the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Oct 2026
Dynamics of Coastal Permafrost Thaw Driven by Seawater Intrusion: A Numerical Study of Coupled Heat, Salt, and Groundwater Flow Processes
Abstract. Global warming poses a growing threat to permafrost stability worldwide. Coastal permafrost is especially vulnerable because it is exposed to both rising ocean temperatures and seawater intrusion. However, the dynamic thermo-hydro-saline coupling mechanisms governing seawater intrusion-driven permafrost thaw remain poorly understood. This study employs a fully coupled groundwater (ice)-salt-heat numerical model to investigate these dynamics in a high-latitude coastal aquifer, with sensitivity analyses on seawater temperature, aquifer permeability, and porosity. Results identify seawater temperature (Ts) as the primary driver, with permafrost thaw volume increasing by ~105% as Ts rises from 0.5 to 3.5 °C. The system evolves from an initial density-driven, clockwise saline circulation to a mature double-circulation pattern, including a thermally-driven counterclockwise cell. The onset of this double circulation occurs earlier at higher Ts, fundamentally reshaping long-term heat transfer. The salt contribution degree (CDs < 0.5) confirms thermal forcing dominates thaw, while salinity modulates early-phase thawing. Aquifer properties strongly modulate thaw sensitivity: higher permeability accelerates heat and solute transport but promotes earlier counterclockwise circulation development, which can limit inland advance. These findings quantify the nonlinear response of coastal permafrost to ocean warming and provide a predictive framework for assessing carbon mobilization and geotechnical risks in vulnerable Arctic regions.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
(20041 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 30 Nov 2026)
- RC1: 'Comment on egusphere-2026-5331', Anonymous Referee #1, 03 Nov 2026 reply
-
RC2: 'Comment on egusphere-2026-5331', Anonymous Referee #2, 04 Nov 2026
reply
This manuscript addresses a timely and important problem: the thermo-hydro-saline coupling that governs seawater-intrusion-driven thaw of coastal permafrost. The authors present a fully coupled numerical model and use it to conduct sensitivity analyses on seawater temperature, permeability, and porosity. The identification of a transition from single to double circulation and the introduction of the salt contribution degree are interesting contributions. However, methodological, and interpretive issues should be addressed before the manuscript can be considered for publication.
- Permafrost is defined as regions where ice saturation exceeds 30% of pore space (Section 2.4), but no justification or citation is given for this threshold. Please state the basis for the 30% criterion. In addition, PV is reported in m², i.e., a two-dimensional equivalent thaw area; this should be stated explicitly at first use so that PV values are not misread as volumetric quantities.
- The Discussion states that "the modeled ice-bearing permafrost table depth after 1400 years of inundation (16.7 m with salt diffusion) matches their field data only when advection is included, whereas a purely diffusive scenario underpredicts that by ~27%". This is potentially confusing because the present simulations extend only to 60,000 days (~164 years). Please rewrite to make clear that the 1400-year figure and the 27% underprediction come from Angelopoulos et al. (2019), and explain how the present advection-inclusive mechanism is consistent with their finding, rather than implying that this study ran 1400-year simulations.
- The manuscript argues that viscosity u can be treated as constant because subsurface temperature differences are within 5 °C. This is reasonable, but a short quantitative statement would strengthen it: over 0-5 °C the dynamic viscosity of water decreases by roughly 15% (from ~1.79×10⁻³ to ~1.52×10⁻³ Pa·s), which is small relative to the temperature- and salinity-induced density contrasts driving flow. More sentences suffice to clarify.
- The sensitivity analysis currently covers seawater temperature Ts, intrinsic permeability k, and porosity n. However, the salinity- and temperature-dependent soil freezing characteristic (SFC) curve in Eq. (6) is controlled by the residual water saturation Swres and the fitting parameter W(c), and only a single value (Swres=0.05) is adopted. Because Swres directly sets the unfrozen water content that persists under fully frozen conditions, it controls the latent-heat release during phase change, the width of the phase-change interval, and hence the sharpness of the thaw front and the timing of the single-to-double circulation transition tdc. A dedicated sensitivity analysis of Swres is therefore warranted.
- In addition, several parameters (geothermal heat flux, top boundary temperature, and dispersivity) that are likely to contribute substantially to model uncertainty are currently fixed without justification or discussion. To strengthen confidence in the reported results, the following should be addressed.
- This distinction between the current permafrost modeling and models from previous study from Xiayang Yu et al., (2026) can be stated clearly, and its implications for the modeled thaw-front morphology.
“Frozen Ground Induces Seawater Retreat in Coastal Unconfined Aquifers” published in Geophysical Research Letters
7. The emergence of the counterclockwise cell is an interesting finding of the study, yet its driving force is described somewhat loosely as "thermal convection." The authors should decompose the buoyancy budget explicitly: how much of the counterclockwise circulation is driven by the temperature contrast between seawater and the cold interior, how much by the salinity contrast, and how much by the interaction between the two (double-diffusive effects)?
