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The two-term infiltration equation (Formula presented.) is commonly used to determine the sorptivity, (Formula presented.) (Formula presented.), and product, (Formula presented.) (Formula presented.), of the dimensionless multiple (Formula presented.) and saturated soil hydraulic conductivity (Formula presented.) (Formula presented.) from cumulative vertical infiltration measurements (Formula presented.) (L) at times (Formula presented.) (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 (Formula presented.) and (Formula presented.). 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 (Formula presented.) and (Formula presented.). 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 (Formula presented.) and (Formula presented.). 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.

Despite previous reports on European growing seasons lengthening due to global warming, evidence shows that this trend has been reversing in the past decade due to increased transpiration needs. To asses this, we used an innovative method along with space-based observations to determine the timing of greening and dormancy and then to determine existing trends of them and causes. Early greening still occurs, albeit at slower rates than before. However, a recent (2011–2020) shift in the timing of dormancy has caused the season length to decrease back to 1980s levels. This shortening of season length is attributed primarily to higher atmospheric water demand in summer that suppresses transpiration even for soil moisture levels as of previous years. Transpiration suppression implies that vegetation is unable to meet the high transpiration needs. Our results have implications for future management of European ecosystems (e.g., net carbon balance and water and energy exchange with atmosphere) in a warmer world.

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.

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]

When estimating field‐scale average soil moisture from sensors measuring at fixed positions, spatial variability in soil moisture leads to "measurement errors" of the spatial mean, which may persist over time due to persistent soil moisture patterns resulting in autocorrelated measurement errors. The uncertainty of parameters that are derived from such measurements may be underestimated when they are assumed to be independent. Temporal autocorrelation models assume stationary random errors, but such error models are not necessarily applicable to soil moisture measurements. As an alternative, we propose a mechanistic error model that is based on the spatial variability of the water retention curve and assumes a uniform water potential. We tested whether spatial soil moisture variability and its temporal covariance could be predicted based on (1) mean soil moisture, (2) water retention variability, and (3) (co)variances of the van Genuchten parameters using a first‐order expansion of the retention curve. The proposed models were tested in a numerical and a field experiment. For the field experiment, in situ sensor measurements and water retention curves were obtained in a field plot. Both experiments showed that water retention variability under a uniform water potential is a good predictor for spatial soil moisture variability, and that soil moisture errors are strongly correlated in time and neglecting them would be an incorrect assumption. The temporal error covariance could be predicted as a function of the mean moisture contents at two observation times. Further research is required to assess the impact of these temporal correlations on soil moisture predictions. Core Ideas: Soil moisture is spatially variable, and spatial variations are correlated in time.Due to spatial variability, the estimated average soil moisture from a limited number of measurements is uncertain.The error of the spatial mean estimated from a limited number of sensors at fixed positions is correlated in time.A mechanistic error modeling approach is presented based on the spatial variability of the water retention curve.Such a model can predict measurement variability and error covariance in time as a function of mean soil moisture. [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]

Root hydraulic properties are key physiological traits that determine the capacity of root systems to take up water, at a specific evaporative demand. They can strongly vary among species, cultivars or even within the same genotype, but a systematic analysis of their variation across plant functional types (PFTs) is still missing. Here, we reviewed published empirical studies on root hydraulic properties at the segment‐, individual root‐, or root system scale and determined its variability and the main factors contributing to it. This corresponded to a total of 241 published studies, comprising 213 species, including woody and herbaceous vegetation. We observed an extremely large range of variation (of orders of magnitude) in root hydraulic properties, but this was not caused by systematic differences among PFTs. Rather, the (combined) effect of factors such as root system age, driving force used for measurement, or stress treatments shaped the results. We found a significant decrease in root hydraulic properties under stress conditions (drought and aquaporin inhibition, p <.001) and a significant effect of the driving force used for measurement (hydrostatic or osmotic gradients, p <.001). Furthermore, whole root system conductance increased significantly with root system age across several crop species (p <.01), causing very large variation in the data (>2 orders of magnitude). Interestingly, this relationship showed an asymptotic shape, with a steep increase during the first days of growth and a flattening out at later stages of development. We confirmed this dynamic through simulations using a state‐of‐the‐art computational model of water flow in the root system for a variety of crop species, suggesting common patterns across studies and species. These findings provide better understanding of the main causes of root hydraulic properties variations observed across empirical studies. They also open the door to better representation of hydraulic processes across multiple plant functional types and at large scales. All data collected in our analysis has been aggregated into an open access database (https://roothydraulic-properties.shinyapps.io/database/), fostering scientific exchange. [ABSTRACT FROM AUTHOR]

