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On the Determination of Unsaturated Hydraulic Conductivity From Soil Moisture Profiles and From Water Retention Curves
Abstract
When solving water flow in a soil using Darcy-Richards' equation, information about the unsaturated hydraulic conductivity of the soil is necessary. However, direct measurement of unsaturated hydraulic conductivity is time consuming and expensive. Therefore, instantaneous profile methods and/or models to estimate the unsaturated hydraulic conductivity from water retention data are preferable. However, results of the instantaneous profile methods are often influenced by how precise we express the relation of measured volume wetness with time and the relation of measured hydraulic heads with soil depth. Here, we introduce three regression functions for expressing these relationships. In addition, an empirical model relating the measured unsaturated hydraulic conductivity with volume wetness was also developed. Evaluations of Burdine and Mualem models to predict the unsaturated hydraulic conductivity from the water retention curves were conducted. The results show Burdine and Mualem models can estimate the unsaturated hydraulic conductivity better for the tested soils at lower volume wetness.
(C) Williams & Wilkins 1993. All Rights Reserved.
... Nonlinear transformations of basic soil parameters (e.g., logarithmic or exponential) and the use of non-linear regression equations appeared to be beneficial . Recently equations built using artificial neural networks (ANN) were found to be more accurate compared with statistical regressions in estimating soil water retention from basic soil properties [Pachepsky and Timlin, 1994;Pachepsky et al., 1996;Schaap and Bouten, 1996]. The ANNs provide an excellent flexibility in mapping complex 'input-output' dependencies [Hecht-Nielsen, 1990]. ...
... The accuracy of both K sat estimates and water retention estimates affects the unsaturated hydraulic conductivity estimates that are relying on these two hydraulic parameters [Alexander and Skaggs, 1984]. There are indications that the capillary pore space models can be used only at relatively high hydraulic heads [Wösten and van Genuchten, 1988;Setiawan and Nakano, 1993]. If the soil water potential is larger than some critical value R c , some part of soil water moves through large pores, and degree of saturation of these pores may not determine their hydraulic conductivity. ...
Pedotransfer functions (PTFs) express relationships between soil properties from soil surveys and soil parameters needed in applications such as modeling or soil quality assessment. The accuracy and the reliability of PTFs vary and depend on the selection of the PTF equation, the availability of soil properties used in the PTF, the homogeneity of the data set, and the scale at which the data were collected. Artificial neural networks and the group method of data handling may generate more accurate PTFs than statistical regression. Soil structure parameters in PTFs improve their accuracy. The accuracy of PTFs increases when a preliminary data grouping is made and separate PTFs are developed for each group. Cross-validation is helpful in assessing whether the grouping will improve the reliability. PTFs are generally reliable in regions different from the region of development when the soil-forming factors are similar in the two regions, or when the region of development comprises a wide range of soils. Model sensitivity analysis or error propagation analysis is needed to define the required PTF accuracy. Aggregating soil data up to soil association level is helpful when PTFs are used in crop modeling at the regional scale. The accuracy of crop simulations with a PTF increases with the temporal scale of the modeling. Development of scale-dependent PTFs is a promising avenue of future research.
... This plane of zero flux can be computed algorithmically given an equation that best fits an H-z profile data. Attempts have been made to describe H-z profile data (Setiawan and Nakano, 1993). Based on the determined average plane of zero flux (z0), drainage flux occurring any depth below the plane of flux can be computed and used to calculate the unsaturated hydraulic conductivity at depth z1, (z1>(z0) by the following equation: ...
... Where, C is concentration in water (g/l), D w is diffusion coefficient (cm 2 /s), x is distance (cm), and t is time (d). Secondly, dispersion coefficient of NaCl solution in soil was measured by meant of the inverse problem of the Convection Dispersion Equation, Equation 2, (Noborio et al., 1996; Feyen et al., 1998; Setiawan B.I. and M. Nakano, 1993), in with the pitcher was buried in the soil having water content distribution in a queasy-steady state. Soil samples were taken and measured analytically in laboratory. ...
