Planetary isotopologue ratios
=============================


==========
1) General
==========

Files with adapted planetary isotopologue ratios have been created and can be
 found in the planets folders in arts-xml-data package.

Isotopic ratios of planets (Mars, Venus, Jupiter) differ from Earth only for
 D/H (all planets) and 15N/14N (Mars and Jupiter, not Venus), while 13C/12C as
 well as 18O/16O and 17O/16O are within 5% of Earth's values.
That is, only species containing H (all 3 planets) and N (Mars, Jupiter) need
 adaptation.

Applied planetary isotopic ratios were provided by L. Rezac under ESA planetary
 toolbox study (see TN1). Earth values were derived from ARTS built-in
 isotopologue ratios separately per molecular species (hence only an approximate
 value given here):

--------------------------------
Planet         D/H       15N/14N
--------------------------------
Earth    (~1.5e-4)     (~3.7e-3)
Venus       1.9e-2      as Earth
Mars        8.1e-4        5.7e-3
Jupiter     2.6e-5       2.25e-3
--------------------------------


===========
2) Approach
===========

Isotopologue ratios of species for those planets are derived from modifying
 the ARTS built-in Earth values for the above listed ratio changes (i.e., we
 do NOT calculate them from scratch from the isotopic ratios of all atomic
 species involved!).

That is, we
(1a) derive molecule-specific isotope ratios D/H and 15N/14N from the
 built-in Earth isotopologue ratios of the individual molecules
(1b) or where molecule-specific isotope ratios are not available set them from N2 and H2
(2) modify those to the above listed values.

Isotopologue ratio is the product of the relative isotopic abundances of all
 the individual atoms in a molecule (times the number of positional permutations).

example:
 IR(CH4)  = ia(C) * ia(H)**4  #1C atom, 4H
 IR(CH3D) = ia(C) * ia(H)**3 * ia(D) * 4 #1C atom, 3H aoms, 1D atom
 IR(CH3D) has a factor 4 since D can be in place of any of the 4H, i.e., for us
 CH3D stands for CHHHD and CHHDH and CHDHH and CDHHH, hence their abundances
 have to be summed up.

The isotopic abundance ia can be expressed in terms of the isotopic ratios ir
 (i.e., abundance of an isotope in relation to the main or another isotope):
 ia(i) = ir(i) / ( sum_j=1^N ir(j) )
 i.e., as the relation of the individual isotope's abundance in relation to a
 fixed (usually the main) isotope to the sum of the relative abundances of all
 isotopes to the fixed (main) isotope.

example:
 ia(H) = 1 / (1+D/H)
 ia(D) = D/H / (1+D/H)
 ia(O-18) = O-18/O-16 / (1 + O-18/O-16 + O-17/O-16) #for O we have 3 common isotopes

with this the isotopologue ratios can be rewritten as:
 IR(CH4)  = ia(C) * 1/(1+D/H)**4  #we don't rewrite C as we do not change C-ir here (but in general those can be handled in the exact same way)
 IR(CH3D) = ia(C) * 1/(1+D/H)**3 * (D/H)/(1+D/H) * 4
          = ia(C) * (D/H) / (1+D/H)**4 * 4


STEP (1a)
---------
molecule-specific isotopic ratios can be derived from ratios of isotopologues
 that apart from the two isotopes we want to derive the ratio of are identical
 (but we need to be a bit careful with positional permutation factors and when
 more than one atom of the species is replaced at once, e.g. two D occuring in
 a molecule)

examples:
 IR(CH3D) / IR(CH4) = [ia(C) * 1/(1+D/H)**3 * (D/H)/(1+D/H) * 4] /
                      [ia(C) * 1/(1+D/H)**4]
                    = (D/H) * 4
 => D/H = IR(CH3D) / IR(CH4) / 4

 IR(D2O) / IR(H2O) = [ia(O) * [(D/H)/(1+D/H)]**2] /
                     [ia(O) * 1/(1+D/H)**2]
                   = (D/H)**2
 => D/H = sqrt( IR(D2O) / IR(H2O) )

simple when only one atom of the species of question occurs, e.g.,
 D/H = IR(O-16D) / IR(O-16H)

In case there are more than one possibility to derive molecul-internal isotopic
 ratios, we take the mean of those. for example , D/H for H2O is derived from
 IR(HDO-16)/IR(H2O-16), IR(HDO-18)/IR(H2O-18), and IR(D2O-16)/IR(H2O-16).

STEP (1b)
---------
For cases, where molecule-specific D/H and 15N/14N can not be derived, we take:
 IR(H2) = 1 / (1+D/H)**2 and  IR(N2) = 1 / (1+15N/14N)**2
 => D/H = 1/sqrt(IR(H2)) - 1 and  15N/14N = 1/sqrt(IR(N2)) - 1

STEP (2)
--------
In the IR formula derived above we now replace (D/H)_earth by (D/H)_planet by
 dividing through its factoral contribution in IR_e and multiplying by its
 planetary replacement:
 IR(CH4_p)  =  IR(CH4_e) /         [1/(1+D/H_e)**4] *         [1/(1+D/H_p)**4]
            =  IR(CH4_e) * [(1+D/H_p) / (1+D/H_e)]**4
 IR(CH3D_p) = IR(CH3D_e) / [(D/H_e) / (1+D/H_e)**4] * [(D/H_p) / (1+D/H_p)**4]
           =  IR(CH3D_e) * [(1+D/H_p) / (1+D/H_e)]**4 * [(D/H_p) / (D/H_e)]

That is, all IR_e get rescaled by [(1+D/H_p) / (1+D/H_e)]**N, where N is the
 number of atoms of the specific species in this molecule (here: atom=H and
 N=4). This is the planetary rescaling factor (rp).
Isotopologues with other than the main isotope furthermore get refactored by
 [(D/H_p) / (D/H_e)]**M, where M is the number of atoms of the isotope
 replacing the main one (here: D and M=1; CD4 would have M=4). This is isotopologue rescaling factor (fac).
Note: using this refactoring method, we do not need to care about the
 positional permutation factors. As they occur in both the Earth and the planet
 IR, they factor out.


===================
3) Species Overview
===================

Below is a list of species implemented in ARTS including tags showing what
 isotopes for (and combinations thereof) the isotopologue ratios were adapted:

* species with both H and N
** species with N
*** species with H

* replaced by x, if only main isotope of the respective species in the molecule
 (e.g., only H, but no D). that is, we can't derive the molecule-internal Earth
 isotopic ratios for them. therefore we fix these from the N2 and H2 values.


#############################
*** H2O
 CO2
  O3
** N2O
  CO
*** CH4
  O2
**  NO
 SO2
xx NO2
* NH3
*/x HNO3 (no internal calc of D/H, only of N14/15)
***  OH
***  HF
*** HCl
*** HBr
***  HI
 ClO
 OCS
*** H2CO
xxx HOCl
**  N2
* HCN
xxx CH3Cl
xxx H2O2
*** C2H2
xxx C2H6
xxx PH3
 COF2
 SF6
*** H2S
*** HCOOH
xxx HO2
   O
xx ClONO2
xx NO+
 OClO
 BrO
xxx H2SO4
 Cl2O2
xxx HOBr
xxx C2H4
xxx CH3OH
xxx CH3Br
* CH3CN
 CF4
* HC3N
 CS
* HNC
 SO
xxx C3H8
*** H2
 He
 Ar
x C4H2
 SO3
#############################

