the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 May 2026
Horizontal sensible heat advection increases snow melt rates: Beyond point measurements
Abstract. In the atmospheric surface layer, it is generally assumed that vertical fluxes dominate near-surface heat transport and heat exchange between the atmosphere and the earth's surface. However, when the earth's surface is covered in patchy snow, near-surface horizontal advection of heat may be significant, and it's impact on snow melt rates is disputed. We estimated the contribution of horizontal sensible heat advection (QH) to snow melt using 8 days of measurements collected in May 2023 in the alpine East River basin in Colorado, Rocky Mountains, USA. We used an infrared video camera and polyester sheet to estimate QH, 3-meter resolution satellite imagery to track fractional snow covered area (fSCA), a scanning lidar to estimate snow melt rates, and micrometeorological and eddy covariance measurements to characterize the surface energy balance. Infrared camera measurements of QH over a single snow patch show that QH contributes to snow melt and is largest at the patch's upwind edge. Lidar-based snow melt measurements show that melt rates are highest at the upwind edge, further suggesting that QH causes snow melt. Over four days when fSCA was less than 62%, QH estimates ranged from 234–584 W m-2 and mid-day net radiation ranged from 331–508 W m-2. When we considered only vertical heat fluxes, radiative fluxes, and snow melt in a snow patch surface energy balance equation, we found a mid-day residual between 267–668 W m-2, and the residual increased as fSCA decreased. The approximate match between the energy balance residual and estimated QH suggests that advection is an important factor to consider when predicting snow melt. On days with low fSCA (< 62%), horizontal advection may contribute as much to snow melt as net radiation.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1633', Anonymous Referee #1, 29 Jul 2026
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RC2: 'Comment on egusphere-2026-1633', Anonymous Referee #2, 21 Sep 2026
Review of ‘Horizontal sensible heat advection increases snow melt rates: Beyond point measurements’ by Eli Schwat et al. submitted to The Cryosphere
Overall comments
This is a very interesting manuscript with many novel measurements. Its strength lies in the rich array of data available including lidar scans of snow melt rates, eddy covariance and radiation observations, satellite observations of snow covered area and novel sensible heat flux measurements using thermal infrared camera and polyester sheet. The lidar-based melt rates indicate complex patterns of melt that highlight enhanced melt at patch edges as well as challenge previous assumptions about spatial variability of melt between snow patches on different topographical locations. Overall, a large energy residual is found between the observed melt rates and the sum of net radiation and turbulent heat fluxes measured over bare ground during periods of patchy snow. This is attributed to horizontally advected turbulent heat flux. The manuscript is well organized with clearly constructed figures that aim to extend our understanding of turbulent heat fluxes in this complex yet important topic.
My main concerns are with the theoretical formulation of some aspects of the analysis, particular assumptions about characteristics of the ABL upwind of the snowpatch and vertical fluxes above the snowpatches, large uncertainties in the observed SEB residual and lidar-derived melt rates, and inconsistencies in the interpretation of the results and the theoretical framework presented.
Given that in heterogenous surface conditions, the boundary upwind of the snowpatch will be constantly evolving and readjusting to the inputs of heat and moisture, and the assumptions of a well-developed boundary layer upwind of the snowpack are likely not valid. Further discussion of this and the limitations it places on the theoretical model are needed.
While the measurement of sensible heat with the polyester sheet are novel, they are very short and do not match real world conditions given the very narrow strip of snow either side of the sheet. Thus, the evolution of the temperature field on the screen is likely to be influenced by lateral horizontal transport of heat from the snow-free areas beside the sheet as the air moves along the sheet. Given this and the wind speed dependence of the calibrated parameters that are discussed, more care needs to be taken to not extrapolate these results into the rest of the analyses.
