Transfer model to determine the above-water remote-sensing reflectance from the underwater remote-sensing ratio

Remote-sensing reflectance, R_rs(λ, θ, Δϕ, θ_s), contains the spectral color information of the water body below the sea surface and is a fundamental parameter to derive satellite ocean color products such as chlorophyll-a, diffuse light attenuation, or inherent optical properties. Water reflectance, i.e., spectral upwelling radiance, normalized by the downwelling irradiance, can be measured under- or above-water. Several models to extrapolate this ratio from underwater "remote-sensing ratio", r_rs(λ), to the above-water R_rs, have been proposed in previous studies, in which the spectral dependency of water refractive index and off-nadir viewing directions have not been considered in detail. Based on measured inherent optical properties of natural waters and radiative transfer simulations, this study proposes a new transfer model to spectrally determine R_rs from r_rs for different sun-viewing geometries and environmental conditions. It is shown that, compared to previous models, ignoring spectral dependency leads to a bias of ∼2.4% at shorter wavelengths (∼400 nm), which is avoidable. If nadir-viewing models are used, the typical 40°-off nadir viewing geometry will introduce a difference of ∼5% in R_rs estimation. When the solar zenith angle is higher than 60°, these differences of R_rs have implications for the downstream retrievals of ocean color products, e.g., > 8% difference for phytoplankton absorption at 440 nm and >4% difference for backward particle scattering at 440 nm by the quasi-analytical algorithm (QAA). These findings demonstrate that the proposed r_rs-to-R_rs model is applicable to a wide range of measurement conditions and provides more accurate estimates of R_rs than previous models.