You are right, the cross dependence would still be there, and come through the 
dry pressure, which gets smaller when there is more water vapor.

Overall, I also still like the option to rescale the VMRs better.


On 16 Sep 2021, at 21:34, Patrick Eriksson wrote:

> Stefan,
>>> 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?
> Bye,
> Patrick

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