本文旨在利用粒子軌跡追蹤方法研發一套能夠完整地模擬海域幼生牡蠣生命週期的遷徙及運動模式，包含牡蠣幼苗誕生、自由漂移、自主性運動、附苗及死亡。模式準確性與合理性透過現場試驗與數學理論進行嚴謹驗證，並將驗證後的模式應用於研究臺灣雲林海域幼生牡蠣遷徙特性、保育及幼苗補充等相關生物傳輸之學理特性。研究結果指出，雲林海域的海流特性在漲潮時候海流流向為西南往東北之方向；退潮時後則為東北往西南方向。殘餘流分析指出當地海流的淨流向為西南往東北，惟影響當地海域中幼生牡蠣傳輸之重要自然因素。根據粒子回溯計算之結果，雲林海域採苗區的的牡蠣幼苗來自南方，包含自身採苗區及南側外傘頂洲的鄰近海域。此外，本文也利用現場與試驗室結果，判定出幼生牡蠣存活在海域中具有擁有向光性之生物行為，此特性並應用在建構牡蠣遷徙模式中的運動模組。數值試驗歸納出能夠較合理模擬海域幼生牡蠣傳輸之運動行為屬於階梯函數 (step function) 之型態，即僅在白天及漲潮時候，幼生牡蠣後期(眼點幼生)之運動現象可藉此方法進行模擬。本文並引入所謂的關連性矩陣 (connectivity matrix) 來瞭解種苗與附苗區域之關連性。分析結果顯示，雲林海域主要採苗區中的幼苗來源，絕大部分來自南部與自身產地。本文也因此建議當地蚵農在傳統的採苗季節(中秋節)前，可以保留部分的成蚵而不需要全數售罄，主因可以使得在採苗區中的成蚵能夠在中秋節前進行生殖，提供更多的幼苗在採苗季時來進行附苗，藉此提高幼苗的附著率。本文計算之滯留時間也顯示雲林海域的海水交換能力良好，適合養殖蚵業的發展。

A Lagrangian-type particle tracking model is developed to simulate a life cycle of oyster larvae in the open sea, including birth, free-swimming transport, biological motion, settlement and death. The model accuracy and applicability are carefully justified against basic mathematics and field data. An application is made to investigate transport characteristics, retention, recruitment of oyster larvae along Yunlin coast of Taiwan. Computed results suggest that typical flow motions along Yunlin coast are that flow moves to southwestward and northeastward during ebb and flood stages, respectively. Residual flows are obvious with a northeastward direction in offshore regions but relatively quiescent in nearshore regions, having predominant effects for driving oyster larvae transport along Yunlin coast. Results of a backward particle tracking simulation indicate that oyster larvae in the harvest regions come from southwest. Field and laboratory clues both suggest that phototropism is a critical environment factor affecting motions of oyster larvae. A set of numerical experiments point out that passive transport for 14 days and a step function of STST (i.e. moves only during daytime and flood stages) is the best assumption for modeling oyster larvae transport along Yunlin coast. Results clearly point out that successful rates of settlement are generally under 19$\%$ in the present case. A connectivity matrix is introduced to quantitatively understand connections between spawning and settlement zones. It is generally observed that recruitment of oyster larvae in the northward zones are contributed by that from the south and harvest region. Therefore, a recommendation is proposed for local oyster farmers by holding certain adult oysters in order to have more opportunities for local recruitment of oyster larvae, especially in the major harvest regions. Computed residence time also suggests that flushing capacity along Yunlin coast is satisfactory, showing a suitable environment for developing oyster production.

Batchelder, H. P. (2006). Forward-in-time/backward-in-time trajectory
(FITT/BITT) modeling of particles and organisms in the coastal ocean,
J. Atmos. Oceanic Technol., 23, 727-741.
Bricker, S. B., Rice, K. C., Bricker III, O. P. (2014). From headwaters
to coast: influence of human activities on water quality of the Potomac
River Estuary, Aquatic Geochemistry, 20, 291-323
Cheng, R. T., Casulli, V., Milford, S. N. (1984). Eulerian-Lagrangian
solution of the convection-dispersion equation in natural coordinates,
Water Resources Res., 20(7), 944-952.
Chu, W. S., Liou, J. Y., Flenniken, K. D. (1989). Numerical modeling
of tide and current in Central Puget Sound: Comparison of a three-
dimensional and a depth-averaged model, Water Resources Research,
25(4), 721-734.
