Review of: “Understanding wind-driven melt of patchy snow cover” by Luuk D. van der Valk, Adriaan J. Teuling, Luc Girod, Norbert Pirk, Robin Stoffer, and Chiel C. van Heerwaarden

This paper is a fascinating modelling approach to address the very challenging process of wind driven local scale advection contributions to snowmelt.  This process has been a persistent challenge on snowmelt modelling but the high complexity of the physical processes has stood in the way of parsimonious/satisfying solutions.  This paper provides a unique/novel modelling approach to the problem, especially with the model not requiring a parametrised stability scheme, and overall I think that this is a very important contribution.  There are a number of areas that I think need work in this manuscript in order to strengthen its conclusions, and place it more completely into the literature context.  With these in mind I would suggest that this paper requires revision prior to publication and would highly encourage the authors to consider what I hope to be constructive comments.  I will begin with a number of general comments followed by more specific/technical comments.

Major Comments:

1. Literature context: I get the impression that the authors may be newer to the snow field and so some of the statements in the introduction (see comments) need revising.  Broadly there is a tremendous amount of research on processed based- energy balance snowmelt modelling that needs a clearer summary/context for this work.  In terms of local-scale advection work there is a much more limited amount but can be found back to the 1970’s.  This needs a more complete treatment to solidify the context of this contribution as well as to distinguish these contributions from previous one. (See comments for examples).

2. Validation with SFM: I’m not exactly clear on the process by which the snow depth difference are calculated via SfM on the observed patch in order to compute expected ranges of turbulent flux contributions and model validation.  Are we only considering snow depth difference for grid cells that were completely uncovered during melt (so we can have a bare ground reference) or are we also considering cells that were not fully uncovered that would have also decreased in snow elevation due to melt?  What areas do these number represent?  Do you observed a decrease in melt from leading edge? Many dynamics can be examined with a spatial dataset but I’m not clear on how this is also processed/what it represents and so would welcome a lot of clarification and perhaps a figure to describe this process.

3. Latent heat flux decay: There is an extensive treatment of the sensible heat flux decay with patch length while this is not discussed with respect to latent heat flux. Can this also be included or is there are reason it is not included.  The heavily cited Harder 2017 paper suggest that latent heat is also an important contributor or at times compensatory (Harder 2018) and so would be very interested in seeing if some of those dynamics could be captured in this modelling scheme.

4. Implications: there are some interesting dynamics explained but I’m not exactly clear on how those could be implemented in larger scale snowmelt prediction.  There is a scaling relationship articulation for sensible heat over a patch length.  Is this considered to be a parameterisation that could be used in basin scale snowmelt prediction models

Specific Comments:

Line 39-40:  Snowmelt, especially over continuous snow cover, is governed by the surface energy balance (radiation AND turbulent exchange processes) with radiation being the dominant source (Male and Granger, 1981).  Turbulent processes, for which air temperature is a proxy, can clearly be important (especially with advection as seen here).  Commonly used empirically based temperature index models erroneously lead to the impression that snowmelt is related to air temperature but if we are to be focused on process interactions this statement is problematic. 

Line 43-45: this contradicts the lines 39-43.  Distinction between the scales of advection are needed. (Shook and Gray, 1997)  Large scale air mass movement can drive turbulent exchange because otherwise the temperature and humidity gradients will tend to equilibrium as noted here.

Line 53-54:  TI models are empirical so another major criticisms is their applicability when applied outside of their calibration periods or domains – especially in prediction of future changes.  There are many other physically based snowmelt models out there besides Alpine3D (which is based on SNOWPACK), such as snobal (Marks et al., 1998), CROCUS (Vionnet et al., 2012) or in the multitude of land surface schemes.

Line 61. Few models parametrise lateral snow distribution processes fully/explicitly (CHM (Vionnet et al., 2021) and APLINE3D are the only 2 that come to mind that have actual process level physics involved)– most others are often based on simplified parameterisations.

Line 61-63: (Harder et al., 2018) provides a simple snowmelt advection model to account for subgrid variability in melt.  (Marsh et al., 1999, 1997) provide an approach to account for sensible heat advection.

