What does these sentences of p-e part mean from the third version of neuralGCM paper?

[weatherforecasterwhai]

Hi,
Thank you for adding more figures and explanation in the third version. Fig C5 is really great to understand more.
Thank you for adding these sentences, which are out of my consideration at all. Good lessons for me.
However, the following sentences are not clear to me:
1."We note that the calculation of P −E assumes that the dynamical core is responsible for all horizontal motions;
thus, P −E could be diagnosed using Eq. H13."
Why do you say this? Sorry, I never heard before. Would you please explain more in detail?

2."However,the physics module might also learn to correct errors originating from inaccuracies in
the dynamical core (e.g., as a result of calculating advective tendencies on a coarse grid), which may
introduce errors into the calculation of P −E. "
Of course, the learned physics might correct the dynamicsal core. Does this sentence hint that the physics module
does not correct some part of dynamical core related to calculating p-e?
Because in Fig C5, "The network tendencies Ψ( ˜X) are added to Φ( ˜X)". Both the moistures and u,v tendencies
predicted by learned physics are considered. What else are not considered?
"as a result of calculating advective tendencies on a coarse grid", could this not contained in the network tendencies?

3."Given that P −E calculated from NeuralGCM-0.7◦ appears generally consistent with ERA5 in the weather
forecasting scenario (Fig.H30), this suggests that any error is likely small."
If adding more learned physics correction as in 2, maybe neuralGCM predicts better for the extreme precipitations.

4. Equation H13 "is the sum of the water species tendencies predicted by the neural network".
   Why not adding the water species tendencies predicted by dynamical part?
   The tendencies are always added by these two parts according to fig1.

5. I found, cloud ice in neuralGCM is almost the same with cloud ice in ERA5, but not accounts cloud snow of ERA5(in my extreme rain case, it lies in the lower layer but 10 times larger).Also, cloud liquid in neuralGCM is almost the same with cloud liquid in ERA5, but not accounts cloud rain of ERA5 (much lower and 10 times larger),
   So, without these two much larger(in my extreme rain case) kinds of moisture, which might affect predicting other three moisture tendencies, and affect the p_e after.
   Why not adding these two moisture species: cloud rain water content and cloud snow water content to neuralGCM ?

[yaniyuval]

The ability to diagnose (and not directly predict) P-E comes from the separation of the dycore from the physics tendencies (NN parameterization). Namely, a pure ML model won't be able to diagnose P-E (it would have to predict it unless it has a way to separate advective tendencies from the physics).
Therefore, if the NN corrects errors also in the dycore, it introduces errors into diagnosing P-E.

About including other tracers (snow and rain) is something we have thought of a long time ago but didn't have the time. Furthermore, we are not really sure it is critical to add (given the fast time scale rain drops fall and the time steps our models take)