the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Mar 2026
Reduced Surface Hoar in a Warming World
Abstract. Surface hoar formation is a critical snow metamorphism process that influences surface roughness, radar-scattering properties, albedo, and avalanche risk of snowpacks. Despite its importance, surface hoar mechanisms and climate sensitivity remain poorly constrained, creating uncertainties in remote sensing of snow properties and infrastructure hazard forecasting. To address these gaps, we use observations from the Surface Atmosphere Integrated Field Lab (SAIL) alongside the Structure for Understanding Multiple Modeling Alternatives (SUMMA) physics-based model to investigate contemporary and future surface hoar dynamics in a representative mid-latitude snow environment in the Colorado Rockies. Modeling and observations are centered around seven high-quality manual measurements of surface hoar mass during February 2023. We confirm that surface hoar is favored on clear nights with snow surfaces that are 10 °C colder than the near-surface air, leading to a favorable humidity gradient for water vapor deposition from the atmosphere onto the snowpack. Nocturnal clouds exert a 30–40 W m-2 radiative forcing that inhibits the snowpack from cooling, thereby limiting deposition. We evaluate stability correction parameterizations and surface roughness parameters for the SUMMA model using colocated vertical gradients and eddy-covariance observed fluxes, finding that models must use an appropriate stability correction for the highly stable surface layers characteristic of surface hoar (Ri > 0.2) to model deposition rates sufficient to explain observed surface hoar mass. After taking these factors into account, both SUMMA and observations agree that deposition fluxes are favored when overnight air temperatures are less than -8 to -10 °C and ωspd is less than 3 m s-1. Sensitivity experiments demonstrate that surface hoar is favored for low-density snowpacks via a thermal conductivity mechanism. Using SUMMA forced by an ensemble of 9 downscaled GCMs shows that, at the annual timescale, the total wintertime nocturnal water vapor flux onto the snowpack decreases at a rate of 6.1 gm2 per degree of warming, yielding an 81 % decrease by the end-of-century under the SSP3-7.0 emission scenario.This decline is driven by a 14 % decrease in nightly surface hoar events per winter and an overall increase in the size and frequency of nocturnal sublimation events. Additional work reconciling observed and modeled amounts of surface hoar mass, turbulent exchanges of water vapor during high stability, and relationships to katabatic winds in complex terrain is warranted in order to improve the understanding of this fundamental snow metamorphosis process.
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Status: open (until 19 May 2026)
- RC1: 'Comment on egusphere-2026-935', Anonymous Referee #1, 11 Apr 2026 reply
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RC2: 'Comment on egusphere-2026-935', Anonymous Referee #2, 13 May 2026
reply
Dear Authors,
This study investigates the formation processes of surface hoar using various meteorological observation data. It also simulates future changes in surface hoar using a numerical model SUMMA. Although the observation area is limited, the study clarifies the formation processes of surface hoar in the study area based on detailed observations. The analysis is also detailed, and I found the study to be carefully conducted. I have no objections to the overall content of the study, but there is room for improvement in the quality of the writing. I hope that revising the manuscript with reference to the comments below will help improve its quality.Major comments
1. When surface hoar forms, does the roughness length of the snow surface change, and consequently the bulk coefficients as well? Looking at the result that Cd deviates from the theoretical curve when Ri is high, could this indicate that surface friction changes due to the formation of surface hoar? In this study, z0, zh, and zq appear to be assumed to be 2 × 10^−4 m. I think it would be better to discuss how the use of these assumed roughness lengths may have affected the results of this study.2. Related to the comment above, if the formation of surface hoar increases friction and enhances turbulence, would this make surface hoar more likely to form? I thought it would be interesting if there were a process similar to positive feedback in surface hoar formation. This is more a matter of my own curiosity than a criticism of the manuscript, but if the authors can develop some discussion on this point, I would appreciate it if they could add it to the manuscript.
