Van Genuchten-Mualem Research Articles

Estimation of hydraulic parameters in a heterogeneous low‐lying farmland near Venice

AbstractEstimating the hydraulic properties of the vadose zone is essential to understand soil‐water dynamics and achieving appropriate water management in agricultural lands. Inverse modelling methods are commonly used to estimate hydraulic properties from field observations. Unlike the extensively applied local search methodologies, data assimilation techniques can fully account for multiple uncertainties and are becoming a widely used tool for estimating hydraulic parameters. However, only few applications on real field tests are available. The main objective of this study was to estimate the van Genuchten‐Mualem (VGM) parameters and the saturated hydraulic conductivity () of a heterogeneous low‐lying farmland at the margin of the Venice Lagoon, Italy, characterized by high peat content, sandy drifts, and a very shallow water table. To this end, two methods were tested, that is, the Ensemble Smoother (ES) and the Levenberg–Marquardt (LM) algorithm associated with hydrological modelling performed with Hydrus‐1D. Volumetric water content (VWC) observations were collected at three monitoring sites from May to September 2011. Results on parameters highlighted that the ES technique effectively reduced the uncertainty of and , but it was less effective on and . The results on VWC showed that the ES efficiency decreased with the increasing non‐linearity of the system (e.g., higher sand content) and when the variability of the experimental data was lower (e.g., deepest soil layers where saturation remained permanently close to 1). Both LM and ES allowed to reproduce the VWC observations in the calibration and validation phases, with the former and the latter performing better in the case of sandy and peat soils, respectively. As concerns the method applicability, the ES was less time‐demanding as it efficiently updated all the parameters at once and was less dependent on the user choices. Finally, the paper points out the importance of previous knowledge of the VGM parameters (e.g., from lab hydraulic analyses) in defining the constraints for the optimization.

Inverse estimation of hydraulic parameters of soils with rock fragments

The application of inverse modeling to determine the hydraulic properties of layered soils with rock fragments (RF > 2 mm) is associated with complex challenges such as selecting suitable hydraulic functions and defining a strategy to optimize many parameters. These two issues were addressed in this study by performing field drainage experiments in layered soil profiles (three layers) with different particle size distributions and different percentages of RF. Water contents (θ) and pressure heads (h) were monitored at different soil depths during drainage experiments (h ≥ −200 cm). Data of θ and h for a drier range (h < −5000 cm) were determined with a dew point potentiometer on disturbed soil samples. The unimodal and bimodal van Genuchten-Mualem functions were evaluated, and their parameters were optimized using the Hydrus-1D “Inverse solution”. The RETC curve fitting software was used to estimate the second set of parameters of the bimodal function. The parameters for the uni- and bimodal models (15 and 27 parameters, respectively) were repeatedly optimized by fixing some parameters while estimating others. The unimodal van Genuchten-Mualem function provided a satisfactory fit of θ and h measurements only when either drainage or dew point potentiometer measurements were used. On the other hand, the bimodal van Genuchten-Mualem function provided a satisfactory fit of θ and h measurements when both sets of data (drainage and dew point potentiometer measurements) were used simultaneously. Furthermore, the optimized parameters were physically consistent except for a few high saturated hydraulic conductivity values. Therefore, bimodal functions should be considered to represent the hydraulic properties of soils with RF. The problem of many calibrated parameters when using bimodal functions can be managed using sequential optimization, which allowed us to estimate 27 parameters for layered soils with RF successfully.

