Review of “On moist ocean-atmosphere coupling mechanisms” by Oguba et al.

This manuscript deals with the details of energy changes associated with water mass exchanges between the ocean and atmosphere. The authors derive energy conservation equations associated with evaporation and precipitation and outline simplifications made in a numerical model (E3SM), and how energy/mass fixers account for those. Instead of investigating the effects of the simplifications in model simulations they go on with exploring the behaviour of the ODEs arising from their different conservation equations. It turns out that the equations underlying E3SM imply unrealistic temperature drifts to reach equilibrium, but they stop there. There is no discussion of implications of their results for the model and the climate it simulates. This makes the manuscript a not so satisfying read as it stands.

Major point #1: After lengthy derivations the reader is left without an interpretation of the results. How do these results impact the simulations of E3SM? I would assume the energetic inconsistencies will introduce a spurious drift but it remains unclear how large this is and what impact it has. This is unsatisfying and I would encourage the authors to explore this more to make the paper more relevant. Ideally, they would conduct model simulations in the spirit of Harrop et al. (2022) to explore the magnitude of the impact of the described energetic inconsistencies.

Major point #2: Despite the lengthy derivations important specifications are missing. In section 2.2.1, there needs to be a discussion on reference temperature. It seems the authors are employing C scale as otherwise their equations would not work. But they should keep in mind that a meteorologist would expect K scale. There also is no discussion of the assumed reference state of water: it appears it is ice at 0 deg C. Lauritzen discussed the equivalence of different choices for the reference state in detail, but here it needs to be specified at least. Furthermore, in line 109 not even Lv and Lf are identified as latent heats of evaporation and fusion. Moreover, it is not said that Lv and Lf are taken as their constant values at 0 deg C (I think) rather than being temperature-dependent. Note also that Mayer et al. (2017) described in some detail the energy changes associated with phase changes as well as the formulation with constant vs variable latent heats.

Minor points:

Line 42: What do the authors mean by “climatological energy trends”?

Line 97: “both the” – space missing

Table 1: in the current model, shouldn’t the energy fluxes received by the atmosphere be scaled by cp_dry?

Line 221: Why do the authors choose delta_K for condensation rate and not delta_C?

Line 296: the authors seem quite confident that eq. (12) is “more correct” than eq. (25), where the difference lies in the use of different specific heats for the evaporated water mass. They seem to assume that the energy required to make evaporation happen is taken equally from the main water mass and the evaporated water mass delta_V (when delta_V is already vaporous). The described processes in nature happen at the same time, and so it is not entirely clear why the sequence of events as insinuated by eq. (25) is the correct one? Can the authors elaborate why this is the more appropriate view on the ongoing processes?

Line 378: in->is; also replace “.” with “,” later on that line.

Line 391: typo in “globally”

Line 397: a similar ref to Harrop et al. has already been made further above.