Chang, Y., Li, H. C., Yang, R. Y. (2011). The preliminary study on
the feasibility of water clarification and CO 2 storage by cultured oyster,
Proc. Twenty-First (2011) International Offshore and Polar Engineer-
ing, Maui, Hawaii, USA, June 19-24
Chang, Y. (2009). The development of using hydro-acoustic technique
to measure oyster larvae swimming ability, The 3rd International Oyster
Symposium(IOS3), Taipei, Taiwan, Nov. 2-4
Canu, D. M., Solidoro, C., Umgiesser, G., Cucco, A., Ferrarin, C. (2012).
Assessing confinement in coastal lagoons, Marine Pollution Bulletin,
64(11), 2391-2398
Cucco, A., Umgiesser, G., Ferrarin, C., Perilli, A., Canu, D. M., Solidoro,
C. (2009). Eulerian and lagrangian transport time scales of a tidal active
coastal basin, Ecological modeling, 220, 913-922
Darmofal, D. L., Haimes, R. (1996). An analysis of 3D particle path
integration algorithms, J. Computational Phyics, 123, 182-195
Davis, H. C. (1958). Survival and growth of clam and oyster larvae at
different salinities, Biological Bulletin, 114(3), 296-307
Dove, M. C., O’Connor, W. A. (2007). Salinity and temperature toler-
ance of Sydney rock oysters Saccostrea glomerata during early ontogeny,
J. Shellfish Res., 26, 939-947
Delhez, É. J. M., Brye, B. d., Brauwere, A. d., Deleersnijder, É. (2014).
Residence time vs influence time, J. Marine System, 132, 185-195
Elder, J. W.(1959). The dispersion of marked fluid in turbulent shear
flow, J. Fluid Mech., 5(4), 544-560.
Edwards, K. P., Hare, J. A., Werner, F. E., Seim, H. (2007). Using
2-dimensional dispersal kernels to identify the dominant influences on
larval dispersal on continental shelves, Marine Ecology Progress Series,
352, 77-87.
Fischer, H. B. (1973). Longitudinal dispersion and turbulent mixing in
open channel flow, Annual Review of Fluid Mechanics, 5, 59-78.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., Brooks, N. H.
(1979). Mixing in inland and coastal waters, Academic Press, New York.
García-Martínez, R., Flores-Tovar, H., 1999. Computer modeling of oil
spill trajectories with a hight accuracy method. Spill Science and Tech-
nology Bulletin, 5(5/6), 323-330.
de Graaf, M., Jager, Z., Vreugdenhil, C. B., Elorche, M. (2004). Numer-
ical simulations of tidally cued vertical migrations of flatfish larvae in
the North Sea, Estuarine, Coastal and Shelf Science, 59(2), 295-305
Hidu, H., Haskin, H. H. (1978). Swimming speeds of oyster larvae Cras-
sostrea virginica in different salinities and temperatures, Estuaries, 1,
252-255
Horn, H. S. (1966). Measurement of "overlap" in comparative ecological
studies, The American Naturalist, 100(94), 419-424.
Hill, A. E. (1991). Vertical migration in tidal currents, Marine Ecology
Progress Series, 75, 39-54
Haase, A. T., Eggleston, D. B., Luettich, R. A., Weaver, R. J., Puckett,
B. J. (2012). Estuarine circulation and predicted oyster larval dispersal
among a network of reserves, Estuarine, Coastal and Shelf Science, 101,
33-43
His, E., Robert, R., Dinet A. (1989). Combined effects oftemperature and
salinity on fed and starved larvae ofthe Mediterranean mussel Mytilus
galloprovincialis and the Japanese oyster Crassostrea gigas, Marine Bi-
ology, 100, 455-463
Hofmann, E. E., Powell, E. N., Bochenek, E. K., Klinck, J. M. (2004).
