Soil Hydraulic Conductivity Curves Research Articles

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.

The effect of amorphous silica on soil–plant–water relations in soils with contrasting textures

This study investigates how amorphous silica (ASi) influences soil–plant–water interactions in distinct soil textures. A sandy loam and silty clay soil were mixed with 0 and 2% ASi, and their impact on soil retention and soil hydraulic conductivity curves were determined. In parallel, tomato plants (Solanum lycopersicum L.) were grown in experimental pots under controlled conditions. When plants were established, the soil was saturated, and a controlled drying cycle ensued until plants reached their wilting points. Soil water content, soil water potential, plant transpiration rate, and leaf water potential were monitored during this process. Results indicate a positive impact of ASi on the sandy loam soil, enhancing soil water content at field capacity (FC, factor of 1.3 times) and at permanent wilting point (PWP, a factor of 3.5 times), while its effect in silty clay loam was negligible (< 1.05 times). In addition, the presence of ASi prevented a significant drop in soil hydraulic conductivity (Kh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${K}_{h}$$\\end{document}) at dry conditions. The Kh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${K}_{h}$$\\end{document} of ASi-treated sandy loam and silty clay at PWP were 4.3 times higher than their respective control. Transpiration rates in plants grown in ASi-treated sandy loam soil under soil drying conditions were higher than in the control, attributed to improved soil hydraulic conductivity. At the same time, no significant difference was observed in the transpiration of plants treated with ASi in silty clay soil. This suggests ASi boosts soil–plant–water relationships in coarse-textured soils by maintaining heightened hydraulic conductivity, with no significant effect on fine-textured soils.

Prediction of absolute unsaturated hydraulic conductivity – comparison of four different capillary bundle models

Abstract. To model water, solute, and energy transport in porous media, it is essential to have accurate information about the soil hydraulic properties (SHPs), i.e., the water retention curve (WRC) and the soil hydraulic conductivity curve (HCC). It is important to have reliable data to parameterize these models, but equally critical is the selection of appropriate SHP models. While various expressions for the WRC are frequently compared, the capillary conductivity model proposed by Mualem (1976a) is widely used but rarely compared to alternatives. The objective of this study was to compare four different capillary bundle models in terms of their ability to accurately predict the HCC without scaling the conductivity function by a measured conductivity value. The four capillary bundle models include two simple models proposed by Burdine (1953) and Alexander and Skaggs (1986), which assume a bundle of parallel capillaries with tortuous flow paths, and two more sophisticated models based on statistical cut-and-random-rejoin approaches, namely those proposed by Childs and Collis-George (1950) and the aforementioned model of Mualem (1976a). To examine how the choice of the WRC parameterization affects the adequacy of different capillary bundle models, we utilized four different capillary saturation models in combination with each of the conductivity prediction models, resulting in 16 SHP model schemes. All schemes were calibrated using 12 carefully selected data sets that provided water retention and hydraulic conductivity data over a wide saturation range. Subsequently, the calibrated models were tested and rated by their ability to predict the hydraulic conductivity of 23 independent data sets of soils with varying textures. The statistical cut-and-random-rejoin models, particularly the Mualem (1976a) model, outperformed the simpler capillary bundle models in terms of predictive accuracy. This was independent of the specific WRC model used. Our findings suggest that the widespread use of the Mualem model is justified.

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).

Developing Pseudo Continuous Pedotransfer Functions for International Soils Measured with the Evaporation Method and the HYPROP System: II. The Soil Hydraulic Conductivity Curve

Direct measurement of unsaturated hydraulic parameters is costly and time-consuming. Pedotransfer functions (PTFs) are typically developed to estimate soil hydraulic properties from readily available soil attributes. For the first time, in this study, we developed PTFs to estimate the soil hydraulic conductivity (log(K)) directly from measured data. We adopted the pseudo continuous neural network PTF (PCNN-PTF) approach and assessed its accuracy and reliability using two independent data sets with hydraulic conductivity measured via the evaporation method. The primary data set contained 150 international soils (6963 measured data pairs), and the second dataset consisted of 79 repacked Turkish soil samples (1340 measured data pairs). Four models with different combinations of the input attributes, including soil texture (sand, silt, clay), bulk density (BD), and organic matter content (SOM), were developed. The best performing international (root mean square error, RMSE = 0.520) and local (RMSE = 0.317) PTFs only had soil texture information as inputs when developed and tested using the same data set to estimate log(K). However, adding BD and SOM as input parameters increased the reliability of the international PCNN-PTFs when the Turkish data set was used as the test data set. We observed an overall improvement in the performance of PTFs with the increasing number of data points per soil textural class. The PCNN-PTFs consistently performed high across tension ranges when developed and tested using the international data set. Incorporating the Turkish data set into PTF development substantially improved the accuracy of the PTFs (on average close to 60% reduction in RMSE). Consequently, we recommend integrating local HYPROPTM (Hydraulic Property Analyzer, Meter Group Inc., USA) data sets into the international data set used in this study and retraining the PCNN-PTFs to enhance their performance for that specific region.

