On the importance of the humidity flux for the surface mass balance in the accumulation zone of the Greenland Ice Sheet

General Comments:

In an effort to increase the accuracy of a regional climate model (MAR), the authors focus on one term in the energy flux of the snow surface over the Greenland Ice Sheet. The method inherent to MAR, a bulk flux estimate, is widely known to be inaccurate. The authors compare fluxes estimated by this bulk approach to fluxes estimated by an eddy-covariance system at the EGRIP drilling site. The authors then use a linear correction to make the bulk estimates more closely match the eddy-covariance estimates. This is an incredibly ambitious problem to approach, and as such the results need to be rigorously supported.

This linear rescaling works relatively well given its simplicity. Such a simple correction is necessary to maintain any sort of numerical economy for a regional climate model. However, the authors opt to rescale the output of an LHF estimation, not the constituent physical variables, which themselves influence other terms in the energy balance. Given this, the way in which the results are presented needs to be very precise. Further comments on my concerns and issues this might create are discussed below.

Furthermore, there is an underlying implication that the eddy covariance method can be used to actually measure the vapor transport away from the snow surface. This is not actually the case and there is 25 years of publication in Boundary Layer Meteorology attempting to understand and better estimate vapor fluxes using Reynolds-decomposition-based methods for both stable and unstable atmospheres. To date, the issues and errors associated with EC over snow are ample, even in relatively homogenous terrain. When reading this manuscript, the feeling that the authors give is that EC calculations can actually be used as a ground truth with which to improve MAR. This is, unfortunately, not scientifically accurate. That being said, the conclusions of the manuscript are not without their own merit. Modifications to the language and conclusions that reflects the underlying lack of an actual “ground-truth” would make this more suitable for publication. Reconsider using “observed LHF” (or justify) as the EC approach is itself also only an estimate.

Specifically, I think the introduction should be improved by being both more precise about the studies they are referencing as benchmarks and including more references to show general issues in using turbulent fluxes in stable boundary layer and over snow-covered terrain to represent water vapor transport (as mentioned above). The authors are suggesting that there are errors in previous experiments and models that represent “humidity flux”, and provide a general view that EC estimates are better than bulk estimates. While few people (if any) would argue bulk estimates are more physically accurate, there are still significant variations between EC studies, especially relating to ice sheet/snow surface conditions and the instruments that are used to measure water vapor.

Fundamentally, I am concerned that there is also no consideration of blowing snow processes in this study, which have been shown to be responsible for sublimating up to 50% of seasonal SWE in some environments. Presumably in the cold, dry interior of Greenland significant latent heat will be exchanged by this specific sublimation contribution. In order to represent an accurate surface energy balance, without specifically addressing blowing snow, both the bulk approach and EC estimates would be influenced by blowing snow sublimation in their calculations (it’s actually happening and affecting the humidity), and potentially other terms that would impact surface mass balance. It appears the authors wish to not specifically address this source of latent heat flux, and wrap its influence up into the corrected bulk estimates. If this is their agenda, it should be specifically addressed and justified why this is a scientifically sound approach.

I was also a bit surprised in the results section when the authors deviate from their proposed objective and instead use lower-frequency observations and a bulk approach for part of the year to compare with the bulk approach in MAR. The justification of this appears to be that they can make bulk estimates from observations close to EC (in linear terms), and thus it’s good to then get close enough to the bulk observations. There’s a compounding error here that has not been commented on, nor has the extensive use of linear statistics and regressions for nonlinear functions.

As well, this EC data referenced does not actually comprise the majority of the data that is used to calculate the humidity flux corrections. It seems that the authors may actually be overstating its influence on the model correction.

I like the idea of the manuscript, but suggest major revisions prior to publication.

Specific Comments:

L25 Reconsider using deposition as this may be confused with deposition of precipitation

L25-27: Are you considering sublimation from blowing snow as well? Sublimation rates of snow particles in transport are much greater than that found from the snow surface. Blowing snow sublimation has been shown to play a significant role in surface mass balance in a wide range of alpine, arctic, Antarctic and other cold regions, and has even been connected to seeding of clouds. Please justify or explain early on.

L42-43: I would suggest against referring to eddy-covariance as a “direct measurement.” There are significant assumptions that need to be satisfied for the eddy-covariance to approximate turbulent fluxes, which themselves are a simplification of the actual vapor flux at a given height in the atmosphere. These assumptions and errors need to be discussed.

L43-44: What is your definition of “humidity flux” that you are using if you are not referring to latent heat flux? I think this needs to be precisely defined as you use both terms, but they do not appear to be interchangeable for you.

L44-47: Again, are these estimates taking into account a mobile snow surface or not? For example, blowing snow sublimation specifically has been attributed to removing 200 mm yr^-1 of SWE on the Antarctic ice sheet (Lenearts et al., 2012). Please clarify the two different methods in this study. Both bulk approaches?

