General

Numerical weather prediction and climate models use surface flux parameterizations depending on Monin Obukhov similarity functions. Various versions of the functions exist in the literature and this paper investigates their effect on model results by using them in the WRF model. The latter is applied to a limited area in the tropics, for which surface flux data exist (the Ranchi data). The focus is on convective conditions. By comparing, e.g. model output with the observations the authors conclude finally that a certain set of functions proposed by Kader and Yaglom (1990) showing non-monotonic behaviour in unstable conditions is superior to other functions. Several sets of functions have been newly implemented by the authors in the model.

The topic is important for model applications but also for theoreticians. I find the paper interesting but the text needs better adjustment to the results shown in the figures. I expect that after such modification the study can be published finally. Before that, some paragraphs (also figures) should be improved and some points need clarification. Perhaps, several unclear issues arose due to language problems, so that I also recommend English editing before publication.   

Major Revisions

• My most important point refers to the differences between the results obtained with different sets of stability functions. To my mind the authors are overinterpreting the differences between the results seen in Figure 4. In my opinion the main finding is here that results obtained by CTRL and experiments 1, 2 and 3 are very similar, when the absolute value of zeta is smaller than about 1.5. Results from CTRL, exp1 and exp2 are even similar in the whole range of zeta. I think, relative to the scatter of observations, only results obtained with exp3 differ really strongly from all other results, but also only when the absolute value of zeta is larger than about 1.5. The discussion of results and conclusions should be reformulated in this direction to reflect the figures 4. The small differences explain also why most results seen in Figures 9,10,11 for different stability functions are so similar. Also here the present text suggests something else.  
• I think that the differences between the offline simulation and what is called here ‘real-case’ simulations using four sets of stability correction functions (default scheme, BD71, CL73, KY90) in WRF should be made clearer. E.g. I recommend to avoid the expression ‘real’ in this connection and to replace the heading ‘Real Case Simulations’ by something like ‘Results of WRF using different sets of integrated stability correction functions’.
• The offline-simulations would become clearer, if they were not called ‘experiment’. What we see in the figure, are the functional dependences of several parameters from stability and surface roughness. The wording ‘experiment’ is more appropriate for the different model applications.
• I wonder also why the observations (Figure 5a) are not shown already in Figure 4. If the different surface roughnesses are the reason, this must be explained. Also, the reader should know why in Figure 5 Ch shows variability for a given zeta, but no scatter is seen in Cd. I guess, the reason is the parametrization of the ratio of momentum roughness and scalar roughness, but this must be said. Which are the values for the observations and which parameterization is used for this ratio in WRF?
• Considering Figure 5a) it seems that the stability range, for which KY results diverge from other results, does not occur in nature, but at least not in the Ranchi data. This should be stressed. Are there other observations, which show a better agreement with the used functions? This should at least be discussed.

These items  result also in the following recommendations:

1. Line 136: all this would be more convincing if data would be added in Figures S1a and b, Also, the reader would like to know if KD had perhaps physical arguments for proposing non-monotonous functions.
2. Line 167: 'without feedback to the atmosphere'...this formulation might be misleading because this offline simulation is completely independent from WRF. So I would recommend writing something like (starting from line 164): The performance of the default and newly installed similarity functions is investigated in two steps. The first one is independent on the WRF model. Namely, we  apply equation A7 to iteratively determine Cd and Ch as a function of zeta by prescribing the bulk Richardson number and surface roughness parameters z_m and z_h...... We call this in the following offline simulation.
3. And later in the text, where you start describing the model application. The second step is to apply all parameterizations of the similarity functions in the model WRF whose output is compared then with observations.
4. Line 203: I do not really see large differences. There is only the function KY90, which produces really large differences to all others. If you think differences between the other functions are also large, this must be better explained. In the present figures I cannot see any relevant difference between results from EXP1, EXP2 and CTRL. There might be a tendency for differences increasing with surface roughness in case of -zeta larger than 1 ? When this is the case, another figure showing this in a zoomed version might be helpful.
5. Line 210: I do not see that they are really ‘substantially’ higher (?)
6. Line 223-225: This last paragraph is the main finding to which I can agree. But this should come earlier, so that this whole subsection could be shortened. But I have another point. Namely, Figure 5 shows that for much stronger instability, differences between all functions become more pronounced. So, why is that not shown already in Section 4.1?
7. Line 237: it should not be only consistent, but results should be identical if the same roughness parameters are used. Please note that the Rib-zeta curves depend only on height and roughness parameters but not on any other external parameter.
8. Line 249: This is not an appropriate formulation. There is a very large disagreement, one should not simply write only that there is no perfect match. Note that the functional forms are completely different.
9. Figures must be improved. E.g., in Figure 7, one cannot read the numbers (especially number 3 is unreadable). Please increase also the font size of headings in all figures showing horizontal cross-sections of model results. These headings are almost unreadable without zooming in, for which, however, the resolution is not good enough.