Line 63-64:  (Harder et al., 2018) provides a advection modelling framework that makes an argument that in some situations upscaling with and including advection will not make any different to discharge predictions.  Ie things can get complicated when the snowmelt is increasing in rate but decreasing in area.

Line 71-76:  missing the advection work of Marsh found in the publications in 1997 and 1999. 

Line 8—81: “spatially highly variable character of melt rates can complicate the observations” - > “high spatial variability of melt rates complicate the observations”

Line 83-90: there is a tremendous body of work on snow remote sensing at high resolutions that far exceed the Offenbach and rittger references which are not the most appropriate to consider local scale advection dynamics.  Perhaps recast this in terms of remote sensing that is suitable for advection (ie high temporal frequency <=daily, and spatial resolution <<10m).  Some high resulting satellite products coming online now but really should focus on aerial platforms (ie ASO (Deems et al., 2013; Painter et al., 2016), drone based (you have many of the UAV-Sfm references but lidar applications are coming online now as well (Harder et al., 2020; Jacobs et al., 2021), and terrestrial laser scanning (Grünewald et al., 2010; Hojatimalekshah et al., 2020), and georectification of oblique time-lapse photography (Härer et al., 2013)

Line 129: of -> from

Line 131-133: wind direction was constant you state.  Can you provide a wind rose or some sort of metric to quantify this?

Line 138-140:  when were these samples taken with respect to the observation interval as snow density is dynamic over melt?  Was a snow tube used? Snow pit? How were 100ml samples collected? Did the melt period have a consistently ripe snowpack?

Line 153: desolated - > isolated?

Line 153-159:  not exactly clear on this methodology.  Base on this and images in Figure A1 we are only looking at the edges and measuring surface change for where the snow melted and a bare ground surface appeared?  Related to figure A1 – how do the upwind and downwind edges line up – unclear as they are plotted in separate rows?

Line 160-165:  How deep was the snowpack and do you have any information to say that the snowpack was ripe at the start of the melt.  Were the cold content requirements satisfied at the start of the period and so all energy could be assumed to be related to melt.

Equation 2: I believe SWE should instead be snow density? 

Figure 3:  how were the surface temperatures and gradients between snow and non-snow generated?  I may be blind but can’t seem to see this.

Figure 4:  I’m not exactly clear on what area constituted an upwind or downwind edge and how that relates to a specific number/boxplot.  There will be a gradient of change.  Can this be clarified? This approach does not consider height changes if it that spot does not become snow free by June 15?

Line 334-336:  It seems SWE and density are being used interchangeably here which is not correct.  Can this be cleared up? These are pretty high densities.  Any observations from field notes about water saturation or other structural attributes. What was the overall snow depth variability? Can you report the SWE of the snow patch? 

Line 353-354:  60-80% based on computing the overall melt energy needed and radiation melt and the turbulent portion as the residual of this energy balance?  If so can that be clarified?

Line 398-403:  Granger et al., 2002 and Weisman, 1977 propose similar power law relationship to describe a sensible heat flux.  Perhaps worth contrasting this formulation and the meaning of your terms with those papers?

Section 5.3: this section exclusively discusses sensible heat flux only.  Your model also considers latent heat flux and observation are available from Harder et al 2017.  Can this also be considered or is there are particular reason you did not bring latent heat flux into the results here?

Line 459-461: same order of magnitude regardless of patch size on the upwind edge?  Sentence seems not complete.

Line 462: “microclimates” - > micrometeorological?  Would suggest that these are very dynamics occurrences unlike what is captured with the “climate” term.

Line 464-467: terrain absolutely plays a role with snow distributions but this is a rather simplistic explanation for very complex physical processes underpinning blowing snow redistribution.  Topography, meteorology, surface characteristics all conspire to make any domain very complex in terms of snowpack distribution variability.  I’d step this back and say that snow patch size distributions (if available) would improve snowmelt predictions.  There are many tools and statistical descriptions of snowpack’s available to do so (see snow pack scaling laws in Harder et al., 2018 and the papers cited therein that consider fractal geometry for example).

Line 467-468: “The melt estimates obtained with the SfM photogrammetry are in line with own expectations based on visual estimations, whereas the estimated errors are relatively small.”  Can you clarify what you mean with “in line with own expectations” - meaning is not apparent to me.

