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The Peters–Durner–Iden (PDI) model system for describing soil hydraulic properties (SHP) has been developed over a decade. Inspired by Rien van Genuchten's seminal work, the PDI system focuses on an efficient and simple parameterization of water retention curves and hydraulic conductivity curves (HCC) across the entire soil moisture spectrum. By combining capillary and non‐capillary components for water retention and conductivity, it aims to reconcile mathematical simplicity and insights on water adsorption and film flow in soils. Recent developments have reduced the number of free parameters of the conductivity model to zero, enhancing the model's applicability in cases of limited data availability. The first reduction was achieved by a prediction of absolute non‐capillary conductivity based on the consideration of film and corner flow on the pore scale, and the second by a prediction of absolute capillary conductivity by a capillary bundle model. This allows a complete characterization of SHP over the entire moisture range with only four retention curve parameters. The inclusion of a maximum pore size in the capillary conductivity model prevents an unrealistic drop of the HCC near saturation. This paper provides a comprehensive overview of the PDI model system, emphasizing its conceptual features and mathematical details. An Excel sheet and a Python code stored in a repository are provided for accessibility. Core Ideas: Compact and comprehensive mathematical overview of the current PDI system.The model integrates elements of capillary and non‐capillary soil water storage and conductivity in a simple manner.Hydraulic conductivity can be completely predicted from the retention curve.Improved applicability in cases where conductivity data are scarce or available only in a limited moisture range. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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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 10.5880/fidgeo.2023.012 (Hohenbrink et al., 2023). [ABSTRACT FROM AUTHOR]

Numerical modeling of soil water dynamics and storage is generally based on the Richards equation. Its solution requires knowledge of the soil hydraulic properties (SHP): the soil water retention function and the hydraulic conductivity function. To determine SHP, laboratory evaporation experiments are particularly popular because they provide data for both SHP functions. The evaluation by the simplified evaporation method (SEM) method, originally proposed by Schindler and subsequently improved by several authors, relies on linearization assumptions that allow for a relatively simple calculation scheme but result in biased conductivity data for some soils. The objective of this study is to propose and test an improved computational scheme for the hydraulic conductivity function. We present the new theory and show that it leads generally to higher accuracy of the conductivity function. The improvement is most pronounced for sandy soils and soil water pressure heads below −100 cm, where the original method provided data with bias. Core Ideas: An improved scheme for the calculation of hydraulic conductivity with the simplified evaporation method (SEM) is presented.Bias in hydraulic conductivity for sandy soils was observed in the original SEM is eliminated.Improvement is most significant for soil water pressure heads in the medium to dry range, below −100 cm.The calculation scheme can be easily implemented in existing computer algorithms. [ABSTRACT FROM AUTHOR]

To model the water, solute and energy transport in porous media, it is essential to have accurate information about the soil hydraulic properties (SHP), i.e. the water retention curve (WRC) and the soil hydraulic conductivity curve (HCC). Having reliable data information to parameterize these models is important, but equally critical is the selection of appropriate SHP models. While various expressions for the WRC are commonly compared, the capillary conductivity model proposed by Mualem (1976a) is widely used but seldom 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. These expressions include two simpler 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). In order to check whether different parametrizations of the WRC interfere with the suitability of the conductivity models, we utilized four different capillary saturation models in combination with each of the conductivity prediction models, resulting in a total of 16 SHP model schemes. All schemes were calibrated using 12 carefully selected datasets 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 datasets 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. [ABSTRACT FROM AUTHOR]

For modeling flow and transport processes in the soil–plant–atmosphere system, knowledge of the unsaturated hydraulic properties in functional form is mandatory. While much data are available for the water retention function, the hydraulic conductivity function often needs to be predicted. The classical approach is to predict the relative conductivity from the retention function and scale it with the measured saturated conductivity, Ks. In this paper we highlight the shortcomings of this approach, namely, that measured Ks values are often highly uncertain and biased, resulting in poor predictions of the unsaturated conductivity function. We propose to reformulate the unsaturated hydraulic conductivity function by replacing the soil-specific Ks as a scaling factor with a generally applicable effective saturated tortuosity parameter τs and predicting total conductivity using only the water retention curve. Using four different unimodal expressions for the water retention curve, a soil-independent general value for τs was derived by fitting the new formulation to 12 data sets containing the relevant information. τs was found to be approximately 0.1. Testing of the new prediction scheme with independent data showed a mean error between the fully predicted conductivity functions and measured data of less than half an order of magnitude. The new scheme can be used when insufficient or no conductivity data are available. The model also helps to predict the saturated conductivity of the soil matrix alone and thus to distinguish between the macropore conductivity and the soil matrix conductivity. [ABSTRACT FROM AUTHOR]

