Inherent optical properties-reflectance relationships revisited

Understanding the relationship between remote sensing reflectance, Rrs(λ) and the inherent optical properties (IOPs) of natural waters is potentially a key to improving our ability to determine biogeochemical constituents from radiometric measurements. These relationships are usually described as a function of absorption, a(λ), and backscattering, bb(λ), coefficients, with the literature providing various forms of equation operating on either bb(λ)/a(λ) or bb(λ)/[a(λ)+bb(λ)] to represent the impact of variations in light field geometries and changes in sea-water composition. The performance of several IOP-reflectance relationships is assessed using HydroLight radiative transfer simulations covering a broad range of Case 1 and Case 2 water conditions. While early versions of IOP-reflectance relationships assigned variability to associated proportionality factors (e.g., f/Q) or low-order polynomial functions, recent studies have demonstrated relationships between Rrs(λ) and bb(λ)/[a(λ)+bb(λ)] are wellcharacterized by nonlinear (high-order polynomial), monotonic functions. This study demonstrates that this approach is also valid for relationships operating on bb(λ)/a(λ) and that there is no intrinsic benefit to functions operating on bb(λ)/[a(λ)+bb(λ)] compared to bb(λ)/a(λ) for Case 2 waters, contrary to recent suggestions in the literature. In all cases it is necessary to carefully consider the performance of best fit relationships across the full range of variability of IOPs and Rrs(λ), with higher order polynomials required to enable equivalent performance across the range of natural variability. The analysis further demonstrates insignificant wavelength sensitivity across the visible region, limited sensitivity to changes in solar zenith angle and extends to relationships for below surface remote sensing reflectance, rrs(λ).