Line 480-490:  have you run any simulations with a higher Re in line with Harder 2017 so that you could make some more conclusive predictions of this RE- decay relationship?

Line 664-665:  please change to the non-discussion version of this paper

References:

Deems, J., Painter, T., Finnegan, D., 2013. Lidar measurement of snow depth: a review. J. Glaciol. 59, 467–479. https://doi.org/10.3189/2013JoG12J154

Granger, R.J., Pomeroy, J.W., Parviainen, J., 2002. Boundary-layer integration approach to advection of sensible heat to a patchy snow cover. Hydrol. Process. 16, 3559–3569.

Grünewald, T., Schirmer, M., Mott, R., Lehning, M., 2010. Spatial and temporal variability of snow depth and ablation rates in a small mountain catchment. Cryosph. 4, 215–225. https://doi.org/10.5194/tc-4-215-2010

Harder, P., Pomeroy, J.W., Helgason, W.D., 2018. A simple model for local scale sensible and latent heat advection contributions to snowmelt. Hydrol. Earth Syst. Sci. Discuss. in review, 1–32.

Harder, P., Pomeroy, J.W., Helgason, W.D., Helgason, W.D., 2020. Improving sub-canopy snow depth mapping with unmanned aerial vehicles: Lidar versus structure-from-motion techniques. Cryosphere 14, 1919–1935. https://doi.org/10.5194/tc-14-1919-2020

Härer, S., Bernhardt, M., Corripio, J.G., Schulz, K., 2013. PRACTISE – Photo Rectification And ClassificaTIon SoftwarE (V.1.0). Geosci. Model Dev. 6, 837–848. https://doi.org/10.5194/gmd-6-837-2013

Hojatimalekshah, A., Uhlmann, Z., Glenn, N., Hiemstra, C., Tennant, C., Graham, J., Spaete, L., Gelvin, A., Marshall, H.-P., McNamara, J., Enterkine, J., 2020. Tree canopy and snow depth relationships at fine scales with terrestrial laser scanning. Cryosph. Discuss. 1–35. https://doi.org/10.5194/tc-2020-277

Jacobs, J.M., Hunsaker, A.G., Sullivan, F.B., Palace, M., Burakowski, E.A., Herrick, C., Cho, E., 2021. Snow depth mapping with unpiloted aerial system lidar observations: A case study in Durham, New Hampshire, United States. Cryosphere 15, 1485–1500. https://doi.org/10.5194/tc-15-1485-2021

Male, D.H., Granger, R.J., 1981. Snow Surface Energy Exchange. Water Resour. Res. 17, 609–627. https://doi.org/10.1029/WR017i003p00609

Marks, D., Kimball, J., Tingey, D., Link, T.E., 1998. The sensitivity of snowmelt processes to climate conditions and forest cover during rain-on-snow : a case study of the 1996 Pacific Northwest Flood. Hydrol. Process. 12, 1569–1587.

Marsh, P., Essery, R., Neumann, N., Pomeroy, J.W., 1999. Model estimates of local advection of sensible heat over a patchy snow cover, in: Tranter, M. (Ed.), Interactions between the Cryosphere, Climate and Greenhouse Gases. IAHS Publ. No. 256, pp. 103–110.

Marsh, P., Pomeroy, J.W., Neumann, N., 1997. Sensible heat flux and local advection over a heterogeneous landscape at an Arctic tundra site during snowtnelt. Ann. Glaciol. 25, 132–136.

Painter, T.H., Berisford, D.F., Boardman, J.W., Bormann, K.J., Deems, J.S., Gehrke, F., Hedrick, A., Joyce, M., Laidlaw, R., Marks, D., Mattmann, C., McGurk, B., Ramirez, P., Richardson, M., Skiles, S.M.K., Seidel, F.C., Winstral, A., 2016. The Airborne Snow Observatory: Fusion of scanning lidar, imaging spectrometer, and physically-based modeling for mapping snow water equivalent and snow albedo. Remote Sens. Environ. 184, 139–152. https://doi.org/10.1016/j.rse.2016.06.018

Shook, K., Gray, D.M., 1997. Snowmelt Resulting from Advection. Hydrol. Process. 11, 1725–1736.

