## 5 Examples of Forward-Inverse Modeling
### Atmospheric Input & Output
#### 5.3.4 Summary of Glint Issues  
The results discussed above may be summarized as follows:  
* A wind-direction dependent Gaussian surface BRDF that uses (1) a 2D slope distribution for singly scattered light, and (2) a 1D slope distribution for multiply scattered light, can be used to successfully simulate BRDF measurements obtained by NASA's Cloud Absorption Radiometer (CAR) at the 1036 nm wavelength. * Upwind and crosswind slope variances, wind direction, and aerosol optical depth, can be accurately retrieved through forward-inverse modeling. * The glint parameters (slope variances and wind direction) can be applied to estimate the glint contribution at visible and NIR wavelengths, resulting in a very good match between model-simulated and measured reflectances. * An advantage of RT simulations of glint reflectance is its inclusion of contributions from the diffuse or multiply scattered light due to scattering by atmospheric molecules and aerosols. The diffuse light reflectance (\"skyglint\") gives an additional glint signal in addition to \"sunglint\" resulting from the direct beam reflectance. * Simulations show that the diffuse glint may contribute more than 4% at 472 nm for a wind speed of 2 m/s, and more than 8% when the wind speed increases to 8 m/s. Hence, the diffuse light reflectance should be considered in the visible bands, especially for large wind speeds. Figure 4: Comparison between model-simulated reflectances assuming a 1D Gaussian BRDF (**left**), a 2D Gaussian BRDF (**middle**), and measurements (**right**) obtained on 10 July 2001. * A simplified version of the pseudo 2D BRDF and glint reflectance method described above has been implemented in the AccuRT model for the coupled atmosphere-ocean system. Retrievals of Atmosphere-Water Parameters from Geostationary Platforms: Challenges and Opportunities  
Simultaneous retrieval of aerosol and surface properties by means of inverse techniques based on a coupled atmosphere-surface radiative transfer model and optimal estimation can yield improved retrieval accuracy in complex aquatic environments compared with traditional methods. At high latitudes low solar elevations is a problem, and if one desires to do satellite remote sensing from a geostationary platform in order to study diurnal variations, then large solar zenith and viewing angles become important issues to be resolved. Satellite remote sensing for such complex situations/environments represents specific challenges due to:  
* (i) the complexity of the atmosphere and water inherent optical properties,
* (ii) the unique bidirectional dependence of the water-leaving radiance, and
* (iii) the desire to do retrievals for large solar zenith and viewing angles. Hence, one needs to consider challenges related to how  
1. atmospheric gaseous absorption, absorbing aerosols, and turbid waters can be addressed by using a _coupled_ forward model in the retrieval process,
2. corrections for _bidirectional effects_ will be accomplished,
3. the _curvature_ of the atmosphere will be taken into account, and
4. _uncertainty assessments_ and error budgets will be dealt with. The generic problem is illustrated in Figures 5 and 6, which show that  
* there is _a significant change_ in sub-surface color with increasing chlorophyll concentration, while at the same time
* there is _only a slight change_ in color at the TOA, where _the spectra are dominated by light from atmospheric scattering_. Figure 5: Simulated upward radiance in the nadir direction at the top of the atmosphere and close to the ocean surface. Solar zenith angle = 45\({}^{\circ}\), US Standard atmosphere with aerosol optical depth = 0.23 at 500 nm. **(Left)** Clear water with chlorophyll concentration = 0.1 mg\(\cdot\)m\({}^{-3}\), MIN = 0.003 g\(\cdot\)m\({}^{-3}\), CDOM443 = 0.003 m\({}^{-1}\) (CCRR bio-optical model). **(Right)** Turbid water with chlorophyll concentration = 10 mg\(\cdot\)m\({}^{-3}\), MIN = 0.1 g\(\cdot\)m\({}^{-3}\), CDOM443 = 0.1 m\({}^{-1}\). Most ocean color algorithms consist of two steps:  
1.