L53-54: You mention limited accuracy of Monin-Obukhov similarity-based approximation, but do not mention any of the limitations to EC calculations in the manuscript (transience, stationarity, gravity waves, etc.). This should be remedied.

L61-62: Is this because blowing snow sublimation saturated their modeled surface layer and effectively turned off the sublimation model? This is a common issue with sublimation modeling over snow when there is no process built in to account for advection to/away from the saturated surface layer.

L65-66: A statement should probably be made that the roughness length itself is not a physical thing to be obtained, rather a term used to describe the influence of turbulence on an assumed log-linear profile. That is, a correction to a simplified model that is trying to represent nonlinear processes.

L66-67: This language is a bit concerning as you have not as of yet shown that the “direct EC method” actually is capable of measuring humidity of water vapor fluxes in this environment. Either rephrase this, or reference literature that shows the accuracy of measuring humidity fluxes with EC. I imagine the latter is not an option as people are still unable to close energy balance models with measured variables (e.g. Helgason and Pomeroy, 2012a,b; Harder et al., 2017). There is always a question in boundary layer studies of, “are you getting the right answer and for the right reason?” It would perhaps be sufficient to show that studies attempting to close the surface energy balance over snow get small discrepancies when using EC versus bulk approaches, but the language needs to be precise if there is no proof the individual flux term is being measured more precisely.

Furthermore, you are specifically talking about estimating EC fluxes of humidity using high temporal resolution water vapor measurements, correct? Accurate measurement would require a closed-path style water vapor measurement as snow particles would impact the signal quality, such as with a KH20. Otherwise, denoising will be required, which can take up a significant amount of a time series during storm events. I do not know of many experiments that actually use this sort of apparatus over snow, and it would significantly benefit you to list such experiments here.

L86: What surface processes are you considering?

L96-99: I don’t understand how turning off blowing snow in your model makes your findings more broadly applicable. This is a complex physical process that is local in nature, and it would be great if you could justify ignoring it

L123-131: This single paragraph on “Atmospheric eddy-covariance system” needs to be significantly expanded. This is essentially the backbone of the manuscript. This data is the data that all subsequent conclusions are based on. I see the data has already been published, and its investigation will not be the focus of the present work, but why was 30-minutes chosen? Was this a statistically stationary window? Were there any large-scale amplitude modulating structures inside this 30-minute threshold? Why do you then average to hourly time scales? To match MAR? How much of the data was thrown out for being noisy? Is there any bias in the data that you selected e.g. did you ignore especially high or low wind speed periods? Especially cold times? Hot times? I see 5304 data points, but there are at least 5700 hours spanning those months in those years. What happened to the rest and why is it not there? As with any model tuning study, it is important to know how representative the data is you are using for tuning and validating your tuned model. Including a figure that shows how representative these values are would be very beneficial, as well as more discussion.

As well, this EC data does not actually comprise the majority of the data that is used to calculate the humidity flux corrections, and the measurements used for the bulk calculation are discussed even less.

L129: Introduce this equivalence earlier when discussing LHF, EC, and humidity flux.

L129-131: I am still a bit confused at this point. Where does this confidence in the EC calculations come from? I get that the EC instrumentation may have been shown to be reliable. However, if I understand correctly, you are using covariance, as calculated from fluctuating time series of your vertical wind speed and some representative of water vapor, to represent the flux of water vapor away from the ice shelf surface to the atmosphere. From this physical standpoint, how do you know you have done that correctly? As mentioned before, I assume you have not been able to perfectly close an energy balance model at this site using measured variables, correct? Or a model of snowpack evolution? As you state in the introduction “This study addresses the uncertainty in regional climate model estimates of the humidity flux contribution to the SMB in the accumulation zone of the GrIS” but is there not already uncertainty in the humidity flux contribution to the SMB from your own measured data because the SMB and EMB have not been closed?

Please rephrase or explain.

L137: Upstream “in” the prevailing wind direction?

L161-162: Why is the summer of 2019 a good representative? Earlier you said that it was warmer and wetter.

L162-163: R-values are not valid for nonlinear regression (e.g. Spies and Neumeyer, 2010). Please use a more representative statistic.

L169: Why is this direct?

L170-171: Is this the PROMICE AWS? Please clarify. It seems like these bulk fluxes constitute the majority of the months where you do your fitting, so this data needs to be in your methods section as it is a significant component of your model correction.

L171-173: What observed roughness length are you referring to? Why would roughness in summer and winter be the same? You have different turbulent mechanisms. Furthermore, what are you comparing to get best agreement with EC of LHF in summer? Did you run the bulk estimate year round? I think it would help to refer to the three LHF calculations as LHF_Mar, LHF_EC, LHG_AWS or something similar. This is getting a bit hard to follow.