Rock fragments (RFs) influence soil hydraulic properties (SHPs), and knowledge about the SHPs of stony soils is important in vadose zone hydrology. However, experimental evidence on effective SHPs of stony soils is still scarce and mostly restricted to water‐saturated conditions and low volumetric contents of RFs. We examined the influence of RFs on SHPs through a series of measurements. Stony soils were prepared by packing 250‐cm3 cylinders with soils of two textures (sandy loam and silt loam) and with different volumes of RFs (up to 50% v/v) with a diameter of 8–16 mm. Samples were prepared in a way that the background soils (diameter smaller than 2 mm) had identical bulk density. The simplified evaporation method was used to determine the effective SHPs of stony soils. We used the obtained SHP data to evaluate the performance of models, which predict the effective SHPs of stony soils from SHPs of the background soil. The results highlight the systematic dependency of SHPs on volumetric content of RFs. The difference between modeled and measured SHPs was substantial for cases in which the soil contained a high amount of RFs. Accounting for the moisture content of RFs improved the prediction of the effective water retention curve of stony soils compared with a simple scaling that used only the content of RFs. Among the evaluated models for the effective hydraulic conductivity, the model based on the general effective medium theory showed the best performance, particularly for low RF contents. Core Ideas: Water retention and hydraulic conductivity curves of stony soils with rock fragments up to 50% (v/v) were measured.Common models for scaling hydraulic properties of stony soils were evaluated.Among the evaluated models of predicting the hydraulic conductivity curve, the GEM performs best. [ABSTRACT FROM AUTHOR]

Stony soils that have a considerable amount of rock fragments (RFs) are widespread around the world. However, experiments to determine the effective soil hydraulic properties (SHPs) of stony soils, i.e., the water retention curve (WRC) and hydraulic conductivity curve (HCC), are challenging. Installation of measurement devices and sensors in these soils is difficult, and the data are less reliable because of their high local heterogeneity. Therefore, effective properties of stony soils especially under unsaturated hydraulic conditions are still not well understood. An alternative approach to evaluate the SHPs of these systems with internal structural heterogeneity is numerical simulation. We used the Hydrus 2D/3D software to create virtual stony soils in 3D and simulate water flow for different volumetric fractions of RFs, f. Stony soils with different values of f from 11 % to 37 % were created by placing impermeable spheres as RFs in a sandy loam soil. Time series of local pressure heads at various depths, mean water contents, and fluxes across the upper boundary were generated in a virtual evaporation experiment. Additionally, a multistep unit-gradient simulation was applied to determine effective values of hydraulic conductivity near saturation up to pF=2. The generated data were evaluated by inverse modeling, assuming a homogeneous system, and the effective hydraulic properties were identified. The effective properties were compared with predictions from available scaling models of SHPs for different values of f. Our results showed that scaling the WRC of the background soil based on only the value of f gives acceptable results in the case of impermeable RFs. However, the reduction in conductivity could not be simply scaled by the value of f. Predictions were highly improved by applying the Novák, Maxwell, and GEM models to scale the HCC. The Maxwell model matched the numerically identified HCC best. [ABSTRACT FROM AUTHOR]

Weber et al. (2019) (W19 in the following) present a modular framework for parametrizing soil hydraulic properties. The W19 model framework is almost identical to the model system developed jointly by Peters (2013), https://doi.org/10.1002/wrcr.20548, Iden and Durner (2014), https://doi.org/10.1002/2014wr015937, and Peters (2014), https://doi.org/10.1002/2014wr016107, to which we will refer as PDI ("Peters‐Durner‐Iden") model in the following. The primary goal of this comment is to uncover some inconsistencies of the W19 formulation. In the following, we (i) comment on the statement made by W19 regarding the number of parameters in the original PDI formulation, (ii) critically analyze the use of their function to parameterize the water retention curve (WRC), and (iii) show that, in contrast to the statement in W19, using their formulation of for parametrizing noncapillary hydraulic conductivity leads to systematic deviations from the physically based film‐conductivity model developed by Tokunaga (2009), https://doi.org/10.1029/2009wr007734. Key Points: Non‐capillary parts of the hydraulic functions of Weber et al. (2019) are analysedSaturation function often agrees neither with experimental data nor with theoretical considerationsContrary to the authors' claim, the hydraulic conductivity function does not agree with Tokunaga's film‐flow model [ABSTRACT FROM AUTHOR]

