General Comments

In this paper, the authors present an empirical model designed to predict the mean summertime diurnal wind speed on valley glaciers. This model, which utilises reanalysis temperature data and a small set of topographic variables, provides a promising approach to overcoming the challenges associated with sparse in-situ meteorological measurements. The potential for applying this model to ungauged glaciers is particularly noteworthy, as it enables more accurate glacier mass-balance calculations in areas where observational data are lacking.

While the authors' methodology is an interesting contribution to the field, I believe some points need further clarification. 

Specific comments

-It’s necessary to specify the reference systems used in the text (see also the following comment). 'Wind speed u' is mentioned, but the reference system is not explained. Since the flow is described over slopes, I’m unsure whether it refers to north-south, planar fit, or slope coordinates.

-Figure 1) It is not clear how this plot was created in terms of normalisation; I think it’s necessary to specify this either in the caption or the text. X and Y represent the longitudinal and transverse distances, but relative to which reference system? It would also be interesting to understand how many of these stations are positioned uphill, or if they follow the glacier downstream.

-In lines 94-96, the paper mentions that the ERA5L wind speed at 10m was not adjusted to 2m due to the complex nature of the boundary layer above glaciers. However, the model’s 10m data is later used to compare with the 2m wind speed observations. While I understand this is based on data availability and what ERA5L provides, this seems inconsistent. The paper acknowledges the challenges associated with sloped flows, which complicate comparisons between wind speeds at different heights. Yet, this issue is only briefly mentioned in lines 94-96, with no further exploration of how it might affect the comparison between the two heights. I suggest that this topic be addressed in more detail in the discussion and limitations sections. 

-Technical corrections

20) You could mention 'anabatic wind' for symmetry.

24) Who do 'they' refer to? Valley wind and glacier winds, or up-valley winds and down-valley winds? The statement is clearly true for both cases.

141) This is not a bilinear regression, but rather a multivariate linear regression (?).

177) Include where these results are presented.

186) Similar to the previous point.

It is advisable to ensure that the order of panels mentioned in the text matches the order in the figure. For example, in Figure 1, panel b is mentioned before panel a.

In general, all figures should be self-explanatory. This means the caption must include explanations of the symbols used. For example, in Figure 2, all abbreviations should be introduced in the caption, and the same applies to the other figures.

This manuscript presents an empirical model for estimating the summertime mean diurnal wind cycle near glaciers using reanalysis temperature and topographic variables. The model is calibrated using observations from 28 glacier and valley weather stations. Relative to ERA5-Land, the model reproduces the observed mean diurnal wind cycle, primarily by correcting biases in mean wind speed.

The analysis focuses on relating fitted model parameters to local geometric and topographic descriptors in order to enable wind-speed estimation at locations without in-situ measurements. While the approach yields improved agreement with observations, the model is highly empirical, and its general applicability relies on assumptions about parameter interpretability and extrapolation beyond the calibration sample.

Overall, the manuscript is well written, but I have concerns about the regression's generalizability and physical interpretation. I have focused the comments below on these major items.

General comments

1. Equation 1 needs to be introduced, derived, and physically motivated. At present, it is unclear where this equation has come from. Because this model is introduced under the auspices of a linear response model, and because the authors end their introduction with “there is a clear need for a simple physically-based model of wind speed...”, it was obfuscated that the model presented here is a harmonic regression. As the authors show, the response functions would be the same in the limit of small ω²τ². However, if τ is a few hours (L121) this is not a valid approximation. In the results, they fit values of τ up to 6. 6 × 0.26 ≈ 2.5, which is very much not asymptotically smaller than 1. Additionally, as this is not a linear response model, τ should not be interpreted as a response time.

2. The uncertainty estimation written in 3.4 assumes the covariance of ū, s, and τ is 0. This is unlikely to be true since they are derived from the same regression, so this uncertainty is an underestimate. Other sources of uncertainty, such as error induced by the finite difference approximation and the ad-hoc handling of outliers, should be considered.

3. The model selection procedure for eq 7–9 searches over a very large space of predictor combinations, but it is unclear whether predictor selection is nested within cross-validation. If variable selection is performed prior to LOOCV, then the cross-validation performance is likely overestimated.

4. The applicability of the regressions in eq 7–9 requires more discussion and analysis. How do the distributions of gauged and ungauged AR, R1, R5, Z10, Zs, and S0.1 compare? Is the training sample representative of the population? Would this model produce realistic results for most ungauged glaciers? Glaciers with long-term measurements tend to be biased to be more accessible and shallower, and already 7% of the training data had to be discarded or modified.

5. A clear physical interpretation of the regression results is required, and compared to examples in literature. For example, what conceptual model can one use to understand why the 1 km relief increases ū, while the 5 km relief decreases it? I'll admit that I am somewhat skeptical of the useability of such a result. While the regression is identifying relationships in the data, it is difficult to interpret these as causal or physically grounded mechanisms rather than empirical correlations. It is surprising, for example, that position along the slope plays no role, since glaciers winds are known to strengthen downslope.

6. Most flux models split the glacier into separate elevation bands due to known changes in u & T along the glacier. The predicted u will change along the glacier as R1, R5, Z10, Zs, and S0.1 change. How do the predicted along-slope profiles of u behave on these glaciers? Is is always physically valid?

7. As the authors note, a lot of the performance improvement in reducing the underestimation comes from the intercept of the regression. Where does this intercept come from? Is it related to any climatological variables? In light of this, I'm not sure RMSE is always the most honest metric throughout -- the RMSE will always improve because of the intercept being added to u.

8. A more careful analysis of the role of τ is required. The three most performant models are identical save for changes in τ. But the relation between τ and S0.1 in figure 6a is not very convincing. From table S3, the correlation is 0.24 and the t-statistics are less than 1.5. Is the model really markedly better with the inclusion of τ? Why would we expect the phase and slope should be related here?

9. The time-scale analysis should be clarified. It is unclear how a diurnal parameterization could be meaningful at multi-day time scales. I suspect the improvement comes from more smoothing and as a result, reduced variance.

10. The distinction between valley wind and glacier wind merits more analysis. Given the difference in scale between the two, consistent model performance between them surprises me. How do the regressions change if only run on on-glacier vs off-glacier observations?

11. Are the heat fluxes from ERA5-L being estimated using 2-m temperature and 10-m wind speed? If so, the exchange coefficients will need to reflect this.

12. Because turbulent heat fluxes are nonlinear functions of u & T computing fluxes from seasonal-mean wind speed and temperature does not, in general, recover the seasonal-mean flux. Some discussion of this is needed.