Stochastic Merging of Soil Hydraulic Properties for Vadose Zone Hydrological Modeling

Soil hydraulic properties (SHPs) are commonly determined in soil samples with replicas. Whether these replicas are taken at a same location to represent a specific point or at several locations to represent a larger area, the results should be merged into a final data set to be used in modeling. For this data set to be representative, standard errors and a correlation matrix must be considered in the merging process. We present a method to perform this merging and give an example using stochastic realizations of van Genuchten-Mualem (VGM) parameters generated by Cholesky decomposition to merge the SHP and associated statistics into a merged parameter set. To do so, we used VGM parameters obtained at sample scale in three replicas from a Brazilian savanna soil through inverse modeling of laboratory evaporation experiments. The effectiveness and representativeness of the proposed methodology were evaluated by observing the frequency distribution of different levels of output, comparing individual and merged sample properties. The outputs include VGM parameters, retention and conductivity characteristics, and water balance components stochastically predicted by a hydrological model. The performed stochastic merging correctly represented the variability of the combined replicas, especially with respect to hydrological model outputs of soil water balance components. Using the mean hydraulic property parameter values to deterministically predict water balance components may yield values that are substantially different from the mean values of stochastic realizations. This suggests that the deterministic prediction using mean parameter values in vadose zone hydrological modeling may result in unrepresentative outputs.

Properties governing flow of solution and air through crushed ore for heap leaching: Part II unsaturated dual-phase flow

Heap leaching of low-grade ores is often restricted by the hydrology of the bed, which limits the rate of dissolution of the target mineral. Although much research has been published on the flow of solution and air through sand, little has been published on the hydrology of coarser rocks. Physical and hydraulic testing of rocks and agglomerates is often incorporated as a part of heap leach design, however, much still relies on experiential rules. Over the past decade, the lead author has performed physical and hydraulic testing of a large number of ore samples considered for heap leaching. In reviewing the data, it was found that the hydraulic conductivity function (HCF), relating the hydraulic conductivity to the degree of saturation, can be modelled with traditional capillary models such as Brooks-Corey (BC) and van Genuchten-Mualem (VGM), but only at lower moisture contents. Furthermore, it was found that the HCF can be modelled as a discontinuous J-curve, with the hydraulic conductivity equal to the saturated hydraulic conductivity (Ks) above the air-entry point, rather than a continuous J-curve with a fitted Ks value, as recommended by other authors. Previous authors have also suggested that the discontinuity represents a transition between capillary- and gravity-controlled flow. However, the author(s) propose that the discontinuity is caused rather by the presence of “dead voids”, which fill up at higher moisture contents without generating additional flow channels. The point of discontinuity was found to correspond to the air-entry value obtained independently from the air conductivity curves. The experiential rule of a maximum void saturation of 65% for heap aeration appears to correspond on average with the experimental data.

In situ estimation of soil hydraulic and hydrodispersive properties by inversion of electromagnetic induction measurements and soil hydrological modeling

Abstract. Soil hydraulic and hydrodispersive properties are necessary for modeling water and solute fluxes in agricultural and environmental systems. Despite the major efforts in developing methods (e.g., laboratory-based, pedotransfer functions), their characterization at applicative scales remains an imperative requirement. Accordingly, this paper proposes a noninvasive in situ method integrating electromagnetic induction (EMI) and hydrological modeling to estimate soil hydraulic and transport properties at the plot scale. To this end, we carried out two sequential water infiltration and solute transport experiments and conducted time-lapse EMI surveys using a CMD Mini-Explorer to examine how well this methodology can be used to (i) monitor water content dynamic after irrigation and to estimate the soil hydraulic van Genuchten–Mualem parameters from the water infiltration experiment as well as (ii) to monitor solute concentration and to estimate solute dispersivity from the solute transport experiment. We then compared the results with those estimated by direct time domain reflectometry (TDR) and tensiometer probe measurements. The EMI significantly underestimated the water content distribution observed by TDR, but the water content evolved similarly over time. This introduced two main effects on soil hydraulic properties obtained by the two methods: (i) similar water retention curve shapes, but underestimated saturated water content from the EMI method, resulting in a scaled water retention curve when compared with the TDR method; the EMI-based water retention curve can be scaled by measuring the actual saturated water content at the end of the experiment with TDR probes or by weighing soil samples; (ii) almost overlapping hydraulic conductivity curves, as expected when considering that the shape of the hydraulic conductivity curve primarily reflects changes in water content over time. Nevertheless, EMI-based estimations of soil hydraulic properties and transport properties were found to be fairly accurate in comparison with those obtained from direct TDR measurements and tensiometer probe measurements.