The mathematical representation of the soil hydraulic properties is of central importance for modeling water, solute and energy transport in soils. The established models of the water retention and hydraulic conductivity curves account for capillary water retention and conductivity, but neglect water adsorption and water flow in films and pore corners. They are therefore suited for modeling flow and transport processes in the medium to wet moisture range, but are susceptible to failure in dry soil. The model system developed by Peters (2013, https://doi.org/10.1002/wrcr.20548; 2014, https://doi.org/10.1002/2014wr016107) and Iden and Durner (2014, https://doi.org/10.1002/2014wr015937) (PDI in the following) is a simple parametric framework that overcomes these structural shortcomings. However, it requires one additional parameter to scale the hydraulic conductivity curve in the moisture range where non‐capillary flow dominates. Measured conductivity data are required to determine this scaling parameter and to compute the hydraulic conductivity over the complete moisture range. In this contribution, we first show that the original PDI model is in close agreement with a comprehensive model for film conductivity in porous media. We then derive a physically‐based approach to predict the film conductivity from the water retention curve. This improved PDI model has the same number of parameters as established models and provides a complete prediction of the hydraulic conductivity curve including non‐capillary flow if water retention data and the saturated conductivity are known. Application to literature data covering a broad range of textures shows an improvement of the conductivity prediction by the factor five if compared to the van Genuchten/Mualem model. Key Points: Simplified model for non‐capillary conductivity is in good agreement with comprehensive physically‐based modelEasy‐to‐compute, physically‐based prediction of non‐capillary conductivity in the medium to dry moisture rangePrediction of conductivity curve from retention curve parameters shows good agreement with measured data [ABSTRACT FROM AUTHOR]

Evaporation experiments are frequently used to determine soil hydraulic properties. We simulated laboratory evaporation experiments with a coupled water, vapor, and heat flow model which includes the surface energy balance. The simulations are performed with different parametrizations of soil hydraulic properties with a focus on soil hydraulic conductivity in medium to dry soil. In previous studies, conductivity in this moisture range has been shown to be influenced not only by water flow in completely filled capillaries ("capillary flow") but also by film and corner flow ("film flow"). Our forward simulations highlight the strong influence of an increased conductivity caused by film flow on evaporation rate, cumulative water loss, soil temperature, and soil water pressure head during evaporation. Film flow extends the duration of stage‐1 evaporation and increases the evaporation rate during stage‐2 even if all other physical material properties are the same. The simulated data were used in inverse simulations with the Richards equation to test whether soil hydraulic properties can be identified without bias. This is a priori questionable because the Richards equation is an isothermal flow model and simplifies the true physics considerably, by ignoring thermal liquid and thermal vapor fluxes, as well as temperature effects on the hydraulic properties. Our results show that the identification of the water retention and hydraulic conductivity curves is bias‐free for media with and without film flow. We conclude that the Richards equation can be safely used to identify hydraulic properties from evaporation experiments by inverse modeling. Key Points: Coupled modeling of water, vapor, and heat flow shows that film‐flow extends stage‐1 and changes the evaporation dynamics during stage‐2Soil hydraulic properties identified by inverse modeling with the Richards equation are unbiased despite strong temperature dynamicsInadequate models for soil hydraulic properties lead to a grossly wrong prediction of the pressure head in medium to dry soils [ABSTRACT FROM AUTHOR]

Bare‐soil evaporation involves coupled flow of liquid water, water vapor, and heat. As evaporation results in non‐isothermal conditions in the soil, the temperature dependence of transport properties and thermal fluxes of water and vapor must be accounted for. In a companion paper, we showed that the Richards equation, that is, a single‐phase flow model assuming isothermal conditions, is applicable to accurately determine soil hydraulic properties including the medium to dry range from evaporation experiments by inverse modeling. This is warranted if pressure head data across a wide moisture range, that is, from almost saturated to almost air‐dry, are used in the objective function and a suitable parameterization of the hydraulic conductivity function including vapor and non‐capillary flow is used. In this article, we confirm the theoretical results by examining real evaporation experiments, in which we measured the temporal dynamics of evaporation rate, soil temperature, and pressure head in laboratory soil columns. Pressure head was measured with mini‐tensiometers and relative humidity sensors. The measurements were evaluated by inverse modeling with the Richards equation assuming isothermal conditions and ambient temperature in the soil. Our results for a sandy and a loamy soil show that the observed transient water and vapor dynamics in the drying soil could be accurately matched, provided the hydraulic conductivity curve considered isothermal vapor diffusion and film flow. These components dominate hydraulic conductivity in the medium to dry soil moisture range and were uniquely identified in agreement with the theoretical analysis in the companion article. Key Points: Identification of soil hydraulic properties across the full moisture range by inverse modeling of evaporation experimentsAdvanced instrumentation with tensiometers and relative humidity sensors allows to identify hydraulic conductivity in medium to dry soilEvaporation experiments can be modeled correctly with Richards' equation, provided hydraulic properties account for vapor and film flow [ABSTRACT FROM AUTHOR]