L174: Nonlinear use of R.

177-178: Linear correlation again.

L179-180: Please rephrase: “twelve values out of four years per season”

L183: I am a bit confused now how you can come up with a seasonal error when the method you are using to generate “observed” LHF is different in winter and summer. I don’t think any seasonal cycle would be meaningful since your observation source is significantly changing.

L190: Again, why good?

Figure 3: Please clarify the source of these observations. All EC here, or are you relying on the AWS as well?

Figure 7: Please improve the explanation of this figure. What is bulk? I thought you were using EC. Is this winter only?

L203-204: If these correction terms are functions of time, please clarify that in your equation.

L209: what do you mean it’s based on q_s,sat? Is it a function of q, or is that just something that influences the bias you are correcting for? Likewise for your explanation of m.

L211-214: Can you explicitly write out the functions that you used, or the periodic functions that you fit for m and b? Right now, I don’t think people could recreate your results. From figure 8 it looks like you did a linear fitting each month? Can you clarify how you did this?

L219-227: If I understand your process correctly, you are taking LHF output from MAR, you found a linear rescaling to match a combination of EC and Bulk observation data on a monthly timescale, adjusted your MAR output accordingly, and then quantified how the adjusted data (now at an hourly timescale) adds up when combined with non-adjusted MAR data to generate an SMB. Is that correct? Given that the other terms in MAR are also likely incorrect, but are as of yet not corrected, how can you make any conclusions about what is actually happening to a given quantity of snow that falls on the ice sheet? It looks like you have kind of brute forced sublimation into your model (Figure 7a) and then conclude how much sublimation is then happening. But there are nonlinear feedbacks between other parts of the surface energy balance that you have no corrected, or adjusted. Why would these changes in sublimation rates not be countered by some other as of yet uncorrected flux term should you do something like include the change in temperature that will result from these increases in sublimation? Or even amplified? Since there is no feedback into other MAR output, I don’t yet understand the impact of tuning the model for more sublimation and then reporting on the magnitude of that sublimation change. I am not trying to be cynical, and I think an explanation of the implications could really help me. Perhaps a deeper explanation in the style of Figure 6 could explain why there are no other terms in the energy balance that NEED to be corrected? How can you make a Figure 6 once you have done your correction?

L230: How did you come to this conclusion? Please rephrase within the constraints of the study.

L258-259: This difference in temperature gradient supports my previous statement as sensible heat fluxes would also be influenced by the sort of physical change that is being imposed on the system by forcing terms in the LHF to be rescaled. In hopes of being clear about this point, q in equation (1) is obviously a function on the state of the system, thus influenced by temperature, as is u. By forcing LHF to change, you are implicitly changing the terms inside 1 that are not constants, but you are not accounting for those changes in other energy balance terms. There appears to also be a potential impact on longwave radiation terms. Why can we disregard the nearly 4 degree difference in 2 meter temperature for longwave radiation, or sensible heat, but state that it is important LHF? And how do we know accounting for ALL the relevant changes won’t result in a different cumulative effect?

L278-281: This should probably be explained back in the methods section.

L285: Why does disregarding blowing snow support validity of your results? I don’t understand this.

L290: Why do you assume blowing snow events are rare and insignificant? A relatively high threshold windspeeds of 5m/s is often met in Figure 6. Sublimation rates of blowing snow have been shown to be relevant even in high accumulation alpine zones.

L314-316: I think this sentence might need rephrasing. I don’t see how a simple linear correction function is appropriate given the complexity and non-linearity you just described.

L316-321: Again these findings should be clearly qualified. These findings are extremely specific to adjusting one term in a model of mass balance, and not adjusting the implicit impact on other terms accordingly.

References:

Helgason, W. and Pomeroy, J. W.: Problems Closing the Energy Balance over a Homogeneous Snow Cover during Midwinter, J. Hydrometeorol., 13(2), 557–572, doi:10.1175/JHM-D-11-0135.1, 2012a.

Helgason, W. and Pomeroy, J. W.: Characteristics of the near-surface boundary layer within a mountain valley during winter, J. Appl. Meteorol. Climatol., 51(3), 583–597, doi:10.1175/JAMC-D-11-058.1, 2012b.

Harder, P., Pomeroy, J. W. and Helgason, W.: Local-Scale Advection of Sensible and Latent Heat During Snowmelt, Geophys. Res. Lett., 44(19), 9769–9777, doi:10.1002/2017GL074394, 2017.

Spiess AN, Neumeyer N. An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC Pharmacol. 2010 Jun 7;10:6. doi: 10.1186/1471-2210-10-6. PMID: 20529254; PMCID: PMC2892436.

Please see attached supplement