Abstract. Increased use of prescribed fire by land managers and the increasing likelihood of wildfires due to climate change require an improved modeling capability of extreme heating of soils during fires. This issue is addressed here by developing and testing the soil (heat–moisture–vapor) HMV-model, a 1-D (one-dimensional) non-equilibrium (liquid–vapor phase change) model of soil evaporation that simulates the coupled simultaneous transport of heat, soil moisture, and water vapor. This model is intended for use with surface forcing ranging from daily solar cycles to extreme conditions encountered during fires. It employs a linearized Crank–Nicolson scheme for the conservation equations of energy and mass and its performance is evaluated against dynamic soil temperature and moisture observations, which were obtained during laboratory experiments on soil samples exposed to surface heat fluxes ranging between 10 000 and 50 000 W m−2. The Hertz–Knudsen equation is the basis for constructing the model's non-equilibrium evaporative source term. Some unusual aspects of the model that were found to be extremely important to the model's performance include (1) a dynamic (temperature and moisture potential dependent) condensation coefficient associated with the evaporative source term, (2) an infrared radiation component to the soil's thermal conductivity, and (3) a dynamic residual soil moisture. This last term, which is parameterized as a function of temperature and soil water potential, is incorporated into the water retention curve and hydraulic conductivity functions in order to improve the model's ability to capture the evaporative dynamics of the strongly bound soil moisture, which requires temperatures well beyond 150 °C to fully evaporate. The model also includes film flow, although this phenomenon did not contribute much to the model's overall performance. In general, the model simulates the laboratory-observed temperature dynamics quite well, but is less precise (but still good) at capturing the moisture dynamics. The model emulates the observed increase in soil moisture ahead of the drying front and the hiatus in the soil temperature rise during the strongly evaporative stage of drying. It also captures the observed rapid evaporation of soil moisture that occurs at relatively low temperatures (50–90 °C), and can provide quite accurate predictions of the total amount of soil moisture evaporated during the laboratory experiments. The model's solution for water vapor density (and vapor pressure), which can exceed 1 standard atmosphere, cannot be experimentally verified, but they are supported by results from (earlier and very different) models developed for somewhat different purposes and for different porous media. Overall, this non-equilibrium model provides a much more physically realistic simulation over a previous equilibrium model developed for the same purpose. Current model performance strongly suggests that it is now ready for testing under field conditions.
Stationary Non-equilibrium Solutions for Coagulation Systems
