1. Dr Heinze presents a local thermal non-equilibrium model for infiltration of water in snow. The motivation is to develop a numerical model to consider the thermal energy related to melting of ice or freezing of liquid water through the snowpack. The non-equilibrium model is interesting. However, it would be worthwhile to compare results from the same thermo-hydraulic scenarios with results from an equilibrium model. It would be useful to evaluate if there are conditions when a simpler equilibrium model is adequate.

1. The coupling with the hydraulic conductivity of the snow is rudimentary in that thermo-hydraulic processes are investigated for influxes of water into snowpacks consisting of spherical grains. The author acknowledges that this is not realistic, but this condition could apply during infiltration through ‘ripe’ snow that has previously been wetted and subjected to grain growth (Colbeck, 1979; Raymond and Tusima, 1979).

1. However, natural snowpacks are typically layered and heterogeneous; during infiltration, the snow structure and density, and flow fingering often evolve rapidly (e.g. Colbeck, 1979; Marshall et al. 1999; Marshall et al., 2014, Hirashima et al., 2017; Katsushima, 2020; Ohara, 2024). Forecasting impacts of ROS on flash floods and snow avalanches requires modeling thermo-hydraulic processes in natural snowpacks.

1. Dr Heinze mentions that different snow morphology and layering also need to be considered; you might be interested in a study using a water transport model, a dual-domain approach and a multi-layer SNOWPACK model to study infiltration of water in a layered snowpack. (Hirashima et al., 2018)

References

Colbeck, SC 1979.Water flow through heterogeneous snow. Cold Regions Sci and Tech/. 1, 37-45

Hirashima, H., F. Avanzi, and S. Yamaguchi, 2017: Liquid water infiltration into a layered snowpack: evaluation of a 3D water transport model with laboratory experiments, Hydrol. Earth Syst. Sci. Discuss., 2017, 1–22, doi:10.5194/hess-2017-200.

Hiroyuki Hirashima, Nander Wever, Francesco Avanzi, Satoru Yamaguchi, Yoshiyuki Ishii 2016. Simulating liquid water infiltration – comparison between a three-dimensional water transport model and a dual-domain approach using snowpack. Proceedings, International Snow Science Workshop, Innsbruck, Austria, 2018

Takafumi Katsushima, Satoru Adachi, Satoru Yamaguchi, Toshihiro Ozeki,Toshiro Kumakura, 2020. Nondestructive three-dimensional observations of flow finger and lateral low development in dry snow using magnetic resonance imaging. Cold Regions Science and Technology 170 (2020) 102956

Marshall, HP, H Conway, LA Rasmussen, 1999: Snow densification during rain Cold Regions Science and Technology 30 1999. 35–41

Marshall, HP and the Cryosphere Geophysics and Remote Sensing (CryoGARS) group, 2014. Water in snow likes to go with the flow: dynamics of liquid water in snow and its impact on stability. Proceedings, International Snow Science Workshop, Banff, 2014

Noriaki Ohara, 2024. Finger flow modeling in snow porous media based on lagrangian mechanics. Advances in Water Resources 185 (2024) 104634

Raymond, CF, Tusima, K, 1979. Grain coarsening of water-saturated snow. J. Glaciology, Vol.22 No.86,1979

Review of the manuscript submitted to HESS Discussion

https://doi.org/10.5194/hess-2024-154

A local thermal non-equilibrium model for Rain-on-Snow events

By T. Heinze

The author presents an up-to-date theoretical model of meltwater infiltration in snow and soil assuming a thermal non-equilibrium (TNE) between the vapor, water and ice phases. The modelling approach, tested in numerical experiments, is novel and interesting but experimental evidences to support the theoretical assumptions and the improvements in the modelling approach are missing. They would provide a significant added value to the research. Otherwise it is not very clear which is the added value of the modelling approach in terms of simulating the actual water and heat dynamics into the snowpack and the frozen soil. Therefore if experimental data are not provided to support the model’s hypothesis at least some simulations under the hypothesis of thermal equilibrium (TE), showing the differences between the TNE and TE assumptions, and simplified traditional hypotheses of advective heat transfer available for melt M (melt rate) as M=PT/80, with P being the Rain on snow intensity, T the air temperature and 80 the ratio of specific heat capacity of water and latent heat of fusion, are recommended. In this way the improvements introduced by the model would be more evident.

