 1972) character recognition (Teague, 1980) and particle recognition ( Costello 1988). It is easy to see that the general moment i s in fact the projection of functionf(x ,y) in space The general space is nonorthogonal and will introduce significant difficulties when higher orders of moments are considered (Teague, 1980). We could, theoretically, use any orthogonal polynomial s, such as Legendre or Zernike polynomials which was demonstrated by Teague ( 1980) Since Zernike polynomials are defined on the unit circle ba s i s, and hence possess the property of rotational invariant, it is simple and fast (Teague 1980 ; Mukundan and Ramakri s hnan 1995 ) due to the fact that a set of mutually 101

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independent descriptors are most efficient since they have least amount of information redundancy We will use this set of moments here. Like the 2 D Fourier transformation, the moments contain image information in a way resembling those descriptions in the frequency space domain, and a few moments can be used to generate the original images fast and with some detail (Teague, 1980). However, when the information to be represented becomes complex, it is no surprise that we need higher-order moments to record this information A good example is given by restoring images from their moments, based on the fact that these representations are mathematically unique (Hu, 1962) It has been shown that the unique patterns could not be discerned unless moments up to orders of 5 or higher are used for the two letters "E" and "F". A good restoration of the images, however could not be accomplished unless at least 12 orders are used while 16 orders would give almost perfect representation (Teague, 1980) The definitions and derived formulas to calculate these invariants for later use in pattern recognitions can be found in Appendix B. 5.1.3 Calculating the Complete Zernike Moment-invariant Set for Large Particles The formulas discussed in Appendix B were incorporated into the ICE system, each particle was measured from MAPPER images, and its moment-invariant set was calculated for future particle classification. We discussed the problem associated with feature extraction in Section 5 1.1. It will be demonstrated that the images of the same particle under different recording resolutions will preserve most lower-order features under its Zernike mom e nt-invariant descriptors. Instead of finding the images of the same particle with different-resolution cameras, we use the reverse approach here. A sample 102

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image (taken from the Friday Harbor, MAPPER, small-field camera in the afternoon of April 20, 1994) is shown in Figure 25 which includes the images of the original highresolution image and images with resolution reduced by 2, 4, 8 and 16 by in each dimension. In practice, these images were generated by averaging neighboring 2x2, 4x4, 8x8 and 16x16 pixels respectively. Figure 25. Sample particle images with reduced resolution, taken from MAPPER small field camera of April 20 night downcast at East Sound, W A The measured Zemike moment-invariants are plotted in Figure 26. Notice the main, low-order features that are described by moment-invariants up to 40, especially those under 20, are mostly preserved throughout these resolution degradations Between the original image (denoted as "orig") and the image at half the resolution (denoted as "by 103

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2"), it appears that all the features are nearly identically presented up to orders of 40 This corresponds to most of the details of the particle, or high frequency features if we put it in terms similar to those of the Fourier transformation. Figure 26. Effect of different resolutions on Zernike moment-invariants for a sample large particle taken from East Sound, W A From Equation 2.10 and B.2, we see that the first moment -invariant contains the information about radius of gyration of the particle, while the second and the third describe the shape and radiance distribution. We notice that the image reduced by 8 is quite different in shape and radius (more in the shape of a slanted stick), which is adequately described in Figure 26. The sharp reduction of the radius of gyration in the last 104

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image (by 16) is explained by the weight (brightness) carried mostly in the bright pixel in the image. Notice for the MAPPER configuration used in Friday Harbor experiment, if the small-field digitized resolution of 17.5 J..Lm pixels is considered, we have de-resolution factors of 5 and 16 for the medium and large fields, respectively. In other words, the images (by 4, by 16) shown in Figure 25 are similar to those observed with the mediumand large-field camera relative to those of the small-field camera (for pictures of such images, see Costello, Hou and Carder, 1994). 1500 . . . . ... . . . . . ... . .. ... ro 1400 Q) 1300 CJ) LlJ 1200 1100 0 : : : : :- 0 1000L_ ____ _L ______ L_ ____ _L ______ L_ ____ _L ______ L_ ____ _L ____ ro Q) 0 2 4 6 8 10 12 14 16 1300 1250 Cf) w 1200 ______ 8L_ ____ Factor to reduce image resolution Figure 27. Effect of reduced resolution on size measurement using different description methods (unit in number of pixels) 105

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Although the resolution has been changed drastically among the three cameras it is worthwhile to mention that the particle size measured changed up to 36% in area from the original resolution to that observed by the 16x lower-resolution system, or 18% in equivalent spherical diameter (Figure 27 upper) When expressed in the empirical spherical projection co-ordinates, this error is significantly less (Figure 27 lower), around 10% in area or 5 % in diameter en 60 55 50 45 40 35 30 25 20 15 2 _....--/ v ----, / 4 6 j[\ A \ \ \ \ I [\ v / \\\ I I \/ I \ 2 / I I / I I / ) v /. 8 10 12 14 16 1 8 20 Threshold Figure 28. The effect of different threshold on calculations of moment-invariants (upper line: traditional pixel selection method; lower line: using all pixels in region ) Last but not least we need to mention an important point regarding calculation of Zernike moments It is advisable to u s e all the pixels within the enclosing region of the particle rather than only those "bright" pixels that exceed a certain preset threshold v alu e which is by definition the image ( f(x,y) in Equation 2.6), even though we might be 106

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enclosing some noise into the calculation. This is illustrated in Figure 28 by examining the effect of various threshold levels on the values of a Zernike moment-invariant (S 1 in this demo case) calculated. Notice that the value of the invariant holds pretty much steady during a wide range of threshold values, while it varies with the changing threshold values steadily in the case of normal calculation. This indicates that when using all the pixels in the region, we could be using a somewhat less than ideal threshold value while still achieving reasonable result. This success lies in the fact that the true noise does not contribute to the moment-invariant as they are averaged out during calculation (like white noise in Fourier transforms), though they are taken into the calculation. When not taken in, since different threshold values would apply different levels of contribution made by true noise we actually make noise looks like signal this way To some extent, this could be another approach to solve the problem caused by electronic overshoot mentioned in other publications (Costello, Hou and Carder, 1994 ). These results indicate that moment-invariants could be used to extract features of targets from a higher-resolution system, and then be applied to a lower one which gives more sampling volume. By taking such patterns from several of these identifiable animals we can use them as a pattern to detect the abundance of certain types of large particles in the ocean. 5.1.4 Characteristics of Some Special Particles in the Ocean By using the procedures described above, we can now calculate the abundance of some of the large particles that are found in the ocean : e g zooplankters such as copepod s, occupied and abandoned larvacean houses aggregates diatom chains and 107