Pitcher is a bottlelike emitter made of porous baked-clay that is designed to be able to release water through its wall into the surrounding soil. In irrigation practice water level inside the pitcher is maintained by means of a constant water level supplier, or mariotte tube. This research looks at how the pitcher can also release nutrients when filled with dissolved fertilizers. For this purpose, we measured hydraulic and hydro-dynamic properties of the pitcher, and simulated solute transport using the convective-dispersive equation, and observed the effectiveness of fertigation in which NPK fertilizers were used on bush pepper plants. The results showed the pitcher was capable to release dissolved solution. Soil water content played significant roles in distributing the dissolved solution. These three nutrients have different distribution patterns. Nitrogen was well distributed, Phosphor was accumulated close to the pitcher's wall, and Potassium increased gradually with distance. These difference patterns were caused by the difference of hydrodynamic coefficients in which Nitrogen was the largest value among the others. The diffusion coefficient ranged at 1.01x10 -7 – 4.1x10 -3 cm 2 /day for NaCl, and 6.7x10 -6 -3.5x10 -3 cm 2 /day for NPK fertilizers. Bush papers planted surrounding a pitcher enabled to extract the nutrients as shown by the progressive growth of the crops: height, branches, leaves and flowers, which were monitored daily. After unearthed, roots of the bush pepper developed only in the wetter soils. This showed the water as well as the dissolved solution were resided concentrically around the pitcher's wall, and were all available to use by the plants effectively.
... Water retention curves of the soils conformed to Genuchten (1980) model which in such way modified by Setiawan (1992) to facilitate the presence of positive water head inside the pitcher. Furthermore, the hydraulic conductivity function of the soils was measured by meant of the instantaneous profile method and the results was well represented by the following equation (Setiawan and Nakano, 1993). Initially, the soil moisture was approximately homogenous and hysteretic effects might be negligible since the water flow would be very slow. ...
Pitcher, a bottle-like irrigation emitter made of baked clayed soils mixed with sands has been recognized as the oldest traditional irrigation. It has high water efficiency since the water seeps directly to and concentrated in the root zones. We conducted numerical and experimental studies to investigate the water flow in the soil surrounding a pitcher and to figure out the availability of soil water for crops. The Darcy and Richards' equation of water flow in a cylindrical coordinate system was applied and was solved using Finite Element Method to describe soil moisture profiles. Two soil textures were used, one was silty clay and the other was sand. The hydraulic conductivity of the pitcher was in order 10 -6 cm/s which was smaller 100 times than that of the two soils. The pitcher was buried in the center axis of a soil box and water was given from Mariotte tube to maintain a constant the water level inside the pitcher. In another studies, we figured out how the pitcher can also release nutrients when filled with dissolved fertilizers. For this purpose, we measured hydraulic and hydro-dynamic properties of the pitcher, and simulated solute transport using the convective-dispersive equation, and observed the effectiveness of fertigation in which NPK fertilizers were used on bush pepper plants. The advancements of wetting front in the soil was very slow and somewhat limited to a radius and depth of no more than 30 cm and 40 cm, respectively for the tested soils. The soil moisture was in a range available for plant growth. Different depths of pitcher placement in the soil produced different reaching distances of the wetting front but showed insignificant different in the water availability. The pitcher was capable to release dissolved solution. The three nutrients have different distribution patterns. Nitrogen was well distributed, Phosphor was accumulated close to the pitcher's wall, and Potassium increased gradually with distance. These difference patterns were caused by the difference of hydrodynamic coefficients in which Nitrogen was the largest value among the others. The diffusion coefficient ranged at 1.01x10 -7 – 4.1x10 -3 cm 2 /day for NaCl, and 6.7x10 -6 -3.5x10 -3 cm 2 /day for NPK fertilizers. Bush papers planted surrounding a pitcher enabled to extract the nutrients as shown by the progressive growth of the crops: height, branches, leaves and flowers, which were monitored daily. After unearthed, roots of the bush pepper developed only in the wetter soils. An accurate placement of pitcher in soil is important to provide effective soil wetness in the root zone and reduce evaporation rate. The right placement of pitcher must be determined based on the hydraulic characteristics of the 1 Presented at Postgraduate GP Education Workshop on From Environmental to Sustainable Science: thinking the shift and the role of Asian agricultural science. pitcher and the soil. From this study we found 5 cm placement depth of the pitcher's shoulder is an appropriate reference for the application of pitcher irrigation.
... One was Sandy Soil and the other was Silty Clay. Water retention curves of the soils conformed to Genuchten (1980) Subsequently the hydraulic conductivity function of the soils was measured by the instantaneous profile method and the results were well represented by the following equation (Setiawan and Nakano, 1993): Source: Saleh (2000). ...
