Review of “A physics-based Antarctic melt detection technique: Combining AMSR-2, radiative transfer modeling, and firn modeling”

The study proposes and evaluates the performance of a new technique to detect meltwater in Antarctica from passive microwave satellite observations. The method is a significant conceptual advance towards a more physics-based estimation of this quantity. Meltwater is of major interest to understand the dynamics of ice shelves (and of the ice sheets). A large corpus of studies use meltwater detected from space and especially from passive microwave observations available from 1979 to day. The potential interest of this study for the snow remote sensing community is very high.

The fact that the method does not outperform the statistical methods is not a surprise, the effect of liquid water on microwave is so strong that a binary detection – melt / no melted – is relatively un-challenging. However, as stated in their conclusion, the potential of a physics-based method is manifold, behind the basic objective of the binary detection. This study is therefore an important step towards a more comprehensive exploitation of microwave data to investigate the liquid water on the ice sheets.

The paper is of high quality, clear, and straight to the point. The method is described with details and the results are abundant. The discussion is excellent. Many minor issues and suggestions are listed below. Nevertheless, remains a major possible issue. The simulations with SMRT seem to have been run with densities > 450 kg/m3 in some instance, which is inaccurate. Even though the consequences for the results are expected to be minor, because the method is self compensating for inputs and model errors as demonstrated in the study, it is recommended to assess and if possible rerun all the simulations. To avoid this issue to happen again in the future, the reviewer – who is a developed of the SMRT model – has added warnings in the code.

After this issue is addressed, I recommend the publication of the study in The Cryosphere.

I sign my reviews: Ghislain Picard

Detailed remarks:

“correlation length“. While this term is commonly used and understood by the snow microwave modeling community, it refers to a general mathematical concept that occurs in many domains, and can result in a confusion here for unaware readers, for instance correlation length is also common for rough surface characterization. Furthermore, without specifying the underlying auto-correlation function this term is loosely defined. This is why some authors have used “exponential autocorrelation function” instead. This issue is one of the motivation for the introduction of the “microwave grain size” concept by the reviewer and colleagues in one of the studies cited by the authors. Mathematically, the definition is independent of the form auto-correlation function, and semantically the term is more specific to the length scale relevant to snow volume scattering. These are some of the advantages of this new concept. Nevertheless, this comment is clearly subjective and opinionated. The authors are free to use correlation length.

L30 suggestion: “in brightness temperature “ → “in brightness temperature timeseries”

L35. There are works by M. Tedesco using MEMLS (doi: 10.1016/j.rse.2009.01.009). See also Thomas Mote works inverting the scattering signal, which is a simple variant of the approach followed in this paper.

L65. There are other recent evaluations with different results, see doi:10.1029/2021GL096599 and doi:10.5194/tc-16-5061-2022. This is particularly important to develop this part in order to understand the representativeness of the effective correlation length obtained by the inverse method.

L75: “too fine”, can you give some numbers ?

L77-80: More than the computational cost, the accuracy of RT calculations requires that the layers are typically thicker than the wavelength. Here 1cm is just ok, smaller is not advised. This constraint, often overlook when using RT models, may be added here.

L86. I’d suggest to move the citation for SMRT out of the parenthesis, that is specific to IBA. Maybe also add original refs for IBA and DMRT.

L88. “ snow microstructure as a single parameter”. Two points:1

1) Depending on the usage “snow microstructure” refers to as the geometry of ice/air matrix in general or more specifically to as “grain size” in a more modern / generalized way. To my knowledge there is no consensus and the authors should clarify here, somehow, that they refer to the latter one.

In the former case (my preference), snow microstructure is described not only by a length scale but also by many other properties (density/fractional volume, convexity, polydispersity, …).

2) strictly speaking, the choice made here is about the snow microstructure representation (exponential versus sticky hard sphere) and not the electromagnetic model (IBA vs DMRT). Traditionally these two formulations have used different microstructure representations, so the amalgam, but now IBA (in SMRT) can easily be use any microstructure type (not that in the original IBA the exponential auto-correlation function was not presented, only in a latter paper describing MEMLS). I’d suggest to indicate that the “exponential microstructure representation” is used here, which is parametrized by two parameters (density and correlation length/microwave grain size), and for this I’d recommend to cite the original Mätzler 1999 MEMLS paper.

