the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Jun 2024
Altimetric Ku-band Radar Observations of Snow on Sea Ice Simulated with SMRT
Abstract. Sea ice thickness is essential for climate studies and numerical weather prediction. Radar altimetry has provided sea ice thickness measurement since the launch of ERS-1 and currently through CryoSat-2, Sentinel-3 and Altika but uncertainty in the scattering horizon used to retrieve sea ice thickness arises from interactions between the emitted signal and snow cover on the ice surface. Therefore, modelling the scattering of the electromagnetic waves with the snowpack and ice is necessary to retrieve the sea ice thickness accurately. The Snow Microwave Radiative Transfer (SMRT) model was used to simulate the low resolution altimeter waveform echo from the snow-covered sea ice, using in-situ measurements as input. Measurement from four field campaigns were used: Cambridge Bay, Eureka Sound and near Alert, Nunavut, Canada in April 2022 in the cold and later winter condition when snow and ice thickness are neat their seasonal maxima prior to melt. In-situ measurements included snow temperature, salinity, density, specific surface area, microstructure from X-ray tomography and surface roughness measurements using structure from motion photogrammetry. Evaluation of SMRT in altimeter mode was performed against CryoSat-2 waveform data in pseudo-low-resolution mode. Simulated and observed waveforms showed good agreement, although it was necessary to adjust sea ice roughness. The retrieved roughness (root-mean-square height) in Cambridge Bay was 2.1 mm and 1.6 mm in Eureka, which was close to the observed value of 1.4 mm for flat sea ice. In addition, simulations of backscatter in preparation for the European Space Agency's CRISTAL mission demonstrated the dominance of scattering from the snow surface at Ku and Ka-band. However, these findings depend on the parameterisation of the roughness. The scattering from the snow surface dominates when roughness is high, but the interface return dominates if the roughness is low ( < 2.5 mm). This is the first study to consider scattering within the snow and demonstrate the origin of CryoSat-2 signals. This work paved the way to a new physical retracker using SMRT to retrieve snow depth and sea ice thickness for radar altimeter missions.
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RC1: 'Comment on egusphere-2024-1583', Anonymous Referee #1, 05 Jul 2024
Review of “Altimetric Ku-band Radar Observations of Snow on Sea Ice Simulated with SMRT” by Julien Meloche et al.
The MS is describing and testing a radar altimeter scattering model implemented as part of the SMRT snow/ice modeling system with in situ observations collected in the Canadian Arctic and satellite CRYOSAT data. The topic is very welcome and altimeter scattering models for sea ice are needed for understanding the uncertainties in sea ice thickness estimation from past, current and future satellite radar altimeter missions. However, the MS seems to be written in a hurry; important info is missing e.g. roughness estimation procedure, key literature is missing from the reference list (see suggested articles), and some initial assumptions about the scattering mechanisms leads to a mismatch between the CRYOSAT observations and simulations with the model. This mismatch is then “fixed” with a calibration factor and this means that conclusions about the surface and volume contributions to the simulated backscatter are biased. In addition, some conclusions are not supported by the results (see specific comments).
Specific comments:
L1: neat-> near
L13: flat->level
L15: “The scattering… “ It is not clear which interface roughness is high or low? I am assuming that it is the snow ice interface roughness…
L16: “This is the first… “ There are studies before this e.g. https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1621086
L1: environment->regions, delete “...for climate prediction”, strong->high
L33: what is meant by “mean return”? Is it the track-point? the mean backscatter? Something else? rewrite the sentence.
L34: tracking point->track-point (throughout).
L36: “tidal” are the tides corrected for when deriving the ice thickness?
L65: “...no volume scattering from brine.” here it is mentioned as a shortcoming of the referenced models but is it really important at all?
L67: “Our understanding …” there are some earlier studies, e.g.: https://ieeexplore.ieee.org/document/9000883, https://tc.copernicus.org/articles/15/1811/2021/
Kwok, R.: Simulated effects of a snow layer on retrieval of CryoSat-2 sea ice freeboard, Geophys. Res. Lett., 41, 5014–5020, 2014.
L69: delete “Snow depth…”
L72: “...scattering horizons…” Is the scattering horizon the same as the track-point? Please define.
L73: If Ka-band is scattered at the snow surface, then is it affected by the same “snow properties” as Ku-band? Please, be specific.
L74: “...must be challenged.” What do you mean? Are you challenging this model?