3. The manuscript does not provide enough information on the experimental settings used for the sensitivity experiments and future projection experiments with SUMMA. Please describe these settings more carefully in the Methods section. Also, as I point out in a later comment, some experimental settings are currently described in the Results section, which is not appropriate. Please revise this point with reference to the comments below.
Specific comments
L40-41: Sublimation is more likely to occur when air temperature is low and the air is dry. Do previous studies suggest that surface hoar formation is more likely to occur under higher air temperatures and moist air conditions? If so, it would be useful to describe such temperature and humidity conditions in this paragraph.L68: I think Section 2 would be easier to read if the structure of the section were briefly described here. Alternatively, a brief overview could be added at the beginning of Section 2.
Section 2.1: Since many abbreviations are used throughout the manuscript, it would be helpful for readers if a table summarizing the meanings of all abbreviations were added to the Supplementary Material.
Section 2.1.1: Starting directly with the equation for the snow surface energy balance felt somewhat abrupt. It would be helpful to add a brief explanation at the beginning of this subsection as to why the discussion starts with the surface mass balance. At present, it gives the impression that this is written simply as a convention. I think it would be useful to briefly describe the relationship between surface hoar and the surface mass balance.
L84: It would be useful to add the values of the emissivity and the Stefan–Boltzmann constant.
L85: Was a fixed value used for the albedo α? Could the formation of surface hoar affect the albedo?
Section 2.1.2: At first, I thought that Eqs. (3), (4), (6), and (7) might be unnecessary if the purpose was only to explain how Fq is calculated. However, since quantities such as Ch are used in the Discussion, it may be helpful to add a brief statement that these equations are used to interpret the behavior of the water vapor flux.
Eqs (2) and (3): Ch and Cq are reversed.
Eq (4): In this equation, the denominator is written as ρ. Since the left-hand sides of Eqs (2) and (3) are expressed using the power of −1, would it be better to write this term as ρ^-1 in the same manner? Also, the friction velocity u* does not appear to be explained in the main text.
L102: The value used for Lv, which is related to Fq, should be stated. Is it treated as a constant, or is it estimated from calculations?
L102: In the text, L is written as an uppercase letter, whereas it is written as a lowercase letter in Eq. (2).
L119: What assumption is made for zh?
L154-155: It would be useful to add the latitude and longitude information for SAIL and SPLASH.
Table2: The term “Fluxes” alone is not sufficiently clear. Please describe what flux each of the three symbols represents.
L224: The manuscript should specify which variables were used as atmospheric forcing inputs to SUMMA, such as air temperature, humidity, and precipitation.
L224: Was the ensemble mean of WUS-D3 used as atmospheric forcing? If this was an ensemble simulation, how many ensemble members were used?
L233: Was the SUMMA simulation conducted at the same spatial resolution as the atmospheric forcing data? It would be easier to understand if the spatial resolution of the model were described earlier in the manuscript.
L244-245: Why was a 41-year period used for the first half, while a 21-year period was used for the latter half? If the former period is intended to represent the early 21st century, would it not be more accurate to define it as 2000–2020?
L247-248: If the “SUMMA GCM-forced experiments” refer to ensemble simulations, the number of ensemble members used in the experiments should also be stated. My understanding is that WUS-D3 provides ensemble forcing data, and that SUMMA was driven by these forcing data, meaning that the model outputs are also an ensemble. It would be helpful to include such an explanation.
Results: There are many incorrect figure reference numbers throughout the Results section. I point out several examples in the comments below, but there appear to be others as well, so please check them carefully throughout the section.
L252-253: Figure 2 appears to include observational results from the M1 site as well, but this sentence mentions only the KP site.
Figure 2: Please clearly indicate which meteorological data were obtained at the M1 site and which were obtained at the KP site. For example, Table 2 states that Tair was obtained at both the M1 and KP sites.
Figure2d: The labels Ts.4m and Ts.9m can be read as 4 m and 9 m, respectively, so it would be better to revise the notation.
