Snow Equi‐Temperature Metamorphism Described by a Phase‐Field Model Applicable on Micro‐Tomographic Images: Prediction of Microstructural and Transport Properties. (7th September 2022) - Bouvet, L.; Calonne, N.; Flin, F.; Geindreau, C.
Abstract: Representing snow equi‐temperature metamorphism (ETM) is key to model the evolution and properties of the snow cover. Recently, a phase‐field model describing mean curvature flow evolution on 3D microstructures was proposed (Bretin et al., 2019, https://doi.org/10.1051/m2an/2018075 ). In the present work, this model is used to simulate snow ETM at the pore scale, considering the only process of moving interfaces by sublimation‐deposition driven by curvatures. We take 3D micro‐tomographic images of snow as input in the model and obtain a time series of simulated microstructures as output. Relating the numerical time, as defined in the model, to the real physical time involves the condensation coefficient α, a poorly constrained parameter in literature. A calibration was performed by fitting simulations to experimental data through the evolution of specific surface area (SSA) of snow under ETM at −2°C. A value of the condensation coefficient was obtained: (9.8 ± 0.7) × 10 −4 and was used in all the following simulations. We then show that the calibrated model enables to well reproduce an independent time series of ETM at −2°C in terms of SSA, covariance length, and mean curvature distribution. Finally, the calibrated model was used to investigate the effect of ETM on microstructure and effective transport properties (thermal conductivity, vapor diffusion, and permeability) for four different samples. As an interesting preliminary result, simulations show an enhancement of the structural anisotropy of snow in the case of initially anisotropic microstructures, such as depth hoar. Results highlight the potential of such microscale models for the development of snow property predictions for large‐scale snowpack models. Plain Language Summary: Snow on the ground is a skeleton of ice in air evolving continuously under different environmental constraints. When the temperature gradient within the snowpack is weak, the snow grains tend to gradually become smoother and rounder. This so‐called equi‐temperature metamorphism (ETM) is one of the main mechanisms of snow evolution and its correct representation is crucial for snow modeling. Here, we use a mean curvature flow model, describing the smoothing of 3D microstructures, to simulate snow ETM. 3D micro‐tomographic images of snow samples are used as input; the output is a time series of 3D images showing ETM evolution. Describing ETM classically relies on the condensation coefficient α, a poorly constrained parameter, which drives the intensity of the evolution. We estimate this parameter for ETM at −2°C by fitting simulations to experimental data. Based on comparisons with an independent data set, we show that the model enables to well reproduce ETM at −2°C when no significant densification occurs. Finally, we use the model to investigate the effect of ETM on microstructure and effective transport properties of snow for four different samples. Overall, this work presents promising tools for snow metamorphism study and the development of predictive means for large‐scale snow models. Key Points: A phase‐field model of mean curvature flow is applied on the process of sublimation‐deposition, describing equi‐temperature metamorphism The model is calibrated through the condensation coefficient parameter by fitting experimental and simulated data at −2°C Equi‐temperature metamorphism is predicted on different snow microstructures; morphological and transport property changes are analyzed