For HSE it is up to the user to apply this "fine tuning" or not. This including
to include adding call of the HSE method in OEM iterations, to make sure that HSE is
maintained after an iteration. The VMR rescaling should also be included in the iteration
agenda, if the retrieval can change H2O close to the ground. That is, a VMR rescaling
would not be something completely new, as I see it.
It seems to me that this leads into a logical loop: If you retrieve H2O and O3,
and the retrieved H2O value directly affects the O3 value due to the rescaling.
As you write, in principle, this should even be in the Jacobian, as a
cross-term. With more water, the lines of all other gases get weaker.
It is true that if there is more of the one there has to be less of the other,
but argh, this is so ugly.
Perhaps the deeper reason why AER went for the other definition? If VMRs refer
to the dry pressure, and the dry gases are all either quite constant or very
rare, then retrievals are more independent.
To switch to the other definition, than the VMR of e.g. N2 would stay
the same in a retrieval of H2O. This is why I initially found this
option nice. But it would not change the physics and the
cross-dependences between species would not disappear. You have to
remember that VMR is a relative measure. To get the absolute amount of
the species, you still need to calculate the partial pressures. That is
you need to "distribute" the total pressure among the gases, and as I
understand it a general expression for this would be:
p_i = VMR_i * p / VMR_sum
where p_i is partial pressure of species i, VMR_i its VMR, p pressure
and VMR_sum the sum of all VMRs.
Our present definition is based on that VMR_sum=1, while in the
alternative version it will deviate, and with more H2O VMR_sum will
increase which will affect p_i even if VMR_i is unchanged.
Or do I miss something?