Soil Hydraulic Conductivity Functions Research Articles

Estimation of hydraulic conductivity function in unsaturated pyroclastic soils

A full understanding of slope failure conditions in unsaturated pyroclastic slope needs a fair analysis of groundwater flow and, therefore, a proper hydraulic soil characterization in terms of either soil water retention curves (SWRC) and hydraulic conductivity function (HCF). A practical method to detect the HCF by processing in situ data is provided, thus, the identification of the HCFs operating on site by applying the Soil Water Balance (SWB) to the pyroclastic soil cover is carried out. In this regard data monitoring (matrix suction and volumetric water content) collected at experimental field of Monteforte Irpino in Southern Italy over four years have been used. Moreover a comparison between the saturated hydraulic conductivity from lab test and from in situ measurements is carried out and the results confirm that the effective hydraulic conductivity operating at the site scale is higher than the hydraulic conductivity obtained in the laboratory for the whole range of suction measured at site.

Modeling of Hydrophysical Properties of the Soil as Capillary-Porous Media and Improvement of Mualem-Van Genuchten Method as a Part of Foundation Arrangement Research

Within the concepts about the capillarity and the lognormal distribution of effective pore radii, a theoretical justification for function of differential water capacity and its antiderivative (function of water-retention capacity in form of a dependence of the soil volumetric water content on capillary pressure of the soil moisture) is presented. Using these functions, the ratio of soil hydraulic conductivity function to the filter coefficient is calculated. Approximations to functions describing the water-retention capacity and relative hydraulic conductivity of the soil have been suggested. Parameters of these functions have been interpreted and estimated with applying the physical and statistical indices of the soil.

Unsaturated Soil Mechanics Principles to Remove and Replace Mitigation for Expansive Clays

The efficacy of removal and replacement as a mitigation alternative for expansive soil is discussed in view of numerical unsaturated flow/deformation results. Observations with respect to selection of depth and replacement soil type (similar, more, or less permeable than underlying expansive clay) are presented in the context of unsaturated flow and stress/deformation principles. Comparisons are made between various remove and replace options on the basis of extent and degree of wetting (changes in soil suction) and on ground surface total and differential movements. Selection of optimal removal and replacement depth and replacement material type requires consideration of unsaturated flow principles and understanding of the role of both net normal stress and matric suction in unsaturated soil response. Complexities in the unsaturated flow process which impact the efficacy of the remove and replace method are primarily because of the highly nonlinear nature of the unsaturated soil storage function (SWCC) and hydraulic conductivity function. Further, because the unsaturated hydraulic conductivity of soils depends on the value of soil suction, placement water content of the replacement layer has significant effect on performance. The net result is that the impact of various remove and replace options is not always intuitive. The findings presented, although not encompassing of all possible removal and replacement configurations or surface flux conditions, set the stage for application of remove and replace mitigation methods based on fundamental unsaturated soil mechanics principles.

Towards Retrieving Soil Hydraulic Properties by Hyperspectral Remote Sensing

In this study, we developed spectrotransfer functions (STFs) that relate soil hydraulic properties (SHPs) to spectral reflectance values to estimate hydraulic parameters of the Mualem–van Genuchten (MvG) model. We investigated the general potential of airborne as well as space‐borne remote sensors to retrieve MvG hydraulic parameters of a bare soil agricultural field. Based on the ASD full spectrum (Scenario I), simple spectral signatures were generated mimicking the hyperspectral EnMAP sensor (Scenario II), and the multispectral Sentinel‐2 sensor (Scenario III). A stepwise multiple linear regression method was used for each scenario to derive STFs. We further tested laboratory‐ and soil‐map‐based HYPRES and Rosetta pedotransfer functions (PTFs) to parameterize MvG parameters and thus provide soil water characteristics and hydraulic conductivity functions in the region. The best results were obtained for Scenarios I and II, with similar R2 values for shape parameters α* and n and the lognormal saturated hydraulic conductivity (Ks*). The R2 values were highest for Ks* in Scenarios I and II (0.58 and 0.57, respectively). The R2 values for α* and n were 0.30 and 0.34 in Scenario I and 0.39 and 0.31 in Scenario II, respectively. In all scenarios, the lowest R2 values were obtained for saturated water content (θs), with values around 0.10 for Scenarios I and II and almost zero in Scenario III. Compared with HYPRES and Rosetta PTFs, the spectral approach performed reasonably well in terms of predicting soil water retention characteristics and unsaturated hydraulic conductivity. These findings suggest that spectral reflectance data provide a promising indirect and quick method for large‐scale parameter estimation.

