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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]

Soil moisture is an essential climate variable of the Earth system. Understanding its spatiotemporal dynamics is essential for predicting weather patterns and climate variability, monitoring and mitigating the effects and occurrence of droughts and floods, improving irrigation in agricultural areas, and sustainably managing water resources. Here we review in depth how soils can remember information on soil moisture anomalies over time, as embedded in the concept of soil moisture memory (SMM). We explain the mechanisms underlying SMM and explore its external and internal drivers; we also discuss the impacts of SMM on different land surface processes, focusing on soil‐plant‐atmosphere coupling. We explore the spatiotemporal variability, seasonality, locality, and depth‐dependence of SMM and provide insights into both improving its characterization in land surface models and using satellite observations to quantify it. Finally, we offer guidance for further research on SMM. Plain Language Summary: Our review paper takes an in‐depth look at soil moisture memory, which is how soil records its moisture history over time and space. Analogous to human psychology, which seeks to understand how a person's/society's memory influences his/her present and future behavior, understanding soil moisture memory encourages consideration of how such memory determines present state and might determine future behavior of soils exposed to environmental disturbances. Soil moisture memory can be affected by a variety of factors, both external (e.g., weather extremes) and internal (soil's unique properties). It affects everything from the air to the way our landscapes respond to disasters like droughts, wildfires, and floods. We also studied how this phenomenon affects the balance of water and energy in our environment, the health of our plants, and even how it communicates with the atmosphere. We show how it can change depending on where you are on the planet, the time of year, and how deep you dig into the soil. We offer scientists insights into how weather and land surface models can become more accurate by accounting for soil moisture memory. Its understanding not only helps us predict and manage our environment, but also provides opportunities for exciting scientific discoveries. Key Points: Atmospheric forcings, land use and management, and soil processes and mechanisms explain how and why soil moisture memory emerges in ecosystemsNonlocality of moisture memory, its spread across different regions, and its interaction with large‐scale climate phenomena are underexploredFurther advances in land surface models and closer integration of model simulations and observations are needed to better characterize moisture memory [ABSTRACT FROM AUTHOR]

In his seminal paper on the solution of the infiltration equation, Philip (1969), https://doi.org/10.1016/b978-1-4831-9936-8.50010-6 proposed a gravity time, tgrav, to estimate practical convergence time and the time domain validity of his infinite time series expansion, TSE, for describing the transient state. The parameter tgrav refers to a point in time where infiltration is dominated equally by capillarity and gravity as derived from the first two (dominant) terms of the TSE. Evidence suggests that applicability of the truncated two‐term equation of Philip has a time limit requiring higher‐order TSE terms to better describe the infiltration process for times exceeding that limit. Since the conceptual definition of tgrav is valid regardless of the infiltration model used, we opted to reformulate tgrav using the analytic implicit model proposed by Parlange et al. (1982), https://doi.org/10.1097/00010694-198206000-00001 valid for all times and related TSE. Our derived gravity times ensure a given accuracy of the approximations describing transient states, while also providing insight about the times needed to reach steady state. In addition to the roles of soil sorptivity (S) and the saturated (Ks) and initial (Ki) hydraulic conductivities, we explored the effects of a soil specific shape parameter β, involved in Parlange's model and related to the type of soil, on the behavior of tgrav. We show that the reformulated tgrav (notably tgrav=F(β)S2/Ks−Ki2, ${t}_{\text{grav}}=\,F(\beta){S}^{2}/{\left({K}_{s}-{K}_{i}\right)}^{2},$ where F(β) is a β‐dependent function) is about three times larger than the classical tgrav given by tgrav,Philip=S2/Ks−Ki2 $\,{t}_{\text{grav},\text{Philip}}={S}^{2}/{\left({K}_{s}-{K}_{i}\right)}^{2}$. The differences between the classical tgrav,Philip and the reformulated tgrav increase for fine‐textured soils, attributed to the time needed to attain steady‐state infiltration and thus i + nfiltration for inferring soil hydraulic properties. Results show that the proposed tgrav is a better indicator of time domain validity than tgrav,Philip. For the attainment of steady‐state infiltration, the reformulated tgrav is suitable for coarse‐textured soils. Still neither the reformulated tgrav nor the classical tgrav,Philip are suitable for fine‐textured soils for which tgrav is too conservative and tgrav,Philip too short. Using tgrav will improve predictions of the soil hydraulic parameters (particularly Ks) from infiltration data compared to tgrav,Philip. Key Points: A new formulation for infiltration characteristic time, tgrav, is providedThe reformulated tgrav seems to be a better criterion for convergence time of Philip's truncated infiltration equationsThe usage of reformulated tgrav improves predictions of soil hydraulic parameters [ABSTRACT FROM AUTHOR]

