Numerical modelling of freezing soil and snow considering coupled water and heat flow

Johanna Ruth Blöcher

Doctoral thesis

Abstract:

In this thesis several coupled water and heat flow models for freezing soil and snow were developed and implemented into DRUtES, and are now available for everyone to use and modify. A novel parameterization for non-equilibrium freezing was developed for freezing soil, which can be used to simulate freezing and thawing. To allow liquid water and snow to exist at 0 deg C, a heat-based non-equilibrium model was developed and implemented. Several rain-on-snow experiments were conducted and processed to be used for model testing. Further tools were developed in cooperation with several master students to analyze these experiments. These include an R package for image processing of flow paths, as well as methodologies for grain size analysis. The results of this thesis showed that the application of regularization of the discontinuous term successfully stabilizes the computation and can remove oscillations in freezing and thawing soil. As the degree of regularization is problem dependent, a simple method to determine optimal regularization parameters was presented. Simulations of volumetric water content and temperature profiles of previously published soil freezing experiments are represented well. This approach can be added to other codebases and the method therefore allows for broad applicability. For the non-equilibrium ice-phase model, the change in the ice content was solved in a separate equation and then linked back as a non-linear zero-order term. The zero-order term contains a non-equilibrium time constant and we found these time constants can vary dramatically. With freezing soil experiments, it was shown that higher equilibrium constants can successfully decrease overestimation reported, but also inhibits the propagation of the freezing front into freezing soils. Non-equilibrium ice-phase models therefore seem promising, but the parameterization may need to be adjusted to depend on the speed of temperature change. For snow, hydraulic and thermal properties are difficult to measure. Some simple cryo-transfer functions based on snow's density and mean snow grain diameter exist. Snow exhibits very steep retention properties. With retention properties based on the snow grain and snow density, the moisture distribution and outflow are difficult to recreate. In this thesis, we confirm that snow often results in complicated flow patterns, showing fingering flow and horizontal flow structures. Some of the horizontal flow structures seemed like capillary barriers, which were impossible to predict based on data from pre-experimental snow pit measurements. Specifically, no remarkably strong difference in grain size and dry snow density were observed, which are the important input values to state-of-the-art cryo-transfer functions for hydraulic properties. It may be that additional mechanisms have to be taken into account to understand how lateral flow patterns are created. One aspect may be to look at anisotropy of permeability of snow. Further, we confirm that the heterogeneity in flow patterns makes it difficult to take representative point measurements of moisture and temperature that can be used for comparison. We also show that image processing could help to obtain a general overview of flow paths after the experiment and may be used to obtain a fast automated overview of preferential flow paths and lateral flow structures as well as regions indicating moisture.

Keywords

cryo-suction, rain-on-snow, Richards equation

Language used: English

Date on which the thesis was submitted / produced: 10. 2. 2022

Thesis defence

• Supervisor: doc. Ing. Michal Kuráž, Ph.D.

Czech University of Life Sciences Prague

Faculty of Environmental Sciences

Doctoral programme / field:
Landscape Engineering / Environmental Modelling