Peters [2013] recently presented a new empirical model of soil hydraulic functions over the entire range of soil water potential. His model is based on established approaches for the retention and conductivity function, and assimilates recently gained knowledge about the shape of hydraulic functions in the medium and dry moisture range. Specifically, the retention function reaches a zero soil water content at a water potential corresponding to oven dryness and approaches this point by a linear decrease of water content with the logarithm of suction, which is in agreement with experimental data [Schneider and Goss, 2012] and physical models of water sorption on surfaces [Tokunaga, 2009]. The Peters [2013] retention function does not require more parameters than traditional models, i.e., it is fully parameterized by a saturated water content, a residual water content, and two parameters which describe the location and width of the pore-size distribution. The unsaturated hydraulic conductivity function represents the flow components capillary flow, film and corner flow, and isothermal vapor flow and requires one additional free parameter as compared to classic models. Peters' model hence offers great potential for modeling soil-water flow in the full moisture range while simultaneously keeping the number of model parameters at a minimum. The objective of this comment is to reference some shortcomings of the model formulation as published by Peters [2013] and to provide solutions to the following points which we regard as problematic: 2013] is not differentiable at suction h5h a [L], the suction below which X(h) is unity. As a result, the soil water capacity function is not continuous but has a discontinuity at h a . (8)). As X(h) is not differentiable at h a , the saturation function S cap is not continuously differentiable if the correction is applied. In cases where the capillary saturation function C(h)[ If the correction discussed under point 2 is applied, closed-form expressions of the conductivity functionbecome unavailable for the models of Kosugi and van Genuchten.4. It is possible that the correction of C(h) is turned on or off during parameter estimation depending on the possible combination of the two parameters describing the pore-size distribution. Unfortunately, the correction S cap ðhÞ5XðhÞCðhÞ changes a large portion of the retention curve and this may affect the performance of the iterative minimization algorithm by generating spurious secondary minima and discontinuities in the objective function [see Kavetski et al., 2007, for examples from rainfall-runoff modeling].In the following, we present solutions to these problems by proposing two modifications of Peters's [2013] retention function and present parameter estimation results for the 10 soils analyzed by him using the new model, which we refer to as Peters-Durner-Iden (PDI) model.

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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.

[1] Inverse modeling is a powerful technique for identifying the hydraulic properties of unsaturated porous media. However, the selection of an appropriate parameterization of the soil water retention and hydraulic conductivity function remains a challenge. In this article, we present an improved algorithm for estimating these two relationships without assigning an a priori shape to them. The approach uses cubic Hermite interpolation and a global optimization strategy. A multilevel routine identifies the adequate number of degrees of freedom by balancing model performance, the statistical interaction of the estimated model parameters, and their number. A first-order uncertainty analysis provides a quantitative measure of how well the soil hydraulic properties can be identified in different ranges of pressure head. This offers great potential for designing optimal experimental procedures for identifying the hydraulic properties of porous media. We demonstrate the effectiveness of the algorithm for the evaluation of multistep outflow experiments by investigating synthetic data sets and real measurements. The free-form approach yields optimal model parameters that show only moderate correlation, indicating well-posed inverse problems. Since parameterization errors are almost completely avoided, the algorithm is well suited to identifying other error sources in unsaturated flow problems, e.g., limitations in the applicability of the Richards equation or problems caused by spatial heterogeneity.Citation: Iden, S. C., and W. Durner (2007), Free-form estimation of the unsaturated soil hydraulic properties by inverse modeling using global optimization, Water Resour. Res., 43, W07451,

The transferability of soil hydraulic properties measured in the laboratory to the field or catchment scale is a key problem in soil hydrology. To narrow the gap between laboratory and field scale we investigated soil water movement at the lysimeter scale. Specific questions of interest are the existence and uniqueness of effective hydraulic properties for lysimeters that are internally heterogeneous. To answer these questions, synthetic measurements of water contents, pressure heads, and fluxes across the system boundaries were generated by forward modelling of water flow, based on the Richards equation, for a variety of homogeneous and layered soils and under varying types of boundary conditions (multistep outflow, evaporation, transient atmospheric). We evaluated the measurements by inverse modelling assuming a homogeneous system. The globally convergent shuffled complex evolution algorithm was applied to avoid parameter estimation problems caused by a rough topology of the objective function. The hydraulic properties of homogeneous soils were always uniquely identified, not only for the classic multistep outflow and evaporation experiments but also under natural atmospheric boundary conditions. Moreover, for the weakly heterogeneous layered soils, the soil water dynamics could be well described with effective homogeneous properties. For highly heterogeneous, layered soils, it was still possible to match the boundary fluxes for all types of experiments. Internal system states could not be matched, however, and the properties identified depended on the type of experiment. For these soils no unique effective soil hydraulic properties exist. We found that for strongly layered soils the simultaneous determination of the hydraulic properties of multiple soil layers by inverse modelling is a practicable alternative to the description with effective parameters.

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.

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.

Inverse modeling of multistep outflow (MSO) experiments is an established and fast method to determine unsaturated hydraulic properties of soils. A disadvantage of the method is its low sensitivity with respect to the hydraulic conductivity function at saturation, which makes the respective estimation very uncertain. Thus, the use of independently measured values for the saturated hydraulic conductivity, Ks, is generally recommended. This involves disadvantages, namely, the effort to conduct additional experiments and the general problems associated with the combination of data from different experimental sources. To overcome this problem, we propose to combine percolation and outflow in one experiment. This extended multistep outflow experiment (XMSO) starts with a completely water‐saturated soil column, on top of which a small amount of water is ponding. The first experimental phase is a saturated percolation under falling‐head conditions. After ponding ceases, the experiment continues as a standard MSO experiment with an unsaturated drainage process. The XMSO experiment is evaluated by inverse modeling, using measurements of cumulative outflow and tensiometric pressure head data. Our analysis of synthetic and real data demonstrates that XMSO yields very accurate estimates of saturated and near‐saturated hydraulic properties, even for soils with structured pore systems. Furthermore, saturated hydraulic conductivities of the supporting porous plate and the soil can be simultaneously determined with great accuracy. We conclude that the XMSO experimental design solves the problem of the identification of near‐saturated hydraulic properties of soil samples and reduces the estimation uncertainty of Ks to a minimum.