Soil bulk density (ρb) is an important indicator of soil quality, productivity, compaction and porosity. Despite its importance, ρb is often omitted from global datasets due to the costs of making many direct ρb measurements and the difficulty of direct measurement on rocky, sandy, very dry, or very wet soils. Pedotransfer functions (PTFs) are deployed to address these limitations. Using readily available soil properties, PTFs employ estimator equations to fit existing datasets to estimate properties like ρb. However, PTF performance often declines when applied to soils outside those in the training dataset. Potentially, recalibrating existing PTFs using new observations would leverage the power of large datasets used in the original PTF derivation, while updating information based on new soil observations. Here, we evaluate such a recalibration approach for ρb estimation, benchmarking its performance against two alternatives: the original, uncalibrated PTFs, and novel, local PTFs derived solely from new soil observations. Using a ρb dataset of N = 360 total observations obtained in West Azerbaijan, Iran, we varied the local dataset size (with N = 15, 30, 60, and 360) and recalibrated four existing PTFs with these data. Local PTFs were generated based on stepwise multiple linear regression for the same datasets. The same PTFs (original, recalibrated, and local) were also applied to the study area, and the resulting ρb estimates were compared with the global SoilGrids dataset. Recalibration of PTFs reduced errors relative to the original uncalibrated PTFs; for instance, the NSE increased from −22.07 to 0.30 (uncalibrated) to 0.20–0.41 (recalibrated), and RMSE decreased from 0.12 to 0.60 Mg m−3 (uncalibrated) to 0.10–0.13 Mg m−3 (recalibrated). The recalibrated PTFs performance was comparable to or better than local PTFs applied to the same data. Recalibration of existing PTFs with local/regional uses provides a viable alternative to the use of global datasets or the development of local PTFs in data‐scarce regions. Highlights: Existing global PTFs were calibrated and tested using a small dataset for local utilisation.Several new local PTFs were also developed using the same datasets.Recalibration of existing global PTFs is comparable to or more accurate than developing new PTFs. [ABSTRACT FROM AUTHOR]

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, {t∼i,I∼i}i=1n$\{ {\tilde t_i},{\tilde I_i}\} _{i = 1}^n$, of cumulative infiltration measurements using curve fitting techniques. The two‐term infiltration equation, I(t)=St+cKst$I(t) = S\sqrt t + c{K_{\rm{s}}}t$, 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, I∼(t∼)$\tilde I(\tilde t)$, beyond t=tvalid$t = {t_{{\rm{valid}}}}$ 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 c(β)$c({{\beta}})$ relationship for 0≤t≤tvalid$0 \le t \le {t_{{\rm{valid}}}}$, 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. Core Ideas: We describe a method that can determine the time validity of infiltration equations.This method infers as well the hydraulic properties of unsaturated soils.We present a robust and efficient numerical solution of Parlange's three‐parameter infiltration equation.Posterior distribution determines how well parameters are defined by calibration to data.Two and a half centimeters of cumulative infiltration is a good proxy for time validity Philip's two‐term equation. [ABSTRACT FROM AUTHOR]

Recently, a novel approach with excellent performance based on the concept of the characteristic infiltration time, the characteristic time method (CTM), is proposed to infer soil sorptivity (S) and saturated hydraulic conductivity (Ks) from one‐dimensional (1D) cumulative infiltration. The current work provides a simplified version of the CTM, called the SCTM, by eliminating the necessity of the iteration method used in CTM and providing a similar accuracy as the original method when estimating S and Ks. We used both synthetic and experimental data to evaluate SCTM in comparison with the original CTM, as well as Sharma (SH) and curve‐fitting methods. In the case of synthetically simulated infiltration experiments, the predicted S and Ks values showed an excellent agreement with their theoretical values, with Nash–Sutcliffe (E) values higher than 0.9 and RMSE values of 0.11 cm h1/2 and 0.35 cm h–1, respectively. In the case of experimental data, the SCTM showed E values larger than 0.73 and RMSE values of 0.64 cm h1/2 and 0.35 cm h–1, respectively. The accuracy and the robustness of SCTM was comparable with the original CTM when applied on synthetic infiltration curves as well as on experimental data. Similar to the original CTM, the simplified approach also does not require the knowledge of the time validity, which is needed when using approaches based on Philip's infiltration theory. The method is applicable to infiltrations with durations from 15 min to 24 h. The supplemental material presents the calculation of S and Ks using SCTM in an Excel spreadsheet. Core Ideas: A simplified version of the CTM is proposed to estimate the S and Ks from a 1D infiltration curve.The SCTM is nearly as accurate as the original CTM in prediction of S and Ks.The SCTM eliminates the necessity of the iteration method used in original CTM. [ABSTRACT FROM AUTHOR]