Determination of Unsaturated Soil Properties and Slope Deformation Analysis Due to the Effect of Varies Rainfall

Recently, landslides often occurs in natural slope in Indonesia, which is associated with the coming rainy season. The increment of ground water level caused by rainfall has affected the properties and behavior of soil especially the unsaturated soil. Generally, the stability of slope is evaluated based on safety factor, but the deformation occure at the soil can also be a good interest in asses the stability of slope. This research is focused to observe the change of pore water pressure and associate deformation considering the hydro-mechanical properties of unsaturated soil due to the effect of varies rainfall. In this research, numerical simulation was carried out to analyze the deformation of the slope affected by pore water pressure change due to rainfall using software-based Finite Element Method of SIGMA/W and SEEP/W from GEO-SLOPE 2004. Unsaturated soil properties, such as Soil Water Characteristic Curve (SWCC) and Hydraulic Conductivity function are obtained from laboratory test and also predicted based on grain-size distribution using psycho-empirical method in SOILVISION Database. HAVARA is used to help rainfall data analysis using statistic approach. Rainfall model is used to vary the moisture content to model unsaturated soil condition. There are six rainfall models, consists of one steady state model and followed by five transient model to accommodate the pore water pressure changes due to rainfall. The results show that rainfall with intensity near saturated permeability of soil gives more significant influence in increasing pore water pressure and deformation than normal rainfall even with long duration. Proposed countermeasure by providing counterweight and sub drain do not significantly take effect the deformation, but it could improves the safety factor significantly, so that the slope is more in stable condition.

Measurement of Thermal Conductivity Function of Unsaturated Soil Using a Transient Water Release and Imbibition Method

AbstractThermal conductivity of unsaturated soil depends on soil water content and soil type. A transient water release and imbibition method (TRIM) is modified to include measurement of the thermal conductivity function (TCF) in conjunction with concurrent measurement of the soil water retention curve (SWRC) and hydraulic conductivity function (HCF). Two pairs of dielectric and thermal needle sensors are embedded in the soil specimen to monitor spatial and temporal variation of water content, thermal conductivity, and thermal diffusivity during drying and wetting processes. Three different soils, including pure sand, silt, and clayey sand are used to examine the effectiveness and validity of the new technique. The thermal conductivity data from the modified TRIM technique accords well with other independent measurements. The results show that the modified TRIM technique provides a fast and accurate way of obtaining thermal properties of different types of soils under both drying and wetting states. The typical testing time for a soil going through a full saturation variation is less than 3 weeks. We observe that the hysteresis in thermal conductivity during a wetting and drying cycle is much less pronounced than that of the hydraulic hysteresis.

Analysis of the impact of surface layer properties on evaporation from porous systems using column experiments and modified definition of characteristic length

The hydraulic properties of the layer at the vicinity of the soil surface have significant impact on evaporation, and could be harnessed to reduce water losses. The effect of the properties of the upper layer on the evolution of phase distribution during the evaporation process is first illustrated from three-dimensional pore network simulations. This effect is then studied from experiments carried out on soil columns under laboratory conditions. Comparisons between homogeneous columns packed with coarse (sand) and fine (sandy loam) materials, and heterogeneous columns packed with layers of fine overlying coarse material and coarse overlying fine material of different thicknesses are performed to assess the impact of upper layer properties on evaporation. Experiments are analyzed using the classical approach based on the numerical solution of Richards’s equation and semi-analytical theoretical predictions. The theoretical analysis is based on the clear distinction between two drying regimes, namely the capillary regime and the gravity-capillary regime, which are the prevailing regimes in our experiments. Simple relationships enabling to estimate the duration of stage-1 evaporation (S1) for both regimes are proposed. In particular, this led to defining the characteristic length for the gravity-capillary regime from the consideration of viscous effects at low water content differently from available expressions. The duration of S1, during which most of the water losses occur, for both the homogeneous and two-layer columns are presented and discussed. Finally, the impact of liquid films and it consequences on the soil hydraulic conductivity function are briefly discussed.