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siphonophores. As a simple test, we will attempt to separate copepod images from the rest of the large-particles imagery using measurements taken at East Sound during our April, 1994 SIGMA cruise. By measuring a group of identified copepods (such as (e) (f) in Figure 1), and aggregate-type particles (such as (a), (b), and (d) in Figure 1), we could calculate high orders of Zernike moment-invariants and compare within group to locate the features in terms of Zernike moment-invariants that are varying least within groups and most between groups, to use them as condensed features for recognition. These descriptors are then used for pattern recognition in automated image processing for every particle measured, via ICE. The decision is made based on minimum mean distance classification in (Jensen 1996; Jain, 1989), stands for the number of features (moment invariants and other variables such as size, reflectance). Since this method leaves no unclassified targets (presumably all patterns are given, which is obviously not in our case), we define two times the standard variations within the group as the "radius" or limitation that an unknown particle belongs to a particular group. This choice ensures no cross-group inclusions will occur. Anything that does not belong to either groups is classified as unknown The Zernike moment invariants for these two types of particles (averaged) are shown in Figure 29, with top one for copepods and bottom one for larvacean houses. The final feature vectors for classification consist of size, reflectance M2, M5 M7,, M8, M9, MlO, M12, M13 M17, M25 M34, M41 and M45 (Zernike moments, notation explained in Appendix B). Detailed procedure could be found in Appendix C. 108

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gives us added sampling volume. For every 5 meter water column, the sample volume is 8 29 liter, when the image sampling area is defined as 640 by 320 to avoid possible noise caused by mechanical pause The total number of large particles exceeding ESP 500 Jl.m are calculated by integration using numbers from Table 10. It is worth mentioning that our classifiers are dealing with particles 500J!m and up but not limited to, therefore the total number of particles detected by MAPPER is slightly larger than the calculation carried out using hyperbolic di s tribution from 500 Jl.m for the top 5 meters. We also notice that the total number of particles is much bigger than the number of copepods and it s eems safe to say that zooplankters at East Sound, though abundant, still compare much les s in number to aggregates and other type particles. copepods copepods Larvacean Unknowns Total % (ICE) (Alldredge) houses (ICE) particles Errors (ICE) (>500J!m) 4/20d 0-5m 1568 m -3 5629 m -3 603m-3 85000 72700 m -3 27 % 5-lOm 2533 2654 126400 172000 10-15m 1086 2037 m -3 3136 137000 160000 23 % 15-20m 483 3378 109400 123000 Table 11. Particles types identified by ICE using imaging pattern recognition Notice our measurements turned out fewer identified copepods than actual measurements. A couple of factors could contribute to this One may be due to the orientation of the particle and its location within the SLS If the particle is not well illuminated by the light sheet or it is po s itioned at an angle to the camera that prevents it's main feature (enlonged body, appendages and tentacles) to be shown in the view our classifier will fail naturally. Another is due to our classification method that we set tight 110

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limitation to our classification radius. A third reason may be obstacle avoidance perhaps due to detection of red light or the large silhouette presented by MAPPER against the night sky (clear sky, 4 days to full moon). Inverting MAPPER and raising it from depth would eliminate the later factor. A better approach might lie in the combination of this supervised classification with non-supervised clustering (Jaine, 1989). Relatively small sample volume is another factor. As we can see, the limit posed by sample volume would be at least one per 5 meters of water column, which is one every 8.29 liters or 8.29x 1 o-3 m3 equivalent of 121 m-3 or 4.2% error compared to field sampling data. 5.2 Optical Scattering Characteristics of Large Particles Even with the reduced size of feature vectors we used, processing still takes a long time due to extensive computations carried out for each particle in each frame. We notice in Section 3.2 that different types of particles present different scattering properties. This might be used along with other simple measurements to classify particles. First, we will look into individual single particle scattering If we recall the geometry of the large-field camera setting (Section 2.2), we notice that the field of view (FOV) is divided into 3 sections, about 270 pixels wide for the center view while about 165 pixels on each side view. To obtain a better signal-to-noise ratio for all 3 views we choose the region in the camera that is close to the laser beam, such that the enclosed center view region defined by four corner as (230,70), (230,250) (330,50), (330,230) with corresponding scattering forward, side and backward scattering angles as (64.7, 94.1, 128.7), (43.4, 82.5, 126 8), (63.5, 100.0, 135.0), (43.3, 90.7, 134.1) respectively. This setting will give us a total sample volume of 7.056 liters 111

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for every 5-meter water column, in order to compare with other measurements We will examine all the particles within this section for the large-fie l d camera and the corresponding sections of forward and backward scattering to measure the scattering property of each i n dividual particle, following geometry like that in Section 3.2 and formu l as in Appendix A. From previous discussions on Mie scattering and multiple scattering by aggregate particles we could expect different scattering properties between different groups of particles in the ocean, which might he l p to identify certain groups using these properties. Exploring such alternative to traditional image pattern recognition could prove beneficial to our understanding of both large-particle scattering and particle classification Some samp l e single particle scattering measurements are listed in Table 1 2, including positions in center view as 640 by 480 digitization, forward (8r), side (8go) and backward (8b) scattering angles, scattering intensities (/fr /go /b) corresponding to these angles, forward maximum (in percentage reflectance compared to 5% standard), forward to backward scattering intensity ratio and the type of the particle Position 8r 8go eb Ir I go 4 Rr Rflb type (301 93) 60.8 96 1 131.7 2751 589 681 0.74 4.04 u (245 187) 51.8 87.4 127. 0 2083 391 243 0 .81 8.57 c (304 119) 57 2 95 0 132.8 3593 442 668 0 .71 5.38 c ( 319 66) 63.3 98 6 133. 0 1460 683 889 0 65 1.64 A (299 156) 52.9 92.4 132 1 2993 512 629 0 78 4.76 c ( 264 86) 62.9 94.8 129 5 1260 407 466 0.42 2 .70 A (290, 178) 51.4 90 5 130.3 2034 642 847 0 79 2.40 u ( 231 ,236) 45.2 83.4 126.8 3459 1230 759 0 .79 4 56 c Table 12 I n divid u a l p art i cle o p t i cal pro p erties used in identification 112

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The type of the particles are shown in Figure 1, with types labeled as "C" for copepod (suc h as (e) and (f)), "A" for larvacean house type aggregate (Figure 1 (a) (b)), and "U" for unknown. We notice that the copepods have a higher forward-to-backward scatteri ng ratio than most of the rest of the particles, and the intensity of their forward scat tering is higher, while some larvacean house type aggregates s how a lower ratio but other unknown types also present a simi l ar property Thus we will not try to identify them at this stage. For this test, we set the rule of classification so that the ratio h as to be greater than 4 for copepods, the maximum forward scattering R r is at least 0.7% (compared pixel grey scale value to standard 5% reflector, equivalent of grey scale value 135), minimum size is 2 pixels on each dimen sion. Copepd s Cope pods cope pods %Errors (scattering) (imaging) (Alldredge ) 4/20d 0-5m 567 1568 m3 5629 m 3 42% 5-IOm 3118 2533 10-15m 1071 1086 2037 m3 2.6% 15-20m 425 483 Table 13. Particles identified by ICE using scattering properties. %errors are obtained by (1-countsscafcountsandredge)*100 Table 13 shows our identification results by scattering phase functio n Considering the simplicity of this identification method, we see a comparable accuracy to imaging which is encouraging. The big difference in accuracy in estimating in the upper and lower water column might be caused by depth separation error, considering that the hydro-cast depth may not be exactly the depth MAPPER samples, and a high concentration lay er of zooplankters were observed near the I 0 meter water depth. The 113

