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Water leaving reflectance that an ocean color mission (such as PACE) measures is inherently bidirectional, i.e., it varies with the position of sun and the viewing direction. This variation, expressed as bidirectional reflectance distribution function (BRDF) is ultimately determined by the volume scattering function (VSF), and in particular its backward shape (called Χ factor). Previous studies investigating BRDF have used the VSFs that evidently underestimate the natural variability of Χ factor and could lead to errors that are greater than the 30% target of retrieving remote sensing reflectance from the PACE mission. On the other hand, the two multi-angle polarimeters (HARP2 and SPEXone) that the PACE will deploy along with the hyperspectral OCI sensor offer an opportunity to measure Χ factor. Taking advantage of this opportunity, we propose to develop a method using multi-angle polarimetry data to derive Χ factor and improve the BRDF correction for PACE's OCI remote sensing reflectance (rrs). The proposed work is based on insight and knowledge that we have gained during past decade in studying the natural variability of the volume scattering function and its impact on ocean color. Specifically, we propose to achieve three objectives. (1) Improve our understanding of natural variability of the Χ factor and its impact on bidirectional remote sensing reflectance. Because of the essential role played by the Χ factor in determining the BRDF effect, addressing this objective will allows us to develop a mechanistic understanding on the source of variability in BRDF. (2) Utilize Zaneveld's theoretical derivation that explicitly includes VSF in rrs formula to retrieve Χ factor from the multi-angle rrs observation. (3) Explore a multi-sensor capability to constrain the BRDF correction for the hyperspectral OCI using Χ factor retrieved from the multi-angle HARP2 and/or SPEXone. In additional to improving BRDF correction, our method will also retrieve Χ factor, which as an important inherent optical property, contains critical information on the composition and structure of the particle assemblages in the oceans. Therefore, it also has potential to derive additional biogeochemical products from the PACE mission.

A key challenge in applying ocean color remote sensing for assessing biogeochemical stocks in the ocean is to link the signal seen by satellite or airborne sensors with the optically active water constituents and their biogeochemical origin. The linkage between ocean color and biogeochemical stocks is established via the inherent optical properties of water, most importantly the volume scattering function (β, m-1 sr-1) and the total absorption coefficient (a, m-1). While our ability to understand and separate the various components of absorption has improved over the last decades, the major challenge remains in the understanding of the sources of variability in the volume scattering function, and particularly the backscattering that are directly relevant to ocean color observation. This has hindered our ability to derive IOPs accurately and to interpret their variability biogeochemically. Of IOPs, the VSF is most difficult to measure with only few data available. The scarcity of data has led to unrealistic assumptions, such as that the phase function of particles can be represented by the average of Petzold's data. This in turn has led to uncertainties in understanding the roles played by particles of different type in generating remote sensing reflectance and the color of the ocean. Recent technological and theoretical advances have allowed us 1) to measure the full angular scattering over a diverse aquatic environments and 2) to interpret the measurements in terms of particle size distribution and composition. We have greatly improved our understanding of natural variability of the VSF and the biogeochemical origin of the variability. However, these improved knowledge has yet to applied to ocean color. The objective of this study is to understand the natural variability of the VSF and its impact on biogeochemical interpretation of ocean color. The answers to this question will help to constrain two major uncertainties affecting both the current and future PACE ocean color missions: bidirectional effect and sources of backscattering. Our approach is centered on in-depth analysis of the field measurements of complete sets of IOPs (including full range VSFs) and biogeochemical stocks covering various aquatic environments through both forward and inverse modeling. The information of biogeochemical stocks is also contained in the detailed angular pattern of the VSF and can be retrieved by VSF-inversion. Applying forward modeling to simulate spectral backscattering from the inversion results will tell what biogeochemical information about particles (such as the size or the type) is retained in, and hence can be possibly retrieved from, the backscattering coefficient derived from ocean color. Comparisons of the modeled and measured biogeochemical stocks and comparisons of the modeled and measured spectral backscattering will aid in the interpretation of the modeling results and will also provide a basis for validating, and possibly refining, the overall modeling approach. The proposed study addresses a fundamental, yet poorly known, linkage between the optical scattering and biogeochemical properties of natural waters. The potential outcome of the study can not only advance our understanding of the VSF as an key IOP parameter but also improve the performance of existing ocean color algorithms by further constraining the uncertainty associated with angular scattering as well as to guide the development of new approaches for ocean color algorithms.