Volume 1 Issue 3 - September 7, 2007
Fast calculation of underwater light field using the radiative transfer model
Cheng-Chien Liu / Institute of Satellite Informatics and Earth Environment, Department of Earth Science, National Cheng-Kung University
Email: ccliu88@mail.ncku.edu.tw

Optics Express 2006, 14(5), pp. 1703-1719.
Fig. 1. Twenty cases of stratified Case 2 waters with vertical profiles of (a) Chl, (b) ag,440 and (c) M. The corresponding profiles of IOPs at wavelength 440 nm are illustrated as (d) a, (e) b and (f) BFp. Source: Liu, C.-C. (2006) Fast and accurate model of underwater scalar irradiance for stratified Case 2 waters. Optics Express, 14(5), pp. 1703-1719.
Sunlight is the main source of natural energy that heats the seawater and causes the vertical convection. It is also responsible for many permanent currents of the ocean, such as the thermohaline circulation. This can be reflected in the diurnal and annual variations of the mixed layer depth. In the sea, photosynthesis is a process by which phytoplankton traps light energy and use it to drive a series of chemical reactions, leading to the formation of carbohydrates. The availability of light at various depths is crucial for this process. The phenomena of diel and seasonal vertical migration of zooplankton are also related to the underwater visibility. Modelers of oceanic system, such as the ocean circulations and the biogeochemical cycles, had been long aware of the significance of light. Furthermore, it is the radiative signal that is detected by most of the sensors used for observing the plankton ecosystem, such as fluorimeters and satellite ocean colour sensors. Therefore, understanding how sunlight interacts with the ocean and distributes below the sea surface is one of the important research topics in oceanography.

The underwater light field was usually described as a function attenuated with depth exponentially. Various empirical models based on some empirical relationships derived from regression analysis on large biooptical data sets. The limitation and possible errors of using the empirical approach have been recognized. For instance, Fasham et al. did a series of sensitivity analyses on various parameters in developing their FDM plankton ecosystem model. They found that the annual primary production was very sensitive to the choice of the attenuation coefficient. Altering the water attenuation coefficient from 0.04 to a lower value of 0.038 results in 160% decrease in annual net primary production. Therefore, they concluded that underwater irradiance distribution is one of the most critical parameters for modelling the plankton ecosystem, and they suggested that it was worth using more complicated light models to simulate the underwater light field.

Many efforts were spent over the past two decades to advance the theorem and numerical model of radiative transfer. Mobley et al. made a comprehensive comparison of various radiative transfer models (RTM). They concluded that these models enable a realistic simulation of underwater light field, such as the physical processes of absorption, scattering, reflection, multiple scattering and Raman scattering, as well as the biological processes of fluorescence and bioluminescence. Although the RTMs are more accurate than the empirical models, the impractical requirement of computational resource prohibits any attempt to embed the accurate RTM in any oceanic models.

This research successfully developed a new RTM that is as accurate as the most advanced and commercially-available model (Hydrolight), yet runs much faster than the full Hydrolight code. Five strategies are formulated and employed in the new model, including (1) reallocating the sky radiance, (2) approximating the influence of the air-water interface, (3) constructing a look-up table of average cosine based on the single-scattering albedo and the backscatter fraction, (4) calculating the phase function of surrogate particles in Case 2 waters, and (5) using the average cosine as an index to cope with stratified waters. A comprehensive model-to-model comparison was made to examine the accuracy, flexibility and applicability of the new model that includes all the aforementioned strategies. A total of 20 cases of Case II waters were compared by randomly specifying values to parameters, including the solar zenith angle, cloudiness, surface wind speed, the backscattering fraction for large and mineral particles, as well as the vertical profiles of chlorophyll, mineral particle and color dissolved organic matter concentrations, as illustrated in Figure 1. For each of the 20 cases described above, the vertical profiles of wavelength-integrated scalar irradiance ranged from 350 to 700 nm E0,PAR(z) were simulated by use of Hydrolight model and the new model developed in this work, respectively, as illustrated in Figure 2. The result shows that the new model runs more than 1,400 times faster than the commercially- available Hydrolight model, while it limits the percentage error to 2.03% and the maximum error to less than 6.81%. This new model can be used interactively in models of the oceanic system, such as biogeochemical models or the heat budget part of global circulation models.
Fig. 2. Comparison of accuracy and speed in simulating E0,PAR(z) (W m-2) between the new model and Hydrolight. A very high correlation (r = 0.999924) as well as a large CSR of 1402.8 was obtained for our model. The percentage error % is 2.03% and the maximum relative error max is not more than 6.81%. Source: Liu, C.-C. (2006) Fast and accurate model of underwater scalar irradiance for stratified Case 2 waters. Optics Express, 14(5), pp. 1703-1719.

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