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• The band structure is specified, and then within each band the high-resolution absorption spectrum of each individual gas is reordered using the median/present-day concentration case from the MMM dataset, with the ordering according to the height of the peak cooling rate. For the NWP applications, all gases except H₂O and O₃ are merged into a single "composite" gas. Note that the same ordering is used at all heights.
• An error tolerance is specified by the user, and the reordered spectra for each gas are divided into as many k terms (g points) as are needed so that the RMSE in heating rate for any individual k term is less than the specified tolerance. The partitioning of the spectrum is adjusted so that the error associated with each k term in a band (for  single gas) is approximately equal. 
• The k terms for the individual gases are combined to obtain a final set of k terms using the hypercube partition method of Hogan (2010).
• The Idealized dataset is used to compute a the look-up tables of absorption coefficient for each gas in each k term.
• A quasi-Newton scheme is used to optimize the coefficients of the look-up table to minimize the errors when computing heating rates and fluxes for the Evaluation-1 dataset.

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Longwave CKD models have been constructed with a range of k terms (g points) using not only the wide and narrow CKDMIP band structures, but also a single band for the entire longwave spectrum (the full-spectrum correlated-k method, FSCK).  Note that the CKD models are optimized by minimizing the errors against the Evaluation-1 CKDMIP line-by-line dataset, so the evaluations here are not truly independent.   Indepdent Independent evaluation will be possible when the Evaluation-2 dataset is produced. The full set of plots are available in PDF files for each of the three CKDMIP "applications":

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Six CKD models have been generated for each of the three applications and three band structures, leading to a total of 54 models.  Some of the detailed information at these links may be summarized in terms of the relationship between accuracy (as quantified by six error metrics) of a CKD model and its efficiency (as characterized by the total number of k terms), which for the "climate" application is as follows:

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Naturally the models tend to become more accurate with increasing numbers of k terms, although there appears to be a limit above which the number of k terms does not improve accuracy.  The FSCK performance is typically better than either of the two band structures for the same number of k terms, and the performance is still reasonable even when the total number of k terms is only of order 20.  The plots for the climate-fsck-27 model are presented and discussed below. The various plots show a few areas where ecCKD could be improved:

• All models show a negative bias in downwelling surface longwave flux that gets systematically worse for warmer and moister atmospheres. No such trend exists for OLR, although there is still a negative bias of typically 0.3 W m-2 that could be improved.
• The radiative forcing by methane tends to be too linear, not capturing the extent of the logarithmic dependence on concentration. This is believed to be because the automated procedure for allocating k terms allocates too few to the methane bands, far fewer than are allocated to carbon dioxide, for which the logarithmic dependence is well captured.  This could be improved by reducing the error threshold for the allocation of methane k terms.
• ecCKD optimizes both broadband fluxes/heating rates, as well as those in individual bands. As a result, there is some compensation of errors between various bands which is larger than it should be in models with large numbers of k terms.

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The following plot evaluates the representation of the overlap of the longwave absorption by carbon dioxide, methane and nitrous oxide. In each case, the x-axis shows the top-of-atmosphere radiative forcing from perturbing a gas to either its climatic minimum or maximum value, using the ranges stated by Hogan and Matricardi (2020). These radiative forcings are computed keeping the concentrations of all other well-mixed gases at their present-day values, except for the gas on the y-axis which is perturbed to its own climatic minimum or maximum values. The main error is associated with methane forcing.

Shortwave

In progress...