The authors present an interesting study on a general formulation (ML) for the several Budyko curves that exist, especially for the non-steady state. The paper is generally well written and shows a good comparison of their ML-formulation and the existing equations.

The authors responded well to the questions and comments of the two reviewers and I think the new manuscript will be an improvement with sometimes a bit more clarification and additional analysis as suggested by the reviewers.

Additional minor comments from my side:
- Figure 1 might be skipped. I don't see the added value of it
- Be consistent with your symbols. Sometimes the storage change is named S, then dS. Besides, I think it will also be better to rename it to dS/dt, since it is storage change (delta) over time (dt). Once using dS/dt it is also more logical to have the dimension [L/T]. Normally S is the actual storage (dimension [L]).
- Maybe you can redefine the upper and lower boundary into Emax and Emin instead of Ex and En.

Regards,
Miriam

The authors changed their manuscript significantly. Although I think the revised version is better structured, I would like an assessment of the 2 reviewers as well since the recommended minor revisions are worked out as major revisions.

Furthermore, I highly recommend to change dS [L/T] into dS/dt. Storage is a stock with dimension [L] and thus has no time dimension. Although the authors define dS correctly in the list of symbols, it can become confusing after seeing Figure 1, where dS is defined as Se-Sb and where Se and Sb are drawn with a line (indicating a storage level with dimension [L])

Please have look at the minor comments of the 2 reviewers.