Understanding snow saltation parameterizations: lessons from theory, experiments and numerical simulations

The authors present a lengthy comparison of several snow saltation studies and compare the assumptions made for the most common snow saltation models in an atmospheric and snow model context. They go to great effort to explain the role that friction velocity plays in many of the scaling rules that have been developed for each model, and compare the results with their own numerical experiments. This is an ambitious undertaking and I applaud the authors for attempting to collect all of these different methods and studies into one review. As snow redistribution is included in more weather and climate models, these sorts of parameterizations will play an important role. I think this could be a highly cited article and provides a nice collection for open questions in future studies of snow transport.

As it stands, the manuscript needs to be improved prior to consideration for publication. The introduction material is currently a bit underdeveloped. The authors are presenting an advancement of a topic that has been studied in a large number of scenarios, which a wide range of applications as is shown in Section 2 when the actual parameterizations are being discussed. As well, the title suggests a kind of review of the state of the field. The authors do not present a sufficiently wide view of the topic in the introduction. I strongly suggest a deeper review of the available studies. Snow transport and snow saltation has been studied and modeled since at least the 1950’s, but the case studies selected to summarize the field and the complexities of the topic are a bit sparse and lacking. For example, the authors have a tendency to cite Antarctic studies in the intro, but the benchmark snow flux profile study of Budd et al. (1966) in Antarctica is not referenced. Perhaps the title would be better suited as "Understanding snow saltation in atmospheric modeling parameterizations".

I have several comments about the analysis and conclusions, as well as some specific comments, outlined below.

L20-22 Sastrugi?

L28-29 Do you have a citation for this convention?

L28-39 This paragraph started off with descriptions of blowing snow, and then focuses solely on Antarctica. Given the amount of time you spend on non-Antarctic snow studies in the remainder of the manuscript, it's a bit strange to limit to such a specific niche here. Please include a broader review.

L37-39 I am certain the authors can find an older reference to this complication than this.

L40-46 Again, this focuses solely on drifting snow in Antarctica. This is a bit strange in a general discussion of drifting snow. Given the number of studies on snow sublimation from field-based, hydrological, and numerical studies, it also seems odd that the authors are using a regional weather model and satellite observations.

L53-54 I do not believe it is widely accepted that snow particles that travel in suspension only arise from particles that have undergone fragmentation. There are no whole snow particles in suspension?

L56: This model of snow redistribution far precedes the referenced literature including, but not limited to (Dyunin, 1967; Lee, 1975; Dyunin, 1980; Pomeroy et al., 1993; Gauer, 1998; Bintanja, 2000)

L62: It would be helpful to cite the sublimation models that use the Thorpe and Mason approximations.

L66: Again, the references to modeling snow redistribution are a bit silo'd as they tend towards recent research from adjacent groups. These issues have been mentioned or studied for many decades, even in mountainous terrain (e.g. Dyunin et al., 1977; Schmidt, 1982; Gauer, 1998)

L65-76: There is again a strange tendency towards Antarctic research, which is not where the majority of drifting snow research has actually been conducted. Snow redistribution was coupled in a GCM by Eric Brun back in the 1980's.

L101: Spanwise?

L103-105: What do you mean statistically invariant? The temporal-average of windspeed is constant on each wall-parallel plane? And can you define "mainly" aligned?

L106-110: Strictly speaking, between the viscous sublayer at the surface and the inertial sublayer is a buffer sublayer where you do not have a fluid velocity profile that provides a constant shear stress. Furthermore, the log-layer or inertial sublayer also only exists for a finite height in the atmosphere. It would benefit the authors and the reader if the authors could address what assumptions we need to make for this sort of shear stress profile they are describing, and what is assumed to happen to the buffer layer in the presence of saltating particles. Typically some sort of roughness height is included in a log-law profile (which comes from the constant shear stress assumption) at which the wind essentially goes to zero above the actual snow surface, though this is widely known to not be physically true, but it helps close the equations. This roughness length is not mentioned anywhere, though often also modified to account for the momentum deficit caused by the saltation layers that the authors are referencing. This dates back to Bagnold.