Core Ideas Temperature dependence of conductivity and retention function was determined simultaneously. Core Ideas Temperature effects were stronger than predicted by surface tension and viscosity theory. Core Ideas Models with soil‐specific parameters could be well fitted to the measured data. Core Ideas Results suggest that surface properties of the matrix influence the temperature dependence. --> The modeling of the water flow in soils under non‐isothermal conditions requires consideration of the temperature influence on the soil hydraulic properties (SHPs). The surface‐tension‐viscous‐flow (STVF) theory considers the influence of temperature on viscosity, density and surface tension and provides a conceptual framework for the temperature dependence of the water retention and hydraulic conductivity curves. Previous research has shown discrepancies between observed temperature effects on SHPs and the STVF theory. Furthermore, experimental investigations, which investigate the temperature effects on both the retention and conductivity curves in a combined manner, are still rare. To overcome this limitation, we measured the SHPs of three different soils at three different temperatures (5, 20, and 35°C) with the evaporation method, which yields highly resolved retention data in the suction range between saturation and 100 kPa, and conductivity data in the range of ∼6 to 100 kPa. The classic STVF‐based model and two alternative models were tested. Results showed that the temperature dependence of SHP was larger than predicted by the STVF theory and depends on the soil. The effect was strongest for the silt loam, followed by the sand and smallest for the sandy loam. Fits of the Grant and Stoffregen models to the experimental data were excellent, but required soil‐specific parameters. This indicates that the surface properties of the soil matrix might contribute to the effects of temperature on SHPs. [ABSTRACT FROM AUTHOR]

Accurate knowledge of the soil water retention curve (WRC) is essential for various hydrological and plant-physiological studies. Currently, there is a lack of a uniform protocol for measuring the wilting point water content (WP) with the dewpoint method (DP), despite its ecological relevance and frequent use to calculate available water capacity. We present a new protocol for measuring the WP with the dewpoint method. In contrast to existing methods which add or remove specific amounts of water to moist, air-dry, or oven-dry soil, we propose to apply the dewpoint method after the evaporation method in which tensiometers measure the pressure head of the soil. We suggest to stop the evaporation experiment when the air-entry of one tensiometer cup is reached, to slice the soil core into slabs, and to apply the dewpoint method to subsamples of the slabs. We test the method by numerical simulations and laboratory experiments on five soils covering a broad range of texture. We investigate the accuracy, robustness, and practicability of the new method and compare it to the existing protocols for the dewpoint method and the pressure plate technique. We find that the proposed method allows a precise determination of the WP and the WRC across the full moisture range. It is easy to perform, robust, accurate, and does not require any a priori guess about the amount of water to be added or removed. By fitting a retention curve to the measured data, any water content, including the WP, can be obtained with great confidence. [ABSTRACT FROM AUTHOR]

Core IdeasThe CDE predicts non‐physical dispersive solute flux against water flow direction.This wrongly directed dispersive solute flux can be as high as the convective flux.This problem occurs around zones with an increase or decrease in concentration.Particular cases are vaporization of water, root water uptake, and biodegradation. The convection–dispersion equation (CDE) is the most widely used model for simulating the transport of dissolved substances in porous media. The dispersion term in the CDE lumps molecular diffusion and hydromechanical dispersion into an effective diffusive solute flux. This is possible by describing hydrodynamic dispersion with Fick's first law of diffusion. We critically analyzed this concept for specific water flow situations where the solute concentration is locally increased by processes like root water uptake or water evaporation. The local accumulation of solutes in these situations leads to high concentration gradients and a dispersive solute flux component opposite to the direction of the water flux. This is physically wrong because it assumes that molecules or ions are moving against the flow direction by dispersion. The aim of this study was to investigate the magnitude of the resulting error by means of numerical modeling. We simulated solute transport from a groundwater table to a bare soil surface during steady‐state evaporation using the HYDRUS‐1D code. The simulations showed that in the region where dissolved substances accumulate due to the transition from liquid water to vapor, the resulting incorrect dispersive flux against the mean transport direction can reach the same order of magnitude as the convective solute flux. Under such conditions, application of the CDE is questionable. [ABSTRACT FROM AUTHOR]

Core Ideas: Unsaturated hydraulic conductivity of stony soils was determined in medium moisture range.Evaporation method works for stony soils, even if stone contents are high.Theoretical scaling models showed a good agreement with measurements for moderate stone contents.Model results and measurements differ markedly for soils with high stone contents. Studying the role of gravel, stones, or rock fragments on effective soil hydraulic properties (SHPs) is crucial for understanding and predicting soil water processes such as evaporation, redistribution, and water and solute transport through soils containing significant amounts of coarse inclusions. We conducted a laboratory study in which we investigated the effect of stones on the water retention and unsaturated hydraulic conductivity curves of soil–stone mixtures. Stony soils were created by packing predefined masses of soil particles (sand and sandy loam) with diameters <2 mm and crushed basalt (2–5 and 7–15 mm). The resulting mixtures ranged from 0 to 40% (v/v) stone content. The SHPs were determined with the simplified evaporation method. The measurements yielded plausible water retention and hydraulic conductivity curves across a wide moisture range. Results qualitatively showed the expected dependencies of SHPs on volumetric stone content, characterized by a reduction of soil water content and hydraulic conductivity across the whole pressure head range. Measured data suggested that coarse inclusions in soil tend to widen the effective pore‐size distribution. Prediction of SHPs of the stony soils, performed by fitting a flexible SHP model to the data of the background soil and scaling it with approaches from the literature, worked well for low stone contents. However, for volumetric stone contents of 25 and 40%, measured SHPs differed substantially from the properties predicted by simple scaling models. [ABSTRACT FROM AUTHOR]