Vionnet, V., Brun, E., Morin, S., Boone, A., Faroux, S., Le Moigne, P., Martin, E., Willemet, J.M., 2012. The detailed snowpack scheme Crocus and its implementation in SURFEX v7.2. Geosci. Model Dev. 5, 773–791. https://doi.org/10.5194/gmd-5-773-2012

Vionnet, V., Marsh, C.B., Menounos, B., Gascoin, S., Wayand, N.E., Shea, J., Mukherjee, K., Pomeroy, J.W., 2021. Multi-scale snowdrift-permitting modelling of mountain snowpack. Cryosphere 15, 743–769. https://doi.org/10.5194/tc-15-743-2021

Weisman, R.N., 1977. Snowmelt: A Two-Dimensional Turbulent Diffusion Model. Water Resour. Res. 13, 337–342.

The paper presents a very interesting study discussing wind-driven processes that affect the energy balance of a melting patchy snow pack. Recent studies have demonstrated that heat advection processes significantly contribute to total snow melt. However, the implementation of the advection process in snow-hydrological studies is very challenging and several approaches have been suggested by other studies. None of these approaches are currently used in larger-scale snow-hydrological models. Thus, the topic of the study is highly relevant and the study is an important contribution to the snow-hydrological community. The paper provides an interesting approach using DNS to calculate turbulent heat fluxes affected by heat advection processes over a patchy snow cover situation. They further present a scaling approach to relate the sensible heat flux to the patch size and conducted snow melt observations at a snow patch. There are several questions regarding the methodology and process description and representation which need clarification and revision. Please consider revising the manuscript considering major and more specific comments below.

General comment:

1. The authors describe a process they term advection of turbulent heat flux and reference studies discussing local advection of sensible heat as described in Mott et al. (2018) and also Harder et al., (2017). It is not clear to me to which term the authors are really relating to as it seems to me that they mix up advection of sensible heat with the vertical turbulent sensible heat flux. The ambiguity becomes particularly clear when the authors compare modelled sensible heat fluxes with estimated advected sensible heat as presented in Harder et al (2017). I recommend to include equations where they clearly state at which terms they are looking at and how these are calculated. Equations for advection of sensible heat are presented in Harder et al. (2017) and Mott et al. (2020).
2. The Introduction of the process and its relevance could be extended to allow the readers an easier access to the very complex interplay of near-surface boundary layer processes that become important over patchy snow covers. I think that the manuscript would particularly benefit from a more detailed background (also including “older” studies) on wind-driven heat exchange processes, the development of internal boundary layers (.e.g. Granger et al., 2002; Essery et al., 2006) and the local advection of sensible heat (e.g. Marsh et al., 1999).
3. The connection between the experimental and the numerical part of the manuscript is not totally clear to me. For the experimental part, the study would particularly benefit from a more detailed analysis on the spatial aspect of the process, i.e. analysis of fetch distance related snow melt and advection estimates. What is the added values of the experimental part?
4. Why are such extreme boundary conditions used for the DNS leading to unrealistically high calculated turbulent heat fluxes? In my view, more representative meteorological boundary conditions (i.e. matching up with the conditions at the observed snow path) would provide more meaningful conclusions. Also, Schlögl et al. (2018a) did a similar modeling study using ARPS. Please set your results more in context of this recent study. What are the benefits of using DNS? How do the results compare? What do we learn? How can we represent the process in larger-scale models?

Specific comments:

