## 3 Results and Discussion
### Algorithm Tuning and Validation
#### 3.2.1 Algorithm Structures and Optimization
Caution is therefore advised when applying this DOC algorithm in regions in which DOC is known to change without commensurate changes in CDOM and/or salinity. For example, the accumulation of DOC in surface subtropical waters including the BATS field station [59; 60] appears to be decoupled from CDOM ([PERSON] and [PERSON], personal communication). Figure 5: MLR retrievals of CDOM plotted against field data for the tuning dataset (i.e., in situ \(R_{rs}(\lambda)\)). The solid line shows the fit through the data, and the 1:1 line is dashed. Another empirical approach tested here was the machine learning approach known as Random Forests [61; 62], which is a method for multivariate, non-linear, non-parametric regression designed to help minimize over-fitting of the training dataset. The method improves on standard decision tree regression performance by using an ensemble of independent decision trees; bootstrapping for the regression is achieved by repeatedly, randomly resampling the original dataset to provide an ensemble of smaller independent datasets, which are each used to grow a decision tree (hence the term random forest tree-bagger, or RFTB). Here, 200 independent decision trees were used, and each tree is trained on approximately 66% of the training dataset. The inputs (i.e., reflectances) and retrievals of the regression (i.e., CDOM, CDOM slope, and DOC) were the same as in the MLR. Model performance and statistics for select bands in the UV and VIS with the training dataset are presented in Figure 6. Comparisons of model retrievals to field data are fairly well correlated, but error and bias are quite high, with _MAPD_ reaching several hundred percent. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(\lambda\) & \(\mathbf{\delta_{0}}\) & \(\mathbf{\delta_{1}}\) & \(\mathbf{\delta_{2}}\) & \(\mathbf{\delta_{3}}\) & \(\mathbf{\delta_{4}}\) & N & \(\mathbf{r^{2}}\) & RMSD & MAPD & \%_Bias_ \\  & & & & & & & & [nm\({}^{-1}\)] & [\%] & [\%] \\ \hline \multicolumn{11}{c}{**MODIS**} \\ \hline
[nm] & & 443 & 488 & 531 & 547 & & & & & \\ \hline
275–295 & \(-\)3.289 & 0.270 & \(-\)0.335 & 1.051 & \(-\)0.921 & 322 & 0.61 & 0.002 & 6.4 & \(-\)0.3 \\
290–600 & \(-\)3.471 & 0.127 & \(-\)0.251 & 1.025 & \(-\)0.843 & 322 & 0.38 & 0.002 & 6.2 & \(-\)0.3 \\
300–600 & \(-\)3.607 & 0.044 & \(-\)0.153 & 0.881 & \(-\)0.722 & 324 & 0.30 & 0.001 & 5.7 & \(-\)0.3 \\
350–400 & \(-\)3.924 & \(-\)0.242 & 0.055 & 0.935 & \(-\)0.710 & 331 & 0.26 & 0.001 & 6.8 & \(-\)0.3 \\
350–600 & \(-\)3.908 & \(-\)0.204 & 0.098 & 0.609 & \(-\)0.463 & 331 & 0.22 & 0.001 & 6.3 & \(-\)0.3 \\
380–600 & \(-\)3.912 & \(-\)0.152 & 0.127 & 0.236 & \(-\)0.173 & 340 & 0.14 & 0.001 & 6.3 & \(-\)0.3 \\
412–600 & \(-\)4.219 & \(-\)0.180 & 0.137 & 0.168 & \(-\)0.131 & 782 & 0.16 & 0.002 & 7.4 & \(-\)0.5 \\
412–555 & 4.195 & \(-\)0.162 & 0.147 & 0.096 & \(-\)0.084 & 760 & 0.10 & 0.002 & 7.6 & \(-\)0.5 \\ \hline \multicolumn{11}{c}{**SeaWiFS**} \\ \hline
[nm] & & 443 & 490 & 510 & 555 & & & & & \\ \hline
275–295 & \(-\)3.012 & 0.427 & \(-\)0.459 & 0.357 & \(-\)0.228 & 424 & 0.77 & 0.002 & 6.8 & \(-\)0.4 \\
290–600 & \(-\)3.425 & 0.131 & \(-\)0.085 & 0.145 & \(-\)0.130 & 424 & 0.46 & 0.002 & 6.6 & \(-\)0.4 \\
300–600 & \(-\)3.615 & 0.004 & 0.014 & 0.160 & \(-\)0.129 & 426 & 0.29 & 0.002 & 6.0 &Semi-analytical approaches included the Quasi-Analytical Algorithm of (QAA) [5; 63; 64], and the Generalized Inherent Optical Property (GIOP) algorithm [65]. These have the advantage that they are based on theoretical models for how the light field is affected by the inherent properties of the water, but can only retrieve IOPs at those wavebands for which \(R_{rs}(\lambda)\) is measured (i.e., they do not