Sparse, Empirically Optimized Quadrature for Broadband Spectral Integration

Abstract Broadband (spectrally‐integrated) radiation calculations are dominated by the expense of spectral integration, and many applications require fast parameterizations for computing radiative flux. Here we describe a novel approach using a linear weighted sum of monochromatic calculations at a small set of optimally‐chosen frequencies. The empirically‐optimized quadrature method is used to compute atmospheric boundary fluxes, net flux profiles throughout the atmosphere, heating rate profiles, and top‐of‐the‐atmosphere forcing by CO2, in the longwave for clear skies. We evaluate the method against two modern correlated k‐distribution models and find that we can achieve comparable errors with 32 spectral points. We also examine the effect of minimizing different cost functions, and find that in order to accurately represent heating rates and CO2 forcing, these quantities must be included in the cost function.