Dear author,

I now received a review report on the revised version of your paper.

"
The revised paper and the responses of the authors are very helpful and clarify the paper. There are a few minor points left that need attention:

1) Check the text one more time in depth. Obvious textual mistakes (such as abstract L.4 “a simple simple model”, p.11 L9: “the resolution… do*es* not…”, etc.) give an impression of carelessness.
2) It would be helpful to identify all “perturbation parameters” (or estimated parameters) in the descriptive text about the model. It is done now for Q_0, it can also be done for chi and alpha_min.
3) Link the observation operator H with the model description in the previous section. H is not linear, yet it is portrayed as a matrix which is not right.
4) I do not think that it is useful/correct to define the mean SWE depth as a separate state variable in the state vector: the observation operator can use the individual SWE elements to diagnose the mean.
5) Why are the obs y not capitalized in the description of the PBS, whereas they are in the ES-MDA? The obs are still a vector of multiple obs in the PBS. "

Can you take these comments into account and resubmit a revised version along with a detailed response to each of the comments ?

Thanks a lot,
Best regards,

Marie Dumont