RFM Numerical Optimisations



 13MAY24

Introduction
The following assumes that the Fortran compiler options have already been
set to produce 'fast' code, eg removing array bound checks, enabling any
compilerspecific optimisations.
The RFM decomposes any problem into a calculation of monochromatic absorption
spectra for a number of singleabsorber, homogeneous paths. The computation
time therefore scales approximately as the time required for a single spectral
calculation multiplied by the number of paths. That is:
(geometric component) ×
(spectral component) ×
(No. absorbing species)
Geometric Component
The principal calculation unit is a 'path',
defined as the segment of a ray path within an atmospheric
profile layer for a single gas. For example, if an atmosphere is defined
at 0, 10, 20 .... 60 km, and a single limbviewing
spectrum from tangent height
35 km is required, there will be 3 paths (for each absorbing species)
corresponding to the altitudes 35–40,
40–50 and 50–60 km.
For zenithviewing from the surface (ZEN
flag) there will be 6 paths (0–10, 10–20, ... 50–60 km)
Adding horizontal structure with limbviewing
(GRA Flag) will
double the number of paths since the upward and downward parts of the
ray path are no longer identical.
If a FieldofView convolution (FOV Flag)
is required the number of paths is again increased by
a factor corresponding to the number of tangent rays required to specify the
FOV.
The following options, starting with the simplest, are suggested to reduce the
number of paths:
 *ATM Section
 The number of paths is also determined
by the height (or pressure range)
and resolution of the atmospheric profile, i.e. the
altitude (or pressure) grid specified in the first file named in the
*ATM section of the Driver Table.

It is generally
adequate to set an upper limit of 120 km for the earth's atmosphere
(unless performing specialist highaltitude calculations)
and to increase the profile spacing in the
upper levels.

Rather than reformat the standard atmosphere files,
the suggested method is to prepare a single height (or pressure) profile in
the .atm file
format which contains the required subset of profile levels
and insert this as the first file in the
*ATM section.
 Something similar to the US Std Atmosphere levels
(hgt_std.atm) is adequate for
limbviewing but even this is probably too fine (particularly in the upper
altitudes) for nadirviewing.

The LAY and/or
BFX Flags can be used for a quick check
whether the layering makes a significant change to the calculated spectra.
 *TAN Section
 Compute as many tangent heights as possible at the same time. This is
because many path sections in the upper
atmosphere have similar CurtisGodson p,T values so the absorption
coefficients only need to be calculated for one path segment and will
be automatically scaled by the absorber amount for similar segments
(the CLC Flag switches off this scaling).

For planeparallel atmospheres
(NAD or
ZEN
flags) this makes no difference as the RFM already
uses the fact that all slant
paths have mathematically identical CG parameters.
 .fov File
(limbviewing)
 The fieldofview (FOV) representation
critically affects the number of calculated paths. For single tangent
heights, the number of paths will be proportional to the number of points
required
to specify the FOV. For multiple, regularlyspaced tangent heights,
efficiency can be gained by using a FOV tabulation on the same spacing
as the tangent heights which allows individual tangent paths to be reused
and adding the FVZ Flag.
For example, the MIPAS trapeziumshape response (0,1,1,1,0) at
relative altitude coordinates (2,1.4,0,+1.4,+2) can be replaced by an
'equivalent' shape (0,y,1,y,0) where y=0.2798 for (3,1.5,0,+1.5,+3),
or y=0.2302 for (2,1,0,+1,+2). For the 1.5km FOV spacing,
a series of n limb views at 3 km increments will
require 2n+3 tangent paths instead of 5n.
Spectral Component
The spectral calculation for an individual molecule can be performed in a number
of ways (see RFM spectral calculations) but generally
the
timeconsuming part will be the linebyline calculations which use the HITRAN
line parameters. This will vary according to molecule simply due to the number
of
lines which have to be considered within the required spectral range but, for
each molecule, the number of calculations required will be the same for each
path.
Speed improvements can be made by reducing the number of spectral points
at which calculations are made, reducing the number of lines
considered, using simplified lineshapes, or replacing the linebyline
calculation with lookup tables.
 REJ Flag
 Sets lower limits on the pathadjusted strength of lines which are
included in the spectral calculation.
Different criteria will be appropriate for different spectral regions and
tangent heights so it is advisable to compare results with and without
this option for specific cases.
 SHP Flag
 By default the RFM uses the Voigt lineshape throughout (=convolution of
Lorentz and Doppler lineshapes). However if it is known that either
Doppler or Lorentz are appropriate, the calculation is quicker if
these lineshapes are used explicitly. (Warning: although the Lorentz
line shape may describe the lineshape at low tangent altitudes it is
often necessary to allow for the Doppler 'core' of lines when performing
calculations using the limbviewing geometry)
 FIN Flag
 If an ILS convolution is required (set by the
ILS or AVG
Flags) the
default is to perform the calculation at 2000 pts/cm^{1}
(i.e. 0.0005 cm^{1} grid)
which is adequate
to resolve Doppler lines at high altitudes (required for limbviewing
calculations) in the midinfrared (~10µm), but for nadirviewing calculations
1000 pts/cm^{1} is usually adequate.
Specifying a coarser resolution will speed up the calculation.
 GRD Flag
 The user can supply irregular grids
(.grd files) to specify the spectral points at
which the lineshapes, absorption coefficients, radiative transfer etc
are calculated instead of using every point on the regular fine grid.
The path radiances, absorptions and transmissions are then interpolated
to the regular grid before output (also prior to any ILS convolution).
Alternatively, the GRD
flag can be used in conjunction with
.tab files to calculate radiances only
at the grid points contained in the files.
 LUT Flag
 The user can supply LookUp Tables (see
See RFM LUTs)
to supply pretabulated absorption coefficients for specific absorbers and
spectral ranges, instead of using a linebyline calculation.
Absorbing Species
 *GAS Section
 The number of paths is proportional to the number of molecules specified in
the driver table, although it is usually the cost of calculating the spectral
component of 'line' molecules (*HIT section)
rather than the number of molecules which is the
main influence.
 Beware of including molecules with overall
weak absorption but a large number of lines (eg COF2 and COCl2 in HITRAN2016).
You can use the WID flag to see how many
lines each molecule contributes.
 Molecules represented by HITRAN crosssection data
(*XSC),
collisioninduced absorption
(*CIA) or by
RFM LookUp Tables
(*LUT) generally impact
the memory usage rather than computation time.