RFM Handling of Isotopologues




Most abundant isotopic variants of atmospheric constituents (expressed as a fraction of the total abundance)
Main IsotopeMinor Isotope Fraction
79Br 81Br 49.3 %
35Cl 37Cl 24.2 %
32S 34S 4.2 %
12C 13C 1.1 %
14N 15N 0.4 %
16O 18O 0.2 %
1H 2H 0.016 %

Isotopologues are variants on molecules where one or more atoms is replaced by a minor isotope, HDO being the classic example where one of the hydrogen atoms in water vapour is replaced by deuterium. In fact there are two more abundant H2O isotopologues where the 16O atom is replaced by 18O or 17O, and also rarer combinations where two atoms are replaced by minor isotopes.

Isotopomers are variants of isotopologues where the order of the minor isotopic atom is changed. For example the ozone isotopologue where one of the 16O atoms is replaced by 18O has two isotopomers, depending on whether the 18O atom is at an end or in the middle (the former being twice as abundant as the latter, as would be expected from simple random distribution of the minor isotope among the 3 atoms).

In general, the relative concentrations of isotopologues just reflect the abundances of their component isotopes. For example, HDO is 0.031% of all H2O, which is twice the abundance of deuterium compared to all hydrogen, there being 2 hydrogen molecues in H2O.

HITRAN line data includes all the major isotopic variants with line strengths scaled by the standard abundances (see www.hitran.org/docs/iso-meta). So, for example, HDO line strengths are scaled by a factor 3.10693x10-4, representing the fraction of all H2O molecules that are HDO. Therefore even the major isotopologue line strengths are slightly reduced (factor 0.997317 for H2O) to allow for the minor isotopologues.

While, at first sight, this scaling might seem an unecessary complication, the result is that you can specify a single concentration for each molecule and the relative abundances of the isotopic variants are all automatically taken into account.

The rest of this section is only for those interested in separating out isotopologues.


Apart from substituting 'D' for 'H' for deuterium (eg 'HDO', 'CH3D') the common notation for isotopologues is to use the last digit of the atomic weights of (some of) the component atoms. So, for example, '626' CO2 refers to the main isotopologue 16O12C16O, the ordering representing the linear structure of the molecule rather than the sequence of letters in the chemical formula.

However, this is not always unambiguous. For example the main isotopologue of Carbonyl Sulphide, known both as OCS and COS, is represented as '622', where the middle '2' refers to the 12C in the centre of the chain, and the last '2' refers to 32S.

HITRAN uses a numbering system starting from 1, representing the main isotopologue, then 2, 3 ... in order of decreasing abundance. However, since the HITRAN 160-character record format only allows 1 digit for isotopic identification, the recently added 10th (838), 11th (837) and 12th (737) isotopologues of CO2 are designated '0', 'A' and 'B' (Note: this is not hexadecimal, which would be 'A', 'B' and 'C')

The RFM follows the HITRAN numbering (using ...10,11,12 rather than ...0,A,B), although with some additions for isotopologues from the GEISA database.

Within the RFM Driver Table and .atm files, an isotopologue is indicated by a number in brackets after the molecule name
H2O(4) CH4(3)
but, just for the above two cases, the commonly used 'D' notation is also accepted

Since the bracket characters can cause problems in filenames, where the RFM generates filenames requiring isotopic information (such as Jacobians), the symbol 'i' is used instead, eg for the above two cases

h2oi4 ch4i3

Isotopic Selection

A subset of isotopologues can be selected from the HITRAN database by specifying isotopic IDs in the
*GAS section of the driver table
   H2O(4) H2O(2) CH3D ! select H2O 162, 181, CH4 212
Isotopologues can also be excluded using a negative number, eg H2O(-1)(-2) excludes the two most abundant H2O isotopologues (161,181).

Note that is only spectroscopic line selection, it has no impact on any other part of the RFM calculation which will proceed as normal but using fewer lines for these molecules.

Isotopic Variation

The standard way to tell the RFM to distinguish between isotopologues is to add isotopic profiles in the .atm files listed in the *ATM section of the Driver Table. These are in addition to a generic profile (which will be used for all the remaining unspecified isotopologues).

Instead of absolute concentrations, isotopic profiles are specified in similar magnitudes to the main isotopologue, since the isotopologue line strengths are already reduced in HITRAN to represent their reduced concentrations (see HITRAN list of scaling factors).
*H2O [ppmv]
10000 8000 6000 4000 2000 1000 500
200 100 50 10 5 5 ...
*H2O(4) [ppmv]
5000 4000 300 200 1000 500 250
100 50 25 5 2.5 2.5 ...
In the above example the HDO profile is set to 50% of the value of the H2O profile (equivalent to a depletion of 500 parts per thousand). HDO line strengths in HITRAN have been scaled by a standard HDO abundance of 3 x 10-4 so the actual modelled surface concentration of HDO molecules would be 5000 x 3 x 10-4 = 1.5 ppmv.


The RFM can be used to create Jacobian spectra of isotopologues, specified in the usual way in the *JAC section of the Driver Table.
   H2O 0 3 6 9 12
   H2O(4) 0 3 6 9 12
In this example, two sets of Jacobian spectra would be created, one set with filenames containing the string 'h2oi4' representing perturbations of just the HDO lines, and another containing string 'h2oi0' representing perturbations of all the other isotopologues, excluding HDO.

Note that if isotopologues are specified in the *JAC section this also forces the RFM to differentiate between these isotopologues even if only a single H2O profile was specified in the *ATM section. This would be equivalent to specifying HDO profile values which are the same as the H2O profile values.

You can specify different isotopic profiles on which to base the Jacobians, as described in the previous section, but unless dealing with large isotopic depletions or enhancements, it's probably sufficient to base Jacobian calculations on the standard abundances.