Estimation Of Saturated Hydraulic Conductivity Research Articles

Representative Sample Size for Estimating Saturated Hydraulic Conductivity via Machine Learning: A Proof‐Of‐Concept Study

AbstractMachine learning (ML) has been extensively applied in various disciplines. However, not much attention has been paid to data heterogeneity in databases and number of samples used to train ML models in hydrology. In this study, we addressed these issues and their impacts on the accuracy and reliability of ML models in the estimation of saturated hydraulic conductivity, Ks. We selected 17,990 soil samples from the USKSAT database and created random subsets N = 2,000, 4,000, 6,000, 8,000, 10,000, 12,000, 14,000, 16,000, and 17,990, 80% of which were used for training. The random subset selection was repeated 50 times. The extreme gradient boosting (XGBoost) algorithm was used to estimate Ks from other soil properties, such as bulk density, soil depth, texture, and organic content. For each subset, we conducted the learning curve analysis on the training and cross‐validation data sets. Results showed that for all training sample sizes the number of samples was not enough for the training and cross‐validation curves to reach a plateau. We also applied the concept of representative elementary volume by plotting the average coefficient of determination, R2, and root mean square log‐transformed error, RMSLE, against the training sample size. For the testing data set, as the number of training sample size increased from 1,600 to 14,392 the average R2 value increased from 0.74 to 0.90, while the average RMSLE value decreased from 1.08 to 0.69. Either the learning curve or representative sample size analysis is required to investigate whether the number of samples is enough or not.

Estimation of soil waterfront velocity and saturated hydraulic conductivity in a Hele-Shaw apparatus with an optical flow method

The estimation of saturated hydraulic conductivity is a key parameter for studying the water flow in the unsaturated zone of the soil. In this work, a combined modelling approach of the waterfront movement is elaborated, integrating a physical analogue type device with image analysis. A customized Hele-Shaw apparatus is designed for the wetting process visual inspection, while an optical flow algorithm is used for the numerical calculation of flow velocity and saturated hydraulic conductivity values at a pixel level of the image processing. Saturated hydraulic conductivity values estimated by the proposed method are in close agreement with values found in the literature under similar soil conditions. Also, the proposed method seems to be a useful tool for a comprehensive analysis of the waterfront movement in the vadose zone.

Estimation of saturated hydraulic conductivity with pedotransfer functions: A review

Saturated hydraulic conductivity (Ks) is a singular parameter in earth system science. Ks not only governs the rate of flow of water under a hydraulic gradient as specified by the Darcy equation for saturated conditions, but also acts as a scaling factor in many unsaturated flow and transport applications that involve pore-size distribution models. Without knowledge of saturated hydraulic conductivity, it would be difficult to accurately describe the transport of water and dissolved or suspended constituents in soils and sediments, or calculate groundwater transport and recharge, and quantify the exchange between soils and the atmosphere. While the determination of Ks is not especially difficult, it is expensive and (in many cases) infeasible to carry out field or lab experiments for large-scale applications. Pedotransfer functions (PTFs) are a class of largely data-driven empirical models that aim to estimate Ks (and often other hydraulic quantities such as water retention characteristics) from easily available data. In this review, we first briefly discuss the history of the development of the concept of saturated hydraulic conductivity and its relation to the Kozeny-Carman (KC) equation. The KC equation serves as a central point in this review because it determines which soil variables affect saturated flow at the pore-scale, a domain which now can also be visited by computational fluid dynamics models. The KC equation also provides us with a structure in which we can classify the large number of PTFs that have been developed for estimating Ks. Datasets and statistical techniques available for PTF development are discussed, and we also describe common metrics used to assess the accuracy and reliability of PTF estimates. The mutual agreement of two main classes (i.e., an effective porosity KC-based and soil texture-based) of PTFs is analyzed using a number of global maps of predicted Ks. Finally, we discuss challenges and perspectives that might lead to PTFs with improved estimates of Ks. In particular, we suggest establishing and utilizing large and completely independent databases to assess the accuracy and reliability of PTFs for global use, while also drawing in information from pedological and remote sensing sources.