L171-172: Did Bagnold show that the necessary shear stress was smaller, or that a smaller friction velocity was sufficient, given that \tau=\rho u_*^2 is only an "effective" shear stress at the surface.

L173: Requires, not implies?

L192-193: What is the fluid threshold friction velocity?

L193-194: Please rewrite this sentence. It is equal because it is assumed to be a fraction, and we assume this fraction is 1?

L196: Nor is it in agreement with experimental evidence dating back to Bagnold.

L196: Now i'm confused. I thought \tau_s was the approximated surface shear stress, which varies with windspeed. I believe you are actually referencing \tau_it, but using its equality with \tau_s in this one instance. Can you replace \tau_s with \tau_it to make the following inequalities clearer?

Does Figure 2 include the decay height of all experiments mentioned in Section 2.2.3?

L552: What is the subgrid-scale relative to the particle size? At what scale can we expect the snow particle to stop responding to fluctuations, and why?

L559-561: This is not a comprehensive list of all forces acting on a particle in a turbulent flow. Beyond gravity (buoyancy) and drag, there are also force terms from the wind, the force from the fluid moving with the particle, and the Basset-Boussinesq memory (Maxey and Riley, 1983; Talaei and Garrett, 2020).

L566: “entrainment”

L570: Is it assumed there is an infinite number of particles that are available to be entrained?

L576: Modulus

Figure 5: Can you discuss these decreases in the inset plots more? This seems like an interesting point that is glossed over rather quickly. As well, it would be helpful to include two more plots that compare the average particle velocities with the average wind speeds in the two directions at each height, for the various scenarios. The influence of vertical winds on ascending saltating particle is particularly interesting to think about as this is a primary factor driving the transition to suspension and away from the paradigms described here. Perhaps a vertical profile of vertical drag (normalized by gravity forces) could reveal these relationships?

L606-607: How many actual lagrangian particles were in transport at a given time? How does this assumption of clustering work? When a splash event occurs at a friction velocity of 0.3, you automatically assume 50 snow particles are ejected at that single location? And when you have an impact of a Lagrangian parcel, are you calculating the force of 50 times the mass equally distributed among the splashed particles? Admittedly this would create more pseudo-particles in transport while not requiring any additional Lagrangian computations, but the fact that each parcel at a given friction velocity has the same number of particles is worrisome. I see it would be difficult to truly track all the particles in a 6 m cube, but you are also manipulating the mass flux by enforcing these rules. I think there may be negligible effect on the relative concentration profiles, but some further explanation is needed here. If you instead chose to have 1000 particles in a lagrangian parcel, would this have a noticeable impact on your snow-wind feedback?

L619: How is steady state quantified? Any subset of the 100 seconds would provide the same mean profiles? Can you please provide some verification of this?

L623-624: Most of the numerical mass flux profiles.

L657: Does the average vertical ejection velocity combine both the splashed particles and the rebounded particles? Please clarify here.

Figure 5, I think v_z^{up} would be a better notation as you are elsewhere using superscripts to denote subsets of velocities in the direction specified in the subscript

L664: Particle velocity profile is mainly invariant

L678-679: Please clarify if this is something you are enforcing in the model, or a result of your model.

Figure 6: As stated above I think it’s weird to be using mass flux instead of a relative number flux given that the mass flux seems to be directly modified by this lagrangian parcel idea.

L682-683: I thought the relationship between impacting particle and splash velocity was stochastic?

L685-686: It would be good to show wind profiles for your full range of friction velocities from the surface to above the saltation layer and that show and quantify this invariance as that is actually a non-trivial conclusion. What do relative velocity changes look like at each height?