T1: Boundary roughness->Interface roughness
L174: RMS roughness should be measured at a horizontal resolution of 1/10 of a wavelength. See e.g Dierking, W. (2000). RMS slope of exponentially correlated surface roughness for radar applications. I E E E Transactions on Geoscience and Remote Sensing, 38(3), 1451-1454. https://doi.org/10.1109/36.843040. Please provide info on the horizontal resolution of your roughness map.
L195: “...antennae collect..”? rewrite this sentence.
L197: “..shallower depths…” What do you mean?
L211: “... assuming a Gaussian height distribution).” Do you need to assume anything when you have the data? Please find the distribution that fits your data best.
L213: there is a good discussion in: https://doi.org/10.1029/GM068p0111
L238: “To allow…” please rewrite, it is not clear.
L296: “Measured… please rewrite.
L311: I think the assumptions behind the model are wrong and that is why there is a mismatch between observations and simulations.
Figure 5: The simulations even after “correction” are missing the “peak backscatter” and it is not making a good prediction of the observations. Further, when all backscatter contributions, from the snow volume and the surfaces are multiplied by 5.9MW then the volume contribution, which I think that you have estimated correctly before the correction, is overestimated after the correction.
L448: Multiple scattering between interfaces would have a very small impact on the peak backscatter and the match between observations and simulations.
L483: It is not “encouraging” that the snow depth retrieval capability of CRISTAL depends on certain conditions of the interface roughness. This will complicate the retrieval of snow depth with CRISTAL.Citation: https://doi.org/10.5194/egusphere-2024-1583-RC1 -
RC2: 'Comment on egusphere-2024-1583', Anonymous Referee #2, 08 Aug 2024
Summary
This manuscript uses recent additions to the snow microwave radiative transfer model (SMRT) to simulate waveforms produced by the SIRAL instrument on board the CryoSat-2 satellite over sea ice. This is informed by a suite of near-coincident field measurements carried out over several seasons in and around the Canadian Archipelago.
The authors then present a sensitivity study to infer the relative contributions to the observed waveform, with particular focus on how much power comes from the snow surface and sea ice surface. The results of their study suggest the dominance of scattering from the snow surface.
Unfortunately I’m sceptical that the modelled waveforms do actually match the observed ones in a meaningful way, since they appear to miss the curvature and amplitude of the waveform leading edges, even after some input values are scaled to improve the fit. I suggest this is unsurprising because the authors (a) have used a symmetrical surface height distribution function when in reality the function is generally skewed (b) did not measure the amplitude of the footprint-scale surface height distribution, instead using values from the literature taken in the Arctic Ocean (c) have assumed that the large-scale ice and snow surface height distributions are the same (d) have not incorporated measurements of the sea ice surface temperature or salinity, and so risk not capturing the dielectric contrast between the snow and the ice, introducing great uncertainty about the contribution of surface scattering from the sea ice surface to the final waveform. Regarding the subsequent sensitivity study, I would argue that meaningful truths about reality cannot be gleaned from a sensitivity study until the model can be demonstrated to have reliable inputs outside the ones under test.
As such I suggest major revisions. However, it is difficult to see a way forward since we cannot go back in time to gather information on the footprint-scale roughness (and sea ice dielectrics) at the field sites.
Model-Observations Fit, and Why There’s a Mismatch
It’s unclear to me from Fig 5 that SMRT is successfully simulating the observed CS2 waveforms. This is a fairly central claim of the manuscript (L11, L405, L425), and is crucial to meaningful interpretation of the ensuing sensitivity study. While it is always valid to investigate the sensitivity of a model to variation in inputs, one can only estimate the sensitivity of the real world to variations in such inputs when all other relevant inputs are roughly correct.
(As a side note, I found it strange that the authors have clipped off the peaks of the observed waveforms from Cambridge Bay and Eureka; this makes it difficult for the reader to compare the model output and observations).
My central point is this: you’ve scaled your s-values at each site (and globally adjusted your l & Λ values) such that the solid-grey, modelled waveforms in Figure 5 best fit the dashed-grey observed ones. So all SMRT has left to simulate is the shape of the dark grey curve: by shape I mean the peakiness/kurtosis, the curvature of the lines on either side of the peak etc. It seems to me the model is missing this shape, and is not actually producing a “good” fit. To phrase things another way: given you have scaled the waveforms in the way that you have, if this is a good fit, what would a bad fit look like?