The manuscript needs to be clearer about the definition of local horizontal heat advection and its relationship to vertical turbulent heat fluxes over the snow surface and large-scale advection of warm air. As noted in Essery (2006), vertical heat fluxes into the snowpack are the mechanism by which horizontal heat advection effects snowmelt
“Snow-free ground has a much lower albedo than snow, and is not limited to a maximum temperature of 0 °C, so it can become substantially warmer than the surrounding snow, and upward fluxes of sensible heat from the snow-free ground warm the air. As this warmed air flows over a snow patch, downward heat fluxes cool the air and warm the snow; heat is thus advected from snowfree ground to snow and provides an additional source of energy for melt.”
And Granger (2006) notes that
“This additional flux of energy to the snow surface cannot be reliably calculated using traditional boundary-layer flux–profile relationships, since these are based on the assumption of a constant flux layer.”
This a key point that seems to be lost in the manuscript – the horizontal advection is occurring in a small frame of reference (a few metres) as the BL adjusts to the new surface. The horizontal transport is a transient response that is not well represented in traditional models of vertical turbulent flux. Once BL has adjusted to the snow surface, it is likely that sensible heat flux towards the surface will continue (due to larger scale advection) but this is likely more well represented by traditional BL flux-profile relationships and is not captured in the framework presented because the source of heat is above the frame of reference used here. Further clarification of the theoretical frame of reference in the introduction is needed to properly introduce the reader.
The key question for those seeking to represent turbulent heat fluxes in land surface and hydrological modelling frameworks is – are the turbulent fluxes enhanced at the patch edge over what you would assume from measurements of air temperature and wind speed made at a single height and classical boundary layer theory – this determines if additional processes control the rate of heat transfer to the snowpack. With this in mind, the manuscript would greatly benefit from a calculation of vertical sensible and latent heat fluxes over the snow patches using traditional bulk methods to highlight the additional flux that may or not be occurring. As part of this, further basic meteorology is needed to give context including timeseries of wind speed and direction, as well as air temperature and humidity from at least one station.
With additional analyses and discussion, the paper should make a valuable contribution to the literature on patchy snow.
Line Comments
Page 1 | line 4: “Qh”- this term is commonly used for vertical turbulent sensible heat flux over snowpack – please consider using a different term to distinguish horizontal advection from vertical turbulent heat flux into the surface or do you consider these to be equal?
Page 1 | line 22: “speed” > rate
Page 2 | line 24: please ensure the references are consistently ordered chronologically or alphabetically
Page 2 | line 39: “influence of sensible”
Page 3 | line 81-83: further references are needed for the formation of the IBL
Page 4 | Figure 1c: this panel needs a north arrow?
Page 4 | Figure 1c: Why were no transects made near D?
Page 5 | Eq. 2 / lines ~99: it is unclear why Hu is part of the formulation for Qh as H0 - H ECV? 0 is a coordinate
Page 5 | line 105: “We can evaluate the integral in Equation 2 to any arbitrary height above zb and find the same estimated advection” It seems unlikely this assumption is valid due to vertical flux divergence above. Check Harder 2017. how does this compare to the formulation of others?
Page 5 | line 103: the wind profile will evolve with x if it is a depression. Please discuss.
Page 12 | line 230: the albedo will also vary diurnally - another source of uncertainty in residual
Page 13 | line 233: what towers was Hu and Eu calculated from?
Page 13 | line 257: “to estimate Qh”
Page 15 | line 289: ‘decent match’ – please provide some quantitative statistics for the match - i.e. uncertainty bounds on each parameter
Page 16 | line 301-302: “surface lowering and melt rates were only calculated for positions on the transects where snow existed throughout the study period” does this mean you have excluded melt rates at upwind positions that may melt quicker?
Page 16 | Figure 7: a consistent y scale would be useful here. it appears that both are in strong depressions/slopes.
Page 17 | lines 312: “melt rates within 5–10 meters of the upwind patch edge were between 1.2–1.5 times larger than average melt rates”. The mean values are higher, but a normalized melt rate of 1 is within the 95% CI for almost all points, so this is not conclusive. Please revise. Also, the relatively abrupt decrease in melt at downwind sites suggests another mechanism is at play to modify melt rates with distance from the patch edge. Please discuss.
