| 27 Jul 2026
Hydrodynamic controls on stable isotopic exchange during meltwater percolation through stratified ice
Abstract. Stable water isotopes are fundamental tracers for interpreting snowpack dynamics, stratigraphy, and meltwater export in the cryosphere. However, the isotopic signals exported from melting snow and ice are often modified internally before release, as natural snowpacks and glacier ice are vertically isotopically heterogeneous and percolating meltwater undergoes dynamic isotopic exchange with the surrounding solid matrix. Here, we quantified how initial isotopic stratigraphy and meltwater flow regimes jointly control this non-conservative isotope transport. We conducted eight controlled column-melting experiments using two-layer ice columns composed of isotopically depleted and enriched layers arranged in reversed vertical sequences under different melting conditions. Effluent δ18O and δ2H were interpreted using a process-based, one-dimensional isotope-exchange model. The experiments show that meltwater isotopic evolution is governed primarily by the vertical order of the isotopically distinct layers and cannot be explained by conservative end-member mixing alone. The model successfully reproduced the observed isotope trajectories using effective exchange parameters, yielding exchange rate constants (kr) of 0.11–0.54 h−1 for oxygen isotopes and 0.11–0.49 h−1 for hydrogen isotopes, with no statistically distinguishable difference between the two isotopic systems within individual experiments. Across the experiments, kr tended to increase with percolation velocity, most clearly in depleted-top configurations, whereas the active exchange fraction (f) decreased under faster-flow conditions within each stratigraphic group. This hydrodynamic decoupling demonstrates that isotopic exchange during meltwater percolation is dictated not only by contact time but also by flow-path organization and the accessibility of ice-water interfaces. Our results highlight that isotopic signatures exported from melting snow and ice must be interpreted as process-modified signals rather than strictly conservative source end-members. Incorporating flow-dependent phase exchange into cryospheric models will improve the interpretation of meltwater export dynamics and the evolution of isotopic stratigraphy in snow- and ice-dominated environments.
General assessment
The manuscript investigates the evolution of stable water isotopes during meltwater percolation through vertically heterogeneous ice layers. The study combines eight controlled column-melting experiments with a one-dimensional isotope-exchange model to evaluate the effects of isotopic layering and meltwater flow conditions on δ18O and δ2H signals. The topic is relevant to isotope hydrology because snowmelt and ice-melt isotope compositions are commonly treated as source end-members in hydrograph separation and catchment-scale mixing analyses, whereas the present study highlights that these signals may be modified during internal percolation before leaving the frozen matrix.
The experimental design, particularly the reversal of enriched and depleted layers, provides a useful framework for exploring this problem. The manuscript contains a clear process-oriented idea and several useful results, especially the demonstration that exported meltwater can depart from a purely conservative two-end-member signal.
However, several aspects of the interpretation currently exceed what can be robustly supported by the experimental dataset. The most important concern is the strength of the claimed hydrodynamic relationships between percolation velocity, the fitted exchange-rate constant kr, and the active exchange fraction f. These relationships are based on only eight experiments in total and, more importantly, on four observations when the experiments are subdivided by isotopic configuration. Therefore, very high Pearson correlations should not be interpreted as evidence for a general or systematic hydrodynamic law (most important!!!).
A second major concern is the interpretation of the differences between depleted-top and enriched-top experiments as being controlled by “initial isotope stratigraphy”. The isotopic sequence is fundamentally a tracer configuration and, unless the two ice types also differ in physical properties, isotopic ordering itself should not determine hydraulic behavior. The manuscript should distinguish more clearly between tracer stratigraphy and physical structure of the porous medium.
A third concern is that kr and f are effective fitted parameters of a simplified one-dimensional model. They should not be interpreted too directly as independently measured physical properties of the ice matrix. This is particularly important because several estimates of f reach the upper optimization bound of 1.0, and because the model assumes uniform melting, one-dimensional vertical flow, constant contact area, and no dispersion.
Overall, the study is potentially suitable for publication after substantial revision. The conclusion that meltwater isotope signals may depart from conservative end-member behavior is supported by the data. However, the mechanistic interpretation in terms of preferential flow, hydrodynamic decoupling, and systematic dependence of kr and f on flow velocity should be presented more cautiously and supported by additional uncertainty, sensitivity, and goodness-of-fit analyses.
Major comments
1. Statistical robustness of relationships among kr, f, u* and S
The manuscript places considerable emphasis on the relationship between the exchange-rate constant kr and percolation velocity u*, particularly for the depleted-top experiments. Once the experiments are divided according to configuration, however, each relationship is based on only four observations. The correlation matrices and regressions shown in Fig. 7 therefore have extremely limited statistical power.
