Dear Prof. Gao,

thank you for the revision of your manuscript and the author's response. All comments were answered sufficiently and following the overall positive response of the reviewers I think there will be no problem in accepting this paper for GMD.

However, unfortunately there was a mix-up in the date of the end of the discussion phase for the manuscript, so that one reviewer had no chance to post his/her comments. Instead, the review is provided below. While your paper is in a good condition already, I think it would be great if you used the additional comments for potential additional benefits to your publication. Sorry for the troubles and unusual process.



Begin of review:
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The paper presents a new methodology to approximate iterative solutions for surface-layer transfer coefficients of momentum and heat with an improved non-iterative solution. The new proposed methodology proves much better accuracy than any previous non-iterative approximation (in particular the recently published wouters et al., 2012). In general, the results are clearly described. I would recommend to publish this paper after dealing with the comments below.

My main concern is that I'm not entirely convinced of the added value of the new non-iterative approximation (that needs 9 pages of parameter values) over the previous approximation WRL2012, and over the iteration with 5 steps. This is also the concern of the anonymous reviewer #1, and needs to be addressed in the paper. In particular, the errors and uncertainty arising from any parameterization or parameter value in the iterative solution can be substancial compared to the errors made by the approximations WRL2012 or the iteration with 5 steps, and needs to be discussed. These parameters include for instance the parameters in the stability function psi_m psi_h (a, b, c, d) , or z_0/z*, kB-1, z/z_0. In order the address this, I recommend to put the comparison of the accuracy of the different non-iterative approximations with the iterative approximations in perspective to the impact of uncertainty in the parameter values of the stability functions psi_m and psi_h (or any other paramete
rization used in the formulations like z_0/z*). Cheng and brutsaert 2005 pointed out that there is some scatter in the observations and thus uncertainty on the stability functions. In particular, when replacing the psi_h-function with the psi_m-function, CB05 only has a minor impact on the error of the stability functions because of uncertainty and natural variability of the observations. Furthermore, the stability functions may include additional errors/uncertainty for urban areas as well (with low z0h). Therefore, it needs to be verified whether the CASES-99 observations used in the Cheng and Brutsaert methodology also includes urban sites. My suggestion is to analyze the propagation of these errors/uncertainties (for instance by effectively replacing psi_h with psi_m) to the iterative transfer coefficients and compare this with the errors made in the non-iterative approximations or iterative solutions with limited iteration steps. This way, one is able to address the added value of
having higher accuracy of the non-iterative approximations (that needs large complexity in the formulations), or to address the consequences of using non-iterative solutions with lower accuracy or iterative solutions with limited iteration steps. In this respect, it also needs to be addressed in later studies what would be the overall impact of either employing an iterative appproximation (either with or without limited iteration step) or else a non-iterative approximation on performance and speed of SVAT-models or atmospheric models, taking urban areas in to account.

You could add a brief discussion of the pros and cons of using any of the iterative (including the one with limited iteration steps) methodologies or non-iterative approximations, for instance by including a small table. This discussion should concern the simplicity in the implementation, computational cost and accuracy. Even though it is not the focus of this paper, maybe you could add some recommendations for the unstable region as well?

MINOR comments:

throughout the text (e.g. r15 6460): the earth's surface'
6460 r. 21 B-D -> BD instead of B-D (seems to be the abbreviation used later on?)
6461 r.1 AND r.7: Jiménez et al. 2012.... also in the remainder of the text
6462 r. 16 'or neglecting/accounting for the roughness sublayer effects.'
6469 r.12: it seems to be suggested that the accuracy by employing the original methodology of WRL12 can be improved? However, this needs to be verified. But maybe you mean that the accuracy of WRL2012 'needs' to be improved by means of a new methodology (so the one presented by the current paper)? But in that case, the 'need' has to be investigated by the paper (see also first major comment).
6469: r.24: 'weather forecasting models' or 'weather prediction models'

please reformulate 6465 r.18. For example:
In order to reduce the complexity, weakly and strongly stable conditions are treated seperately in previous studies (e.g., Launiainen, 1991; Li et al., 2010; WRL12). Analogously, multiple regions are considered for z0 and z 0h for the regression of ζ = f( RiB , L0M , kB-1) in this paper.


pp. 6468
r.1 : leave away 'here'
r.5 : where (lowercase)
r.15: Here, AverageError(zeta) ...
please reformulate r. 18, e.g.: 'The results indicate that the maximum delta zeta exceeds... when using CB05 with 5 iteration steps or WRL12, whereas the averaged delta zeta exceeds 15%. On the contrary, the maximum delta zeta ...."

please recheck (consistency of) references:
e.g.
pp.6465 r. 19: lauriainen 1991 -> launiainen 1995 ??

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end of review

Thank you very much for the second revision and considering the third reviewer's comments. The new table 11 is a very good addition to the paper.