L258: Looking at Figure 2d, Tsfc appears to be higher than Tair almost throughout the period. Is this the opposite of what is stated in the text?
L264: Should this be January 27–31?
L271-274: Is there a reason why 25% was chosen to define clear-sky conditions?
Figure 4: I am concerned that panels a–g are not arranged in chronological order. Is there a reason for this?
L309: Figure 9 -> Figure 4
L310-311: Please add a statement indicating that this sentence refers to the results shown in Figure 4h.
L318-319: It would be easier to compare this statement with Figure 2c if the specific wind direction were also described.
Figure 5d: The notation on the horizontal axis should be revised, as the overbar and slash are too close together and look like a square-root symbol.
L330-339: Most of this paragraph describes content that should be included in the Methods section, so it would be better to move it there. There does not appear to be a subsection on the SUMMA parameterizations in the Methods section, so I think it would be useful to add such a subsection.
Figure 6: The caption does not seem to explain what the gray and light-blue markers and the black circles represent. Also, it seems unnatural for the vertical axis to show only “dimensionless” as the unit. Would it be better to label it as “bulk transfer coefficient (dimensionless)”?
L360-364: This paragraph should also be moved to the Methods section.
L365-369: Please make it clear that the results described in this paragraph refer to Figure 7.
L366: If the correlation coefficients are 0.75 and 0.94, why are the corresponding squared values, R², 0.13 and 0.75?
Figure 7a, b, d: Please ensure that the dashed 1:1 lines do not terminate in the middle of the plots. Also, for panel d, it is better to set the minimum value of the axis to 0, since relative humidity cannot be negative.
Figure 8: It feels unnatural that the dates on the horizontal axis are not arranged in chronological order. I recommend rearranging them in chronological order. It is also difficult to tell which bar each date label on the horizontal axis refers to. For example, the SUMMA bar for Feb. 11 appears to be the rightmost bar, but the SUMMA bar for Feb. 4 is located very close to the label for Feb. 11. In addition, there does not seem to be any explanation of SB1 and SB2 in the legend, so please add one. Please also explain the meaning of the purple V-shaped symbols.
L375-377: This statement is more interpretive in nature, so it would be more appropriate to move it to the Discussion section.
L375-377: The Louis formulation for Cd does not reproduce Cd well under high Ri conditions. How is Cd calculated in the SUMMA model? Even if wind speed is weak, a high Cd would allow momentum to be transferred to the snow surface more efficiently. In such a case, could more efficient water vapor deposition occur?
L402-403: The expression “decline” is somewhat misleading. Would it be better to state that Δq “closes to zero”?
L403-404: The figure reference is incorrect. It should be Figure 9, not Figure 7.
L406-408: The abstract states the following, and the wind speed threshold given there is slightly different from the one stated here. The specific values should be made consistent between the two sections:
“both SUMMA and observations agree that deposition fluxes are favored when overnight air temperatures are less than -8 to -10 degC and wspd is less than 2 to 3 ms^-1.”L412-417: I think this paragraph should also be moved to the Methods section. Overall, some parts of the experimental settings and assumptions are described in the Results section, which makes the manuscript difficult to follow.
L417: Is the figure being referred to here Figure 10?
Figure 10a: The caption does not explain the difference between the solid and dashed Tsfc lines for each value of λ.
L443: Looking at Figure 13b, the trend appears to increase year by year, but the description in the text seems to imply the opposite. I assume the authors mean that the amount of surface-hoar deposition is decreasing, but since the flux itself is actually increasing, the current wording is inappropriate. Because the same expression appears throughout the manuscript, it would be better to describe this point more carefully or revise the wording.
図13: Because sublimation flux increases under warming, the total flux also increases. However, the deposition flux also appears to show a slight increasing trend. Since the number of nights on which surface hoar forms decreases under warming, could it be that a larger amount of surface hoar forms during each individual formation night? If so, the risk of hazards such as avalanches related to surface hoar may also increase.