With n = 4, high r or R² values can be strongly affected by one point and should not be interpreted as robust evidence of a general relationship. The manuscript should explicitly state sample size for each regression, report uncertainty or p-values where appropriate, and present subgroup regressions as exploratory trends rather than established statistical laws.
The language should be revised consistently across the Abstract, Introduction, Discussion and Conclusions. Expressions such as “systematically increases”, “demonstrates”, and “fundamental advance” should be replaced by more cautious formulations such as “shows a tendency to increase under the investigated conditions” or “is consistent with”.
2. Isotopic stratigraphy versus physical hydrodynamic control
The manuscript repeatedly states or implies that hydrological behavior depends on the “initial isotope stratigraphy”. Yet the depleted and enriched layers are primarily tracer end-members. If the two ice types are hydraulically and structurally equivalent after freezing, reversing their isotopic sequence should not itself modify permeability, pore connectivity, preferential flow or effective saturation.
The authors should clarify whether DW-derived and SW-derived ice differed physically in residual solute concentration, freezing texture, density, morphology, roughness, or any other property that could affect meltwater routing. If such differences were not measured, the manuscript should avoid assigning causality to isotope stratigraphy and instead refer to “experimental configuration” or “layer configuration”.
3. Physical interpretation and identifiability of kr and f
Both kr and f are obtained through calibration of the same model against the isotope time series. They should therefore be described throughout the manuscript as effective or apparent parameters.
The authors should report numerical confidence intervals, discuss covariance between kr and f, describe how the confidence regions in Fig. 6 were calculated, and provide a sensitivity/identifiability analysis. This is particularly important because several f estimates reach exactly 1.00, the imposed upper bound. These cases should be identified as boundary-constrained solutions rather than interpreted literally as evidence that 100% of the ice participated in exchange.
4. Quantitative model-performance metrics are needed
The manuscript repeatedly states that the model reproduces the isotope trajectories successfully or with high fidelity, but evaluation is almost entirely visual. Since parameters are optimized by minimizing squared residuals, the authors should report quantitative performance metrics for each experiment and isotope, for example RMSE, MAE and bias. These values could be included in Table 2 or in supplementary material.
5. Preferential flow is inferred, not directly observed
The manuscript attributes several observations to preferential flow, channelized flow, flow-path organization and changing accessibility of ice-water interfaces. These interpretations are plausible, but the internal flow paths were not directly imaged or measured.
The manuscript should systematically distinguish observed variables (discharge, meltwater isotope composition, melt duration), calculated variables (u*, S), fitted parameters (kr, f), and inferred processes (preferential flow, flow-path accessibility, channelization).
6. Constant hydraulic properties versus evolving flow structure
Table 2 assigns identical intrinsic permeability and hydraulic conductivity values to all experiments, while the central interpretation of the paper is that internal hydrodynamic conditions differ substantially among experiments. The authors should explain whether these hydraulic properties are merely reference values, whether they enter the calculations of u* or S, and how sensitive the inferred relationships are to these assumptions.
7. Experimental replication and treatment effects
The paired design is useful, but there are no true replicate runs within each heat-forcing/configuration combination. Therefore, treatment effects cannot be cleanly separated from run-to-run variability associated with packing or stochastic development of flow pathways.
The manuscript should acknowledge this limitation explicitly and avoid wording that implies a statistically replicated factorial experiment.
8. Transferability from ice cubes to natural snowpacks
The 3 × 3 × 2.5 cm ice cubes provide experimental control but differ substantially from natural snow in pore geometry, specific surface area, capillary retention, grain structure and likely preferential-flow behavior. The limitations section recognizes this, but several statements elsewhere extrapolate rather directly to natural snowpacks and catchments.
The paper should distinguish clearly between process-level evidence from the artificial coarse ice matrix, plausible implications for natural snow, and demonstrated catchment-scale consequences.
9. Mass-balance and measurement uncertainty
Meltwater recovery ranges from below 95% to above 100%, including 102.6% for Exp-5. A recovery above 100% indicates non-negligible experimental and/or measurement uncertainty. The balance resolution should be reported, uncertainty quantified, and the effect on discharge and derived hydrological variables discussed. The wording “negligible uncertainty” should be replaced by a quantitatively justified statement.
10. Interpretation of δ18O-δ2H slopes and GMWL
The GMWL is a familiar visual reference, but the experimental end-members are distilled water and desalinated seawater rather than natural meteoric precipitation. The manuscript should clarify that slope deviations relative to 8 do not have exactly the same interpretation as in conventional meteoric-water datasets. The GMWL may remain as a reference line, but the discussion should avoid overinterpreting the observed slopes as a conventional meteoric evaporation signal.