Abstract: While boreal lowland bogs have been extensively studied using the eddy‐covariance (EC) technique, less knowledge exists on mountainous peatlands. Hence, half‐hourly CO2 fluxes of an ombrotrophic peat bog in the Harz Mountains, Germany, were measured with the EC technique during a growing season with exceptionally dry weather spells. A common biophysical process model for net ecosystem exchange was used to describe measured CO2 fluxes and to fill data gaps. Model parameters and uncertainties were estimated by robust inverse modelling in a Bayesian framework using a population‐based Markov Chain Monte Carlo sampler. The focus of this study was on the correct statistical description of error, i.e. the differences between the measured and simulated carbon fluxes, and the influence of distributional assumptions on parameter estimates, cumulative carbon fluxes, and uncertainties. We tested the Gaussian, Laplace, and Student's t distribution as error models. The t‐distribution was identified as best error model by the deviance information criterion. Its use led to markedly different parameter estimates, a reduction of parameter uncertainty by about 40%, and, most importantly, to a 5% higher estimated cumulative CO2 uptake as compared to the commonly assumed Gaussian error distribution. As open‐path measurement systems have larger measurement error at high humidity, the standard deviation of the error was modeled as a function of measured vapor pressure deficit. Overall, this paper demonstrates the importance of critically assessing the influence of distributional assumptions on estimated model parameters and cumulative carbon fluxes between the land surface and the atmosphere. [ABSTRACT FROM AUTHOR]

In ombrotrophic peatlands, the moisture content of the acrotelm (vadoze zone) controls oxygen diffusion rates, redox state, and the turnover of organic matter. Thus, variably saturated flow processes determine whether peatlands act as sinks or sources of atmospheric carbon, and modelling these processes is crucial to assess effects of changed environmental conditions on the future development of these ecosystems. We show that the Richards equation can be used to accurately describe the moisture dynamics under evaporative conditions in variably saturated peat soil, encompassing the transition from the topmost living moss layer to the decomposed peat as part of the vadose zone. Soil hydraulic properties (SHP) were identified by inverse simulation of evaporation experiments on samples from the entire acrotelm. To obtain consistent descriptions of the observations, the traditional van Genuchten-Mualem model was extended to account for non-capillary water storage and flow. We found that the SHP of the uppermost moss layer reflect a pore-size distribution (PSD) that combines three distinct pore systems of the Sphagnum moss. For deeper samples, acrotelm pedogenesis changes the shape of the SHP due to the collapse of inter-plant pores and an infill with smaller particles. This leads to gradually more homogeneous and bi-modal PSDs with increasing depth, which in turn can serve as a proxy for increasing state of pedogenesis in peatlands. From this, we derive a nomenclature and size classification for the pore spaces of Sphagnum mosses and define inter-, intra-, and inner-plant pore spaces, with effective pore diameters of >300, 300-30, and 30-10 μm, respectively. [ABSTRACT FROM AUTHOR]

In ombrotrophic peatlands, the moisture content of the vadose zone (acrotelm) controls oxygen diffusion rates, redox state, and the turnover of organic matter. Whether peatlands act as sinks or sources of atmospheric carbon thus relies on variably saturated flow processes. The Richards equation is the standard model for water flow in soils, but it is not clear whether it can be applied to simulate water flow in live Sphagnum moss. Transient laboratory evaporation experiments were conducted to observe evaporative water fluxes in the acrotelm, containing living Sphagnum moss, and a deeper layer containing decomposed moss peat. The experimental data were evaluated by inverse modeling using the Richards equation as process model for variably-saturated flow. It was tested whether water fluxes and time series of measured pressure heads during evaporation could be simulated. The results showed that the measurements could be matched very well providing the hydraulic properties are represented by a suitable model. For this, a trimodal parametrization of the underlying pore-size distribution was necessary which reflects three distinct pore systems of the Sphagnum constituted by inter-, intra-, and inner-plant water. While the traditional van Genuchten-Mualem model led to great discrepancies, the physically more comprehensive Peters-Durner-Iden model which accounts for capillary and noncapillary flow, led to a more consistent description of the observations. We conclude that the Richards equation is a valid process description for variably saturated moisture fluxes over a wide pressure range in peatlands supporting the conceptualization of the live moss as part of the vadose zone. [ABSTRACT FROM AUTHOR]