In particular, the model does not appear to capture the curvature or total height of the leading edge (particularly in panels f & h). In log-space, the waveforms look very triangular when the real waveforms are curved and highly peaked, so I think the model is missing a key element of the physics at play. For instance, the peak power of the observed waveforms in panels e & g (which would inform the retrack threshold) are more than double the values which are modelled. Missing these aspects matters to sea ice altimetry, since the leading edge is the key source of information when obtaining a radar freeboard estimate.
I suggest that there are a couple of reasons why you might be seeing such a large mismatch between the shape of the modelled waveforms and the shape of the observed ones, particularly at the leading edge:
- You’ve assumed a Gaussian function for the large-scale sea ice roughness in this modelling exercise, which is unlikely to be appropriate. Figures 1 & 2 of Landy et al. (2020) indicate clearly that both the snow surfaces and the ice surfaces in the paper have skewed distributions. A Gaussian distribution is commonly used for open ocean altimetry, but sea ice can be described as being made of flat pans with occasional roughness, skewing the distribution away from the symmetry of the Gaussian. To state the obvious, the shape of an altimetry waveform’s leading edge strongly reflects the shape of the height distribution of the surface in the footprint, so you absolutely have to characterise this before you try to model the waveform; it’s non-negotiable.
- If it were possible to simply convert your Eq 6 to a log-normal curve (rather than a Gaussian), we still wouldn’t have an appropriate value for the rms height on the footprint scale: I see you have taken values from the literature.The FYI values given by Landy et al. 2020 were generated in the Arctic Ocean, not in the Canadian Archipelago where FYI is likely much less deformed. But even if they were taken from your field sites, the RMS height of the sea ice surface is quite a variable quantity in both space and time, and is critical to successful modelling of the waveform shape. I should say: if a sensitivity analysis implies that your chosen values of σ_surf do not actually matter to within the range that they typically vary, then I’ll happily accept that.
- I might be wrong about this, but have you used the same surface height pdf (your Eq. 6) for both the snow and the ice? I’m not aware of any evidence supporting this, and Landy 2020 makes a statement which implies the contrary (“The average standard deviation of the height distribution (σ) is significantly higher for the snow surface (0.28 m) than the ice surface (0.19 m), although we did not analyze identical sections between the two instruments.”). I’m open to the idea that your surface height pdfs for snow and ice are (happily) the same at your field site, but I can’t see any reason for this to be the case given there’s quite a lot of prior evidence to the contrary. I think this will be especially the case at FYI, where you often see bedforms even when the ice is very level. I appreciate that in response to this comment one might shout “we don’t know the relationship between the surface height pdfs of snow and sea ice!”. Unfortunately this is probably true, but it is nonetheless probably quite important, and thus quite limiting, to the modelling exercise at hand. Certainly a sensitivity analysis is justified here to ensure that your results aren’t contingent on these unknowns.
- L278-281: For a study setting out to model the backscatter from snow-covered sea ice, there appears to be a paucity of key measurements of the sea ice itself. The backscattered power from the sea ice surface will scale with the dielectric contrast between the sea ice and the snow cover above (at least it does in surface scattering models like those contained within SMRT). So it scales with the ratio of the dielectric permittivity of the snow to the dielectric permittivity of the ice. You’ve provided a good treatment of the snow dielectrics by considering measured temperature and salinity, from which the brine volume fraction can be calculated and ɛ derived. Unfortunately the sea ice permittivity (the other half of the ratio) seems to be dubiously calculated by comparison. Thickness values of 2m & 3m (where did you get these?) are plugged into a formula designed to yield the bulk salinity of sea ice. The result is then implicitly assumed to reflect the surface salinity (which can be much higher than the bulk value over FYI due to upward brine rejection). You’ve then combined this surface salinity figure (which has no basis in measurements carried out) with an ice surface temperature which also has no basis in measurement (how did you come to the value of 260K?). These values are then combined to reach a BVF and an ɛ value for the sea ice. So your sea ice temperature and salinity is unmoored from that of the snow, casting doubt on whether your dielectric contrast is realistic. The uncertainty in these assumptions risks propagating into your results. Have you looked at the impact of these figures (2m, 3m, 260K) on the modelling that follows? If you change them do you get a different partitioning of ice surface backscatter to snow surf backscatter?
The upshot of the above is that the quality of your inputs implies that SMRT may well not produce good results, and the results don’t indicate (at least to me) that it has performed well. By “well”, I mean to the extent that allows the individual components of the scattering (surface, interfaces, volume) to be “backed out”. I certainly don’t think that you can claim to have “demonstrated the dominance of scattering from the snow surface at Ku and Ka-band” in real life, given the uncertainty of the inputs.
