## 4 Results
### Assessment with Global NOMAD Data Set  
Figure 6A shows results for the ZTT model applied to a subset of 80 measurements from the NASA NOMAD global data set. IOPs were averaged over the first optical depth. Match up MAPE %\(\delta_{abs}\) of 20% was observed for this global data set, comparing favorably to the error of 16% observed with the high quality data set from [PERSON] et al. [29] (Table 1; see Table 2 for spectral breakdown). This is especially true considering the different IOP and \(r_{rs}\) processing approaches (e.g., there are several scattering error correction options for in-water absorption measurements) used for these data sets. If \(\widetilde{b}_{bp}\) is constrained to 0.006, MAPE %\(\delta_{abs}\) increases to 23% (Figure 6B). Results from ZTT runs for other fixed \(\widetilde{b}_{bp}\) are shown in Table 1, where the dependency of performance on \(\widetilde{b}_{bp}\) is again apparent.  
If the [PERSON] et al. [7] approach for deriving the phase function from [Chl] is used as input into the ZTT model, %\(\delta_{abs}\) increased from 20% to 26% for the NOMAD data (Table 1). If measured \(\widetilde{b}_{bp}\) are used to derive \(P_{bb,FF}(\psi\widetilde{b}_{bp})\) following [67], %\(\delta_{abs}\) increased to 25% for the ZTT model.  
Match ups are also shown for implementation of the full M02 and L11 models with the NOMAD data set (Figure 6C,D). MAPE statistics are summarized in Tables 1 and 2. There are several possibilities for the systematically lower measured \(r_{rs}\) in the red spectral region for these data: (1) Suboptimal surface extrapolation of radiances due to water Raman effects [80; 81], (2) residual scattering errors in reported in-water absorption measurements that may promote a bias to higher values of modeled \(r_{rs}\) (e.g., [29; 49]), and/or (3) suboptimal corrections for sensor self-shading, which can be strong in clear water at longer wavelengths due to water absorption [82; 83].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{_Approach_} & \multirow{2}{*}{\(\beta_{p}\) (\(\psi\psi\)/\(b_{bp}\) Input} & \multirow{2}{*}{\(\tilde{b}_{bp}\) Input} & \multirow{2}{*}{\(\lambda\) (nm)} & \multicolumn{2}{c}{**\%\(\delta_{abs}\)**} \\ \cline{5-6}  & & & & **SORTIE and** & **NOMAD** \\  & & & & **OCVAL** & **(80 Stations)** \\ \hline \multirow{6}{*}{ZTT} & \multirow{6}{*}{\(P_{bb,ST}(\psi)\)} & & 412 (410) & 20 & 17 \\  & & 440 & 16 & 20 \\  & & 488 (490) & 16 & 20 \\  & & 510 & 19 & 19 \\  & & 532 & 13 & - \\  & & 555 & 14 & 23 \\  & & 650 & 13 & - \\  & & 665 & - & 63 \\ \hline \multirow{6}{*}{ZTT} & \multirow{6}{*}{\(P_{bb,ST}(\psi)\)} & & 412 (410) & 20 & 20 \\  & & 440 & 16 & 23 \\  & & 488 (490) & 19 & 23 \\  & & 510 & 13 & 25 \\  & & 532 & 14 & - \\  & & 555 & 13 & 26 \\  & & 650 & 22 & - \\  & & 665 & - & 63 \\ \hline \multirow{6}{*}{[PERSON] et al. [7] (M02)} & \multirow{6}{*}{\(\mathrm{N/A}\)} & 412 (410) & 17 & 22 \\  & & 440 & 14 & 25 \\  & & 488 (490) & 16 & 25 \\ \cline{1-1}  & & 510 & 18 & 26 \\ \cline{1-1}  & & 532 & 22 & - \\ \cline{1-1}  & & 555 & 38 & 21 \\ \cline{1-1}  & & 650 & 17 & - \\ \cline{1-1}  & & 665 & - & 71 \\ \hline \multirow{6}{*}{[PERSON] et al. [11]} & \multirow{6}{*}{Blend of Petzold average and 1%} & 412 (410) & 22 & 22 \\  & & 440 & 21 & 26 \\ \cline{1-1}  & & 488 (490) & 24 & 27 \\ \cline{1-1}  & \(\widetilde{b}_{p}\) Fournier-Forand & & 510 & 21 & 27 \\ \cline{1-1}  & & 532 & 20 & - \\ \cline{1-1}  & & 555 & 19 & 24 \\ \cline{1-1}  & & 650 & 26 & - \\ \cline{1-1}  & & 665 & - & 66 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary MAPE %\(\delta_{abs}\) results for calculated \(r_{rs}\) vs measured \(r_{rs}\) for each \(\lambda\), for SORTIE and OCVAL data sets (see Figure 4) and NOMAD data (see Figure 6).