The particle-size distribution (PSD) of a soil expresses the mass fractions of various sizes of mineral particles which constitute the soil material. It is a fundamental soil property, closely related to most physical and chemical soil properties and it affects almost any soil function. The experimental determination of soil texture, i.e., the relative amounts of sand, silt, and clay-sized particles, is done in the laboratory by a combination of sieving (sand) and gravitational sedimentation (silt and clay). In the latter, Stokes' law is applied to derive the particle size from the settling velocity in an aqueous suspension. Traditionally, there are two methodologies for particle-size analysis from sedimentation experiments: the pipette method and the hydrometer method. Both techniques rely on measuring the temporal change of the particle concentration or density of the suspension at a certain depth within the suspension. In this paper, we propose a new method which is based on the pressure in the suspension at a selected depth, which is an integral measure of all particles in suspension above the measuring depth. We derive a mathematical model which predicts the pressure decrease due to settling of particles as function of the PSD. The PSD of the analyzed sample is identified by fitting the simulated time series of pressure to the observed one by inverse modeling using global optimization. The new method yields the PSD in very high resolution and its experimental realization completely avoids any disturbance by the measuring process. A sensitivity analysis of different soil textures demonstrates that the method yields unbiased estimates of the PSD with very small estimation variance and an absolute error in the clay and silt fraction of less than 0.5%. [ABSTRACT FROM AUTHOR]

Understanding the influence of attached microbial biomass on water flow in variably saturated soils is crucial for many engineered flow systems. So far, the investigation of the effects of microbial biomass has been mainly limited to water-saturated systems. We have assessed the influence of biofilms on the soil hydraulic properties under variably saturated conditions. A sandy soil was incubated with Pseudomonas Putida and the hydraulic properties of the incubated soil were determined by a combination of methods. Our results show a stronger soil water retention in the inoculated soil as compared to the control. The increase in volumetric water content reaches approximately 0.015 cm3 cm−3 but is only moderately correlated with the carbon deficit, a proxy for biofilm quantity, and less with the cell viable counts. The presence of biofilm reduced the saturated hydraulic conductivity of the soil by up to one order of magnitude. Under unsaturated conditions, the hydraulic conductivity was only reduced by a factor of four. This means that relative water conductance in biofilm-affected soils is higher compared to the clean soil at low water contents, and that the unsaturated hydraulic conductivity curve of biofilm-affected soil cannot be predicted by simply scaling the saturated hydraulic conductivity. A flexible parameterization of the soil hydraulic functions accounting for capillary and noncapillary flow was needed to adequately describe the observed properties over the entire wetness range. More research is needed to address the exact flow mechanisms in biofilm-affected, unsaturated soil and how they are related to effective system properties. [ABSTRACT FROM AUTHOR]

The authors comment regarding the "Simple consistent models for water retention and hydraulic conductivity in the complete moisture range" by A. Peters. Topics discussed include the empirical model for soil hydraulic functions and soil water potential, basis of the models such as conductivity functions and hydraulic functions, and representation of hydraulic conductivity such as capillary flow, corner and film flow, and isothermal vapor flow.

Highlights: [•] Biochar amendments directly affected the soil carbon cycle. [•] Biochar reduced organic matter (OM) mobilization from a soil. [•] Carbon oxidation state of OM mobilized from a soil increased after biochar amendment. [•] Soil released more aromatic OM after turning anoxic. [ABSTRACT FROM AUTHOR]

Abstract: Weighable lysimeters are powerful measurement systems for identifying soil hydraulic processes and properties, because the boundary fluxes (precipitation, actual evapotranspiration, and seepage across the bottom) can be determined very precisely. However, root water uptake by plants and the soil water flux are interrelated. Thus, the simultaneous estimation of root water uptake parameters and soil hydraulic parameters from macroscopic state observations is a challenge. In this study we investigated the possibility of simultaneously estimating root water uptake and soil hydraulic parameters by inverse simulation of soil water flow in monolithic lysimeters under atmospheric boundary conditions. We used the Richards equation and a macroscopic root water uptake model to simulate the processes. The amount of information needed for the unique identification of parameters was analyzed and the magnitude of their uncertainties was investigated. To check the principal feasibility of our approach, we first examined synthetic data sets for different scenarios and instrumentation campaigns that differed in their information content and complexity of soil properties. The investigations of synthetic data showed that for homogeneous profiles, cumulative outflow and profile-averaged water content data contained enough system information to allow the simultaneous estimation of soil hydraulic properties and root-distribution parameters. In contrast, for soil profiles consisting of two layers, unique soil hydraulic parameters and the correct rooting depth could only be estimated if matric potential measurements from both layers were included in the objective function. To test the procedure with real data, soil hydraulic properties of the grass-reference lysimeter at Wagna (Austria) were estimated using actual measurements. Water dynamics in the lysimeter could be described well by an effective parameterization assuming a homogeneous soil profile. Furthermore, the system behavior under different boundary conditions could be predicted adequately with the estimated parameters. [Copyright &y& Elsevier]