L457-458: The statement “but some mechanistic descriptions are not accurate from a climatic perspective” seems somewhat excessive. I agree that this study reveal the formation process of surface hoar using detailed meteorological observation data, but it should be noted that the validation is limited to a restricted region. Of course, I still think this is a sufficiently valuable study. However, in other regions, the formation processes of surface hoar may differ from those observed in this study.
L480-485: In this paragraph, rather than using a shortened explanation such as “The effect is described in part by climatology,” please explain clearly and carefully why weak wind speed is important for surface hoar formation. I think the content of this paragraph is one of the important findings clarified by this study.
Citation: https://doi.org/10.5194/egusphere-2026-935-RC2
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- 1
This manuscript is the first report mentioned climate change effects on surface hoar events. Stability correction is a critical factor in discussing surface hoar formation, and this paper focuses on its parameterization. As for the observation results of the surface heat balance (Fig. 2, Fig. 3), the findings are essentially consistent with those of Hachikubo and Akitaya (1997) and Stossel et al. (2010). Although I would assess the novelty as limited, the observed data are valuable, and I do not see any issues with the content. This is likely the first instance of upper-air meteorological observations during surface hoar formation, and it is interesting that latent heat flux was demonstrated to be downward from the upper troposphere to the snow surface. I feel like I've read an impressive paper in a while. I can recommend its publication, because the manuscript will be of interest to the readers of EGUsphere. Minor revision will be needed, my comments are as follows:
Because I am an field researcher rather than a modeler, I will focus exclusively on observation results.
1) I have a question regarding the Stossel box. When surface hoar forms, the relative humidity profile reaches its minimum at the snow surface, as shown in Fig. 4. In addition to surface hoar, another "frost", which generates near-surface faceted crystals, should also form under the box. Removing this frost is considerably difficult. I understand this should have been addressed in this study, but I would like to confirm that the frost on the underside of the box is properly removed before each measurement. Based on this point, I believe that the automatic measurements described in the section of Discussion are practically impossible.
2) An infrared hygrometer is required to measure latent heat flux using the eddy covariance method. When surface hoar forms, it is likely that frost will also form on the window of the infrared hygrometer. How was this phenomenon overcome?
3) I would like to confirm whether the specific heat of air (cp) is a function of temperature and pressure in the turbulent flux calculations. In Fig. 2, the atmospheric pressure is approximately 700 hPa. Compared to zero meters above sea level, sensible heat flux is relatively smaller at high altitudes such as mountainous regions.
4) There is no explanation for Fig. 1e in the figure caption, there are two instances of (d). The relationship between (a) and (e) is unclear. Latitude and longitude information might be required for Fig. 1a.
Small points:
L285: Fig. 3c is wrong, 3d is correct?
L309: (Fig.9))?
L373-: It is incorrect that the explanation for Fig. 8 appears before that for Fig. 7 in the text. The figure cited in Section 3.4.1 is listed as Fig. 7, but Fig. 9 is correct. The original Fig. 7 is not cited in the text. The figure citations throughout the manuscript should be checked again.
L481-485:I do not understand the meaning of "apparent paradox". I do not find it obvious that surface hoar accumulation increases with increasing wind speed. As Hachikubo (2001) Ann. Glaciol. demonstrates, an increase in wind speed promotes sensible heat, raises the snow surface temperature, and reduces delta q. On the other hand, under calm conditions, only molecular diffusion of water vapor occurs, which is insufficient to maintain the surface hoar growth. Therefore, it is clear that an optimal wind speed range exists.
L526-531: This is a comment. The snow surface is "layer", not "plane". Even when sublimation dominates in the energy budget, surface hoar may still be maintained on the snow surface (Hachikubo and Akitaya, 1998, Ann. Glaciol.; Stossel et al., 2010).