RFM Spectral Grids
Contents
15JAN24

Introduction

With the default set-up, the user specifies (in the *SPC section of the driver file) the set of regular spectral grid points on which the RFM calculations are performed and output.

It is emphasised that RFM performs monochromatic radiative transfer calculations at a set of discrete spectral points, whereas the 'real' spectrum is a continuous function.

If the RFM grid is fine enough to capture the underlying spectral structure of the real atmosphere, then e.g., joining up the RFM output points with straight line segments will be a reasonable approximation to the 'real' spectrum. But if the RFM calculations are on too coarse a grid, complete spectral lines may be missed.

Other options are:

Spectral Structure

How fine a grid is required to capture atmospheric spectral structure? An atmospheric absorption/emission lines represents transition between rotational/vibrational energy levels within a molecule. Since these energy levels are well defined, these spectral lines should be infinitely narrow. However, there are two mechanisms which contribute to broadening of lines Lorentz broadening is proportional to pressure, but Doppler broadening is independent of pressure, so at the upper levels of any atmosphere the line widths will be limited by Doppler broadening. Assuming molecular velocities of the order of 300 m/s, a factor 106 smaller than the speed of light, this suggests Doppler widths of the order of 10-6 ν0, where ν0 is the wavenumber at the line centre. For ν0=1000 cm-1 (i.e. 10μm, mid-infrared) this gives a Doppler width of 0.001 cm-1.

that for the Earth's atmosphere, in the mid-infrared (around 10μm, or 1000 cm-1, pressure broadening dominates in the troposphere, Doppler broadening in the mesosphere, with a transition in the stratosphere.

In terms of actual line width, pressure broadening is approximately 0.1 cm-1 at surface pressure. Since the width in wavenumber (or frequency) space corresponds directly to energy uncertainty, set by collisionaly frequency, this number approximately holds for all molecules at all wavelengths, and varies proportional to pressure (with some additional temperature dependence).

Doppler broadening, on the other hand, depends on the average speed of the molecules, which is of the order of 10-6 the speed of light (i.e. 300 m/s compared to 3x108 m/s), consequently the Doppler width is approximately 10-6 x the line centre frequency (it also depends on temperature and molecular mass but these generally vary by less than an order of magnitude). Thus, for the mid-infrared (1000 cm-1) Doppler widths are of the order of 0.001 cm-1, hence take over from pressure broadening for pressures less than 10 hPa. However, for microwave spectra (10~cm-1) the Doppler width is 10-5 cm-1 and so Pressure broadening dominates up to 0.1 hPa, i.e. well into the mesosphere.

There are three basic ways of specifying the RFM spectral grid:

  1. User specifies the grid used for monochromatic spectral calculations and on which output spectra are written ('sampling') - default
  2. User specifies the output grid for which each point represents an average of monochromatic values calculated on a fine, internal grid ('averaging') - AVG flag
  3. User specifies the output grid for which each point represents a convolution of monochromatic values calculated on a fine, internal grid with a user-supplied convolution function ('convolution') - ILS flag + *ILS section.

Cases (2) and (3) are actually very similar, the difference being that for (2) the RFM calculates its own triangular ILS shape. In these two cases the RFM performs calculations on a fine grid set by default to 0.0005 cm-1 (2000 pts per cm-1), which is suitable for limb-viewing in the mid-infrared (for Earth) but may need to be increased for longer wavelengths and/or cooler atmospheres (FIN flag + *FIN section).

Fine Grid

By default this is 0.0005 cm-1 (or 2000 pts/cm-1, which is determined by the typical mid-infrared Doppler half-width of 0.001 cm-1 in the Earth's atmosphere.

Since Doppler width scales as wavenumber (set by 1/DEFFIN set in rfmcon_dat.f90),

However, the RFM may can also perform convolutions in the spectral domain (ILS or AVG flags). In this case it is necessary to distinguish between the output grid (which is what the user specifies *SPC section) and the fine grid, which is used internally for the RFM monochromatic calculations before applying the convolution, which has a default value of 0.0005 cm-1.

The RFM, by default, uses a regular fine grid, but there is also the option of providing it with an irregular fine grid, usually with the aim of reducing compuation time.

The RFM spectral grid is specified by default in wavenumber (i.e., 1/wavelength, with wavelength defined in cm), but can also be specified in GHz. It cannot be specified in wavelength.