I have some more minor comments below:
L14: I’m not sure it’s possible to make statements like this without reference to the viewing geometry, and relatedly the mode (LRM vs SAR). For instance, the look angle is on average higher for LRM than for SAR (no beam sharpening so wider beam), which will affect the relative contributions of your surfaces to the total backscatter, no? So just needs some clarification that you’re not simulating the geometry that CRISTAL will have, so may be underestimating the degree of specularity it will experience.
L17: “This is the first study to consider scattering within the snow, and demonstrate the origin of CryoSat-2 signals”. With respect, I found this statement quite uncomfortable to read given how long and hard the sea ice altimetry community has considered scattering within the snow. For instance, I think it’s fair to say that Giles et al. (2008), Ricker et al (2015), Nandan et al (2017), Nandan et al. (2020), Tonboe et al. (2021) and Nab et al (2023) considered scattering of CS2 radar pulses within the snow. People have also considered this issue extensively using surface-based and airborne radars (e.g. Willatt et al., 2010; 2011; 2023; King et al., 2018; De Rijke Thomas et al 2023).
L57: it would be good to have some information about how the pLRM waveforms are constructed. For instance the exact data source wasn’t included in your data availability statement. From the github it looks like it’s now included in the L1B product, but which baseline did you use etc? The github readme just links to the ftp and not the product.
Figure 1: You’ve averaged several CS2 pLRM waveforms to produce the ones which you then compare to your model, which I think is a good idea. But it’s important to know what the “spread” of these individual waveforms was prior to averaging. That is to say, are your averaged waveforms representative of their inputs?
Relatedly to the above: I couldn’t quite understand why the waveforms were taken from so far apart, but this is probably because I don’t understand the nature of the plrm processing chain. Is SIRAL not chirping at 20Hz, allowing the construction of a plrm waveform for every conventional doppler-sharpened waveform? If so, you would have many, very closely spaced plrm waveforms. I understand that you probably want to use independent (i.e. non-overlapping) waveforms, but is it really necessary to choose waveforms spaced so far apart and thus risk introducing quite a lot of along-track variability in the sea ice properties?
Table 3: suggest you order the rows in this the same as the rows of Figure 5
Figure 4b: Am I right in saying you cleared the snow off the ice surface to perform photogrammetry to retrieve small scale roughness? If so, I would be interested to know how this was done, since this is a notoriously difficult task. I’ve seen and heard of people trying it with brushes, shovels and even wet-vacs, but all generally either fail to remove all the basal snow or end up removing part of the surface scattering layer and artificially flattening the surface. So a bit of practical methodology needs to be presented here to justify these measurements, beyond the technical method which is very well presented in lines 165-176.
Figure 4: Could do with some information about the KDE method used: what was the kernel shape and how is it justified? Seems like a lot of information in the shaded regions based on quite few scatter points.
L2: “Measurements of sea ice thickness”. It is unusual to see SIT retrievals by CryoSat-2 described as “measurements”. This is obviously a somewhat philosophical point, but it’s the convention in the literature that CS2 is described as measuring ranges, but we then estimate sea ice thickness using range measurements as a proxy. I think you should probably stick to this convention because it reinforces the point that the hydrostatic conversion (and also the lead interpolation to make freeboard) is very uncertain, and describing the SIT retrieval as a measurement somewhat belies this major uncertainty. Indeed I note that in the first sentence of the introduction, SIT retrievals are described as being “estimated”.
L40 - 44: This statement needs more nuance. The most popular CS2 SAR-SIT product used by sea ice scientists is perhaps the AWI product which uses an empirical retracker? The CPOM retracker is also empirical, and has historically been heavily used for CS2 SIT analysis.
L109 - 111: Producing a “complete suite of in-situ field measurements” is a challenge.. I would argue you didn’t measure the most critical parameter of all (wrt waveform shape), which is the footprint scale height distributions of the snow and sea ice. You’ve also used arbitrary figures for ice thickness, ice surface salinity and ice temperature in the modelling which implies (and tell me if I’m wrong) that you also didn’t measure these? Perhaps I’m mistaken, but I don’t think “complete” can be justified in this paper.
L199/200: Can you explain this a bit more? SIRAL’s range sampling is twice this (~1.5ns, i.e. half the range res) to preserve the frequency domain due to Nyquist etc.