A hysteretic hydraulic constitutive model for unsaturated soils and application to capillary barrier systems

Unsaturated soils exhibit water retention hysteresis, with different water retention behaviour during drying and wetting paths. Water retention hysteresis has often been modelled using expressions for the main drying and main wetting water retention curves that are unsatisfactory at low values of degree of saturation. In addition, the effect of retention hysteresis on the unsaturated hydraulic conductivity behaviour has typically not been explicitly considered. This paper presents a new hysteretic hydraulic constitutive model for the water retention and hydraulic conductivity behaviour of unsaturated soils, which is effective and easy to apply. The model includes: (i) main wetting and main drying water retention curves modelled with a modified version of the van Genuchten model, improved at low degree of saturation; (ii) hysteretic scanning water retention curves modelled using a bounding surface approach; (iii) the effect of hydraulic hysteresis on a soil hydraulic conductivity curve (SHCC) model improved at low degree of saturation and including the effect of liquid film conductivity. The new hysteretic hydraulic model is then validated against experimental data. After implementation in the finite element software Code_Bright, the new hydraulic constitutive model is applied in a numerical study of the impact of hydraulic hysteresis on the behaviour of capillary barrier systems (CBSs). Water retention hysteresis, which has typically been neglected in the modelling of the hydraulic behaviour of CBSs, is shown to have a significant impact on: (i) movement and redistribution of water within the finer layer of a CBS; (ii) the phenomenon of water breakthrough across the interface between the finer and coarser layers of a CBS and the subsequent restoration of the CBS after infiltration at the ground surface ceases; (iii) the prediction of evaporation from a CBS into the atmosphere.

Utilizing Splintex 2.0 for estimating the soil hydraulic conductivity curve measured with instantaneous profile method

Soil hydraulic conductivity curve (SHCC) is a key-physical-function in hydrological and environmental studies. Measuring SHCC is a difficult and onerous task and often unfeasible in large-scale monitoring. Therefore, pedotransfer functions (PTFs) have been an alternative way for estimating SHCC. In this study, the novel version of Splintex model (Splintex 2.0) is analyzed to estimate the unsaturated soil hydraulic conductivity (K) as a function of water content (θ). Splintex 2.0 estimates the function K(θ) assuming that soil pores can be represented by equivalent capillary tubes and that the water flow rate is a function of pore size distribution. Then, the estimates of K(θ) data are fitted to the SHCC described by the van Genuchten (1980); Mualem (1976) (VGM) equation. In this study, the goodness-of-fit of K(θ) estimation was evaluated with selected 198 measured SHCCs by the instantenous profile method. Each data set contains measured information of textural composition, solid and bulk densities, total porosity, and K(θ) data. Estimated and measured SHCCs were compared dividing the analyzed soil data in four textures and computing Pearson correlation coefficient (r), mean error (ME), and root mean square error (RMSE) measures. The estimation using Splintex 2.0 revealed a mean RMSE of log10[K(θ)] of 1.17, ranging from 0.77 to 1.22, pointing for an acceptable performance for PTFs purposes.

Parametric soil water retention models: a critical evaluation of expressions for the full moisture range

Abstract. Few parametric expressions for the soil water retention curve are suitable for dry conditions. Furthermore, expressions for the soil hydraulic conductivity curves associated with parametric retention functions can behave unrealistically near saturation. We developed a general criterion for water retention parameterizations that ensures physically plausible conductivity curves. Only 3 of the 18 tested parameterizations met this criterion without restrictions on the parameters of a popular conductivity curve parameterization. A fourth required one parameter to be fixed. We estimated parameters by shuffled complex evolution (SCE) with the objective function tailored to various observation methods used to obtain retention curve data. We fitted the four parameterizations with physically plausible conductivities as well as the most widely used parameterization. The performance of the resulting 12 combinations of retention and conductivity curves was assessed in a numerical study with 751 days of semiarid atmospheric forcing applied to unvegetated, uniform, 1 m freely draining columns for four textures. Choosing different parameterizations had a minor effect on evaporation, but cumulative bottom fluxes varied by up to an order of magnitude between them. This highlights the need for a careful selection of the soil hydraulic parameterization that ideally does not only rely on goodness of fit to static soil water retention data but also on hydraulic conductivity measurements. Parameter fits for 21 soils showed that extrapolations into the dry range of the retention curve often became physically more realistic when the parameterization had a logarithmic dry branch, particularly in fine-textured soils where high residual water contents would otherwise be fitted.

