the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Jan 2025
Modeling L-band Microwave Brightness Temperature Time Series for Firn Aquifers
Abstract. Firn aquifers play an important role in polar ice sheet hydrology and the associated mass and energy transport processes. Although firn aquifer extent has been mapped using passive microwave satellite observations, models to predict L-band brightness temperature time series have remained elusive. This paper implements a radiative transfer model for time series L-Band V and H pol brightness temperature (TB) observations from the 3 km SMAP enhanced resolution data product. The model relates the firn aquifer permittivity and properties of the dry firn layer above the aquifer to SMAP observations. Results are presented for aquifers within both the Greenland and Antarctic ice sheets. The results show that the brightness temperature is more sensitive to aquifer liquid water content changes when the water table is closer to the surface. The model developed is expected to find application in future studies of aquifer property retrieval from satellite remote sensing.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2395', Anonymous Referee #1, 28 Feb 2025
- AC1: 'Reply on RC1', Haokui Xu, 28 Jul 2025
- AC3: 'Reply on RC1', Haokui Xu, 28 Jul 2025
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AC4: 'Reply on RC1', Haokui Xu, 28 Jul 2025
Please refer to the second uploaded responses file. The first pdf fail to correctly give the color of the words.
There is one comment I want to add. In of the points, the reviewer asked about the temperature profile of Wilkins ice sheet and asked why the exponential like function can represent the temperature.
We use the exponential like function to fit the FA-13 temperature and the results show a good fit. The figure is provided in the attached file.
- AC5: 'Reply on RC1 final', Haokui Xu, 06 Aug 2025
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RC2: 'Comment on egusphere-2024-2395', Melody Sandells, 28 Jun 2025
This paper concerns the modelling of L-band brightness temperatures for dry firn overlying aquifers in Greenland and Antarctica. This is an application of the Huang et al (2024) permittivity model and extension of this work from backscatter modelling in the original paper to brightness temperature in this paper, and comparison of the radiative transfer model with enhanced resolution 3km SMAP data. The paper uses sensitivity studies to examine the impact on different parameters, but stops short of using the model to retrieve aquifer liquid water content. This is a potentially exciting application of this work. The paper would benefit from clarifications and further discussions to highlight the significance of this work, as detailed below.
Specific comments:
- Representation of the dry firn layer. In this model framework, the dry firn layer, up to ~15m deep, is represented by a single layer that contains density fluctuations around the mean. Figures 4 and 5 show (as expected) vertical variation in density from 350-800 kg / m3. It would be useful to gain some insight as to how good the assumption of a single layer is. It seems some of the observed fluctuations in brightness temperatures are rather extreme e.g. at a depth of 4m in Figure 5, it looks like there may be an ice lens between two lower density layers of around 500 kg / m3. Existing multi-layer radiative transfer theory models (SMRT, LS-MEMLS, DMRT) could be used to test the impact of these layers compared with a single layer approach and thereby demonstrate whether the experimental set-up here is appropriate.
- Fitted versus physically-derived parameters. It would be useful to highlight which of the parameters applied in the model have been derived directly from the measurements and which have been fitted to the SMAP observations. As far as I understand, the mean densities, temperature profiles and aquifer depths were from observations, whereas the density fluctuations, liquid water content, and vertical and horizontal correlation length were all fitted to the SMAP observations – is this correct? I would recommend parameters for all sites (Tables 3, 4, 5) be combined into a single table, and highlight (perhaps in bold) which ones were directly from the observations. It would be useful to overlay the mean density and a shaded region for fluctuations on to the density profiles to demonstrate how representative the model is.
- Difference in parameters between two Greenland sites. These two sites are 5-6km apart (different values given in different parts of the paper), leading to the assumption that some of the parameters (density, temperature) are transferable. However, the aquifers have different liquid water assumptions and consequently effective permittivity. What is the reason for the 10% difference? The SMAP data presented show rather different signatures, but are likely adjacent or near adjacent pixels within the same radiometer footprint. A scatterplot comparison between the two may be informative - what in the footprint is causing the difference in TB, given that it’s likely coming from the radar? Is there something specific about the topography that could cause differences in the aquifer water content?
- Aquifer liquid water assumption. How were the values used derived? Are they realistic for the regions?