Minor Revisions

Most of these minor revisions refer to language problems, e,g, at many places the English article ‘the’ is not used correctly or it needs to be added. I give many examples.

1. Line 12: is ‘all’ really correct, aren’t there more such functions?
2. Line 12: replace ‘used phi_m’ by ‘used similarity functions phi_m’ . (The symbols need to be explained at their first occurrence.)
3. Line 28: replace near neutral’ by ‘near-neutral’. This occurs at many places in the text, I will not repeat it. So please check it.
4. Line 20: do you mean here in the WRF model or in other numerical models as well? The formulation leaves this open. So, what do you mean with 'the ... model? Perhaps a language problem.....
5. Line 52: when you write WRF model, then it should always be ‘the model’. Only when you write just WRF (without the word model) then ‘the’ can be omitted. This arises at many places in the whole text.
6. Line 65: Replace perhaps ‘the available’ by all available’ ?
7. Line 68: no comma after which
8. Lines 82-84: The structure is a little puzzling here and I recommend therefore to replace the sentence by something like: Their determination based on MOST using integrated forms of the similarity functions is explained in Appendix A. In the following, the default similarity functions used in WRF are explained and further functions are introduced in Section 2.2.
9. Line 100: Already here the abbreviation F96 must be introduced, which is used later (?)
10. Line 102: At this point, the formulation is somehow unclear and I was not yet sure here if these functions are already implemented in WRF or if this implementation is the topic of the paper. It should become clear already here.
11. Line 106: replace ‘these functions’ by ‘They’
12. Line 112: Better write: equations (B3) and (B4) (Appendix B)
13. Line 113: Have not been analyzed by you or by others as well?
14. Line 114: are given by Equation (6)
15. Line 127: Mentioning this program parameter is a very specific information for those who are using this model. I suggest describing this more generally or add this very technical description in an appendix.
16. Line 144: replace ‘strong’ by ‘strongly’
17. Line 145: replace ‘KY90’ by ‘the KY90’
18. Line 148: replace ‘other’ by ‘the other’
19. Line 148: replace part after functions by: while results of all other functions (BD71, CL73 and KY90) are very similar to each other.
20. Line 164: The wording is not correct: I recommend replacing everywhere in the text (including captions) the formulation ‘incorporated functions’ by ‘newly installed functions’ (note that the default function is also an incorporated function in the model).
21. Line 166: brackets are not correct (see above)
22. Line 185: replace ‘of 1st’ by ‘of the first’
23. Line 191: replace ‘brief’ by ‘a brief ’ and use better’ given in’ than stated in’
24. Lines 199-201: Can these sublayers be explained briefly? Not every reader is an expert for this. E.g., what is dynamic convective-free convective?
25. Line 218: This is now in contrast to the description in the preceding paragraph where it is written that differences are large.
26. Line 238: I guess it should be written almost identical, Identical results can only be achieved, when the same formula is used. This should be corrected at all occurrences.

Review of the manuscript gmd-2024-3

An Updated Parameterization of the Unstable Atmospheric Surface Layer in WRF Modeling System

By Namdev et al.

Summary: The paper discusses how the free convection limit needs to be implemented in NWP models, i.e. that fact that in case of vanishing wind speed the friction velocity drops out of the Monin Obukhov scaling. Within the context of the WRF mesoscale model several formulations are discussed and implemented in the surface layer scheme of WRF and tested for a long period of offline and online simulations. It is shown the model is (moderately) sensitive to the selected similarity functions for operational forecasts for a 3 month period.