We investigated the release of chloride, sulfate, sodium, copper, chromium, and dissolved organic carbon from a demolition waste material and a municipal waste incineration product. Batch leaching tests at the liquid-to-solid ratios (L/S ratios) 1, 2, 5, 10, and 50 L kg-1 were carried out and the parameters of a mass balance-partitioning model were estimated from measured concentrations in the extracts by applying a Bayesian approach using a Markov Chain Monte Carlo sampler. We assessed the uncertainty of the model parameters, the desorption isotherms, and the model-predicted concentrations, respectively. Both the excellent fit to the experimental data and a comparison between the model-predicted and independently measured concentrations at the L/S ratios of 0.25 and 0.5 L kg-1 showed the applicability of the model for almost all studied substances and both materials. Since experimental difficulties impede extraction tests at L/S ratios representative of field soil-water contents, the predictability of concentrations in this range is of great practical relevance for risk assessments. We conclude that batch extraction tests at varying L/S ratios provide, at moderate experimental cost, a powerful complement to established test designs like column leaching or single batch extraction tests. [ABSTRACT FROM AUTHOR]

The simplified evaporation method is frequently applied to determine soil hydraulic properties in the laboratory. In the past, numerical simulations have been used to quantify the accuracy of the SEM. These tests have led to the conclusion that the method yields accurate estimates of hydraulic properties, but they neither accounted for heat flow, nor thermal fluxes of liquid water and water vapor, nor temperature effects on the transport properties. This is problematic because evaporation experiments are under most circumstances non-isothermal. The objective of this study was to test the accuracy of the simplified evaporation method using numerical simulations with a coupled model based on the Philip-de Vries theory. The model includes the fluxes of water, vapor, and heat flow, solves the surface energy balance and therefore provides a state-of-the-art description of the fluxes of water, vapor and energy occurring in laboratory evaporation experiments. We first present simulation results for three soil textures and different evaporation rates during stage-one, and analyze the accuracy of the evaporation method using the simulation data. The mean error for the estimated volumetric water content as function of matric head is smaller than 0.0025 and the relative error of hydraulic conductivity ranges from 5-15 % for sandy loam and clay loam. For sandy soil, the error in hydraulic conductivity is markedly higher but the shape of the hydraulic conductivity curve is still identified well. The average error of the SEM turned out to be only slightly higher compared to previous analyses of the evaporation method which used isothermal flow modeling. [ABSTRACT FROM AUTHOR]

A new model is presented which predicts the effective hydraulic conductivity of stony soils. It is based on the generalized effective medium (GEM) theory in a three-dimensional medium consisting of a homogeneous background soil and ellipsoidal inclusions. The formulation accounts for the hydraulic conductivities of background soil and stones, volumetric stone content, and the shape and orientation of the stones. One advantage of the new model over existing approaches is that it considers the hydraulic conductivity of the stones and is therefore applicable to soils containing permeable inclusions. Furthermore, effective hydraulic conductivity can be calculated for mixtures which consist of more than two constituents with contrasting hydraulic conductivities and for mixtures which contain tightly packed and even intersecting stones. As a consequence, soils with high stone content (>50 % v/v) and soils close to the percolation threshold can be treated. In the case of non-porous, spherically-shaped stones, the model reduces to the Maxwell model which has been used in vadose zone hydrology before. We illustrate the behavior of the model for different binary mixtures and compare its results with those of numerical simulations in three spatial dimensions. Model results lie well within the Hashin-Shtrikman bounds over the whole range of volumetric stone content. The generality and simplicity of the model make it attractive for practical applications in vadose zone flow and transport studies. [ABSTRACT FROM AUTHOR]

Solute transport in porous media is typically simulated with the convection dispersion equation (CDE). Hydrodynamic dispersion is usually assumed to behave similarly as molecular diffusion and is therefore formulated using Fick's law. In this contribution, the application of the CDE for modeling solute transport in porous media is critically analyzed for situations in which the solute concentration changes locally while water is flowing. A local increase or decrease of concentration caused by root water uptake or evaporation (phase change) leads to concentration gradients in all spatial directions and induces diffusive as well as dispersive solute fluxes in all directions. These fluxes include a dispersive flux opposite to the direction of the water flux which is physically wrong. The aim of this study was to investigate the magnitude of the resulting error by means of numerical simulations. We simulated solute transport during steady-state evaporation from a groundwater table to a bare soil surface with the Hydrus-1D code. The solute was assumed to originate from the groundwater. The simulation lead to the correct result that the solute accumulates around the evaporation plane located close to the soil surface. However, because Fick's law is used to model the dispersive flux, both diffusive and dispersive solute fluxes were directed downward, i.e. opposed to the gradient in solute concentration. While this is physically correct for the diffusive flux, it is fundamentally wrong for the dispersive flux. We show that the erroneous dispersive flux can have the same order of magnitude as the convective solute flux. Under such conditions, application of the CDE is questionable. [ABSTRACT FROM AUTHOR]

