Van Genuchten-Mualem Research Articles

Inverse analysis of soil hydraulic parameters of layered soil profiles using physics‐informed neural networks with unsaturated water flow models

AbstractInformation about the spatial distribution of soil hydraulic parameters is necessary for the accurate prediction of soil water flow and the coupled movement of chemicals and heat at the field scale using a process‐based model. Physics‐informed neural networks (PINNs), which can provide physical constraints in deep learning to obtain a mesh‐free solution, can be used to inversely estimate soil hydraulic parameters from less and noisy training data. Previous studies using PINNs have successfully estimated soil hydraulic parameters for homogeneous soil but estimating such parameters of layered soil profiles where the interface depth and the parameters are unknown still has some difficulties. The objective of this study was to develop PINNs to inversely estimate the distribution of soil hydraulic parameters, such as saturated hydraulic conductivity and α and n of the Mualem–van Genuchten model directly within layered soil profiles by predicting changes in the pressure head from training data based on simulation results at given depths during infiltration. The impact of factors affecting PINNs performance, such as the weights assigned to each component of the loss function, time range used in error computations, and number of samples used to assess the physical constraint, was investigated. By assigning a larger weight to the physical constraint and excluding the earlier stage of infiltration in the loss function, the changes in the pressure head and the three soil hydraulic parameter distributions within the layered soil were successfully estimated. The developed PINNs can be further applied to more complex soils and can be improved.

Hydro-pedotransfer functions: a roadmap for future development

Abstract. Hydro-pedotransfer functions (PTFs) relate easy-to-measure and readily available soil information to soil hydraulic properties (SHPs) for applications in a wide range of process-based and empirical models, thereby enabling the assessment of soil hydraulic effects on hydrological, biogeochemical, and ecological processes. At least more than 4 decades of research have been invested to derive such relationships. However, while models, methods, data storage capacity, and computational efficiency have advanced, there are fundamental concerns related to the scope and adequacy of current PTFs, particularly when applied to parameterise models used at the field scale and beyond. Most of the PTF development process has focused on refining and advancing the regression methods, while fundamental aspects have remained largely unconsidered. Most soil systems are not represented in PTFs, which have been built mostly for agricultural soils in temperate climates. Thus, existing PTFs largely ignore how parent material, vegetation, land use, and climate affect processes that shape SHPs. The PTFs used to parameterise the Richards–Richardson equation are mostly limited to predicting parameters of the van Genuchten–Mualem soil hydraulic functions, despite sufficient evidence demonstrating their shortcomings. Another fundamental issue relates to the diverging scales of derivation and application, whereby PTFs are derived based on laboratory measurements while often being applied at the field to regional scales. Scaling, modulation, and constraining strategies exist to alleviate some of these shortcomings in the mismatch between scales. These aspects are addressed here in a joint effort by the members of the International Soil Modelling Consortium (ISMC) Pedotransfer Functions Working Group with the aim of systematising PTF research and providing a roadmap guiding both PTF development and use. We close with a 10-point catalogue for funders and researchers to guide review processes and research.

Influence of precipitation infiltration recharge on hydrological processes of the karst aquifer system and adjacent river

Understanding the hydrological processes of the karst aquifer system (KAS) and adjacent river can further accurately evaluate karst water storage. However, the mechanism of the KAS and adjacent river hydrological processes under precipitation infiltration recharge conditions, the micro-flow behavior of groundwater in the KAS, and changes in media saturation remain unclear. This study coupled the KAS and adjacent river through the Volume of Fluid (VOF), simulated the flow behavior of groundwater in different medium of the KAS and coupled the free flow process of the adjacent river by using the multiphase Darcy-Brinkman-Stokes (DBS) equation, applied the van Genuchten-Mualem and van Genuchten-modified Mualem equations to characterize the seepage processes in soil. The results indicate that the saturation of different porous media controlled by recharge intensity directly influences the flow behavior and flow paths of the porous media. The main groundwater flow path under low precipitation intensity (b=3) is primarily the lower porous medium, while under moderate precipitation intensity (3<b≤8), the main flow path of groundwater is the karst conduit. During heavy precipitation (8<b≤12), due to the limited capacity of karst conduit, they cannot bear the large amount of groundwater supplied from upper porous medium. The peak conduit saturation in laminar flow is 0.3 lower than that in turbulent flows. Under laminar flow conditions, the conduit drainage leads to a rapid decrease in saturation, making it easier for porous media to recharge to the conduit and discharge towards the adjacent river. The turbulent state conduit maintains a high saturation recession, but the discharge is consistently lower than laminar flow. The variation process line of average flow velocity and interfacial flow velocity are obtained using the DBS method and N-S simulation method respectively. There is a certain discrepancy between the simulation results of the two methods since the N-S simulation scheme dose not consider the water retention characteristics of the porous medium.