Page 17 | line 327: please provide some more detail on temporal and spatial extent of this average.
Page 17 | lines ~325-328: “melt rates measured over a snow patch in a depression (UW) were actually larger than melt rates measured over a snow patch not in a depression (D)”. It appears so, but D is downwind of UW so we would also expect some cooling of the air to occur that would depress melt rates at D. Also, D is still on a slope and this may have an impact. Please discuss.
Page 18 | line 331; what were typical wind speeds during the daytime? These would give some additional context for the likelihood of decoupling (more likely in lower wind speed)
Page 18 | line 334: Are the lidar-based melt rates in Figure 9 for all points or only for points that were always snow covered?
Page 18 | line 343: this sentence does not make sense – which melt rates were higher?
Page 19 | line 377: “matched within 0.01%” this seems unrealistically small – is this the melt rate over the full period? please check
Page 19 | lines 346-347: It seems that the lidar matches more closely those pillows that have shallower snow (i.e. UE and C earlier on, and UW and D later). Please comment
Page 19 | lines 351-356: These three sentences contradict each other - you say it's patchy by 13th at latest, the 12th is ‘bareground patchy’, but snow cover dominated on 13th, and the period of patchy snow started 15th. Some more precise definition of what you consider patchy is needed here.
Page 19 | line 374: “snow beneath the surface may have remained below 0°C later into the day” this could be confirmed by relatively straightforward modelling using observed snow surface temperatures, depths and densities. Consider adding this to reduce uncertainties in the residuals.
Page 19 | lines ~374-375: “Res became positive between” this reads as if the positive Res occurred from 0600 to 1200 rather than started at that point. please reword: “Res switched to a positive sign at some point between 0600 and 1200 each day, remained…”
Page 20 | Figure 10c: where does large residual on Friday 12th come from?
Page 20 | Figure 10c: where has the data gone for Thursday 11th? looks like a large offset between Rnet and Emelt that deserves discussion.
Page 21 | Table 1 caption: why wouldn't we compare Mid-day estimates of Qh with the values also for midday?
Page 22 | line 391: “net radiation balanced snow melt” this is an over simplification - on 10th May, Hu appears to contribute significantly to Melt - perhaps due to regional scale advection of warm air? Please revise.
Page 22 | line 402: “It is possible that a portion of Res is due to QE” some simple analysis of vapor pressures measured over the snowpack would allow you to assess how much condensation played a role here. Do you have observation of air temperature and humidity over the snowpack?
Page 22 | line 409: “Future work should analyze the snow patch energy balance” this is a key limitation and deserves further discussion given the aims of the paper. In particular it would be worth reflecting on what parts of the energy balance more complex parameterisations would help constrain?
Page 23 | line 423: The Hu and Eu bulk analysis should be included here or an appendix.
Page 23 | line 424: on what basis were the bulk Eu estimates deemed to be wrong?
Page 25 | Appendix A lines 484-485: in the caption for Figure 3 zb(x) is defined as the height at which temperature over the patch equals the temperature over the upwind bareground, but here it is defined as where the vertical sensible heat flux equals the vertical sensible heat flux over the upwind bareground. It is not clear why these two should be equal – please discuss this more clearly.
Citation: https://doi.org/10.5194/egusphere-2026-1633-RC2
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- 1
This study examines sensible heat advection over a snow patch over an 8-day period in an alpine valley in the Rocky Mountains of Colorado. The few studies that have examined this term have suggested that it may be significant, particularly during the snowmelt season when snow patches are present. An ambitious experimental setup was thus implemented to quantify the key terms of the energy balance over the snow patch. The main innovative feature is the deployment of a polyester sheet that is imaged by a thermal camera; this sheet has the property of capturing the air temperature distribution above the snow patch and visualizing the growth of the internal boundary layer (IBL). This setup is installed at the center of an array comprising several flux towers - which measure turbulent sensible and latent heat fluxes - radiometers, and satellite measurements to provide a detailed description of snow cover changes, as well as a lidar to measure changes in snow depth over the patch.