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combined overall accuracy in this case would be more realistic, and a value of 32% is acceptable compared to the image recognition method and other acoustic approaches (Chapter I). Again, MAPPER avoidance due to sky silhouetting is more likely than bottle avoidance. The identification method seems to work nicely in certain parts of the water column, although this exercise is not conclusive at this stage. The approach could be of greater value if some improvements could be made. One problem observed during measurement is that the alignment of 3 images of the same particle is very important. If, for any reason the frame is not paused perfectly (bad sync by TBC bad timing during freeze improper advance of frame by VTR) the geometry of 3-D scattering could be easily lost. Sensitivity tests show that for every ten pixels misalignment in the center view, it could cause eight pixel in side views That is equivalent to about a 0.25 to 0.7 variation in center view, and 0 7 to 2 .2 on the side. The signal-to-noise ratio is also controlled in part by the quality of the freeze. Therefore storage of original video in digital format could be very helpful, and successive processing could give much improved results Other factors that might affect our measurement includes the relative small sampling volume examined. Outside this region, either the signal-to-noise ratio is too low to make any valid measurement, or weaker power prevents signals to appear in all three views at the same time This also happens from time to time even within the detection box, when light sheet blocked by other particles (that are not in our detection range). 114

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5.3 Summary In this chapter, we tested hypotheses #7 and #8 and both of them are true. For #7, we conclude that in-situ video microscopy technique can be used to separate major zooplankter groups from marine-snow-type particles It is demonstrated here that for a multiple-camera system, Zernike moment-invariants of target particles could be extracted from the higher resolution system, and then applied to lower resolution system to identify different types of particles, with added sampling volume and signal-to-noise ratio. While in the case of #8, we used optical signatures of large particles to successfully identify particle origins with similar accuracy to imaging method. This faster and simpler approach utilizing particle optical properties via HMM including forward to backward scattering ratio, maximum reflectance, and size, is tested against copepod-like particles, with 32 % accuracy, compared with that of 24 % using image processing method. Both methods may be affected by obstacle avoidance behavior around MAPPER triggered by its large silhouette against the night sky. Inverting and raising MAPPER might obviate this possibility. The identification of different types of large particles in the ocean can be beneficial to other applications, such as modeling flux in ecosystems, zookplankton physiology succession, aggregation process modeling as well as light scattering and transmis s ion. With MAPPER-ICE system, these automated measurements could be done in situ, to provide systematic mapping about abundance of different types of particles in the natural environment, without introducing sampling error or disturbing the environment. 115

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Better results could be expected with improvements in computing and laser power in the near future, possibly towards real time processing. 116

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CHAPTER 6 SUMMARY 6.1 Conclusion Throughout this presentation, we see that the amount of large particles in the ocean, especially in the shallow water in coastal regions, plays an important role in the understanding of the underwater light field, and their enhanced back-scattering has significant implications on remote sensing of world ocean. The following is a list of conclusions regarding our hypotheses : ( 1) True. The MAPPER/ICE system can accurately measure the large-particle (>I OO,um) size distribution, supported by both comparison with beam attenuation estimates and results from other instruments operated independently (which are conclusions of previous publications). Also, it seems that this particle size distribution can be defined by a single parameter, it's hyperbolic slope. The concentration constant appears to be highly correlated to the slope, which might be location-dependent and for enclosed system only, but held for both East Sound and Monterey Bay data (2) False The hyperbolic distribution of large particles can not be directly applied to small-particle size distribution, although possible correlations might exist. (3) True. Forward scattering corrections for beam attenuation measurements are applied using in-situ particle size distribution measured by MAPPER, and calculations 117

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show an average error of 15% when not applied. Further, measured large-particle size distributions indicate possible correlation between slope and total particle attenuation ratio between 450 and 660 nm although correlations were rather low. (4) True. The beam attenuation measurement provides an important lOP quantity which contains information from both smalland large-sized particles It is further estimated that in the coastal region such as our project site, a typical reading from a 25cm c-meter pathlength reflects scattering by particles up to the size of 1 mm in diameter. (5) True. Our estimations of small-particle size distributions, using beam attenuation and large-particle size distribution information measured by MAPPER, provide reasonable accuracy compared to Coulter Counter measurements (5.07%). Further analysis excluding high gradient regions shows excellent result (3.05%), indicating that in-situ instruments such as MAPPER may be more suitable for ocean research in regions of rapid change. (6) True. Our first in-situ estimation of large marine particles seems to be a success, in providing unique scattering phase function for a class of large particles that are difficult to handle and measure The increased backscattering is consistent with those derived for other media, and in part can be explained by our Monte Carlo simulations. (7) True. Our test indicates that we can use a in-situ video microscopy technique to identify large marine particles, separating a major zooplankter group from marine snow-type particles, by solving the dilemma of choice between higher resolution and larger sample volume using Zemike moment-invariants. (8) True. Optical signatures of large particles can be used to identify particle origins with a certain degree of success (32% ), compared to net samples Sampling 118

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consistency may have been reduced by vertical concentration gradients and visual, obstacle-avoidance behavior typical of zooplankters. 6.2 Future Work (I) More power output from the diode lasers would improve the signal-to-noise ratio and increase dynamic range of measurements. (2) Possible processing and data recording entirely in digital domain can significantly increase signal-to-noise ratio, and allow real-time in-situ data reduction (3) Further research with MAPPER at different locations is desirable, and necessary modeling could be carried out to further test some of the above hypothesis and conclusions These include the relationship between concentration constants and PSD slopes, and relationships between PSD slopes and beam-attenuation ratios at different wavelengths, which might lead to a simpler faster, and commonly accessible method of measuring particle size distributions in-situ. (4) In order to better quantify zoolplankton abundance, future MAPPERs should consider an inversion of current deployment pattern, from surface-down to bottom-up with SLS leading its path, to minimized possible underestimation caused by obstacle avoidance of zooplankters 119

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REFERENCES Akleson, S. and R. W Spinrad 1988. Size and refractive index of individual marine particulates: a flow cytometric approach. Appl. Opt. 32:1270-1277 Alldredge, A. L. and C. Gotschalk, 1995. SIGMA Friday Harbor study: Aggregates abundance and background data. SIGMA Data Report #3 to the Office of Naval Research under the Accelerated Research Initiative, Significant Interactions Governing Marine Aggregation II: 1-41 Alldredge, A. L. U. Passow and B. E. Logan 1993 The abundance and significance of a class of large, transparent organic particles in the ocean. Deep-Sea Res. 40: 1131-40 Alldredge A. L. and M W. Silver 1988. Characteristics, dynamic s and significance of marine s now Progr ess in Oceanography 20:41-82. Alldred ge, A. L. and C. Gotschalk, 1988. In situ settling behavior of marine snow. Limnol Oceanogr. 33:339-351 Alldredge, A. and E. 0. Hartwig, editors 1986. Aggregate Dynami cs in the Sea Workshop R e port Office of Naval Research, Asilomar Pacific Grove, Ca. 211 pp. Alldredge. A. L. 1976 Di scare d appendicularian houses as so urces of food surface habitats and particulate organic matter in planktonic environments Limnology and Oceanography, 21:14-23 Alldredge, A. L., 1972. Abandoned larvacean houses: A unique food source in the pelagic environment. Science, 117:885 887 A sper, V L. 1987. Measuring the flux and sinking speed of marine snow aggregates. De e p-Sea R esea rch. 34: 1-17 Asano S 1979. Light scattering properties of spheroidal particles. Appl. Opt. 18:712-723 A sa no S, M. Sato 1980 Light scattering by randomly oriented spheroidal particle s. Appl. Opt. 19:962-974 1 20

