## 5 Discussion
### Suitability for Inversion  
The ZTT model can be used to directly solve for \(b_{b}/a\) using least-squares minimization of a \(r_{rs}\) measurement at any wavelength. This is shown in Figure 7 for the validation data set from [PERSON] et al. [29], assuming a constant \(\widehat{b}_{bp}\) of 0.006. The typical value for \(V\) of 15 km was assumed. MAPE %\(\delta_{abs}\) in the inversion was 17%, which matches results from full RT simulations of closure in the forward direction. Residual errors thus appear almost entirely comprised of the inherent errors of the data set arising from IOP and radiometric measurements [29]. With respect to the use of \(P_{bb,ST}(\psi)\), another potential approach to estimating VSF shape as it relates to the upcoming PACE mission is using planned multi- and hyper-angular polarimetry data from the Hyper-Angular Rainbow Polarimeter-2 (HARP2; contributed by University of Maryland, Baltimore County) and the Spectrometer for Planetary Exploration--one (SPEXone; contributed by the Netherlands Institute for Space Research) [94]. If information on the backward shape of the VSF could be gleaned with sufficient accuracy from angular polarimetry data (only a few angles would be necessary), this could be used directly in the ZTT model. The ZTT model described here only addresses in-water RT, although the current approach to normalize water-leaving radiances measured by a satellite imager is expected to directly apply (see [15], Sections 3.1 and 6]). The BRDF is built-in to the Zaneveld model so an additional step to conceptually shift the geometry to a normalized geometry standard would not be required for IOP inversion. A normalized geometry (to nadir viewing or other geometry) could still be applied to intercompare reflectances in images. Translation to water-leaving radiance by accounting for all the reflection and refraction effects through the air-sea interface i.e., \(\mathcal{R}(\theta_{s},\theta_{v})\)[6; 15], can still be applied. Similarly, the effects of varying Earth-Sun distance and atmospheric attenuation can be removed following the current approach. Moreover, we would expect a practical implementation of this analytical model to have similar computational requirements as the current M02 LUT-based approach. The ZTT model shows \(\widetilde{b}_{bp}\) exerts some influence on \(r_{rs}\) (Table 1) and the potential to invert \(r_{rs}\) for \(\widetilde{b}_{bp}\) is also being investigated. The parameter \(\widetilde{b}_{bp}\) has not historically been associated with \(r_{rs}\) and could provide new insights into particle composition in natural waters (e.g., [41]). Even a retrieval of \(\widetilde{b}_{bp}\) with relatively large errors could be useful for many research applications. The ZTT model is fully spectral and can be applied over the full anticipated ocean color hyperspectral wavelength range for the future PACE mission (350-800 nm). A primary goal in model development was parameterization entirely in terms of \(a\) and \(b_{b}\). Inversion approaches, such as the General IOP (GIOP) inversion using a least-squares minimization to solve for IOP subcomponents [16] may consequently be readily applied. Spectral \(b_{bp}\) and \(a_{pg}\) can be solved using assumptions for subcomponent IOP spectra through least squares minimization of Equation (18). This is the step where empiricism prominently enters the problem as spectral shapes for IOP subcomponents must be assumed. This is being examined in ongoing work. Further investigation is needed to determine IOP subcomponent spectra with a high spectral resolution for error minimization over this full spectral range in inversion, which is currently being assessed by the PACE Science Team [13; 95]. Hyperspectral (i.e., 5 nm) resolution for PACE is expected to improve fidelity in inverting for subcomponents (and potentially \(\widetilde{b}_{bp}\)) as there will be higher degrees of freedom than for multi-spectral imagers [96; 97]. Code for the ZTT model in MATLAB is available at ioccg.org. Conceptualization, M.T. ; Methodology, M.T.