Estimation of saturated hydraulic conductivity of coarse-grained soils using particle shape and electrical resistivity

Based on the similarity in the underlying mechanisms between electrical and hydraulic conduction in porous media, Archie's equation can be combined with the Kozeny-Carman (KC) equation to estimate the hydraulic conductivity (K) of coarse-grained soils. However, the assumption of the exponent m in Archie's equation, which is equivalent to the assumed porosity at specific soil electrical properties, reduces the accuracy of the value of K predicted using the combination of Archie's equation and the KC equation. Therefore, this study introduces a depolarization factor, which allows the exponent m in Archie's equation to be estimated from the shape of the particles. Consequently, this study proposes a formula for estimating K for coarse-grained soils based on the combination of Archie's equation, the KC equation, and the depolarization factor. Data from laboratory experiments performed in this work and available data from the literature were used to validate the proposed model. In addition, the optimal value for the exponent m was recommended for predicting hydraulic conductivity using the proposed K estimating formula in the absence of particle shape data. Data obtained in the experiments and literature revealed that the proposed model is comparatively reliable in predicting K.

Pedotransfer Functions for the Estimation of Saturated Hydraulic Conductivity for Some Indian Sandy Soils

Determination of the saturated hydraulic conductivity (ks) is needed in many studies and applications related to irrigation, drainage, water movement and solute transport in the soil. Although many advances are made for direct measurements of ks, they are usually time consuming and costly. Some attempts have been made to indirectly predict the saturated hydraulic conductivity from the more easily or readily available basic soil properties. The objective of this study was to develop and validate Pedotransfer Functions (PTFs) for estimation of saturated hydraulic conductivity using multiple non-linear regression technique. One hundred and one soil samples were collected from agricultural and forest soils at different depths, at different locations in the Pavanje River basin that lies in the southern coastal region of Karnataka, India. Saturated hydraulic conductivity was measured, by variable falling head method through Permeameter in the laboratory. Prediction accuracies were evaluated using coefficient of determination, root mean square error, mean error, geometric mean error ratio and geometric standard deviation of the error ratio between measured and predicted values. The results show that, the PTFs for the estimation of saturated hydraulic conductivity could be used appropriately for the soils with loamy sand and sandy loam textures falling in this area of the coastal region of southern India.

Impact of soil surface and subsurface properties on soil saturated hydraulic conductivity in the semi-arid Walnut Gulch Experimental Watershed, Arizona, USA

The estimation of saturated hydraulic conductivity (Ks) is of high relevance to correctly reproduce water fluxes, such as infiltration rates or surface runoff in hydrological simulations. Yet, estimation of Ks is challenging especially in semi-arid regions with particular soil surface characteristics like crusting and sealing. This study presents results of a field campaign in the semi-arid Walnut Gulch Experimental Watershed, Arizona (US), where surface and subsurface Ks measurements were undertaken across the watershed. Data of saturated hydraulic conductivity on crust covered and crust-free surfaces was collected and compared to results of commonly used methods to retrieve spatially distributed Ks data. Results reveal that methods typically used for estimating Ks, such as exponential decay functions or pedo-transfer functions (PTFs), can be inadequate in such regions. The analysis shows that in our study area the presence of surface crust is the dominating factor for determining the spatial distribution of Ks. Furthermore, the results reveal that remote sensing data can provide useful information for estimating surface Ks values as it could be successfully applied for the spatial detection of surface crust characteristics.

