Search

Many different equations have been proposed to describe quantitatively one-dimensional soil water infiltration. The unknown coefficients of these equations characterize soil hydraulic properties and may be estimated from a n record, (Formula presented.), of cumulative infiltration measurements using curve fitting techniques. The two-term infiltration equation, (Formula presented.), of Philip has been widely used to describe measured infiltration data. This function enjoys a solid mathematical–physical underpinning and admits a closed-form solution for the soil sorptivity, S [L T−1/2], and multiple, c [−], of the saturated hydraulic conductivity, Ks [L T−1]. However, Philip's two-term equation has a limited time validity, tvalid [T], and thus cumulative infiltration data, (Formula presented.), beyond (Formula presented.) will corrupt the estimates of S and Ks. This paper introduces a novel method for estimating S, c, Ks, and tvalid of Philip's two-term infiltration equation. This method, coined parasite inversion, use as vehicle Parlange's three-parameter infiltration equation. As prerequisite to our method, we present as secondary contribution an exact, robust and efficient numerical solution of Parlange's infiltration equation. This solution admits Bayesian parameter estimation with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and yields as byproduct the marginal distribution of Parlange's β parameter. We evaluate our method for 12 USDA soil types using synthetic infiltration data simulated with HYDRUS-1D. An excellent match is observed between the inferred values of S and Ks and their “true” values known beforehand. Furthermore, our estimates of c and tvalid correlate well with soil texture, corroborate linearity of the (Formula presented.) relationship for (Formula presented.), and fall within reported ranges. A cumulative vertical infiltration of about 2.5 cm may serve as guideline for the time-validity of Philip's two-term infiltration equation.

Many different equations ranging from simple empirical to semi-analytical solutions of the Richards equation have been proposed for quantitative description of water infiltration into variably saturated soils. The sorptivity, S, and the saturated hydraulic conductivity, Ks, in these equations are typically unknown and have to be estimated from measured data. In this paper, we use so-called characteristic time (tchar) to design a new method, referred to as the characteristic time method (CTM) that estimates S, and Ks, from one-dimensional (1D) cumulative infiltration data. We demonstrate the usefulness and power of the CTM by comparing it with a suite of existing methods using synthetic cumulative infiltration data simulated by HYDRUS-1D for 12 synthetic soils reflecting different USDA textural classes, as well as experimental data selected from the Soil Water Infiltration Global (SWIG) database. Results demonstrate that the inferred values of S and Ks are in excellent agreement with their theoretical values used in the synthetically simulated infiltration experiments with Nash–Sutcliffe criterion close to unity and RMSE values of 0.04 cm h−1/2 and 0.05 cm h−1, respectively. The CTM also showed very high accuracy when applied on synthetic data with added measurement noise, as well as robustness when applied to experimental data. Unlike previously published methods, the CTM does not require knowledge of the time validity of the applied semi-analytical solution for infiltration and, therefore, is applicable to infiltrations with durations from 5 min to several days. A script written in Python of the CTM method is provided in the supplemental material.

Infiltration in soils is a key process that partitions precipitation at the land surface into surface runoff and water that enters the soil profile. We reviewed the basic principles of water infiltration in soils and we analyzed approaches commonly used in land surface models (LSMs) to quantify infiltration as well as its numerical implementation and sensitivity to model parameters. We reviewed methods to upscale infiltration from the point to the field, hillslope, and grid cell scales of LSMs. Despite the progress that has been made, upscaling of local-scale infiltration processes to the grid scale used in LSMs is still far from being treated rigorously. We still lack a consistent theoretical framework to predict effective fluxes and parameters that control infiltration in LSMs. Our analysis shows that there is a large variety of approaches used to estimate soil hydraulic properties. Novel, highly resolved soil information at higher resolutions than the grid scale of LSMs may help in better quantifying subgrid variability of key infiltration parameters. Currently, only a few LSMs consider the impact of soil structure on soil hydraulic properties. Finally, we identified several processes not yet considered in LSMs that are known to strongly influence infiltration. Especially, the impact of soil structure on infiltration requires further research. To tackle these challenges and integrate current knowledge on soil processes affecting infiltration processes into LSMs, we advocate a stronger exchange and scientific interaction between the soil and the land surface modeling communities.