Inverse modeling of frequency domain-based one-dimensional soil water flow in layered soils

Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (Ks) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of Ks everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying Ks utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between Ks and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of Ks. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of Ks. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous Ks. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK Ks is very similar to that of the VG Ks, although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK Ks can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation.

Implementation and efficient evaluation of backpropagation network training algorithms in parametric simulations of soil hydraulic conductivity curve

The estimation of the soil hydraulic conductivity curve (SHCC) through machine learning tools for determining pedotransfer functions (PTFs) is essential in various agriculture, hydrological, and environmental management-related studies. The accuracy and reliability of machine learning tools such as backpropagation neural network (BNN) for estimating SHCC mainly depends on the optimization of its architecture, specifically the selection of the network training algorithms. By comparing the performance of network training algorithms, various researchers related to agriculture science, hydrology and environmental can choose the appropriate algorithm that provides the best balance of accuracy, speed, computational efficiency, and robustness for hydrological modeling purposes. Therefore, the present study assessed and compared the performance of 4 training algorithms including, gradient descent with momentum (GDM), Quasi-Newton (QN), Bayesian regularization (BR) and Levenberg-Marquardt (LM) for the estimation of the parametric-based PTFs of the van Genuchten-Mualem hydraulic conductivity equation as novelty of this research, which has not been investigated, so far. In this study four GDM, BR, LM and QN-based PTFs were derived to estimate the SHCC from different combinations of readily available properties of 86 soil samples from UNSODA database. The integral root mean square error (IRMSE) and coefficient of determination (R2) and were used to assess the estimations. The performance of BR algorithm-based PTFs on testing data varied from 4.634 to 6.690 with average 5.476 cm day−1 in terms of IRMSE, and 0.958 to 0.966 with average 0.963 in terms of R2, which provided better simulation than other training algorithms. The outcome of the present study on testing data showed that the BR algorithm was stable and robust to heterogeneous and noisy data compared to other training algorithms. Finally, development of accurate and reliable PTFs using efficient algorithms can play a crucial role in soil resource assessments, water resource management, irrigation planning, and designing effective drainage systems, because accurate knowledge of SHCC is vital for optimizing irrigation and fertilization practices and minimizing wastage of water and nutrients.

Comment on “Modified expression for unsaturated hydraulic conductivity according to Mualem–van Genuchten to allow proper computations at low pressure heads” by M. Heinen

AbstractThis comment concerns evaluation of the Mualem–van Genuchten (MvG) unsaturated soil hydraulic functions at very low (negative) pressure heads as described recently in an important study by Heinen. He showed that below some critical pressure head, the unsaturated hydraulic conductivity should be approximated by a power function, even when evaluated using double precision computations. We show that a more precise approximation is possible when the approximation is formulated in terms of effective fluid saturation (Se) rather than the pressure head, h. More general constraints are also provided when the approximated hydraulic conductivity equation should be used. The alternative formulation and constraints were implemented earlier in the SOHYP and RETC software packages.