Data sets
Dynamics of Coastal Permafrost Thaw Driven by Seawater Intrusion: A Numerical Study of Coupled Heat, Salt, and Groundwater Flow Processes Shaobo Gao https://doi.org/10.5281/zenodo.22242291
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 238 | 144 | 24 | 406 | 30 | 27 |
- HTML: 238
- PDF: 144
- XML: 24
- Total: 406
- BibTeX: 30
- EndNote: 27
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Zheng et al. have conducted a numerical modeling investigation of the influence of seawater intrusion on coastal permafrost thaw using a simulator that links energy (with phase change), groundwater, and solute (salt) transport. In my opinion, the most interesting finding in this study is the double circulation cell in the salt wedge. I think there are a lot of issues with this manuscript as presented, and so I highlight them below.
Major issues.
1). There are no new field data or model capacity (the particular COMSOL set of equations appears to be a new implementation in COMSOL, but it overlaps with several other models out there) and relatively few new ideas in this study. It overlaps considerably with Guimond et al., 2021 GRL, although there are definitely some new aspects to the present study (i.e., a bit more of a sensitivity analysis and the focus on the double circulation cell). In my view, this present manuscript is way too long a study (figures and text) for the amount of discovery. It should be confined to a technical note in HESS in terms of length, while making use of a supplement for more tangential aspects for the few readers wanting more details.
2). The intro is too long and goes into topics that simply do not need to be included in an introductory section for a paper of this content. For example, the authors talk about the greenhouse gas effect (L47-48) and the sinks of the planet’s energy (L48-51). The influence of solute vs. thermal diffusivity (L68-70) is also too narrow for an introduction, as is the influence of microstructures and hysteresis etc. (L70-74). The authors need to think about what is interesting and important as introductory matter and refocus better. Also, in the first sentence of the last introduction paragraph (which is usually where the main point of a paper is stated), the authors say “to address these gaps, this study developed a fully coupled…model.” But such a model already exists (several of them in fact), so that is itself a weak contribution. That needs to be reframed.
3) This study is only about deep seawater intrusion and does not address flood-driven, downward saltwater intrusion. This latter process is highly relevant in the Arctic with a loss of sea ice and more intensive coastal storms driving more flooding. I think the focus on only deeper seawater intrusion must be stated somewhere.
4) The authors don’t use the term cryopeg (unfrozen permafrost) in this manuscript but talk a lot about it. They should remember that permafrost is still permafrost even when the ground is unfrozen (due to freezing point depression) since permafrost has a temperature-based definition. Really, much of the thaw simulated in the study is conversion of frozen permafrost to cryopeg. For example, on L240, they say that “permafrost is defined as regions where ice saturation exceeds 30%”. Why change the meaning of permafrost (which is stated correctly in the first sentence of the introduction)?
5) Figure 1 looks like an AI product, but no credit is given for that. Also, the sea level is well above the water table at the coastal interface, which can’t happen. There is a white arrow which appears to refer to sea level rise, but this isn’t explicit or obvious what the significance is. Also, the salt wedge concavity is flipped (look at a salt wedge in any textbook, and they don’t look this way) – this is the shape produced by the model, but it should not be so exaggerated and should be acknowledged up front that this is atypical. The land surface is warming, but based on the figure it looks like the only warming that matters is the ocean.
6) The model equations have issues. Where did the form of equation (1) come from? (a citation would be helpful). Equation 3 has units issues. For example Cw is not volumetric heat capacity as stated; rather it is specific heat. Cp IS volumetric heat capacity, but the authors have oddly given it the wrong units (per mass instead of per volume). V is stated as the porewater velocity vector, but it should actually be the Darcy flux vector. Frankly these issues make a reader wonder if anything is actually set up correctly in the model. Also, the explanation around L171-178 seems overly detailed and confusing. It is also unclear where Eq. (6) comes from (is it from the cited Mohammed study that is mentioned later?). Also, a 2020 paper is used to justify the form of Eq. 7, but this equation is older than 2020, and the authors should be using the correct, original citation.
7) The model boundary conditions have issues. What is meant by “the top boundary is impermeable and has a prescribed constant temperature to simulate the effects of snow cover”? How does assigning a constant temperature simulate snow cover? This is nonsensical without comparing it to air temperature or something. The geothermal heat flux magnitude should be accompanied by a citation. What is the horizontal hydraulic gradient imposed by the hydraulic boundary conditions? Is there any (if not, then wedge movement will be exaggerated)? Why is the right boundary condition vertical and not sloping like the bathymetry of an ocean? This is not how coastal groundwater models are set up. This treats the ocean as a vertical interface, which it is not. This might cause too much seawater to enter the model domain, resulting in an exaggeration of the seawater thermal influence. Also, Figure 2 presents only one boundary condition on each side (e.g. hydraulic or thermal or solute), but you need one boundary condition for each equation (hydraulic + thermal + solute) on each model boundary.