Some key references are missing as suggested in the review.

Line 30 Literature in the 70s and 80s posed the bases for multiphase snowpack dynamics and meltwater infiltration into snow. I added some fundamental references (Colbeck, 1972, 1978: Colbeck and Anderson, 1982; Dunne et al., 1976; Morris, 1991; Akan, 1984a, 1984b) that cannot be neglected, also in view of the model’s parameterization and verification with experimental data.

Line 35 About soil freezing and thawing I would refer also to Leuther and Schlüter (2021)

Line 52 I would spell out LTE Local Thermal Equilibrium

Line 75 I suggest to give some more references about the capacity of the van Genuchten model (developed for soils) to explain water saturation-hydraulic head relationship also for snow.

Line 125 Explain better the assumption about a similar flow velocity for air and infiltrating water. Water is forced by gravity and capillary forces that cannot be treated in the same way for air.

Line 130 Specify the meaning of subscript ij (the 3 phases of water?) for Qij, hij and Aij

Line 212 In Table 1. Ice density is assumed 917 kg/m3 a value generally adopted in  the literature. Why is ice density assumed 940 kg/m3 at line 212?

Line 212 The assumption of a spherical shape for snow crystals with low density as 0.1 kg/m3 is not very realistic as for that density a dendritic shape of snow crystals is more appropriate. Which are the implications of this assumption for the model proposed?

Line 230 The explanation of the mechanical compaction of snow needs to be better explained.

Line 250 A rainfall depth of 0.1 m is assumed but over which time period does rainfall occur?

Then it seems that in the modelling approach a constant hydraulic head of 0.1 m holds at the top boundary (see figure 1, 2, 3, 4, 5, 6, 7). Is this the head of a constant water depth (totally unrealistic) or does it include the capillary head?

Line 254-292 This numerical simulation is interesting. But how would the melt

Discussion. Some discussion about perspectives of the modelling approach to test its results for instance testing its results with measurements of snowpack properties and passive microwave monitoring of the freezing/melting  processes as in Cagnati et al. (2004) would be useful.

How would the infiltration fluxes  change if a hydraulic head of 0.001 m is assumed at the top boundary? The top boundary hydraulic head conditions are not very clear (see comment to line 250).

Line 408. If experimental data are not provided to support the model’s hypothesis at least some simulations under the hypothesis of thermal equilibrium (TE), showing the differences between the TNE and TE assumptions, and simplified traditional hypotheses of advective heat transfer would be useful.

References

Akan, A. O.: 1984a, ‘Mathematical Simulation of Snowmelt and Runoff from Snow Covers’, Frontiers in Hydrology, Water Resources Publications, pp. 79–92. https://doi-org.proxy.unibs.it/10.1029/WR020i006p00707

Akan, A. O. (1984b). Simulation of runoff from snow‐covered hillslopes. Water Resources Research, 20(6), 707-713.

Cagnati, A., A. Crepaz, G. Macelloni, P. Pampaloni, R. Ranzi, M. Tedesco, M. Tomirotti  and  M. Valt,  Study of the snow melt–freeze cycle using multi–sensor data and snow modelling, J. of Glaciology, 50(170), 419-426, 2004

Colbeck, S. C.: 1972, ‘A Theory of Water Percolation in Snow,’ Journal of Glaciology 11(63), 369–385.

Colbeck, S. C. (1978). The physical aspects of water flow through snow. In Advances in hydroscience (Vol. 11, pp. 165-206). Elsevier.

Colbeck, S. C., and E. A. Anderson: 1982, ‘The Permeability of a Melting Snow Cover,’ Water Resources Research 18(4), 904–908.  

https://doi-org.proxy.unibs.it/10.1029/WR018i004p00904

Dunne, T., Price, A. G., & Colbeck, S. C. (1976). The generation of runoff from subarctic snowpacks. Water Resources Research, 12(4), 677-685.  

https://doi.org/10.1029/WR012i004p00677

Morris, E.M. (1991). Physics-Based Models of Snow. In: Bowles, D.S., O’Connell, P.E. (eds) Recent Advances in the Modeling of Hydrologic Systems. NATO ASI Series, vol 345. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3480-4_5

Leuther, F. and Schlüter, S.: Impact of freeze–thaw cycles on soil structure and soil hydraulic properties, SOIL, 7, 179–191, https://doi.org/10.5194/soil-7-179-2021, 2021.