Implementation of the Brunswick model system into the Hydrus software suite

AbstractThe Brunswick modular framework for modeling unsaturated soil hydraulic properties (SHP) over the full moisture range was implemented in the Hydrus suite. Users can now additionally choose between four different variants of the Brunswick model: (i) van Genuchten–Mualem (VGM), (ii) Brooks–Corey, (iii) Kosugi, and (iv) modified van Genuchten. For demonstration purposes, simulation results for two different setups, (i) bare soil evaporation and (ii) root water uptake, are presented, along with a comparison of the original VGM model and its Brunswick variant. Results show that the original VGM model underestimates the simulated cumulative evaporation and cumulative transpiration due to the inconsistent representation of the SHP in the dry moisture range. We also implemented a two‐step hydro‐PTF (pedotransfer function) into the Hydrus suite that converts the parameters of the original VGM model (from Rosetta) to the corresponding Brunswick variant. In that way, physically comprehensive simulations are ensured if no data on SHP are directly available, but information on physical soil properties (e.g., texture and bulk density) exists.

Analytical solution for steady vertical flux through unsaturated soils based on van Genuchten-Mualem model

Various analytical solutions for steady-state vertical flux through unsaturated soils exist in the literature. These solutions often assume specific hydraulic conductivity forms such as exponential form, rational power form, or power-law form such as the Brooks-Corey model. The van Genuchten-Mualem model is widely used in practical applications of flow through unsaturated soils. It is among the most complicated hydraulic conductivity forms for which no analytical solutions are available. This paper deals with the development of an analytical solution for steady-state vertical flux using van Genuchten-Mualem model. The analytical solution is obtained using Maclaurin series expansions and the multinomial theorem. The general form expresses the depth as a function of pressure head. The analytical solution can be used to model both infiltration (positive flux rate) and evaporation (negative flux rate). The derived analytical solution is compared with numerical results and shows excellent agreement. It can also be used to identify the hydraulic parameters analytically, eliminating the need of a numerical inverse procedure. As far as the author’s knowledge, the proposed solution is the first analytical solution dealing with van Genuchten-Mualem model, which is directly derived from the flow equation without any predefined mathematical form of the pressure head.

Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments

Green roofs can be a valid solution for stormwater management in urban environments. The objective of this study was to develop a laboratory procedure for the hydraulic characterization of artificial substrates, used in the realization of green roofs, based on transient evaporation and steady-state unit hydraulic gradient (UHG) experiments. The retention, θ(h), and hydraulic conductivity, K(h), curves of two commercial substrates Terra Mediterranea® (TMT) and AgriTERRAM® (ATV) and a specifically developed substrate made by mixing peat, compost and sandy loam soil (MIX) were investigated. The unimodal van Genuchten–Mualem (VGM) hydraulic functions obtained by the direct evaporation method with different choices of the fitting parameters were compared with UHG measurements of K(h) conducted close to saturation. A numerical inversion of the transient evaporation experiments performed by Hydrus-1D software was also conducted, assuming that the hydraulic properties could be expressed either by unimodal or bimodal VGM models. The results indicated that an appropriate a priori choice of the residual water content parameter improved the estimation of the water retention curve. Moreover, the water retention data estimated from the direct evaporation method were not statistically different from those obtained with the inverse Hydrus-1D. The unsaturated hydraulic conductivity estimations obtained by the direct and inverse methods were highly correlated and the use of the bimodal VGM model improved the estimation of K(h) in the wet range. The numerical inversion of laboratory evaporation data with the hydraulic characteristics expressed by the bimodal VGM model proved to be a reliable and effective procedure for hydraulic characterization of artificial substrates, thus improving the reliability of simulated water fluxes in green roofs.

Stochastic analysis of plant available water estimates and soil water balance components simulated by a hydrological model

AbstractThe uncertainty in soil hydraulic parameters is often not taken into account in process‐based hydrological modeling. Performing runs with 104 stochastic parameter realizations, we evaluated the propagation of uncertainty in the Van Genuchten–Mualem (VGM) parameters into estimates of the threshold values of soil water content used to calculate the total and readily available water, and on the long‐term (30 years) simulations of evaporation, transpiration, bottom flux, and runoff by the SWAP hydrological model. The simulated scenarios included weather data from a location in southeast Brazil and seven soils from the same region cropped with maize, comprising a wide range of texture classes. The results showed that uncertainties in VGM parameters affect the estimates of total and readily available water. Water balance components obtained by a deterministic simulation with average VGM parameters did not always agree with the average or median of stochastic simulations, and stochastic simulations including parameter uncertainties should be preferred. Variations in yearly rainfall characteristics were more important for bottom flux and evaporation, while transpiration and runoff were more strongly influenced by the variations in soil hydraulic properties.

