Dear Authors,

thank you for the revised version of your manuscript.
Your paper improves considerably, however, according to a second review of your paper there are still open issues.
I encourage you to thoroughly go through the reviewers comments (see below) and consider them in a second revision. In particular the description of the method (scaling procedure) should be precise and easy to follow in a technical journal as GMD.

all the best
Hella Garny

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General comments

Although the authors have improved the manuscript with the revision, there are still open questions that need to be addressed before final publication.

Specific comments


The description of the approach by Nissen et al. (2007) is still misleading. As currently written in the manuscript the reader could suppose that the original 4-band SW parametrization of E5 has been refined with the same approach as Fouquart and Bonnel (1980) to a 49-band SW parametrization by Nissen et al. (2007). Instead they replaced the UV-visible band of standard E5 4-band SW radiation scheme at model levels where the pressure is less than 70 hPa, by a 49-band parametrization based on Strobel (1978) (Schumann-Runge bands and continuum) Shine and Rickaby (1989) (Herzberg-, Hartley-, Huggins-, Chappuis-Band), and Chabrillat and Kockarts (1997) (Lyman-alpha). The Nissen et al. (2007) method (FUBRAD) is therefore also comparable to the methods of Egorova (2004) or Formichev et al. (2004).


The comparison of the E4 UV heating rates (250--680 nm) with the E5c UV heating rates (200--441 nm) in figure 2 indicates the E4 scheme up to 6.5 K/day weaker near the stratopause. Figure 1 of Cagnazzo et al. (2007) shows a similar comparison between the E5 and the E5c short wave heating rates, indicating the original E5 scheme only 3.5 K/day weaker than E5c.
Furthermore the comparison in Nissen et al. (2007) of the UV-Vis part of the original E5 (250--683 nm) scheme with LibRadtran (Figure 1, equator) shows a good agreement of the E5 heating rates with LibRadtran (121--683 nm). The comparison in the current paper of the E4 UV heating rates (250--680 nm) with the LibRadtran UV heating rates (120.5--440 nm) in figure 2 indicates the E4 scheme up to 5 K/day weaker near the stratopause than LibRadtran.
Can the authors give some explanations for these large discrepancies?


Page 5, line 32:
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Page 6, line 1:
replace ... underestimation ... with ... overestimation ...
replace ... (E5) ... with ... (E5c) ...


There are still no details given about the scaling procedure itself.

Page 8, line 20--26:
... the inclusion of these parameterizations does not introduce any additional deviation to the absolute values of the heating rates compared to LibRadtran but only makes the difference between LibRadtran and E5c and E6 constant in time. The mean difference over the whole modelling time will be greater with extra heating than without extra heating, however the second one is less only because of the bad representation of the solar signal, and the first one will be equal to the difference in the "grand minimum" and will be constant in time.

It is not possible to follow the argumentation of the paragraph above, as long as no details about the scaling procedure are given. I would like to encourage the authors to include more details about the method used to create the scaling coefficients, and how they are applied to the additional parametrizations.

References

Chabrillat, S. and Kockarts, G.: Simple parameterization of the absorption of the solar Lyman-alpha line, Geophys. Res. Lett., 24, 2659--2662, 1997.

Fouquart, Y. and Bonnel, B.: Computations of solar heating of the earth's atmosphere: A new parameterization, Beitr. Phys. Atmos., 53, 35--62, 1980.

Shine, K. P. and Rickaby, J. A.: Solar radiative heating due to the absorption by ozone, in: Ozone in the atmosphere, edited by: Bojkov, R. D. and Fabian, P., A. Deepak, Hampton, Va., p. 597--600, 1989.

Strobel, D. F.: Parameterization of the atmospheric heating rate from 15 to 120 km due to O2 and O3 absorption of solar radiation, J. Geophys. Res., 83, 6225--6230, 1978.

