Examining Biases In Diurnally Integrated Shortwave Irradiances Due To Two- And Four-Stream Approximations In A Cloudy Atmosphere

Shortwave irradiance biases due to two- and four-stream approximations have been studied for the last couple of decades, but biases in estimating Earth's radiation budget have not been examined in earlier studies. To quantify biases in diurnally averaged irradiances, we integrate the two- and four-stream biases using realistic diurnal variations of cloud properties from Clouds and the Earth's Radiant Energy System (CERES) synoptic (SYN) hourly product. Three approximations are examined in this study: delta-two-stream-Eddington (D2strEdd), delta-two-stream-quadrature (D2strQuad), and delta-four-stream-quadrature (D4strQuad). Irradiances computed by the Discrete Ordinate Radiative Transfer model (DISORT) and Monte Carlo (MC) methods are used as references. The MC noises are further examined by comparing with DISORT results. When the biases are integrated with one day of solar zenith angle variation, regional biases of D2strEdd and D2strQuad reach up to 8 W m(-2), while biases of D4strQuad reach up to 2 W m(-2). When the biases are further averaged monthly or annually, regional biases of D2strEdd and D2strQuad can reach -1.5 W m(-2) in SW top-of-atmosphere (TOA) upward irradiances and +3 W m(-2) in surface downward irradiances. In contrast, regional biases of D4strQuad are within +0.9 for TOA irradiances and -1.2 W m(-2) for surface irradiances. Except for polar regions, monthly and annual global mean biases are similar, suggesting that the biases are nearly independent to season. Biases in SW heating rate profiles are up to -0.008 K day(-1) for D2strEdd and -0.016 K day(-1) for D2strQuad, while the biases of the D4strQuad method are negligible.