Pitcher, a bottle-like irrigation emitter made of baked clayed soils mixed with sands has been recognized as the oldest traditional irrigation. It has high water efficiency since the water seeps directly into and concentrated in the root zones. Numerical and experimental studies were conducted to investigate the water flow in the soil surrounding a pitcher and to figure out the availability of soil moisture for crops. The Darcy and Richards’ equations of water flow in a cylindrical coordinate system was applied and was solved using Finite Element Method to describe soil moisture profiles. Two soil textures were used, one was silty clay and the other was sand. The hydraulic conductivity of the pitcher was in order 10-6 cm/s which was 100 times smaller than that of the two soils. The pitcher was buried in the center axis of a soil box and water was given from Mariotte tube to maintain a constant water level inside the pitcher. The results showed the infiltration rates decreased linearly rather than exponentially even though the soil was initially dry. The advancement of wetting front was very slow and somewhat limited to a radius and depth of no more than 30 cm and 40 cm, respectively for both tested soils. The surrounding soil moisture was in a range available for plant growth. Different depths of pitcher placement in the soil produced different reaching distances of the wetting front but showed insignificant differences in water availability. Accurate placement of pitcher depth in soil is important to provide effective soil wetness in the root zone and reduce evaporation rate. The right placement of pitcher must be determined based on the hydraulic characteristics of the pitcher and the soil. In this study, 5 cm placement depth of the pitcher’s shoulder is an appropriate reference for the application of pitcher irrigation.
Keywords: pitcher irrigation, infiltration rate, soil moisture profile
Infiltration regulates the movement and storage of water at the soil–atmosphere interface and is, therefore, a key component of many related physical and biogeochemical processes. Numerous studies have examined infiltration over the past two centuries. These efforts have resulted in the development of numerous models that capture the effects of specific soil properties and initial and boundary conditions. This proliferation of models has advanced our collective ability to understand infiltration processes but has also made it challenging for researchers to select appropriate approaches for analyzing experimental infiltration data or for conducting basic research on soil parameters like saturated hydraulic conductivity or sorptivity. Here, we aimed to reduce this uncertainty by developing a comprehensive literature review of published infiltration models, including their underlying philosophies and evolution over the years. Through this effort, we compiled and examined 138 unique infiltration models. We grouped models into two major categories, empirical and conceptual, noting that boundaries between those two categories are at times debatable. After classifying and providing a full historical retrospective of these models, we examined specific model parameters and how their usage has changed with time. We also reviewed different methods applied to estimate infiltration parameters, as well as the challenges that arise when using such methods. Finally, we proposed a framework for identifying suitable models depending on field conditions, experimental plan, and data availability.
Pitcher Irrigation is one of the artificial water supply techniques to overcome the lack of soil water content. The Pitcher Irrigation can save water so it is suitable for use on dry land. The research purposes was to determine the effect of various hydraulic conductivity of the picther on changes in soil water content around the pichter through program simulation. The methods used are direct measurement methods in the field and simulation methods. The measurement and simulation results are then calibrated with a solver and validated to obtain a small RMSE value and R2 was high. The results showed that the hydraulic conductivity of the picther had a significant effect on the soil water content. If the higher the hydraulic conductivity of the picther, the higher the water content around this pcther. And if the hydraulic conductivity of the picther is lower, the water content around the picther be lower. From the results of model validation, it can be said that the simulation program in this study is feasible to use because the value obtained R2 is 56.1%.
Abschließend wird ein Überblick über Methoden zur Ermittlung der hydraulischen Leitfähigkeit gegeben. Die ungesättigte hydraulische Leitfähigkeit kann durch direkte (stationäre und instationäre) Methoden, durch inverse Methoden und durch Pedotransferfunktionen bestimmt werden. Bei der Behandlung von Beispielen wird der Instantaneous Profile Method und den Infiltrationsmethoden für die Anwendung im Felde (Bohrlochpermeameter, Tensionsinfiltrometer, Infiltrationsmessungen mit gesättigter Bodenoberfläche) besondere Aufmerksamkeit gewidmet. Das große Gebiet der Pedotransferfunktionen konnte nur durch wenige Beispiele berücksichtigt werden.
There is high motivation to develop pitcher irrigation system due to its effectiveness in wetting the root zone. Many experiments have been conducted to study water flow in soils with the application of pitcher irrigation. The objective of this research is to develop models to study solute transport in the soils. Numerical approaches with 2-D finite difference method were applied and verified. The results show the models are more or less confirmed well with measured data.
