Estimation of soil hydraulic properties and their uncertainty through the Beerkan infiltration experiment

The Beerkan method based on in situ single‐ring water infiltration experiments along with the relevant specific Beerkan estimation of soil transfer parameters (BEST) algorithm is attractive for simple soil hydraulic characterization. However, the BEST algorithm may lead to erroneous or null values for the saturated hydraulic conductivity and sorptivity especially when there are only few infiltration data points under the transient flow state, either for sandy soil or soils in wet conditions. This study developed an alternative algorithm for analysis of the Beerkan infiltration experiment referred to as BEST‐generalized likelihood uncertainty estimation (GLUE). The proposed method estimates the scale parameters of van Genuchten water retention and Brooks–Corey hydraulic conductivity functions through the GLUE methodology. The GLUE method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the goodness‐of‐fit between modelled and observed data. The results showed that using a combination of three different likelihood measurements based on observed transient flow, steady‐state flow and experimental steady‐state infiltration rate made the BEST‐GLUE procedure capable of performing an efficient inverse analysis of Beerkan infiltration experiments. Therefore, it is more applicable for a wider range of soils with contrasting texture, structure, and initial and saturated water content. Copyright © 2015 John Wiley & Sons, Ltd.     

Validity limits for the van Genuchten–Mualem model and implications for parameter estimation and numerical simulation

The calculation of the relative hydraulic conductivity function based on water retention data is an attractive and widely used approach, since direct measurements of unsaturated conductivities are difficult. We show theoretically under which conditions an air-entry value for water retention data is definitely required when using the statistical approach of Mualem. Moreover we rigorously specify the conditions for which the classical van Genuchten–Mualem model leads to wrong predictions of relative hydraulic conductivity and, hence, an alternative formulation including an air-entry value should be used. Significant consequences are demonstrated for the inverse parameter estimation based on multistep outflow experiments. Furthermore it is shown that the use of a physically correct formulation of the water retention curve including an air-entry value and the derived hydraulic conductivity function influences not only the stability of numerical simulations but also their final results. This is especially grave as simulations with van Genuchten–Mualem parameters are frequently used to compare experiments and simulations and to draw conclusions on the correctness of Richards’ equation.     

Consistent parameter constraints for soil hydraulic functions

Parameters of functions to describe soil hydraulic properties are derived from measurements by means of parameter estimation. Of crucial importance here is the choice of correct constraints in the parameter space. Often, the parameters are mere shape parameters without physical meaning, giving flexibility to the model. A fundamental requirement is that the hydraulic functions are monotonic: the retention function and the conductivity function can only decrease as the capillary suction increases. A stricter physical requirement for the conductivity function is that its decrease with respect to saturation is at least linear. This linear decrease would occur if all pores of a capillary bundle had an equal radius. In the first part of this contribution, we derive constraints for the so-called tortuosity parameter of the Mualem conductivity model, which allow highest possible flexibility on one hand and guarantee physical consistency on the other hand. In combination with the retention functions of Brooks and Corey, van Genuchten, or Durner, such a constraint can be expressed as a function of the pore-size distribution parameters. In the second part, we show that a common modification of retention models, which is applied to reach zero water content at finite suction, can lead to the physically unrealistic case of increasing water content with increasing suction. We propose a solution for this problem by slightly modifying these models and introducing a correct parameter constraint.     

Including prior information in the estimation of effective soil parameters in unsaturated zone modelling

