Abstract
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.
Highlights
Since the development of the theory of Philip and de Vries (PdV model) almost 60 years ago (Philip and de Vries, 1957; de Vries, 1958), virtually all models of evaporation and condensation in unsaturated soils have assumed that soil water vapor at any particular depth into the soil is in equilibrium with the liquid soil water at the same depth
The present model further improves on its companion by including the possibility of soil water movement and better parameterizations of thermophysical properties of water and water vapor
TK − TK,in where TK,in [K] is the initial temperature of the laboratory experiments and Eav −Mwψ [J mol−1] is an empirically determined surface condensation/evaporation activation energy. (Note that (a) TK ≥ TK,in, valid most of the time for any simulation, guarantees Kc ≤ 1. (b) The enthalpy of vaporization, hv(TK), is a logical choice for Eav; but, model performance was significantly enhanced by assigning a constant value for Eav ≈ 30–40 kJ mol−1 rather than assigning Eav ≡ hv.) The present formulation ensures that ∂Kc/∂TK < 0, in accordance with experimental and theoretical studies (Tsuruta and Nagayama, 2004; Kon et al, 2014)
Summary
Since the development of the theory of Philip and de Vries (PdV model) almost 60 years ago (Philip and de Vries, 1957; de Vries, 1958), virtually all models of evaporation and condensation in unsaturated soils have assumed that soil water vapor at any particular depth into the soil is in equilibrium with the liquid soil water (or soil moisture) at the same depth. The present study develops and evaluates a non-equilibrium (liquid–vapor phase change) model for simulating coupled heat, moisture, and water vapor transport during extreme heating events It assumes thermal equilibrium between the soil solids, liquid, and vapor. Unlike its predecessor, this study allows for the possibility of liquid water movement (i.e., it includes a hydraulic conductivity function for capillary and film flow) It improves on and corrects (where possible and as noted in the text) the mathematical expressions used in the previous paper to parameterize the high-temperature dependency of latent heat of vaporization, saturation vapor density, diffusivity of water vapor, soil thermal conductivity, water retention curve, etc. In order to facilitate comparing the present model with the earlier companion model the present study displays all graphical results in a manner very similar to those of Massman (2012)
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