Simple one-parameter models for predicting changes in unsaturated soil hydraulic properties with changing soil-water content are useful, considering the great uncertainty and variability in the hydraulic parameters, and the models are often used for stochastic simulations of water and solute transport under field conditions. Two general one-parameter models for predicting relative hydraulic conductivity between water saturation and -350 cm H2O of soil-water potential are presented. The two new hydraulic conductivity models were labeled the Double Log Conductivity (DLC) and the Single Log Conductivity (SLC) models and represent modifications of the Campbell and the Libardi et al. conductivity models, respectively. The DLC and SLC model constants were optimized based on conductivity and retention data from a broad texture group of 40 sieved soils, but they can be calibrated easily to specific series of soils. The main parameter in both models (the Campbell soil-water retention parameter, b) can be estimated readily from soil texture or water retention data. Both models gave improved predictions of relative hydraulic conductivity in sieved soils compared with traditionally used one-parameter models. DLC and SLC model predictions were further compared with conductivity data from 10 undisturbed soils. The results suggested that the new models are also useful for predicting both relative and absolute hydraulic conductivity in undisturbed soil, but in this case, a calibration of the model constants based on a larger undisturbed soil data set is recommended.
Hydraulic conductivity is likely the most important soil property controlling water and solute movement in soils. It is also one of the most variable and uncertain soil properties. Models for predicting soil hydraulic conductivity from other soil characteristics are, therefore, useful in both deterministic and stochastic transport studies. A new model for predicting saturated hydraulic conductivity (KS) in undisturbed soils from macroporosity (∊100), defined as the air-filled porosity at a soil-water potential of Ψ = -100 cm H2O, was developed using data for 23 undisturbed soils (90 horizons). The new KS model compared well with measurements when tested against independent data sets for 73 undisturbed soils (191 horizons) from the UNSODA database and gave improved predictions (accuracy within one order of magnitude) compared with existing KS models. Two new models for predicting relative hydraulic conductivity (K/KS) in relatively moist, (Ψ > -350 cm H2O) undisturbed soils from soil-water content (θ) and the Campbell soil-water retention parameter, b, were developed using conductivity and water retention data for the 73 soils from UNSODA. The new K/KS models represent modifications of the recently presented DLC and SLC models (Poulsen et al. 1998. Soil Science 163:425-435) for predicting K/KS in sieved, repacked soils. The modified DLC and SLC models were combined with the new KS model, yielding new two-parameter (∊100, b) models for unsaturated hydraulic conductivity (K(θ)) in undisturbed soil. The two new K(θ) models were successfully tested against independent K(θ) data. Also, the classical Campbell (Campbell. 1974. Soil Science 117:311-314) K/KS model, combined with the new, more accurate KS model, gave K(θ) prediction accuracy almost as good as the modified DLC and SLC K(θ) models. The suggested two-parameter K(θ) models require knowledge of only the soil-water retention curve, including a measurement at Ψ = -100 cm H2O, and seem promising for use in deterministic and stochastic models for water transport in natural, undisturbed soils.
Over the past 30 years, numerous studies have been carried out into groundwater behavior in volcanic areas, with particular attention being paid to unsaturated volcanic tuffs.The volcanic formations of the Chaîne des Puys (Massif Central, France) have long been regarded as valuable sources of fresh water and many aquifers associated with volcanic flows have been tapped for domestic water supply or as sources of bottled mineral water. It has often been postulated that these volcanic flows are recharged by groundwater from the volcanic cones located upstream, although no efforts have been made to validate this theory. We tested the physical basis of this hypothesis by characterizing the unsaturated hydrodynamic properties of the packed lapilli and scoria that form the most important constituents of the Strombolian cones in this area. The model derived from the results of the characterization experiments was compared with data obtained from a field site. The unsaturated properties of this site (Puy de Louchadière Strombolian cone) are discussed qualitatively and in terms of “memory effect”.Further investigations are now needed to determine the exact behavior of the Strombolian cone and to produce complete models of the saturated and unsaturated zones of the aquifer system.