Drought is a serious constraint to crop growth and production of important staple crops such as maize. Improved understanding of the responses of crops to drought can be incorporated into cropping system models to support crop breeding, varietal selection and management decisions for minimizing negative impacts. We investigate the impacts of different soil types (stony and silty) and water regimes (irrigated and rainfed) on hydraulic linkages between soil and plant, as well as root: shoot growth characteristics. Our analysis is based on a comprehensive dataset measured along the soil-plant-atmosphere pathway at field scale in two growing seasons (2017, 2018) with contrasting climatic conditions (low and high VPD). Roots were observed mostly in the topsoil (10–20 cm) of the stony soil while more roots were found in the subsoil (60–80 cm) of the silty soil. The difference in root length was pronounced at silking and harvest between the soil types. Total root length was 2.5–6 times higher in the silty soil compared to the stony soil with the same water treatment. At silking time, the ratios of root length to shoot biomass in the rainfed plot of the silty soil (F2P2) were 3 times higher than those in the irrigated silty soil (F2P3) while the ratio was similar for two water treatments in the stony soil. With the same water treatment, the ratios of root length to shoot biomass of silty soil was higher than stony soil. The observed minimum leaf water potential (ψleaf) varied from around -1.5 MPa in the rainfed plot in 2017 to around -2.5 MPa in the same plot of the stony soil in 2018. In the rainfed plot, the mimimum ψleaf in the stony soil was lower than in silty soil from -2 to -1.5 MPa in 2017, respectively while these were from -2.5 to -2 MPa in 2018, respectively. Leaf water potential, water potential gradients from soil to plant roots, plant hydraulic conductance (Ksoil_plant), stomatal conductance, transpiration, and photosynthesis were considerably modulated by the soil water content and the conductivity of the rhizosphere. When the stony soil and silt soil are compared, the higher 'stress' due to the lower water availability in the stony soil resulted in less roots with a higher root tissue conductance in the soil with more stress. When comparing the rainfed with the irrigated plot in the silty soil, the higher stress in the rainfed soil resulted in more roots with a lower root tissue conductance in the treatment with more stress. This illustrates that the 'response' to stress can be completely opposite depending on conditions or treatments that lead to the differences in stress that are compared. To respond to water deficit, maize had higher water uptake rate per unit root length and higher root segment conductance in the stony soil than in the silty soil, while the crop reduced transpired water via reduced aboveground plant size. Future improvements of soil-crop models in simulating gas exchange and crop growth should further emphasize the role of soil textures on stomatal function, dynamic root growth, and plant hydraulic system together with aboveground leaf area adjustments. [ABSTRACT FROM AUTHOR]

Drought is a serious constraint to crop growth and production of important staple crops such as maize. Improved understanding of the responses of crops to drought can be incorporated into cropping system models to support crop breeding, varietal selection and management decisions for minimizing negative impacts. We investigate the impacts of different soil types (stony and silty) and water regimes (irrigated and rainfed) on hydraulic linkages between soil and plant, as well as root: shoot growth characteristics. Our analysis is based on a comprehensive dataset measured along the soil-plant-atmosphere pathway at field scale in two growing seasons (2017, 2018) with contrasting climatic conditions (low and high VPD). Roots were observed mostly in the topsoil (10-20 cm) of the stony soil while more roots were found in the subsoil (60-80 cm) of the silty soil. The difference in root length was pronounced at silking and harvest between the soil types. Total root length was 2.5 - 6 times higher in the silty soil compared to the stony soil with the same water treatment. At silking time, the ratios of root length to shoot biomass in the rainfed plot of the silty soil (F2P2) were 3 times higher than those in the irrigated silty soil (F2P3) while the ratio was similar for two water treatments in the stony soil. With the same water treatment, the ratios of root length to shoot biomass of silty soil was higher than stony soil. The observed minimum leaf water potential (ψleaf) varied from around -1.5 MPa in the rainfed plot in 2017 to around -2.5 MPa in the same plot of the stony soil in 2018. In the rainfed plot, the mimimum ψleaf in the stony soil was lower than in silty soil from -2 to -1.5 MPa in 2017, respectively while these were from -2.5 to -2 MPa in 2018, respectively. Leaf water potential, water potential gradients from soil to plant roots, plant hydraulic conductance (Ksoil_plant), stomatal conductance, transpiration, and photosynthesis were considerably modulated by the soil water content and the conductivity of the rhizosphere. When the stony soil and silt soil are compared, the higher 'stress' due to the lower water availability in the stony soil resulted in less roots with a higher root tissue conductance in the soil with more stress. When comparing the rainfed with the irrigated plot in the silty soil, the higher stress in the rainfed soil resulted in more roots with a lower root tissue conductance in the treatment with more stress. This illustrates that the 'response' to stress can be completely opposite depending on conditions or treatments that lead to the differences in stress that are compared. To respond to water deficit, maize had higher water uptake rate per unit root length and higher root segment conductance in the stony soil than in the silty soil, while the crop reduced transpired water via reduced aboveground plant size. Future improvements of soil-crop models in simulating gas exchange and crop growth should further emphasize the role of soil textures on stomatal function, dynamic root growth, and plant hydraulic system together with aboveground leaf area adjustments. [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]