- Spatial extent of application. This model assumes dry firn above aquifers, which may form under ‘certain conditions’ (line 24). What are the conditions that cause this situation and how frequently / on what scale do they occur. This is important to understand how significant this problem is. Although potential contribution to sea level rise is given as 0.4mm for total aquifer drainage, it would be useful to understand whether this a few large aquifers or many small ones.
- Generalisation of modelling. Borehole / GPR were used to parameterize the model – how could modelling be approached without these data i.e. extended to other locations? This also ties in with point 10 below: what would you need to know to be able to do the aquifer liquid water retrievals.
- Credit to earlier work. In particular, this work leverages earlier permittivity work by Huang et al. (2024). Figures 2 and 6 in this paper are rather similar to figures in the Huang paper, which is understandable, but please be explicit about how the work in this paper builds on the work of Huang, particularly placing into context here the treatment of effective permittivity, which is studied much more comprehensively in Huang. There are also numerous other radiative transfer models available – please be explicit about how the one used here is different, and why it is used rather than any other. I would really like to have seen the impact of different permittivity model assumptions on TB – this would be helpful to the community and would again help demonstrate the impact of this work.
- Apparent sensitivity to aquifer wetness in Figure 10. Please explain the physical mechanism for the decrease in TB with increasing wetness here. This is counterintuitive to the increase in permittivity to near blackbody behaviour for wet snow.
- Temporal resolution of simulations. Five data points are presented for each site, to represent the seasonal evolution over a year. What are the temporal resolution of observations available for the in situ data and how were these particular points chosen? Is it possible to include other data points? It is not clear how this varied in time, and how the aquifer depth was inferred from these observations.
- Aquifer liquid water content retrievals. As the application of this paper is for aquifer liquid water content retrievals, it would be hugely beneficial to attempt this in the paper, and use the sensitivity study to indicate how well the parameters need to be known. In lieu of this, please could you suggest a methodology for liquid water retrieval, particularly how some of these unmeasured parameters may be estimated. As it stands, this paper does not support the last sentence in the abstract.
- Structure of material. Site data from other studies should be in the methodology section, along with the map of the sites. These are other people’s work with no new analysis in this study.
- Code and data availability. The authors are strongly encouraged to make the code publicly available. ‘Code available upon request’ does not conform to FAIR principles and has meant that it is much more difficult to interpret how the authors have undertaken their research. ‘Upon request’ is more or less unjustifiable and incompatible with how research is conducted in present times. Links download the data need to be provided in this section.
Technical comments:
Line 37: ‘logistic-like’: should this be logarithmic?
Line 44: Explain the polarization signal that is not captured by a single layer model, and why the single layer model here is different.
Section 2.1 A figure showing the geometry and nomenclature would be useful here.
Figure 3: needs to be in the context of a larger map (and in the methodology)
Figure 5: Show water table location
Line 215. Explain how this fitting was done.
Line 216. Figure 6 does not show this.
Line 258. Where does this assumption come from? Is it reasonable?
Line 260. Explain the mechanism for squeezing the temperature profile.
Line 261. Why tune the density fluctuations? Why not use the observations?
Table 2. Explain what is meant by ‘TB reductions’ i.e how these are calculated. How are boundary effects separated, given multiple scattering?
Figure 8, caption. How and why is the temperature gradient changed ‘to have a slower changing speed’ – please clarify what this means.
Line 288. ‘As indicated in…’ – please rephrase to clarify what this sentence means.
Line 314. ‘higher aquifer water content’ in Wilkins is inconsistent with values indicated in simulation parameter tables.
Line 383. The vertical correlation length lz controls the layer-like behaviour, not the horizontal.
Citation: https://doi.org/10.5194/egusphere-2024-2395-RC2 - AC2: 'Reply on RC2', Haokui Xu, 28 Jul 2025
- AC6: 'Reply on RC2 final', Haokui Xu, 06 Aug 2025
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-2395', Anonymous Referee #1, 28 Feb 2025
Review of paper egusphere-2024-2395.
General comments
The paper is interesting and shows a theoretical explanation of passive microwave time series collected over aquifers in Greenland and Antarctica. The text is well written and easy to understand. It opens by introducing the scientific problem, the test sites and relative geophysical parameters, the electromagnetic models used for the analysis. Then it keep on with a suitable description of the results along with a fair discussion about these achievements and the uncertainties in the process. The workflow is fine although I found some major issues in the many assumptions made due to the lack of ground data. Assumption that often are unreferred and somewhat strong. In my opinion this point must be stressed clearly both in the abstract and in the introduction, in order to provide the reader with a clear overview of what will follow. Provided this, the paper is not a breakthrough but a first attempt to understand the relationship between aquifers evolution and microwave signatures although the many assumptions made can weak the reach of the work.