Coupled hydrogeophysical inversion of an artificial infiltration experiment monitored with ground-penetrating radar: synthetic demonstration

Abstract. In this study, we investigate the use of ground-penetrating radar (GPR) time-lapse monitoring of artificial soil infiltration experiments. The aim is to evaluate this protocol in the context of estimating the hydrodynamic unsaturated soil parameter values and their associated uncertainties. The originality of this work is to suggest a statistical parameter estimation approach using Markov chain Monte Carlo (MCMC) methods to have direct estimates of the parameter uncertainties. Using the GPR time data from the moving wetting front only does not provide reliable results. Thus, we propose to use additional information from other types of reflectors to optimize the quality of the parameter estimation. Water movement and electromagnetic wave propagation in the unsaturated zone are modeled using a one-dimensional hydrogeophysical model. The GPR travel time data are analyzed for different reflectors: a moving reflector (the infiltration wetting front) and three fixed reflectors located at different depths in the soil. Global sensitivity analysis (GSA) is employed to assess the influence of the saturated hydraulic conductivity Ks, the saturated and residual water contents θs and θr, and the Mualem–van Genuchten shape parameters α and n of the soil on the GPR travel time data of the reflectors. Statistical calibration of the soil parameters is then performed using the MCMC method. The impact of the type of reflector (moving or fixed) is then evaluated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. GSA results show that the sensitivities of the GPR data to the hydrodynamic soil parameters are different between moving and fixed reflectors, whereas fixed reflectors at various depths have similar sensitivities. Ks has a similar and strong influence on the data of both types of reflectors. Concerning the other parameters, for the wetting front, only θs and α have an influence, and only at long time steps since the total variance is zero at the very beginning of the experiment. On the other hand, for the fixed reflectors, the total variance is not zero at the very start and the parameters θs, θr, α and n can have an influence from the very beginning of the infiltration. Results of parameter estimation show that the use of calibration data from the moving or fixed reflectors alone does not enable a good identification of all soil parameters. With the moving reflector, the error between the estimated mean value and the exact target value for θr and α is 9 % and 45 %, respectively, and less than 3 % for the other parameters. The best reduction of the size of the parameter distribution is obtained for n, with a posterior distribution 9 times smaller than the prior one. For the others, this reduction ratio varies between 1 and 5. For the fixed reflectors, the estimated mean values are far from the target values for α, θr and n, representing for a reflector located at 120 cm 15 %, 27 %, and 121 %, respectively. On the other hand, when both data are combined, all soil parameters can be well estimated with narrow confidence intervals. For instance, when using both data from the moving wetting front and a fixed reflector located at 120 cm for calibration, the estimated mean values of the errors of all parameters are less than 5 %. Moreover, all parameter distributions are well reduced, with a maximum reduction for Ks, leading to a posterior distribution being 46 times smaller than the prior one, and the worst but still satisfactory being for θr for which the posterior distribution is 8 times smaller than the prior one. The methodology was applied to fine, medium, and coarse sands with very good results, particularly for the finest soil. The thickness of the unsaturated zone was also tested (0.5, 1, and 2 m) and a better estimation of the hydrodynamic parameters is obtained when the water table is deeper. In addition, the height of water applied in the infiltrometry test influences the speed of the test without affecting the performance of the proposed method.

Approximation of van Genuchten Parameter Ranges from Hydraulic Conductivity Data.

The use of retention function and relative conductivity function is essential for the calculation of flow in a variably saturated media using the Richards equation. A widely used mathematical model for this is the Mualem-van Genuchten model which requires the shape parameters and . These, however, are difficult to obtain. When data is scarce, and are often taken from literature and may deviate largely from actual values. The current study presents a novel mathematical model for the approximation of and and for the further estimation of realistic value ranges, which may be used as parameter space, for example, for the calibration of a numerical model. The model was developed for cases where data is scarce and only values of saturated hydraulic conductivity are available. It is based on a large data set from literature and it is demonstrated that the model estimates mean values from that data set with a good accuracy. In order to show the applicability of the model, a second data set has been compiled anew (provided as Supporting Information). The model is incorporated into the current version of the freeware computer program HYPAGS, which enables easy usage.

