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Evaporation and condensation in bare soils govern water and energy fluxes between the land and atmosphere. Phase change between liquid water and water vapor is commonly evaluated in soil hydrology using an assumption of instantaneous phase change (i.e. chemical equilibrium). Past experimental studies have shown that finite volatilization and condensation times can be observed under certain environmental conditions, thereby questioning the validity of this assumption. A comparison between equilibrium and non-equilibrium phase change modeling approaches showed that the latter is able to provide better estimates of evaporation, justifying the need for more research on this topic. Several formulations based on irreversible thermodynamics, first order reaction kinetics, or the kinetic theory of gases have been employed to describe non-equilibrium phase change at the continuum scale. In this study, results from a fully coupled non-isothermal heat and mass transfer model applying four different non-equilibrium phase change formulations were compared with experimental data generated under different initial and boundary conditions. Results from a modified Hertz-Knudsen formulation based on kinetic theory of gases, proposed herein, were consistently in best agreement in terms of preserving both magnitude and trends of experimental data under all environmental conditions analyzed. Simulation results showed that temperature dependent formulations generally better predict evaporation than formulations independent of temperature. Analysis of vapor concentrations within the porous media showed that conditions were not at equilibrium under the experimental conditions tested. This article is protected by copyright. All rights reserved.

[1] Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance. However, there is no agreement on the best modeling methodology to determine evaporation under different atmospheric boundary conditions. Also, there is a lack of directly measured soil evaporation data for model validation to compare these methods to establish the validity of their mathematical formulations. Thus, a need exists to systematically compare evaporation estimates using existing methods to experimental observations. The goal of this work is to test different conceptual and mathematical formulations that are used to estimate evaporation from bare soils to critically investigate various formulations and surface boundary conditions. Such a comparison required the development of a numerical model that has the ability to incorporate these boundary conditions. For this model, we modified a previously developed theory that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. Precision data under well-controlled transient heat and wind boundary conditions were generated, and results from numerical simulations were compared with experimental data. Results demonstrate that the approaches based on different boundary conditions varied in their ability to capture different stages of evaporation. All approaches have benefits and limitations, and no one approach can be deemed most appropriate for every scenario. Comparisons of different formulations of the surface boundary condition validate the need for further research on heat and vapor transport processes in soil for better modeling accuracy.

[1] In the shallow subsurface immediately below the land-atmosphere interface, it is widely recognized that the movement of water vapor is closely coupled to thermal processes. However, their mutual interactions are rarely considered in most soil water modeling efforts or in practical applications where it becomes necessary to understand the spatial and temporal distribution of soil moisture. The validation of numerical models that are designed to capture these processes is difficult due to the scarcity of field or laboratory data with accurately known hydraulic and thermal parameters of soils, limiting the testing and refinement of heat and water transfer theories. The goal of this paper is to perform controlled experiments under transient conditions of soil moisture and temperature and use this data to test existing theories and develop appropriate numerical models. Water vapor flow under varying temperature gradients was implemented on the basis of a concept that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion. To validate this new approach, we developed a long column apparatus equipped with a network of sensors and generated data under well-controlled thermal boundary conditions at the soil surface. The nonequilibrium approach yielded good agreement with the experimental results, validating the hypothesis that transport in the gas phase is better suited to be modeled with nonequilibrium liquid/gas phase change for highly transient field conditions where the thermal conditions at the land-atmosphere interface are constantly changing.

[1] Recently improved ECH2O soil moisture sensors have received significant attention in many field and laboratory applications. Focusing on the EC-5 sensor, a simple and robust calibration method is proposed. The sensor-to-sensor variability in the readings (analog-to-digital converter (ADC) counts) among 30 EC-5 sensors was relatively small but not negligible. A large number of ADC counts were taken under various volumetric water contents (θ) using four test sands. The proposed two-point α-mixing model, as well as linear and quadratic models, was fitted to the ADC – θ data. Unlike for conventional TDR measurements, the effect of sensor characteristics is lumped into the empirical parameter α in the two-point α-mixing model. The value of α was fitted to be 2.5, yielding a nearly identical calibration curve to the quadratic model. Errors in θ associated with the sensor-to-sensor variability for the two-point α-mixing model were ±0.005 cm3 cm−3 for dry sand and ±0.028 cm3 cm−3 for saturated sand. In the validation experiments, the highest accuracy in water content estimation was achieved when sensor-specific ADCdry and ADCsat were used in the two-point α-mixing model. Assuming that α = 2.5 is valid for most mineral soils, the two-point α-mixing model only requires the measurement of two extreme ADC counts in dry and saturated soils. Sensor-specific ADCdry and ADCsat counts are readily measured in most cases. Therefore, the two-point α-mixing model (with α = 2.5) can be considered as a quick, easy, and robust method for calibrating the ECH2O EC-5 sensor. Although further investigation is needed, the two-point α-mixing model may also be applied to calibrating other sensors.