8) Model setup: why would setting a deliberately high temperature for initial temp (20C) cause the model to “accelerate convergence to steady state”? I don’t get the point of some of the sensitivity runs. For example, I don’t think running sensitivity on porosity is that interesting since that is a relatively constrained parameter (unlike k for example). Also, it doesn’t have a huge influence later in the results, which is not overly surprising. Many of the metrics for model run evaluations (L245-251) could (and should) be easily shown on a conceptual model figure (or a numerical model domain figure). I also think the model setup is weird where the results indicate very low temperatures at the top (due to -4 top boundary condition) and the warm seawater temperatures at depth. Does this make sense? Would you actually have mean seawater temperature that is so much warmer than the mean land surface temperature? If so, some citations should be provided. I think the thermal gradients are too high and are an artifact of the unusual boundary condition combinations, at least for the runs with higher seawater temperature. I also don’t understand why the authors just use fixed temperature for all their runs. Why not increase the land surface and ocean temperatures at some rate?
There is also some conflicting information throughout about seasonal temperature variation. Even if very shallow flow isn’t considered (so perhaps a seasonally variable land-surface thermal boundary isn’t necessary), the authors also bring up the basal active layer in the introduction, and mention the appearance of a narrow active layer in the results (L307). This can only appear if there is seasonal variation in the temperature forcing (the active layer characteristically thaws and freezes seasonally). The authors say both that seasonal freeze-thaw cycles are not considered (L126) and that seasonal freeze-thaw cycles are captured (L562). In the “future work” paragraph the authors state that spatial heterogeneity, seasonal cycles, and erosion should be included (L584) although “why” these are important factors is not discussed.
I question the utility of the extensive investigation of the salt wedge development from “zero”. The development of the double circulation cell is interesting, and may be representative of true subsurface conditions. However, in reality, ocean forcing isn’t imposed suddenly upon fully frozen ground, and the development of the salt wedge from zero is not the most important result in this paper. The equilibrium state should certainly be presented, but then it feels more valuable to gradually increase the ocean temperature and describe the response during re-equilibration.
9) I have questions about CDs (eq. 8). For example, you can (and should under the boundary conditions given) have a stable salt wedge. That is not “seawater intrusion” per se. Intrusion is when the wedge moves (e.g. due to sea-level rise, pumping, reduced recharge). So some of the change in volume just has to do with the influence of a salt wedge being present -> not seawater intrusion.
10) The Results section needs a lot more sign posting for the reader. First, it is simply too long. Results are mostly over-explained, particularly when they are only model-generated. The subsections are too long and cascading and hard to follow. If this length is required, these need to be broken down further. Section 3.1 is a good example of this. There are some insightful results in general throughout the results section, but the interesting parts are hidden in all the extra text. This is one reason why I think forcing this to be a technical note length would make it a much better contribution.
11) A lot of figures show isolines for 0C, but it might make more sense to ALSO show the isoline for whatever the freezing temperature of seawater is as this is more relevant in the wedge.
12) The authors make statements, including in the Conclusions, that are only true for their particular boundary condition combinations and parameters. It is better to be careful about this and to state “For the model setups considered in this study, X was true”.
Minor points:
L20, rising land surface temperatures likely matter more than rising ocean temperatures, except perhaps right at the coastal interface
L29, there is no point bringing up the “salt contribution degree” in the abstract if it isn’t defined.
L63, need to specify that the isothermal conditions are between the groundwater and the seawater.
L72-76, the Xu et al. example (depth affects hysteresis of water retention) does not relate to the following sentence (permeability must be considered when modelling thermo-hydro-saline processes) even though it is implied they should be connected by the sentence structure.
L81-82, rising sea levels push the saltwater interface further inland IF all else (for example, aquifer recharge) stay the same. The saltwater interface location is the product of multiple factors (terrestrial and oceanic) balancing each other.
L96, I don’t think this would be an active layer unless it is seasonally freezing and thawing
L118, there are not “materials” in this paper, so I would just call this section methods.
L121, this list doesn’t make sense. Either all the items in the list refer to concentration fields (which doesn’t make sense since you can’t have a phase change concentration field) or they stand along by themselves (and that does not work for “thermal”)
L122 and surrounding text: the model limitations/assumptions focus on weird things. The assumption of constant solute diffusivity is less of an assumption than, say, the complete ignoring of geomechanics and cryosuction. For example, the modeled ground in the model is fully saturated. But what happens when pore ice converts to porewater or vice versa? They have different densities, so the same mass can’t keep the pore space saturated. It might be reasonable to ignore those volume changes, but surely that is more important to acknowledge than some of these other points. Also, the list in L122-129 is not parallel writing.
L153: “Regarding u:” is an awkward way to start a sentence
L156, “minimally” – why not say how much in terms of a %
L161, tell the reader what the impedance factor accounts for
L221, “unchanged” is repetitive in this sentence
Table 2 – the last column is “results” not “methods”, and I don’t think it makes sense to blend this with a methods table.
L333-337, sounds very AI and a bit opaque
L549 and following text, is your model domain/forcing based on Angelopoulos et al.’s data and are you comparing it to their results? I believe that is what is being implied in this sentence, but it isn’t clear or referenced in the methodology at all.
L564, is there evidence that this is represents real phenomena better than those other models?
L569, be more direct about what you mean by gravitational instabilities (are you using this as a synonym for convective fingering?) and how this actually relates to the double circulation cells. Do Li et al. also have multi-directional circulation?