Specific and line-by-line comments
Abstract, lines 16-22: The statement that the isotope trajectories cannot be explained by conservative end-member mixing alone is supported, but it would be useful to state explicitly that this conclusion is based on comparison with the theoretical two-layer conservative signal. Suggested wording: “The observed meltwater isotope trajectories deviated from the conservative signal expected from sequential melting of the two isotopically distinct layers, indicating substantial modification by internal exchange.”
Abstract, lines 20-23: Retain the cautious expression “kr tended to increase with percolation velocity” throughout the manuscript. Replace “This hydrodynamic decoupling demonstrates…” with “This contrasting behavior suggests…” or “is consistent with…”.
Abstract, lines 24-25: Replace “will improve” with “may improve”, because improved predictive performance has not been directly tested.
Introduction, lines 34-53: The framing is relevant but broad. Consider shortening the first paragraph and maintaining tighter focus on isotope modification during snowmelt and percolation.
Introduction, lines 45-48: Consider changing “can severely bias” to “can bias” unless the magnitude of the bias is directly documented by the cited studies.
Introduction, lines 57-68: Introduce an explicit distinction between isotopic heterogeneity and physical heterogeneity. Suggested addition: “Importantly, isotopic stratification and physical stratification need not be equivalent, and their respective roles in controlling meltwater transport should therefore be distinguished.”
Introduction, lines 69-85: Clarify the distinction between exchange-rate constant, total exchange efficiency, residence time and exchangeable ice fraction. These quantities should not be used interchangeably.
Introduction, lines 87-98: The description of kr and f as effective parameters is appropriate and should be maintained consistently throughout Results and Discussion.
Introduction, lines 99-108: The wording is too strong. Remove “As a fundamental advance”, “unifies previous contradictory literature”, and “systematically increases”. Suggested replacement: “The experiments provide evidence that the apparent relationship between exchange parameters and percolation velocity may depend on the internal flow configuration.”
Introduction, lines 108-116: Replace “delivers a robust physical foundation” with “provides process-level experimental constraints”.
Materials and methods, lines 119-130: Provide physical characterization of DW- and SW-derived ice, including any differences in electrical conductivity/residual salinity, density, texture, or freezing behavior. This is essential for evaluating whether configuration-dependent hydrodynamics could reflect physical differences between the two ice types.
Materials and methods, lines 125-129: Replace “enabling a robust optimization” with “facilitating estimation” unless formal identifiability diagnostics are provided.
Materials and methods, lines 131-136: Replace “systematic evaluation” with “paired comparison”, since there are no replicated treatments.
Materials and methods, lines 137-140: Specify meltwater sampling resolution and protocol: fixed time interval, fixed mass/volume, or variable sampling.
Materials and methods, lines 141-153: Provide the explicit equation for u*, define effective saturation clearly, report units, and discuss uncertainty propagation.
Materials and methods, lines 167-176: Use a single isotope notation throughout the manuscript, preferably δ2H rather than alternating between δ2H and δD.
Materials and methods, lines 183-187: Discuss why dispersive mixing can be neglected, particularly because the later interpretation invokes heterogeneous and preferential flow.
Materials and methods, lines 195-198: Justify the use of constant equilibrium fractionation factors at 0 °C under infrared heating, or provide a sensitivity argument.
Materials and methods, lines 210-217: Rephrase the interpretation of f. Suggested wording: “f is treated as an effective parameter representing the fraction of solid ice accessible to isotopic exchange within the model framework.”
Materials and methods, lines 217-226: Describe the optimization method in full: algorithm, parameter ranges and bounds, initial guesses, convergence criteria, whether kr and f were fitted simultaneously, whether isotopes were fitted independently, and how confidence regions were obtained.
Results, lines 227-236: The differences in melt duration between nominally paired experiments should be treated as evidence of substantial run-to-run variability and discussed later as a limitation.
Results, lines 253-262: Replace “Such differences likely reflect…” with “Such differences may reflect…”, because grain-size and channelized flow were not measured directly.
Table 1: Explain the 102.6% recovery in Exp-5. Report the balance resolution and measurement uncertainty, and clarify whether and how this uncertainty affects discharge calculations.
Results, lines 274-290: The correspondence between F ≈ 0.5 and the physical layer interface should be described as approximate, because percolating water can cross the interface before half of the total ice mass has melted.
Results, lines 292-308: The conclusion that slopes below 8 imply minimal evaporation/sublimation should be stated more cautiously. A slope lower than 8 alone does not exclude these processes, especially with artificial end-members.
Results, lines 309-321: Replace “does not compromise overall model validity” with “appears to have limited influence on the overall fitted trajectories” unless this is demonstrated quantitatively. A useful sensitivity test would be to refit excluding F < 0.05.