L99. What is this amount ? Kelvins ? How many ?

L110. Figure 2c uses densities > 400 kg/m3 in a range where modeling snow as “ice in air” is becoming increasingly wrong (this equally applies to IBA and DMRT and to any snow RT models). The consequence is that Tb are increasing while they should decreases. See doi: 10.5194/tc-16-3861-2022 for details and especially Fig 2. To solve the issue easily, I’d recommend to invert the medium (that is use air in ice) above fractional volume 50% (density > 917/2 kg/m3). A more advanced alternative is to use SCE instead of IBA (see the mentioned paper) but the stability of this more recent and more numerically-challenging method may be an issue. Unfortunately, it means that re-running all the simulations is required if densities >450 kg/m3 are present in the profiles in the upper 1-2 m of the snowpack. I suggest to first assess the proportion of such cases, and second to assess the impact in the worst cases. Then decide. It is likely to impact the estimate of correlation length, but the melt detection won’t be affected because the inverse method tends to incorporate all the artifacts into the correlation length, including this modeling artifacts.

Note: SMRT code has been updated on 29 sept 2023:

- a warning has been added to avoid this frequent kind of issue in the future.

- a new argument is available in IBA “dense_snow_correction” to make it easy to apply an automatic (yet imperfect) correction. The user is responsible to activate this option, until positive feedback is received from the community, to make it as a default.

L133 “shorter” → lower or smaller. Shorter is used with wavelength… which appears to be longer at 18.7 GHz compare to 89 and 150 GHz used in the cited paper.

L146. I think what you describe is the “Secant method”, (e.g. https://en.wikipedia.org/wiki/Secant_method). The Brent method is supposed to be better (Brent, R. P., Algorithms for Minimization Without Derivatives. Englewood Cliffs, NJ: Prentice-Hall, 1973. Ch. 3-4). Comment based on scipy.optimize.brentq documentation.

L175. 0.01 K is a very small error compared to satellite accuracy. This could be relaxed to 0.1 K to reduce inversion computational cost.

L180-185. Maybe this paragraph should be earlier, it is indeed difficult to understand why L147 paragraph is needed after L139 paragraph which seems to be a complete and sufficient description of the process. I’d suggest at least to start L139 paragraph with “To further decrease the computation cost …”. If I understand well the purpose of these extra steps.

L208. I’d remove “more”

L219. Please add the value for the bias.

L219. “remove it by linear regression”. Why not by subtraction ? Is this bais has a seasonal variability ? Give details about this linear regression, in short.

Fig 4. I’d expect to see AMSR-2 data in Fig 4c and Fig 4d. Do they overlap ? If yes, maybe use small crosses for the AMSR-2 data.

I think the data you are using are coming from Picard et al. 2014, not from Brucker et al. (2011) which was limited to 2m in depth. I don’t understand “Refl.” in the legend in Fig b.

L228. penetration depth of AMSR-2 → add “at 18 GHz”

L234 Figure 3e → Figure 4e. In addition I’d suggest to remove this last panel, the value of 0.02K in the text is sufficient for the reader to understand that it is extremely small and negligible.

Fig 7. To avoid overlapping symbols, I’d suggest to use thin vertical bars as symbols in the panels b and d.

L308. The Mosaic was referred before in the paper as an abbrevation and without reference. This should be corrected.

L310 and L320. I’m not sure what kind of mathematical correlation is used here.

L340. It is nice to recall that the threshold proposed in Picard et al. 2022 was not intended to be optimal. It does surprisingly well.

L368. This final part of the discussion should be developed a bit. Retrieving correlation is a useful side product of this work, but the representativeness of the value is a big issue. In particular, because there is a circular indetermination between the correlation length and the penetration depth. Usually large correlation lengths imply low penetration depths (for a given density) which means that the values obtained here are representative of depths that depends on the values.

L370. It is worth mentioning that the SEB estimates are not pure observations, a model is involved. Despite the relatively weak assumptions required to compute melt for the raw meteorological observations, some assumptions are required.

L390 in MERRA-2 → consider to add “and in SMRT”.

Discussion: I suggest to add a few items regarding scalability of the technique at the continental scale. It could be mainly about computation time as I don’t see any other difficulties.