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Azam, F. and D. C. Smith, 1991. Bacterial influence on the variability in the ocean's biogeochemical state: a mechanistic view NATO AS/ Series, Particle Analysis in Oceanography edited by S. Demers, Springer Verlag Berlink Heidelberg, 027:214-236 Bader, K. S. and R. C. Smith, 1979. The hyperbolic distribution of particle sizes, J. Geophys. Res. 75:2822 Bale, A. J. and A. W. Morris, 1987. In-situ measurement of particle size in estuarine waters. Estuarine and Coastal Shelf Science, 24:253-263 Bartz, R., J R. Zaneveld and H. Pak, 1978. A transmissometer for profiling and moored observations in water. OCEAN OPTICS V 160: 102-108 Bergougnoux, L., J. Misguich-Ripault, J. L. Firpo and J Andre, 1996. Monte Carlo calculation of backscattered light intensity by suspension: comparison with experimental data. Appl. Opt 35:1736-1741 Bird, R. E. I 972. Scattering of light from large infinite ice cylinders at normal incidence Appl. Opt II: 16-22 Bishop, J. K. B., J. C. Stepien and P. H. Wiebe, 1986. Particulate matter distributions, chemistry and flux in the Panama Basic: response to environmenta l forcing. Profress in Oceanography, I7: 1-59 Bohren C. F ., Donald R Huffman, I 983. Absorption and scattering of light by small particles x iv + 530. Wiley, New York. Bourrely, P. C. and B.Torresani, 1986. Light scattering by particles of arbitrary shape: a fractal approach, J. Opt Soc. Am. A. 3:250 256 Bricaud A. and D Stramski 1990. Spectral absorption coefficients of living phytoplankton and nonalgal biogenous matter: a comparison between the Peru upwelling area and th e Sargasso Sea. Limnology and Oceanography, 35:562-582 Brown 0. B. and H. R. Gordon, 1974. Size-refractive index distribution of clear coastal water particu lat es from scattering Appl. Opt., 13:2874 Calvert S.E. and M. J. McCartney, 1979. The effect of imcomplete recovery of lar ge particles from water samplers on the chemical composition of oceanic particulate matter. Limnology and Oceanograph y 24:532-536 Carder, K.L. and R.G. Steward, 1985 A Remote sensing Reflectance Model of a Red Tide Dinoflagellate off West Florida Limmnol. Oc e anogr. 30:286-298 1 2 1

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Carder, K. L. and D. K. Costello, 1994 Optical effects of large particles. Ocean Optics. K.L. Carder, M.J. Perry, and R.W. Spinrad, editors, Oxford University Press, New York, N.Y. 243-257 Carder, K. L., R. D. Tomlinson, and G. F. Beardsley Jr. 1972. A technique for the estimation of indices of refraction of marine phytoplankters. Limnol. And Oceanogr. 17:833-839 Carder, K. L., G. F. Beardsley Jr., and H. Pak, 1971. Particle size distributions in the eastern equatorial Pacific. J. Geophys. Res. 76:5070-5077 Carson, Rachel, 1951. The Sea Around Us. New York, Oxford University Press Cattrall, C., 1996. Investigation of remote sensing reflectance dependencies using Hydrolight 3.0 Cohen, A. and P. Alpert, 1979. Extinction efficiency of obliquely and randomly oriented infinite cylinders J. Appl. Phys. 50:8262 -64 Cohen A. 1980. Scattering of a linearly polarized incidence at arbitrary angle to incident plane of infinite tilted cylinders Opt. Lett. 5:150-152 Costello, D K., K. L. Carder, and W. Hou 1995. Aggregation of a diatom bloom in a mesocosm: bulk and individual-particle optical measurements. Deep-Sea Research II. 42 : 29-45 Costello, D. K., W. Hou and K. L. Carder, 1995 Bulk and individual particle optical measurements. April 14-22, 1994, East Sound San Juan Islands, W A. In: SIGMA Data Report #3 to the Office of Naval Research under the Accelerated Research Initiative, Significant Interactions Governing Marine Aggregation. Vll: 1-46 Costello D K. W. Hou and K. L. Carder, 1994 Some effects of the sensitivity threshold and spatial resolution of a particle imaging system on the shape of the measured particle size distribution. In: Ocean Optics XII, Jules S. Jaffe, Editor, Proc. SPIE 2258, Bergen Norway. Costello, D. K. K. L. Carder and W. Hou, 1992. Structured visible diode laser illumination for quantitative underwater imaging. Ocean Optics XI. Gary D. Gilbert, Editor, Proc. SPIE 1750 : 95-103. Costello, D. K., K. L. Carder and R. G. Steward, 1991. Development of the Marine Aggregated Particle Profiling and Enumerating Rover (MAPPER) Underwater Imaging,Photography, and Visibility, Richard W. Spinrad, Editor, Proc. SPIE 1537:161-172 122

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Costello, D. K., K. L. Carder, and R. G. Steward. 1988 Computer enhancement of in-situ holographic images with preliminary algorithms for marine particle pattern recognition. EOS, 69:1124-1129 Deirmendjian D., 1969. Electromagnetic Scattering on Spherical Polydispersions Elsevier, New York. Deuser, W G. F. E. Muller-Karger, R. H Evans, 0. B. Brown W. E. Esaias and G. C. Feldman, 1990. Surface-ocean color and deep-ocean carbon flux: how close a connection? Deep Sea Res 37 : 1331-1343 Dukunda,R and K. R. Ramakrishnan,1995. Fast computation of Legendre and Zemike moments Pattern Re cogn ition 28 : 1433-1442 Fowler, S W. and G A. Knauer 1986. Role of Large Particles in the Transport of Elements and Organic Compounds Through the Ocean Water Column Prog. Oceanog. 16:147-194 Gibbs, R. J. and L. N. Konwar, 1983. Sampling of mineral floes using Niskin Bottles. Environmental Science and Technology. 17:374-375 Gordon, H. R., 0. B. Brown and M. M. Jacobs 1975. Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean. Appl. Opt 14:417427 Gordon, H R., D K. Clark, J W. Brown, 0. B. Brown, R. H. Evans, and W. W Broenkow, 1983. Phytoplankton pigment concentration in the Middle Atlantic Bight: Comparison of ship determinations and CZCS estimates. Appl. Opt. 22:20-36 Gregg, W. W. and K. L. Carder, 1990 A simple spectral solar irradiance model for cloudless maritime atmospheres, Limnol Oceanogr 35:1657-1675 Harris, J. E., 1977. Characterization of suspended matter in the Gulf of Mexico-IT. Particle size analysis of suspended matter from deep water. Deep Sea Res. 24: 1055-1061 Hawley, Nathan, 1982. Settling velocity distribution of natural aggregates. J Geophys. Res. 87:9489-9498 Hill P S 1992. Reconciling aggregation theory with observed vertical fluxes following phytoplankton blooms. J. Geophys. Res. 97:2295-2308 Hill, P.S. and A. R. M Nowell 1990. The potential role of large, fast-sinking particles in clearing nepheloid layers Phil. Trans. R. Soc. Land. A 331: 103-117 123