Observations of soil moisture content from remote sensing platforms can be used in conjunction with hydrological models to inversely estimate soil hydraulic properties (SHPs). In recent years, cosmic-ray neutron sensing (CRNS) has proven to be a reliable method for the estimation of area-average soil moisture at field scales. However, its use in the inverse estimation of the effective SHPs is largely unexplored. Thus, the main objective of this study was to assess the information content of aboveground fast-neutron counts to estimate SHPs using both a synthetic modeling study and actual experimental data from the Rollesbroich catchment in Germany. For this, the forward neutron operator COSMIC was externally coupled with the hydrological model HYDRUS-1D. The coupled model was combined with the Affine Invariant Ensemble Sampler to calculate the posterior distributions of effective soil hydraulic parameters as well as the model-predictive uncertainty for different synthetic and experimental scenarios. Measured water contents at different depths were used to assess estimated SHPs. The analysis of both synthetic and actual CRNS data from homogenous and heterogeneous soil profiles, respectively, led to confident estimations of the shape parameters a and n, while higher uncertainty was observed for the saturated hydraulic conductivity. Furthermore, results demonstrated that neutron data are less influenced by local sources of uncertainty compared with near-surface point measurements. The simultaneous use of CRNS and water content data further reduced the overall uncertainty, opening up new perspectives for the combination of CRNS with other remote sensing techniques for the inverse estimation of the effective SHPs.

The two‐term infiltration equation I(t)=St+At$I(t) = S\sqrt {t} + A t$ is commonly used to determine the sorptivity, S$S$(LT−1/2)$({\text{LT}}^{-1/2})$, and product, A=cKs$A = c K_{\text{s}}$(LT−1)$({\text{LT}}^{-1})$, of the dimensionless multiple c$c$ and saturated soil hydraulic conductivity Ks$K_{\text{s}}$(LT−1)$({\text{LT}}^{-1})$ from cumulative vertical infiltration measurements I∼1,...,I∼n$\tilde{I}_{1},\ldots,\tilde{I}_{n}$ (L) at times t1,...,tn$t_{1},\ldots,t_{n}$ (T). This reduced form of the quasi‐analytical power series solution of Richardson's equation of Philip enjoys a solid physical underpinning but at the expense of a limited time validity. Using simulated infiltration data, Jaiswal et al. have shown this time validity to equal about 2.5 cm of cumulative infiltration. The goals of this work are twofold. First, we investigate the extent to which cumulative infiltration measurements larger than 2.5 cm bias the estimates of S$S$ and Ks$K_{\text{s}}$. Second, we investigate the impact of epistemic errors on the inferred time validities and parameters. Partial infiltration curves up to 2.5 cm of cumulative vertical infiltration improve substantially the agreement between actual and least squares estimates of S$S$ and Ks$K_{\text{s}}$. But this only holds if the data generating infiltration process follows Richardson's equation and experimental conditions satisfy assumptions of soil homogeneity and a uniform initial water content. Otherwise, autocorrelated cumulative infiltration residuals will bias the least squares estimates of S$S$ and Ks$K_{\text{s}}$. Our findings reiterate and reinvigorate earlier conclusions of Haverkamp et al. and show that epistemic errors deteriorate the physical significance of the coefficients of infiltration functions. As a result, the parameters of infiltration functions cannot simply be used in storm water and vadose zone flow models to forecast runoff and recharge at field and landscape scales unless these predictions are accompanied by realistic uncertainty bounds. We conclude that the time validity of Philip's two‐term equation is an elusive theoretical quantity with arbitrary physical meaning. Core Ideas: Structural model errors of infiltration functions bias the values of S$S$ and Ks$K_s$.Least squares estimates of Ks$K_s$ compare poorly to measured values.Epistemic uncertainty turns coefficients of infiltration functions into fitting parameters.The time validity of Philip's two‐term equation is an elusive theoretical quantity.Treatment of epistemic errors enhances usefulness of plot‐scale infiltration experiments for large‐scale prediction. [ABSTRACT FROM AUTHOR]