General: I wasn’t able to find out what the air temperatures were at the field sites. I looked on the github repo but the data directory hasn’t been pushed, which is fair enough at this stage. Nonetheless, some information should be given about the snow temperatures at each site, even if just to assure the reader that everything was “cold” in a microwave sense. This is done in the abstract, but not in the manuscript body. But also, why not use the measured basal snow temperatures to inform the ice surface temperatures?
L302: “lack a precise”
L309: How many did you exclude, and out of a total of how many? Could you perhaps mark them on Figure 1?
Competing interests: This is not often discussed but I write this in response to a growing issue (which may not apply here). If this publication is required to hit a contractually agreed project deliverable as part of AKROSS, and so is required to release funding, then this should be declared as a competing interest. Assuming it’s not explicitly & contractually required (even if implicitly favoured, as is generally the case) then I think nothing needs to be done.
Relatedly: the Copernicus competing interests policy suggests declaring positions on advisory boards etc. So I think it would also be appropriate to declare any memberships of altimetry-relevant ESA MAGs etc, including concurrent applications to the newest round of the CRISTAL MAG that might be affected by the content or publication of this manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-1583-RC2
Status: closed
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RC1: 'Comment on egusphere-2024-1583', Anonymous Referee #1, 05 Jul 2024
Review of “Altimetric Ku-band Radar Observations of Snow on Sea Ice Simulated with SMRT” by Julien Meloche et al.
The MS is describing and testing a radar altimeter scattering model implemented as part of the SMRT snow/ice modeling system with in situ observations collected in the Canadian Arctic and satellite CRYOSAT data. The topic is very welcome and altimeter scattering models for sea ice are needed for understanding the uncertainties in sea ice thickness estimation from past, current and future satellite radar altimeter missions. However, the MS seems to be written in a hurry; important info is missing e.g. roughness estimation procedure, key literature is missing from the reference list (see suggested articles), and some initial assumptions about the scattering mechanisms leads to a mismatch between the CRYOSAT observations and simulations with the model. This mismatch is then “fixed” with a calibration factor and this means that conclusions about the surface and volume contributions to the simulated backscatter are biased. In addition, some conclusions are not supported by the results (see specific comments).
Specific comments:
L1: neat-> near
L13: flat->level
L15: “The scattering… “ It is not clear which interface roughness is high or low? I am assuming that it is the snow ice interface roughness…
L16: “This is the first… “ There are studies before this e.g. https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1621086
L1: environment->regions, delete “...for climate prediction”, strong->high
L33: what is meant by “mean return”? Is it the track-point? the mean backscatter? Something else? rewrite the sentence.
L34: tracking point->track-point (throughout).
L36: “tidal” are the tides corrected for when deriving the ice thickness?
L65: “...no volume scattering from brine.” here it is mentioned as a shortcoming of the referenced models but is it really important at all?
L67: “Our understanding …” there are some earlier studies, e.g.: https://ieeexplore.ieee.org/document/9000883, https://tc.copernicus.org/articles/15/1811/2021/
Kwok, R.: Simulated effects of a snow layer on retrieval of CryoSat-2 sea ice freeboard, Geophys. Res. Lett., 41, 5014–5020, 2014.
L69: delete “Snow depth…”
L72: “...scattering horizons…” Is the scattering horizon the same as the track-point? Please define.
L73: If Ka-band is scattered at the snow surface, then is it affected by the same “snow properties” as Ku-band? Please, be specific.
L74: “...must be challenged.” What do you mean? Are you challenging this model?
T1: Boundary roughness->Interface roughness
L174: RMS roughness should be measured at a horizontal resolution of 1/10 of a wavelength. See e.g Dierking, W. (2000). RMS slope of exponentially correlated surface roughness for radar applications. I E E E Transactions on Geoscience and Remote Sensing, 38(3), 1451-1454. https://doi.org/10.1109/36.843040. Please provide info on the horizontal resolution of your roughness map.
L195: “...antennae collect..”? rewrite this sentence.
L197: “..shallower depths…” What do you mean?
L211: “... assuming a Gaussian height distribution).” Do you need to assume anything when you have the data? Please find the distribution that fits your data best.
L213: there is a good discussion in: https://doi.org/10.1029/GM068p0111
L238: “To allow…” please rewrite, it is not clear.
L296: “Measured… please rewrite.
L311: I think the assumptions behind the model are wrong and that is why there is a mismatch between observations and simulations.
Figure 5: The simulations even after “correction” are missing the “peak backscatter” and it is not making a good prediction of the observations. Further, when all backscatter contributions, from the snow volume and the surfaces are multiplied by 5.9MW then the volume contribution, which I think that you have estimated correctly before the correction, is overestimated after the correction.