PENENTUAN SIFAT TEKNIS TANAH JENUH SEBAGIAN DAN ANALISIS DEFORMASI LERENG AKIBAT PENGARUH VARIASI HUJAN

Abstract
 Recently, landslides often occurs in natural slope in Indonesia, which is associated with the coming rainy season . The increment of ground water level cause by rainfall is affected the properties and behavior of soil especially the unsaturated soil. Generally, the stability of slope is evaluated based on safety factor, but the deformation occured at the soil can also be a good interest in assesing the stability of slope. This research is focused to observe the change of pore water pressure and ascoociate deformation considering the hydro-mechanical properties of unsaturated soil due to the effect of varies rainfall. In this research, numerical simulation was carried out to analysis the deformation of the slope affected by pore water pressure change due to rainfall using software-based Finite Element Method of SIGMA/W and SEEP/W from GEO-SLOPE 2004. Unsaturated soil properties, such as Soil Water Characteristic Curve (SWCC) and Hydraulic Conductivity function are obtained from laboratory test and also predicted based on grain-size distribution using psycho-empirical method in SOILVISION Database. HAVARA is used to help rainfall data analysis using statistic approach. Rainfall model is used to vary the moisture content to model unsaturated soil condition. There are six rainfall models, consists of one steady state model and followed by five transient model to accomodate the pore water pressure changes due to rainfall. The results show that rainfall with intensity near saturated permeability of soil gives more significant influence in increasing pore water pressure and deformation than normal rainfall even with long duration. Proposed countermeasure by providing counterweight and subdrain do not significantly effect the deformation, but it could improves the safety factor significantly, so that the slope is more in stable condition.
 
 Keywords : landslide, unsaturated soil properties, pore water pressure, slope deformation, numerical simulation, finite element method, countermeasures.

Texture-depending performance of an in situ method assessing deep seepage

Summary Deep seepage estimation is important for water balance investigations of groundwater and the vadose zone. A simplified Buckingham-Darcy method to assess time series of deep seepage fluxes was proposed by Schindler and Muller (1998) . In the method dynamics of water fluxes are calculated by a soil hydraulic conductivity function. Measured soil moistures and matric heads are used as input data. Resulting time series of flux dynamics are scaled to realistic absolute levels by calibrating the method with the areal water balance. An assumption of the method is that water fluxes at different positions exhibit identical dynamics although their absolute values can differ. The aim of this study was to investigate uncertainties of that method depending on the particle size distribution and textural heterogeneity in non-layered soils. We performed a numerical experiment using the two-dimensional Richards Equation. A basic model of transient water fluxes beneath the root and capillary zone was setup and used to simulate time series of soil moisture, matric head, and seepage fluxes for 4221 different cases of particle size distribution and intensities of textural heterogeneity. Soil hydraulic parameters were predicted by the pedotransfer function Rosetta. Textural heterogeneity was modeled with Miller and Miller scaling factors arranged in spatial random fields. Seepage fluxes were calculated with the Buckingham-Darcy method from simulated soil moisture and matric head time series and compared with simulated reference fluxes. The median of Root Mean Square Error was about 0.026 cm d −1 and the median of maximum cross correlation was 0.96 when the method was calibrated adequately. The method’s performance was mainly influenced by (i) the soil textural class and (ii) the time period used for flux calibration. It performed best in sandy loam while hotspots of errors occurred in sand and silty texture. Calibrating the method with time periods that exhibit high variance of seepage fluxes yielded the best performance. The geostatistical properties of the Miller and Miller scaling field influenced the performance only slightly. However, the Miller and Miller scaling procedure generated heterogeneous flow fields that were addressed as main reason for mismatches of simulated reference fluxes and fluxes obtained with the Buckingham-Darcy method.

Prediction of spatially variable unsaturated hydraulic conductivity using scaled particle‐size distribution functions

Simultaneous scaling of soil water retention and hydraulic conductivity functions provides an effective means to characterize the heterogeneity and spatial variability of soil hydraulic properties in a given study area. The statistical significance of this approach largely depends on the number of soil samples collected. Unfortunately, direct measurement of the soil hydraulic functions is tedious, expensive and time consuming. Here we present a simple and cost‐effective hybrid scaling approach that combines the use of ancillary information (e.g., particle‐size distribution and soil bulk density) with direct measurements of saturated soil water content and saturated hydraulic conductivity. Our results demonstrate that the presented approach requires far fewer laboratory measurements than conventional scaling methods to adequately capture the spatial variability of soil hydraulic properties.