Recommendation: Revisions needed

Major comments

1.Earlier studies, especially the ones done in the GABLS model intercomparison projects have studied the impact of the shape of the stability functions on the modelled profiles and fluxes (though for stable conditions mostly). However, they learnt that applying different stability functions in the surface layer parameterization and in the boundary-layer parameterization may trigger unnatural kinks in the wind speed profiles in models like WRF. This happens in practice quite often in modelling approaches for all kind of reasons. It would be good if the authors can add some discussion about this aspect, and check for (in)consistency of phi-functions in PBL and SL in their updated KY90 formulation. And whether kinks are seen in temperature and wind profiles in the WRF output.

1. The paper is silent on the impact of potential clipping that is present in the WRF model. In many schemes the stability (psi) is kept in a certain range, as is the friction velocity, and some other parameters. Hence it is interesting to learn whether the WRF model got the complete freedom to show its sensitivity to the tested similarity functions. Hence please add some discussion to what is the range of -zeta the model could reach.
2. There is some discussion about the free convection limit that could be added to the paper. On one hand the idea is that if the mean wind drops completely, then the CH should go to zero to allow the friction velocity to become zero too, so it disappears from the problem. However there are some other LES studies that show that despite the mean wind speed can drop to zero, the friction velocity will NOT drop to zero, i.e. that there is a “minimum friction velocity ” that is proportional the w* (see Schumann 1980). Please discuss how the KY90 approach and implementation matches the minimum friction velocity approach.
3. I find the description of the observational site too limited. Please extend. What is the time frequency of the output of the obs? 10-min or 60 min? What is the vegetation of the measurement site? Idem for typical roughness length.
4. Concerning the real cases, it would be good to add some discussion about how many model grid cells are affected by the changed psi functions for how many time slots in the simulations, and in which weather regimes this occurs. That offers a more detailed insight in the modelling impacts.

Minor comments:

CD and CH are never formally defined in the paper. I think it is good to add that for a more easy read.

Ln 28: tuned. I think this is not the right wording in the sense that to fit the relation between dimensionless groups, one must use observations

Ln 84: Appendix B was referred to before Appendix A was referred to.

Ln 86: …the CASES-99 dataset

Equation 7: something seems to be missing between the brackets for the formula in the upper regime

Equation 8: Same here, they look like loose hanging minuses.

Ln 132: here the notations for phi’s are suddenly in italic, while they are not in the rest of the manuscript so far.

Ln 169: For the computation, z is taken as 10 m and RiB is in the range −2 ≤ RiB ≤ 0. Can you justify the 10m and the RIB regime?

Ln 347: typo in “moemntum”

Ln 487: the bias is the mean of the difference between model and observations, so better to type the overbar over (p_i-o_i).

Figure 1: In the box for the stable boundary layer, “Change” should be “Cheng”

Figure 2: From these plots and the captions it is not directly clear which of the lines represents the new model implementation.

Figure 2: the caption says “default”, but none of the labels in the figure indicates which of the four is the default.

Figure 4: the legend box is overlying the vertically dashed lines three times

Figure 4: the caption is incomplete since the explanation is missing for DNS, DFS, FCS, DCS-FCS, DNS-DCS. I must say I find these graphs rather chaotic since these texts about the regimes are scattered all over the place. Can this not be solved by coloring the background of the diagram for the regimes in contrasting color. The caption is also incomplete since it does not explain what are Exp1-3. Better to label these BD71, CL73, and KY90. This applies to all figures afterwards.

Figure 4: headers: z0 must have a unit.

Figure 4: the vertical axes have somewhat unnatural steps. Why not start at y=0?

Figure 8: RMSE must have a unit

All tables: Put the table caption above the caption.

Table 2: The number of decimals is really too large in this table. The typical measurement error of a temperature measurement including its representativeness error is about 0.3K, then 3 decimals for RMSE and MAE is really high. Friction velocity does not have more than 2 decimals significance, so 3 is too many here. Please reconsider also for the other variables, and in Table 3.

Reference:

Schumann, U.: 1988, ‘Minimum Friction Velocity and Heat Transfer in the Rough Surface Layer of a Convective Boundary Layer’, Boundary-Layer Meteorol. 44, 311–326.