In this paper we propose a methodology to include prior information in the estimation of effective soil parameters for modelling the soil moisture content in the unsaturated zone. Laboratory measurements on undisturbed soil cores were used to estimate the moisture retention curve and hydraulic conductivity curve parameters. The soil moisture content was measured at 25 locations along three transects and at three different depths (surface, 30 and 60 cm) on an 80×20 m hillslope for the year 2001. Soil cores were collected in 84 locations situated in three profile pits along the hillslope. For the estimation of the effective soil hydraulic parameters the joint probability distribution of measured parameter values was used as prior information. A two-horizon single column 1D MIKE SHE model based on Richards' equation was set-up for nine soil moisture measurement locations along the middle transect of the hillslope. The goal of the model is to simulate the soil moisture profile at each location. The shuffled complex evolution (SCE) algorithm has been applied to estimate effective model parameters using either wide parameter ranges, referred to as the ‘no-prior’ case, or the joint probability distribution of measured parameter values as prior information (‘prior’ case). When the prior information is incorporated in the SCE optimisation the goodness-of-fit of the model predictions is only slightly worse compared to when no-prior information is incorporated. However, the effective parameter estimates are more realistic when the prior information is incorporated. For both the no-prior and prior case the generalised likelihood uncertainty estimation procedure (GLUE) was subsequently used to estimate the uncertainty bounds (UB) on the model predictions. When incorporating the prior information more parameter sets were accepted for the estimation of the predictive uncertainty and the parameter values were more realistic. Moreover, UB better enclosed the observations. Thus, incorporating prior information in GLUE reduces the amount of model evaluations needed to obtain sufficient behavioural parameter sets. The results indicate the importance of prior information in the SCE and GLUE parameter estimation strategies.     

Delineation of hydrologically similar units in a watershed based on fuzzy classification of soil hydraulic properties

Evaluation of flow and transport processes in a watershed‐scale requires that the watershed be divided into homogenous spatial units referred to as hydrologically similar units (HSUs). Although a few discretization schemes are already in use, a universally acceptable method of obtaining HSUs is yet to emerge. In this study, we developed a fuzzy inference system (FIS) to classify the saturated hydraulic conductivity (K_s) and two water‐retention parameters α and n into fuzzy logic‐based soil hydrologic classes (FSHCs). Analysis of these classes showed that soil properties within an FSHC have less variability and those between two FSHCs have large variability. This result suggested that soils belonging to a specific FSHC may be more similar than those across different FSHCs and may be grouped together to represent an HSU. Soils within a specific hydrologic class were aggregated to delineate HSUs within the watershed. For the Dengei Pahad micro‐watershed (DPW), this approach showed five distinct regions representing a discretized zone having similar soil hydraulic properties. Application of this approach on a larger international database of soil hydraulic properties revealed that the developed hydrologic classes are quite comparable across different databases. The delineated HSUs based on these FSHCs were also better than the soil series map of the watershed in maintaining the soil heterogeneity of the watershed. Moreover, this new discretization scheme using the SWAT modelling environment showed better performance than the soil series‐based discretization approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Impact of land use on the hydraulic properties of the topsoil in a small French catchment

The hydraulic properties of the topsoil control the partition of rainfall into infiltration and runoff at the soil surface. They must be characterized for distributed hydrological modelling. This study presents the results of a field campaign documenting topsoil hydraulic properties in a small French suburban catchment (7 km²) located near Lyon, France. Two types of infiltration tests were performed: single ring infiltration tests under positive head and tension‐disk infiltration using a mini‐disk. Both categories were processed using the BEST—Beerkan Estimation of Soil Transfer parameters—method to derive parameters describing the retention and hydraulic conductivity curves. Dry bulk density and particle size data were also sampled. Almost all the topsoils were found to belong to the sandy loam soil class. No significant differences in hydraulic properties were found in terms of pedologic units, but the results showed a high impact of land use on these properties. The lowest dry bulk density values were obtained in forested soils with the highest organic matter content. Permanent pasture soils showed intermediate values, whereas the highest values were encountered in cultivated lands. For saturated hydraulic conductivity, the highest values were found in broad‐leaved forests and small woods. The complementary use of tension‐disk and positive head infiltration tests highlighted a sharp increase of hydraulic conductivity between near saturation and saturated conditions, attributed to macroporosity effect. The ratio of median saturated hydraulic conductivity to median hydraulic conductivity at a pressure of − 20 mm of water was about 50. The study suggests that soil texture, such as used in most pedo‐transfer functions, might not be sufficient to properly map the variability of soil hydraulic properties. Land use information should be considered in the parameterizations of topsoil within hydrological models to better represent in situ conditions, as illustrated in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterizing the hydraulic properties of unsaturated sand considering various porosities and drying‐wetting paths of the retention curve