Analyzing dual porosity in soil hydraulic properties using soil databases for pedotransfer function development

AbstractCurrent databases of soil hydraulic properties (SHPs) have typically been used to develop pedotransfer functions (PTFs) to estimate water retention [θ(h)] assuming a unimodal pore‐size distribution. However, natural soils often show the presence of bimodal to multimodal pore‐size distributions. Here, we used three widely spread databases for PTF development: UNsaturated SOil hydraulic DAtabase (UNSODA) 2.0, Vereecken, and European hydropedological data inventory (EU‐HYDI), to analyze the presence of structural effects in both θ(h) and hydraulic conductivity [K(h)]. Only undisturbed samples were included in the analysis that contained enough datapoints for both θ(h) and K(h) properties, especially in the wet range. One‐hundred ninety‐two samples were suitable for our analysis, which is only 1% of the total samples in the three databases. Results showed that 65% of the samples exhibited a bimodal pore‐size distribution, and bimodality was not limited to fine‐textured but also coarser‐textured soils. The Mualem–van Genuchten (MvG) expression for both unimodal and bimodal soils was not able to predict the observed unsaturated K. Only a joint fitting of measured θ(h) and K(h) functions provided parameter estimates that were able to describe unsaturated K for uni‐ and bimodal soils. In addition, we observed a negative relationship between α and n in the case of low sand content (&lt;52%) for both unimodal and bimodal matrix domain properties, contradicting the classical notion. The ratio of α for the macropore and matrix domain was positively correlated with the fraction of macropores and sand content. We anticipate that the results will contribute to deriving PTF for structured soils and avoid unrealistic combinations of MvG parameters.

On several numerical strategies to solve Richards’ equation in heterogeneous media with finite volumes

We propose several numerical approaches building on upstream mobility two-point flux approximation finite volumes to solve Richards’ equation in domains made of several rock-types. Our study encompasses four different schemes corresponding to different ways to approximate the nonlinear transmission condition systems arising at the interface between different rocks consisting in the continuity of the pressure and the fluxes, as well as different resolution strategies based on Newton’s method with variable switch. We benchmark the robustness and accuracy of the different methods on filling and drainage test cases with standard nonlinearities of Brooks-Corey and van Genuchten-Mualem type, as well as with challenging steep nonlinearities.

Tracing lateral subsurface flow in layered soils by undisturbed monolith sampling, targeted laboratory experiments, and model‐based analysis

AbstractLateral subsurface flow (LSF) is a phenomenon frequently occurring in the field induced by local water saturation along horizon boundaries under nonequilibrium conditions. However, observations of LSF in undisturbed soils under controlled irrigation in the laboratory are limited but needed for model improvement, prediction, and quantification of LSF. We present a method for extracting an undisturbed soil monolith along a soil horizon boundary and introduce an experimental setup for the measurement of LSF and an irrigation device for simulating rainfall. An experimental test run was simulated using HYDRUS 2D. Water infiltrating into the monolith and flowing either laterally along the horizon boundary or vertically through the bottom horizon could be separately captured by suction discs at the side and the bottom. Thus, a clear distinction between lateral and vertical flow was possible. Pressure heads and water contents were recorded by tensiometers and frequency domain reflectometry (FDR) sensors distributed across the monolith in a regular two‐dimensional, vertical, cross‐sectional pattern. Sensor readings indicated the presence of nonequilibrium conditions within the monolith. Modeling results could reproduce the lateral and vertical outflow of the monolith under constant irrigation, thus showing that water flow within the monolith under steady‐state conditions can be explained by the Richards equation and the van Genuchten–Mualem model. The presented method can be used to improve and verify models designed for the prediction of the onset of LSF including that induced by local nonequilibrium conditions.

