## 1 Introduction
To minimize the magnitude of BRDF correction, this angle could be chosen as the centroid angle of the maximum in the frequency distribution of in-water single scattering angles observed for polar orbiting satellites, which is about 150\({}^{\circ}\) (Figure 1). Since we can accurately measure \(\beta\) at or near 150\({}^{\circ}\) with commercially available instrumentation (e.g., WET Labs ECO, In-situ Marine Optics IMO-SC6, and legacy HOBI Labs Hydroscat sensors), there would appear to be potential to reduce uncertainties with \(\beta(150^{\circ})\)-based algorithms matched to a \(\beta(150^{\circ})\)-based BRDF correction using M02 relative to the current \(b_{b}\)-based algorithms applied to a \(\beta(\pi)\)-based BRDF correction. In the former approach, uncertainties associated with the phase function are thus mostly restricted to the BRDF correction step. Herein we explore a different approach, working with a RT expression from [PERSON] [27; 28] that explicitly incorporates a dependency on VSF shape, as well as specific viewing geometry. A path to inversion to IOPs is also presented where SAA steps 1 and 2 mentioned above are combined in a single relationship and uncertainties related to VSF shape and other parameters can be directly assessed. This approach has several potential benefits, including (1) a single, fully analytical and invertible expression describing the RT process for all remote sensing geometries, (2) optimal retention of native RT relationships with more degrees of freedom than the first order approximation, directly linked to physically meaningful terms, (3) all parameters including the VSF are explicit in the model with readily characterized uncertainties, (4) model can be readily enhanced by tuning one or more terms rather than developing new LUTs from complete recomputations of full RT, and (5) native viewing geometries produce scattering at angles that can be resolved with available instrumentation. A challenge in an explicitly VSF-dependent approach is amenability to inversion, as some information about the phase function is ostensibly required [1; 20]. However, it should be pointed out this is also the case with any model, including the M02 BRDF correction, and subsequent inversion algorithms and their inherent assumptions about VSF shape. In fact, as is assessed herein, the same assumptions of M02 in linking changes in VSF shape with an independent estimate of chlorophyll can be directly applied to this RT model, with the benefit of being able to directly quantify associated errors. In this paper we focus on the performance of a forward implementation of the Zaneveld expression using a modified formulation in terms of IOPs that is now amenable to inversion. Performance of the inversion to IOPs is being fully assessed in ongoing work. A key advance promoting inversion is the finding by Sullivan and [PERSON] [26] that the shape of the particulate VSF in the backward direction is relatively constant for a wide range of water types, and so may be represented by a constant function in an algorithm without introducing significant error. Importantly, we have also now overcome a limitation in practically assessing this approach by collecting a database of measured VSFs resolved over a large dynamic range concurrently with other high quality IOPs and radiometry under ideal cloud-free environmental conditions [29].