Soil water retention and hydraulic conductivity measured in a wide saturation range

Abstract. Soil hydraulic properties (SHPs), particularly soil water retention capacity and hydraulic conductivity of unsaturated soils, are among the key properties that determine the hydrological functioning of terrestrial systems. Some large collections of SHPs, such as the UNSODA and HYPRES databases, have already existed for more than 2 decades. They have provided an essential basis for many studies related to the critical zone. Today, sample-based SHPs can be determined in a wider saturation range and with higher resolution by combining some recently developed laboratory methods. We provide 572 high-quality SHP data sets from undisturbed, mostly central European samples covering a wide range of soil texture, bulk density and organic carbon content. A consistent and rigorous quality filtering ensures that only trustworthy data sets are included. The data collection contains (i) SHP data, which consist of soil water retention and hydraulic conductivity data, determined by the evaporation method and supplemented by retention data obtained by the dewpoint method and saturated conductivity measurements; (ii) basic soil data, which consist of particle size distribution determined by sedimentation analysis and wet sieving, bulk density and organic carbon content; and (iii) metadata, which include the coordinates of the sampling locations. In addition, for each data set, we provide soil hydraulic parameters for the widely used van Genuchten–Mualem model and for the more advanced Peters–Durner–Iden model. The data were originally collected to develop and test SHP models and associated pedotransfer functions. However, we expect that they will be very valuable for various other purposes such as simulation studies or correlation analyses of different soil properties to study their causal relationships. The data are available at https://doi.org/10.5880/fidgeo.2023.012 (Hohenbrink et al., 2023).

Development and functional evaluation of pedotransfer functions for estimating soil hydraulic properties in Portuguese soils: Implications for soil water dynamics

Accurate knowledge of soil hydraulic properties is essential for effectively simulating soil water dynamics in field plots. However, determining these properties directly can be challenging, especially when a large amount of data is required. Therefore, the primary objective of this study was to develop four hierarchical pedotransfer functions (PTFs) to estimate the soil hydraulic parameters of the Mualem-van Genuchten model. The PTFs that were developed ranged from utilizing a limited set of variables to those comprising a more comprehensive set of variables. These included particle size distribution, soil bulk density, soil depth, and soil water contents at matric potentials of −33 and − 1580 kPa. The functional performance of these PTFs was also assessed in simulations of the soil water balance in ten agricultural fields over two growing seasons using the HYDRUS-1D model. The simpler PTFs exhibited moderate accuracy in estimating soil water contents at different matric potentials, while the more complex PTFs with a greater number of variables yielded increasing accuracy. However, estimation errors were more noticeable in the drier range of the soil water retention curve. The inclusion of bulk density as a predictor only affected the wetter range of the same curve. Estimation of log Ks improved from the simpler to the more complex PTFs, but the statistical indicators were consistently modest. The functional performance of the PTFs showed increased errors in simulating soil water contents in the ten study sites compared to reference simulations. The more complex PTFs with the greatest number of variables provided the best predictions in most cases. The PTFs primarily affected flow conditions in the soil profile, resulting in increased soil water storage and impacting predictions of deep percolation the most. Water availability in the soil profile then influenced actual transpiration, alleviating stress in some cases but causing waterlogging in one situation. The study emphasizes the cautious use of the PTFs and the need for additional information on clay-rich soils and hydraulic conductivity data to enhance their performance.

Modified expression for hydraulic conductivity according to Mualem–van Genuchten to allow proper computations at low‐pressure heads

AbstractWater retention and hydraulic conductivity characteristics are key input data in studies on soil water dynamics in the vadose zone. The most well‐known analytical functions to describe these characteristics are those given by Mualem and van Genuchten, where van Genuchten showed that both can be described by a limited set of shared parameters. Analytically, there are no restrictions on the range of pressure heads for which these characteristics can be used. Experience, however, has shown that for certain sets of parameters, the hydraulic conductivity cannot be computed accurately at low‐pressure heads. This is due to the accuracy of (double precision) floating point operations in computer code. It is shown that for low‐pressure heads, the Mualem function approaches a power function. An adapted version of the Mualem–van Genuchten (MvG) expression for the hydraulic conductivity is proposed: between saturation and a soil‐dependent critical pressure head, the classical Mualem expression is valid and below this critical pressure head a power function is used. The power function is defined such that it matches the Mualem value at the critical pressure head. No accuracy problems will occur when using the power function until the result approaches the smallest possible (double precision) floating point value that significantly differs from zero.