Thank you for the revised version of your manuscript.
All comments of the reviewer were addressed, however unfortunately not all of them satisfactory.

In particular the answer to the issue on the description of the scaling procedure reveals that the authors estimated the scaling coefficients "by eye", rather than applying a mathematical, scientific sensible, method. In particular given that there appear to have been problems in the fit of the absolute values versus the solar signal amplitude, a fit method that finds the best estimates of the coefficients (both with respect to absolute values and solar signal) would be highly desirable, and as the authors state, possible. I consulted again the reviewer of the last versions of the paper, and he agrees in that the paper should show a scientific sound way to estimate the coefficients
(see below for his comments). I'm afraid that the fit "by eye" does not meet the scientific standards of a journal as GMD.
Therefore, I have to ask the authors to revise their paper accordingly to be acceptable for GMD. Sorry for this strong request at this stage, but the information on the scaling procedure was revealed only now.

Please also consider the other comments by the new reviewers report, as given below.


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1 General comments
Although the authors have clarified some open questions with the 2nd revision, they have not considered all points of the second review. As one essential part of the method described in this paper to include the 11–year solar cycle to GCMs and CCMs is based on scaling additional heating rates, the authors should include a mathematical procedure to obtain the scaling coefficients.

2 Specific comments
The authors now indicate that the scaling coefficients were estimated by eye, but
in general can be calculated by a definite mathematical procedure. As this paper
shall be a contribution to a journal especially designed to document the numerical procedures, leading to scientific results, I would like to asked the authors to document their scaling procedure in the paper. I guess the aim of the authors is to give good reasons to choose their method to include the 11–year solar cycle variations to GCMs and CCMs. It is therefore essential to include a full documentation of the method.

The authors still ignore the fact that also the approach of Nissen et al. (2007) is based on the Beer–Lambert law as used in Strobel (1978), i.e. the approach is also physically comparable to the methods of Egorova (2004) or Formichev et al. (2004), although more bands are used. This should be clear to the reader. On page 3, line 23 it is still written in the 2nd revision of the paper:
Another way is to apply parametrizations for the missed extra heating due to solar UV enhancement based on the Beer–Lambert law ...
This is misleading, as it implies that the physical basis of Egorova (2004) or Formichev et al. (2004) is different compared to Nissen et al. (2007). The authors should rewrite this paragraph.

The authors still stress the high computational costs caused by a higher spectral resolution of any radiation code. In general this is true, but the cited references (Nissen et al., 2007; Kubin et al., 2011) do not include any statement about computational costs (this is also mentioned by the authors). For this reason I still do not understand the chosen references in this context. When mentioning the increase in computational time for the Nissen et al. (2007) method, by increasing the spectral resolution from 6 bands to 49 bands, the authors should avoid any speculations about the increased computing time, as long as they cannot provide a proper reference. It would be best to delete this paragraph completely.

In the paragraph discussing the results of the new Figure 3, the authors have to be more specific when stating an overestimation of the E4 absolute values compared with E5c and libRadtran, which is only true in the height range below 40 km. Near the maximum in heating rates E4 slighly underestimates E5c and still overestimates libRadtran.

Although the authors claim to have replaced the following statements, they are still unchanged in the 2nd revision:
Page 5, line 32:
replace ... underestimate ... with ... overestimate ...
Page 6, line 1:
replace ... underestimation ... with ... overestimation ...
replace ... (E5) ... with ... (E5c) ...

3 Technical corrections

Page 6, Line 20:
replace (Formichev (2009)) with (Formichev, 2007)
Page 9, Line 17:
remove one bracket after (McClatchey et al., 1972)
Page 16, Figure 2 top row:
correct right axis label: solar minimum
Page 16, Line 4:
replace nad with and

Dear Authors,

Thank you for the revised version of your manuscript. As the scaling factors are now estimated with a proper mathematical procedure as requested I can recommend the paper for puplication after a few technical corrections as listed in the reviewer report.