Specific comments
- The main issue of the paper is the lack of ground measurements to be used both in the modelling phase and in the verification of results. This lack has led to many assumptions and has weakened the work. For instance, density and temperature profiles at site 2 are not known and assumed as site FA-13 (line 59), temperature profile and liquid water content are not known for the Antarctic test site (line 64). The aquifer’s liquid water content is let range from 5% to 25% but no reference is provided (line 188, it seems that these values comes from other papers or simulations, not from ground measurements). Also, temperature profile at Wilkins Ice Shelf test site is derived from a model but no references are given (lines 213-215 and 219-223).
The depletion trend of the aquifers is just assumed, and no ground truth is available but the one on April (lines 258-259 and 297) for Greenland and December for Antarctica. Given the work found that the water table level is one of the main drivers of Tb timeseries trend, the water table level must be derived in a more robust way. Maybe from a geophysical model.
The snow temperature profile changes in time due to changes in water level and thermal forcing from above, no details are provided about its modelling (at line 261 is cited just a “squeezed”). For FA-13 the firn permittivity is set to a fixed value corresponding to a given liquid water content (line 279), however no references are provided to justify this geophysical value.
For the second Greenland site, the assumptions are similar to FA-13 but in this case the liquid water content of the aquifer is set to 10% (line 303). No justification is provided for this value.
For the Antarctic test site, the water table level is “adjusted as shown in figure 10” (lines 315-316).
Overall, it seems that the work relies on too many assumptions, in several cases without proper reference.
- In Fig.4 and 5 it is possible to see two temperature profiles, but nothing is said about the day of the year on which they were collected. Considering that the paper analyze a time series of 4 months, the temperature swing in the snow/firn is appreciable and not considered.
- Ice permittivity models from Mätzler 1996 and Tiuri 1984 are appreciably different (line 191). More details should be provided about the use of these models.
- In the simulations it is not cited the inclusion of the temporal temperature swing in the upper layers that, given the shallow thickness of the snow (about 10m) can have an impact on the Tb. And maybe contribute to the “cooling” trend of SMAP Tb.
- Having the model parameterized in section 3.1, a sensitivity analysis is provided in section 3.2. However, given the many assumptions often not referenced, the representativeness of the trends found seems at least questionable.
- At line 397 the paper says “This model eliminates the ambiguities…..where different parameters ae needed to explain ….”. Actually, given the number of assumptions made, this sentence sounds too optimistic.
Minor points
- line 26, there is a red “s” in aquifers.
- line 56, here the second test site is 5km far from FA-13 while at line 298 is 6km. It is better to use a single value for coherency.
- What is the Tb reduction? It is not a common parameter and should be described in the text, not in a table (line 289).
- section 2.1. This section is redundant and the formulation can be found in many books and papers. I strongly suggest removing this section that adds nothing to the discussion and leave just some proper references.
- Figure 3 must be improved, for instance by using inset with large-scale maps, a clearer (lat, lon) grid, etc.
- section 3.1.2 seems misplaced and should be moved close to the model description.
- in line 332 the first “H pol” should be “V pol”
- the panels in figures 10 and 11 should be represented in a unique figure each to ease the comparison of the curves.
- In figure 12, the different limits of y-axes makes the comparison of the two different cases difficult. Better to merge the two panels into one.
- What “the increased water content contributes constructively to the decreased water table depth” means at line 367?
- lines 388-394 are redundant and can be shortened or deleted at all.
Citation: https://doi.org/10.5194/egusphere-2024-2395-RC1 - AC1: 'Reply on RC1', Haokui Xu, 28 Jul 2025
- AC3: 'Reply on RC1', Haokui Xu, 28 Jul 2025
-
AC4: 'Reply on RC1', Haokui Xu, 28 Jul 2025
Please refer to the second uploaded responses file. The first pdf fail to correctly give the color of the words.
There is one comment I want to add. In of the points, the reviewer asked about the temperature profile of Wilkins ice sheet and asked why the exponential like function can represent the temperature.