Validation of a Centrifuge Permeameter for Investigation of Transient Infiltration and Drainage Flow Processes in Unsaturated Soils

Abstract This paper focuses on the validation of a centrifuge permeameter and testing methodology developed to investigate transient water flow processes in unsaturated soils. The centrifuge permeameter is capable of controlling the boundary conditions for infiltration and drainage and contains instrumentation to measure profiles of the volumetric water content and matric suction with height in a soil layer during centrifugation. Evaluations of the measured matric suction and volumetric water content profiles from a series of infiltration and drainage tests performed on a fine sand at centrifuge acceleration levels ranging from 20 to 50 times earth gravity indicate that the established equations for calculating the hydraulic conductivity of unsaturated soil at steady-state conditions might not be appropriate, except at higher centrifuge accelerations. The transient profiles were also analyzed using a form of the instantaneous profile method in which the centrifuge acceleration was incorporated into the hydraulic gradient. Although the calculated soil water retention curve and hydraulic conductivity function data show some scatter, the hysteretic behavior of the soil during wetting and drying could be assessed.

A Transient Water Release and Imbibitions Method for Rapidly Measuring Wetting and Drying Soil Water Retention and Hydraulic Conductivity Functions

Abstract A transient water release and imbibitions (TWRI) method for measuring the soil water retention curve (SWRC) and hydraulic conductivity function (HCF) under drying and wetting states is presented. The intellectual merit of the TWRI method is its integration of physical and numerical experiments: it employs the simple and reliable measurement of transient water content by electronic balance to record the signature of transient unsaturated flow in soil sample, and it takes advantage of the robust inverse modeling capability to simulate the physical process. The TWRI method; therefore, has two integrated components: testing and modeling. The testing consists of water release upon two-steps increase in matric suction and water imbibitions upon one-step decrease in matric suction. Each process lasts sufficient time in order to obtain transient water content. The data is then used as an objective function in an inverse numerical modeling process to obtain the unsaturated hydrologic parameters that fully define the SWRC and HCF of the soil. A novel feature of the TWRI method is its capability to measure SWRC and HCF under wetting state. The apparatus can accommodate both undisturbed and remolded samples. The testing time required for completing a full drying and wetting loop is approximately one week for most soils. Validation of the technique has been performed both experimentally and numerically. Comparisons between data obtained with the TWRI method and the independent Tempe cell method verify the reliability, applicability, and accuracy of the TWRI method. Results from three different soils are presented to illustrate the procedure and performance of the TWRI method for different soils from fine sand to clayey silt. The TWRI method provides a fast, accurate, and simple testing tool for obtaining SWRC and HCF of various types of soils under both wetting and drying states with high range of matric suction several orders of magnitude above the air-entry pressure of the ceramic stone used in the experimental setup.

Infiltration models for soil profiles bounded by a water table

Approximate solutions of Richards' equation are developed for rational forms of the soil hydraulic conductivity and moisture retention functions using a perturbation expansion method. A novel approach is devised in the perturbation technique whereby a priori introduced parameters are estimated in an optimal context to ensure the accuracy of the perturbation solution at all times and for all flow conditions. The perturbation model describes the one‐dimensional nonlinear nonsteady infiltration for arbitrary initial conditions under either a time‐dependent surface flux or a constant head boundary condition into either a semi‐infinite or a finite medium bounded from below by a shallow water table. The optimal perturbation approach proved to be an effective method by which closed‐form linear solutions can be adapted to nonlinear soils through proper scaling factors. The results show that the first‐order linear term of the optimal perturbation solution is sufficiently accurate for practical applications, especially for shallow water table conditions. They offer the means to analyze the effect of nonuniform initial conditions and the influence of the water table on the infiltration process. Practical results in terms of well‐defined soil water parameters and the antecedent moisture content include algebraic expressions for the surface moisture content variation under variable rainfall conditions, time‐to‐ponding expressions and infiltration equations for deep and shallow water table conditions, and a prediction formula for the water table recharge rate.

