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.

The remarkable complexity of soil and its importance to a wide range of ecosystem services presents major challenges to the modeling of soil processes. Although major progress in soil models has occurred in the last decades, models of soil processes remain disjointed between disciplines or ecosystem services, with considerable uncertainty remaining in the quality of predictions and several challenges that remain yet to be addressed. First, there is a need to improve exchange of knowledge and experience among the different disciplines in soil science and to reach out to other Earth science communities. Second, the community needs to develop a new generation of soil models based on a systemic approach comprising relevant physical, chemical, and biological processes to address critical knowledge gaps in our understanding of soil processes and their interactions. Overcoming these challenges will facilitate exchanges between soil modeling and climate, plant, and social science modeling communities. It will allow us to contribute to preserve and improve our assessment of ecosystem services and advance our understanding of climate-change feedback mechanisms, among others, thereby facilitating and strengthening communication among scientific disciplines and society. We review the role of modeling soil processes in quantifying key soil processes that shape ecosystem services, with a focus on provisioning and regulating services. We then identify key challenges in modeling soil processes, including the systematic incorporation of heterogeneity and uncertainty, the integration of data and models, and strategies for effective integration of knowledge on physical, chemical, and biological soil processes. We discuss how the soil modeling community could best interface with modern modeling activities in other disciplines, such as climate, ecology, and plant research, and how to weave novel observation and measurement techniques into soil models. We propose the establishment of an international soil modeling consortium to coherently advance soil modeling activities and foster communication with other Earth science disciplines. Such a consortium should promote soil modeling platforms and data repository for model development, calibration and intercomparison essential for addressing contemporary challenges.

Abstract. A conceptual model based on the assumption that soil structure evolves from a uniform random fragmentation process is proposed to define the water retention function. The fragmentation process determines the particle size distribution of the soil. The transformation of particles volumes into pore volumes via a power function and the adoption of the capillarity equation lead to an expression for the water retention curve. This expression presents two fitting parameters only. The proposed model is tested on water retention data sets of 12 soils representing a wide range of soil textures, from sand to clay. The agreement between the fitted curves and the measured data is very good. The performances of the model are also compared with those of the two-parameter models of van Genuchten [1980] and Russo [1988] for the water retention function. In general, the proposed model exhibits increased flexibility and improves the fit at both the high and the low water contents range. IntroductionThe solution of the flow equation of water in soils requires the expression of two soil hydraulic characteristics, the water retention curve (WRC) and the hydraulic conductivity function (HCF). The WRC describes the relationship between the soil capillary head, ½, and the volumetric water content, 0. The HCF describes the relationship between the unsaturated hydraulic conductivity, K, and 0. Different models permit defining the HCF in terms of the WRC [Mualem, 1986]. Therefore the WRC can be considered to be one of the most fundamental hydraulic characteristics of a soil. The experimenfal determination of the WRC is tedious and time consuming. Therefore the WRC is not always present in the usual data sets presenting the basic properties of soils. When it is available, it is a discrete representation of a limited number of volumetric water content-capillary head points within the range of the water matric tensions under interest. Consequently, intensive efforts were and are still invested in developing mathematical functions to be fitted to the available set of measured points in order to provide a continuous expression of the WRC. This study is a contribution to this effort. It assumes that the soil particle size distribution (PSD) stems from a fragmentation process and derives the void size distribution (VSD) from the PSD. Approaches inwhere ½o is the capillary head at the inflection point and Se, the effective saturation degree, is defined as A different approach was to develop expressions for the WRC starting from the particle size distribution (PSD) of the soil. Arya and Paris [1981] developed a model to predict the WRC of a soil from its PSD, bulk density, and particle density on the basis of the similarity in shape between the WRC and the PSD of a soil. They proposed the relationship between the mean pore radius, r, and the mean particle radius, R:where e is the void ratio, n is the number of spherical particles with radius r, and a is an empirical constant ranging from In terms of the similarity hypothesis used, a...

The formation of structural seals at the surface of bare soils exposed to the direct impact of raindrops is Rainfall-induced soil surface sealing can have severe agricultural, dominated by a wide variety of factors involving soil hydrological, and environmental effects. Seal formation is a complex phenomenon dominated by a wide variety of factors involving soil properties, rainfall characteristics, and flow conditions. properties, rainfall characteristics, and flow conditions. It has beenThe complexity of the phenomenon has challenged studied through extensive experimental investigations as well as simumany scientists, and it has been studied during the last lation models. This study reviews some of the main issues, in terms four decades through extensive experimental investigaof morphology, phenomenology, and both conceptual and empirical tions as well as simulation models. A large number of modeling approaches to improve our perception of the phenomenon experimental studies have investigated the effect of the and our ability to simulate its effects on flow processes. The effects factors involved in seal formation, either during its dyof different factors on infiltration during seal formation and in sealed namic stage, or after it has already reached its final stage soil profiles are highlighted, including seal representation, soil and when the seal layer is fully developed. Laboratory as rainfall properties, and field heterogeneity. New research opportuniwell as field experiments were performed on various ties toward a generalized formulation of the processes involved in soil sealing and a reliable quantitative prediction of its effects on flow soil types under either saturated or unsaturated flow processes are identified. These are related mainly to the ability to conditions, and for a wide range of natural and simuquantify and predict the relationships between soil hydraulic properlated rainfall intensities and kinetic energies. Different ties and physical, chemical, and biological factors that affect the soil conceptual as well as empirical models of seal formation, resistance to destruction.properties, and effects on infiltration were suggested.Dealing with soil surface sealing requires the ability to understand, characterize, and quantitatively repre-

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