Beware of scaling artefacts and implicit model characteristics when fitting soil water release and moisture capacity data

The primary objectives of this study were to: ( i) elucidate the impacts of nonlinear scale transformations on the shapes and parameter values of soil water release and moisture capacity curves; and ( ii) demonstrate how implicit characteristics of some established soil water release and moisture capacity models can impact model-data fits and estimates of model parameters. Nonlinear scale transformations of the tension head ( h) axis (e.g., log10 h, h1/2) were found to distort release and capacity curve shapes, create fictitious curve inflections and modes, and occasionally erase visual evidence of actual inflections and modes. The popular van Genuchten–Mualem and Assouline–Grant models were shown to always generate a release curve inflection and a capacity curve mode, even when inflections and modes did not exist in the data, and this in turn caused poor model-data fits in the critical near-saturated region. The van Genuchten model with four independently fitted parameters and the Dexter–Weibull model could accurately fit data sets with no inflection or mode, but this resulted in a physically unrealistic zero-angle intersection between the release curve and the water content axis. It was concluded that nonlinear h axis transforms should not be used when determining inflections, modes, pore size distributions, soil structure parameters, or soil quality indexes from soil water release and moisture capacity data-sets. It was also recommended that more flexible release curve models should be developed that do not assume the existence of inflections and modes, and also produce physically realistic angles of intersection between the water content axis and the fitted model.

Experimental study on gas permeability of cement-based materials

Gas permeability is an important property associated with the durability of cement-based materials. In this study, an experimental method based on applying a quasi-stationary flow is adopted to evaluate the gas permeability of cement-based materials. The results indicate that the intrinsic permeability of dried cement-based materials is affected by the addition of limestone powder, fly ash, and aggregate. The Katz-Thompson equation could predict the intrinsic permeability by using the capillary porosity, average diameter, and pore tortuosity. The intrinsic permeability of partially saturated cement-based materials decreases when the water saturation increases. The Van Genuchten-Mualem model could describe the relative gas permeability of partially saturated cement-based materials, and the model parameters n value between 1 and 2 while m value ranging from 0.64 to 0.69 for cement and mortar. Moreover, the power function relationship between the intrinsic permeability and Klinkenberg constant of cement-based materials has also been corroborated. Finally, a prediction model of gas permeability of cement-based materials under arbitrary water saturation and pressure gradient is proposed.

КАЧЕСТВО ВОСПРОИЗВЕДЕНИЯ СОСТОЯНИЯ ПОЧВЫ МОДЕЛЬЮ ДЕЯТЕЛЬНОГО СЛОЯ СУШИ ИВМ РАН - МГУ В СОСТАВЕ МОДЕЛИ ПРОГНОЗА ПОГОДЫ ПЛАВ

In situ soil moisture and temperature observations are used to evaluate soil moisture and temperature analysis of the global atmospheric model SL-AV for the summer season of 2014 across Western Europe. It is shown that the seasonal temperature analysis trends are reproduced better than the seasonal trends of soil moisture. Numerical experiments with the offline land surface scheme demonstrated that the implementation of the Mualem-van Genuchten water retention curve has the advantage for describing the processes of soil moisture transfer in comparison with Brooks-Corey parameterization. The last one is used in the basic version of the model. The Mualem-van Genuchten function provides better computational stability of the soil model in case of soils with high coarse grain content. An important contribution to the soil moisture error in the analysis and forecast is caused by specifying an inaccurate profile of the soil granulometric composition. It indicates a need to involve state-of-the-art databases for soil characteristics