L686-687: This is an interesting point as well. When do particles in saltation have a change in sign for the drag? Assuming a non-slip velocity at the immediate snow surface, it should always occur somewhere. Is this accounted for in your snow-wind feedback? As we approach steady-state, and snow particles are already quickly moving, at what fraction of maximum trajectory height does that of transition drag sign-change occur? How does this momentum source for the wind balance with the momentum sink caused by the presence of particles? In turn, what role does this play in modifying u* or u*,s?

L732-733: What do you mean perturbed? How was this set of trajectories filtered? It sounds like you may be intentionally neglecting the impact of wall-normal winds and trying to only focus on ballistic-like?

L735-736: The particles never reach the surface? Does the wind field extend all the way to the surface?

Figure 9: In the splash-dominated saltation regime, it appears the saltation height is constant with variations in u*, and with constant mean particle velocity, correct? Then, researchers that are studying blowing snow in highly-unsteady wind should always measure the same snow particle velocities near the surface, as long as the windspeeds stay above the threshold and are averaged for 100 seconds? This seems like an unphysical conclusion to come to as there is no upper limit on wind speeds at the snow surface above the splash-dominated threshold, but you are imposing a clear upper limit on particle speeds. As well, would the height of the saltation layer not actually decrease with increasing windspeed as near-surface wind fluctuations (and fast particles) lead to quick suspension? This seems like a highly relevant question, especially for polar (and even high mountain regions) where 100km windspeeds are easily attained and shape the landscape.

Dyunin, A. K. (1967), Fundamentals of the mechanics of snow storms, in Physics of Snow and Ice: proceedings, pp. 1065–1073.

Lee, L. W., and L. Wah (1975), Sublimation of Snow In Turbulent Atmosphere, PhD Dissertation, Department of Mechanical Engineering, University of Wyoming.

Dyunin, A. K., Anfilofiyev, B. A., Istrapilovich, M. G., Mamayeva, N. T. and Kvon, Y. D.: Strong Snow-Storms, their Effect on Snow Cover and Snow Accumulation, J. Glaciol., 19(81), 441–449, 1977.

Dyunin, A. K., and V. Kotlyakov (1980), Redistribution of snow in the mountains under the effect of heavy snow-storms, Cold Reg. Sci. Technol., 3, 287–294.

Schmidt, R. A.: Properties of blowing snow (1982), Rev. Geophys., 20(1), 39–44.

Pomeroy, J. W., D. M. Gray, and P. G. Landine (1993), The Prairie Blowing Snow Model  :characteristics, validation, operation, J. Hydrol., 144, 165–192.

Gauer, P. (1998), Blowing and drifting snow in Alpine terrain: numerical simulation and related field measurements, Ann. Glaciol., 26, 174–178.

Maxey, M., and J. Riley, 1983: Equations of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids, 26, 883–889, https:// doi.org/10.1063/1.864230.

Talaei, A. and Garrett, T. J.: On the Maxey-Riley equation of motion and its extension to high Reynolds numbers, , 1–19 [online] Available from: http://arxiv.org/abs/2006.16577, 2020.

Bintanja, R. (2000), Snowdrift suspension and atmospheric turbulence. Part I: Theoretical background and model description, Boundary-layer Meteorol., 95, 343–368.

Budd, W. F., Dingle, W. R. J. and Radok, U. (1966): The Byrd Snow Drift Project: Outline and Basic Results, pp. 71–134.

Overview:  Overall, this paper was an engaging review of the current state of snow saltation science that examined, from first principles, numerous related disciplines from aeolian to atmospheric science.  Further, this review is neatly tied together and contextualized with LES simulations, which begets broader discussion on the future of snow saltation research and better identifies gaps in the currently available parameterizations.  The figures are informative, and the paper is very well written with very few typographic errors.  As it stands, the paper is in excellent shape and with some minor changes made to improve readability and some additional more holistic discussion on the state-of-the-science, it has the potential to be of significant impact to the greater community.  In light of that, I would like to congratulate the authors’ ambitious and well executed study.  Please see below for specific comments.

