RFM Use of Look-Up Tables of Absorption Coefficient
RFM Use of Look-Up Tables of Absorption Coefficient |
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08JUN24 | ||
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.
Creating LUTs
The TAB Flag can be used to switch
the RFM from generating spectral output files to generating LUTs as individual
.tab files, one for each absorber
for each spectral range. In this case the contents of the
*TAN section of the driver table,
which usually specify the path geometry, instead specify
the axes for the LUTs
(see *DIM section).
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.
Using LUTs
The LUT Flag can be used to enable
the RFM to use .tab files as input,
with
filenames specified in the *LUT
section.
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 all spectral ranges for each specified absorber, the RFM will also require a HITRAN binary file (*HIT section) or a cross-section file (*XSC), 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.
LUT Axes
The following suggestions are provided for specifying the range and
spacing of the p, T axes in the
*DIM section of the Driver Table.
See also tabcmp_x.
Binary LUTs
Unless you want transfer between different computers, or
to examine the file contents, the
BIN Flag is recommended:
creating LUTs as binary files which are more compact and faster to read.
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.
Atmospheric Profiles
Although the calculation of LUTs in principle only involves applying a fixed
set of (p,T) values to the HITRAN parameters it is still necessary
to provide the RFM with atmospheric profile information via the
*ATM section, or at least homogeneous
path conditions (HOM flag).
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.
VMR Dependence
By default, absorption coefficient values k(ν,p,T)
are tabulated as functions of wavenumber, pressure and temperature.
H2O Continuum
The H2O continuum is unsuitable for inclusion in a
LUT: it has strong dependence
on (p,T,q), which would require a dense tabulation
to be properly represented, but on the other hand can be calculated explicitly
relatively quickly. This suggests only the H2O 'line-only' component should be
stored as LUTs, with the continuum component added separately when required.
Irregular Grids
The LUT format allows for irregular spectral grid spacing; ideally with dense
spectral sampling near line centres, coarser sampling in line wings and no
sampling where absorption is negligible. This reduces both the file size and the
access time.
Cross-section (.xsc) files
Since there is no saving in the 'line-by-line' aspect for such molecules,
the only advantage of converting
.xsc files
to .tab files is the saving of
internal array space required to hold the full
k(ν,p,T)
matrix
.xsc files.
Microwave Region
The number of line transitions, per unit wavenumber, is less dense in the
microwave (a few 10s of cm-1) compared to the mid infrared
(1000 cm-1) so the main advantage of using LUTs is lessened.
Accuracy Criteria
Several of the Auxiliary Programs compress the
.tab files subject to a
user-defined 'accuracy criterion'.
Auxiliary Programs
There are several standalone FORTRAN programs for manipulating
.tab files.
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