## 1 Introduction
The M02 BRDF tables were developed from extensive RT modeling using VSF shapes (also known as phase functions \(P(\psi)\)), defined as the VSF normalized to total scattering, \(P(\psi)=\beta(\psi)/b\), with units sr\({}^{-1}\)) tied to estimated chlorophyll concentrations [Chl]. To obtain \(P(\psi)\) for modeling, [PERSON] et al. [7] first mixed two phase functions for populations dominated by large and small particles representing high and low [Chl] extremes, respectively, and then mixed that particulate phase function with the phase function for molecular seawater to a degree that was also linked to estimated [Chl]. The [Chl] estimate was initially derived from \(R_{rs}\) with an empirical band ratio algorithm. Uncertainty is thus associated with how close the assumed \(P(\psi)\) used in the BRDF modeling matches the actual \(P(\psi)\) associated with any given \(L_{w}\) measurement. While the M02 model has been validated in Case 1 waters with atmospheric conditions and IOPs that presumably agree with the underlying atmospheric and bio-optical models [17; 18], there have been limited attempts to assess any embedded phase function uncertainties with actual VSF measurements in diverse water types [19; 20]. No subsequent BRDF approach has demonstratedenhanced performance for Case 1 waters relative to the M02 approach while being feasible to implement for ocean color. However, [PERSON] et al. [21] have recently shown the [PERSON] et al. [11] LUT-based approach was more accurate for Case 2 waters sampled in the Adriatic, Baltic, and Black Seas. Uncertainty also arises from exclusively using the \(b_{b}\) term in the inversion algorithm, i.e., in step two of the SAA approach described above. Effort has been devoted to trying to correct this uncertainty by layering additional VSF dependence in the \(f/Q\) proportionality [22]. Interestingly, after the current M02 BRDF normalization is applied (i.e., measurement geometry transferred to Sun at zenith and nadir viewing), the scattering parameter that should be most closely linked to \([L_{w}]_{N}^{ex}\), and thus presumably should provide the lowest associated uncertainties in IOP retrievals, is \(\beta(\pi)\) if single scattering is assumed, which is typically a good approximation [23]. We are not aware however of any algorithm using \(\beta(\pi)\) in lieu of \(b_{b}\). The practical but still arbitrary choice of converting measured \(L_{w}\) to \([L_{w}]_{N}^{ex}\) with Sun at zenith and nadir viewing may thus not optimize uncertainties in inversion algorithms. The parameter \(\beta(\pi)\) is almost completely unknown in the ocean, as there are virtually no direct measurements of \(\beta(\pi)\) in the literature and typical models of particle scattering with simplified particle shapes do not account for possible particle-particle coherent scattering that may cause significant, but poorly understood, enhancement near \(\beta(\pi)\)[24]. For example, a recent estimate of \(b_{b}/\beta(\pi)\) made with a combination of airborne lidar and in situ \(b_{b}\) measurements [25] was 50% the value expected from extrapolation of available \(\beta\) measurements [26]. Although the M02 BRDF correction as currently applied can be considered \"conceptual\" at \(L_{w}(0,\pi)\) without creating a problem from a geometry point of view (i.e., \(L_{w}\) at any viewing geometry can be corrected to a conceptual standard \(L_{w}\) at another geometry as long as it is consistent), it will be problematic if we try to develop algorithms based on \(\beta(\pi)\) to reduce uncertainties because the necessary data for algorithm development and validation are lacking. This would also suggest a possible benefit in using the BRDF correction to obtain \([L_{w}]_{N}^{ex}\) at another unique geometry (solar zenith, viewing angle, and azimuth), one that was representative of single scattering at an angle that we can measure directly with available instrumentation.