the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Sep 2024
Improved permafrost modeling in mountain environments by including air convection in a hydrological model
Abstract. Permafrost occurrence in mountainous regions is influenced by complex topography and surficial geology, leading to high spatial heterogeneity. Coarse sediments create a unique thermal regime that allows permafrost to persist even under positive mean annual air temperatures due to natural convection lowering ground temperatures. Although this process has been recognized as a key factor in explaining the persistence of permafrost formation within coarse sediments, studies assessing the impact of natural convection on ground temperatures and permafrost are limited, partly due to the absence of hydrological models that take this process into account. This article expands on a well-established hydrological model to incorporate the effects of natural air convection on heat transfer. The modified model includes airflow through Darcy’s equation and the Oberbeck-Boussinesq approximation to account for density-driven buoyancy effects, as well as a heat advection-conduction equation for the air phase without assuming local thermal equilibrium between the air and the other phases. The model was tested on a talus slope in the Canadian Rockies, where conventional models failed to represent field-based evidence of permafrost. The results revealed that coarse-size sediments can lower ground temperatures by several degrees when natural convection is considered. Additionally, the study demonstrated that the local thermal equilibrium approach hinders the impact of natural convection. This enhanced model improves our understanding of permafrost dynamics in alpine landforms and enables a more accurate analysis of permafrost extent and its influence on groundwater discharges.
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Notice on discussion status
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
(21120 KB)
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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.
- Preprint
(21120 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
- CC1: 'Comment on egusphere-2024-2575', Giacomo Medici, 06 Sep 2024
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RC1: 'Comment on egusphere-2024-2575', Anonymous Referee #1, 11 Nov 2024
Permafrost and its reaction on climate change are key issues of cryosphere research and thus also in TC. As the processes that change permafrost are very complex, process understanding is still comparatively limited. Improving the modelling of permafrost is an important approach to close this research gap. The work of Zegers et al. addresses relevant scientific questions in the context of permafrost research by improving its modelling through introduction of air convection and its effects (heat advection-conduction without assuming a local thermal equilibrium between the air and matrix) into the 3D hydrology model GEOtop. In this way, new methods and results for permafrost modelling based on the existing theory of air convection and density-driven buoyancy flow of air and heat advection conduction in a porous matrix are presented.
I found the paper very interesting, generally well written, well structured and easy to follow. Only the large number of acronyms sometimes made it difficult to follow the storyline. The title of the paper is well chosen and reflects the content well. The abstract is short and concise and contains key information of the paper. Due to the topic of the study, the paper contains a larger number of mathematical formulae, but these are balanced in scope, well presented and explained in the text as well as are useful for understanding the content. Results are clearly sufficient to support the interpretations and conclusions, which are clear and useful for the research community. In general, the paper is well embedded in appropriate international references (see also my minor comment below).
I suggest only minor revision before the paper can be accepted in the Cryosphere.
Minor comments:
Supercooled talus slopes are an interesting phenomenon in the context of permafrost processes. This is well described and introduced in the paper, but I suggest to mentioned that supercooled talus slopes have been known for a long time (e.g. since the end of the 18th century).
I also wondered to what extent the distinction between summer and winter situations for air circulation in the talus slopes is too general. In principle, the difference between day and night often has a similar effect, especially if, for example, long-wave radiation at the surface (radiation night) causes a strong cooling of the upper talus sediment layers near the surface at night. Then a corresponding density gradient of the air in the talus body should also occur. Of course, the time available to drive this process is very limited, but at least it can counteract the daytime situation in summer. Perhaps this process is taken into account in the paper, but I couldn't find it in the text. It also appears that the winter and summer simulations shown are driven by constant temperature values and do not take into account daily temperature variations. In the long-term simulation in Chapter 4.3.1, it is also not clear at which temporal resolution the driving data (e.g. of air temprature, radiation etc. ) are used. This should be clarified.
I am not familiar with the study area presented, but it seems to me that there are simpler situations with supercooled talus slopes (e.g. in the European Alps) where the temperature effects are measurable (and have actually been measured). These conditions would be much more suitable for evaluating the model, as the temperature could be evaluated directly (and air convection could actually be measured). In the supercooled talus slopes of the Alps, the temperature effect is also very clearly visible in the vegetation. Is there such evidence in the vegetation of the study area in Canada?