L448: Multiple scattering between interfaces would have a very small impact on the peak backscatter and the match between observations and simulations.
L483: It is not “encouraging” that the snow depth retrieval capability of CRISTAL depends on certain conditions of the interface roughness. This will complicate the retrieval of snow depth with CRISTAL.Citation: https://doi.org/10.5194/egusphere-2024-1583-RC1 -
RC2: 'Comment on egusphere-2024-1583', Anonymous Referee #2, 08 Aug 2024
Summary
This manuscript uses recent additions to the snow microwave radiative transfer model (SMRT) to simulate waveforms produced by the SIRAL instrument on board the CryoSat-2 satellite over sea ice. This is informed by a suite of near-coincident field measurements carried out over several seasons in and around the Canadian Archipelago.
The authors then present a sensitivity study to infer the relative contributions to the observed waveform, with particular focus on how much power comes from the snow surface and sea ice surface. The results of their study suggest the dominance of scattering from the snow surface.
Unfortunately I’m sceptical that the modelled waveforms do actually match the observed ones in a meaningful way, since they appear to miss the curvature and amplitude of the waveform leading edges, even after some input values are scaled to improve the fit. I suggest this is unsurprising because the authors (a) have used a symmetrical surface height distribution function when in reality the function is generally skewed (b) did not measure the amplitude of the footprint-scale surface height distribution, instead using values from the literature taken in the Arctic Ocean (c) have assumed that the large-scale ice and snow surface height distributions are the same (d) have not incorporated measurements of the sea ice surface temperature or salinity, and so risk not capturing the dielectric contrast between the snow and the ice, introducing great uncertainty about the contribution of surface scattering from the sea ice surface to the final waveform. Regarding the subsequent sensitivity study, I would argue that meaningful truths about reality cannot be gleaned from a sensitivity study until the model can be demonstrated to have reliable inputs outside the ones under test.
As such I suggest major revisions. However, it is difficult to see a way forward since we cannot go back in time to gather information on the footprint-scale roughness (and sea ice dielectrics) at the field sites.
Model-Observations Fit, and Why There’s a Mismatch
It’s unclear to me from Fig 5 that SMRT is successfully simulating the observed CS2 waveforms. This is a fairly central claim of the manuscript (L11, L405, L425), and is crucial to meaningful interpretation of the ensuing sensitivity study. While it is always valid to investigate the sensitivity of a model to variation in inputs, one can only estimate the sensitivity of the real world to variations in such inputs when all other relevant inputs are roughly correct.
(As a side note, I found it strange that the authors have clipped off the peaks of the observed waveforms from Cambridge Bay and Eureka; this makes it difficult for the reader to compare the model output and observations).
My central point is this: you’ve scaled your s-values at each site (and globally adjusted your l & Λ values) such that the solid-grey, modelled waveforms in Figure 5 best fit the dashed-grey observed ones. So all SMRT has left to simulate is the shape of the dark grey curve: by shape I mean the peakiness/kurtosis, the curvature of the lines on either side of the peak etc. It seems to me the model is missing this shape, and is not actually producing a “good” fit. To phrase things another way: given you have scaled the waveforms in the way that you have, if this is a good fit, what would a bad fit look like?
In particular, the model does not appear to capture the curvature or total height of the leading edge (particularly in panels f & h). In log-space, the waveforms look very triangular when the real waveforms are curved and highly peaked, so I think the model is missing a key element of the physics at play. For instance, the peak power of the observed waveforms in panels e & g (which would inform the retrack threshold) are more than double the values which are modelled. Missing these aspects matters to sea ice altimetry, since the leading edge is the key source of information when obtaining a radar freeboard estimate.
I suggest that there are a couple of reasons why you might be seeing such a large mismatch between the shape of the modelled waveforms and the shape of the observed ones, particularly at the leading edge:
- You’ve assumed a Gaussian function for the large-scale sea ice roughness in this modelling exercise, which is unlikely to be appropriate. Figures 1 & 2 of Landy et al. (2020) indicate clearly that both the snow surfaces and the ice surfaces in the paper have skewed distributions. A Gaussian distribution is commonly used for open ocean altimetry, but sea ice can be described as being made of flat pans with occasional roughness, skewing the distribution away from the symmetry of the Gaussian. To state the obvious, the shape of an altimetry waveform’s leading edge strongly reflects the shape of the height distribution of the surface in the footprint, so you absolutely have to characterise this before you try to model the waveform; it’s non-negotiable.
