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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.

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]

The Alpi Apuane (Italy) are located a few kilometres from the coast of the Ligurian Sea, and they are characterized by peak elevations up to two thousand meters above sea level, as well as narrow, deeply incised valleys and steep slopes. Due to these morphoclimatic conditions, heavy rains are frequent, causing floods, landslides, and debris flows, particularly within the Vezza catchment. In this work we applied two different hydrological-hydraulic models to this catchment, focusing on the catastrophic debris flow event of June 19, 1996. Firstly, recent, well-documented rainfall events were used to validate the engineering geological model of the study area, then we began to analyse the rainfall-runoff and debris flow event of 1996 in the Cardoso sub-catchment. As models, we used the FLO-2D and a novel experimental model, developed by some of the authors and based on TRENT2D, in which the dynamic of a debris flow is fully coupled with the rainfall-runoff response of a basin. Preliminary results show how the used approach allowed us to gain some insight into the hydrological behaviour and debris flows formation, erosion, transport, and deposition in the Cardoso sub-catchment.

This comment challenges Gao et al. (2023)'s perspective rejecting the role of soil processes in hydrology. We argue that the authors present a false dichotomy between soil-centric and ecosystem-centric views. These two views of hydrology are complementary and reflect on the inherent multiscale complexity of hydrology where soil processes dominate at certain scales but other processes may become important at catchment scale. We recognize the need for a new scale aware framework that reconciles the interplay between soil processes at small scales with emergent behaviors driven by vegetation, topography and climate at large scales. [ABSTRACT FROM AUTHOR]

Toxic breakdown products of young Camelina sativa (L.) Crantz, glucosinolates can eliminate microorganisms in the soil. Since microorganisms are essential for phosphate cycling, only insensitive microorganisms with phosphate-solubilizing activity can improve C. sativa's phosphate supply. In this study, 33P-labeled phosphate, inductively coupled plasma mass spectrometry and pot experiments unveiled that not only Trichoderma viride and Pseudomonas laurentiana used as phosphate-solubilizing inoculants, but also intrinsic soil microorganisms, including Penicillium aurantiogriseum, and the assemblies of root-colonizing microorganisms solubilized as well phosphate from apatite, trigger off competitive behavior between the organisms. Driving factors in the competitiveness are plant and microbial secondary metabolites, while glucosinolates of Camelina and their breakdown products are regarded as key compounds that inhibit the pathogen P. aurantiogriseum, but also seem to impede root colonization of T. viride. On the other hand, fungal diketopiperazine combined with glucosinolates is fatal to Camelina. The results may contribute to explain the contradictory effects of phosphate-solubilizing microorganisms when used as biofertilizers. Further studies will elucidate impacts of released secondary metabolites on coexisting microorganisms and plants under different environmental conditions. [ABSTRACT FROM AUTHOR]

Augmented reality and virtual reality technologies are witnessing an evolutionary change in the 5G and Beyond (5GB) network due to their promising ability to enable an immersive and interactive environment by coupling the virtual world with the real one. However, the requirement of low-latency connectivity, which is defined as the end-to-end delay between the action and the reaction, is very crucial to leverage these technologies for a high-quality immersive experience. This paper provides a comprehensive survey and detailed insight into various advantageous approaches from the hardware and software perspectives, as well as the integration of 5G technology, towards 5GB, in enabling a low-latency environment for AR and VR applications. The contribution of 5GB systems as an outcome of several cutting-edge technologies, such as massive multiple-input, multiple-output (mMIMO) and millimeter wave (mmWave), along with the utilization of artificial intelligence (AI) and machine learning (ML) techniques towards an ultra-low-latency communication system, is also discussed in this paper. The potential of using a visible-light communications (VLC)-guided beam through a learning algorithm for a futuristic, evolved immersive experience of augmented and virtual reality with the ultra-low-latency transmission of multi-sensory tracking information with an optimal scheduling policy is discussed in this paper. [ABSTRACT FROM AUTHOR]

Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation, while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic function – even with infinite hydraulic diffusivity or positive air-entry water pressure heads – and any boundary condition, including infinite initial water pressure head, h→-∞. Lastly, we show the benefits of using the proposed formulation for modeling water into soil with analytical models that use sorptivity. [ABSTRACT FROM AUTHOR]

Conserving water resources is a current challenge that will become increasingly urgent in future due to climate change. The arid and semi-arid areas of the globe are expected to be particularly affected by changes in water availability. Consequently, advances in ecohydrology sciences, i.e., the interplay between ecological and hydrological processes, are necessary to enhance the understanding of the critical zone, optimize water resources' usage in arid and semi-arid areas, and mitigate climate change. This Special Issue (SI) collected 10 original contributions on sustainable land management and the optimization of water resources in fragile environments that are at elevated risk due to climate change. In this context, the topics mainly concern transpiration, evapotranspiration, groundwater recharge, deep percolation, and related issues. The collection of manuscripts presented in this SI represents knowledge of ecohydrology. It is expected that ecohydrology will have increasing applications in the future. Therefore, it is realistic to assume that efforts to increase environmental sustainability and socio-economic development, with water as a central theme, will have a greater chance of success. [ABSTRACT FROM AUTHOR]

