# A New Algorithm for Simultaneous Retrieval of Aerosols and Marine Parameters
## 3 Results and Discussion
Figure 7 shows a comparison between input values and retrieved values for the aerosol volume fraction with correlation coefficients of 0.97, 0.87, 0.92, and 0.92 for SZAs of 45\({}^{\circ}\), 53\({}^{\circ}\), 63\({}^{\circ}\), and 75\({}^{\circ}\), respectively. For all values of the SZA, the retrieval algorithm is seen to accurately predict the aerosol volume fraction. Figure 8 shows the effect of the SZA on the TOA radiance contribution from the ocean. The ratio between the average total TOA radiance and the average TOA radiance contribution from the ocean is seen to increase significantly (note the logarithmic scale on the vertical axis in Figure 8) with increasing SZA, implying that the oceanic contribution to the TOA radiance is reduced as the SZA is increased. This may explain why the accuracy \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Testing Data Set**} & \multicolumn{4}{c}{**Training Data Set**} \\ \hline  & \multicolumn{4}{c}{**Solar Zenith Angle**} & \\ \hline Retrieved Parameter & 45\({}^{\circ}\) & 53\({}^{\circ}\) & 63\({}^{\circ}\) & 75\({}^{\circ}\) & 45\({}^{\circ}\) & 53\({}^{\circ}\) & 63\({}^{\circ}\) & 75\({}^{\circ}\) \\ \hline CDOM & 0.97 & 0.82 & 0.72 & 0.64 & 1.00 & 0.80 & 0.97 & 0.84 \\ Chlorophyll Concentration & 0.98 & 0.78 & 0.82 & 0.73 & 1.00 & 0.95 & 0.99 & 0.97 \\ Mineral Concentration & 1.00 & 0.94 & 0.93 & 0.96 & 1.00 & 0.67 & 0.96 & 0.87 \\ Aerosol fine-mode fraction & 0.82 & 0.67 & 0.93 & 0.91 & 1.00 & 0.98 & 1.00 & 1.00 \\ Aerosol volume fraction & 0.97 & 0.87 & 0.92 & 0.92 & 0.99 & 0.82 & 0.97 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients between input parameters and retrieved parameters for different solar zenith angles in absence of noise. Figure 3: Comparison between input values and retrieved values for the CDOM absorption coefficient at 443 nm for different solar zenith angles (SZAs). of the retrieved ocean parameters (CDOM absorption and chlorophyll concentration) in Figures 3 and 4 reduced as the SZA is increased. Figure 4: Comparison between input values and retrieved values for the chlorophyll concentration for different solar zenith angles (SZAs). Figure 5: Comparison between input values and retrieved values for the mineral concentration for different solar zenith angles (SZAs). To test for robustness of the retrieval algorithm we introduced white Gaussian noise in all eight TOA radiance channels using the MATLAB function \(awgn(X,SNR)\), where \(X\) is the vector signal and SNR is the signal-to-noise-ratio. Figure 9a-e show how the algorithm predicts CDOM absorption, chlorophyll concentration, mineral concentration, aerosol volume fraction, and volume fraction of fine-mode aerosol particles for four different values of the SZA and the SNR. As discussed earlier, we first generated 10,000 randomly distributed sets of the five input parameters. Then we used a well-tested forward RTM to compute TOA radiances for eight of the MODIS channels for each of the 10,000 sets of input parameters for training (90%) and validation (10%) of a RBF-NN. To speed up the inversion, we used TOA radiances predicted by the RBF-NN as input to the retrieval algorithm, which was based on fminsearch. We then added varying amounts of white Gaussian noise to the TOA radiances before starting the retrieval without re-training the RBF-NN. Figure 9a,b show how the algorithm retrieves the CDOM absorption coefficient at 443 nm and the chlorophyll concentration, respectively, for varying values of the SNR and four different SZA values. It is clearly seen that for low noise the algorithm retrieves the two parameters very well and that the performance decreases as one increases the SZA and the noise level. Figure 6: Comparison between input values and retrieved values for the volume fraction of fine-mode aerosol particles for different solar zenith angles (SZAs).