Equation makes the important assumption that the circulating air is assumed to be incompressible and the temperature is only a consequence of the density (if I understood it correctly). However, if the air in the soil/talus layers sinks downwards parallel to the slope (as indicated in Figures 5, 7 and 9), then it reaches regions of higher air pressure and undergoes compression, which is cannot be neglected over larger vertical distances (or conversely expansion as the air rises). Figure 5 also shows that the air in the talus body is in equilibrium with the outside air (i.e. corresponds to the respective air pressure). Was the assumption made here that the vertical movement is not large enough (maybe 10-20m) and therefore the vertical pressure change is not large enough and is neglected? However, this would limit the applicability of the model.
On page 18 the performance of GEOtop in comparison to the UEB model is described. It is stated that the GEOtop is well performing and show similar snow cover patterns as UEB. However, the difference of simulated SWE is rather large and also the time of maximum SWE is quite different. It seems that GEOtop is calibrated towards UEB in a way that it represents snow depletion well. I don’t believe that differences in snow simulation change results in Figure 12 significantly. But I would rephrase the description of the performance of snow simulations of GEOtop more accurately according to the simulations. Also the discharge simulations shown in Figure 12 are with significant deviations from observations (could add some skill measures here). This is explained in the text but it also stated that the GEOtop simulations align with observations in June and July. Though it is not easy to see exactly from Figure 12, it seems that also for June und July deviations are significantly (but the daily cycle is strong and give the impression of high coincidence).
Equations (13) and (14): wn is not used consistently here (does not appear in equation (13), but is stated afterwards)
Figures 7 and 9: Please add a x-axis scaling, the arrows of air flow are hard to identify
The labelling of Figures 6, 8 and 11 could be improved to make it easier for the reader, e.g. indicate the profile name above the figure. A short description instead of the acronyms of the model configurations would also help (depending on the space available).
Figure 12: Please explain with more text
Citation: https://doi.org/10.5194/egusphere-2024-2575-RC1 -
AC1: 'Reply on RC1', Gerardo Zegers, 19 Apr 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2575/egusphere-2024-2575-AC1-supplement.pdf
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AC1: 'Reply on RC1', Gerardo Zegers, 19 Apr 2025
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RC2: 'Comment on egusphere-2024-2575', Martin Hoelzle & Dominik Amschwand (co-review team), 17 Feb 2025
This co-review was done by Dominik Amschwand and Martin Hoelzle
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AC2: 'Reply on RC2', Gerardo Zegers, 19 Apr 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2575/egusphere-2024-2575-AC2-supplement.pdf
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AC2: 'Reply on RC2', Gerardo Zegers, 19 Apr 2025
Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2024-2575', Giacomo Medici, 06 Sep 2024
General comments
Good and novel research in the field of hydrology that needs some minor and further detail before publication.
Specific comments
Line 11. “Canadian Rockies”. Better Canadian Rocky Mountains for an international audience.
Lines 20-24. “Within mountains… relatively small area”. Please, add recent papers on mountain hydrology that incorporate the impact of snow and ice melt on runoff and groundwater recharge:
- Joshi, S. K., Swarnkar, S., Shukla, S., Kumar, S., Jain, S., Gautam, S. (2023). Snow/ice melt, precipitation, and groundwater contribute to the Sutlej River system. Water, Air, & Soil Pollution, 234(11), 719.
- Lorenzi, V., Banzato, F., Barberio, M. D., Goeppert, N., Goldscheider, N., Gori, F., Lacchini A, Manetta M, Medici G, Rusi S, Petitta, M. (2024). Tracking flowpaths in a complex karst system through tracer test and hydrogeochemical monitoring: Implications for groundwater protection (Gran Sasso, Italy). Heliyon, 10(2).
Lines 83-90. Paragraph 2.1. Specify that you are dealing with fluid flow in the unsaturated zone.
Line 141. “GEOtop” really novel model or can you insert a reference?
Line 393 “A low conductivity layer”. Please, specify which type of conductivity.