- If it were possible to simply convert your Eq 6 to a log-normal curve (rather than a Gaussian), we still wouldn’t have an appropriate value for the rms height on the footprint scale: I see you have taken values from the literature.The FYI values given by Landy et al. 2020 were generated in the Arctic Ocean, not in the Canadian Archipelago where FYI is likely much less deformed. But even if they were taken from your field sites, the RMS height of the sea ice surface is quite a variable quantity in both space and time, and is critical to successful modelling of the waveform shape. I should say: if a sensitivity analysis implies that your chosen values of σ_surf do not actually matter to within the range that they typically vary, then I’ll happily accept that.
- I might be wrong about this, but have you used the same surface height pdf (your Eq. 6) for both the snow and the ice? I’m not aware of any evidence supporting this, and Landy 2020 makes a statement which implies the contrary (“The average standard deviation of the height distribution (σ) is significantly higher for the snow surface (0.28 m) than the ice surface (0.19 m), although we did not analyze identical sections between the two instruments.”). I’m open to the idea that your surface height pdfs for snow and ice are (happily) the same at your field site, but I can’t see any reason for this to be the case given there’s quite a lot of prior evidence to the contrary. I think this will be especially the case at FYI, where you often see bedforms even when the ice is very level. I appreciate that in response to this comment one might shout “we don’t know the relationship between the surface height pdfs of snow and sea ice!”. Unfortunately this is probably true, but it is nonetheless probably quite important, and thus quite limiting, to the modelling exercise at hand. Certainly a sensitivity analysis is justified here to ensure that your results aren’t contingent on these unknowns.
- L278-281: For a study setting out to model the backscatter from snow-covered sea ice, there appears to be a paucity of key measurements of the sea ice itself. The backscattered power from the sea ice surface will scale with the dielectric contrast between the sea ice and the snow cover above (at least it does in surface scattering models like those contained within SMRT). So it scales with the ratio of the dielectric permittivity of the snow to the dielectric permittivity of the ice. You’ve provided a good treatment of the snow dielectrics by considering measured temperature and salinity, from which the brine volume fraction can be calculated and ɛ derived. Unfortunately the sea ice permittivity (the other half of the ratio) seems to be dubiously calculated by comparison. Thickness values of 2m & 3m (where did you get these?) are plugged into a formula designed to yield the bulk salinity of sea ice. The result is then implicitly assumed to reflect the surface salinity (which can be much higher than the bulk value over FYI due to upward brine rejection). You’ve then combined this surface salinity figure (which has no basis in measurements carried out) with an ice surface temperature which also has no basis in measurement (how did you come to the value of 260K?). These values are then combined to reach a BVF and an ɛ value for the sea ice. So your sea ice temperature and salinity is unmoored from that of the snow, casting doubt on whether your dielectric contrast is realistic. The uncertainty in these assumptions risks propagating into your results. Have you looked at the impact of these figures (2m, 3m, 260K) on the modelling that follows? If you change them do you get a different partitioning of ice surface backscatter to snow surf backscatter?
The upshot of the above is that the quality of your inputs implies that SMRT may well not produce good results, and the results don’t indicate (at least to me) that it has performed well. By “well”, I mean to the extent that allows the individual components of the scattering (surface, interfaces, volume) to be “backed out”. I certainly don’t think that you can claim to have “demonstrated the dominance of scattering from the snow surface at Ku and Ka-band” in real life, given the uncertainty of the inputs.
I have some more minor comments below:
L14: I’m not sure it’s possible to make statements like this without reference to the viewing geometry, and relatedly the mode (LRM vs SAR). For instance, the look angle is on average higher for LRM than for SAR (no beam sharpening so wider beam), which will affect the relative contributions of your surfaces to the total backscatter, no? So just needs some clarification that you’re not simulating the geometry that CRISTAL will have, so may be underestimating the degree of specularity it will experience.
L17: “This is the first study to consider scattering within the snow, and demonstrate the origin of CryoSat-2 signals”. With respect, I found this statement quite uncomfortable to read given how long and hard the sea ice altimetry community has considered scattering within the snow. For instance, I think it’s fair to say that Giles et al. (2008), Ricker et al (2015), Nandan et al (2017), Nandan et al. (2020), Tonboe et al. (2021) and Nab et al (2023) considered scattering of CS2 radar pulses within the snow. People have also considered this issue extensively using surface-based and airborne radars (e.g. Willatt et al., 2010; 2011; 2023; King et al., 2018; De Rijke Thomas et al 2023).