SPATIAL VARIABILITY OF HYDRO-RELATED PHYSICAL PROPERTIES OF AL-RASHEED LOAM

A field study was conducted on 2 hectare area at Al- Rashid district, south of Baghdad to analyze the spatial variability of saturated hydraulic conductivity (Ks), initial infiltration rate (IR), Porosity (F) and bulk density (BD). Based on measured BD values Rosetta software was used in this study to estimate water retention parameters, water content at θ33 and θ1500 kPa and unsaturated hydraulic conductivity at 33 kPa(k33), 100 kPa(k100) and 1500 kPa(k1500) according to Van Genuchten-Mualem model. Measured and predicted data were analyzed both statistically and geostatistically and, the results showed a strong to moderate spatial dependence for the studied characteristics. The spatial correlation values (r2) were obtained with a spherical model for Ks, θ33, θ1500, k33, k100 and k1500, an exponential model for IR, and a Gaussian model for F and BD. Ks increased significantly with increasing of IR (r2 = 0.49**) and decreased with increasing of F and BD, IR increased with decreasing of BD (r2 = -0.326*) and BD increased with increasing of F (r2 = 0.989 **). In general the spatial distribution was moderately skewed (-0.5 to 0.5) for the studied characteristics with pronounced kurtosis (&gt;2.5). The limit distance for the search radius to estimating spatial dependency varied from 29.9 m for BD to 105 m for IR.

Comment on Cabrera et al. A User-Friendly Tool to Characterize the Moisture Transfer in Porous Building Materials: FLoW1D. Appl. Sci. 2020, 10, 5090

In July 2020, this journal published “A User-Friendly Tool to Characterize the Moisture Transfer in Porous Building Materials: FLoW1D”. That article presents and applies a forward-Euler-based tool, implemented in Visual Basic for Applications in Excel, for simulating moisture transfer in building materials. In that tool, the building materials’ hygric properties are described via the unimodal van Genuchten and Mualem equations. All parameters needed therein are inversely identified from only a capillary absorption experiment. These are three feats that, if valid, would strongly progress the state-of-the-art on moisture transfer simulation, hygric property description, and hygric property characterisation. This critique voices severe doubts, however, about the applicability of FLoW1D, the adequacy of the van Genuchten-Mualem equations, and (most fundamentally) the uniqueness of the inverse characterisation.

Physical-hydric properties of Oxisols as influenced by soil structure and clay mineralogy

The soil water retention curve (SWRC) and soil hydraulic conductivity (K) are important soil hydraulic properties. In Oxisols, the degree of microaggregation depends on the amount of iron and aluminum oxides, kaolinite and biological activity engaged in modifying the pore size distribution (PSD) of the soil porous system. The objectives of this study were (i) to characterize four Brazilian Oxisols in terms of SWRC and PSD, using undisturbed (structural SWRCs) and disturbed (textural SWRCs) soil samples; (ii) to apply the van Genuchten-Mualem (vGM) model to the prediction of K and (iii) to correlate the classes of porosity and saturated hydraulic conductivity (Ksat) with the physical, chemical and mineralogical properties. Four soils were studied: Xantic Kandiustox, Rhodic Haplustox, Anionic Acrustox and Typic Hapludox. The soil samples were collected from the Bw horizon of each soil. The structural SWRCs were determined by Haine’s funnels and Richards’ chambers, whereas the textural SWRCs were determined by dew point meter. Ksat was evaluated by constant head permeameter and, additionally, soil chemical and mineralogical analyses were prepared. It was concluded that: (i) the four soils showed bimodal PSD; (ii) the four soils presented the maximum frequency of equivalent radius in the class of macropores (structural SWRCs) with rmax varying between 43.37 and 88,98 μm, and in the class of cryptopores (textural SWRCs) with rmax varying between 0.012 and 0.014 µm; (iii) the higher the Ksat, the higher the K predicted by the vGM model over the entire soil water content range of the structural SWRCs, except for Xanthic Kandiustox and Typic Hapludox in which this phenomenon occurred closer to saturation; (iv) the K values estimated by the vGM model from textural SWRCs were very low, varying approximately from 10−25 to 10−11mm h−1 for the four soils; (v) the degree of microaggregation of Rhodic Haplustox and Anionic Acrustox resulting from the high levels of Fe and Al oxides, leading to the formation of greater inter-aggregate space, had an influence on the high Ksat and showed that the mineralogy of the clay fraction was decisive in the physical-hydric behavior of these soils.