Lines 513-672. Insert recent and relevant literature on snow and ice melts recharging the groundwater in mountain areas.
Figures and tables
Figure 1. Add the approximate scale to the conceptual scheme.
Figure 5A and B. Add the spatial scale.
Figure 7. All graphs are very clear. Difficult to read this one even at a second look. Please, improve graphic resolution, and description of caption.
Figure 9. Same here. Difficult to read also this one. Please, improve graphic resolution, and description of caption.
Citation: https://doi.org/10.5194/egusphere-2024-2575-CC1 -
RC1: 'Comment on egusphere-2024-2575', Anonymous Referee #1, 11 Nov 2024
Permafrost and its reaction on climate change are key issues of cryosphere research and thus also in TC. As the processes that change permafrost are very complex, process understanding is still comparatively limited. Improving the modelling of permafrost is an important approach to close this research gap. The work of Zegers et al. addresses relevant scientific questions in the context of permafrost research by improving its modelling through introduction of air convection and its effects (heat advection-conduction without assuming a local thermal equilibrium between the air and matrix) into the 3D hydrology model GEOtop. In this way, new methods and results for permafrost modelling based on the existing theory of air convection and density-driven buoyancy flow of air and heat advection conduction in a porous matrix are presented.
I found the paper very interesting, generally well written, well structured and easy to follow. Only the large number of acronyms sometimes made it difficult to follow the storyline. The title of the paper is well chosen and reflects the content well. The abstract is short and concise and contains key information of the paper. Due to the topic of the study, the paper contains a larger number of mathematical formulae, but these are balanced in scope, well presented and explained in the text as well as are useful for understanding the content. Results are clearly sufficient to support the interpretations and conclusions, which are clear and useful for the research community. In general, the paper is well embedded in appropriate international references (see also my minor comment below).
I suggest only minor revision before the paper can be accepted in the Cryosphere.
Minor comments:
Supercooled talus slopes are an interesting phenomenon in the context of permafrost processes. This is well described and introduced in the paper, but I suggest to mentioned that supercooled talus slopes have been known for a long time (e.g. since the end of the 18th century).
I also wondered to what extent the distinction between summer and winter situations for air circulation in the talus slopes is too general. In principle, the difference between day and night often has a similar effect, especially if, for example, long-wave radiation at the surface (radiation night) causes a strong cooling of the upper talus sediment layers near the surface at night. Then a corresponding density gradient of the air in the talus body should also occur. Of course, the time available to drive this process is very limited, but at least it can counteract the daytime situation in summer. Perhaps this process is taken into account in the paper, but I couldn't find it in the text. It also appears that the winter and summer simulations shown are driven by constant temperature values and do not take into account daily temperature variations. In the long-term simulation in Chapter 4.3.1, it is also not clear at which temporal resolution the driving data (e.g. of air temprature, radiation etc. ) are used. This should be clarified.
I am not familiar with the study area presented, but it seems to me that there are simpler situations with supercooled talus slopes (e.g. in the European Alps) where the temperature effects are measurable (and have actually been measured). These conditions would be much more suitable for evaluating the model, as the temperature could be evaluated directly (and air convection could actually be measured). In the supercooled talus slopes of the Alps, the temperature effect is also very clearly visible in the vegetation. Is there such evidence in the vegetation of the study area in Canada?
Equation makes the important assumption that the circulating air is assumed to be incompressible and the temperature is only a consequence of the density (if I understood it correctly). However, if the air in the soil/talus layers sinks downwards parallel to the slope (as indicated in Figures 5, 7 and 9), then it reaches regions of higher air pressure and undergoes compression, which is cannot be neglected over larger vertical distances (or conversely expansion as the air rises). Figure 5 also shows that the air in the talus body is in equilibrium with the outside air (i.e. corresponds to the respective air pressure). Was the assumption made here that the vertical movement is not large enough (maybe 10-20m) and therefore the vertical pressure change is not large enough and is neglected? However, this would limit the applicability of the model.
