## Abstract

Rayleigh-scattering radiance (*L _{r}*) calculations based on the standard algorithm are often associated with significant uncertainties leading to inconsistent water-leaving radiance retrievals, both spatially and temporally across latitudes and altitudes. The uncertainty could result from the use of Rayleigh lookup tables generated for the standard surface atmospheric pressure and hence the Rayleigh optical thickness (ROT) at the specific atmospheric pressure regardless of its daily and seasonal variations. This study presents a new algorithm (hereafter referred to as the refined algorithm) to compute the Rayleigh-scattering radiance that relies on accurate calculations of the ROT as a function of the composition of air (CO

_{2}volume concentration), surface atmospheric pressure and relative air mass for given sun-sensor geometries. As CO

_{2}is well mixed throughout the atmospheric column, the CO

_{2}volume concentrations derived from this study agree well with measurements in different seasons across studied latitudes. Relative air mass has a significant effect on the ROT and that is calculated as a function of apparent sun-sensor zenith angles with the variations in pressure and thermal characteristics of the atmosphere. Thus, the results indicate significant variations of ROT and air mass with location on the earth’s surface and their influence on the

*L*, particularly in the UV-Blue region of the spectrum. The refined algorithm for calculating the

_{r}*L*is tested on several MODIS-Aqua Level 1A data and the relative errors in Rayleigh-scattering radiance and normalized water-leaving radiance (

_{r}*Lwn*) retrievals between the refined algorithm and standard (SeaDAS) algorithm are compared using in-situ measurement data collected at MOBY (clear ocean), AERONET (turbid coastal ocean), and NOMAD (clear ocean) sites. The results indicate that the

*L*calculated using the SeaDAS algorithm are mostly underestimated and show significant departures with the

_{r}*L*calculated using the refined algorithm. This departure induced by the SeaDAS algorithm to

_{r}*L*becomes larger with decreasing wavelength (Δ

_{r}*L*from −2.38% at 412 nm to 1.69% at 678 nm), which causes errors in

_{r}*Lwn*retrievals (Δ

*Lwn*) of up to 26.48% at 412 nm and 13.34% at 678 nm. The overall improvements in the retrieved

*Lwn*values achieved vary from 56% at 412 nm to 29% at 678nm, which yield similar improvements in

*Lwn*retrievals with lower errors and higher slopes and correlation coefficients when compared with the in-situ

*Lwn*data. These results indicate that the refined algorithm for computation of the

*L*can yield more accurate

_{r}*Lwn*retrievals and produce spatially and temporally consistent biogeochemical products at different latitudes and altitudes as desired by the scientific community.

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