Previous studies have shown that water retention curve (WRC) and the hydraulic conductivity vary because of changes of the void ratio or porosity of soil. However, limited documents pointed out the change of hydraulic properties of soil when compacted to different porosities while considering both of the drying and wetting processes of the WRC. This information is sometimes necessary for research like finger flow analysis or the occurrence of wetting and drying cycles as what would be seen in the field. Therefore, this study aims to examine the change of WRC characteristics with varied porosity considering both of the drying and wetting path in WRC by conducting a sand box experiment. Results show that the same type of sand compacted to various porosities have different hydraulic parameters. Hydraulic conductivities generally decrease with reduced porosities; shape parameter α of the van Genuchten equation (1980) linearly decreases with declining porosity and shape parameter n in a reversal manner for the sands of interest whether in the drying process or wetting process. The unsaturated properties of sand are further characterized by inspecting the variations of moisture content, matric suction and vertical displacement of soil body subject to periodic changes of the water level by another sand box experiment. The outcomes suggest that the saturated water content and residual water content are changing during the wetting–drying process, which can be an implication of the changed properties of WRC. The characteristics of volumetric deformation might be varied as well because of the observation of the dissimilar patterns of the changing vertical displacements among each wetting–drying process. Infiltration patterns of the sands also are identified through numerical modelling by introducing a constant infiltration flux from the surface followed by a no‐influx condition. Results indicate that less water accumulates in the sand near the surface for the sand compacted to higher porosity, but water can move deeper. Hydraulic conductivity is found as the prime factor dominating the evolvement of wetting fronts. However, shape parameters of water retention curves also affect the infiltration pattern to some extent. In addition, different sands with similar porosities can have quite different infiltrating characteristics. Copyright © 2012 John Wiley & Sons, Ltd.     

Examining the information content of time-lapse crosshole GPR data collected under different infiltration conditions to estimate unsaturated soil hydraulic properties

Time-lapse geophysical data acquired during transient hydrological experiments are being increasingly employed to estimate subsurface hydraulic properties at the field scale. In particular, crosshole ground-penetrating radar (GPR) data, collected while water infiltrates into the subsurface either by natural or artificial means, have been demonstrated in a number of studies to contain valuable information concerning the hydraulic properties of the unsaturated zone. Previous work in this domain has considered a variety of infiltration conditions and different amounts of time-lapse GPR data in the estimation procedure. However, the particular benefits and drawbacks of these different strategies as well as the impact of a variety of key and common assumptions remain unclear. Using a Bayesian Markov-chain-Monte-Carlo stochastic inversion methodology, we examine in this paper the information content of time-lapse zero-offset-profile (ZOP) GPR traveltime data, collected under three different infiltration conditions, for the estimation of van Genuchten–Mualem (VGM) parameters in a layered subsurface medium. Specifically, we systematically analyze synthetic and field GPR data acquired under natural loading and two rates of forced infiltration, and we consider the value of incorporating different amounts of time-lapse measurements into the estimation procedure. Our results confirm that, for all infiltration scenarios considered, the ZOP GPR traveltime data contain important information about subsurface hydraulic properties as a function of depth, with forced infiltration offering the greatest potential for VGM parameter refinement because of the higher stressing of the hydrological system. Considering greater amounts of time-lapse data in the inversion procedure is also found to help refine VGM parameter estimates. Quite importantly, however, inconsistencies observed in the field results point to the strong possibility that posterior uncertainties are being influenced by model structural errors, which in turn underlines the fundamental importance of a systematic analysis of such errors in future related studies.     

Inverse upscaling of hydraulic parameters during constant flux infiltration using borehole radar

Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil.     