Results, lines 321-325: A <12.5% difference between oxygen and hydrogen kr values does not itself establish statistical equivalence. The later confidence-region analysis is the more appropriate evidence.
Table 2: Add uncertainties/confidence intervals for u*, f and kr, plus a model-performance metric. Mark solutions that hit parameter bounds.
Table 2: The heading “Porosity, φ, %” is inconsistent with values around 0.40-0.42. Either report 40-42% or label the variable as dimensionless porosity.
Table 2: Clarify whether hydraulic conductivity and intrinsic permeability are measured, assumed, or literature reference values, and indicate whether they enter any derived calculations.
Figure 3: Add quantitative model-fit statistics in the text or table rather than relying only on visual agreement.
Figure 4: State explicitly in the caption or text that the GMWL is shown only as a familiar reference because the experimental end-members are not natural meteoric waters.
Figure 5: Define precisely how the conservative two-layer reference signal is calculated. If it is a step function at F = 0.5, state this explicitly.
Discussion section numbering: The manuscript begins with “3. Discussion” but uses subsections “4.1”, “4.2” and “4.3”. Correct the numbering.
Discussion, lines 541-548: Provide methodological details for the 95% confidence regions and discuss parameter covariance/identifiability, not only overlap between oxygen and hydrogen fits.
Discussion, lines 550-556: When comparing kr across previous studies, clarify whether the same model formulation and parameter definition were used.
Discussion, lines 557-564: Pearson correlations based on n = 4 should be treated as exploratory tendencies. State n explicitly and avoid strong statistical language.
Discussion, lines 565-577: The phrase “show a contrasting tendency” is appropriately cautious; retain this tone consistently elsewhere.
Discussion, lines 587-596: Because Exp-4 strongly influences the enriched-top relation, this caveat should also be reflected in the Abstract and Conclusions.
Discussion, lines 597-611: Frame preferential-flow interpretation as a plausible mechanism: “One possible explanation is that faster or more organized flow…” rather than presenting it as directly demonstrated.
Section 4.2, lines 612-618: Notation error: “active exchange fraction for oxygen isotopes (kr,18O)” should be f18O.
Section 4.2, lines 625-631: Replace “the hydrological response of the ice columns depends on the initial isotope stratigraphy” with a non-causal formulation such as “The two layer configurations exhibited contrasting relationships between effective saturation and percolation velocity.”
Section 4.2, lines 632-647: The conceptual comparison between fine-grained snow and coarse ice is useful but should be clearly framed as interpretation based on previous studies rather than direct evidence from these experiments.
Section 4.2, lines 647-651: Consider replacing “highlights the sensitivity” with “suggests potential sensitivity” given the limited sample size.
Section 4.3, lines 673-688: Explicitly separate measured processes, model-inferred parameters and hypothesized hydrodynamic mechanisms.
Section 4.3, lines 689-700: Add three limitations: lack of treatment replication, small n for statistical relationships, and potential physical differences between the two ice end-members.
Conclusions, lines 707-722: Replace “These patterns indicate…” with “These patterns suggest…” when referring to hydrodynamic controls.
Conclusions, lines 707-722: The statement that stable-isotope signals can be process-modified is a strong outcome, but consider changing “should therefore be interpreted” to “may therefore behave as process-modified tracers” to avoid overgeneralization.
Data and code availability: The statement that information is available upon request is weak for a modeling study. Deposit isotope data, discharge data, model code, optimization settings and parameter files in a public repository if possible.
Editorial consistency: Use δ2H or δD consistently; correct “how much ice involved in the isotopic exchange”; check “Materials and methods”; standardize hyphenation and notation for ice-water, melt rate and kr; correct the repeated comma in Author Contributions.
Suggested recommendation text
The manuscript addresses a relevant problem in isotope hydrology and presents an interesting combination of controlled melting experiments and process-based modeling. The experimental evidence convincingly shows that isotopic layering and internal liquid-solid exchange can modify the isotope composition of exported meltwater relative to a purely conservative two-end-member signal. However, the manuscript currently overstates the robustness and mechanistic significance of the inferred relationships between percolation velocity, exchange-rate constant, and active exchange fraction. These relationships are based on a very small number of experiments, particularly after subdivision by layer configuration, and several key hydrodynamic processes invoked in the interpretation were not directly observed. In addition, the physical meaning and identifiability of the fitted parameters require further clarification. I therefore recommend major revision, with particular attention to statistical robustness, parameter uncertainty, model evaluation, causal interpretation of isotope stratigraphy, and the distinction between observed and inferred hydrodynamic processes.