Dependence of the Bidirectional Reflectance Distribution Function Factor ƒ′ on the Particulate Backscattering Ratio in an Inland Lake

The bidirectional reflectance distribution function (BRDF) factor ƒ′ provides a bridge between the inherent and apparent optical properties (IOPs and AOPs) of inland waters. The previous BRDF studies focused on ocean waters, while few studies examine inland waters. It is meaningful to improve the theory of remote sensing of water surface and the accuracy of image derivation in inland waters. In this study, radiative transfer simulation was applied to calculate the ƒ′ values using appropriate IOPs based on in situ combined with realistic boundary conditions (N = 11,232). This study shows that ƒ′ factor varied over the range of 0.33–16.64 in Lake Nansihu, a finite depth water, higher than the range observed for the ocean (0.3–0.6). Our results demonstrate that the factor ƒ′ depends on not only solar zenith angle (θs) but also the average number of collisions (n−) and particulate backscattering ratio (b~bp). The ƒ′ factor shows a continuous geometric increase as the solar zenith angle increases at 400–650 nm but is relatively insensitive to solar angle in the 650–750 nm range in which ƒ′ increases as b~bp and n− decreases. To account for these findings, two empirical models for ƒ′ factor as a function of θs, n− and b~bp are proposed in various spectral wavelengths for Lake Nansihu waters. Our results are crucial for obtaining Hyperspectral normalized reflectance or normalized water-leaving radiance and improving the accuracy of satellite products.