L57: it would be good to have some information about how the pLRM waveforms are constructed. For instance the exact data source wasn’t included in your data availability statement. From the github it looks like it’s now included in the L1B product, but which baseline did you use etc? The github readme just links to the ftp and not the product.
Figure 1: You’ve averaged several CS2 pLRM waveforms to produce the ones which you then compare to your model, which I think is a good idea. But it’s important to know what the “spread” of these individual waveforms was prior to averaging. That is to say, are your averaged waveforms representative of their inputs?
Relatedly to the above: I couldn’t quite understand why the waveforms were taken from so far apart, but this is probably because I don’t understand the nature of the plrm processing chain. Is SIRAL not chirping at 20Hz, allowing the construction of a plrm waveform for every conventional doppler-sharpened waveform? If so, you would have many, very closely spaced plrm waveforms. I understand that you probably want to use independent (i.e. non-overlapping) waveforms, but is it really necessary to choose waveforms spaced so far apart and thus risk introducing quite a lot of along-track variability in the sea ice properties?
Table 3: suggest you order the rows in this the same as the rows of Figure 5
Figure 4b: Am I right in saying you cleared the snow off the ice surface to perform photogrammetry to retrieve small scale roughness? If so, I would be interested to know how this was done, since this is a notoriously difficult task. I’ve seen and heard of people trying it with brushes, shovels and even wet-vacs, but all generally either fail to remove all the basal snow or end up removing part of the surface scattering layer and artificially flattening the surface. So a bit of practical methodology needs to be presented here to justify these measurements, beyond the technical method which is very well presented in lines 165-176.
Figure 4: Could do with some information about the KDE method used: what was the kernel shape and how is it justified? Seems like a lot of information in the shaded regions based on quite few scatter points.
L2: “Measurements of sea ice thickness”. It is unusual to see SIT retrievals by CryoSat-2 described as “measurements”. This is obviously a somewhat philosophical point, but it’s the convention in the literature that CS2 is described as measuring ranges, but we then estimate sea ice thickness using range measurements as a proxy. I think you should probably stick to this convention because it reinforces the point that the hydrostatic conversion (and also the lead interpolation to make freeboard) is very uncertain, and describing the SIT retrieval as a measurement somewhat belies this major uncertainty. Indeed I note that in the first sentence of the introduction, SIT retrievals are described as being “estimated”.
L40 - 44: This statement needs more nuance. The most popular CS2 SAR-SIT product used by sea ice scientists is perhaps the AWI product which uses an empirical retracker? The CPOM retracker is also empirical, and has historically been heavily used for CS2 SIT analysis.
L109 - 111: Producing a “complete suite of in-situ field measurements” is a challenge.. I would argue you didn’t measure the most critical parameter of all (wrt waveform shape), which is the footprint scale height distributions of the snow and sea ice. You’ve also used arbitrary figures for ice thickness, ice surface salinity and ice temperature in the modelling which implies (and tell me if I’m wrong) that you also didn’t measure these? Perhaps I’m mistaken, but I don’t think “complete” can be justified in this paper.
L199/200: Can you explain this a bit more? SIRAL’s range sampling is twice this (~1.5ns, i.e. half the range res) to preserve the frequency domain due to Nyquist etc.
General: I wasn’t able to find out what the air temperatures were at the field sites. I looked on the github repo but the data directory hasn’t been pushed, which is fair enough at this stage. Nonetheless, some information should be given about the snow temperatures at each site, even if just to assure the reader that everything was “cold” in a microwave sense. This is done in the abstract, but not in the manuscript body. But also, why not use the measured basal snow temperatures to inform the ice surface temperatures?
L302: “lack a precise”
L309: How many did you exclude, and out of a total of how many? Could you perhaps mark them on Figure 1?
Competing interests: This is not often discussed but I write this in response to a growing issue (which may not apply here). If this publication is required to hit a contractually agreed project deliverable as part of AKROSS, and so is required to release funding, then this should be declared as a competing interest. Assuming it’s not explicitly & contractually required (even if implicitly favoured, as is generally the case) then I think nothing needs to be done.
Relatedly: the Copernicus competing interests policy suggests declaring positions on advisory boards etc. So I think it would also be appropriate to declare any memberships of altimetry-relevant ESA MAGs etc, including concurrent applications to the newest round of the CRISTAL MAG that might be affected by the content or publication of this manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-1583-RC2
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