Unsaturated soil hydraulic conductivity K is a fundamental transfer property of soil but its measurement is costly, difficult, and time-consuming due to its large variations with water content (θ) or matric potential (h). Recently, C. Doussan and S. Ruy proposed a method/model using measurements of the electrical conductivity of soil core samples to predict K(h). This method requires the measurement or the setting of a range of matric potentials h in the core samples--a possible lengthy process requiring specialised devices. To avoid h estimation, we propose to simplify that method by introducing the particle-size distribution (PSD) of the soil as a proxy for soil pore diameters and matric potentials, with the Arya and Paris (AP) model. Tests of this simplified model (SM) with laboratory data on a broad range of soils and using the AP model with available, previously defined parameters showed that the accuracy was lower for the SM than for the original model (DR) in predicting K (RMSE of logK = 1.10 for SM v. 0.30 for DR; K in m [s.sup.-1]). However, accuracy was increased for SM when considering coarse- and medium-textured soils only (RMSE of logK= 0.61 for SM v. 0.26 for DR). Further tests with 51 soils from the UNSODA database and our own measurements, with estimated electrical properties, confirmed good agreement of the SM for coarse-medium-textured soils ( Additional keywords: electrical conductivity, hydraulic conductivity, particle size distribution, scaling parameter., Introduction Unsaturated soil hydraulic conductivity, K(θ) or K(h), which is a highly non-linear function of water content (θ) or matric potential (h), is a fundamental property for estimating transfer/transport processes [...]

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]

Numerous communications and networking challenges prevent deploying unmanned aerial vehicles (UAVs) in extreme environments where the existing wireless technologies are mainly ground-focused; and, as a consequence, the air-to-air channel for UAVs is not fully covered. In this paper, we address the crucial problem of beamforming in the UAV-based communications by utilizing a spatial estimation algorithm, which relies on the theory of observers in the control systems literature. The proposed spatial estimation algorithm relies on using a delay-tolerant observer-based predictor, which can accurately predict the positions of the target UAVs in the presence of uncertainties due to factors such as wind gust. The solution, which uses discrete-time unknown input observers (UIOs), reduces the joint target detection and communication complication notably by operating on the same device and performs reliably in the presence of channel blockage and interference. The effectiveness of the proposed approach is demonstrated using simulation results. [ABSTRACT FROM AUTHOR]

Well test analysis is a method for evaluating the average properties of the reservoir by characterizing the ability of the fluid to flow through the reservoir and to the well. Well test output parameters that descript reservoir are permeability, reservoir heterogeneities, boundaries and pressure; also, parameters that descript well are skin factor, productivity index and well geometries. The suggested models for prediction of pressure drop in vertical well have obtained from the solution of diffusivity equation for radial and elliptical regime. The purpose of this project is to generate a model for the horizontal well in fracture reservoir and estimate a parameter for this type of well by ANN method and compare the results with well test software. In this study, pressure data versus time was obtained for horizontal wells in naturally fractured reservoirs by solving diffusivity Equation using Stehfest algorithm, and for each set of data, a polynomial was developed for pressure derivative data by applying Chebyshev polynomials method. The polynomial coefficients along with reservoir and horizontal well data were fed into Artificial Neural Network (ANN) as input data and as a result, a model was presented for the horizontal well in naturally-fractured reservoir. In addition, output of the model was compared to the well log and well test software’s data and it was found that the presented model has better and higher performance than well test software’s. [ABSTRACT FROM AUTHOR]

Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. Parlange (1975) proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving the hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic functions - even with infinite hydraulic diffusivity or positive air-entry water pressure heads - and any boundary condition, including infinite initial water pressure head, h → - ∞. [ABSTRACT FROM AUTHOR]

Sorptivity is a parameter of primary importance in the study of unsaturated flow in soils. This hydraulic parameter is required to model water infiltration into vertical soil profiles. Sorptivity can be directly estimated from the soil hydraulic functions (water retention and hydraulic conductivity curves), using the integral formulation of. However, calculating sorptivity in this manner requires the prior determination of the soil hydraulic diffusivity and its numerical integration between initial and final saturation degrees, which may be difficult in some situations (e.g., coarse soil with diffusivity functions that are quasi-infinite close to saturation). In this paper, we present a procedure to compute sorptivity using a scaling parameter, cp , that corresponds to the sorptivity of a unit soil (i.e., unit values for all parameters and zero residual water content) that is utterly dry at the initial state and saturated at the final state. The cp parameter was computed numerically and analytically for five hydraulic models: delta (i.e., Green and Ampt), Brooks and Corey, van Genuchten–Mualem, van Genuchten–Burdine, and Kosugi. Based on the results, we proposed brand new analytical expressions for some of the models and validated previous formulations for the other models. We also tabulated the output values so that they can easily be used to determine the actual sorptivity value for any case. At the same time, our numerical results showed that the relation between cp and the hydraulic shape parameters strongly depends on the chosen model. These results highlight the need for careful selection of the proper model for the description of the water retention and hydraulic conductivity functions when estimating sorptivity. [ABSTRACT FROM AUTHOR]