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Honjo, S., K. W. Doherty, Y. C. Agrawal, and V. Asper, 1984. Direct optical assessment of large amorphous aggregates (marine snow) in the deep oceans. Deep-Sea Res. 31:67-76 Hou, W., D. K. Costello, K.L. Carder and R. G Steward, 1994. High-resolution Marine Particle data from MAPPER, a new in-situ optical ocean instrument. EOS AGU/ASLO 75:21-24 Hou, W., K. L, Carder and D. K. Coste llo, 1996 Large particle scattering phase function. Ocean Optics XIII, Halifax Canada Hunt, J .R. 1980 Prediction of oceanic particle size distributions from coagulation and sedimentation mechani s ms Particulate s in Wat er. M C. Kavanaugh and J O Leckie, editors American Chemical Society 243 -257 Hu, M-K., 1962 Visual pattern recognition by moment-invariants, IRE Transactions on Info rmation Theory. 179 187 Jackso n, G. A., R. Maffione D. K. Costello, A. A Alldredge B. E. Logan H. G Dam, 1997. Particle size spectra, from 1 J..Lm to 1 em, at Monterey Bay as determined by multiple instruments. accepted by Deep Sea Res. Jackso n G A. 1995, SIGMA Data Report 3 to the Office of Naval Research under the A cce l era t ed Research Initiative Si g nifi cant Int e ractions Governing Marine Aggregation. Jack son G A. and W Kimsey, 1995. Acoustic Doppler Current Profiler (ADCP) data analysis. In: SIGMA Data Report #3 to the Office of Naval Resear c h under th e Accelerated R esea rch Initiative, Significant Int erac ti ons Governing Marine A gg regation ill: l-23 Jackson G A. 1990. A model of the formation of marine algal floes by phys ical coagulation processes, Deep Se a R es. 37: l 197-121 1 Jain, Ani) K., 1 989. Fundamentals of Digital Image Processing Prentice Hall Englewood C l iffs, NJ Jensen J R., 1996. Introdu c t ory Di gi tal Imag e Proc ess ing, A remote sensing perspective Prentice-Hall Inc. Jerlov N G. 1 976. Marine Optics, Elsevier Ams terdam, 231pp Kitchen J C., J. R. V. Zaneveld and H. Pak, 1982 Effect of Particle size distribution and chlorophyll content on beam atte nu a tion s pectra Appl. Opt 21 : 3913-18 Kirk J T. 0., 1983 Li ght and photosynthesis in aquatic ecosystems. Cambridge Univers i ty Press 124

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Koike, I. S Hara, K. Terauchi and K. Kogure, 1990 Role of sub-micrometer particles in the ocean, Nature, London, 345:242-243 Krone, R B. 1976. Engineering interest in the benthic boundary layer. In I. McCave ( ed): The Benthic Boundary Layer, Plenum, New Yo r k, 143-156 Kuga, Y. and A. Ishimaru, 1989. Backscattering enhancement by randomly distributed very large particles Appl. Opt. 28:2165-2169 Lambert, c E C. Jehanno, N. Silverberg, J. C. Brun-Cottan and R. Chesselet, 1981. Log normal distributions of suspended particles in the open ocean Journal of Marine Research 39 : 77-98 Latimer, P 1980. Predicted scattering by spheroids. Comparison of approximate and exact methods. Appl. Opt. 19:3039-3041 Latimer, Paul. 1984 Light sca ttering by a structured particle: the homogeneous sphere with holes. Appl. Opt. Vol.23:1844-1847 Lerman, A. K. L. Carder and P. R. Betzer 1977. Elimination of fine suspensoids in the oceanic water column. Earth Planet Sci. Lett. 37:61-70 Lee, Z. P., K. L. Carder, S. K. Hawes R G. Steward, T. G. Peacock and C. 0 Davis 1994. A Model for interpretation of hyperspectral remote sensing reflectance Appl. Opt. 33:5721-32 Li, X and B. E Logan 1995. Size distributions and fractal dimensions of small particles. In: SIGMA Data Rep o rt #3 to th e Office of Naval Research under the Accelerated R ese arch Initiative, Si g nificant Interactions Governing Marine Aggregation. VI : 1 -17 Logan, B. E D. B Wilkinson 1990 Fractal geometry of marine snow and other biological aggregates, Limnol. Oceanogr 35: 130-136 Lord Rayleigh, 1897. Phil. Mag., 41:107 447 Mann K. H., and J R.N. Lazier, 1991. Dynamics of marine ecosystems: bi o logical physical interactions in the oceans. Blackwell Scientific Publications Mandt, C. E and L. Tsang, 199 2. Backscattering enhancement from a random distribution of large discrete spherical scatterers with a size distribution, J Opt Soc. Am. A. 9 :22 46-2251 McCave, I. N ., 1984 Size spectra and aggregation of suspended particles in the deep ocean. Deep S e a Res. 31 :329:352 125

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Mie, G 1908 Beitrage zur optik triiber median speziell kolloidaler metallOsungen, Ann. Phys., 25 : 377-442 Mishchenko M. I., D. W. Mackowski and L. D Travis, 1995 Scattering of light by bispheres with touching and separated components. Appl. Opt. 34:4589-4599 Mitchell, B G and D A. Kiefer, 1988. Chlorophyll-a specific absorption and fluorescence excitation spectra for light-limited phytoplankton. D eep -Sea Res 35:635663 Mobley, C. D. 1994 Light and Water: Radiative Transfer in Natural Waters. Academic Pre ss, Morel A. 1974 Optical properties of pure water and pure sea water, in Optical Aspects of Oceanography, N G. Jerlov and E S. Nielsen, Eds, Academic, New York Morel, A. and L. Prieur, 1977. Analysis of variations in ocean color Limnol. Oceano gr. 22:709-722 Morel, A., 1988 Optical modeling of the upper ocean in relation to its biogenous matter content (Case I Waters), J. Geophys. Res 93:10,749-68 Mukundan, R, and K. R. Ramakrishnan, 1995. Fast computation of Legendre and Zernike moments Pattern R ecognition, 28:1433-1442 Nelson, J R. J R Beers, R. W Eppley G A. Jackson, J. J McCarthy and A. Soutar 1987 A particle flux study in the Santa Monica-San Pedro Basin off Los Angles: particle flux, primary production and transmissometer survey. Continental Shelf Res. 7 : 307-328 Parsons T. R. Y Maita and C. M. Lalli 1984. A manual of chemical and biological methods for seawater analysis Pergamom Press, N.Y., 173pp Preisendorfer, R.W., 1961. Application of radiative transfer theory to light measurements in the sea. UGGI Mono gr. I 0: 11-30. Perrin J M and P. Chiappetta, 1985. Light scattering by large particles I. A new theoretical description in the eikonal picture. Optica Acta 32: 907 921 Perrin, J M, P L. Lamy, 1983. Light scattering by large rough particles, Optica Acta 30:1223-44 Risovic, D. 1993 Two-component model of sea particle size distribution Deep-Sea Res. 40 : 1459-73 126

