## 3 Results and Discussion
### Algorithm Tuning and Validation  
#### 3.2.1 Algorithm Structures and Optimization  
Both empirical and semi-analytical approaches to ocean color retrievals of CDOM, \(S_{S}\), and DOC were explored using the GOCAD dataset. Of the former, a band ratio, single exponential decay model similar to that presented by [PERSON] (2008) was tested, but found to be better suited for the continental shelf waters for which it was derived rather than for the deep ocean, and will not be presented here. A multiple linear regression (MLR) approach was tested matching the natural logarithm of \(R_{rs}\) in four ocean color bands with the logarithm of \(a_{g}(\lambda)\) and \(S_{S}\) at each waveband described in Section 2.2.1, and DOC. The least square difference minimization regression, performed using Matlab's _regstats_ function (www.mathworks.com), follows the form:  
\[ \begin{array}{c}\ln(Y)=\beta_{0}+\beta_{1}\times\ln(R_{rs}(\lambda_{1}))+ \beta_{2}\times\ln(R_{rs}(\lambda_{2}))+\beta_{3}\times\ln(R_{rs}(\lambda_{3})) \\ \hskip 142.26378 pt+\beta_{4}\times\ln(R_{rs}(\lambda_{4}))\end{array}  \tag{8}\]  
where \(\beta_{0}\)-\(\beta_{4}\) are the regression coefficients, \(Y\) is the retrieval parameter, and \(\lambda_{1}\)-\(\lambda_{4}\) are the sensor-specific wavelengths (i.e., 443, 488, 531, and 547 nm for MODIS, 443, 490, 510, and 555 nm for  
Figure 4: Examples of CDOM absorption at 412 nm (top row), and CDOM spectral slope in the UVB (middle row) and VIS (bottom row) from GOCAD show patterns which reflect the sources and age of CDOM in environments stretching from estuarine, such as the Chesapeake Bay in the eastern U.S., to stations sampled well offshore. SeaWiFS). Using monthly, binned L3 Aqua imagery for 2010, MLR retrievals were used to establish the 99 th percentiles for each retrieval waveband of \(a_{g}\). Retrievals above these values were considered outside the scope of this global algorithm, and eliminated. Regression coefficients, statistics, and thresholds are presented in Figure 5, and Tables 3-5. Model retrievals plotted against field data are well organized about the 1:1 line with low scatter, particularly in the UVA, which is reflected in high correlation coefficients and low error and bias. _MAPD_ is below 30% for all bands below 488 nm; from this band to higher wavelengths, the CDOM signal becomes very weak in most of the global ocean. For the reasons outlined in Section 1.4 (i.e., a large and variable portion of DOC is unpigmented), DOC derived directly from ocean color alone using MLR was not robust (Table 5; MLR1). However, satellite retrievals of sea surface salinity are now available thanks to the Aquarius mission ([[http://aquarius.nasa.gov/](http://aquarius.nasa.gov/)]([http://aquarius.nasa.gov/](http://aquarius.nasa.gov/))), and for CDOM, salinity was a reasonable choice as an additional proxy for water type considering it will generally reflect proximity to sources of fresh water and CDOM as well as distinguishing water masses (e.g., Gulf Stream). Using GOCAD, a multiple linear regression approach was developed for retrieving DOC from \(a_{g}(355)\) (in place of \(R_{rs}(\lambda_{1})\) in Equation (8)) and salinity (in place of \(R_{rs}(\lambda_{2})\)), and proved very robust (e.g., \(\text{r}^{2}=0.91\), %\(Bias=0\)). Using CDOM and salinity as predictors significantly improved retrievals of DOC (Table 5; MLR2), with \(\text{r}^{2}\) increasing from 0.76 to 0.91, and _MAPD_ dropping by about three percentage points. The strength of the correlation between field and retrieved DOC to CDOM and salinity is stronger than expected, considering the many ways in which changes in DOC, CDOM, and salinity may diverge across seasons or from region to region. It is worth pointing out that other factors may be contributing to the stronger statistical performance of MLR2 over MLR1, such as the higher number of coincident predictors and retrievals, as well as the absence of uncertainties associated with reflectance data in the tuning dataset (i.e., DOC is derived directly from CDOM absorption and salinity).