A modeling study of the influence of environment and food supply on
survival of Crassostrea gigas larvae, J. Marine Science, 61, 596-616
Isobe, A. Kako, S., Chang, P. H., Matsuno, T. (2009). Two-way particle-
tracking model for specifying sources of drifting objects: application
to the East China Sea Shelf, J. Atmospheric and Oceanic Technology,
26(8), 1672-1682
Jouon, A., Douillet, P., Ouillon, S., Fraunié, P. (2006). Calculations of
hydrodynamic time parameters in a semi-opened coastal zone using a 3D
hydrodynamic mode, Continental Shelf Research, 26(12-13), 1395-1415
Komar, P. D. (1998). Beach processes and sedimentation, 2nd Edition,
Prentice-Hall, Upper Saddle River, New Jersery
Kowalik, Z., Murty, T. S., (1993). Numerical modeling of ocean dynam-
ics, Advanced series on ocean engineering
Kininmonth, S., Beger, M., Bode, M., Peterson, E., Adams, V. M.,
Dorfman, D., Brumbaugh, D. R., Possingham, H. P. (2011). Dispersal
connectivity and reserve selection for marine conservation, Ecological
Modelling, 222(7), 1272-1282
Kim, C. K., Park, K., Powers, S. P., Graham, W. M. (2010). Oyster
larval transport in coastal Alabama: Dominance of physical transport
over biological behavior in a shallow estuary, J. Geophysical Res., 115,
C10019
Lin, T. C., Liou, J. Y., Chang, Y. H., Chiang, W. S., Hsiao, S. C., Hsieh,
C. M. (2013). A numerical study on passive water particle transport in
Zhoushei estuary, Taiwan, Proc. 2013 IAHR World Congre., Sep. 8-13,
Chengdu, China
Liou, J. Y. (1996). Numerical modeling water quality in Tamshui coastal
area, Proc. 18th Conf. on Ocean Engineering, 467-478 (in Chinese)
Longuet-Higgins, M. S., Stewart, R. W. (1964). Radiation stress in water
waves: a physical discussion with application, Deep-Sea Research, 11,
529-562.
Longuet-Higgins, M. S. (1970). Longshore currents generated by
obliquely incident sea waves, J. Geophy. Res., 75, 6778-6801.
Leendertse, J. J. (1970). Water quality model for well-mixed estuaries
and coastal seas, Principles of Computation, Rep. RM-6230-RC, The
RAND Corporation, Santa Monica, Calif.
Leendertse, J. J., Liu, S.-K. (1977). A three-dimensional model for es-
tuaries and coastal seas, Turbulent Energy Computation, Rep. R- 2187-
OWRT, The RAND Corporation, Santa Monica, Calif.
Leendertse, J. J., Alexander, R. C., Liu, S.-K. (1973). A three-
dimensional model for estuaries and coastal seas, Principles of Com-
putation, Rep. R-1417-OWRR, The RAND Corporation, Santa Monica,
Calif.
Leendertse, J. J. (1967). Aspects of a computational model for long
period water-wave propagation, RM5294-PR, The RAND Corporation,
Santa Monica, Calif.
Li, M., Zhong, L., Boicourt, W. C. (2005). Simulations of Chesapeake
Bay estuary: sensitivity to turbulence mixing parameterizations and
comparison with observations, J. Geophysical Research, 110, C12004.
Lin, H.-J., Shao, K.-T., Hsieh, H.-L. Lo, W.-T. Dai, X.-X. (2009). The
effects of system-scale removal of oyster racks from Tapong Bay, south-
western Taiwan: model exploration and comparison with field observa-
tions, ICES J. Marine Science, 66(5), 797-810
Land, L. S. (2014). Oysters’ impact on water quality in the Potomac
River estuary, Aquatic Geochemistry, 20(5), 465-466
Ma, G., Shi, F., Liu, S., Qi, D. (2011). Hydrodynamic modeling of
Changjiang estuary: Model skill assessment and large-scale structure
impacts, Applied Ocean Research, 33, 69-78.
Miyake, Y., Kimura, S., Itoh, S., Chow, S., Murakami, K., Katayama, S.,
Takeshige, A., Nakata, H. (2015). Roles of vertical behavior in the open-
ocean migration of teleplanic larvae: a modeling approach to the larval
transport of Japanese spiny lobster, Marine Ecology Progress Series,
539, 93-109
Metaxas, A., Megan, S. (2009). Quantifying the "Bio-" Components in
Biophysical Models of Larval Transport in Marine Benthic Invertebrates:
Advances and Pitfalls, Biological Bulletin, 216(3), 257-272.
Monsen, N. E., Cloern, J. E., Lucas, L. V. (2002). A comment on the
use of flushing time, residence time and age as transport time scales,
Limnology and Oceanography, 47(5), 1545-1553.
Murman, E. M., Powell, K. G. (1989). Trajectory integration in vortical
flows, AIAA J., 27(7), 982-984.