Modeling of the land surface water‐, energy‐, and carbon balance provides insight into the behavior of the Earth System, under current and future conditions. Currently, there exists a substantial variability between model outputs, for a range of model types, whereby differences between model input parameters could be an important reason. For large‐scale land surface, hydrological, and crop models, soil hydraulic properties (SHP) are required as inputs, which are estimated from pedotransfer functions (PTFs). To analyze the functional sensitivity of widely used PTFs, the water fluxes for different scenarios using HYDRUS‐1D were simulated and predictions compared. The results showed that using different PTFs causes substantial variability in predicted fluxes. In addition, an in‐depth analysis of the soil SHPs and derived soil characteristics was performed to analyze why the SHPs estimated from the different PTFs cause the model to behave differently. The results obtained provide guidelines for the selection of PTFs in large scale models. The model performance in terms of numerical stability, time‐integrated behavior of cumulative fluxes, as well as instantaneous fluxes was evaluated, in order to compare the suitability of the PTFs. Based on this, the Rosetta, Wösten, and Tóth PTF seem to be the most robust PTFs for the Mualem van Genuchten SHPs and the PTF of Cosby for the Brooks Corey functions. Based on our findings, we strongly recommend to harmonize the PTFs used in model inter‐comparison studies to avoid artifacts originating from the choice of PTF rather from different model structures. Plain Language Summary: Hydrological models need information about the soil physical characteristics (soil hydraulic parameters), which are in general not available if the models are applied at larger scales (region to global scale). Therefore, pedotransfer functions (PTFs) are classically used, which relate easily available soil properties such as sand‐, silt‐, clay‐content, soil organic carbon content, and soil bulk density, which are available from soil maps, to the soil hydraulic parameters. Unfortunately, there are many different PTFs available in literature. In the study presented, we analyzed the impact of different PTFs on the simulation results of water fluxes and found, that the choice of PTF impacts the simulation results. Further, some PTFs were identified as being less robust compared to others. In general, the study shows that harmonizing PTFs in model‐inter‐comparisons is needed to avoid artifacts originating from the choice of PTF rather from different model structures. Key Points: Using different PTFs in hydrological models causes substantial variability in predicted fluxesWe strongly recommend to harmonize the PTFs used in model inter‐comparison studies [ABSTRACT FROM AUTHOR]

Soil sorptivity, S, and saturated hydraulic conductivity, Ks, can be estimated from the inverse analysis of a disc infiltrometer cumulative infiltration curve using the quasi‐exact implicit (QEI) analytical Haverkamp et al. (1994) equation, which is a function of Ks, S, the parameters β and γ, the disc radius, rd, and the water content increase, ∆θ. Given the complexity of solving QEI, this paper presents three‐term, 3T, and four‐term, 4T, QEI expansions to estimate S and Ks. The interplays between β, γ, Ks and S employing S‐Ks, γ‐Ks, γ‐S, γ‐β, S‐β and Ks‐β error maps generated for a loam soil synthetic infiltration were analyzed with QEI. To reduce the number of variables, Δθ, rd and γ were packed into the A=γrd∆θ term. Five different QEI expansion analyses were evaluated: (i and ii) optimization of 3T using A, 3TA, or β, 3Tβ, as fixed variables; (iii and iv) optimization of 3T, 3TAβ, and 4T, 4TAβ, using constant β and A values; and (v) optimization of 4T leaving all coefficients free, 4TF. The different methods were evaluated with synthetic infiltrations for homogeneous sand, loam and silt soils, and for an uniform loam soil with a contact sand layer. The QEI expansions were applied to experimental infiltrations, and the results were compared to those obtained with QEI, using β = 0.6 and γ = 0.75. Infiltrations were performed at zero cm of soil tension. Global optimization with QEI demonstrates that γ and β are extremely linked. This makes it difficult to estimate these two parameters. All procedures applied to synthetic homogeneous soils resulted in good Ks and S approaches. However, only 3TA, 3TAβ and 4TAβ obtained accurate estimates of Ks and S when applied to a synthetic homogeneous soil with a contact sand layer. Application of the different methods to the experimental infiltrations showed that 3TAβ and 4TAβ gave the most accurate and robust estimates of S and Ks. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Weighable lysimeters were used to study the relation between soil water content (SWC) and the actual evapotranspiration (ETa) of grassland under two different climate regimes of Rollesbroich and Selhausen but for an identical soil from Rollesbroich. All components of the water balance were determined from 2012 until 2018. Budyko analysis was used to characterize the hydrological status of the studied sites. Wavelet analysis was also applied to study the power spectrum of ETa, vegetationheight- adjusted reference evapotranspiration (ETcrop), and water stress index (WSI) defined as ETa/ETcrop, as well as SWC at three different depths and the coherence between SWC and ETa and WSI. The Budyko analysis showed that 2018 resulted in a shift of both locations towards more water-limited conditions, although Rollesbroich remained an energy-limited system. Based on the power spectrum analysis, the annual timescale is the dominant scale for the temporal variability of ETa, ETcrop, and SWC. The results also showed that increasing dryness at the energy-limited site led to more temporal variability of SWC at all depths at the annual timescale. Wavelet coherence analysis showed a reduction of the phase shift between SWC and ETa at an annual scale caused by the increase in dryness during the measurement period. We found that phase shifts between SWC and ETa and SWC and WSI were stronger at the water-limited site than at the energy-limited site. The wavelet coherence analysis also showed that from 2014 to 2018, the control of ETa and WSI on SWC increased due to higher dryness of soil. [ABSTRACT FROM AUTHOR]