On page 18 the performance of GEOtop in comparison to the UEB model is described. It is stated that the GEOtop is well performing and show similar snow cover patterns as UEB. However, the difference of simulated SWE is rather large and also the time of maximum SWE is quite different. It seems that GEOtop is calibrated towards UEB in a way that it represents snow depletion well. I don’t believe that differences in snow simulation change results in Figure 12 significantly. But I would rephrase the description of the performance of snow simulations of GEOtop more accurately according to the simulations. Also the discharge simulations shown in Figure 12 are with significant deviations from observations (could add some skill measures here). This is explained in the text but it also stated that the GEOtop simulations align with observations in June and July. Though it is not easy to see exactly from Figure 12, it seems that also for June und July deviations are significantly (but the daily cycle is strong and give the impression of high coincidence).
Equations (13) and (14): wn is not used consistently here (does not appear in equation (13), but is stated afterwards)
Figures 7 and 9: Please add a x-axis scaling, the arrows of air flow are hard to identify
The labelling of Figures 6, 8 and 11 could be improved to make it easier for the reader, e.g. indicate the profile name above the figure. A short description instead of the acronyms of the model configurations would also help (depending on the space available).
Figure 12: Please explain with more text
Citation: https://doi.org/10.5194/egusphere-2024-2575-RC1 -
AC1: 'Reply on RC1', Gerardo Zegers, 19 Apr 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2575/egusphere-2024-2575-AC1-supplement.pdf
-
AC1: 'Reply on RC1', Gerardo Zegers, 19 Apr 2025
-
RC2: 'Comment on egusphere-2024-2575', Martin Hoelzle & Dominik Amschwand (co-review team), 17 Feb 2025
This co-review was done by Dominik Amschwand and Martin Hoelzle
-
AC2: 'Reply on RC2', Gerardo Zegers, 19 Apr 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2575/egusphere-2024-2575-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Gerardo Zegers, 19 Apr 2025
Peer review completion
Journal article(s) based on this preprint
Model code and software
GeoTOP-CE Gerardo Zegers https://github.com/gzegers/geotop-CE
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Cited
2 citations as recorded by crossref.
- Sub-surface processes and heat fluxes at coarse blocky Murtèl rock glacier (Engadine, eastern Swiss Alps): seasonal ice and convective cooling render rock glaciers climate-robust D. Amschwand et al. 10.5194/esurf-13-365-2025
- Global evidence that cold rocky landforms support icy springs in warming mountains S. Brighenti et al. 10.1088/1748-9326/adf07f
Gerardo Zegers
Masaki Hayashi
Rodrigo Pérez-Illanes
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(21120 KB) - Metadata XML
General comments
Good and novel research in the field of hydrology that needs some minor and further detail before publication.
Specific comments
Line 11. “Canadian Rockies”. Better Canadian Rocky Mountains for an international audience.
Lines 20-24. “Within mountains… relatively small area”. Please, add recent papers on mountain hydrology that incorporate the impact of snow and ice melt on runoff and groundwater recharge:
- Joshi, S. K., Swarnkar, S., Shukla, S., Kumar, S., Jain, S., Gautam, S. (2023). Snow/ice melt, precipitation, and groundwater contribute to the Sutlej River system. Water, Air, & Soil Pollution, 234(11), 719.
- Lorenzi, V., Banzato, F., Barberio, M. D., Goeppert, N., Goldscheider, N., Gori, F., Lacchini A, Manetta M, Medici G, Rusi S, Petitta, M. (2024). Tracking flowpaths in a complex karst system through tracer test and hydrogeochemical monitoring: Implications for groundwater protection (Gran Sasso, Italy). Heliyon, 10(2).
Lines 83-90. Paragraph 2.1. Specify that you are dealing with fluid flow in the unsaturated zone.
Line 141. “GEOtop” really novel model or can you insert a reference?
Line 393 “A low conductivity layer”. Please, specify which type of conductivity.
Lines 513-672. Insert recent and relevant literature on snow and ice melts recharging the groundwater in mountain areas.
Figures and tables
Figure 1. Add the approximate scale to the conceptual scheme.
Figure 5A and B. Add the spatial scale.
Figure 7. All graphs are very clear. Difficult to read this one even at a second look. Please, improve graphic resolution, and description of caption.
Figure 9. Same here. Difficult to read also this one. Please, improve graphic resolution, and description of caption.