Identification of optimal soil hydraulic functions and parameters for predicting soil moisture

Abstract

The accuracy of six combined methods formed by three commonly-used soil hydraulic functions and two methods to determine soil hydraulic parameters based on a soil hydraulic parameter look-up table and soil pedotransfer functions was examined for simulating soil moisture. A novel data analysis and modelling approach was used that eliminated the effects of evapotranspiration so that specific sources of error among the six combined methods could be identified and quantified. By comparing simulated and observed soil moisture at six sites of the USDA Soil Climate Analysis Network, we identified the optimal soil hydraulic functions and parameters for predicting soil moisture. Through sensitivity tests, we also showed that adjusting only the soil saturated hydraulic conductivity, K_s , is insufficient for representing important effects of macropores on soil hydraulic conductivity. Our analysis illustrates that, in general, soil hydraulic conductivity is less sensitive to K_s than to the soil pore-size distribution parameter.

Editor D. Koutsoyiannis; Associate editor D. Hughes

Citation Pan, F., McKane, R.B. and Stieglitz, M., 2012. Identification of optimal soil hydraulic functions and parameters for predicting soil moisture. Hydrological Sciences Journal, 57 (4), 723–737.     

Using a H∞ filter assimilation procedure to estimate root zone soil water content

Root zone soil water content impacts plant water availability, land energy and water balances. Because of unknown hydrological model error, observation errors and the statistical characteristics of the errors, the widely used Kalman filter (KF) and its extensions are challenged to retrieve the root zone soil water content using the surface soil water content. If the soil hydraulic parameters are poorly estimated, the KF and its extensions fail to accurately estimate the root zone soil water. The H‐infinity filter (HF) represents a robust version of the KF. The HF is widely used in data assimilation and is superior to the KF, especially when the performance of the model is not well understood. The objective of this study is to study the impact of uncertain soil hydraulic parameters, initial soil moisture content and observation period on the ability of HF assimilation to predict in situ soil water content. In this article, we study seven cases. The results show that the soil hydraulic parameters hold a critical role in the course of assimilation. When the soil hydraulic parameters are poorly estimated, an accurate estimation of root soil water content cannot be retrieved by the HF assimilation approach. When the estimated soil hydraulic parameters are similar to actual values, the soil water content at various depths can be accurately retrieved by the HF assimilation. The HF assimilation is not very sensitive to the initial soil water content, and the impact of the initial soil water content on the assimilation scheme can be eliminated after about 5–7 days. The observation interval is important for soil water profile distribution retrieval with the HF, and the shorter the observation interval, the shorter the time required to achieve actual soil water content. However, the retrieval results are not very accurate at a depth of 100 cm. Also it is complex to determine the weighting coefficient and the error attenuation parameter in the HF assimilation. In this article, the trial‐and‐error method was used to determine the weighting coefficient and the error attenuation parameter. After the first establishment of limited range of the parameters, ‘the best parameter set’ was selected from the range of values. For the soil conditions investigated, the HF assimilation results are better than the open‐loop results. Copyright © 2010 John Wiley & Sons, Ltd.     

Beerkan multi-runs for characterizing water infiltration and spatial variability of soil hydraulic properties across scales

A method is presented for characterizing the spatial variability of water infiltration and soil hydraulic properties at the transect and field scales. The method involves monitoring a set of 10 Beerkan runs distributed over a 1-m length of soil, and running BEST (Beerkan estimation of soil transfer parameters) methods to derive hydraulic parameters. The Beerkan multi-runs (BMR) method provides a significant amount of data at the transect scale, allowing the determination of correlations between water infiltration variables and hydraulic parameters, and the detection of specific runs affected by preferential flow or water repellence. The realization of several BMRs at several transects on the same site allows comparison of the variation between locations (spatial variability at the field scale) and at the transect scale (spatial variability at the metre scale), using analysis of variance. From the results, we determined the spatial variability of water infiltration and hydraulic parameters as well as its characteristic scale (transect versus field).     