Closed-form expressions for quantifying the unsaturated soil hydraulic properties are widely used in computer programs to model subsurface flow and transport in porous media and to investigate indirect methods for estimating these properties. For example, water retention data, which relate soil-water pressure head (h) and effective water saturation (Se), are frequently used to predict the unsaturated hydraulic conductivity (K). However, the suitability of different functions to describe unsaturated hydraulic data has rarely been investigated comprehensively. We attempted to fit 14 retention and 11 conductivity functions to 903 sets of water retention and hydraulic conductivity data measured on soil and rock samples or horizons reported in the unsaturated hydraulic database UNSODA. Some of the best mean values for r2 and MSE for fitting Se(h) data were obtained with the retention functions reported by van Genuchten (1980), Globus (1987), and Hutson and Cass (1987). A function reported by Gardner (1958) could describe K (h) data quite well whereas functions reported by Brooks and Corey (1964) and van Genuchten (1980), which are respectively based on the conductivity models by Burdine and Mualem, yielded a relatively good description of K(SC) data.
Reliable prediction models for unsaturated hydraulic conductivity (K) based on a minimum of easily measurable input parameters are valuable for assessing water and chemical transport in the vadose zone. Recently, the Three Region Campbell (TRC) model for predicting K in undisturbed soil in three separate pore size regions (corresponding to 0 to -10, -10 to -350, and -350 to -15,000 cm H2O of soil-water matric potential) was suggested and calibrated, but not tested. In this study, the TRC model is tested against independent data for 36 undisturbed soils from the Netherlands, and the number of necessary input parameters is reduced. The TRC model yielded accurate K predictions for the 36 soils in all three pore-size regions. Two different methods for using the TRC model with reduced sets of input parameters were proposed. Method I requires two measurements of hydraulic conductivity (at saturation and at -10 cm H2O) and three measurements of soil-water retention (swr) (at -10, -100 and about -250 cm H2O). Method II requires only a measurement of soil total porosity and the three swr measurements, and it is based on estimating saturated and near-saturated hydraulic conductivity from the air-filled porosity at -100 cm H2O (representing pores larger than 30 mum equivalent pore diameter). Root mean square error (RMSE) of prediction of Log(K) for the 36 soils increased by 18% (Method I) and 78% (Method II) compared with using the nonreduced parameter input in the TRC model. However, the prediction accuracy (typically around one order of magnitude) is still sufficient for many modeling purposes and, in comparison, the RMSE (Method II) was still four times lower than the original Campbell single-region K model. Data from six additional soils were used to evaluate the possibility of adding a fourth region (film flow, < - 15,000 cm H2O) in the TRC model. The results imply that the TRC model concept, with its advantage, could be expanded to a four-region model when additional data for K in very dry soil become available.
Studies to predict the impact of deforestation on climate in Amazonia have stimulated interest in the hydraulic properties of the soils of the region and the surrounding areas, Few directly measured hydraulic conductivity data are available; these were used to derive parameters to allow the unsaturated hydraulic conductivity-water content (K-theta) curve to be obtained from the more easily measured water retention curve, Relative hydraulic conductivity was modeled using the Brooks-Corey formula, whereas the saturated conductivity was calculated as a function of effective porosity from the expression proposed by Ahuja et al, Empirical relationships were fitted to seven different Brazilian soils, from 13 different sites, assembling about 2650 field conductivity values, The data for six of the soil types could be represented by a single set of parameters, with kaolinitic yellow latosolic soils from Amazonia requiring a separate set, Fitted relationships showed very high statistical significance, and the parameters derived were significantly different from those derived by Ahuja et al, for North American soils, To verify the proposed methodology, the parameters were derived using the complete data set (without the kaolinitic yellow latosol), excluding one soil type at a time, and checking the ability of the relationships to predict the conductivity of the soil not included in the fitting, In addition, the parameters obtained from the complete data set predicted hydraulic conductivities from the water release curves of five other Brazilian soils for which measured conductivity values were available. Pages: 703-712
This paper gives a review of our current conceptual understanding of the basic processes of water flow and chemical transport in the untsaturated (vadose) zone and of various deterministic mathematical models that are being used to describe these processes. During the past few decades, tremendous effort has been directed toward unravelling the complexities of various interactive physical, chemical, and microbiological mechanisms affecting unsaturated flow and transport, with contributions being made by soil scientists, geochemists, hydrologists, soil microbiologists, and others. Unfortunately, segmented, disciplinary research has contributed to a lack of experimental and theoretical understanding of the vadose zone, which, in turn, has precluded the accurate prediction and management of flow and contaminant transport through it. Thus a more unified and interdisciplinary approach is needed that considers the most pertinent physical, chemical, and biological processes operative in the unsaturated zone. Challenges for both fundamental and applied researchers to reveal the intricacies of the zone and to integrate these with currently known concepts are numerous, as is the urgency for progress inasmuch as our soil and ground water resources are increasingly subjected to the dangers of long-term pollution. Specific research areas in need of future investigation are outlined.
