A Correlated K-Distribution (CKD) tool generates CKD gas-optics models in a number of steps, sometimes requiring human intervention. This page compares how the various tools perform each step. One of the most interesting parts of CKDMIP will be to understand how differences in how each step is performed feed through to differences in the accuracy of fluxes and heating rates. The page is an attempt to gather information about how the CKD tools perform these steps, specifically:
Reference(s): Relevant paper(s) describing the method.
Implementation language(s): Fortran, Python etc.
Select band boundaries: Band boundaries are always chosen manually, but what are the restrictions on band width, e.g. to minimize the number of major gases in each band, or the variation in the Planck function?
Reorder spectrum: Is reordering done separately at each pressure level, or is there a unique mapping from wavenumber to g space?
Choose number of g points: Is this specified manually, or is an automated procedure used to determine the appropriate number of g points for a particular band and gas?
Partition g space for one gas: Is g space partitioned using a fixed formula (e.g. Gaussian Quadrature), or a more adaptive method?
Partition g space for multiple gases: How are the g points for the individual active gases in a band combined to produce the total number of g points?
Compute absorption of one gas: How are the LBL spectral absorption values averaged to obtain the absorption by one gas in one g point, e.g. logarithmic averaging? How is the pressure/temperature/concentration dependence of absorption handled in the gas-optics model generated, e.g. parametrically or as a look-up table?
Compute combined absorption of multiple gases: How are the absorptions from multiple gases combined, potentially accounting for non-random spectral overlap?
Compute Planck function for each longwave g point: Is the Planck function first computed for the band and then partitioned amongst the g points, or is account made for exactly where in the band the energy contributing to a particular g point comes from?
Compute incoming solar radiation for each shortwave g point: How is the incoming solar radiation computed for each g point, and using which reference spectrum?
ecCKD
Reference: Hogan (JAS 2010), although there have been several improvements since then such as extension to the shortwave.
Implementation language(s): C++ programs called from shell scripts.
Select band boundaries: There are no restrictions on the width of a band, and indeed ecCKD can be used to generate full-spectrum correlated-k (FSCK) models.
Reorder spectrum: The spectra for the "median" CKDMIP present-day profile are reordered. Reordering is performed for "major" gases, which for the "climate" application are H2O, O3, CO2, CH4, N2O and in the shortwave only a composite gas of O2+N2. For the "NWP" application the major gases are H2O, O3 and a composite gas containing all other CKDMIP gases. Each major gas is reordered separately (where a composite gas is treated as a single gas). A unique ordering is produced for each gas that is constant with pressure, i.e. we don't reorder separately at each pressure level. In the longwave, ordering is in terms of the height of the peak cooling rate for an idealized temperature profile, monotonically decreasing with height. In the shortwave, ordering is in terms of the height at which the zenith optical depth to top-of-atmosphere is 0.25.
Choose number of g points: The number of g points required to represent each major gas is computed in turn. The user specifies a heating-rate error tolerance, and the code calculates the number of g points needed to ensure that the RMS heating rate error (compared to the LBL reference) for each g point is less than this tolerance, taking the concentration of the target gas from the "median" CKDMIP profile. The RMS error is computed assuming that the spectral variation of absorption for the target gas is replaced by a single value, but all other gases are represented with full LBL spectral resolution. The concentrations of all other gases are held at their "minimum" value, which for the greenhouse gases in climate applications is the concentrations from the Glacial Maximum scenario. This adaptive method to choose the number of g points ensures that fewer g points are used for gases with weak absorption in a particular band, or in a band with little energy.
Partition g space for one gas: For each gas, an equipartition algorithm is used to shuffle the boundaries in g space to ensure that each g point contributes roughly equally to the RMS error in heating rate and fluxes, again just considering the "median" CKDMIP profile.
Partition g space for multiple gases: If we have M major gases then g space in a band consists of an M-dimensional hypercube. Hogan (2010) described a technique to partition this cube such that the total number of g points required is N = N1+N2+...+NM + 1 - M, where Ni is the number of g points required for gas i. Note that if gas i is declared as major but turns out to have weak absorption in a particular band then it will not lead to unnecessary g points because Ni will be 1 (i.e. a single g point representing the entire band).
Compute absorption of one gas: The CKDMIP "Idealized" dataset is used to construct a look-up table for each gas (major and minor): for a given input temperature, pressure and concentration, the look-up table provides the absorption coefficient of that gas at all N g points. The absorption coefficient in a g point is computed by averaging the spectral absorption coefficients contributing to that g point such that the transmittance of the layer to diffuse radiation is preserved. For all gases except water vapour, the absorption coefficient is assumed to be proportional to concentration (i.e. the look-up table provides the molar absorption coefficient from temperature and pressure, which is then multiplied by the mole fraction of the gas to obtain the absorption coefficient). The look-up table for water vapour allows a nonlinear dependence of absorption on concentration. Composite gases represent those whose concentrations are fixed or depend only on pressure, i.e. O2+N2 in CKD models for climate and CO2+CH4+N2O+O2+N2+CFC11+CFC12 for NWP; in this case the look-up table is a function of temperature and pressure with no dependence on concentration.
Compute combined absorption of multiple gases: Gas optics models produced by ecCKD assume that the total optical depth of a layer in one g point is the sum of the contributions from individual gases (each computed from a look-up table). However, the "out of the box" performance using absorptions from the previous step is poor. Therefore, an optimization step is performed in which the coefficients of the look-up tables are adjusted such that the resulting fluxes best agree (in a least squares sense) with reference fluxes from the 50-profile CKDMIP Evaluation-1 dataset (the 50 profiles sampling wide variations in temperature, water vapour and ozone). Typically in optimizing the coefficients for a CKD gas optics model to be used for climate modelling, this is done in several steps. Firstly, the look-up table coefficients for water vapour, ozone and carbon dioxide are optimized using line-by-line flux calculations in which CO2 is varied (CKDMIP scenarios 5-9), but with present-day concentrations of the other well-mixed greenhouse gases. Subsequent steps then optimize the coefficients of CH4 and N2O, each time training with LBL calculations varying only these gases. These optimization steps ensure that when more than one gas is important in a particular spectral range, the coefficients are chosen such that the fluxes are as accurate as they can be over the range of concentrations used in the training. This does, however, mean that an ecCKD-generated gas-optics model is not independent of the Evaluation-1 dataset, so should be evaluated with the independent Evaluation-2 dataset.
Compute Planck function for each longwave g point: The Planck function is computed for each g point as a look-up table against temperature with 1 K resolution. Since each g point maps on to the same points of the original spectrum regardless of pressure, this look-up table is created simply by integrating over the spectral Planck function from those spectral points.
Compute incoming solar radiation for each shortwave g point: The incoming solar radiation for a g point is found by integrating over the points of the Coddington et al. (BAMS 2016) reference spectrum used by CKDMIP which contribute to that g point.