Understanding saturated hydraulic conductivity under seasonal changes in climate and land use

The goal of this study was to understand better the co-play of intrinsic soil properties and extrinsic factors of climate and management in the estimation of saturated hydraulic conductivity (Ksat) in intensively managed landscapes. For this purpose, a physically-based, modeling framework was developed using hydro-pedotransfer functions (PTFs) and watershed models integrated with Geographic Information System (GIS) modules. The integrated models were then used to develop Ksat maps for the Clear Creek, Iowa watershed and the state of Iowa. Four types of saturated hydraulic conductivity were considered, namely the baseline (Kb), the bare (Kbr), the effective with no-rain (Ke-nr) and the effective (Ke) in order to evaluate how management and seasonality affect Ksat spatiotemporal variability. Kb is dictated by soil texture and bulk density, whereas Kbr, Ke-nr, and Ke are driven by extrinsic factors, which vary on an event to seasonal time scale, such as vegetation cover, land use, management practices, and precipitation. Two seasons were selected to demonstrate Ksat dynamics in the Clear Creek watershed, IA and the state of Iowa; specifically, the months of October and April that corresponded to the before harvesting and before planting conditions, respectively.Statistical analysis of the Clear Creek data showed that intrinsic soil properties incorporated in Kb do not reflect the degree of soil surface disturbance due to tillage and raindrop impact. Additionally, vegetation cover affected the infiltration rate. It was found that the use of Kb instead of Ke in water balance studies can lead to an overestimation of the amount of water infiltrated in agricultural watersheds by a factor of two. Therefore, we suggest herein that Ke is both the most dynamic and representative saturated hydraulic conductivity for intensively managed landscapes because it accounts for the contributions of land cover and management, local hydropedology and climate condition, which all affect the soil porosity and structure and hence, Ksat.

Estimation of saturated hydraulic conductivity using fuzzy neural network in a semi-arid basin scale for murum soils of India

Saturated hydraulic conductivity, Ks is an important input parameter in modeling flow process in soil. Measurement of Ks in field is time consuming and costly. Also, due to inherent temporal and spatial variability of this parameter, large number of samples are required to characterize the areas of site. In this study, a hybrid approach consists of Fuzzy Neural Network (FNN), has been proposed to estimate Ks from limited number of field measurements using Guelph permeameter. The various soil properties such as bulk density, porosity, specific gravity, sand, clay, silt and organic matter were used as input variables and Ks was kept as output. In this study, 175 field measurements and soil samples were collected in a grid of 40 m × 200 m with uniform spacing along the slope of barren land in the site of Punanaka (Solapur city), India. To quantify the prediction accuracy, this FNN approach is compared with regression, Fuzzy Mamdani approach and artificial neural network with BP algorithm. The various statistical performance indices like root mean square error, coefficient of determination (R2), and Mean relative error were used for evaluation of model performance. It was found that the hybrid FNN approach in comparison with others could more accurately predict saturated hydraulic conductivity.

Estimation of saturated hydraulic conductivity from ring infiltrometer test taking into account the surface moisture stain extension

Abstract A large single-ring infiltrometer test was performed in order to characterize the saturated hydraulic conductivity below an infiltration basin in the well field of Lyon (France). Two kinds of data are recorded during the experiment: the volume of water infiltrated over time and the extension of the moisture stain around the ring. Then numerical analysis was performed to determine the saturated hydraulic conductivity of the soil by calibration. Considering an isotropic hydraulic conductivity, the saturated hydraulic conductivity of the alluvial deposits is estimated at 3.8 10−6 m s−1. However, with this assumption, we are not able to represent accurately the extension of the moisture stain around the ring. When anisotropy of hydraulic conductivity is introduced, experimental data and simulation results are in good agreement, both for the volume of water infiltrated over time and the extension of the moisture stain. The vertical saturated hydraulic conductivity in the anisotropic configuration is 4.75 times smaller than in the isotropic configuration (8.0 10−7 m s−1), and the horizontal saturated hydraulic conductivity is 125 times higher than the vertical saturated hydraulic conductivity (1.0 10−4 m s−1).