The particle-size distribution (PSD) is a basic physical property of soils. Its experimentaldetermination in the silt range is based on gravitational sedimentation in an initiallyhomogeneous suspension. Two classic methods that use this principle are the hydrometermethod and the pipette method. Recently, Durner et al. (2017) have presented the integralsuspension pressure method (ISP) for the accurate, disturbance-free determination of the PSDin high resolution. In this method, a time series of suspension pressure at a fixed depth in thesedimentation cylinder is monitored, and the PSD is identified by simulating thesedimentation process and numerically solving the inverse problem. We present an extension of the experimental protocol called ISP+, which makes theinverse problem better-posed. At the end of the ISP measurement, a part of the suspensionis drained laterally from the sedimentation cylinder through an outlet, collectedand oven-dried. The resulting dry mass of the soil particles is integrated into theobjective function of the inverse problem. This markedly reduces the uncertainty of theidentified PSD towards the finest particles. We present theoretical studies usingcomputer-generated data and first experimental results evaluated by inverse modelingto illustrate the new experimental design and the improved accuracy of the ISP+method. Reference: Durner, W., S.C. Iden, and G. von Unold, 2017: The integral suspension pressuremethod (ISP) for precise particle-size analysis by gravitational sedimentation, Water ResourcesResearch, doi:10.1002/2016WR019830. [ABSTRACT FROM AUTHOR]

Modeling water flow in the soil–plant–atmosphere continuum with the Richards equation requires a model for the sink term describing water uptake by plant roots. Despite recent progress in developing process-based models of water uptake by plant roots and water flow in above-ground parts of vegetation, effective models of root water uptake are widely applied and necessary for large-scale applications. Modeling root water uptake consists of three steps, (i) specification of the spatial distribution of potential uptake, (ii) reduction of uptake due to various stress sources, and (iii) enhancement of uptake in part of the simulation domain to describe compensation. We discuss the conceptual shortcomings of the frequently used root water uptake model of Feddes and suggest a simple but effective improvement of the model. The improved model parametrizes water stress in wet soil by a reduction scheme which is formulated as function of air content whereas water stress due to low soil water potential is described by the original approach of Feddes. The improved model is physically more consistent than Feddes’ model because water uptake in wet soil is limited by aeration which is a function of water content. The suggested modification is particularly relevant for simulations in heterogeneous soils, because stress parameters are uniquely defined for the entire simulation domain, irrespective of soil texture. Numerical simulations of water flow and root water uptake in homogeneous and stochastic heterogeneous soils illustrate the effect of the new model on root water uptake and actual transpiration. For homogeneous fine-textured soils, predicted root water uptake never achieves its potential rate. In stochastic heterogeneous soil, predicted water uptake is more pronounced at the interfaces between fine and coarse regions which has potential implications for plant growth, nutrient uptake and depletion. [ABSTRACT FROM AUTHOR]

Simultaneous determination of soil hydraulic properties and a rooting depth parameter was studied by inverse modeling of unsaturated water flow with root water uptake in weighable lysimeters under transient atmospheric boundary conditions. Inclusion of pressure head data in the objective function yielded unique parameter estimates even for layered profiles. We investigated the feasibility of simultaneous identification of soil hydraulic and root-distribution parameters by inverse simulation of soil water flow in monolithic lysimeters under atmospheric boundary conditions using the Richards equation and a macroscopic root water uptake model. Weighable lysimeters are powerful test systems for this purpose because the boundary fluxes (precipitation, actual evapotranspiration, and seepage across the bottom) can be determined very precisely. We analyzed the amount of information needed for the unique identification of parameters and investigated the magnitude of their uncertainties. First, we examined synthetic data sets for different scenarios and instrumentation campaigns that differed in their information content and complexity of soil properties. Atmospheric boundary conditions as measured at the lysimeter station in Wagna, Austria, were used as forcing data. The results show that for homogeneous profiles, cumulative outflow and profile-averaged water content data contain enough system information to allow the simultaneous estimation of soil hydraulic properties and root-distribution parameters. In contrast, for soil profiles consisting of two layers, unique soil hydraulic parameters and the correct rooting depth could only be estimated if matric potential measurements from both layers were included in the objective function. Finally, soil hydraulic properties of the grass-reference lysimeter in Wagna were estimated using real measurements. Water dynamics in the lysimeter could be described well by an effective parameterization assuming a homogeneous soil profile. Furthermore, the system behavior under different boundary conditions could be predicted adequately with the estimated parameters. This demonstrates the usefulness of the identified system properties for predictive modeling. [ABSTRACT FROM AUTHOR]