傳統上，水庫的水質監測方法主要是在少數的特定點進行量測，相當地耗時費力。如果能夠藉由遙測的手段進行水質監測，就能即時地掌握水庫的水質概況。然而，欲連結遙測資料與水質，必須先建立水中物質與相對應的光學性質之關係。要得到單一水質參數 對光學訊號的影響，可在實驗室進行水槽試驗，控制不同的水質參數。吾人藉由前向蒙地卡羅光束追蹤法(Forward Monte Carlo ray-tracing technique, FMCR)模擬水槽中的輻射傳輸過程，以模擬遙測儀器所測量的光學訊號。藉由此模式的模擬，可以發現固有光學性質(IOP)與外顯光學性質(AOP)之間的量化關係。
根據前人研究(Liu and Woods, 2004)，FMCR的概念為，將光束分為大量的光子，依據大量亂數以及各種現象的發生機率決定光子在水體中的行進路徑，最後得到的光場分布即為所有光子的整體貢獻。此模式的模擬條件為，邊界均為朗伯表面(Lambertian surfaces)的正立方體水槽，單一光源放置於水槽上方，感測器可放置在水槽的任意位置。模式可任意指定水體的IOP參數。
吾人從無限深到有限深度的水體條件下，使用軟體Hydrolight驗證FMCR模式。加上水槽的側向邊界後，從模擬結果可以發現，調整模式參數後，將側向邊界設置在離光源較遠的距離，感測器放置在固定的位置，將邊界距離逐漸縮小，則感測器所偵測到的輻射量會逐漸增加。
本研究調整模擬參數後，可得到輻射值變化的合理趨勢，例如：在較高的單一散射反照率以及邊界反射率的模擬條件下，感測器接收的輻射量較大。藉由FMCR模式可有系統地大量產生IOP與AOP的對照表，藉由此對照表可將量測的AOP得到相對應的IOP資訊。

The general approach of monitoring the water quality in a reservoir relies on the point measurements made at ground stations, which is both time and labor consuming. Employing the technique of remote sensing, by contrast, would enable us to acquire a near-real-time and synoptic view of the entire reservoir. To relate the remote sensing data to the water quality, however, we need to establish the relationship between the water constituents and various optical properties. This can be investigated in a water tank with detailed measurements of optical properties for various water samples of controlled constituents. By employing the forward Monte Carlo ray-tracing (FMCR) technique to simulate the radiative transfer process in a water tank, we attempt to establish a quantitative relationship between the Inherent Optical Properties (IOP) and the Apparent Optical Properties (AOP).
As described in the earlier work by Liu and Woods (2004), the basic principle of our FMCR model is to simulate a beam of light by a very large number of photons. Following the path of each photon, we can use a series of random numbers to determine the photon’s life history according to different probabilities for different phenomena. The final light field is the cumulative contribution of total photons. The water tank is a cubic box with Lambertian surfaces. One unit light comes from the top of the box and the detectors can be deployed at any place in the box to collect photons. For each simulation, the IOPs are specified by various constituent-optical models.
We carefully validate our FMCR model against the commercial Hydrolight model for the case of infinitely deep bottom and the case of one-dimensional parallel bottom. The results verify the simulation of interaction between the photon and the Lambertian surface. After adding the walls of the box, the light near eight corners of the box is apparently brighter than the one simulated in the case without walls. This phenomenon is further enhanced as the size of box is reduced.
From simulations of model, there are some reasonable phenomenons we could discover, like high single scattering albedo or high reflectance will lead to high radiance. This FMCR model can be employed to systematically investigate the relationship between IOPs and AOPs by running a comprehensive FMCR simulation to generate a look-up-table (LUT). This LUT would assist us to derive the IOPs directly from the measurements of AOPs in the future.

Bannister, T. T., EMPIRICAL EQUATIONS RELATING SCALAR IRRADIANCE TO A, B/A, AND SOLAR ZENITH ANGLE, Limnology and Oceanography, 35(1), 173-177. (1990)
Bielajew, A. F., Advanced Monte Carlo for radiation physics, particle transport simulation, and applications :proceedings of the Monte Carlo 2000 Conference, Lisbon, 23-26 October 2000, Springer, Berlin, 1-6. (2001)
Buiteveld, H., et al. (1994), Optical properties of pure water, paper presented at Ocean Optics XII, SPIE, Bergen, Norway.
