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 more common 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 (eg, a factor 0.997317 for 'standard' H2O) to allow for the minor isotopologues.

At first sight this scaling might seem an unecessary complication, but 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 page is only for those interested in separating out isotopologues, or altering their concentrations.


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.

Knowing the order can be important. For example, the main isotopologue of the linear molecule Carbonyl Sulphide, known both as OCS and COS, is represented as '622'. In this case you need to know that carbon is the middle atom, so 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'). Confusing, maybe, but it's a result of historical evolution — the format was designed back in the day when 9 isotopic variants seemed more than sufficient.

The RFM identifies isotope by their HITRAN numbering, but using ...10,11,12 rather than ...0,A,B.

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. E.g., for the above two cases

h2oi4 ch4i3
(Hydrogen Iodide (HI), and the recently added CH3I, are the only molecules in the HITRAN database with the letter 'i', so this should not create too much confusion.)

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, eg
*GAS H2O(4) H2O(2) CH3D ! select H2O 162, 181, CH4 212
Specific 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 standard, generic profile for the molecule which will be used for all/any remaining, unspecified, isotopologues.

Since the isotopologue line strengths are already scaled in HITRAN to represent their reduced concentrations (see HITRAN list of 'Abundances'), isotopic profiles should have similar magnitudes to the generic molecular profile (i.e., not the absolute concencentrations of the isotopologues), eg

*H2O [ppmv] 10000 8000 6000 4000 2000 1000 500 200 100 50 10 5 5 ... *H2O(4) [ppmv] 5000 4000 3000 2000 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 concentration of HDO molecules at the lowest profile level 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.
*JAC 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 (i.e. excluding HDO).

Note that even if only a single H2O profile was specified in the *ATM section, specifying isotopologues in the *JAC section, as above, will also force the RFM to differentiate between these isotopologues, equivalent to to specifying separate but identical HDO and H2O profiles in the *ATM section.

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 (so no need for explicit isotopologue profiles in the *ATM section).

Recognised Isotopologues

The RFM holds an internal list (in module isolst_sub.f90) of all the isotopologues found in HITRAN 2020 and GEISA 2015 linelists. This is required because, in order to compute the Doppler width (or the Doppler part of the Voigt lineshape), it needs the mass of the isotopologue, which is not something contained in the HITRAN .par format.

If you present the RFM with an isotopologue which is not in its internal list a fatal error is reported. However it should be straightforward to edit isolst_sub.f90 to allow it.

The other piece of code with explicit isotopic data is for the Total Internal Partition Sums (TIPS) calculation. TIPS data are not provided for the GEISA isotopologues, and adding new isotopologues to the TIPS data isn't really a practical option, so, faced with an isotopologue for which it has no specific TIPS data, the RFM defaults to using the TIPS data for the main isotopologue with just a warning message printed to the rfm.log file.