Extension of the Gardner exponential equation to represent the hydraulic conductivity curve: Inclusion of macropore flow effects

In soil hydraulics, it is crucial to establish an accurate representation of the relative hydraulic conductive curve (rHCC), K_r(h). This paper proposes a simple way to determine K_r(h), called the Modified Gardner Dual model (MGD), using a logarithmic extension of the classical Gardner exponential representation and including macropore flow effects. MGD has five parameters which are hydraulic constants clearly identified in the bilogarithmic representation of K_r(h). Two of them are related to the main inflection point coordinates of rHCC; from them, it is possible to determine the macroscopic capillary length of the infiltration theory. The model was tested in the suction interval 0 < h < 15,000 cm with a total of 249 soil samples from two databases, and employing a flexible representation of the Mualem-van Genuchten (MVG) equation as a reference. Using the RMSE statistics (with log base) to measure the fitting errors, we obtained a 31% reduction in errors (RMSE_MGD = 0.27, RMSE_MVG = 0.39). In 74% of the soils, including samples from the two databases, the reduction was 53% (RMSE_MGD = 0.19, RMSE_MVG = 0.40); the rHCC data fitting of this group was accurate over all the suction h intervals, with RMSE_MGD < 0.32 in each soil sample. In the remaining 26% of the samples, the quality of the MGD fitting degraded due mainly to the presence of multiple rHCC data inflection points. Therefore, in soils without this structural peculiarity, the proposed model revealed to be quite accurate in addition to being analytically simple. Another advantage of MGD is that its parameters depend mainly on the data with h around and lower than the main inflection suction value, which, in turn, never exceeded the 300-cm limit in this study. Hence, in soils that do not have multiple inflections, the extrapolations of the model in drier intervals (1000 cm < h < 15,000 cm) are reliable. The MGD parameter optimization software has been called KUNSAT. It is available in the Supplementary Material or from the corresponding author on request.

Reduce uncertainty in soil hydrological modeling: A comparison of soil hydraulic parameters generated by random sampling and pedotransfer function

Numerical simulation of unsaturated soil hydrology relies on calibrated soil hydraulic parameters, which are subject to uncertainty due to imperfect information during the inverse modelling. This study investigates the effectiveness of reducing parameter uncertainty using the recently developed Rosetta 3 pedotransfer function. The GLUE method was employed for numerical modeling using the Darcy-Richards equation under two strategies for sampling Mualem-van Genuchten (MvG) parameters: the first uses conventional random generation of MvG parameters (GLUE-random), while the second adopts Rosetta 3 to transfer soil particle composition to MvG parameter (GLUE-Rosetta). Both approaches were used for inverse modeling of 9 typical soils, each with a recommended parameter set defined as true values and associated soil moisture dynamics as observations. The posterior parameters selected with both GLUE-random and GLUE-Rosetta show an equifinality phenomenon. GLUE-random fails to provide well-constrained posterior parameters to recover the pre-defined true values, and its posterior results of soil water characteristic curve (SWCC) and soil hydraulic conductivity function (HCF) are poorly constrained. In contrast, GLUE-Rosetta significantly improves the accuracy of the inversely-estimated soil hydraulic parameters, and the ensemble of posterior SWCC and HCF also encompasses the predefined true curves. The results demonstrate the effectiveness of using Rosetta 3 to reduce the dimensionality of the optimization problem, which results in reliable estimation of soil hydraulic parameters and soil particle compositions. Moreover, GLUE-Rosetta outperforms GLUE-random in predicting soil moisture dynamics under different rainfall intensities. Overall, it is recommended to integrate Rosetta 3 with existing optimization tools to reduce the uncertainty of soil parameters and support more reliable modeling of unsaturated soil hydrology.