Scaling soil water retention functions using particle-size distribution

The presented study explores the prediction of soil water retention and its variability from soil texture and bulk density measurements, using a physically-based scaling technique. Specifically, the Arya–Paris (AP) physico-empirical model is applied to two soil datasets that are collected from two catchments located in different areas of Southern Italy. Laboratory-measured soil water retention functions are scaled to characterize soil variability. The laboratory-measured and AP-predicted reference water retention functions are compared by evaluating the lognormal distribution of derived scaling factors, relative to the mean reference retention function. Since the scaling theory assumes geometric similitude for the investigated soils, successful application of using particle-size distribution to estimate soil water retention requires separation of soils with different textures, using variance analysis. We conclude that variability in soil water retention can be determined from limited soil water retention data using the scaling approach when combined with particle-size distribution measurements. This method can potentially be used as an effective tool for identifying soil hydrologic response at catchment scales.     

Ecohydrological modelling in a deciduous boreal forest: Model evaluation for application in non-stationary climates

Soil moisture is an important driver of growth in boreal Alaska, but estimating soil hydraulic parameters can be challenging in this data-sparse region. Parameter estimation is further complicated in regions with rapidly warming climate, where there is a need to minimize model error dependence on interannual climate variations. To better identify soil hydraulic parameters and quantify energy and water balance and soil moisture dynamics, we applied the physically based, one-dimensional ecohydrological Simultaneous Heat and Water (SHAW) model, loosely coupled with the Geophysical Institute of Permafrost Laboratory (GIPL) model, to an upland deciduous forest stand in interior Alaska over a 13-year period. Using a Generalized Likelihood Uncertainty Estimation parameterisation, SHAW reproduced interannual and vertical spatial variability of soil moisture during a five-year validation period quite well, with root mean squared error (RMSE) of volumetric water content at 0.5 m as low as 0.020 cm³/cm³. Many parameter sets reproduced reasonable soil moisture dynamics, suggesting considerable equifinality. Model performance generally declined in the eight-year validation period, indicating some overfitting and demonstrating the importance of interannual variability in model evaluation. We compared the performance of parameter sets selected based on traditional performance measures such as the RMSE that minimize error in soil moisture simulation, with one that is designed to minimize the dependence of model error on interannual climate variability using a new diagnostic approach we call CSMP, which stands for Climate Sensitivity of Model Performance. Use of the CSMP approach moderately decreases traditional model performance but may be more suitable for climate change applications, for which it is important that model error is independent from climate variability. These findings illustrate (1) that the SHAW model, coupled with GIPL, can adequately simulate soil moisture dynamics in this boreal deciduous region, (2) the importance of interannual variability in model parameterisation, and (3) a novel objective function for parameter selection to improve applicability in non-stationary climates.     

Pedotransfer functions estimating soil hydraulic properties using different soil parameters

Estimates of soil hydraulic properties using pedotransfer functions (PTF) are useful in many studies such as hydrochemical modelling and soil mapping. The objective of this study was to calibrate and test parametric PTFs that predict soil water retention and unsaturated hydraulic conductivity parameters. The PTFs are based on neural networks and the Bootstrap method using different sets of predictors and predict the van Genuchten/Mualem parameters. A Danish soil data set (152 horizons) dominated by sandy and sandy loamy soils was used in the development of PTFs to predict the Mualem hydraulic conductivity parameters. A larger data set (1618 horizons) with a broader textural range was used in the development of PTFs to predict the van Genuchten parameters. The PTFs using either three or seven textural classes combined with soil organic mater and bulk density gave the most reliable predictions of the hydraulic properties of the studied soils. We found that introducing measured water content as a predictor generally gave lower errors for water retention predictions and higher errors for conductivity predictions. The best of the developed PTFs for predicting hydraulic conductivity was tested against PTFs from the literature using a subdata set of the data used in the calibration. The test showed that the developed PTFs gave better predictions (lower errors) than the PTFs from the literature. This is not surprising since the developed PTFs are based mainly on hydraulic conductivity data near saturation and sandier soils than the PTFs from the literature. Copyright © 2007 John Wiley & Sons, Ltd.     