PREDICTION OF SOIL HARD-SETTING USING SOIL MOISTURE RETENTION DATA AND ITS RELATION WITH DEGREE OF GYPSIFEREOUS SOIL COMPACTNESS

A laboratory experiment was carried out to predict soil hard-setting index (H-index) depending on soil moisture retension curve and its relationship soil degree of soil compactness (%DC) for seven soil samples with different gypsum content (62-443 g kg-1). Soil samples with (G2) 106, (G3) 153, (G4) 202, (G5) 245 and (G6) 337 g kg-1 gypsum content were prepared by mixing of surface soil layer soil with low gypsum content (G1) 62 g kg-1 with sub-surface with high gypsum content (G7) 443 g kg-1. The soil moisture retension curve of the soil samples were measured at tensions 0,5, 15, 33, 100, 500, 700, 1000 and 1500 kPa and at the soil bulk densities 1.2, 1.4, 1.6 and 1.8 Mg m-3. Soil hard setting (H-index),was determined according to van Genuchten-Mualem equation. The results indicate that soil hard setting index ( H-index) was negatively correlated with soil gypsum content. It decreases with increasing soil gypsum content. The soil bulk density was positively correlated with H-index, and Degree of soil compaction (%DC) was positively correlated with H-index for all gypsiferous soil samples.

Modeling seasonal soil moisture dynamics in gley soils in relation to groundwater table oscillations in eastern Croatia

This study aims to explain complex vadose zone hydrology of fine-textured (gley) agricultural soils influenced by a shallow and dynamic groundwater (GW) levels. The field site was located in the Biđ field (Eastern Croatia), where a detailed soil survey was performed. The simulations included a three-year period (2016–2018) at four locations. Soil hydraulic parameters (SHP) were estimated based on variables determined in the laboratory, while soil water flow was monitored using in-field zero-tension lysimeters. Piezometers were installed and used to monitor daily oscillations of groundwater levels (average depth to GW 2.2 m), while data from nearby Sava River was monitored. Unsaturated flow and water regime assessment was performed using HYDRUS-1D numerical modeling. Additional SHP optimization of van Genuchten-Mualem parameters (α and n) was performed using Shuffled Complex Evolution algorithm (SCE). The autocorrelation analysis was used to detect patterns in the precipitation, GW, and river level time series, while the Mutual Information (MI) was used to estimate the codependence of the processes in unsaturated zone and the main hydrological events. The model successfully (R2 0.72 – 0.94) reproduced measured lysimeters outflows. The outflows from lysimeters were connected to precipitation patterns, transpiration intensity, and soil moisture content influenced by the shallow water table. Comparable MI values obtained for precipitation, GW, and river level suggest a concurrent role of these parameters in the unsaturated flow dynamics. The relationship between upward flux/water storage change into the domain, and transpiration/growth stages, suggests a strong connection between the water fluxes and the root water uptake. Results confirm the importance of GW for the agricultural production due to the major influence on upper soil layer moisture.

Determining the unsaturated hydraulic conductivity of remoulded loess with filter paper method and soil column seepage test

Loess is very widely distributed, and the unsaturated hydraulic conductivity of loess is related to many engineering issues. To determine the unsaturated hydraulic conductivity of remoulded loess more conveniently and at a lower cost, filter paper test and soil column seepage test were carried out. The results indicate that in the one-dimensional soil column seepage process, the unsaturated hydraulic conductivity of loess increases with the increase of the volumetric water content, and as the seepage time continues, the unsaturated hydraulic conductivity of loess from the top to the depth of 40 cm gradually becomes uniform. The changes in the microstructure indicate that the collapsible settlement will occur during the seepage process, which will change the pore structure of loess, thereby reducing the unsaturated hydraulic conductivity of the underlying loess. Compared with the experimental results, the soil hydraulic conductivity curve (SHCC) obtained by the van Genuchten–Mualem model (VG–M model) underestimates the magnitude of unsaturated hydraulic conductivity in the part with a low volumetric water content (< 20%). and the Childs and Collis-George model (CCG model) has more consistent results with the experimental results, because it is based on more segments of the soil–water characteristic curve (SWCC).