Bukata, R. P., Optical properties and remote sensing of inland and coastal waters, CRC Press, Boca Raton, 103. (1995)
Carder, K., Illumination and turbidity effects on observing faceted bottom elements with uniform Lambertian albedos, Limnology and Oceanography, 48(1), 355. (2003)
Chang, C. H., et al., Integrating semianalytical and genetic algorithms to retrieve the constituents of water bodies from remote sensing of ocean color, Opt. Express, 15(2), 252-265. (2007)
Dadson, S. J., et al., Links between erosion, runoff variability and seismicity in the Taiwan orogen, Nature, 426(6967), 648-651. (2003)
Dekker, A. G., and H. J. Hoogenboom, The remote sensing of inland water quality., John Wiley & Sons Ltd., New York, 123-142. (1995)
Gordon, H. R., Modeling and Simulating Radiative Transfer in the Ocean, Ocean Optics, 3-39. (1994)
Haltrin, V. I., Monte Carlo modeling of light field parameters in ocean with Petzold laws of scattering, Proceedings of the Fourth International Conference Remote Sensing for Marine and Coastal Environments: Technology and Applications, I, 503-508. (1997)
Han, L., Spectral Reflection with Varying Suspended Sediment Concentrations in Clear and Algae-Laden Waters, Photogrammetric Engineering & Remote Sensing, 63, 701-705. (1997)
Karabulut, M., and N. Ceylan, The Spectral Reflectance Responses of Water with Different Levels of Suspended Sediment in The Presence of Algae, Turkish J. Eng. Env. Sci., 29, 351-360. (2005)
Kirk, J. T. O., Monte Carlo procedure for simulating the penetration of light into natural waters, Division of Plant Industry, CSIRO, P. O. Box 1600, Canberra City, A.C.T. 2601. (1981)
Lee, Z. P., et al., Remote Sensing of Inherent Optical properties: Fundamentals, Tests of Algorithms and Applications, IOCCG, Canada, 105-110. (2006)
Liu, C. C., and J. D. Woods, Prediction of ocean colour: Monte Carlo simulation applied to a virtual ecosystem based on the Lagrangian Ensemble method, Int. J. Remote Sens., 25(5), 921-936. (2004)
Mobley, C. D., A NUMERICAL-MODEL FOR THE COMPUTATION OF RADIANCE DISTRIBUTIONS IN NATURAL-WATERS WITH WIND-ROUGHENED SURFACES, Limnology and Oceanography, 34(8), 1473-1483. (1989)
Mobley, C. D., Light and Water, Academic Press, Inc, California. (1994)
Orlov, M. Y., et al., Monte-Carlo calculation of the gamma-ray dose distribution inside a wall of a building and in air, Atomic Energy, 94(6), 428-433. (2003)
Ostlund, C., et al., Mapping of the water quality of Lake Erken, Sweden, from Imaging Spectrometry and Landsat Thematic Mapper, Science of the Total Environment, 268(1-3), 139-154. (2001)
Oyama, Y., et al., A new algorithm for estimating chlorophyll-a concentration from multi-spectral satellite data in case II waters: a simulation based on a controlled laboratory experiment, Int. J. Remote Sens., 28(7-8), 1437-1453. (2007)
Petzold, T. J., Volume Scattering Functions for Selected Ocean Waters, Light in the Sea, 152–174. (1977)
Plass, G. N., and G. W. Kattawar, Monte Carlo Calculations of Light Scattering from Clouds, Appl. Opt., 7(3), 415-419. (1968)
Plass, G. N., and G. W. Kattawar, Radiative Transfer in an Atmosphere-Ocean System, Appl. Opt., 8(2), 455-466. (1969)
Plass, G. N., and G. W. Kattawar, Radiance and Polarization of the Earth's Atmosphere with Haze and Clouds, Journal of the Atmospheric Sciences, 28(7), 1187-1198. (1971)
Plass, G. N., and G. W. Kattawar, Monte Carlo Calculations of Radiative Transfer in the Earth's Atmosphere-Ocean System: I. Flux in the Atmosphere and Ocean, Journal of Physical Oceanography, 2(2), 139-145. (1972)
Pope, R. M., and E. S. Fry, Absorption spectrum (380-700 nm) of pure water .2. Integrating cavity measurements, Applied Optics, 36(33), 8710-8723. (1997)
Press, W. H., et al., Numerical Recipes in C++: The Art of Scientific Computing, Cambridge University Press, United States of America,278-320. (2002)
Robinson., I. S., Satellite oceanography :an introduction for oceanographers and remote-sensing scientists, Chichester, West Sussex, England ;Halsted Press, New York, 22.(1985)
Sathe, P. V., and S. Sathyendranath, A FORTRAN-77 PROGRAM FOR MONTE-CARLO SIMULATION OF UPWELLING LIGHT FROM THE SEA, Computers & Geosciences, 18(5), 487-507. (1992)
Sathyendranath, S., et al., Remote Sensing of Ocean Colour in Coastal, and Other Optically-Complex, Waters., IOCCG, Canada, 23. (2000)
Sears, F. W., Principles of Physics: 3. Optics, Addison-Wesley, Cambridge, Mass,167-176. (1949)
Tolk, B. L., Han, L. , and Rundquist, D. C. , The impact of bottom brightness on spectral reflectance of suspended sediments, INT. J. REMOTE SENSING, 21, 2259-2268. (2000)
Tyler, J. E., Radiance distribution as a function of depth in an underwater environment, Bull. Scripp. Inst. Oceanogr., 7(5), 363-412. (1960)
Zhai, P. W., et al., Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method, Appl. Opt., 47(8), 1037-1047. (2008)
王奕婷, 流體在微渠道流動之數值模擬, 國立中山大學機械與機電工程學系研究所. (2002)
李三畏, 集水區的經營治理, 中興工程基金會, 頁13. (2005)
金紹興.虞國興, 永續水資源, 中興工程基金會. (2005)
紀金輝, 蒙地卡羅方法於臨床光子射束劑量分佈研究, 中台醫護技術學院放射科學研究所. (2007)
黃慶祥, 水庫水質與光學性質模式之建立及其應用, 國立成功大學環境工程學系. (2006)
經濟部水利署 (2006), 水資源供需情勢統計調查方式改善與彙編 94-96 年各項用水統計報告(2/3)總報告.
廖福全.趙家民, 桃園地區水資源異常之供水因應策略, 空大學訊. (2007)
潘國樑, 遙測學大綱, 成陽出版股份有限公司, 頁7. (2006)
蔡在宗., 含砂水體反射率峰值對應波長偏移現象研究, 成功大學碩士論文. (2007)
韓震.惲才興.蔣雪中, 懸浮泥沙反射光譜特性實驗研究, 水利學報, 第七期, 頁118-122. (2003)