Plant water uptake and plant and soil water status are important for the soil water balance and plant growth. They depend on atmospheric water demand and the accessibility of soil water to plant roots, which is in turn related to the hydraulic properties of the root system and the soil around root segments. We present a simulation model that describes water flow in the soil–plant system mechanistically considering both root and soil hydraulic properties. We developed an approach to upscale three‐dimensional (3D) flow in the soil toward root segments of a 3D root architecture to a model that considers one‐dimensional flow between horizontal soil layers and radial flow to root segments in that layer. The upscaled model couples upscaled linear flow equations in the root system with an analytical solution of the nonlinear radial flow equation between the soil and roots. The upscaled model avoids simplifying assumptions about root hydraulic properties and water potential drops near roots made in, respectively, soil‐ and root‐centered models. Xylem water potentials and soil–root interface potentials are explicitly simulated and show, respectively, large variations with depth and large deviations from bulk soil water potentials under dry soil conditions. Accounting for hydraulic gradients in the soil around root segments led to an earlier but slower reduction of transpiration during a drought period and a better plant water status with higher nighttime plant water potentials. Core Ideas: Root water uptake depends on root and soil hydraulic properties.Water uptake at root element scale was upscaled to the root system scale.The upscaled model can be implemented in one‐dimensional soil water flow models.Low conductance of dry soil prevents low nighttime plant water potentials. [ABSTRACT FROM AUTHOR]

Non‐invasive imaging of processes within the soil–plant continuum, particularly root and soil water distributions, can help optimize agricultural practices such as irrigation and fertilization. In this study, in‐situ time‐lapse horizontal crosshole ground penetrating radar (GPR) measurements and root images were collected over three maize crop growing seasons at two minirhizotron facilities (Selhausen, Germany). Root development and GPR permittivity were monitored at six depths (0.1–1.2 m) for different treatments within two soil types. We processed these data in a new way that gave us the information of the "trend‐corrected spatial permittivity deviation of vegetated field," allowing us to investigate whether the presence of roots increases the variability of GPR permittivity in the soil. This removed the main non‐root‐related influencing factors: static influences, such as soil heterogeneities and rhizotube deviations, and dynamic effects, such as seasonal moisture changes. This trend‐corrected spatial permittivity deviation showed a clear increase during the growing season, which could be linked with a similar increase in root volume fraction. Additionally, the corresponding probability density functions of the permittivity variability were derived and cross‐correlated with the root volume fraction, resulting in a coefficient of determination (R2) above 0.5 for 23 out of 46 correlation pairs. Although both facilities had different soil types and compaction levels, they had similar numbers of good correlations. A possible explanation for the observed correlation is that the presence of roots causes a redistribution of soil water, and therefore an increase in soil water variability. Core Ideas: Analying spatial and temporal belowground GPR signal variability and root images for maize crop roots.Root images and GPR data show differences for different treatments.Linking of root volume fraction and GPR permittivity variability. [ABSTRACT FROM AUTHOR]

Copyright of Vadose Zone Journal is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article focuses on the evaluation of different methods for gap filling of long-term actual evapotranspiration time series measured by lysimeters. It explore four different gap filling methods namely potential terrestrial evapotranspiration method, the ratio method, and the FAO-based water balance method, and HYDRUS modeling. It also mentions that gap-filling methods do not perform very differently for dry and wet conditions.

Core Ideas: Parameters of different RWU models were optimized using data from a rhizotron facility.The same soil hydraulic properties were obtained for models considering RWU compensation.Feddes–Jarvis and Couvreur models predicted similar root‐system‐scale stress functions.The obtained RWU parameters were consistent with data reported in the literature.The models with compensation predicted similar total uptake but different local RWU. The spatiotemporal distribution of root water uptake (RWU) depends on the dynamics of the root distribution and compensatory uptake from wetter regions in the root zone. This work aimed to parameterize three RWU models with different representations of compensation: the Feddes–Jarvis model that uses an empirical function, the Feddes model without compensation, and the Couvreur model that is based on a physical description of water flow in the soil–root system. These models were implemented in HYDRUS‐1D, and soil hydraulic parameters were optimized by inverse modeling using soil water content and potential measurements and observations of root distributions of winter wheat (Triticum aestivum L.) in horizontally installed rhizotubes. Soil moisture was equally well predicted by the three models, and the soil hydraulic parameters optimized by the models with compensation were comparable. The obtained RWU parameters of the Feddes–Jarvis model were consistent with data reported in the literature, although the pressure heads h3l and h3h for lower and higher transpirations rates, respectively, could not be uniquely identified. Response surfaces of the objective function showed that the root‐related parameters of the Couvreur model could be identified using inverse modeling. Furthermore, these parameters were consistent with combined root architectural and hydraulic observations from the literature. The Feddes–Jarvis and Couvreur models simulated similar root‐system‐scale stress functions that link total RWU to the effective root zone water potential, suggesting that parameters may be transferable between the two models. Simulated RWU profiles differed due to different water redistribution by the root system, but the measurements were not sufficiently precise to observe this redistribution. [ABSTRACT FROM AUTHOR]