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Sheldon R. W., A. Prakash and W H Sutcliffe, Jr., 1972 The size di s tribution of particles in the ocean. Limnol. Oceanogr 27: 327-340 Spinrad, R. W and Brown, J W., 1986. Relative real refractive index of marine microorganisms : a technique for flow cytometric estimation. Appl Opt., 25:1930-4 Stolzenbach, Keith D., 1993. Scavenging of small particles by fast-sinking porous aggregates,. D ee p-Sea Res. 40:359-369 Stramski D. and D. A. Kiefer, 1991. Light scattering by microorganisms in the open ocean Prog. Oceanogr 28:343-383 Suzuki N. and K. Kato, 1953 Studies on suspended materials Marine snow in the sea I. Sour ces of marine snow. Bull eti n of the Faculty of Fisheries of Hokkaido University. 4:132-135 Teague, M R., 1980. Image analysis via the general theory of moment s. J Opt Soc. Am. 70 : 920-930 Tsunogai, S. and S. Noriki 1991. Particulate fluxes of carbonate and organic carbon in the ocean. Is the marine biological activity working as a sink of the atmospheric carbon? T e llus. 43b:256-266 Ulloa, 0., S. Sathyendranath and T Platt, 1994 Effect of the particle -s ize distribution on the backscattering ratio in seawater. Appl. Opt. 33:7070-77 Van de Hulst, H. C. 1957 Light Scattering by Small Particles. John Wiley, New York Wallin, A. a nd Olaf Kubler 1995 Complete sets of complex Zemike moment-invariants and the role of the pseudoinvariants. IEEE Transactions on Pattern Analysis and Machine Int elligence. 17:1106-1110 Walsh, I. D. and W. D. Gardner 1992 A comparison of aggregate profiles with sediment trap fluxes. Deep-Sea Res. 39:1817 1834 Well s, J T and A. L. Shanks, 1987 Observations and geological significance of marine s now in a s h a llow-water, partiall y enclosed marine embayment. J. Geophys. Res 92: 13,185 190 Wells M. L., E D. Goldberg 1992 Marine sub micron particles Marine Ch e mistry 40: 5 -18 Weller sha u s, S ., L Goke and P Frank, 1973. Size distribution of suspended particles in sea water. Meteor Fors chu ngs ergebenisse, S eries D, 16:1-16 127

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Xu, Y-L., I 995. Electromagnetic scattering by an aggregate of spheres. Appl. Opt. 34: 4573-4588 Zaneveld J. R. V., R. W. Spinrad, R. Bartz, I979. Optical Properties of turbidity standards. SPIE Ocean Optics VI: 159 I 68 Zhang-Fan Xing and J Mayo Greenberg, 1994 Efficient method for the calculation of mean extinction. II. Analyticity of the complex extinction efficiency of homogeneous spheroids and finite cylinders. Appl. Opt. 33:5783-95 Zurk, L. M., T Tsang K. H. Ding, and D P. Winebrenner 1995 Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries. J. Opt. So c Am. A 12: 1772-1781 128

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APPENDICES 129

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APPENDIX A Single-particle-scattering Geometry As shown in Figure 20 assume Cartesian coordinates origin is at center of 4 laser diode and we will first list all coordinates for laser diode, camera and the particle in SLS so that the exact scattering angles of these 3 scattering path could be solved exactly. The camera is located at (xO,yO,zO), where xO = -15, yO = 25.4 are the verticle offset of the camera from the coordinate origin, zO = 215, all units are in em, the laser diode is at (xa, ya za=O). To ease the calculation, recall from geometrical optics that the optical path is exactly the same for the forward scattering if we assume the receiving camera is at the position in mirror of P2, and the "virtual camera" in P2 (right) is xO xOr = 2sm(H)cos(H)(cen +tan( H)+ z O + ) xO yOr =yO xO-xOr z0r=z0+-tan(H) tan( H) and for the forward scattering calculations, we could calculate the lengths of all three that consist the triangle point "a" (laser diode), point "1" (position of the particle in SLS) and point "R" (position of shadowing camera in mirror P2) and all angles can be derived from these lengths 130

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Appendix A (Continued) Rat= (xa-xt)(xa-xl) + (ya-yt)(ya-yt) + (za-zt)(za-zt) Rtr = (xOr-xt)(xOrxt) + (yOr-yt)(yOryt) + (zOr-zt)(zOrzt) Rar = (xaxOr)(xa-xOr) + (yayOr)(ya-yOr) + (zaz Or)(za-z Or) so that forward scattering angle between line "a" to "t" and "t" to "r" is, e t80 (Rat+ Rlr-Rar) = t80--acos( ) 3.14 2(Ral)112(Rtr)112 Similar results could be obtained for side e 8 t80 (Rat+ ROt RaO) -1 0--acos( ) -3.14 2(Ral)112(ROt) 112 and backward t80 (Ral+Rlt-Rat) B= t803.14 acos( 2(Ral)I'2(Rll)ll2 ) For a particle within the laser sheet in any location, with distance to the laser as Rat, the incident irradiance per unit volume could be expressed as (Costello et al. t993) E Io R al*c =--e Rat Considering the attenuation involved in each scattering angle before reach the camera, we could restore the amount of light scattered at the particle location, rather than camera received as: near 90 e = I; =I eROI*c (Rat)eRIII*c srdt r t3t

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Appendix A (Continued) forward e = ( = I Rlr* c(Rai)eRal*c fon v ard E ,e backward e = I; = I eROI* c(Ral)eRal*c srde E r 132

