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The solution of many field‐scale flow and transport problems requires estimates of unsaturated soil hydraulic properties. The objective of this study was to calibrate neural network models for prediction of water retention parameters and saturated hydraulic conductivity, Ks, from basic soil properties. Twelve neural network models were developed to predict water retention parameters using a data set of 1209 samples containing sand, silt, and clay contents, bulk density, porosity, gravel content, and soil horizon as well as water retention data. A subset of 620 samples was used to develop 19 neural network models to predict Ks. Prediction of water retention parameters and Ks generally improved if more input data were used. In a more detailed investigation, four models with the following levels of input data were selected: (i) soil textural class, (ii) sand, silt, and clay contents, (iii) sand, silt, and clay contents and bulk density, and (iv) the previous variables and water content at a pressure head of 33 kPa. For water retention, the root mean square residuals decreased from 0.107 for the first to 0.060 m3 m‐3 for the fourth model while the root mean square residual Ks decreased from 0.627 to 0.451 log(cm d‐1). The neural network models performed better on our data set than four published pedotransfer functions for water retention (by ≈0.01–0.05 m3 m‐3) and better than six published functions for Ks (by ≈0.1–0.9 order of magnitude). Use of the developed hierarchical neural network models is attractive because of improved accuracy and because it permits a considerable degree of flexibility toward available input data.

We reviewed the use of the van Genuchten–Mualem (VGM) model to parameterize soil hydraulic properties and for developing pedotransfer functions (PTFs). Analysis of literature data showed that the moisture retention characteristic (MRC) parameterization by setting shape parameters m = 1 − 1/n produced the largest deviations between fitted and measured water contents for pressure head values between 330 (log10 pressure head [pF] 2.5) and 2500 cm (pF 3.4). The Schaap–van Genuchten model performed best in describing the unsaturated hydraulic conductivity, K The classical VGM model using fixed parameters produced increasingly higher root mean squared residual, RMSR, values when the soil became drier. The most accurate PTFs for estimating the MRC were obtained when using textural properties, bulk density, soil organic matter, and soil moisture content. The RMSR values for these PTFs approached those of the direct fit, thus suggesting a need to improve both PTFs and the MRC parameterization. Inclusion of the soil water content in the PTFs for K only marginally improved their prediction compared with the PTFs that used only textural properties and bulk density. Including soil organic matter to predict K had more effect on the prediction than including soil moisture. To advance the development of PTFs, we advocate the establishment of databases of soil hydraulic properties that (i) are derived from standardized and harmonized measurement procedures, (ii) contain new predictors such as soil structural properties, and (iii) allow the development of time‐dependent PTFs. Successful use of structural properties in PTFs will require parameterizations that account for the effect of structural properties on the soil hydraulic functions.

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In many vadose zone hydrological studies, it is imperative that the al., 1998). Far fewer alternatives exist for unsaturated soil's unsaturated hydraulic conductivity is known. Frequently, the Mualem-van Genuchten model (MVG) is used for this purpose be-hydraulic conductivity. Although some pedotransfer cause it allows prediction of unsaturated hydraulic conductivity from functions are available (Saxton et al., 1986; Schuh and water retention parameters. For this and similar equations, it is often Bauder, 1986; Vereecken et al., 1990), pore-size distriassumed that a measured saturated hydraulic conductivity (K s) can bution models by Burdine (1953) and Mualem (1976), be used as a matching point (K o) while a factor S L e is used to account among others, are more popular. for pore connectivity and tortuosity (where S e is the relative saturation Generally speaking, the Burdine and Mualem models and L ϭ 0.5). We used a data set of 235 soil samples with retention infer the pore-size distribution of a soil from its water and unsaturated hydraulic conductivity data to test and improve preretention characteristic. By making assumptions about dictions with the MVG equation. The standard practice of using K o ϭ continuity and connectivity of pores, integral expres-K s and L ϭ 0.5 resulted in a root mean square error for log(K) sions can be derived that describe unsaturated conduc-(RMSE K) of 1.31. Optimization of the matching point (K o) and L to the hydraulic conductivity data yielded a RMSE K of 0.41. The fitted tivity in terms of water content or pressure head. A K o were, on average, about one order of magnitude smaller than general expression can be given as (after Hoffmannmeasured K s. Furthermore, L was predominantly negative, casting Riem et al., 1999): doubt that the MVG can be interpreted in a physical way. Spearman rank correlations showed that both K o and L were related to van

Soil, through its various functions, plays a vital role in the Earth's ecosystems and provides multiple ecosystem services to humanity. Pedotransfer functions (PTFs) are simple to complex knowledge rules that relate available soil information to soil properties and variables that are needed to parameterize soil processes. In this paper, we review the existing PTFs and document the new generation of PTFs developed in the different disciplines of Earth system science. To meet the methodological challenges for a successful application in Earth system modeling, we emphasize that PTF development has to go hand in hand with suitable extrapolation and upscaling techniques such that the PTFs correctly represent the spatial heterogeneity of soils. PTFs should encompass the variability of the estimated soil property or process, in such a way that the estimation of parameters allows for validation and can also confidently provide for extrapolation and upscaling purposes capturing the spatial variation in soils. Most actively pursued recent developments are related to parameterizations of solute transport, heat exchange, soil respiration, and organic carbon content, root density, and vegetation water uptake. Further challenges are to be addressed in parameterization of soil erosivity and land use change impacts at multiple scales. We argue that a comprehensive set of PTFs can be applied throughout a wide range of disciplines of Earth system science, with emphasis on land surface models. Novel sensing techniques provide a true breakthrough for this, yet further improvements are necessary for methods to deal with uncertainty and to validate applications at global scale.

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We propose a method for approximating the adhesion parameters in the Shan and Chen multicomponent, multiphase lattice Boltzmann model that leads to the desired fluid-solid contact angle. The method is a straightforward application of Young's equation with substitution of the Shan and Chen cohesion parameter and a density factor for the fluid-fluid interfacial tension, and the adhesion parameters for the corresponding fluid-solid interfacial tensions.