## 5 Examples of Forward-Inverse Modeling
### Sunglint: A Nuisance or Can Can It Be Used to Our Advantage? For clarity, we should note that \"glint\" here refers only to Fresnel reflectance from the (calm or \"wind-roughened\") water surface. In the presence of glint, satellite remote sensing remains a challenging problem [97]. The contribution from glint to the TOA radiance is large enough to dominate the signals received by sensors deployed in space. Algorithms developed for current satellite sensors such as the Sea-viewing Wide Field of view Sensor (SeaWiFS), the MODerate-resolution Imaging Spectroradiometer (MODIS), the MEdium Resolution Imaging Spectrometer (MERIS), the Polarization and Directionality of Earth Reflectances (POLDER) instrument, and the Global Imager (GLI), use different correction algorithms [77; 98; 99] based on the same principle: estimate the glint contribution inferred from a statistical glint model and a direct beam reflectance and then remove its contribution from the signal received by the sensor. To analyze remotely sensed radiances obtained by instruments such as SeaWiFS, MODIS, and MERIS, NASA has developed a comprehensive data analysis software package (SeaWiFS Data Analysis System, SeaDAS), which performs several tasks, including cloud screening and calibration, required to convert the raw satellite signals into calibrated TOA radiances. The SeaDAS software package also has tools aimed at quantifying and removing the atmospheric contribution to the TOA radiance (atmospheric correction) as well as contributions from whitecaps and sunlight due to reflections from the ocean surface [81]. In the SeaDAS algorithm (and similar algorithms) a sunlight flag is activated to mask out pixels for which the reflectance or BRDF, exceeds a certain threshold. If the reflectance for a given pixel is above the threshold, the signal is not processed. If the reflectance is below the threshold, a directly transmitted radiance (DTR) approach is used to calculate the TOA sunlight radiance in the SeaDAS algorithm. Thus, it is computed assuming that the direct beam and its reflected portion only experience exponential attenuation through the atmosphere [77], that is  
\[I_{\text{glint}}^{\text{TOA}}(\mu_{0},\mu,\Delta\phi)=F_{0}(\lambda)T_{0}( \lambda)T(\lambda)I_{\text{GN}} \tag{152}\]\[T_{0}(\lambda)T(\lambda)=\exp\Big{\{}-[\tau_{M}(\lambda)+\tau_{A}(\lambda)]\Big{(} \frac{1}{\mu_{0}}+\frac{1}{\mu}\Big{)}\Big{\}} \tag{153}\]  
where \(\mu_{0}\) and \(\mu\) are cosines of the solar zenith angle and polar viewing angle, respectively, and the normalized sunlight radiance \(I_{GN}\) is the radiance that would result for a transparent atmosphere if the incident solar irradiance were \(F_{0}(\lambda)=1\). The Rayleigh (molecular) and aerosol optical thicknesses are denoted \(\tau_{M}(\lambda)\) and \(\tau_{A}(\lambda)\), respectively. The downward diffuse incident light (sunlight being multiply scattered by atmospheric molecules and aerosols before hitting the rough sea surface) also contributes to the upward reflectance. In the SeaDAS algorithm, such diffuse light reflectance that accounts for the effect of ocean surface roughness has been included only in the Rayleigh lookup tables [100]. Radiative transfer (RT) simulations may provide a more complete look at the glint problem [87]. An RT model can be used for accurate quantification of contributions not only from direct sunlight, but also from skygint due to multiply scattered light [101]. Hence, RT simulations can be used to test current correction methods and explore the potential for extending remote sensing into strong glint situations masked out by the current SeaDAS algorithm. As alluded to in Section 4.1.3, plane parallel RT models assume that the BRDF depends only on the difference in azimuth between the sun-sensor directions. Therefore, they are intrinsically one-dimensional, and cannot be used to simulate the directional dependence of realistic slope distributions that require a wind-direction dependent (hereafter referred to as 2D BRDF) treatment.