Core Ideas: Transversal relaxation time spectra were a good proxy to determine pore size distribution.Chitosan provides more degradable C to the soil microbial community than Arabic gum.The water retention curve showed that 10 g Arabic gum kg−1 soil decreased plant‐available water.The same amount of chitosan increased available water content compared with the reference soil. The pore size distribution (PSD) of biopolymeric‐amended soils is rarely investigated due to difficulties in its quantification using classical methods. In this study, we analyzed the impact of biopolymeric soil amendments on the PSD of a dryland loamy soil based on its physical and biological properties using a completely randomized design with four treatments consisting of two different dosages (10 and 5 g kg−1) of two different biopolymers, (chitosan [CH] and Arabic gum [AG]) plus a reference soil. To determine the effects of CH and AG on the PSD, nuclear magnetic resonance relaxometry (NMRR) measurements were used to determine the longitudinal (T1) and transversal (T2) relaxation times. A set of soil structure–related characteristics was also determined in the laboratory. The results revealed that T2 spectra provided a good proxy to determine the PSD, showing good agreement between the PSD from T2 spectra and that calculated from the water retention curve (WRC) (R2 > 0.78; RMSE <1.38 μm). The application of CH also increased the zeta potential of the soil to −18.5 mV, compared with −20 mV obtained for the reference soil. The WRC measurements revealed that AG decreased the available water content for plant use compared with the reference soil, whereas CH increased the available water in comparison to the reference soil. Considering the parameters of the van Genuchten model, the application of AG and CH mainly affected the parameter α, confirming the dominant changes in macropores. This finding was confirmed by NMRR relaxation spectra. Furthermore, the application of CH and AG stimulated the microbial activity of the amended soil, leading to an increase in soil respiration. [ABSTRACT FROM AUTHOR]

Since the direct measurement of soil hydraulic conductivity [Kw(θ)] is time consuming and difficult, several methods have been suggested for its prediction. However, their application still reθuires some kind of direct or experimental measurement, even after calibration. Considering much easier measurement of the air permeability [Ka(θ)] and the water and air flows in the soil medium, several attempts have been made to link Kw(θ) and Ka(θ), most of which have used Ka(θ) to predict the saturated hydraulic conductivity (Ks). The current research was aimed to model the air permeability and evaluate its application for Kw(θ) prediction. In this regard, laboratory measurements were conducted for Kw(θ) and Ka(θ) at different soil moisture contents (θ). Then, we introduced a semitheoretical model and evaluated it using measured data. Results showed that the proposed model can predict Kw(θ), with an average evaluation error of 3.69% and average R2 of 0.88. Regarding the fast and nondestructive measurement of Ka(θ) compared with Kw(θ), the proposed model seems to be more practical to characterize unsaturated soil hydraulic conductivity and can improve the accuracy and efficiency of Kw(θ) estimation. [ABSTRACT FROM AUTHOR]