Sparse, Empirically Optimized Quadrature for Broadband Spectral Integration.

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. Plain Language Summary: Quantifying the way radiation flows through the atmosphere is computationally expensive, and most applications require fast approximation. In this paper, we develop an empirically‐optimized quadrature method that can compute quantities of interest in climate science and weather prediction such as radiative flux throughout the atmosphere, heating rates, and forcing by carbon dioxide. The method uses a simple optimization algorithm, combined with a linear model, to achieve accuracy and computational cost of similar order of magnitude to the modern correlated k‐distribution models. Depending on the focus of the application, the algorithm can easily be adapted to prioritize desired quantities. Key Points: Spectrally integrated radiative quantities can be estimated from a small weighted set of monochromatic calculationsTradeoffs between computational cost and accuracy are commensurate with correlated k‐distribution modelsOptimization priorities can be tailored to a specific applications [ABSTRACT FROM AUTHOR]