We use the exponential like function to fit the FA-13 temperature and the results show a good fit. The figure is provided in the attached file.
- AC5: 'Reply on RC1 final', Haokui Xu, 06 Aug 2025
-
RC2: 'Comment on egusphere-2024-2395', Melody Sandells, 28 Jun 2025
This paper concerns the modelling of L-band brightness temperatures for dry firn overlying aquifers in Greenland and Antarctica. This is an application of the Huang et al (2024) permittivity model and extension of this work from backscatter modelling in the original paper to brightness temperature in this paper, and comparison of the radiative transfer model with enhanced resolution 3km SMAP data. The paper uses sensitivity studies to examine the impact on different parameters, but stops short of using the model to retrieve aquifer liquid water content. This is a potentially exciting application of this work. The paper would benefit from clarifications and further discussions to highlight the significance of this work, as detailed below.
Specific comments:
- Representation of the dry firn layer. In this model framework, the dry firn layer, up to ~15m deep, is represented by a single layer that contains density fluctuations around the mean. Figures 4 and 5 show (as expected) vertical variation in density from 350-800 kg / m3. It would be useful to gain some insight as to how good the assumption of a single layer is. It seems some of the observed fluctuations in brightness temperatures are rather extreme e.g. at a depth of 4m in Figure 5, it looks like there may be an ice lens between two lower density layers of around 500 kg / m3. Existing multi-layer radiative transfer theory models (SMRT, LS-MEMLS, DMRT) could be used to test the impact of these layers compared with a single layer approach and thereby demonstrate whether the experimental set-up here is appropriate.
- Fitted versus physically-derived parameters. It would be useful to highlight which of the parameters applied in the model have been derived directly from the measurements and which have been fitted to the SMAP observations. As far as I understand, the mean densities, temperature profiles and aquifer depths were from observations, whereas the density fluctuations, liquid water content, and vertical and horizontal correlation length were all fitted to the SMAP observations – is this correct? I would recommend parameters for all sites (Tables 3, 4, 5) be combined into a single table, and highlight (perhaps in bold) which ones were directly from the observations. It would be useful to overlay the mean density and a shaded region for fluctuations on to the density profiles to demonstrate how representative the model is.
- Difference in parameters between two Greenland sites. These two sites are 5-6km apart (different values given in different parts of the paper), leading to the assumption that some of the parameters (density, temperature) are transferable. However, the aquifers have different liquid water assumptions and consequently effective permittivity. What is the reason for the 10% difference? The SMAP data presented show rather different signatures, but are likely adjacent or near adjacent pixels within the same radiometer footprint. A scatterplot comparison between the two may be informative - what in the footprint is causing the difference in TB, given that it’s likely coming from the radar? Is there something specific about the topography that could cause differences in the aquifer water content?
- Aquifer liquid water assumption. How were the values used derived? Are they realistic for the regions?
- Spatial extent of application. This model assumes dry firn above aquifers, which may form under ‘certain conditions’ (line 24). What are the conditions that cause this situation and how frequently / on what scale do they occur. This is important to understand how significant this problem is. Although potential contribution to sea level rise is given as 0.4mm for total aquifer drainage, it would be useful to understand whether this a few large aquifers or many small ones.
- Generalisation of modelling. Borehole / GPR were used to parameterize the model – how could modelling be approached without these data i.e. extended to other locations? This also ties in with point 10 below: what would you need to know to be able to do the aquifer liquid water retrievals.
- Credit to earlier work. In particular, this work leverages earlier permittivity work by Huang et al. (2024). Figures 2 and 6 in this paper are rather similar to figures in the Huang paper, which is understandable, but please be explicit about how the work in this paper builds on the work of Huang, particularly placing into context here the treatment of effective permittivity, which is studied much more comprehensively in Huang. There are also numerous other radiative transfer models available – please be explicit about how the one used here is different, and why it is used rather than any other. I would really like to have seen the impact of different permittivity model assumptions on TB – this would be helpful to the community and would again help demonstrate the impact of this work.
- Apparent sensitivity to aquifer wetness in Figure 10. Please explain the physical mechanism for the decrease in TB with increasing wetness here. This is counterintuitive to the increase in permittivity to near blackbody behaviour for wet snow.