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APPENDIXB General Theory of Moments If we have an image which is defined as f(x,y and limited to a finite region R, we can define the pth,qth order moment as (B.l) mp.q = fJ f(x, y)xpyqdxdy R p,q = 0,1,2, ... and moment-invariants could be constructed from these quantitie s so that general feature s described using these invariants do not change under image transformations such as sca ling and rotation. Here we will pre se nt the formulation to compute the moment invariant of Zemike type to any order. Two dimentional complex Zemike moments are defined by project the image region onto the well -k n o wn Zemike polynomials, ( B .2) V,m(x y) = V,m(psin 6,pcos6) = R,m(p)exp(im6) and we have complex Zemike moments (B.3) n + 1llfTr -jm8 Z,m R ,m(r)e f(r, 8)rdrd8 1l 0 -Tr notice that the image is written in polar form, however, the calculations are carried out in Cartesian coordinates where (B.4) 1
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Appendix B (Continued) (B.5) (11-jm)/21 ( ) 1 s n-s n-2s R"m(r) = ..,; (-I) n+lrrzl n-lrrzl r s=O S ( S) ( S) 2 2 and (B.6) o:::;lrrzl:::; n; n -lml is given; n>O and the real C11111 and imaginary part Snm separately are, (B.7) 2n + 2 l lftc C""' = Rnm(r)cos(m8)j(r,8)rdrd8 JZ 0 -IC (B.8) 2n + 2 lJIC Mnm = Rnm(r)sin(m8)f(r,8)rdrd8 1l -tc Transform the R equation will give us (Teague I980) II (B.9) Rnm(r) = L Bnms r s s = m where (Mukundan and Ramakrishnan, I995) (B.IO) ( -l)'2(( n + s) I 2)! B ,,,.f ((n s) I 2) !((s + m) I 2) !((s-m) I 2)! With the Zernike moments calculated we could make the complete set of the (n+ I ) invariants (Wall in, Kubler I995), and for the first (n+ I )/2, (B.II) M = Ik = lz"-2kl2 t n n where and for even n, we could simply use (B.12) M = /"'2 = zo 1 n n where n = [;].2 134

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Appendix B (Continued) and next (n-1)12 invariants and pseudo invariants (which could be changing signs under transformation) are (B. l3) P; = where and IE[n-2,n-4, ... ] lastly, (B.14) wherej=1 when n is odd andj=2 when n is even, and P stands for pseudo invariants here. Pseudo invariants will change signs under some transformation (Teague 1980), which is not important in this application, therefore we choose not to calculate, although some researchers show that it also contribute to minor image details such as slight phase change when reconstruct images from moments (Wallin, Kubler, 1995). The last moment-invariant as in Equation B 15 is not calculated for the large particles neither as some extra calculation will significantly increase the computing time while this single value does not seem to po se special impact a nd the author believe it is justifiable to skip this one among dozens of value s. So our final Zernike moments invariants calculated at those from 135

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Appendix B (Continued) Equation B.11, B.12 and B.13 without pseudo ones, in the orders described by the descending values in the subscript, labeled thereafter M 1, M2, M3 etc 136

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(C. I) APPENDIXC Effect of Unit Change on xa We have a particle size distribution that s expressed in em unit d2N --=ADk dDdV k>O where D is the particle diameter, dV is the sample volume, N is the total number of particles between size rangeD and D + dD. It is equivalent to the following form (C.2) d2N IOD k lOdD 103dV = A(Wf k>O 10 103 Now notice we could simple substitute JOdD with dD to transform the equation into mm base unit similar applies to dV (C.3) k>O Assume another PSD (C.4) k'>O and follow Equation (2.16), the aggregation point x0 in em unit is at (C.5) log(A')-log(A) X ----oM k'-k I For convenience we use base-l 0 logrithm here so in mm unit using Equation (C.3) 137

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Appendix C (Continued) (C.6) (log( A') -4 + k')-(log( A) -4+ k) k'-k log( A ) -log( A)+ (k'k) log( A ) -log( A) ----1 k'-k k '-k Comparing Equation C.5 to C.6, we could see that the aggregation size expressed in 1 oxo is the same. 138

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APPENDIXD Pattern Recogn ition With improvement in computing speed, automatically identifying features or patterns from images or signals by computers is becoming more feasible A pattern is defined as a set of variables (pattern descriptor) that describe certain feature(s) of an object, usually in digital domain such as di s crete or continuous digital signals, and digital images (Jain, 1989 Jen sen, 1996) One can def i ne patterns in many ways. By examining a known feature from an im ag e for example one can extract this feature and express it in variables that describes it and discerns it from other features and computers can be programmed to automatically identify this feature. For instance if we have a mixed set of images of ellipse and circles we can u se the major and minor axis to represent ellipses (when they are not equal) and to separate them from circles. This approach, called supervised pattern recognition, is based on the fact that patterns are known a priori. Another common approach, called unsupervised pattern recognition, involves procedures that computers automatically identify features among images by clustering variables into groups that are close to each ot her and a n alysts later determine if certain groups should be combined or eliminated 139

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Appendix D (Continued) The above two methods are sometimes referred to as hard pattern recognition (Jensen, 1996), versus soft approaches that involve fuzzy logic or neural network applications. We will focus on supervised classifications in our exercise here. Our goal is to identify two types of particles from all other particles that are present in the MAPPER images. First, we need to define our pattern descriptors. With identified groups of zooplankters (copepods, Figure 1 (e) (f) (h) ), and aggregate-type particles ((a), ( b) and (d)), we can obtain variables that best describes the features of these particle s, namely, by means of Zernike moment-invariant (Costello, 1988 Teague, 1980). As seen in Appendix B, these invariants to any high orders can be calculated. Following conclusion of Teague (1980), we will only calculate M;'s to the order of 100, as displayed in Figure 29. Since all these calculation s are carried out for each individual particle within the image for all video se quences (30 frames per second average downcast last s about 3 minutes ), it is necessary to limit the calculations to the most contributing variables, which will reduce the processing time significantly. The variables we want to keep are the ones that have minimum variations within the group, while at the same time have maximum variations between groups This high contrast will prevent mixing up among groups, though errors could occur that might lead to underestimation The standard deviations of measured M;'s are calculated for each groups for this purpose we found that among first 100 Zernike moment-invariants, M2, M5, M7 M9 MJO, MJ2 MJ3 M17 M25, M34 41 and M45, best satisfy the above criteria. We choose this set of variables as our 140

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Appendix D (Continued) pattern descriptors. To use these descriptors to identify the particles, we apply a modified minimum mean distance classification in k-space, where here k stands for the number of dimensions (variables or invariants here) which in our case, is 12 (Figure 30). The standard minimum mean distance classification basically involves calculating the mean distance to all classified group centers ink-dimensional space, k ( D .l) D; = L,C Mii -M0 ) 2 j=l and then compare all the distances calculated to find the minimum value (closest to a classified group center), where D; is the distance to i1h centers, Moj is the }-component of the t' center (Figure 30). Figure 30. Sketch of minimum mean distance classification in k-space 141

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Appendix D (Continued) Note that we only have two groups and the rest are unknown, hence we do not have a complete group centers therefore our classification approach needs to be modified slight ly. By testings done with two sample groups, we define 2cri as the range radius that will classify the target to the group, where 2cri (i = 1 ,2) is the two times standard deviation of M o 1 (dashed circle in Figure 30, for zooplankters) and M02 (dashed circle, for aggregates), respectively. Considering this modification is rather tight, errors might be introduced, most probably on the underestimation side 142