Controlling effects of surface crusts on water infiltration in an arid desert area of Northwest China

Purpose Surface crusts are important features in arid desert areas and are critical to hydrological processes and ecosystem development. This paper aims to understand the effects of crusts on water movement in the soil and the factors that affect this and to provide the soil parameters for estimation of saturated hydraulic conductivity (Ks) in ecohydrological models.

Estimation of saturated hydraulic conductivity from double‐ring infiltrometer measurements

SummaryThis research aims to determine soil vertical saturated hydraulic conductivity (Ks) in situ from the measured steady infiltration rate (I), initial soil properties and double‐ring infiltrometer (DRI) test data. Characterizing the effects of these variables on the measured steady infiltration rate will enable more accurate prediction of Ks. We measured the effects of the ring diameter, head of ponding, ring depth, initial effective saturation and soil macroscopic capillary length on measured steady infiltration rates. We did this by simulating 864 DRI tests with the finite element program HYDRUS‐2D and by conducting 39 full‐scale in situ DRI tests, 30 Mini‐Disk infiltrometer experiments and four Guelph Permeameter tests. The M5′ model trees and genetic programming (GP) methods were applied to the data to establish formulae to predict the Ks of sandy to sandy‐clay soils. The nine field DRI tests were used to verify the computer models. We determined the accuracy of the methods with 30% of the simulated DRI data to compare I/KS values of the finite element models with estimates from the suggested formulae. We also used the suggested formulae to predict the Ks values of 30 field DRI experiments and compared them with values measured by Guelph Permeameter tests. Compared with the GP method, the M5′ model was better at predicting KS, with a correlation coefficient of 0.862 and root mean square error (RMSE) of 0.282 cm s−1. In addition, the latter method estimated Ksvalues of the field experiments more accurately, with an RMSE of 0.00346 cm s−1.

Estimation of saturated hydraulic conductivity of Korean weathered granite soils using a regression analysis

Estimation of saturated hydraulic conductivity of Korean weathered granite soils using a regression analysis

Application of EM38 and ERT methods in estimation of saturated hydraulic conductivity in unsaturated soil

Soil apparent electrical conductivity is being considerably used as a surrogate measure for soil properties and hydraulic parameters. In this study, measurements of electrical conductivity were accomplished with electrical resistivity tomography (ERT) and EM38 to develop multiple datasets for defining spatiotemporal moisture content variations and estimating saturated hydraulic conductivity under natural conditions in an experimental site located in Lisbon, Portugal. In addition, EM38 capability in monitoring electrical conductivity variations in comparison with ERT method was examined. In order to achieve these objectives, appropriate relationships were derived based on determination of experimental curve resistivity vs. degree of saturation by in-situ investigation to convert electrical resistivity maps inferred from ERT and EM38 data to moisture content distribution maps. In addition, the surface temperature variations during the experiment were measured and the effects of the temperature variations were removed by assuming 2% change in electrical resistivity per °C change in temperature. The conducted experiment proves that the soil is fairly homogenous and semi-pervious sediment and the spatiotemporal moisture content variations during the experiment barely exceed 10%. Our calculations constrain the range of saturated hydraulic conductivity to be 3–9 (cm/day) range.

Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects

Electrical impedance tomography (EIT) is gaining importance in the field of geophysics and there is increasing interest for accurate borehole EIT measurements in a broad frequency range (mHz to kHz) in order to study subsurface properties. To characterize weakly polarizable soils and sediments with EIT, high phase accuracy is required. Typically, long electrode cables are used for borehole measurements. However, this may lead to undesired electromagnetic coupling effects associated with the inductive coupling between the double wire pairs for current injection and potential measurement and the capacitive coupling between the electrically conductive shield of the cable and the electrically conductive environment surrounding the electrode cables. Depending on the electrical properties of the subsurface and the measured transfer impedances, both coupling effects can cause large phase errors that have typically limited the frequency bandwidth of field EIT measurements to the mHz to Hz range. The aim of this paper is to develop numerical corrections for these phase errors. To this end, the inductive coupling effect was modeled using electronic circuit models, and the capacitive coupling effect was modeled by integrating discrete capacitances in the electrical forward model describing the EIT measurement process. The correction methods were successfully verified with measurements under controlled conditions in a water-filled rain barrel, where a high phase accuracy of 0.8 mrad in the frequency range up to 10 kHz was achieved. The corrections were also applied to field EIT measurements made using a 25 m long EIT borehole chain with eight electrodes and an electrode separation of 1 m. The results of a 1D inversion of these measurements showed that the correction methods increased the measurement accuracy considerably. It was concluded that the proposed correction methods enlarge the bandwidth of the field EIT measurement system, and that accurate EIT measurements can now be made in the mHz to kHz frequency range. This increased accuracy in the kHz range will allow a more accurate field characterization of the complex electrical conductivity of soils and sediments, which may lead to the improved estimation of saturated hydraulic conductivity from electrical properties. Although the correction methods have been developed for a custom-made EIT system, they also have potential to improve the phase accuracy of EIT measurements made with commercial systems relying on multicore cables.

Simple Predictive Models for Saturated Hydraulic Conductivity of Technosands

Accurate estimation of saturated hydraulic conductivity (Ks) of technosands (gravel-free, coarse sands with negligible organic matter content) is important for irrigation and drainage management of athletic fields and golf courses. In this study, we developed two simple models for predicting Ks of technosands based on either (i) the classic Kozeny-Carman (K-C) model modified by considering the content of finer particles (fines) less than 200 μm to estimate an immobile water fraction or (ii) the Revil-Cathles (R-C) model modified by using the characteristic particle diameter from the Rosin-Rammler particle size distribution (PSD) function. The Ks and PSD data of 14 golf course sands from literature as well as newly measured data for a size fraction of Lunar Regolith Simulant, packed at three different dry bulk densities, were used for model evaluation. The pore network tortuosity-connectivity parameter (m) obtained for pure coarse sand after fitting to measured Ks data was 1.68 for both models and in good agreement with m values obtained from recent solute and gas diffusion studies. Both the modified K-C and R-C models are easy to use and require limited parameter input, and both models gave comparable accuracy as more complex Ks models. The models are therefore recommended for preliminary assessment and design of technosand layers, for example, with regard to selecting sand PSD for optimal hydrological performance at athletic fields or golf courses.

Near Surface Electrical Characterization of Hydraulic Conductivity: From Petrophysical Properties to Aquifer Geometries—A Review

This paper reviews the recent geophysical literature addressing the estimation of saturated hydraulic conductivity (K) from static low frequency electrical measurements (electrical resistivity, induced polarization (IP) and spectral induced polarization (SIP)). In the first part of this paper, research describing how petrophysical relations between electrical properties and effective (i.e. controlling fluid transport) properties of (a) the interconnected pore volumes and interconnected pore surfaces, have been exploited to estimate K at both the core and field scale is reviewed. We start with electrical resistivity measurements, which are shown to be inherently limited in K estimation as, although resistivity is sensitive to both pore volume and pore surface area properties, the two contributions cannot be separated. Efforts to utilize the unique sensitivity of IP and SIP measurements to physical parameters that describe the interconnected pore surface area are subsequently introduced and the incorporation of such data into electrical based Kozeny–Carman type models of K estimation is reviewed. In the second part of this review, efforts to invert geophysical datasets for spatial patterns of K variability (e.g. aquifer geometries) at the field-scale are considered. Inversions, based on the conversion of an image of a geophysical property to a hydrological property assuming a valid petrophysical relationship, as well as joint/constrained inversion methods, whereby multiple geophysical and hydrological data are inverted simultaneously, are briefly covered. This review demonstrates that there currently exists an opportunity to link, (1) the petrophysics relating low frequency electrical measurements to effective hydraulic properties, with (2) the joint inversion strategies developed in recent years, in order to obtain more meaningful estimates of spatial patterns of K variability than previously reported.