Temporal and spatial variation of infiltration in urban green infrastructure

Infiltration is the primary mechanism in green stormwater infrastructure (GSI) systems to reduce the runoff volume from urbanized areas. Soil hydraulic conductivity is most important in influencing GSI infiltration rates. Saturated hydraulic conductivity (Ksat) is a critical parameter for GSI design and post-construction performance. However, Ksat measurement in the field is problematic due to temporal and spatial variability and measurement errors. This review paper focuses on a comparison of methods for in-situ Ksat measurement and the causes of temporal and spatial variations of Ksat within GSI systems. Automated infiltration testing methods, such as the Modified Philip–Dunne (MPD) and SATURO infiltrometers, show promise for efficient Ksat measurements. Soil Ksat values can change over time and substantially vary throughout a GSI, which can be attributed to multiple factors, including but not limited to temperature changes, soil composition and properties, soil compaction level, plant root morphology and distribution, biological and macrofauna activities in the soil, inflow sediment characteristics, quality of infiltrating water, and measurement errors. There is evidence that infiltration rates in vegetated urban GSI systems are sustained given an appropriate GSI design, reasonable concentration of suspended sediments in the inflow runoff, and routine maintenance procedures. These observations indicate that clogging can be counteracted by processes that tend to increase the soil hydraulic conductivity (e.g., plant root and biological activities). This self-sustainability underlines that infiltration-based GSI systems are a reliable long-term stormwater management solution. Recommendations on how to incorporate the temporal changes of Ksat in GSI design and on obtaining a spatially-representative Ksat for the GSI design are presented.     

Sensitivity of nitrate concentration-discharge patterns to soil nitrate distribution and drainage properties in the vertical dimension

We propose a conceptual model that examines the ‘variable source area’ (VSA) and ‘nitrate flushing’ hypothesis in the vertical direction, and use this approach to explain nitrate concentration–discharge relationships in a semi-arid watershed. We use an eco-hydrology simulation model (RHESSys) to show that small changes in the vertical distribution of nitrate mass and their interaction with soil hydraulic conductivity can result in abrupt changes in the nitrate concentration–discharge relationship. We show that the estimated concentration–discharge relationship is sensitive to the parameters governing soil vertical nitrate distribution and soil hydraulic conductivity, at both patch scale and watershed scale, where lateral redistribution of water and nitrate is also accounted for. Given heterogeneity in nitrogen inputs, uptake processes, soil drainage and storage processes, substantial variation in parameters that describe rate of changes in vertical distribution of soil nitrate and hydraulic properties is likely both within and between watersheds. Thus, we argue that vertical ‘variable source area’ processes may be as important as lateral VSA in determining concentration discharge relationships.     

Development of a three‐dimensional watershed modelling system for water cycle in the middle part of the Heihe rivershed,in the west of China

A three‐dimensional numerical modelling system is developed to study transformation processes of water resources in alluvial fan and river basin along the middle reaches of the Heihe River Basin, Northwest China, an arid and semi‐arid region. Integrating land utilization, remote sensing and geographic information systems, we have developed a numerical modelling system that can be used to quantify the effects of land use and anthropogenic activities on the groundwater system as well as to investigate the interaction between surface water and groundwater. Various hydraulic measurements are used to identify and calibrate the hydraulic boundary conditions and spatial distributions of hydraulic parameters. In the modelling study, various water exchanges and human effects on the watershed system are considered. These include water exchange between surface water and groundwater, groundwater pumping, lateral water recharges from mountain areas, land utilization, and infiltration and evaporation in the irrigation and non‐irrigation areas. The modelling system provides a quantitative method to describe spatial and temporal distributions and transformations between various water resources, and it has application to other watersheds in arid and semi‐arid areas. Copyright © 2011 John Wiley & Sons, Ltd.