# A New Algorithm for Simultaneous Retrieval of Aerosols and Marine Parameters
## 3 Results and Discussion  
To validate the performance of our inverse algorithm described in Section 2.4, we compared the two aerosol and the three marine parameters that were used as inputs to the RTM for generating computed TOA radiances for the MODIS channels with the corresponding retrieved parameters. To test for robustness we considered two cases: (i) low and high sun without white Gaussian noise added to the computed TOA radiances and (ii) low and high sun with different levels of white noise added to the computed TOA radiances. In both cases, we used the RTM for computation of TOA radiances, and trained the RBF-NN separately for each SZA, and in the latter case, we added white Gaussian noise to the computed TOA radiances in order to check how much added white Gaussian noise the inverse algorithm would tolerate. All statistics about algorithm performance validation and robustness testing were conducted on testing data set. For each of the five input parameters, the correlation coefficient \(r_{j}\) (\(j=1,2,3,4,5\)) between input parameter number \(j\) and the corresponding retrieved parameter was computed using  
\[r_{j}=\frac{\sum_{i=1}^{M}(p_{j,i}^{s}-\overline{p_{j}^{s}})(p_{j,i}^{t}- \overline{p_{j}^{t}})}{\left[\sum_{i=1}^{M}\left(p_{j,i}^{s}-\overline{p_{j}^{ s}}\right)^{2}\sum_{i=1}^{M}\left(p_{j,i}^{t}-\overline{p_{j}^{t}}\right)^{2} \right]^{1/2}}, \tag{26}\]  
where \(p_{j,i}^{s}\) is the \(i^{th}\) data point for input parameter number \(j\) and \(p_{j,i}^{t}\) is the corresponding retrieved parameter, and \(M\) is the total number of data points, which is equal to the number of parameter sets used for validation, i.e., \(M=10,000\). The average values in Equation (26) are given by  
\[\overline{p_{j}^{s}}=\frac{1}{M}\sum_{i=1}^{M}p_{j,i}^{s}\ \ ;\ \ \overline{p_{j}^{t}}=\frac{1}{M}\sum_{i=1}^{M}p_{j,i}^{t}. \tag{27}\]  
At Rost local noon solar zenith angles (SZAs) of \(45^{\circ},53^{\circ},63^{\circ},\) and \(75^{\circ}\) correspond to the dates of 5 June, 1 May, 1 April, and 1 March, respectively. Table 2 shows correlation between input and retrieved parameters for different solar zenith angles, and different sets of data in absence of noise. The algorithm performed well in retrieving all the five parameters in both data sets in absence of noise. Figures 3-7 show comparisons between input parameters and retrieved parameters for different solar zenith angles, and the correlation coefficients are given in Table 2 under testing data set. Figure 3 shows a comparison between input values and retrieved values for the CDOM absorption coefficient for different SZAs. The correlation coefficients are 0.97, 0.82, 0.72, and 0.64 for SZAs of \(45^{\circ},53^{\circ},63^{\circ},\) and \(75^{\circ}\), respectively. Figure 4 shows a comparison between input values and retrieved values for the chlorophyll concentration with correlation coefficients of 0.98, 0.78, 0.82, and 0.73 for SZAs of \(45^{\circ},53^{\circ},63^{\circ},\) and \(75^{\circ}\), respectively. It follows that the chlorophyll concentration is retrieved well, both for low and high sun. Figure 5 shows a comparison between input values and retrieved values for the mineral concentration. The correlation coefficients between input values and retrieved values are 1.00, 0.94, 0.93, and 0.96 for SZAs of 45\({}^{\circ}\), 53\({}^{\circ}\), 63\({}^{\circ}\), and 75\({}^{\circ}\), respectively. Thus, the mineral concentration is retrieved accurately, both for low and high sun. Figure 6 shows a comparison between input and retrieved values for the volume fraction of fine-mode aerosol particles, where the correlation coefficients between input and retrieved values are 0.82, 0.67, 0.93, and 0.91 for SZAs of 45\({}^{\circ}\), 53\({}^{\circ}\), 63\({}^{\circ}\), and 75\({}^{\circ}\), respectively. For all four values of the SZA, we see that the retrieval algorithm predicts the volume fraction of fine-mode aerosol particles very well.