Infiltration models for semi‐infinite soil profiles

Infiltration models for hydrological applications are developed for rational forms of the soil hydraulic conductivity and moisture retention functions. The models are based on the traveling and kinematic wave solutions of the governing equation that proved to be highly accurate in specific flow conditions. The approximate solutions describe the one‐dimensional infiltration into a semi‐infinite medium for uniform initial conditions under either a time‐dependent flux or a constant head boundary condition. They capture the profile development from early to late time accurately due to the proper derivation of the wetting front speed in terms of the time‐varying surface boundary potential and flux rate. Algebraic expressions of theoretical and practical importance are derived in terms of well‐defined soil water parameters and include the effect of the antecedent moisture content in a specific fashion. Practical results include simple expressions for the surface moisture variation for variable rainfall patterns, time‐to‐ponding expressions and infiltration equations that account explicitly for the initial condition, formulas for the depth of the wetting zone, and algebraic equations for parameter estimation of the soil hydraulic parameters by inverse analysis.

Structure and parameter schematization of the vadose zone for groundwater recharge modeling

On the basis of published soil profile data typical retention curves and hydraulic conductivity functions were obtained that depend on soil depth, lithological characters, and different surface landscape conditions. The corresponding average soil hydraulic parameters for M.Th.Van Genuchten equations were estimated. These average soil parameters are suitable for groundwater recharge estimations based on unsaturated flow modeling.

Influence of Unsaturated Soil Properties Uncertainty on Moisture Flow Modeling

The quality of a numerical modeling solution of moisture flow through unsaturated soil, in part, depends on properly described unsaturated soil properties. The variability of the Soil Water Characteristic Curve, SWCC, is attributed to hysteresis and reproducibility of measurement. Because the unsaturated conductivity function is rarely directly measured, the variability of the unsaturated soil hydraulic conductivity function is attributed to the uncertainty associated with the estimation of this parameter with currently available fitting functions, and hence a range of reasonable variation was considered. One-dimensional modeling of expansive soil under dry initial conditions (suction of 1,500 kPa) was performed; both potential evaporation and infiltration boundary conditions were considered. It was found that small variations in the unsaturated soil hydraulic conductivity function result in significantly different modeling outputs, as expected, while substential variation in SWCC alone (assuming the same unsaturated soil hydraulic conductivity for all SWCCs) produced almost identical soil response in terms of soil suction when the slope of the SWCC is similiar. Thus, proper characterization of the slope of the SWCC is important to proper suction profile determination.

The relationship between surface fractal dimension and soil water content at permanent wilting point

Permanent wilting point (PWP) is an important soil water parameter available from the soil water retention curve. Soil water content held at 1500 kPa determines plant survival or death. Recently, the application of fractal geometry concepts has been widely used for modeling soil and its hydraulic properties (e.g. soil water retention curve and unsaturated hydraulic conductivity). The objective of this study was to investigate the relationship between surface fractal dimension ( D s ) and soil water content held at permanent wilting point, θ PWP For this purpose, we used five datasets corresponding to Puckett et al. [Puckett, W.E., Dane, J.H., Hajek, B.F., 1985. Physical and mineralogical data to determine soil hydraulic properties. Soil Sci. Soc. Am. J. 49, 831–836], UNSODA [Leij, F.J., Alves, W.J., van Genuchten, M.T.h., Williams, J.R., 1996. Unsaturated Soil Hydraulic Database, UNSODA 1.0 user's manual. Rep. EPA/600/R96/095. USEPA, Ada, OK], GRIZZLY [Haverkamp, R., Zammit, C., Boubkraoui, F., Rajkai, K., Arrúe, J. L., Keckmann, N., 1997. GRIZZLY, Grenoble soil catalogue: Soil survey of field data and description of particle-size, soil water retention and hydraulic conductivity functions. Laboratoire d'Etude des Transferts en Hydrologie et en Environnement. Grenoble, France], Huang et al. [Huang, G., Zhang, R., Huang, Q., 2006. Modeling soil water retention curve with a fractal method. Pedosphere 16, 137–146], and Fooladmand [Fooladmand, H.R., 2007. Measurement of soil specific surface area and its relation to some soil physico-chemical properties. Ph.D. Thesis. Department of Irrigation. Science and Research Unit of Islamis Azad University, Tehran]. This yielded a total of 172 soil samples. The results showed that D s was positively related to both θ PWP and clay content. The D s versus θ PWP and D s versus clay content relationships were well fitted by logarithmic functions (goodness of fit R 2 = 0.97 and R 2 = 0.88, respectively). Soil quality index (S-index) and D s were also significantly correlated ( R = 0.911). The water film retained at 1500 kPa (PWP) delineates the complex geometrical structure of the pore–solid interface which could be determined by the relative amount and orientation of clay particles.