Newell, R. I. E., Kennedy, V. S., Manuel, J. L., Meritt, D. (2005). Behav-
ioral responses of Crassostrea ariakensis and Crassostrea virginica larvae
to environmental change under spatially realistic conditions, Final report
to Maryland and Department of Natural Resources, May 2005
Nielsen, P. (2009). Coastal and Estuarine Processes, Advanced series on
ocean engineering, World Scientific
Narváez, D. A., Klinck, J. M., Powell, E. N., Hofmann, E. E., Wilkin,
J., Haidvogel, D. B. (2012). Modeling the dispersal of eastern oyster
(Crassostrea virginica) larvae in Delaware Bay, J. Marine Research, 70,
381-409
North, E. W., Hood, R. R., Chao, S. Y., Sanford, L. P. (2006). Us-
ing a random displacement model to simulate turbulent particle motion
in a baroclinic frontal zone: A new implementation scheme and model
performance, J. Mar. Syst., 60, 365-380
North, E. W., Schlag, Z., Hood, R. R., Li, M., Zhong, L., Gross, T.,
Kennedy, V. S. (2008). Vertical swimming behavior influences the dis-
persal of simulated oyster larvae in a coupled particle-tracking and hy-
drodynamic model of Chesapeake Bay, Mar. Eco. Pro. Ser., 359, 99-115
O’Connor, S., Moltschaniwskyj, N., Bolch, C. J. S., O’Connor, W.
(2015). Assessment of temperature or salinity effects onlarval develop-
ment by catecholamine-inducedmetamorphosis of hatchery-reared at oys-
ter, Ostreaangasi (Sowerby 1871) larvae, Aquaculture Res., 46, 2501-2511
Qin C., Robert, A. D., James T. K., Andrew, B. K., Merrick C. H.
(1999). Boussinesq modeling of a rip current system, J. Geophysical Re-
search, 104, C9, 20617-20637
Salamon, P., Fernàndez-Garcia, D., Jaime, Gómez-Hernandez, J. (2006).
A review and numerical assessment of the random walk particle tracking
method, J. Contaminant Hyd., 87, 277-305.
Seliger, H. H., Boggs, J. A., Rivkin, R. B., Biggley, W. H., Aspden, K. R.
H. (1982). The transport of oyster larvae in an estuary, Maine Biology,
71, 57-72.
Simons, R. D., Siegel, D. A., Brown, K. S. (2013). Model sensitivity
and robustness in the estimation of larval transport: A study of particle
tracking parameters, J. Marine System, 119-120, 19-29.
Sundelöf, A., Jonsson, P. R. (2012). Larval dispersal and vertical mi-
gration behavior-a simulation study for short dispersal times, Marine
Ecology, 33, 183-193
Sheng, Y. P., Liu, T. (2011). Three-dimensional simulation of wave-
induced circulation: comparison of three radiation stress formulations,
J. Geophysical Research, 116, C05021
Savina, M., Lacroix, G., Ruddick, K. (2010). Modelling the transport of
common sole larvae in the southern North Sea: Influence of hydrody-
namics and larval vertical movements, J. Marine Systems, 81, 86-98
Thomas, Y., Dumas, F., Andréfoët, S. (2014). Larval dispersal modeling
of Peral Oyster (Pinctada margaritifera) following realistic environmen-
tal and biological forcing in Ahe Atoll lagoon, PLOS one, 9(4), e95050
Thomann, R. V., Mueller, J. A. (1987). Principles of Surface Water
Quality Modeling and Control, Harper & Row, Publishers, New York.
Vaschenko, M. A., Hsieh, H.-L., Radashevsky, V. I. (2013). Gonadal state
of the oyster Crassostera Angulata Cultivated in Taiwan, J. Shellfish
Res., 32(2), 471-482.
Weare, T. J. (1979). Errors arising from irregular boundaries in ADI
solutions of the shallow-water equations, Int. J. Num. Meth. Eng., 14,
921-931
Wilmott, C.J., (1981). On the validation of models. Physical Geography,
2(2), 184194.
Wilson, C., Scotto, L., Scarpa, J., Volety, A., Laramore, S., Haunert, D.
(2005). Survey of water quality, oyster reproduction and oyster health
status in the ST. Lucie estuary, J. Shellfish Res., 24(1), 157-165
Zimmerman, K. M., Pechenik, J. A. (1991). How do termperature and
salinity affect relative rates of growth, morphological differentiation, and
time to metamorphic competence in larvae of the marine gastropod
Crepidula plana, Biological Bulletin, 180, 372-386.
Zimmerman, J. T. F. (1976). Mixing and flushing of tidal embayments
in the western Dutch Wadden Sea. Part I: Distribution of salinity and
calculation of mixing time scales, Netherlands J. Sea Research, 10(2),
149-191.