Review of “A Prototype Passive Microwave Retrieval Algorithm for Tundra Snow Density” by Welch and Kelly

The authors present a new algorithm to estimate bulk density for tundra snow. This is potentially a really interesting contribution! Bulk density identified from satellite observations is potentially of great value for understanding global snow. The authors show a result that I found counter-intuitive: I would not have thought that bulk density would be able to be predicted following their methods. I found it counterintuitive that the difference in 19 and 37 GHz v-polarization data while holding other variables approximately constant would lead to a change in brightness temperature that is truly measurable. After reviewing the various ways that the retrieval is constrained by the in situ data via calibration, I’m a little bit confused. I’m even a little bit worried that the skill they are seeing is more simply getting out what they put in: just reproducing the first station density basically. Perhaps that that is unlikely, but that worry combined with the surprising nature of the result and the potential excitement if this method really works everywhere. I think other readers may well have these questions as well, and so I would want to see these answered and included in a revised manuscript. Really nice work overall, and I’m very excited to see this algorithm running globally if that is in the authors future plans!

First, as this is a fundamental new contribution, I think the paper should include both a paragraph and a figure describing why brightness temperature is so sensitive to the snow density in the first place. I suppose packing more snow grains into the same space should drop the brightness temperature, but in any case if that’s what the mechanism is then it would be useful to explicate. And on the other hand, if you hold SWE constant and vary density (e.g. during mid-winter compaction), then this Tb observation wouldn’t be expected to change, correct? That is how I normally think about density sensitivity, but the algorithm using snow depth from the weather station changes things somewhat. For the suggested figure, a demonstration of the sensitivity will really help make the case that the sensitivity exists, and that it is enough to be measured from space. So the goal would be varying density on the independent axis and see the response of 19 GHz, 37 GHz, and the difference between the two plotted as the dependent variable. I’d suggest doing these with model simulations where you configure the model using the parameters in the paper, including the mapping between bulk density and the depth hoar and wind slab density. I’d give really careful thought to whether to hold depth or SWE constant; it would really be ideal to show both!  You may even be able to use data from Figure 2? In any case, all that together will help make the case for the other pieces that come later.

Second, related to this first point, I think Figure 2 really needs to have the units shown for the quantity presented: In fact, could you actually show the square root of the objective function shown in (1), in kelvins? Then these values can be related to expected uncertainty of the space borne brightness temperatures allowing readers to have a sense of signal-to-noise.

Third, Figure 3 should also show the brightness temperature gradient. This is the primary data that the density estimates are based on, and I think a sense of how this all works is key to this paper. Showing the range of values itself will be useful. If the density is a linear transformation of the Tb gradient then simply showing a second y-axis would be adequate, although it doesn’t seem that the algorithm is a linear transformation, requiring another set of panels, but I really think it’s necessary to see some Tb timeseries.

Fourth, I found some aspects related to the heterogeneity parameter H a bit confusing. At first I thought that H might be the ratio of the two densities? That doesn’t quite make sense though since the authors say that H is zero at the lower boundary (line 172). In any case, I think the equation relating H and the two densities should be provided in the paper. 

Fifth, I found the fixed 2:1 ratio of depth hoar to wind slab thickness quite surprising. For example King et al 2015 found that over the 50 CASIX pits at Churchill, depth hoar was half of the snow depth on average. And Zhu et al. 2018 cite spatial variability in the hoar/slab layer as a dominant control on backscatter, implying spatial variability. It may be that the fixed ratio is unavoidable in order to keep number of unknowns and observations at parity, e.g.. However, I think at minimum: 1) the paper ought to present a sensitivity test showing how the accuracy varies with the fixed ratio 2) some comments ought to be added about the importance of this assumption and possible future work to relax the assumption in places that don’t have the 2:1 ratio.

Sixth, I think the paper ought to show the equation that predicts bulk density from H and from the ratio of depths. This will really help readers follow what’s going on, and tie the various pieces together.

Seventh and finally, I at least found myself getting lost in trying to understand what calibrating H does. If for example the one station where H gets calibrated has H and depth hoar to wind slab ratio far from 2:1, what does that mean for other locations? Is there reason to think the stations have the same value or different? What is the calibrated value of H? How do results change if you change H? Can you visualize the fixed value of H in Figure 2 or a similar figure? Some additional comments on that in the discussion would be most helpful. 

King, J., Kelly, R., Kasurak, A., Duguay, C., Gunn, G., Rutter, N., et al. (2015). Spatio-temporal influence of tundra snow properties on Ku-band (17.2 GHz) backscatter. Journal of Glaciology, 61(226), 267-279(13). https://doi.org/10.3189/2015jog14j020

Zhu, J., Tan, S., King, J., Derksen, C., Lemmetyinen, J., & Tsang, L. (2018). Forward and Inverse Radar Modeling of Terrestrial Snow Using SnowSAR Data. IEEE Transactions on Geoscience and Remote Sensing, 56(12), 7122–7132. https://doi.org/10.1109/tgrs.2018.2848642