Analysis of Soil–Water Characteristics and Stability Evolution of Rainfall-Induced Landslide: A Case of the Siwan Village Landslide

This paper aimed to study the soil–water characteristics and stability evolution law of rainfall-induced landslide. Taking the two landslide events in Siwan village as an example, the formation conditions of the disaster and landslide characteristics were analyzed. Additionally, the deformation characteristics and destruction mechanisms of landslides were discussed in-depth. The soil–water characteristics and hydraulic conductivity of the landslides were analyzed based on TRIM experiment results. Geo-Studio numerical software was further used for typical sections to analyze the stability of the evolution of the landslide events under rainfall conditions. The results showed that (1) The soil–water characteristic curve (SWCC) inversely varies with water content volume, and the sliding body has lower saturated water content and matrix suction than the sliding zone. The hydraulic conductivity function (HCF) increases with water content volume, and the sliding body has higher hydraulic conductivity (0.43 m/d) than the sliding zone (0.03 m/d). (2) Rainfall is the primary cause of landslides, and there is a hysteretic effect. Heavy rainfall will inevitably accelerate the formation of landslides in the analysis of the deformation characteristics and destruction mechanisms of rainfall-induced landslides. (3) Compared with the engineering analogy of the Fredlund and Xing (FX) model, the Van Genuchten–Mualem (VGM) model of the soil–water characteristics test based on the TRIM experimental system can better reflect the actual field situation. The numerical simulation method based on the TRIM experiments of the soil–water characteristics test is scientifically sound and reliable for the stability evolution of overburden rainfall-induced landslides.

Estimating Soil Hydraulic Parameters during Ponding Infiltration Using a Hybrid Algorithm

Accurate inversion of soil hydraulic parameters based on the van Genuchten–Mualem model has received much attention in soil science research. Herein, a hybrid algorithm method using particle swarm optimization and vector-evaluated genetic algorithm was used to invert the parameters θs, α, n, and Ks, with the objective functions of infiltration rate, cumulative infiltration, and soil water content. Then, numerical experiments were conducted on four typical soils at three initial water content levels (20, 40, and 60% effective saturation) to verify the accuracy of the inverse method. The results showed that the inversed soil water retention and conductivity curves were approximately the same as the real curves, with the root mean square errors of 0.00101–0.00192 cm3·cm−3, 0.00800–0.02519 cm3·cm−3, respectively, and both the Nash-Sutcliffe coefficients were approximately 1.0. Additionally, laboratory experiments were also performed to compare with the inversed parameters for verification, within small root mean squared errors and approximately 1.0 Nash–Sutcliffe coefficients. Furthermore, the method can also achieve acceptably accurate parameter inversion even with substantial measurement errors included in the cumulative infiltration, initial water content, and final water content. Thus, the method is effective and robust and found to be practical in field experiments.

Soil water diffusivity as function of the pore size distribution and precompression stress

The idea of the study was to combine the saturation-dependent hydraulic conductivity, K(Se), as intensity parameter with the volume fraction related to the fractional capillary potential for each of the characteristic pore size classes that based on the matric flow potential, φ, and the soil water diffusivity, D(θ). The analysis is focused on the soil hydraulic properties of differently textured soils with differences in the pore size distribution, PSD. The soil-moisture retention, θ(h), and K(Se) as function of the effective saturation were determined with undisturbed samples for each soil profile and horizon and fitted by Mualem–van Genuchten type analytical function. The results indicate a strong linear relationship between φ values and the soil water diffusivity, D(θ), of soils with its volume fractions of macropores (r2: 0.65–0.91), wide coarse pores (r2: 0.55–0.77), and medium pores (r2: 0.83–0.85). The precompression stress, Pc, as mechanical soil strength parameter affects the soil water diffusivity of the chosen datasets especially in the wide coarse pore range (r2: 0.85). The results suggest that the PSD’s-related φ and D(θ) values are affected by both textural and structural effects. The soil water diffusivity itself strongly depends on the PSD and is an effective link between soil’s intensity and capacity parameter.