New theoretical formulation for the determination of radiance transmittance at the water-air interface

Radiative transfer across the water-air interface has important implications for optics and remote sensing of natural waters. The upward radiance emerging from the water suffers a critical change when it passes through the water-air interface. Upwelling radiance transmittance τw,a is an optical process occurring at the water-air interface that determines the in-water radiances propagating through the interface. In previous studies, τw,a was successfully derived for determining the water-leaving radiances in open ocean waters, despite being oversimplified with a constant value. The constant τw,a value becomes rapidly invalid in high scattering and absorbing waters within nearshore and inland environments. In this study, we attempt to quantitatively solve the upwelling radiance transmittance τw,a (i.e., the percentage of in-water photons that escape through the water-air interface) for varying coefficients of scattering and absorption within the range of natural waters. The two important optical phenomena which are ignored in the previous studies have been fully accounted: (i) the particulate contribution to the refractive index (RI) of seawater and (ii) the multiple interactions of the upwelling photons with the water-air interface. As a result, this study leads to a new theoretical formulation of the upwelling radiance transmittance applicable to all natural waters. The effect and variation of the new formulation on the water-leaving radiance and remote sensing reflectance is further studied for coastal and inland waters. Particular attention is also focused on the conversion of sub-surface remote sensing reflectance (rrs) to above-surface remote sensing reflectance (Rrs), which is important for calibration and validation of the remote sensing algorithms. The results show substantial improvement in the ocean color quantities (Lw and Rrs) by up to factor 33% for scattering waters and <5% for absorbing waters.