I feel that the reviewers comments are quite positive, specific and relatively easy to address (but see below).I am convinced you will have no problems in accommodating them. In any case, I will wait for your final version and response to comments to decide whether or not to request another round of revisions prior to final publication in HESS.

I'd suggest to emphasize the following issues in your response:
1) storage. I need you want to write another paper with a formal method to include the energy storage. Still, it is clear to me that you need to address the issue here. Since you have the temperature data, you evaluate the energy storage variation and deduce the kind of errors you make. In fact, this can be a good motivation for your later paper.
2) You also need to address the comments by Patrick Le Moigne (but I would not change A(t) by A_{z=zsurf}(t), which looks awful, just call it A(t) and mention in the text that it represent the area at the surface elevation which chages…, or something alike that).
Just bear in mind that you want your paper to be attractive!

The paper is good! Go ahead!

Beautiful work!
Congratulations!