Evaporation from porous media involves mass and energy transport including phase change, vapor diffusion, and liquid flow, resulting in complex displacement patterns affecting drying rates. Force balance considering media properties yields characteristic lengths affecting the transition in the evaporation rate from a liquid-flow-based first stage limited only by vapor exchange with air to a second stage controlled by vapor diffusion through the medium. The characteristic lengths determine the extent of the hydraulically connected region between the receding drying front and evaporating surface (film region) and the onset of flow rate limitations through this film region. Water is displaced from large pores at the receding drying front to supply evaporation from hydraulically connected finer pores at the surface. Liquid flow is driven by a capillary pressure gradient spanned by the width of the pore size distribution and is sustained as long as the capillary gradient remains larger than gravitational forces and viscous dissipation. The maximum extent of the film region sustaining liquid flow is determined by a characteristic length L_{C} combining the gravity characteristic length L_{G} and viscous dissipation characteristic length L_{V} . We used two sands with particle sizes 0.1-0.5 mm ("fine") and 0.3-0.9 mm ("coarse") to measure the evaporation from columns of different lengths under various atmospheric evaporative demands. The value of L_{G} determined from capillary pressure-saturation relationships was 90 mm for the coarse sand and 140 mm for the fine sand. A significant decrease in drying rate occurred when the drying front reached the predicted L_{G} value (viscous dissipation was negligibly small in sand and L_{C} approximately L_{G} ). The approach enables a prediction of the duration of first-stage evaporation with the highest water losses from soil to the atmosphere.

[1] Prediction of drying rates from porous media remains a challenge due to complex interactions between ambient conditions and porous medium properties. Evaporation from a gradually drying porous surface across air boundary layer exhibits nonlinear behavior due to enhanced diffusive fluxes from increasingly isolated active pores. These nonlinear interactions were quantified by modeling evaporation from surfaces composed of individual pores considering surface water content dynamics and internal transport within the medium. Wind tunnel experiments show that in contrast with nearly constant evaporation rates obtained at low atmospheric demand (typically <5 mm/d), evaporation fluxes under high atmospheric demand (high air velocities) exhibit a continuous decrease with surface drying even in the absence of internal capillary flow limitations. The isolated pore evaporation model captures surface drying dynamics for a range of atmospheric demands associated with air velocity and boundary layer thickness. As a surface dries under low atmospheric demand (low air speed, thick boundary layer), the remaining active pores become gradually isolated with a conforming vapor concentration field becoming increasingly three-dimensional thereby enhancing evaporative flux per pore. Such enhancement may fully compensate for reduced evaporative surface area leading to observed constant evaporation rate under low demand. For high evaporative demand, limitations to vapor field configuration within thin boundary layer limit flux compensation efficiency and leads to decreasing evaporative flux with surface drying irrespective of internal supply capacity. The model provides new insights into the intrinsic links between surface properties and atmospheric conditions in determining a range of evaporative dynamics for similar surface wetness conditions. Citation: Shahraeeni, E., P. Lehmann, and D. Or (2012), Coupling of evaporative fluxes from drying porous surfaces with air boundary layer: Characteristics of evaporation from discrete pores, Water Resour. Res., 48, W09525,

Globally, evaporation consumes about 25% of solar energy input and is a key hydrologic driver with 60% of terrestrial precipitation returning to the atmosphere via evapotranspiration. Quantifying evaporation is important for assessing changes in hydrologic reservoirs and surface energy balance and for many industrial and engineering applications. Evaporation dynamics from porous media reflect interactions between internal liquid and vapor transport, energy input for phase change, and mass transfer across air boundary layer. We reviewed recent advances on resolving interactions between soil intrinsic properties and evaporation dynamics with emphasis on the roles of capillarity and wettability affecting liquid phase continuity and capillary driving forces that sustain Stage I evaporation. We show that soil water characteristics contain information for predicting the drying front depth and mass loss at the end of Stage I and thus derive predictions for regional‐scale evaporative water losses from soil textural maps. We discuss the formation of secondary drying front at the onset of Stage II evaporation and subsequent diffusion‐controlled dynamics. An important aspect for remote sensing and modeling involves nonlinear interactions between wet evaporating surfaces and air boundary layer above (evaporation rate is not proportional to surface water content). Using pore scale models of evaporating surfaces and vapor transport across air boundary layer, we examined the necessary conditions for maintenance of nearly constant evaporation while the surface gradually dries and the drying front recedes into the soil. These new insights could be used to improve boundary conditions for models that are based on surface water content to quantify evaporation rates.

A review of present modelling approaches for root reinforcement in vegetated steep hillslopes reveals critical gaps in consideration of plant-soil interactions at various scales of interest for shallow landslide prediction. A new framework is proposed for systematic quantifi cation of root reinforcement at scales ranging from single root to tree root system, to a stand of trees. In addition to standard basal reinforcement considered in most approaches, the critical role of roots in stabilizing slopes through lateral reinforcement is highlighted. Primary geometrical and mechanical properties of root systems and their function in stabilizing the soil mass are reviewed. Stress-strain relationships are considered for a bundle of roots using the formalism of the fi ber bundle model (FBM) that offers a natural means for upscaling mechanical behavior of root systems. An extension of the FBM is proposed, considering key root and soil parameters such as root diameter distribution, tortuosity, soil type, soil moisture and friction between soil and root surface. The spatial distribution of root mechanical reinforcement around a single tree is computed from root diameter and density distributions based on easy to measure properties. The distribution of root reinforcement for a stand of trees was obtained from spatial and mechanical superposition of individual tree values with regard to their positions on a hillslope. Potential applications of the proposed approach are illustrated in a numerical experiment of spatial strength distribution in a hypothetical slope with 1000 trees randomly distributed. The analyses result in spatial distribution of weak and strong zones within the soil where landslide triggering is expected in large and continuous zones with low reinforcement values. Mapping such zones would enhance the quality of landslide susceptibility maps and optimization of silvicultural measures in protection forests.