The introduction provides an excellent review of the literature, clearly outlining the current state of knowledge and the gaps that this article aims to fill. The theoretical frameowrk is clear and well-structured. This type of study is rare and important, as there is considerable uncertainty regarding the processes controlling snowmelt when snow cover becomes patchy. This study addresses two main research questions: 1) to quantify the magnitude of sensible heat advection; 2) to determine the contribution of sensible heat advection to the melting of the snow patch. Unfortunately, the experimental setup is not fully in line with these research objectives, forcing the authors to propose multiple assumptions, such as :
As such, the level of confidence in the results is, at best, moderate. Some of these assumptions need to be revisited and discussed in greater detail to improve the level of confidence in the results.
Main Comments
1) Wind Speed Profile
The assumption of a logarithmic wind profile under neutral atmospheric conditions does not hold up, in my opinion, especially when considering the estimated profiles above a snow patch shown in Figure 5 of Haugeneder et al. (2023). I encourage you to revisit your treatment of the wind profile and explore the possibility of using the “wind field estimation from infrared data” (WEIRD) approach presented in their article.
2) Height of the IBL
First, it would be helpful to present air temperature profiles at various locations along the snow patch, as shown in Fig. 5 of Haugeneder et al. (2023). A more robust approach than visual inspection should also be used to determine zb, which was set at 0.75 m.
3) Determination of QH
QH is determined based on 30 minutes of data. The evolution of QH is then linked to the relative position with respect to the leading edge of the snow patch, and a regression model is trained to estimate QH using the width of each snow patch in the following days. What were the weather conditions like during this 30-minute period? What was the main factor limiting the use of other data blocks to increase the robustness of this estimate? Is it possible to be a little more flexible regarding wind direction? The fits used do not seem to perform very well between 0 and 1 m. Overall, you need to improve the robustness of your approach to determining QH.
4) Disturbed Snow Patch
Well, it is not ideal, but the snow patch was manually shoveled around the screen for the purposes of the study (see lines 131–133). What are the effects of this disrupted snow on melting? For example, the surface is surely rougher than a natural snow patch, no? What is the impact on albedo? These effects need to be discussed.
5) Albedo
Is it possible to see the albedo data on which the assumption of a constant value of 0.6 was based? I find this value rather high for snow during the melting period. Why not show the data collected in situ just before the snow melted at the site?
More Specific Comments
Fig. 1: This figure would benefit from being revised to make it look more professional. The number of colors used should be minimized, font sizes should be standardized, all boxes should be properly aligned, the blue diagram of the towers should not be superimposed on the photo in (b), text elements within the boxes should be centered, etc. The focus should be on the towers relevant to the study. Furthermore, Figures (d) through (i) are a bit too small to be easily readable. Perhaps fewer days should be selected and the figures enlarged? Also, the fourth line of the legend should read “locations.”
Fig. 3. This figure has great potential, but would benefit from being simplified. Add downward-pointing lenses for the radiometer, even though that data is not used here. Add actual arrows at (a) and standardize the font size and line thickness. Minimize the number of frames to avoid cluttering the figure. Is the shape of the temperature profiles representative?
L2: its impact
L102: sensible
L123: µm should not be in italics
L145: add space between 4.5 and m
L179–180: What is the basis for the claim that heat fluxes between the ground and the base of the snow cover are negligible?
L345: within .01%, really?
REFERENCE
Haugeneder M, Lehning M, Reynolds D, Jonas T, Mott R. A Novel Method to Quantify Near-Surface Boundary-Layer Dynamics at Ultra-High Spatio-Temporal Resolution. Boundary Layer Meteorol. 2023;186(2):177-197.