Evaluation of the water content‐suction relation applicable to field soil horizons that differ widely in texture was considered. Except for coarse‐textured, organic matter‐deficient horizons, it is concluded that soil water retention of sieved samples is significantly modified and does not represent the natural soil volume. Water content‐suction data from measurements on carefully procured core samples of each horizon of a Typic Hapludult adequately represent their water retention characteristics. Using appropriate water content‐suction data, the hydraulic conductivity‐water content relation calculated by published procedures was compared with hydraulic conductivity measured on similar samples by a transient outflow procedure. The calculated hydraulic conductivity‐water content relations for coarse grained systems or systems having a relatively narrow range of pore size and well‐defined bubbling pressure was sufficiently accurate for many purposes. However, to obtain a useful evaluation of the unsaturated hydraulic conductivity of fine‐textured horizons with a very wide range of pore size and a poorly defined bubbling pressure, the Marshall or Millington and Quirk methods had to be matched at a water content in the 0.1‐ to 0.3‐bar range. Indiscriminate use of such methods of calculating hydraulic conductivity is inadvisable.
A practical new field method is proposed to evaluate hydraulic
conductivity in partially saturated media near a water impoundment. The
new method is an inverse procedure which utilizes a flow net constructed
from the steady state total hydraulic head distribution around the water
source. In the vicinity of constant head sources and downstream along
any stream tube, wetness and conductivity generally decrease. Knowing
the stream tube geometry and hydraulic gradient from the flow net,
Darcy's law is used to determine unsaturated hydraulic conductivities
within the stream tube relative to some segment of the stream tube where
conductivity is known. This approach was used successfully to predict
the unsaturated hydraulic conductivity which was input to two variably
saturated numerical models, utilizing total hydraulic head fields
generated by the models. This procedure is also applied to pressure head
and water content data collected in the field surrounding a constant
head borehole infiltration test originally designed to determine only
saturated hydraulic conductivity above the water table. For practical
purposes the new procedure compares very favorably with (1) results of a
field experiment to obtain unsaturated hydraulic conductivity in situ
using the instantaneous profile method and (2) values of unsaturated
conductivity calculated from field and laboratory measurements of water
content and pressure head.
The application of numerical approximation has been greatly enhanced by the introduction of digital computers. The main purpose for the use of approximating functions is to represent a set of known data points by means of simple and elementary functions so that values at some unknown points can be evaluated, as well as to perform many common operations such as differentiation and integration.
Many phases of soil science still remain largely empirical because the soil is such a complex system. For instance, there is no known function to define the soil-water characteristic curve required to establish the relation between water content and water pressure in studying soil-water behavior. To determine soil-water diffusivity by infiltrating water into an air-dried soil, knowledge of how water distributes within the soil profile is needed and it is rather tedious to evaluate d[theta]/dx manually. It is obvious that statistical approaches are not applicable to these instances and piecewise linear approximation does not always provide satisfactory results.
The purpose of this paper is to formulate a relatively simple approximation method to provide a continuous and smooth curve through all points of interest, one which is differentiable as well as integratable everywhere throughout the specified domain. This spline function method has been developed only recently and is not included in most numerical analysis texts.
(C) Williams & Wilkins 1972. All Rights Reserved.
A simple analytic model is proposed which predicts the unsaturated
hydraulic conductivity curves by using the moisture content-capillary
head curve and the measured value of the hydraulic conductivity at
saturation. It is similar to the Childs and Collis-George (1950) model
but uses a modified assumption concerning the hydraulic conductivity of
the pore sequence in order to take into account the effect of the larger
pore section. A computational method is derived for the determination of
the residual water content and for the extrapolation of the water
content-capillary head curve as measured in a limited range. The
proposed model is compared with the existing practical models of
Averjanov (1950), Wyllie and Gardner (1958), and Millington and Quirk
(1961) on the basis of the measured data of 45 soils. It seems that the
new model is in better agreement with observations.