This page evaluates the ECMWF CKD tool "ecCKD", which builds on the methods described by Hogan (JAS 2010) and is under active development; the longwave results are from version 0.5 and the shortwave results from version 0.6. CKD models are generated from CKDMIP datasets using the following automated steps:

  • 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 in the longwave, and the height at which the optical depth from TOA reaches 0.25 in the shortwave. 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.

1. Longwave (ecCKD v0.5)

1.1. Overview

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.   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":

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:

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 longwave 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.

1.2. Detailed evaluation of the climate-fsck-27 model

To illustrate the performance of ecCKD, the plots are shown for one of the better CKD models it produced, targeting the climate application with the FSCK band structure and 27 k terms. The parts of the spectrum contributing to each k term are illustrated below. The first term represents the most optically thin parts of the spectrum while terms 2-27 target the absorption by an individual gas.  Most of the terms are for CO2 and H2O, except for terms 2, 17 and 21 for O3, term 10 for N2O and term 11 for CH4.

The following plots evaluate fluxes and heating rates for the four CKDMIP greenhouse-gas scenarios "Present", "Preindustrial", "Glacial Maximum" and "Future" (click on individual plots to expand). The evaluation has been performed using radiative transfer with four zenith angles in each hemisphere (8 streams). The shaded regions in the central three panels of each plot encompass 95% of the data. As with most models generated by ecCKD version 0.5, the upwelling TOA fluxes are underestimated by 0.3-0.4 W m-2, and the downwelling surface fluxes are are unbiased for values up to around 200 W m-2, but increasingly underestimated as the downwelling flux increases (which we assume to be associated with warmer and moister atmospheres).

The following plot compares the instantaneous radiative forcing (change to net flux) at top-of-atmosphere and the surface, from perturbing the concentrations of individual well-mixed greenhouse gases from their present-day values, found by averaging over the 50 profiles of the Evaluation-1 dataset. For the minimum and maximum concentrations, the change to mean atmospheric heating rate is also evaluated. In this case we see that the model represents the radiative forcing of all gases well except for methane for which the dependence of forcing on concentration is too linear.  As shown in an earlier plot, only one of the k terms is dedicated to methane absorption, so it is likely that more terms would need to be added to improve this dependence.

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.


2. Shortwave (ecCKD v0.6)

2.1. Overview

Shortwave CKD models have been constructed with a range of k terms using the wide and narrow CKDMIP band structures. The full-spectrum correlated-k method was tried but the results are not yet satisfactory. As in the longwave, the CKD models are optimized by minimizing the errors against the Evaluation-1 CKDMIP line-by-line dataset, so the evaluations here are not yet truly independent. The full set of plots are available in PDF files for each of the three CKDMIP "applications":

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:

Naturally the models tend to become more accurate with increasing numbers of k terms and in terms of RMSE in fluxes there appears to be scope for further increasing accuracy by futher increasing the number of k terms. When comparing models using the narrow and wide band structure for the same number of k terms, the narrow-band models tend to have a larger flux bias but a lower upper-atmosphere heating-rate RMSE. 

2.2. Detailed evaluation of the climate-wide-38 model

To illustrate the performance of ecCKD, the plots are shown for one of the better shortwave CKD models it produced, targeting the climate application with the wide band structure and 38 k terms. The parts of the spectrum contributing to each k term are illustrated below. ecCKD automatically selects k terms with the aim of each one having a roughly similar error in reproducing the fluxes and heating rates in the parts of the spectrum it represents. It can be seen here that in the first three wide bands the k terms have been selected similarly to the longwave according to the locations of the strongest and weakest absorption lines. In the fourth wide band where line absorption is very weak, five k terms are used stacked in order of increasing Rayleigh optical depth. In the final wide band the k terms are selected according to the strength of continuum absorption by ozone and molecular oxygen.

The following plots evaluate fluxes and heating rates for the four CKDMIP greenhouse-gas scenarios "Present", "Preindustrial", "Glacial Maximum" and "Future" (click on individual plots to expand). Five solar zenith angles have been used with a fixed surface albedo of 0.15, the approximate global-mean value. The evaluation has been performed using two-stream radiative transfer for both the CKD and LBL models. The red line in the central column of panels quantifies the bias averaging over all five solar zenith angles, so should be considered as a daytime average (divide by two to get an approximate diurnal average). The shaded regions in these panels encompass 95% of the data. The upwelling TOA fluxes are overestimated by a little under 0.5 W m-2.


To understand the broadband errors further, the following figure evaluates fluxes and irradiances in each of the 5 wide CKDMIP shortwave bands.

The following plot compares the instantaneous radiative forcing (change to net flux) at top-of-atmosphere and the surface, from perturbing the concentrations of individual well-mixed greenhouse gases from their present-day values. It has been found by averaging over the 50 profiles of the Evaluation-1 dataset, and averaging over the five solar zenith angles; therefore these forcings correspond to daytime only. The CFCs have a tiny shortwave effect so have been excluded. For the minimum and maximum concentrations, the change to mean atmospheric heating rate is also evaluated. For modest perturbations to these gases, the forcing is well captured, but for 8x CO2 or the very low concentrations at glacial-maximum, the forcing is less well captured.



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