## 4 Results
### Assessment with High Quality Validation Data
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{_Approach_} & \multirow{2}{*}{\(\beta_{p}(\psi)\)/\(\widetilde{b}_{bp}\) Input} & \multirow{2}{*}{\(\widetilde{b}_{bp}\) Input} & \multicolumn{2}{c}{\(\widetilde{\gamma}\)\(\delta_{abs}\)} \\ \cline{3-5}  & & & \multicolumn{1}{c}{**SORTIE and OCVAL**} & \multicolumn{1}{c}{**NOMAD**} \\  & & & **(23 Stations)\({}^{\text{1}}\)** & **(80 Stations)** \\ \hline Full RT \({}^{\text{2}}\) & directly measured & N/A & 17 & nd \({}^{\text{4}}\) \\ Full RT \({}^{\text{2}}\) & Fournier-Forand \({}^{\text{3}}\) & measured & 20 & nd \({}^{\text{4}}\) \\ ZTT & directly measured & measured & 17 & nd \({}^{\text{4}}\) \\ ZTT & Fournier-Forand \({}^{\text{3}}\) & measured & 19 & 25 \\ ZTT & \(P_{bb,ST}(\psi)\) & measured & 16 & 20 \\ ZTT & \(P_{bb,ST}(\psi)\) & 0.005 & 18 & 22 \\ ZTT & \(P_{bb,ST}(\psi)\) & 0.006 & 17 & 23 \\ ZTT & \(P_{bb,ST}(\psi)\) & 0.008 & 18 & 25 \\ ZTT & \(P_{bb,ST}(\psi)\) & 0.010 & 19 & 27 \\ ZTT & \(P_{bb,ST}(\psi)\) & 0.015 & 22 & 29 \\  & Large and small population & & & \\ ZTT & phase functions with \(\widetilde{b}_{bp}\) of & & & \\  & 0.19\% and 1.4\%, blended & & & \\  & according to [Chl] \({}^{\text{5}}\) & & & \\ [PERSON] et al. [7] & phase functions with \(\widetilde{b}_{bp}\) of & N/A & 21 & 25 \\ (M02) & 0.19\% and 1.4\%, blended & & & \\  & according to [Chl] \({}^{\text{5}}\) & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \end{tabular} \({}^{\text{1}}\) see [29]; \({}^{\text{2}}\) Hydrolight, \({}^{\text{3}}\) derived from \(\widetilde{b}_{bp}\) according to [67]; \({}^{\text{4}}\) not determined; \({}^{\text{5}}\) algorithm of [7]; \({}^{\text{6}}\)[79].  
\end{table} 
Table 1: Summary MAPE %\(\delta_{abs}\) results for simulated or calculated \(r_{rs}\) vs measured \(r_{rs}\) for all \(\lambda\). Figure 4: \(r_{rs}\) computed from (**A**) ZTT, (**B**) ZTT with \(\widetilde{b}_{bp}\) fixed at 0.006, (**C**) M02, and (**D**) L11 models, compared to measured \(r_{rs}\) in the high quality validation data set from [PERSON] et al. [29]. Note L11 does not account for Raman scattering. Chlorophyll input for M02 was derived from spectral absorption using the Nardelli and Twardowski [78] line height algorithm. MAPE %\(\delta_{abs}\) was 16%, 17%, 21%, and 21%, in A through D, respectively. defined as \(f/Q\), which is a function of viewing geometry, wind speed, and [Chl]. [Chl] can be estimated from an empirical \(r_{rs}\) band ratio algorithm. For the assessment here, [Chl] input was either quantified directly from discrete samples or derived from spectral particulate absorption measurements using the line height method with specific absorption \(a_{p}\)*(676) of 0.0108 m\({}^{2}\) mg\({}^{-1}\) after [78]. Note that bootstrapping exercises have shown relatively large errors in this estimated [Chl], i.e., up to \(+/-50\%\), affect \(\%\delta_{abs}\) in match ups by typically no more than 1%. The other inputs were measured \(a_{pg}\) and \(b_{bp}\). Match up \(\%\delta_{abs}\) for M02 was 21% for the data set from [29] (Table 1). Notably, M02 performed well in the blue spectral region (Table 2). To derive phase functions, [PERSON] et al. [7] used randomly-oriented spheroidal particles, computing the scattering phase function with the T-matrix method. Because the computations for spheroids were lengthy, a single refractive index \(n_{p}\) of 1.06 was considered with sizes ranging from 0.02 to 14 \(\upmu\)m. A Junge-type particle size distribution was assumed, i.e., a power law model, with exponents of 3.1 and 4.2 representing two end-member populations. Particulate scattering phase functions were then calculated from (see Figure 5):  
\[P_{p}(\psi)=\alpha_{s}([Chl])P_{ps}(\psi)+\alpha_{l}([Chl])P_{pl}(\psi),\]  
\[\text{with }\alpha_{s}+\alpha_{l}=1,\text{ and }\alpha_{s}([Chl])=0.855\big{[}0. 5-0.25\log_{10}([Chl])\big{]}.\]  
If the [PERSON] et al.