• L 39: Warm air advection is AN important source for the energy balance but not generally the main cause of snow melt. Please change the sentence accordingly.
• L 46-50: While the introduction to the process is correct, the sentence in L46/47 does not describe the process that is typically described as local advection of sensible heat (as by Mott et., 2018; Harder et al., 2017): Local heat advection is generally understood as a process where the mean wind that transports the warm air from snow-free towards snow-covered area. It is NOT the horizontal gradient in air temperature which initiates this process like sea breezes. The process is defined in Mott et al. (2020) as “Horizontal transport of sensible (and latent) heat with the mean flow” and can be written as wind speed*dT/dx (For further details also see Mott, R., Stiperski, I., and Nicholson, L.: Spatio-temporal flow variations driving heat exchange processes at a mountain glacier, The Cryosphere, 14, 4699–4718, https://doi.org/10.5194/tc-14-4699-2020, 2020.). The process as described in studies of Mott el. (2015,2018, 2020) and Harder et al. (2017) not refer to the advection of turbulent heat fluxes which would be defined as: U * d/dx(w’T’) + U*d/dx(w’q’). As you refer to advection of turbulent heat fluxes throughout the manuscript, it is very important that you include equations on the terms you are analysing.
• The process of advection of heat was found to be not only an important process over snow patches but also for ice fields (Mott et al., 2019) and glaciers (Sauter and Galos, 2016; Mott et al., 2020) potentially affecting snow melt processes there. Please include this in your intro to provide a more complete picture of the process and the importance for glaciers mass balance studies as well.
• L 59: Please also mention rain on snow events as situations where TI models drastically fail.
• L 76; as you reference both Schlögl et al (2018) paper you should introduce 2018a and 2018b.
• L79: this is not entirely correct as Schlögl et al. (2018b) did snow ablation and turbulence measurements over three entire ablation periods.
• L 83: “This advocates the use of spatial field observations, however, most methods for estimates
• on small spatial scales are relatively expensive or come with low precision and accuracy” here you should reference studies using TLS to measure high-resolution snow ablation rates (Grünewald et al., 2010; Egli et al., 2012; Schlögl et al., 2018b).
• L110: Although not being an expert on photogrammetry, I think it is not fully correct that you state that you are using SfM – you are actually using stereophotogrammetry as structure from motion implies that the 3D structure was created using camera movement.
• L114: can you shortly explain how those measurements serve as a basis?
• L129: Please elaborate on how you used the meteorological data in 2.5 km distance from the actual field site. Have you applied any spatial interpolation to data to account for elevation difference or local terrain effects (e.g. wind, radiation)?
• L134: Why did you not measure the spatial distribution of snow ablation over the entire snow patch? How did you determine the local wind direction? Also, was the wind fetch always constant through the measurement time period?
• L139: why did you not measure SWE for the entire snowpack? Doing so at different sites with different snow depths would allow a more precise information on SWE of the snowpack at the snow patch. Was the snow pack already isothermal at the start of the measurement campaign?
• L159: would be nice to show the resulting snow ablation map of the snow patch retrieved from SfM.
• Figure 1: the small figure is not clear to me. Are white areas still snow-covered? Is this an orthofoto? How did you determine the local wind direction?
• L 161: what do you mean by assuming a snow albedo between 0.6 and 0.8? changed the value in time? Can you provide a reference for choosing those numbers? The albedo value has an extreme effect on your energy balance calculation and your estimated contribution from turbulent heat fluxes.
• L174: the relative humidity was measured at the large-distance test site?
• L 187: local scale advection of what? Also, it is not clear how measurements of Harder have been used for the idealised system. What did you use for what exactly?
• Figure 2: Please insert the meaning of the parameters in the figure caption. It is not easy to understand what the figure is showing.
• L 195: if theta_atm is the temperature of the atmosphere – what is theta then? The surface temperature of snow/bare ground? Please define.
• L 318: how do you define up-wind and downwind edge? is it the first grid cell? How do you deal with grid cells which become snow-free during the observation day? The daily-melt rate will be underestimated if you also consider pixels which become snow-free during a measurement day. Would be interesting to see a snow ablation rate curve depending on fetch distance.
• L336 and table 4: Please provide more precise explanation on your estimate ranges. Please also state whether any spatial interpolation is done to the meteorological variables or not.
• L337: is that the length of the sow patch?
• L343: I assume that you are taking the difference of snow melt due to radiation (equation2) and the actual snow melt to estimate the contribution of the turbulent heat flux. Please add more information how you exactly calculate the turbulent heat flux (latent and sensible turbulent heat flux?)
• L353/354: and how does this compare to the contribution at the downwind edge? As mentioned earlier it would be extremely interesting to have a fetch distance related estimate of the contribution of turbulent heat fluxes (sensible and latent). Also, if you provide a number of 60-80% contribution at the upwind edge – what does this exactly mean? Over which area? As known from other studies, the contribution strongly changes with fetch distance. These high numbers of 60-80% might be very misleading looking at the relevance for the catchment scale snow melt. It would be very interesting to see an analysis on the contribution of heat advection to total snow melt for varying snow patch sizes and snow cover fractions. Furthermore, the relative contrition of heat advection to total snow melt strongly depends on the spatial variability of snow depths as snowpacks with a high spatial variability of end of season snow depths are typically characterized by a longer time period of the patchy snow cover stage and therefore a higher importance of the heat advection process. A more detailed discussion would allow a better comparison to the study of Schlögl et al., 2018a. Please relate to results of Schlögl et al. (2018), who tried to put the local scale estimations into the catchment scale context to draw conclusions for its relevance.
• Section 4.1: These estimations include many uncertainties (snow density differences depending on snow height, differences in shortwave radiation between snow patch and actualmeasurement location due to terrain shading, albedo). The high number of turbulent heat fluxes at the surface do not tell us how much of this turbulent heat flux originates from the higher air temperatures at the upwind edge caused by the local advection of sensible heat. Regarding the uncertainty in the net shortwave radiation the authors should consider doing radiation modelling for the area for the respective time period including high-resolution terrain information.
• Figure 5: the authors are quite lazy with terms – please clearly state sensible turbulent heat flux as it has to be clear that this is the turbulent exchange of sensible heat.
• L366: if I understand it correctly you describe here the turbulent sensible heat flux per grid cell and not the heat advection. These values are extremely high. You compare these with estimates of Harder et al (2017) (L273) but they are providing estimates on the advected sensible and latent heat between two points and not the advected turbulent heat flux (paper Harder et al., 2017; equation 2 and 3).
• L405: I do not fully understand the sentence here. For the local advection of sensible heat not the difference between snow surface temperature and air temperature is important but the horizontal air temperature difference (and mean horizontal wind speed).
• L406: the reduction in the turbulent sensible heat flux of 20% in downwind distance is most probably the result of a decreasing contribution of the advection of sensible heat with increasing fetch distance over snow.
• L409: yes, exactly, the difference arises as you compare the simulated turbulent sensible heat flux at the surface (by your model) to an estimation of the advected sensible heat calculated by Harder et al. (2017).