Specific comments:

1. The authors go through great lengths to distinguish the different types of shear stresses within the surface layer (e.g., fluid, surface, impact, etc). Given that this paper has a strong focus on the atmospheric aspects, I think it’s worth discussing how u_star is determined through atmospheric models and how that value can relate to the different u_star values that comprise the different surface stresses.  Further, I think it is also worth a brief discussion of drag partitioning (i.e., the loss of surface momentum to non-erodible elements) (e,g., Marsh et al., 2020, as an example of a parameterization with drag-partitioning).  While maybe not critically important for much of the work performed in this paper, since much of this paper reviews the details of snow saltation at very small scales, it may be worth some brief discussion to tie in with other parameterzations used at regional atmosheric modeling scales.

As a sub-point, I think it may improve readability to have a table somewhere in section 2.1.1 listing the different surface stresses, though I will leave that choice to the authors.  It can be hard to keep all of these straight, especially when many models use only one friction speed value.

1. The authors several times make reference to the fact that “snow surface” characteristics are critically important for accurately simulating the different variables that contribute the particle mass flux at the top of the saltation layer, however there is very little comment on the research that has been performed characterizing the threshold friction speeds for blowing snow algorithms, or any of the existing parameterizations in the literature. A brief discussion here may be warranted, especially an explanation on how values for u_star_threshold tie into the fluid stress and impact stress thresholds discussed here.  A good “first principles” reference is in Schmidt, 1980.
2. The authors claim on lines 317 – 322 that the linear relationship between u* and Q suggested by Pomeroy and Gray is not in agreement with most saltation models. I think this may be, at least partially, a consequence of that fact that many of the snow a majority saltation parameterizations referenced throughout (e.g., Vionnet et al., 2014) are based on parameterizations originally configured for soils.  In consideration of the fact that Pomeroy and Gray, specifically claim that the linear relationship is a consequence of snow vs. soil, and that soil parameterizations are not “directly applicable to snow,” I think this is worth elaborating on here.  While understanding this is an older paper, and that more recent work (e.g., Melo et al. 2022) provides some evidence that PG is incomplete even when taking into reasonable account interparticle forces, it’s worth making the distinction between PG and other parameterizations here, since PG was based on measurements of natural snow in the field instead of wind-tunnels.  I think this is important, especially in light of the fact that the LES simulations in this paper specifically ignore the inter-particle forces of the snow surface in an effort to replicate wind-tunnel measurements.
3. Equation 5 and Lines 595 – 602: The value of 0.1 for A in equation 5 for the aerodynamic fluid threshold, was that tuned to match the “disintegrated individual particles?” How were the equations for splash and rebound tuned to match this assumption?  Were any other roughness lengths tried, I’ve often seen snow reported as 2x10-4 meters (double that of the value used here), and even higher for some land surface models.  Presumably, the roughness length of the surface is used to generate the log-wind profile in the LES?
4. Figure 4: “The decay height …. Follows approximately the trend proposed by NH (2002)”.  I’d disagree, to me it looks like there is simulations follow a relationship that looks more continuously proportional to the square-root of u_star, even below 0.3 m/s. It never appears to me that it is proportional to u^2.  Though it would be helpful to see a value lower that 0.2 (if there is one).  Given that this “agreement” is used to support a statement on Lines 653 – 654, it’s worth a second look.
5. Figure 9: Great figure!
6. Line 847: “particle mas flux” should be “particle mass flux”

References:

Marsh, C.B., Pomeroy, J.W., Spiteri, R.J. and Wheater, H.S., 2020. A finite volume blowing snow model for use with variable resolution meshes. Water Resources Research, 56(2), p.e2019WR025307.

Schmidt, R.A., 1980. Threshold wind-speeds and elastic impact in snow transport. Journal of Glaciology, 26(94), pp.453-467.