A Tool for Generating Fast k‐Distribution Gas‐Optics Models for Weather and Climate Applications

Abstract

Perhaps the most fundamental part of a climate model is the gas-optics module of its radiation scheme; in fact, one of the most influential (and indeed Nobel-prize-wining) studies of the climatic impact of increased greenhouse gases used a climate model consisting of little more than a radiation scheme coupled to a convective-adjustment scheme (Manabe & Wetherald, 1967). The correlated k-distribution (CKD) method (Goody et al., 1989;Lacis & Oinas, 1991) has emerged as the leading technique for treating the radiative effects of gases that is fast enough to use in 3D weather and climate models. Many models still use older alternatives; DeAngelis et al. ( 2015) reported a large spread in the magnitude of the near-infrared (NIR) water vapor feedback amongst 14 climate models, but those using the CKD method were found to be much the most accurate compared to benchmark line-by-line (LBL) radiation calculations.CKD models are very time consuming to develop from scratch, so when writing a new radiation scheme one must usually incorporate one of the small number of off-the-shelf models, even though it may not be optimized for ones particular application. The perceived high computational cost of radiation schemes has spurred numerous ideas to accelerate them, such as replacement of the radiation scheme (or only its gas-optics component) by a neural network (e.g., Ukkonen et al., 2020), or sub-sampling of model columns (Barker et al., 2021). The computational cost of a radiation scheme scales with the number of pseudo-monochromatic calculations (hereafter referred to as "k-terms" or spectral intervals) required to represent the entire spectrum, which is determined by the

Optimized Alternate Mapping Correlated K‐Distribution Method for Atmospheric Longwave Radiative Transfer

“…Ultimately, the optimal process converges in each band. Hogan and Matricardi (2022) also minimized an objective function with a similar form to Equation , using the L‐BFGS‐B method, but optimized many thousands of absorption coefficients (for all the temperatures and pressures in a look‐up table) to minimize the squared error against several hundred profiles spanning different climate conditions. Hogan (2010) first demonstrated the optimization approach with a much smaller data set of training profiles.…”

“…Hogan (2010) proposed an optimization algorithm to adjust the absorption coefficients in each spectral interval to minimize the deviation of broadband radiation fluxes and heating rates produced by the CKD model from the LBL model for several “training” profiles, in the least squares sense. And this method is also used by Hogan and Matricardi (2022) as part of their wider “ecCKD” tool. However, at present, there is a lack of exploration of using similar optimization methods to improve the accuracy of the AMCKD scheme.…”

Fast computation of cloud 3D radiative effects in dynamical models by optimizing the ecRad scheme

“…Since version 1.4, ecRad has the capability to use ecCKD gas-optics models. Hogan and Matricardi (2022) used three techniques to reduce the number of spectral intervals while retaining accuracy: the full-spectrum correlatedk method, the hypercube partition method for treating the spectral overlap of gases, and the optimization of look-up table coefficients against a set of training profiles. We use their models with 32 spectral intervals in each of the longwave and shortwave; since this is several times fewer than used by RRTMG, we expect a speed-up of the entire radiation scheme.…”

“…Fortunately, the reliable radiative transfer equations need not be sacrificed at the altar of efficiency. Algorithmic developments can, for instance, substantially reduce the number of spectral terms required for a given level of accuracy (Hogan & Matricardi, 2022).…”

Sparse, Empirically Optimized Quadrature for Broadband Spectral Integration

“…The sorting and averaging creates a much smoother integral that can be evaluated with just tens or hundreds of quadrature points, as compared to the millions of points required by line‐by‐line models. These parameterizations seek to minimize the number of these quadrature points, called g ‐points, to limit computational cost (Hogan & Matricardi, 2022).…”