RFM use of Look-Up Tables
RFM use of Look-Up Tables |
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05JAN25 | ||
For absorbing species represented by line parameters (i.e., molecules#1–63) the calculation of k is 'line-by-line': each transition has its strength and linewidth adjusted for local p,T conditions, and the contributions from all (local) lines are summed at each spectral grid point.
This 'line-by-line' approach is computationally expensive and, where a large number of transitions are involved (mid-infrared) it is quicker to use pre-tabulated look-up tables (LUTs) of k [m2/kmol] (1 kmol approx 6e26 molecules).
There will be some loss of accuracy since the set of (p,T) values used for the tabulation will generally not match the actual Curtis-Godson (p,T) values required for the RFM calculations, resulting in an interpolation error in the p,T domain. This error can be reduced by dense sampling of the p,T domain when constructing the tables or, if working on a fixed pressure grid, ensuring that the p tabulation values are at the Curtis-Godson pressures for the grid.
The RFM has the ability both to create such LUTs and to use them, and there are various (Fortran) programs to manipulate these LUTs.
The spectral range(s) (*SPC) and list of absorbers (*GAS) have their usual definitions, allowing multiple tables to be generated in a single RFM run. The atmospheric profiles included in the *ATM section have a more subtle influence, described below.
For the 'plain' LUT calculation, the user would specify uniformly spaced axes in pressure and temperature, and the RFM would calculate one or more .tab files containing tabulations of k(ν,p,T) for different spectral ranges and/or absorbers.
To be used, the LUT file has to contain one of the absorbers specified in the *GAS section of the Driver Table, and completely span one or more of the spectral ranges specified in the *SPC section.
Unless a LUT file can be found for every spectral ranges for every specified absorber, the RFM will also require a HITRAN binary file (*HIT section) or a cross-section file (*XSC section), depending on the molecule, even if these files contain no absorption feature for the molecule in the spectral range.
Note the distinction between LUTs, which are assumed to specify absorption only within the spectral range covered by the LUT, and the HITRAN and cross-section files which are assumed to contain all the spectral features of the absorber. This allows LUTs to be 'plugged into' any spectral range over-riding HITRAN or cross-section data without ambiguity.
See also TABMRG.
See also tabcmp_x.
Different compilers have different interpretations of binary files, so if you do decide to use binary LUTs you should use the same fortran compiler for all of
The various Auxiliary Programs for manipulating .tab files can also be used to convert between ASCII and binary formats.
The main reason for this is that the 'line-by-line' calculations involve some dependence on absorber concentration (see VMR Dependence), which is obtained from the user-specified VMR profile interpolated to the LUT pressure grid.
A second reason is if the user uses LUT axis options related to the atmospheric profile itself, such as PCG, or 'relative temperatures', where the LUT temperature axes are temperatures relative to some temperature which varies as a function of the pressure axis.
The temperature and VMR profiles, interpolated to the pressure axis, are always written to the LUT file. If the user specifies a homogeneous atmosphere then the temperature and VMR profile values will be constant, but still contain as many values as points on the pressure axis.
However, when calculating these k values, it is necessary to make some assumption about the volume mixing ratio (VMR): HITRAN has different Lorentz half-width parameters for self-broadening and air-broadening, and molecular continua may also contain different self- and air-broadening components,
Usually the VMR is obtained from the user-supplied profiles of pressure and VMR (see Atmospheric Profiles) to interpolate VMR to the pressure axis values, so for each pressure value a single VMR value is assumed.
However, the .tab file format allows for a fourth-dimension: k(ν,p,T,q), where q is the explicit dependence on the VMR.
For most species in the Earth's atmosphere the actual concentrations are too small for this to be significant, and for other molecules such as O2 or N2 the concentrations are almost constant so no tabulation as a function of VMR variability is required. In fact this extra dimension is only likely to be needed for tropospheric H2O.
The tabulated q-axis values are defined to be % scaling factors for the embedded VMR profile, thus the actual VMR used to calculate k(ν,p,T,q), will also vary with the p-axis value.
In the absence of any explicitly defined q-axis the .tab file contains a single value '100' [%] for this dimension.
There is an additional complication in that H2O lines are calculated slightly differently when combined with the continuum. When calculating the line-only component of a H2O LUT, the RFM's default behaviour is to assume that this LUT will be subsequently be used in conjunction with the continuum, so the recommendation is
It is possible to generate LUTs on predefined grids using the GRD option, but there is also a dedicated Auxiliary program, tabcmp_v which takes as input a .tab file generated on a full regular grid, examines the spectral structure of the tabulated data to determine a reduced, irregular set of grid points, and automatically creates a reduced LUT file on the irregular grid.
The suggested procedure is to use the RFM to generate .tab files on the full grid (which will be huge), then run the tabcmp_v program to remove spectral points which can be interpolated, thereby reducing the files to a more manageable size.
A number of mostly heavier molecules (molecules#100+) are already represented by tabulated absorption cross-sections k(ν,p,T) rather than individual transitions (although note that k in these .xsc files is in units of [cm2/molecule] cf [m2/kmol] in the .tab files).
These are usually species where the individual line transitions are too closely spaced to be distinguished so lab measurements are restricted to the general shape of the absorption feature for a variety of different p,T conditions.
These .xsc files files are in principle the same as the RFM-generated .tab files in that the absorption coefficient k is interpolated in the (ν,p,T) domain but with the following differences
Note also the GHZ Flag which converts the .tab file table spectral axes from cm-1 to GHz. When using these as input files, the RFM automatically determines which spectral axis units are used.
While defining accuracy in terms of the reconstructed k values would be straightforward (either in absolute terms or as a fractional error), it is not actually that useful. The problem is that the user probably wants to specify accuracy in transmittance or radiance spectra, which are non-linearly related to k.
The approach is to assume that the pressure axis of the .tab file approximates to the vertical layering required by the user, and that the temperature and VMR axes represent the range of atmospheres to be modelled. Following the RFM treatment (see Introduction) the (p,T,q) axes of the .tab file can then be used to define a set of Np × NT × Nq homogeneous cells, with each cell (pi, Tj, qk) containing an absorber amount uijk [kmol/m2] defined by the pressure-axis interval and embedded VMR profile as if these were layers in a vertical path through the earth's atmosphere
Each cell ijk will have a monochromatic transmittance given by
The user then defines the accuracy Δτ with which the transmittance of every cell matches the original transmittance as spectral points are removed and interpolated.