A modeling framework to quantify the effects of compaction on soil water retention and infiltration

AbstractThe water retention curve (WRC) of arable soils from the southeastern United States at different levels of compaction (no compaction, and 10 and 20% increases in soil bulk density) was estimated using the van Genuchten–Mualem (VG) model. The VG water retention parameters of the noncompacted soils were obtained first by fitting measured soil hydraulic data. To construct the WRC of the compacted soils, gravimetric values of the permanent wilting point (θgw, 1,500 kPa) and the residual (θgr) water content were assumed to remain unchanged with compaction. The VG parameter α and exponent η after compaction were estimated using two approaches. In Approach 1, α and η were estimated from saturation, the permanent wilting point, and the residual water content. In Approach 2, the value of η was assumed to remain unchanged with compaction, which allowed α to be estimated immediately from the VG equation. Approach 2 was found to give slightly better agreement with measured data than Approach 1. The effect of compaction on the saturated hydraulic conductivity (Ks) was predicted using semitheoretical approaches and the VG‐WRC function. HYDRUS‐1D was further used to simulate vertical infiltration into a single‐layered soil profile to determine the impact of compaction on the infiltration characteristics of the soils used in our analyses. Results showed that a 10–20% increase in soil bulk density, due to compaction, reduced cumulative infiltration (Ic) at time T = Tfinal (steady‐state) by 55–82%, and the available water storage capacity by 3–49%, depending upon soil type.

Non-isothermal water retention curve model for adsorption

Non-isothermal water retention curve (WRC) in high suction range is a fundamental and interpretative tool to describe the behavior of bentonite and is crucial to ensure the safety and effective operation of high-level nuclear waste repository. In this study, an adsorption equation at given water content is proposed according to Kelvin equation, Clausius-Clapeyron equation and the adsorption enthalpy equation. Then, the proposed adsorption equation is incorporated into van Genuchten-Mualem model to establish a non-isothermal WRC model for adsorption. Four series of non-isothermal WRC data in a temperature range (293∼353 K) and high suction range (>1 MPa) from four different soils are employed to illustrate the application and performances of the proposed model. The proposed WRC model provides good agreement between the calibrated/predicted and measured non-isothermal WRCs.

A scaling procedure for straightforward computation of sorptivity

Abstract. Sorptivity is a parameter of primary importance in the study of unsaturated flow in soils. This hydraulic parameter is required to model water infiltration into vertical soil profiles. Sorptivity can be directly estimated from the soil hydraulic functions (water retention and hydraulic conductivity curves), using the integral formulation of Parlange (1975). However, calculating sorptivity in this manner requires the prior determination of the soil hydraulic diffusivity and its numerical integration between initial and final saturation degrees, which may be difficult in some situations (e.g., coarse soil with diffusivity functions that are quasi-infinite close to saturation). In this paper, we present a procedure to compute sorptivity using a scaling parameter, cp, that corresponds to the sorptivity of a unit soil (i.e., unit values for all parameters and zero residual water content) that is utterly dry at the initial state and saturated at the final state. The cp parameter was computed numerically and analytically for five hydraulic models: delta (i.e., Green and Ampt), Brooks and Corey, van Genuchten–Mualem, van Genuchten–Burdine, and Kosugi. Based on the results, we proposed brand new analytical expressions for some of the models and validated previous formulations for the other models. We also tabulated the output values so that they can easily be used to determine the actual sorptivity value for any case. At the same time, our numerical results showed that the relation between cp and the hydraulic shape parameters strongly depends on the chosen model. These results highlight the need for careful selection of the proper model for the description of the water retention and hydraulic conductivity functions when estimating sorptivity.