- Temporal resolution of simulations. Five data points are presented for each site, to represent the seasonal evolution over a year. What are the temporal resolution of observations available for the in situ data and how were these particular points chosen? Is it possible to include other data points? It is not clear how this varied in time, and how the aquifer depth was inferred from these observations.
- Aquifer liquid water content retrievals. As the application of this paper is for aquifer liquid water content retrievals, it would be hugely beneficial to attempt this in the paper, and use the sensitivity study to indicate how well the parameters need to be known. In lieu of this, please could you suggest a methodology for liquid water retrieval, particularly how some of these unmeasured parameters may be estimated. As it stands, this paper does not support the last sentence in the abstract.
- Structure of material. Site data from other studies should be in the methodology section, along with the map of the sites. These are other people’s work with no new analysis in this study.
- Code and data availability. The authors are strongly encouraged to make the code publicly available. ‘Code available upon request’ does not conform to FAIR principles and has meant that it is much more difficult to interpret how the authors have undertaken their research. ‘Upon request’ is more or less unjustifiable and incompatible with how research is conducted in present times. Links download the data need to be provided in this section.
Technical comments:
Line 37: ‘logistic-like’: should this be logarithmic?
Line 44: Explain the polarization signal that is not captured by a single layer model, and why the single layer model here is different.
Section 2.1 A figure showing the geometry and nomenclature would be useful here.
Figure 3: needs to be in the context of a larger map (and in the methodology)
Figure 5: Show water table location
Line 215. Explain how this fitting was done.
Line 216. Figure 6 does not show this.
Line 258. Where does this assumption come from? Is it reasonable?
Line 260. Explain the mechanism for squeezing the temperature profile.
Line 261. Why tune the density fluctuations? Why not use the observations?
Table 2. Explain what is meant by ‘TB reductions’ i.e how these are calculated. How are boundary effects separated, given multiple scattering?
Figure 8, caption. How and why is the temperature gradient changed ‘to have a slower changing speed’ – please clarify what this means.
Line 288. ‘As indicated in…’ – please rephrase to clarify what this sentence means.
Line 314. ‘higher aquifer water content’ in Wilkins is inconsistent with values indicated in simulation parameter tables.
Line 383. The vertical correlation length lz controls the layer-like behaviour, not the horizontal.
Citation: https://doi.org/10.5194/egusphere-2024-2395-RC2 - AC2: 'Reply on RC2', Haokui Xu, 28 Jul 2025
- AC6: 'Reply on RC2 final', Haokui Xu, 06 Aug 2025
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Haokui Xu
Leung Tsang
Julie Miller
Brooke Medley
Jeol Johnson
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2365 KB) - Metadata XML
Review of paper egusphere-2024-2395.
General comments
The paper is interesting and shows a theoretical explanation of passive microwave time series collected over aquifers in Greenland and Antarctica. The text is well written and easy to understand. It opens by introducing the scientific problem, the test sites and relative geophysical parameters, the electromagnetic models used for the analysis. Then it keep on with a suitable description of the results along with a fair discussion about these achievements and the uncertainties in the process. The workflow is fine although I found some major issues in the many assumptions made due to the lack of ground data. Assumption that often are unreferred and somewhat strong. In my opinion this point must be stressed clearly both in the abstract and in the introduction, in order to provide the reader with a clear overview of what will follow. Provided this, the paper is not a breakthrough but a first attempt to understand the relationship between aquifers evolution and microwave signatures although the many assumptions made can weak the reach of the work.
Specific comments
The depletion trend of the aquifers is just assumed, and no ground truth is available but the one on April (lines 258-259 and 297) for Greenland and December for Antarctica. Given the work found that the water table level is one of the main drivers of Tb timeseries trend, the water table level must be derived in a more robust way. Maybe from a geophysical model.
The snow temperature profile changes in time due to changes in water level and thermal forcing from above, no details are provided about its modelling (at line 261 is cited just a “squeezed”). For FA-13 the firn permittivity is set to a fixed value corresponding to a given liquid water content (line 279), however no references are provided to justify this geophysical value.
For the second Greenland site, the assumptions are similar to FA-13 but in this case the liquid water content of the aquifer is set to 10% (line 303). No justification is provided for this value.
For the Antarctic test site, the water table level is “adjusted as shown in figure 10” (lines 315-316).
Overall, it seems that the work relies on too many assumptions, in several cases without proper reference.
Minor points