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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]

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]

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]

Developing accurate and reliable pedo-transfer functions (PTFs) to predict soil non-readily available characteristics is one of the most concerned topic in soil science and selecting more appropriate predictors is a crucial factor in PTFs’ development. Group method of data handling (GMDH), which finds an approximate relationship between a set of input and output variables, not only provide an explicit procedure to select the most essential PTF input variables, but also results in more accurate and reliable estimates than other mostly applied methodologies. Therefore, the current research was aimed to apply GMDH in comparison with multivariate linear regression (MLR) and artificial neural network (ANN) to develop several PTFs to predict soil cumulative infiltration point-basely at specific time intervals (0.5–45 min) using soil readily available characteristics (RACs). In this regard, soil infiltration curves as well as several soil RACs including soil primary particles (clay (CC), silt (Si), and sand (Sa)), saturated hydraulic conductivity ( K s ), bulk ( D b ) and particle ( D p ) densities, organic carbon ( OC ), wet-aggregate stability ( WAS ), electrical conductivity ( EC ), and soil antecedent ( θ i ) and field saturated ( θ fs ) water contents were measured at 134 different points in Lighvan watershed, northwest of Iran. Then, applying GMDH, MLR, and ANN methodologies, several PTFs have been developed to predict cumulative infiltrations using two sets of selected soil RACs including and excluding K s . According to the test data, results showed that developed PTFs by GMDH and MLR procedures using all soil RACs including K s resulted in more accurate (with E values of 0.673–0.963) and reliable (with CV values lower than 11 percent) predictions of cumulative infiltrations at different specific time steps. In contrast, ANN procedure had lower accuracy (with E values of 0.356–0.890) and reliability (with CV values up to 50 percent) compared to GMDH and MLR. The results also revealed that K s exclusion from input variables list caused around 30 percent decrease in PTFs accuracy for all applied procedures. However, it seems that K s exclusion resulted in more practical PTFs especially in the case of GMDH network applying input variables which are less time consuming than K s . In general, it is concluded that GMDH provides more accurate and reliable estimates of cumulative infiltration (a non-readily available characteristic of soil) with a minimum set of input variables (2–4 input variables) and can be promising strategy to model soil infiltration combining the advantages of ANN and MLR methodologies. [ABSTRACT FROM AUTHOR]

A close correlation between water conductivity (K(θ)) and air permeability (Ka), measured at various water contents, is expected due to tight dependence of water filled porosity to air filled porosity of soils. Finding such a relation will greatly facilitate the prediction of unsaturated water conductivity (K(θ)). So, the purpose of the current investigation was to find out if a reliable relation or function between the two permeabilities can be established. In this regard, K(θ) and Ka were measured by pressure plate outflow and variable head methods, respectively, at the range of 0 to -100 kPa matric potential (ψm). A linear regression function between relative water conductivity (Kr(θ)) and Ka(LogK, (θ)=a+bLogKa) with the correlation coefficient (R) from 0.884 to 0.999 were established for the 22 examined soils. The overall R for 128 data pairs (Kr(θ) and Ka) became 0.821 (being significant at P<0.01) with the slope (b) of -2.54 and intercept (a) of -10.93. For the comparison propose Kr(θ) were also predicted from RETC using experimental SMC data and van Genuchten and Brooks-Corey models. The reliability of the Kr(θ) prediction from Ka based on root mean square error (RMSE), geometric mean error ratio (GMER), and geometric standard deviation of error ratio (GSDER) criteria became considerable greater than those predicted from the two mentioned models. [ABSTRACT FROM AUTHOR]

• Saturated soil hydraulic conductivity was predicted reasonably using easily accessible environmental data and limited soil observations. • Random Forest outperformed best, resulting in high-resolution hydraulic conductivity which can be used in the hydrological model at a large scale. • Silt content, Bands 7, 6, 4, 2, NDPI, and NDVI covariates explained most of the soil hydraulic conductivity variations. Saturated soil hydraulic conductivity (K sat) is a key component in hydrogeology and water management. This study aimed at evaluating popular tree-based machine learning algorithms (Random forest (RF), Quantile random forest (QRF), Cubist (Cu), and Decision tree regression (DTr)) to assess the spatial distribution of K sat in a sandy agricultural field. Soil surface reflectance derived from Landsat-8 (OLI/TIRS) (several remotely sensed data including original surface reflectances of spectral bands and 22 remote sensing indices) as well as limited ground measured soil data were used as predictor covariates. Using collected disturbed and undisturbed soil samples, physicochemical properties (K sat , porosity, organic matter, and texture contents) were determined. Based on novel supervised feature selection, covariates including Landsat-8 spectral Band2, Band4, Band6, and Band7, normalized difference pond index (NDPI), normalized difference vegetation index (NDVI), and silt content were identified as the most important factors in K sat prediction. Variable importance analysis showed Band7 and Band6 were explaining 54% of the total K sat variation. The model evaluation, using five statistics cretria, Taylor diagram and the Kruskal–Wallis (KW) test, demonstrates the outperformance of RF being followed by QRF, Cu, and DTr models. Accordingly, the RF method combined with an optimized sampling approach provides the most accurate digital soil K sat map. The uncertainty analysis showed no significant different trend in K sat predictions by applying more dense datasets confirming original-limited data (n = 28) was efficient and sufficient to derive a reliable K sat -map. The developed approach, which can be scaled up at a large scale, seems to be useful in modelling water flow and solute transport for water and nutrient management purposes toward precision agriculture. [ABSTRACT FROM AUTHOR]