Multiscale Pedotransfer Functions for Soil Water Retention

Parametric soil water retention and hydraulic conductivity functions are often used for predicting soil hydrologic behavior using hydrologic, hydroclimatic, and contaminant transport models. The prediction accuracy of any such model is critically dependent on the quality of the input parameters. Limited availability of (detailed) soil hydraulic data for large‐scale hydroclimatic models (with grids ranging from several kilometers to several hundred kilometers) is a major challenge. To address this need, pedotransfer functions (PTFs) have been used to estimate the required soil hydraulic parameters from other available or easily measurable soil properties. While most previous studies derive and adopt these parameters at matching spatial scales (1:1) of input and output data, we have developed a methodology to derive soil water retention functions at the point or local scale using the PTFs trained with coarser scale input data. This study was a novel application of an artificial neural network (ANN)‐based PTF scheme across two spatial support scales within the Rio Grande basin in New Mexico. The ANN was trained using soil texture and bulk density data from the SSURGO database (scale 1:24,000) and then used for predicting soil water contents at different pressure heads with point‐scale data (1:1) inputs. The resulting outputs were corrected for bias before constructing the soil water characteristic curve using the van Genuchten equation. A hierarchical approach with training data derived from multiple clustered subwatersheds (with varying spatial extent) was used to study the effect of the increase in spatial extent. The results show good agreement between the soil water retention curves constructed from the ANN‐based PTFs and field observations at the local scale near Las Cruces, NM. The robustness of the multiscale PTF methodology was further tested with a separate data set from the Little Washita watershed region in Oklahoma. Overall, ANN coupled with bias correction was found to be a suitable approach for deriving soil hydraulic parameters at a finer scale from soil physical properties at coarser scales and across different spatial extents. The approach could potentially be used for downscaling soil hydraulic properties.

Free‐form estimation of the unsaturated soil hydraulic properties by inverse modeling using global optimization

Inverse modeling is a powerful technique for identifying the hydraulic properties of unsaturated porous media. However, the selection of an appropriate parameterization of the soil water retention and hydraulic conductivity function remains a challenge. In this article, we present an improved algorithm for estimating these two relationships without assigning an a priori shape to them. The approach uses cubic Hermite interpolation and a global optimization strategy. A multilevel routine identifies the adequate number of degrees of freedom by balancing model performance, the statistical interaction of the estimated model parameters, and their number. A first‐order uncertainty analysis provides a quantitative measure of how well the soil hydraulic properties can be identified in different ranges of pressure head. This offers great potential for designing optimal experimental procedures for identifying the hydraulic properties of porous media. We demonstrate the effectiveness of the algorithm for the evaluation of multistep outflow experiments by investigating synthetic data sets and real measurements. The free‐form approach yields optimal model parameters that show only moderate correlation, indicating well‐posed inverse problems. Since parameterization errors are almost completely avoided, the algorithm is well suited to identifying other error sources in unsaturated flow problems, e.g., limitations in the applicability of the Richards equation or problems caused by spatial heterogeneity.

On the use of soil hydraulic conductivity functions in the field

The estimation of soil water fluxes using the Darcy–Buckingham flux-gradient approach is, after a century of use, still problematic under field conditions. Two features of the soil hydraulic conductivity ( K) function are the main causes of failure, first the exponential character of the K versus soil water content ( θ) relations, which lead to large variations in K for minimal variations of θ. Due to this, the level of precision of field measurements of θ and the spatial variability of θ itself, make the deterministic estimation of soil water fluxes unfeasible using this approach. Secondly, the spatial variability of the parameters of the K( θ) relations also contribute heavily to errors in soil water flux estimation from site to site. In a coffee crop water balance experiment, soil water fluxes below the root zone were estimated over one year, comparing the use of a soil hydraulic conductivity function obtained in the field, with an indirect climatologic approach in which the deep drainage is estimated from a water balance excess. Five replicates gave the possibility of calculating variances of both forms of calculation and their respective coefficients of variation (CV). Results show that CVs of the estimates made through the Darcy–Buckingham approach varied from 78 to 122%, in comparison to 8–23 for the indirect climatologic approach. It is therefore concluded that Darcy–Buckingham approach used deterministically under field conditions does not yield consistent results.