Reference suggestions:

Egli, L., Jonas, T., Grünewald, T., Schirmer, M., and Burlando, P. (2012). Dynamics of snow ablation in a small Alpine catchment observed by repeated terrestrial laser scans. Hydrol. Process. 26, 1574– 1585. doi: 10.1002/hyp.8244.

Grünewald, T., Schirmer, M., Mott, R., and Lehning, M. (2010). Spatial and temporal variability of snow depth and ablation rates in a small mountain catchment. Cryosphere 4, 215–225 doi: 10.5194/tc-4-215-2010

Marsh, P., Essery, R., Neumann, N., and Pomeroy, J. W. (1999). “Model estimates of local advection of sensible heat over a patchy snow cover,” in Interactions between the Cryosphere, Climate and Greenhouse Gases, Vol 256, ed M. Tranter (Burmingham: IAHS Publ.), 103–110

Granger, R.J., Pomeroy, J.W., Parviainen, J., 2002. Boundary-layer integration approach to advection of sensible heat to a patchy snow cover. Hydrol. Process. 16, 3559–3569.

Mott, R., Stiperski, I., and Nicholson, L.: Spatio-temporal flow variations driving heat exchange processes at a mountain glacier, The Cryosphere, 14, 4699–4718, https://doi.org/10.5194/tc-14-4699-2020, 2020,

Sauter, T. and Galos, S. P.: Effects of local advection on the spatial sensible heat flux variation on a mountain glacier, The Cryosphere, 10, 2887–2905, https://doi.org/10.5194/tc-10-2887-2016, 2016. 

Mott, R., Wolf, A., Kehl, M., Kunstmann, H., Warscher, M., and Grünewald, T.: Avalanches and micrometeorology driving mass and energy balance of the lowest perennial ice field of the Alps: a case study, The Cryosphere, 13, 1247–1265, https://doi.org/10.5194/tc-13-1247-2019, 20