Importance of soil heating, liquid water loss, and vapor flow enhancement for evaporation

Abstract

Field measurements conducted by Cahill and Parlange (1998) are reanalyzed to verify if their conclusion that daytime peak values of 60–70 W m−2 of latent heat flux divergence occurred in the 7–10 cm soil layer of a drying Yolo silt loam when maximum values of surface latent heat flux are estimated to have been about 100 W m−2. The new analyses, as similar to theirs as possible, are validated using a numerical simulation of coupled soil moisture and heat flow based on Philip and de Vries (1957) as a test bed. The numerical simulation is extended to include the flow of air induced by diurnal soil heating and evaporative water loss to verify the flux divergence calculations reported in Parlange et al. (1998) that explained the findings of Cahill and Parlange (1998). It is shown that the conclusions of both of these papers are in error, so that the original version of the Philip and de Vries (1957) theory is consistent with their field measurements after all and the effects of airflow associated with soil heating and liquid water loss (and low‐frequency barometric pressure variations also considered) are negligible in practice. In an additional investigation, enhancement of diffusive vapor flow (first postulated by Philip and de Vries (1957)) and discussed extensively in the literature since is shown to have negligible effects on cumulative evaporation under field conditions.

Validity of Assuming Equilibrium Between Liquid Water and Vapor for Simulating Evaporation

“…For a one‐dimensional vertical soil domain the continuum‐scale conservation equations for liquid water and water vapor are, respectively, given by where θ is the volumetric water content (m 3 water m −3 soil), t is the time (s), q l is the liquid water flux density (m s −1 ; all soil flux densities positive downward), z is the depth below the soil surface (m), S e is the subsurface evaporation rate per unit volume of soil (m 3 water m −3 soil s −1 ), K l is the liquid water hydraulic conductivity (m s −1 ), ψ is the matric potential (m), q v is water vapor flux density (m s −1 ), D s is the soil vapor diffusivity (m 2 s −1 ), ρ w is the density of water (kg m −3 ), and ρ v is the vapor density in the air‐filled pore space (kg m −3 ). In agreement with PdV57 and Novak (, ) neglects the variation of water vapor storage, a simplification with negligible effect in most cases. The expression in the brackets in , after multiplication by −1, is Darcy's law while similarly that in is Fick's law.…”

“…This section describes the fundamental dynamical equations governing coupled moisture and heat flow essentially as in PdV57 and Philip (), except with soil matric potential as dependent variable based on Milly () and as in Novak (, ). For a one‐dimensional vertical soil domain the continuum‐scale conservation equations for liquid water and water vapor are, respectively, given by where θ is the volumetric water content (m 3 water m −3 soil), t is the time (s), q l is the liquid water flux density (m s −1 ; all soil flux densities positive downward), z is the depth below the soil surface (m), S e is the subsurface evaporation rate per unit volume of soil (m 3 water m −3 soil s −1 ), K l is the liquid water hydraulic conductivity (m s −1 ), ψ is the matric potential (m), q v is water vapor flux density (m s −1 ), D s is the soil vapor diffusivity (m 2 s −1 ), ρ w is the density of water (kg m −3 ), and ρ v is the vapor density in the air‐filled pore space (kg m −3 ).…”

“…Grifoll () examined the effect of mechanical dispersion of vapor on evaporation and found that although it contributed significantly to the effective vapor diffusion coefficient in the dry surface layer, corresponding changes to evaporation rate were small. His numerical simulations assumed equilibrium, and the vapor dispersion was associated with advective air‐flow due to soil heating and liquid water loss, as in Novak (). Grifoll () indicated that his results were consistent with Hanks and Gardner () who showed that evaporation is limited by upward liquid flow resistance rather than by the dry surface layer resistance, which essentially adjusts to the upward flow rather than vice versa.…”

“…Their enhancement accounted for the expectation that the temperature gradient in the air‐filled pore space is greater than the cross‐sectionally averaged soil temperature gradient, which is determined also by heat flow in the more conductive mineral/organic solid and liquid water phases, and that the presence of “islands” of liquid water would shorten the diffusion path length for water vapor via an evaporation/distillation mechanism. These enhancement processes have been the subject of extensive further investigation since the PdV57 paper was published (e.g., Cary, ; Cass et al, ; Jury & Letey, ; Sakai et al, ; Shahraeeni & Or, ; Shokri et al, ; Webb & Ho, ), although their ultimate importance in determining cumulative evaporation under field conditions is apparently small (Novak, ).…”

Evaluation of Model Concepts to Describe Water Transport in Shallow Subsurface Soil and Across the Soil–Air Interface

“…Difficulty lies in choosing the appropriate soil resistance formulations and the definition of the formulation's parameters. Finally, for Richards vapor model, one other commonly used top boundary condition is evaporation flux which is expressed as the vapor pressure difference between the surface (calculated based on the local equilibrium assumption) and the atmosphere (Novak 2010(Novak , 2016Sakai et al 2011). The surface vapor pressure can also be obtained based on simulation of non-equilibrium models, and the corresponding evaporation flux has been used as the top boundary condition (e.g., Smits et al 2011;Trautz et al 2015).…”