Relating relative hydraulic and electrical conductivity in the unsaturated zone

Numerical modeling was used to generate pore-scale structures with different structural properties. They were partially saturated according to wetting and drainage regimes using morphological operations for a range of saturations. The hydraulic and electrical conductivities of the resulting partially saturated grain packs were numerically computed to produce relative hydraulic conductivity versus saturation and relative electrical conductivity versus saturation curves. The relative hydraulic conductivities were then compared to the relative electrical conductivities for the same saturations and it was found that relative hydraulic conductivity could be expressed as relative electrical conductivity to a power law exponent, β. This exponent β was not correlated to porosity, specific surface area, or tortuosity. It did change according to whether the soil was wetting or draining. However, a β value of 2.1 reproduced relative hydraulic conductivity from relative electrical conductivity with little added error. The effects of surface conduction on the observed power law relationship due to either low fluid electrical conductivity or increased clay content were analyzed. The relationship was found to hold for fluid conductivities typical of groundwater and for clay content of less than 5% if the clays were layered perpendicular to electrical flow. The relationship breaks down for electrical flow parallel to clay layers, which makes the choice of electrode arrangement important in cases where clay may be present. This relationship can be used with secondary pressure or saturation data to characterize a soil's hydraulic conductivity curve.

Combining a Single Hydraulic Conductivity Measurement with Particle Size Distribution Data for Estimating the Full Range Partially Saturated Hydraulic Conductivity Curve

We have developed an approach for predicting the soil hydraulic conductivity curve (HCC) of soil using soil particle‐size distribution (PSD) data and one single measurement of the hydraulic conductivity in the wet range of the HCC. Unlike other models, our approach does not need a prior determination of the soil moisture characteristic curve. The development was motivated by the fact that PSD data are often available or can be inferred from soil maps and also that the hydraulic conductivity at low matric suction can be determined easily with field infiltrometer devices. The HCC prediction was good at low matric pressures, but the model performance diminished at high matric pressures. The RMSE ranged from 0.165 to 2.016, the average being 0.755 (log‐transformed hydraulic conductivity [cm d−1]). We propose to improve the accuracy of prediction models in the dry range of the HCC in future studies.

Dynamical process upscaling for deriving catchment scale state variables and constitutive relations for meso-scale process models

Abstract. In this study we propose an uspcaling approach to derive time series of (a) REW scale state variables, and (b) effective REW scale soil hydraulic functions to test and parameterise models based on the REW approach. To this end we employed a physically based hydrological model, that represents the typical patterns and structures in the study catchment, and has previously been shown to reproduce observed runoff response and state dynamics well. This landscape- and process-compatible model is used to simulate numerical drainage and wetting experiments. The effective soil water retention curve and soil hydraulic conductivity curve are derived using the spatially averaged saturation and capillary pressure as well as averaged fluxes. When driven with observed boundary conditions during a one year simulation the model is used to estimate how the spatial pattern of soil moisture evolved during this period in the catchment. The time series of the volume integrated soil moisture is deemed as best estimate for the average catchment scale soil moisture. The approach is applied to the extensively monitored Weiherbach catchment in Germany. A sensitivity analysis showed that catchment scale model structures different from the landscape- and process compatible one yielded different times series of average catchment scale soil moisture and where not able to reproduce the observed rainfall runoff response. Hence, subscale typical heterogeneity leaves a clear fingerprint in the time series of average catchment scale saturation. In case of the Weiherbach catchment local scale heterogeneity of ks could be neglected and a simple representation of the typical hillslope scale patterns of soil types and macroporosity was sufficient for obtaining effective REW scale soil hydraulic functions. Both the effective soil hydraulic functions and time series of catchment scale saturation turned out to be useful to parameterise and test the CREW model, which is based on the REW approach and was applied to the Weiherbach catchment in a companion study Lee et al. (2006, this issue).