Dear Gerrit,

I hope you will be able to rewrite the paper taking into account all reviewers comments (as you can see a major overhaul is required). Please keep in mind that initial reviewer grades were not good and convincing changes must be made for the paper to pass the next step of review process.

Sincerely yours,
Andrey

Dear Gerrit,

I think that significant improvements were made in the paper. I hope that remaining (rather serious though) comments from one of the reviewers can be addressed during "minor revision" procedure. But please do not treat these questions as "minor" ones.

Best regards,
Andrey Gritsun

The paper still has several significant issues that must be addressed or corrected.

1. First one was mentioned by the reviewer in his major comments #1, #2, #4.

I completely agree with the reviewer (major comment 1) that no one is using EBMs in the way described by Eq4. It is physically inconsistent and gives unrealistic range of temperatures (0K-407K) by obvious reasons. So there is little sense to provide a page (starting from line 20 page 3) of technical calculations for its average temperature. It is enough to give the final result (163K) and formulate correct model (eq9).

2. Also “major comment 2” (i.e. calculations on lines 1-8 of page 5 use essentially the same zero heat capacity assumption as for eq.4) should be better explored. Indeed, it is easily seen that (11) and (12) could be obtained from (4) by exactly the same approach as in the section 3: integrate (4) over Theta from zero to 2pi, replace Theta integral over T**4 by (Theta integral over T)**4 , get (11), average it over latitude and finally get (12). This basically means that for the stationary solutions of Eq.9 (or small heat capacities or strong Theta-dependence of the solution) approach of the section 3 does not work. So the same legit question remains – is it correct to drop the left hand side in (10) for zonally averages? How accurate will be the estimate (12) for solutions with weaker dependence on Theta or large heat capacities)? Unless author provides a better analysis of eq.9 I suggest removing lines 1-8 of page 5, removing red line on figure 3, and proceeding with results obtained with numerical experiments only.

By the way, it is unclear to me what norm (L1 or L4) is used for Fig.3 and Fig.4? If the L1 norm is used I would expect to see eq7 for small (tending to zero) heat capacities and estimate from eq12 for large ones. Also I do not understand why on Fig.3 and Fig.4 several lines do not approach to 0.0K on the poles as suggested by eq.9. It would be helpful to add temperature profile of the real Earth atmosphere to figures 3, 4, 6, 7.

Text on page 5 (lines 10-15) should be reformulated as linearization could be performed successfully around time-dependents states which is natural for the system with strong time dependency as Eq.9 (this is also connected with the major comment 5 of the reviewer).

3. I think that the statement “large seasonality gives colder climate” should be better explained (end of section 4). All experiments and calculations in the paper have the following procedure – prescribe heat capacity and look what will happen with the zonally averaged temperature profile. Amplitudes of the seasonal cycle (for two very different setups) appear only on figure 8. So I think that the statement “large seasonal contrast gives colder climate” is not properly supported. The last paragraph of the section 4 does not explain anything either. Models from fig.7 are all nonlinear, have different T_winter’s and T_summer’s, different zonal temperature profiles. So it is difficult to understand how the Holder inequality could be applied to get the result. After reading the paper the conclusion “small heat capacities give colder climates with larger variability near the poles” seems more logical.

I think that the manuscript now is very close to the “be accepted” status and required corrections are very minor indeed. Please look at the attached file.