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APPENDIXE Multi-sphere Mie Scattering General Mie theory that was finalized by Lorenz ( 1898) and Mie ( 1908) describes the scattering and absorbing behavior by any single particle with arbitrary size and index of refraction. Others efforts were made to calculate other related shapes such as homogeneous spheroids (Asano and Yamanoto, 1975), cylinders by Lord Rayle ig h (1897), spheres with hole s (Latimer 1984 ), and touching spheres (Mishchenko et al., 1995). A recent effort was made to expand the situation to multi -s phere system with any configuration of spheres of different size and locations, by Yu lin Xu at the University of Florida. A brief summary of this theory will be given here, mostly based on several of his recent publications (Y. Xu, 1995, Y. Xu, 1996) A test run of his theory with marine type particles (relative index of refraction to the seawater 1 05) is carried out for a 4-particle aggregate stacked in a pyramid shape, to demonstratie the backscattering enhancement by aggregated particles The general equations governing time harmonic electromagnetic wave (electric field vector E magnetic field vector H) propagating in a homogenous isotropic medium with no so urce are (E.1) VxVxE-k2E=O V xVxH-k2H =0 143

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Appendix E ( Continued) where k is the wave number k = 2rt//... Since we are going to deal with scattering by multiple spheres, it is more convenient to express the plane wave in spherical harmonics in polar coordinates, with base vectors like (E.2) zu> (kr) =i,n(n+l) P ,"'( cos8) "kr exp(imqJ)+ + [i9-r"',(cos8)-i91i1tm,(cos8)]-1 !{_[rz!J)(kr)]exp(imqJ) kr dr where i9 ir are unit vector s, is the spherical Bessel functions (J= 1 ,2 ,3,4 for first second and third kind, which contains Hankel functions first and second kind). Th e basic vector spherical harmonic s are ( E.3 ) where P;" (cos 8) represents the Legendre function with degree n and order m We can expand the electromagnetic field for any /h sphere in a cluster of spheres in the se forms the scattered field (E5 H5 ) and the internal field HI) are n ( E.4 ) E ( ) -'"" '"". E [ j N <3> b j M <3>] s J ...J ...J l mn a mn mn + mn mn n=l m=n k n H ( .) '"" '""E [ j M <3> bj N <3> ] s J ...J ...J mn a mn mn + mn mn (J) Jl n=l m =-11 144

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Appendix E (Co ntinued ) .. n (E.5) E ( .) ""' ""':'C' [d i N> i M <1> ] I 1 -L...J L...JlDmn mn mn + Cmn mn n=l m=-n kj oo n H ( .) ""' ""E [ i N <1> d i M<1> ] I 1 --L...J L...J mn Cmn mn + mn mn COjl n=l m=n where E =IE lin(2n+1)(n-m)! mn o (n+m)! It is easy to see that for a cluster of single sp here, incident plane wave, m = 1, we have (E.6) E = E IE lin 2n + 1 In n= 0 n(n + 1 ) which i s exact ly what appears in general Mie theory (see Borhen and Hoffman 1983, chapter 4). The l ast part of a complete set of electromagnetic filed upon the jth sphere is the incident field, and following Equations E.4 and E.5, we assign oo n (E.7) E ( .) ""' ""' .E [ i N<1> i M0> ] i 1 -L...J L...Jl mn Pmn mn +qmn mn n=l m=-n k .. n H ( .) ""' ""'E [ i N <1> i M0> ] i 1 --L...J L...J mn qmn mn + Pnm mn COjl n = l m=-n The boundary conditions of jth sphere sat i sfy (E.8) 145

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Appendix E (Continued ) with which, along Equations E.4 E.5 E 7 we can solve a L , which are the total scattering coefficients for the jth sphere: (E.9 ) a j a j p j mn n mn' b j b jqj mn n mn cj c j p j IIIII-II ltltl' Note a b c d are exactly the same as the Mie coefficient s for isolated single sphere s found in Borhen and Hoffman (1983) which are combinations of spherical harmonic Bessel functions (1=1, 2, 3, 4), and the relative index of refraction ( detail s s ee Xu, 1995) From Equation E 9, we see that the scattering contribution from a single sphere of a cluster of spheres is additive The result can be viewed as a combination of linear modifications of normal s ingle Mie scattering functions The tas k of determining multisphere s cattering is now reduced to the determinations of P L which includes all the geometry and boundary conditions. To s implify the process we will transform coordinate to eac h sph e re in a cluster so that a generalized formul a can be u s ed for all different individuals within the system Assuming a system with multi-sphere s and the incident field of /h sphere takes both the initial incident wave EoU), and all s cattered fields from neighboring spheres (E. 10) H ;(j) = H0(j) + L H_t(l, }) 146

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Appendix E (Continued) From the addition theorem, the translation from lth sphere to fh sphere takes the form (Stein and Cruzan ( 1962)) v = L (l, (}) + (E.11) v = O p=-v v = L + v=O p=-v where M u > N <'> are the basis spherical vectors in each coordinate system, and jJV jJV are the so-called translation or addition coefficients Summarize the results from Equation E.4 E 5, E.9 E.IO and E 11, we obtain the total addition coefficient for the fh sphere, ( l L ) v P!,, L L (l, j) + (l, j) (E.12) /;t. j v = l p =-v (l.L) v q!rn L L (l, j) + (l, j) /;t. j V = l jl=-V and (E 13) =iv -11 (2v +1)(n+m)!(v -JL)! Jl (2n+l)(n-m)!(V+f.1)! Jl sm: =iv-n (2v+l)(n+m)!(v-f.1)! P (2n+1)(n-m)!(V+J.1)! Jl with E 12 we can calculate all a!rn, bL, c!rn, d !.n with which Muller matrix element S i (E.l4) 147

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Appendix E (Continued) and the scattering cross-section Csca can be calculated via basic summation For Csca (E.I5) 4n .. (n-m)! 2 2 csca = 2 I I n(n + 1)(2n + 1) Clamnl + lbmn l k n=l m=-n (n + m)! and note when m= 1, it has the form (E.16) which is the single sphere scattering cross-section from Mie theory (Bohren and Hoffman, 1983) Using the above theory, a 4-sphere scattering situation was calculated, using medium index of refraction 1.33 (seawater), relative index of refraction of the sphere taken as 1.05, which is typical of small marine particles such as phytoplankton cells (Stramski and Kiefer 1991). The 4 sphere are stacked up in a pyramid shape as shown in Figure 31. Since we only need the total scattering intensity of un-polarized field, we assume the incident plane wave as x-polarized, in Z direction, and the equivalent of S 11 of BHMIE code (Bohren and Hoffman, 1983) will give us the intensity 148

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Appendix E ( Continued ) X Figure 31. Sketch of multi-sphere aggregate scattering calculation 149

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VITA Weilin Hou received a Bachelor's Degree in Physics from the Fudan University of Shanghai, China in 1988. He enrolled in the Ocean Optics Program in the Ocean University of Qingdao as a Master degree seeking student in the same year and attended classes there. He enrolled as a PhD stu dent in Marine Science at the University of South Florida in the Fall of 1990. He is a member of SPIE and AGU. He is also the semor author on two publications completed during his tenure as a graduate student.


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