The indirect estimation of saturated hydraulic conductivity of soils, using measurements of gas permeability. I. Laboratory testing with dry granular soils

A comprehensive knowledge of soil hydraulic conductivity is essential when modelling the distribution of soil moisture within soil profiles and across catchments. The high spatial variability of soil hydraulic conductivity, however, necessitates the taking of many in situ measurements, which are costly, time-consuming, and labour-intensive. This paper presents an improved method for indirectly determining the saturated hydraulic conductivity of granular materials via an in situ gas flow technique. The apparatus employed consists of a cylindrical tube which is embedded in the soil to a prescribed depth. Nitrogen at a range of pressures was supplied to the tube and allowed to escape by permeating through the soil. A 3-dimensional, axisymmetric, steady-state, finite element flow model was then used to determine the value of the soil intrinsic gas permeability which produces the best fit to the pressure–air flow data. Saturated hydraulic conductivities estimated from the application of the gas flow technique to 5 granular soils covering a wide range of permeabilities were in close agreement with values determined using a conventional permeameter. The results of this preliminary study demonstrate the potential of this approach to the indirect determination of saturated hydraulic conductivity based on measurement of gas flow rates in granular and structured soils.

A geostatistically based inverse model for three-dimensional variably saturated flow

We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.

Improving the field estimation of saturated hydraulic conductivity in soil survey

Prediction of the movement and storage of water in soil is central to quantitative land evaluation. However, spatial and temporal predictions have not been provided by most Australian soil surveys. The saturated hydraulic conductivity (Ks) is an essential parameter for description of water movement in soil and its estimation has been considered too difficult for logistic and technical reasons. The Ks cannot be measured everywhere and relationships with readily observed morphological variables have to be established. However, conventional morphology by itself is a poor predictor of Ks. We have developed a more functional set of morphological descriptors better suited to the prediction of Ks. The descriptors can be applied at several levels of detail. Measurements of functional morphology and Ks were made on 99 horizons from 36 sites across south-eastern Australia. Useful predictions of Ks were possible using field texture, grade of structure, areal porosity, bulk density, dispersion index, and horizon type. A simple visual estimate of areal porosity was satisfactory, although a more quantitative system of measurement provided only slightly better predictions. Regression trees gave more plausible predictive models than standard multiple regressions because they provided a realistic portrayal of the non-additive and conditional nature of the relationships between morphology and Ks. The results are encouraging and indicate that coarse-level prediction of Ks is possible in routine soil survey. Direct measurement of Ks does not appear to be generally feasible because of the high cost, dynamic nature of Ks, and substantial short-range variation in the field. Prediction is further constrained by the limited returns from more sophisticated morphological predictors. The degree to which this limits practical land evaluation is yet to be demonstrated.

Indirect estimation of soil hydraulic properties to predict soybean yield using GLYCIM

GLYCIM, a mechanistic model of soybean ( Glycine Max L.) growth and development, requires soil hydraulic parameters as input. These data are usually not readily available. The objective of this study was to compare yields calculated with measured hydraulic properties to those calculated with hydraulic properties estimated from soil texture and bulk density. We reviewed estimation methods and chose two methods to estimate a soil moisture release function and two methods to obtain saturated hydraulic conductivity. Both methods use soil texture and bulk density as predictors. Soil water retention predicted by these methods correlated well with measured soil water retention whereas the estimation of saturated hydraulic conductivity was poor. Soybean yields were simulated using GLYCIM with and without irrigation for seven locations in Mississippi, USA, using seven years of weather records. Simulated yields were affected more by the method of estimating the moisture release curve than by the method of estimating saturated hydraulic conductivity. The average simulated yields from estimated properties were higher than those from measured properties because estimated water retention provided more available water. Correlation between yields simulated using measured and estimated hydraulic properties was higher under non-irrigated conditions than with irrigation. Averaging yields over years with different weather conditions greatly improved the correlations.