A Correlated K-Distribution (CKD) tool generates CKD gas-optics models in a number of steps. 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 particular steps are performed feed through to differences in accuracy. The steps are:

Reference(s): 

Implementation language(s): 

Select band boundaries:

Reorder spectrum:

Choose number of g points:

Partition g space for one gas:

Partition g space for multiple gases:

Compute absorption of one gas:

Compute combined absorption of multiple gases:

Compute Planck function for each longwave g point:

Compute incoming solar radiation for each shortwave g point:

ecCKD

Reference: Hogan (JAS 2010), although there have been numerous 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. Each major gas is reordered separately, although there is the option to use "composite" gases for NWP applications. 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 monotonically decreasing temperature profile. 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 separately. The user specifies a heating-rate error tolerance, and code calculates the number of g points needed to ensure that the RMS heating rate error (compared to 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 in a band then g space consists of an M-dimensional hypercube. Hogan (2010) described a technique to partition this cube such that for the total number of g points required is N = N₁+N₂+...+N_M + 1 - M, where N_i is the number of g points required for gas i. 

Compute absorption of one gas:

Compute combined absorption of multiple gases:

Compute Planck function for each longwave g point:

Compute incoming solar radiation for each shortwave g point: