75: Determining Soil Hydraulic Properties

WOLFGANG DURNER AND KAI LIPSIUS

Institute of Geoecology, Department of Soil Physics, Braunschweig Technical University,Braunschweig, Germany

Hydraulic properties are required for modeling water and solute transport in unsaturated soils. The bottleneckfor the successful application of numerical simulation models lays usually in their parameter estimationrequirements. Methods to determine hydraulic properties can be classified into indirect and direct approaches.Indirect methods encompass the estimation of hydraulic properties by pedotransfer functions from more easilymeasured soil properties, and the prediction of the unsaturated hydraulic conductivity function from the waterretention curve (WRC ). In direct methods, observations of flow attributes from laboratory or field experiments areevaluated. This article reviews common methods to estimate the hydraulic conductivity function from the waterretention characteristic and various direct measurement techniques in the laboratory and the field. We concludewith an outlook on contemporary developments in measurement techniques, stressing the key role of inversemodeling of experiments to derive optimum hydraulic properties and the importance of a future combination ofnoninvasive measurement techniques with inverse modeling by stochastic data fusion.

INTRODUCTION

A proper characterization of water flow processes is neededin nearly all basic and applied aspects of soil, water,nutrient, and salinity management research (van Genuchtenet al., 1999b). Water flow in soils is typically describedwith the Richards equation (Richards, 1931)

C(h)∂h

∂t= ∂

∂z

[K(h)

(∂h

∂z− 1

)]+ s (1)

where t is time [T], z is a spatial coordinate [L], positivedownward, h is the matric potential, expressed as pres-sure head [L], C(h) is the specific water capacity [L−1],defined by the change of the volumetric water content θ [L3

L−3], with pressure head, C = ∂θ/∂h,K(h) is the unsatu-rated hydraulic conductivity [L T−1], and s is a source/sinkterm [T−1]. The model is completed by appropriate initialand boundary conditions. Since C and K are nonlinearlydependent on h, its solution generally requires numericalmethods. Equation (1) is derived from the combination ofthe Darcy-Buckingham equation and continuity considera-tions in the framework of the continuum theory, and is validfor the measurement scale (see Durner and Fluhler, 2005;

Chapter 74, Soil Hydraulic Properties, Volume 2). It isalso frequently used as process model for water transport atmuch larger scales. The coefficients C and K are then usedas effective properties, which have the same names as forthe local scale, but their values are no longer necessarilyconsistent with the local definition. Determining hydraulicproperties is the process of deriving the constitutive rela-tionships θ(h) and K(θ ), or K(h), as used in equation (1).The relationship θ(h) is called (water retention curve)WRC . The dependence of the hydraulic conductivity, K(h),on water content or pressure head is called ‘hydraulic con-ductivity curve’.

This article reviews the indirect and direct methodsfor the determination of soil hydraulic properties. Directmethods are based on flow experiments in the field orwith soil samples in the laboratory. They rely on obser-vations of flow attributes, such as water potential, watercontent or water flux density. These measurements are farfrom simple. Water content measurement is treated in thisencyclopedia in Chapter 72, Measuring Soil Water Con-tent, Volume 2 (Topp and Ferre, 2005), soil water poten-tial measurement is treated in Chapter 73, Soil WaterPotential Measurement, Volume 2 (Durner and Or, 2005).Water flux density can be determined at system boundaries,

Encyclopedia of Hydrological Sciences. Edited by M G Anderson. 2005 John Wiley & Sons, Ltd.

2 SOILS

using scales or burettes in the laboratory. For measuringfluxes in situ, there are no reliable and accurate methods.Accordingly, in situ flux measurements are not used up todate for the determination of hydraulic properties (Dirksen,1999b).

Indirect methods are used to estimate hydraulic proper-ties from more easily measured data, using regression orneural network algorithms. In particular, the unsaturatedconductivity function is seldom measured, but commonlyestimated from the WRC and matched to a single mea-sured conductivity value. Because of the shortcomings ofdirect measurement procedures, indirect estimation methodsare gaining popularity. All estimation procedures, however,need the results of direct measurements as benchmarks forvalidation. Furthermore, reliable and efficient experimentalprocedures are critical to improve the understanding of flowand transport processes in variably saturated media, regard-less of the advances in the formulation of indirect methods.

A review on measurement methods needs to addressaspects of sensor technology, instrumentation, experimentaldesign, techniques to evaluate observed data, scale issues,parameterization of hydraulic functions, parameter estima-tion techniques, and uncertainty estimation and propagation.Covering all these issues in the required depth would be farbeyond this contribution. So the focus is on principles ofindirect estimation procedures (Section “Indirect estimationof hydraulic functions”), on direct laboratory measure-ment methods (Section “Laboratory methods”), and on fieldmethods (Section “Field methods”). Topics that are closelyrelated to soil hydraulic measurements are treated in theaccompanying contributions in this encyclopedia. Theseare, in particular, soil water potential measurement (Durnerand Or (2005), Chapter 73, Soil Water Potential Mea-surement, Volume 2), water content measurement (Toppand Ferre (2005), Chapter 72, Measuring Soil WaterContent, Volume 2), estimation of hydraulic properties bypedotransfer functions (Schaap, 2005, Chapter 76, Mod-els for Indirect Estimation of Soil Hydraulic Prop-erties, Volume 2), scale issues (Hopmans and Schoups,2004, Chapter 66, Soil Water Flow at Different Spa-tial Scales, Volume 2), recent developments in parameterestimation techniques (Vrugt and Dane, 2005, Chapter 77,Inverse Modeling of Soil Hydraulic Properties, Vol-ume 2), and uncertainty propagation in hydrologic mod-els (Brown and Heuvelink, 2005, Chapter 79, Assess-ing Uncertainty Propagation Through Physically basedModels of Soil Water Flow and Solute Transport, Vol-ume 2). The definition of hydraulic functions in the frame-work of the continuum theory, the parameterization of thehydraulic functions including hysteresis, and the issue ofscale dependence of hydraulic properties are treated byDurner and Fluhler (2005)).

Methods and techniques to measure soil hydraulicproperties are described in a series of monographs. The

reference with the widest distribution is the classic mono-graph “Methods in Soil Physics – Physical Methods” ofthe American Society of Agronomy. The previous edi-tion (Klute, 1986) has recently been revised (Dane andTopp, 2002), and covers almost all practical measurementtechniques including soil sampling, uncertainty, and sen-sor technology. Hydraulic measurement methods are furtherdiscussed in some textbooks, for example, Kutilek andNielsen (1994), Dirksen (1999a), and Fluhler and Roth(2004). The scientific state of knowledge on direct, inverse,and indirect measurement methods at the time of the millen-nium is documented on 1600 pages in the “Proceedings ofthe International Workshop on Characterization and Mea-surement of the Hydraulic Properties of Unsaturated PorousMedia” (van Genuchten et al., 1999a). Direct measurementmethods cover about a fourth of the volumes.

The Purpose of Hydraulic Measurements

Methods to determine hydraulic properties differ withrespect to their accuracy, measurement range, difficulty ofimplementation, and demand for time and capital. Beforeselecting a specific measurement method, the purpose of themeasurements must be manifest. Purposes may be classifiedinto three groups.

(i) Soil hydraulic properties are often needed for ahydraulic classification of soils, in a similar manneras the particle size distribution is used for a texturalclassification. Knowledge of basic hydraulic proper-ties, such as field capacity or plant available watercontent, is useful for a variety of purposes, wheresoil moisture storage, soil wetness (affecting oxygensupply for plant roots and redox state of soil), sur-face runoff, susceptibility to soil erosion, and otherlarge-scale properties of soils are of interest. Indirectmethods are often appropriate for this group (Schaap,2005, Chapter 76, Models for Indirect Estimationof Soil Hydraulic Properties, Volume 2).

(ii) Today’s prevalent demand for hydraulic properties istheir use in numerical simulation of water transportby Richards’ equation. Estimation of water rechargethrough the vadose zone for water balance calcula-tions are a classic application, but more importantis now their use for agricultural, ecological, andenvironmental purposes, such as irrigation control,fertilizer management, and contaminant fate mod-eling. The focus of subsurface models of waterand solute transport has increasingly been shiftedtoward environmental research, with the primary con-cern on the subsurface fate and transport of varioussubstances, such as nutrients, pesticides, pathogens,pharmaceuticals, viruses, bacteria, colloids, and toxictrace elements (Simunek, 2005, Chapter 78, Models

DETERMINING SOIL HYDRAULIC PROPERTIES 3

of Water Flow and Solute Transport in the Unsat-urated Zone, Volume 2). The crucial bottleneck forthe successful application of these models is theirparameter estimation requirements.

(iii) Finally, accurate measurement of soil hydraulic prop-erties is required for a further improvement in thebasic understanding of soil hydraulic processes, thatis, in order to test and improve the process knowl-edge we have. Examples are the understanding andassessment of nonequilibrium phenomena in waterflow, further progress in describing hysteresis in soilwater flow, and the question up to which scale theRichards equation process model provides an appro-priate effective process representation for unsaturatedwater transport (Durner and Fluhler, 2005).

Whereas the demand on accuracy, resolution, precision,and reliability of the measurements is moderate for the firstgroup, it is higher for the second and third. For the secondgroup, we are particularly faced with scale considerations.For the third group, the precision, reliability, and validity ofmeasurements are of utmost importance, in order to avoidmisconceptions.

The Challenge of Determining Soil Hydraulic

Properties

Determining soil hydraulic properties is demanding fora variety of reasons. Soils are porous media with athree-dimensional arrangement of interconnected voids thatform a highly complex pore system. The topology ofthis system shows, in general, a hierarchical arrangement,with spatial and temporal variability on a multitude ofscales. The microscopic properties of the pore systemdetermine the macroscopic hydraulic behavior. A completeunderstanding of water flow in soils requires a thoroughunderstanding of processes on scales much smaller thanthe usual measurement scale and the ability to expresseffective hydraulic properties at scales much larger than themeasurement scale (Durner and Fluhler, 2005; Hopmansand Schoups, 2004, Chapter 66, Soil Water Flow atDifferent Spatial Scales, Volume 2).

A specific problem in the determination of soil hydraulicproperties lays in the fact that quality control and valida-tion of measurement results is extremely difficult. Contraryto soil chemical analysis, there is virtually no possibilityfor reliable interlaboratory comparisons (Dirksen, 1999b).The reasons for this are: (i) as opposed to consolidatedporous media, the soil pore system is not a stable struc-ture. Just those parts of the pore system, which controlthe water transmission near saturation, are most fragile,and there is always a danger that the measurement pro-cess itself changes the system (Ghezzehei and Or, 2003).Therefore, repetitive measurements on the same soil sample

by different laboratories are impractical. The sampling pro-cess itself often causes the most severe disturbance, whenan “undisturbed” soil sample is isolated from the naturalembedding. (ii) Soils exhibit considerable temporal vari-ability (Mapa et al., 1986; Ahuja et al., 1998; Leij et al.,2002). Thus, measurements at the same site may yield dif-ferent results if applied at different times (van Es et al.,1999). (iii) Soil is a living organism and the pore system isaffected by a variety of interacting biological, chemical, andphysical processes. Matrix surface properties are variegatedand may change depending on physical, chemical, and bio-logical factors, thereby changing the macroscopic hydraulicbehaviour. (iv) Spatial variability of hydraulic properties,finally, is probably the biggest problem (Nielsen et al.,1973, 1986). Different measurement methods use differentsample volumes and sample numbers, dictated by stan-dard procedures and the apparatus available for the variousmethods. This implies that, in a comparison of measure-ment methods, considerable uncertainty about the result ofthe comparison will always be induced by natural variabil-ity (Stolte et al., 1994; Munoz-Carpena et al., 2002). Forexample, the determination of field-saturated conductivity,Kfs, may vary two or more orders of magnitude amongdifferent field and laboratory methods.

Testing measurement methods on synthetic soil-likeporous media is not a solution to this dilemma. Thepore system properties of repacked soil samples are oftenvery different from the properties of an undisturbed soil(Torquato, 2001). It is notable that especially uniform finesand, being the favorite material used for research pur-poses in soil physics, has properties that are quite untypicalfor a structured natural soil. Since the early observationsof Kozeny (1927) on particle segregation during packing,the problem of constructing a synthetic porous mediumin a fully reproducible manner, with pore system proper-ties comparable to a natural soil, has remained unresolved(Lebron and Robinson, 2003).

An overview on various field and laboratory methodsfor determining unsaturated hydraulic properties shows thatmany techniques have been proposed, but most of them arelimited to relatively narrow ranges of water potential (h) orwater content (θ ). Figure 1 illustrates this, showing resultsof five different measurement methods to determine thehydraulic conductivity. The existing experimental proce-dures all have their own unique advantages and limitations(Gee and Ward, 1999), and selecting the most appropriatemeasurement for a specific task is usually not trivial.

Classification of Methods

Determining hydraulic properties of soil encompasses directmeasurements and indirect estimation methods. Because ofthe shortcomings of direct measurement procedures, indi-rect estimation methods are gaining popularity. Computersoffer the possibility to generate indirect estimates using

4 SOILS

104

101

102

102

103

103

100

10−1

10−2

|h| (

m)

|h| (m)

101

101

100

100

10−1

10−1

10−2

10−2

10−3

10−4

10−5

10−6

10−7

10−8

10−9

K (

m/d

)

0 0.1 0.2 0.3 0.4 0.5

q

Fluviatile silt loam Fluviatile silt loam

(a) (b)

Crust method

Drip infiltrometer method Hot-air method (median withminimum and maximum)

One-step outflow method (medianwith 20th and 80th percentiles)

Evaporation method

Figure 1 Hydraulic properties of a fluviatile silt loam. (a) Water retention curve measurements. (b) Unsaturatedconductivity measurements, determined by five different methods (Reproduced from Stolte et al., 1994 by permission ofSoil Science Society of America)

regression or neural network algorithms. In practice, unsat-urated conductivity is seldom measured, but estimated fromthe saturated conductivity (or preferably an other matchingpoint) and the WRC. The principles of indirect estimationprocedures are outlined in Section “Indirect estimation ofhydraulic functions”.

All estimation procedures need the results of direct mea-surements as benchmarks for validation of their results.Reliable and efficient experimental procedures are critical toimprove the understanding of flow and transport processesin variably saturated media, regardless of the advances inthe formulation of indirect methods. Experiments for mea-suring hydraulic properties are based on hydrostatic, steadystate, or transient flow conditions. The methods can begrouped in those that aim at measuring (i) water retentivity,(ii) saturated conductivity, (iii) unsaturated conductivity orwater diffusivity, and (iv) simultaneously retentivity andconductivity. We may further distinguish between labora-tory methods and field methods. The reason for treatinglaboratory (Section “Laboratory methods”) and field exper-iments (Section “Field methods”) in this review in separatesections is less motivated by the different scale, but by thefact that in the laboratory a much better control of bound-ary conditions, fluxes across boundaries, and integral watercontent measurements can be achieved.

Finally, methods differ in how the observations of flowattributes, such as pressure heads, water contents or fluxes

are evaluated. In the early stages of soil physics, methodshave been developed for determining the WRC or thesaturated conductivity (Gardner, 1986). Determination ofthe water retention characteristic can be done directly, bypairing water content and water potential measurements inthe laboratory or in the field. The determination of saturatedconductivity is achieved by a closed-form inversion ofthe flow equation. Analytical solutions for the unsaturatedconductivity can be obtained in the laboratory by a seriesof consecutive unit-gradient experiments, where a constantflux or pressure head is applied at the top of a sample, and acorresponding suction at the bottom (Dirksen, 1991, 1999a,1999b). These methods are conceptually straightforwardand easy to implement. Their main disadvantage is thatthey take a long time, and are therefore tedious andexpensive. In order to achieve hydraulic equilibrium, thesample sizes must be kept small and sizes are often belowthe representative elementary volume, REV (Durner andFluhler, 2005). Accordingly, the resulting properties aregenerally highly variable.

Measurement of unsaturated hydraulic conductivity andwater diffusivity poses greater obstacles. The methods arebased on solving the inverse problem, where a modelof the flow process is optimized to match observations(Russo et al., 1991; Hopmans et al., 2002; Vrugt and Dane,2005, Chapter 77, Inverse Modeling of Soil Hydraulic

DETERMINING SOIL HYDRAULIC PROPERTIES 5

Properties, Volume 2). For some simplified cases, solv-ing the inverse problem is accomplished by closed-formsolutions, such as the determination of diffusivity froma quasi-analytical solution of the Richards’ equation. Inmost other cases, solution of the inverse problem canonly be achieved by fitting numerically simulated data toobservations. This requires the use of nonlinear parameterestimation techniques. In doing this, the next logical stepis to simultaneously estimate retentivity and conductivityparameters by inverse modeling.

METHODS TO DETERMINE SOIL HYDRAULICFUNCTIONS

Indirect Estimation of Hydraulic Functions

Estimation by Pedotransfer Functions

In pedotransfer functions, the water retention and conduc-tivity functions are derived from more easily measured soilproperties, such as soil texture, bulk density, and organicmatter content. Methods to derive soil hydraulic propertiesindirectly include multiple regression, classification, andneural network predictions (van Genuchten et al., 1999a).Comparisons of indirectly determined hydraulic propertiesto directly measured properties are manifold and remaina topic of ongoing research (Schaap, 2005, Chapter 76,Models for Indirect Estimation of Soil Hydraulic Prop-erties, Volume 2). In general, it is found that the accuracyof pedotransfer estimates of hydraulic functions for char-acterizing field average is comparable to simple directmeasurements, if spatial variability is considered. Depend-ing on the desired use of these properties, indirect methodshave evolved to a point where they provide reliable answersfor many problems. However, further improvement of indi-rect methods hinges on experimental data, which must beobtained with direct procedures.

Conductivity Estimation by Statistical EstimationMethods

The most frequently practiced way to determine the unsat-urated hydraulic conductivity function is by estimatingits shape from the WRC. The equilibrium WRC can beregarded as an effective statistical cumulative distribu-tion of equivalent pore sizes of a porous medium. Fromthat, attempts to predict the conductivity curve basedon capillary models of the pore space by applicationof Poiseuille’s law have been early set (Kozeny, 1927;Purcell, 1949; Childs and Collis-George, 1950; Burdine,1953; Fatt, 1956; Wyllie and Gardner, 1958; Marshall,1958; Millington and Quirk, 1961; Mualem, 1976; Alexan-der and Skaggs, 1984). Capillary pore-bundle models arenow routinely applied in an implicit manner, because they

yield closed-form equations for the hydraulic conductiv-ity function if combined with specific retention functions.Notable are the models Brooks-Corey/Burdine (Brooks andCorey, 1964), van Genuchten/Mualem (van Genuchten,1980;), or Russo/Gardner (Russo, 1988). The model of vanGenuchten/Mualem is nowadays the most frequently used.It is given by

Se = (1 + (α|h|)n)−m (2)

where Se = (θ − θr)/(θs − θr) is a scaled water content,called “effective saturation”, and α > 0 [L−1], n > 1 [−]and m > 0 [−] are empirical curve shape parameters. Ifm is related to n by m = 1 − 1/n, the correspondingconductivity function is given by

Kr(Se) = Sle

[1 − (1 − S1/m

e )m]2

(3)

where the parameter l [−] is called “tortuosity factor”.When applying the van Genuchten/Mualem conductivitymodel (3), the user should be aware of a model artifactfor small values of the parameter n, which is discussed inDurner and Fluhler (2005).

Despite the fact that these models often rely on over-simplified representations of the medium’s pore space asa bundle of cylindrical capillaries, there is much empiri-cal evidence that capillary models yield reasonable shapesfor the conductivity curve in a limited range of matricpotentials. However, the prediction of the absolute level ofconductivities was never successful (Jackson et al., 1965).Hence, “matching factors” are needed to match the unsatu-rated conductivity curve with observed conductivity values.A matching factor is used to scale a predicted value of therelative conductivity curve, Kr (θ ), to a directly measuredconductivity, Kref (θref), at a reference water content, θref.

K(θ) = Kref(θref)

Kr(θref)Kr(θ) (4)

In practice, most often the saturated conductivity, Ks,is used as matching factor, because measurement of thesaturated conductivity is relatively easy, both with respectto the experimental procedure and with respect to theinversion the Darcy-Buckingham flux equation. However,already as early as in the 1960s, the notorious instability ofmatching the predicted conductivity function to a measuredvalue at saturation was evident (Jackson et al., 1965). Thisis due to the extreme dependency of the conductivity nearsaturation on pore structure (Durner, 1994), which causes anenormous variability of the saturated conductivity in naturalstructured soils and makes the mathematical predictionnear saturation unstable. The current recommendation isto use an unsaturated reference measurement, which leadsto a more reliable description of the overall conductivityfunction (Hopmans et al., 2002). This, however, leaves the

6 SOILS

question open as to how the shape of the conductivityfunction close to full saturation should be described.

Also, the usual predictive models tend to fail at lowmatric potentials (Nimmo, 1999), with deviations up to fiveorders of magnitude (e.g. Kosugi, 1999). This was oftenattributed to the moisture dependence of pore tortuosityand connectivity, and was accounted for by introducinga tortuosity/connectivity term θ l . Contrary to theoreticalconsiderations of, for example, Mualem (1976), the analysisby Hoffmann-Riem et al. (1999) shows that the tortuosityfactor l must be regarded as a (second) purely empiricalmatching factor, with a high variation from soil to soil.This is confirmed by the study of Schaap et al. (1999) whofound an overall averaged optimum value of l = −1 forthe van Genuchten/Mualem model when testing soils ofthe UNSODA database. If interpreted in the original modeltheory of Mualem (1976), this value would be “unphysical”.Tuller and Or (2001) argue that the failure of predictedconductivity functions in the low moisture range is dueto the lack of consideration of flow in thin liquid filmsand in crevices and corners of angular pores. In a seriesof papers (Tuller et al., 1999; Or and Tuller, 1999; Tullerand Or, 2001) they developed a thermodynamically basedconductivity estimation model that improves the predictionsat low saturations significantly.

Estimation of Constitutive Relationships byPore-network ModelsComputational pore-scale network models describe two-phase porous media flow systems by resolving individualinterfaces at the pore scale, and tracking these interfacesthrough the pore network (Celia et al., 1995). Coupledwith volume-averaging techniques, these models can repro-duce relationships between macroscopically measurablevariables like capillary pressure, water content, and rela-tive permeability. Over the last decade, this approach hastaken a tremendous development. This is due to rapidadvances in instrumental techniques for a noninvasivethree-dimensional characterization of the pore spaces andfor flow and transport processes (Blunt and Hilpert, 2001).In connection to this, the use of fast computers allows touse sophisticated image analysis tools and tomography toreconstruct three-dimensional statistically equivalent pore-scale network models (for an overview, see Blunt andHilpert, 2001). Also, simulation of water and air distribu-tion and transport in reconstructed porous networks on themicroscale, for example, by Lattice-Boltzmann techniques(Krafczyk and Rank, 1995), can be used to infer macro-scopic hydraulic properties. On a macroscopic level, Liuand Bodvarsson (2003) modeled effective constitutive rela-tionships for fracture networks and for dual-permeabilitymedia. Currently, the use of these techniques is in a researchstate, and aims more toward understanding various flowphenomena than on practical determination of hydraulicproperties.

Laboratory Methods

Laboratory methods have the advantage of being conductedin a controlled environment. On the experimental side,significant progress has been achieved through the useof improved computer technology that lead to automationof experimental devices with flexible control of boundaryconditions and precise data acquisition at high temporalresolution (Durner et al., 1999a). Dirksen (1999b) statesthat measurements of hydraulic properties should be madein the laboratory, unless there are overriding reasons toperform them in situ, such as the presence of stronglylayered soil profile, large unstable structural elements, andan abundance of stones. Vogel and Roth (2001) put forwardthat direct measurements of the hydraulic functions areonly feasible on the scale of core samples treatable inthe laboratory. Laboratory methods are, however, subjectto the limitation that some disturbance is introduced inmanipulating the sample, even if “undisturbed” soil coresare used. In addition, the measurements may be affectedby hydraulic effects not present in the field (Munoz-Carpena et al., 2002). Santos et al. (1999) pointed out theimportance of in situ methods to obtain reference valuesagainst which laboratory methods should be tested.

Direct laboratory measurement methods can be groupedinto static equilibrium methods to determine water reten-tivity (Section “Hydrostatic equilibrium methods”), steady-state flux methods to determine conductivity (Section“Steady-state laboratory methods”), and transient meth-ods to determine unsaturated conductivity or diffusivity(Section “Transient laboratory methods”). Transient meth-ods are increasingly replacing the conventional equilibra-tion and steady-state methods, because they can be appliedto larger soil samples and speed up the experiments consid-erably. Traditionally, transient methods focus on determin-ing the unsaturated hydraulic diffusivity or conductivity bymeasuring water fluxes at the system boundary. However,simultaneous measurements of water content and pressurein a soil sample during computer-controlled transient exper-iments are probably the best and quickest method to derive,also directly, the water retention function (Schultze, 1998;Zurmuhl, 1998).

Hydrostatic Equilibrium MethodsHydrostatic equilibrium methods can be used to determinethe WRC. There are several standard methods. For ref-erences to the primary literature and for details in theapplication of the methods, the reader is referred to Kutilekand Nielsen (1994) and Dane and Topp (2002). Nimmo(2002) compiled a table with useful guidelines for the selec-tion of the most appropriate method for a given purpose,considering aspects of sample size, measurement range, dif-ficulty, duration, and cost.

• Long column method : A long homogeneous column isput in contact with a water reservoir at its lower end.

DETERMINING SOIL HYDRAULIC PROPERTIES 7

Dependent on the initial state of the column, saturatedor dry, an imbibition process or a drainage process willtake place. After equilibration, the column is sliced andthe water contents are determined. Problems of thismethod lie in the extreme long time demand necessaryfor equilibration, the limited pressure range, and inthe difficulty of obtaining a homogeneous soil column.Advantage of the method is an almost arbitrary fineresolution with respect to θ(h).

• Hanging water column: A sample is placed on a finesand bed or a porous plate. Suction is applied via ahanging water column, with a length smaller than thecorresponding air-entry pressure of the sand, or viaa controlled vacuum, which is applied to the spacebelow the porous plate. After the sample has reachedhydraulic equilibrium, its water content is determinedgravimetrically. Advantages of this classic method areits relatively low cost and technical operating expense,which allows measuring many samples simultaneously.

• Suction table: the method is similar to the hanging watercolumn, but instead of a water column, a technicallycontrolled vacuum can also be applied to the waterphase. The range of the method is limited by theatmospheric pressure.

• Pressure plate extractor : A sample is placed on aporous plate inside a pressure container. Air pressureis applied to the container, which induces displacementof water toward and through the porous plate to thefree atmosphere. After reaching equilibrium, the watercontent is determined gravimetrically. This method canbe applied in combination with the Hanging watercolumn method, where it yields values for the dry rangeof the θ(h).

• Pressure cell (Tempe cell ): A ring sample is mountedon a porous plate and connected to a top, through whichthe gas phase pressure can be regulated. Increasing theair pressure induces displacement of water through theporous plate, which can be measured in a burette thatis connected to the outlet.

• Centrifuge method : An initially saturated sample isplaced in a centrifuge and spinned with a specificvelocity. After the centrifugal and capillary forcesreach equilibrium the saturation can be determined.The method is well suited to determine residual watersaturation. It has also been applied to measure hydraulicconductivity. The pressure range depends on the powerof the centrifuge. Problems are costs and the mechanicaldestruction of the sample under high acceleration.

• Controlled liquid volume: In this method, defined pointsof θ(h) are determined by adding or extracting con-trolled volumes of liquid. Water then redistributeswithin the sample until the pressure is equalized. Themain advantage of this method is that it achieves fasterequilibration. However, during water redistribution part

of the sample will be draining, and the other part will bewetting, and therefore hysteresis may affect the overalldistribution.

The above listed methods are in most cases used in aseries of equilibration steps to desaturate a soil from fullsaturation, thus yielding a drying curve. Common to allhydrostatic equilibrium methods is the considerable timerequirement, in particular, if saturations at low potentialsare to be determined. Since equilibrium time grows withthe square of the length of the sample (Miller, 1980),equilibration times of large samples become prohibitivelylong for high suctions. Nonequilibration is in particulara problem for sands, where higher tensions can only bereached by equilibration via the gas phase (Gee et al.,2002). For the dry range of a retention curve, thereare not many alternatives. In the literature, the freezingmethod is described (Spaans and Baker, 2002; Bittelli et al.,2003), which makes use of the thermodynamic equivalencebetween freezing and drying. Recently, vapor pressuremeasurements of soil with known water contents have beendiscussed (Nimmo and Winfield, 2002).

The usual way to evaluate equilibrium measurementsis to pair the pressure at the center of the sample withthe average water content of the whole sample. Thislinearization results in a retention characteristic that issmoothed around the air-entry point, as compared to thetrue point characteristic, in particular, for coarse porousmedia and for large samples. Liu and Dane (1995) andJalbert and Dane (2001) provide correction procedures forthis problem.

Steady-State Laboratory MethodsSteady-state methods aim at obtaining the hydraulic con-ductivity at a particular saturation, by inversion of Darcy’slaw. The procedure is based on the fundamental assump-tion that the rate of flow is proportional to the pressuregradient and the permeability constant is a property of theporous medium (Klinkenberg, 1941). We will restrict ourdiscussion to methods that use water as a fluid. For practicalrecommendations and details on influences of temperature,ion composition, and other factors affecting fluid properties,see Dane and Topp (2002).

Steady-state in water flow is reached by applying eitherconstant head or constant flux boundary conditions to thetop or the bottom of soil samples. A flux boundary conditioncan be realized by drip irrigation (mostly through needles),by spraying (Dirksen and Matula, 1994), or by pumpingwater via a porous plate onto the top of the sample.None of these procedures is trivial. At the lower boundary,suction can be applied through a porous plate (sinteredglass, metal, ceramic, or nylon). It is generally advisable tocheck the pressure head inside the sample by tensiometricmeasurements (Dirksen, 1991). For methods that aim atthe saturated conductivity, Ks [L T−1], it is important

8 SOILS

that the flow resistance of the experimental device, inparticular the membrane, is kept smaller than the resistanceof the soil. Since Ks is extremely dependent on continuousmacropores along the flow direction, any change of soilstructure (compaction, sealing of water entry surface), andany bypass of water (gap between column casing and soil)must be avoided.

• Constant head permeameter : Water is applied by meansof a mariotte device to the top of a soil sampleat a constant head. Water leaving the sample at thebottom is also kept at a constant head, either atzero pressure by free drainage through a suspensionmesh to the atmosphere, or to a positive pressure viaan overflow vessel. The experiment can equally beperformed with the flow direction of water from thebottom to the top. Ks is calculated by rearranging theDarcy equation. Limitations of the method are related tosmall or inadequate sample size, soil disturbance duringcore collection, and possible short-circuit flow throughmacropores along the core wall. On the other hand themethod is simple, inexpensive, and convenient. Despitepotential limitations, the method remains as one of themost popular means for measuring Ks and is often usedas a benchmark for evaluating other methods (Reynoldset al., 2000).

• Crust method : The crust method (Bouma et al., 1983)determines hydraulic conductivity, K(h), by measuringthe water flux density into an unsaturated soil sample.Unsaturated conditions are obtained by supplying waterthrough a crust made of sand and special cement witha lower hydraulic conductivity than the soil sample. Ina typical setup, a saturated soil sample is placed on along sand column to attain nearly gravitational flow inthe sample. Water is supplied to the crust by ponding,using a Mariotte burette. A tensiometer is placed inthe soil few centimeters below the top of the sample.The flux density is derived from the discharge fromthe burette. If only gravitational flow is assumed andsteady-state is reached (e.g. 24 h no change in pressurehead), the flux density, q [L T−1], equals the unsaturatedhydraulic conductivity. To obtain information about thewhole range of K(h), several crusts would be needed.This makes the crust method very tedious. The crustmethod is also used in the field.

• Drip Infiltrometer Method : The drip infiltrometermethod (Dirksen, 1991) determines the hydraulicconductivity by infiltration. Typically, the soil sampleis placed on a sand box with a hanging water column.Water is applied from a reservoir through hypodermicneedles on top of a sample. Tensiometers are placed inthe soil at different depths. The pressure head gradient(dh/dz) in the sample can be controlled by adjustingthe height of a hanging water column with overflow,attached to the sand box. Measurements start after

steady-state is reached. By measuring the flux density(q) and the pressure heads (h), the unsaturated hydraulicconductivity K(h) is calculated for each compartmentbetween two tensiometers with Darcy’s law. Again itis very laborious to measure the whole range of K(h).Obtaining values for low flux densities is limited by theapplication of a constant flux rate and very long timesto attain steady-state.

• Atomized Water Spray Method : Delivery of water uni-formly to the soil surface can also be accomplished witha controlled atomized spray. Dirksen and Matula (1994)constructed and tested a water spray system that deliv-ers water accurately to the surface of a 20-cm diametersoil column at rates ranging from 10−4 to 10−7 cm s−1.The advantage of this method over more conventionallaboratory methods is that large samples can be testedand it requires no ceramic plates and therefore does nothave a contact resistance problem. However, the sys-tem is relatively cumbersome and does require thermalcontrol for optimal results.

• Steady-state evaporation method : Fujimaki and Inoue(2003) introduced a method that determines hydraulicconductivity from a water content profile under steady-state upward flow. Steady-state was induced by settingboth constant meteorological conditions and a con-stant inflow rate from the bottom, with evaporationdemand being higher than the supply rate. After steady-state is reached, the soil column is sectioned to mea-sure the water content profile. Isothermal water vaporflux is evaluated via inverse optimization. An indepen-dently determined θ(h) is also required. Unlike mostother methods, this method is not limited to the wetrange/tensiometer range (h > −700 cm).

• Disc Infiltrometer method : In the disc infiltrometermethod (Simunek et al., 1999), water is applied at neg-ative pressure using a tension disc (see Section “Fieldmethods”) that is placed on top of the sample. Thesoil profile is instrumented with both Time domainreflectometers (TDR) (at one location) and tensiometers(at several locations). The measured data are analyzedusing Wooding’s (1986) analytical solution. Wooding’sanalysis requires steady-state infiltration rates at differ-ent supply pressure heads. Simunek et al. (1999) com-pared analysis by numerical inversion against results ofWooding’s solution. Unsaturated hydraulic conductivi-ties corresponded well, but Ks was overestimated.

• Heat Pipe Method : Very low unsaturated K(h) mea-surements (10−7 –10−12 cm s−1) have been reported byGlobus and Gee (1995) using a heat pipe method. Themethod uses a partially wetted sample that is sealedand equilibrated with an applied thermal gradient. Inthe heat pipe method, equilibrium is attained when liq-uid water flow from the cool end equals water vaporflow from the warm end, and the water content profile

DETERMINING SOIL HYDRAULIC PROPERTIES 9

has become stable. After a given period, ranging fromdays to several weeks, the soil is removed from the col-umn and sampled for water content. Water diffusivityvalues for the soil are determined from the measuredwater content gradients. K(h) is subsequently computedfrom an independently measured θ (h) for the soil. Themethod requires temperature control and is time con-suming. K(h) is actually a lumped parameter, since itrepresents a combined estimate of the vapor and liquidconductivity (Gee and Ward, 1999).

Transient Laboratory MethodsWith decreasing pressure head, steady-state methods loosetheir attractiveness, because constant fluxes and unit gra-dients are hard to obtain. Transient laboratory techniquesdo not employ equilibrium steps and are therefore muchmore rapid. Traditional transient laboratory methods, suchas outflow or evaporation experiments, however, show rel-atively little sensitivity to the hydraulic conductivity atnear-saturated conditions. Thus it is advisable to determinethe hydraulic conductivity in the wet range with steady-stateexperiments, whereas transient conditions are used for thedrier range (Wendroth and Simunek, 1999).

In the last few decades, several transient methods havebeen proposed for characterizing soil hydraulic properties,including one-step outflow, multistep outflow, evaporation,downward, and upward infiltration methods (UIMs). Eachof these methods uses the change in column weight versustime to infer hydraulic properties. If simultaneous deter-mination of retention and conductivity is sought, additionalmonitoring of matric potential changes at one or more posi-tions in the samples, or independently determined θ(h) arerequired. Otherwise, only diffusivity can be determined.All transient methods assume uniform one-dimensional fluxaccording to Richards’ equation in a homogeneous porousmedium, and apply constant or changing heads or constantor changing fluxes to the top or to the bottom of a soil sam-ple. For unsaturated experiments, where matric potential isnegative, a porous plate or a membrane with appropriatepore sizes is required to apply the pressure. In the fol-lowing, the principles of the various methods are shortlydescribed. For details in the experimental and evaluationprocedures, the reader is referred to Kutilek and Nielsen(1994) and Dane and Topp (2002).

• Falling Head Permeameter : This method is used todetermine Ks for samples with low conductivity. Theupper surface of a soil sample is connected to a water-filled burette, and the lower face to a constant boundarypressure. When water is allowed to flow, the water levelfalls, and the pressure difference between the upperand lower boundary decreases exponentially. Since thepressure difference is large as compared to the length ofthe soil sample and the diameter of the burette is usuallychosen to be considerably smaller than the diameter of

the soil sample, a high hydraulic gradient is appliedand the flux can be monitored with high precision.This speeds up the measurement process for soils withlow hydraulic conductivity, as compared to the constanthead method. Other shortcomings of the constant headpermeameter method, however, cannot be overcome.The conductivity is calculated by

Ks = 1

(t2 − t1)

ABLS

ASln

(h2

h1

)(5)

where AB and AS are the areas of the burette and thesoil, respectively, LS = height of the soil, and h1 andh2 are the head differences between the upper and lowerboundary at times t2 and t1, respectively.

• One-step and Multistep Outflow method : The one-stepmethod was originally introduced by Gardner (1958) todetermine the diffusivity, D(θ ). Saturated soil sampleson top of a ceramic plate are exposed to a high airpressure on top of the sample or to a sudden reductionin water pressure below the ceramic plate. The pres-sure change induces unsaturated flow in the soil sample,with the ceramic plate remaining saturated. The cumu-lative outflow of water is recorded in a burette or bya scale. The historic reasons for favoring the one-stepmethod (Doering, 1965) lie in the possibility to applysemianalytical solutions of the flow equation to identifythe hydraulic diffusivity function, provided the conduc-tivity curve follows an exponential function (Gardner,1958; Gardner, 1962). Since the mid-80s, following thepioneering work of Kool and coworkers (Kool et al.,1985a,b; Kool and Parker, 1987) outflow methods arenow evaluated by inverse modeling to determine thesoil hydraulic functions θ(h) and K(h) simultaneously(Hopmans et al., 2002). Because one-step experimentsoften yielded nonunique inverse solutions, investigatorsrecommended to include additional θ(h) data (van Damet al., 1992; Bohne et al., 1993), or tensiometric mea-surements in the object function (Toorman et al., 1992;Eching and Hopmans, 1993). A major point of critiquewith respect to the one-step method has always beenthat the quick change of the boundary condition doesnot represent natural conditions (van Dam et al., 1992,1994), and the sensitivity of the method can be low if, asa result of a large pressure drop, a very thin drained soillayer next to the porous plate controls the total flow rate(van Dam et al., 1992). For these reasons, the multistepmethod was suggested, where the pressure at the bound-ary is changed in several small steps (van Dam et al.,1990). Eching et al. (1994), van Dam et al. (1994),Crescimanno and Iovino (1995), and Zurmuhl (1996)demonstrated for the van Genuchten/Mualem model thatthe multistep method is superior to the one-step methodbecause the hydraulic parameters are less correlated.

10 SOILS

The outflow methods are constrained to the wet mois-ture range by the air-entry pressure of the porous plate.

• Continuous Inflow/Outflow method : Even with severalsmall pressure changes as applied in the multistepoutflow method, the pressure changes at the soil’sboundary still occur shock-wise, which – at least forthe drainage process – never occurs under naturalconditions. As an alternative, Durner et al. (1999b)suggested a continuous smooth change of the boundarypressure, which showed to yield good results. A soilsample is placed on a membrane plate in contact witha pressure-controlled reservoir. The reservoir headspaceis controlled by air pressure manipulation (Butters andDuchateau, 2002) to initiate water flow in the soilsample. Theoretically, both wetting and draining θ(h)

and K(h), up to the air-entry value of the membraneplate, including saturation can be measured. Butters andDuchateau (2002) used a combination of direct Darciananalysis and numerical inversion of Richards’ equationfor estimation of the hydraulic properties. The directanalysis provides Ks and θs that can be used to anchorthese parameters in the inverse analysis. As a limitation,the direct K estimate applies to fairly short samplesand is susceptible to tensiometer errors, especiallyof systematic nature. Durner (1994) recommended todirectly and independently measure K(h) in the rangeclose to saturation where the inverse estimation fromoutflow experiments is insensitive.

• Wind’s Evaporation Method : Similar to the outflowmethods, Wind’s evaporation method (Wind, 1968)aims at determining simultaneously θ(h) and K(h). Ten-siometers are installed at regular depth intervals ina saturated soil sample. The sample is placed on abalance and its surface is exposed to free or forcedevaporation. Weight and pressure heads are recordedperiodically. After completing the experiment, the vol-umetric water content of the sample is determined,which allows to recalculate the total water contentsduring the experiment. The water contents in the com-partments around the tensiometers at different timesare estimated from the measured pressure heads andthe total water contents by fitting a parametric modelof water retention characteristic to the observations.The subsequent evaluation is identical to the instan-taneous profile experiment (see the Section on “FieldMethods”) by calculating the flux density from thedecrease of the water contents of the compartments,and the pressure head gradient from the pressure headsof two adjacent compartments. Finally, the unsatu-rated hydraulic conductivity can be calculated withDarcy’s law. The program package METRONIA (Hal-bertsma and Veerman, 1994; http://dino.wiz.uni-kassel.de/model db/mdb/metronia.html) is avail-able for this analysis. Bertuzzi et al. (1999) found that

small uncertainties in tensiometer data greatly influ-ence the hydraulic conductivity determined under wetconditions, but θ(h) estimates are relatively robust.Also, thermal effects on hydraulic conductivity esti-mates were far from negligible. Wendroth and Simunek(1999) reported that Wind’s method (1968) method doesnot yield valid estimates of θ(h) and K(h) for layeredsoil samples. Finally the evaporation method fails in thenear-saturation range where the hydraulic conductivityis highest, leading to very small hydraulic gradients thatcannot be determined with sufficient accuracy (Wen-droth and Simunek, 1999).

• Hot-air Method : The hot-air method (Arya et al., 1975)determines the diffusivity function D(θ ). With thismethod, hot air is blown over the surface of aninitially uniformly wet soil column. Before the watercontent at the bottom of the sample starts decreasing,evaporation is stopped and the sample is cut into smalllayers. The water content of each layer is determinedgravimetrically. The diffusivity D(θ) = K(θ)/C(θ),defined by the ratio of hydraulic conductivity, K , andthe specific water capacity, C, at a water content, θ , canbe calculated from

D(θx) = 1

2t

dx

dθ

∣∣∣∣x

∫ θi

θx

x dθ (6)

where t = time [T], θi = initial volumetric water con-tent [−], θx = volumetric water content [−] at distancex [L] from the evaporating surface. The method isknown to be greatly affected by thermal effects.

• Other Evaporation Methods: Gabele and Hoch (1999)proposed to adapt the evaporation rate to the K-rangeof interest by either dividing the experiment into two orthree sections, each starting with a different evaporationrate after a zero-flux period of several hours or contin-uous variation of the evaporation rate in response tomeasured state variables. Simunek et al. (1998) simul-taneously estimated the van Genuchten parameters forθ(h) and K(h) from an evaporation experiment withparameter optimization techniques. Some uncertaintyexists in the soil hydraulic parameters caused by highcorrelation between θr and n. Pressure heads measuredclose to the soil surface were found to be more valu-able for the parameter estimation technique than thosemeasured at lower locations. Tensiometer readings atone position are already sufficient to guarantee preciseestimation of the soil hydraulic characteristics withinthe range of measurements (Simunek et al., 1998).Extrapolation beyond this range involved a high levelof uncertainty. Romano and Santini (1999) extendedthe analysis to compare various expressions for soilhydraulic properties. As for Wind’s method, accuracy ofhydraulic conductivity estimates is limited mainly due

DETERMINING SOIL HYDRAULIC PROPERTIES 11

to (i) near-zero hydraulic gradients close to saturationand (ii) extremely steep h-gradients at low conductivi-ties.

• Combined Outflow/Evaporation Method : To reduce theduration of the evaporation experiment and to obtainthe retention data in the low suction range, an outflowexperiment can be conducted before the initiation ofevaporation. After attaining near-equilibrium at nega-tive pressure, the bottom boundary is sealed, the soilsurface uncovered, and the evaporation rate at a con-trolled constant temperature measured. Fujimaki andInoue (2003) determined θ(h) by curve-fitting of theequilibrium outflow and psychrometric data obtainedfrom soil samples after evaporation, while the K(θ )was estimated inversely using cumulative evaporationamounts and the final water content profile.

• Sorptivity Method : This and the following methodscombine laboratory experiments and parameter estima-tion for determining soil hydraulic properties in thewetting direction, rather than in the drying direction,as obtained through outflow methods. The sorptivitymethod (Dirksen, 1974) determines the soil water dif-fusivity function D(θ ) by means of a series of one-dimensional absorption experiments in soil of constantinitial water content θ0. The sorptivity S [L T−1/2] isdefined as proportionality constant between the cumu-lative amount of freely supplied water, I [L], infiltratinginto an initially unsaturated horizontal soil column, andthe square root of time, S = I/

√t . Infiltration is con-

trolled by mechanically supplying water to the absorp-tion interface proportional to t1/2. After supplying waterfor a certain time, the final water content of the top layerθ1 is determined gravimetrically. The diffusivity can becalculated from

D(θ1) = πS2

4(θ1 − θ0)2

[(θ1 − θ0)

(1 + γ ) loge× d

dθ1(log S2) − 1 − γ

1 + γ

](7)

where D = diffusivity [L2 T−1], θ = volumetric watercontent, S = sorptivity [L T1/2], and γ = weightingparameter [−]. For details, see Klute and Dirksen (1986)and Clothier and Scotter (2002).

• Water Absorption into a Horizontal Column: A hori-zontally placed soil column is connected to a waterreservoir, causing absorption of water. The advance ofthe wetting front with time and the amount of waterinfiltrated are recorded. From these data, Shao and Hor-ton (1998) estimated the van Genuchten parameters n

and α by an approximate analytical solution. Additionalinformation about Ks is needed. Wang et al. (2002) usedanalytical solutions of horizontal infiltration to estimateBrooks and Corey parameters. Input data needed are

infiltration rate, cumulative infiltration, and distance ofthe wetting front with infiltration time.

• Upward Infiltration Method : In the upward infiltrationmethod, UIM (Hudson et al., 1996), a constant flux ofwater is imposed at the bottom of the soil sample,and pressure heads are measured inside the sampleusing tensiometers. To maximize information for theinverse analysis, Young et al. (2002) suggested toinitiate infiltration by a certain tension at the bottomof the sample, using a Mariotte system, rather than byimposing a boundary flux. For tension infiltration, thesoil controls the total amount of water being taken up,thus providing additional information and control for thenumerical inversion. The method is most useful in thewet range of the retention and conductivity functions.Simunek et al. (2000) suggested a method based onmodification of the UIM to capture nonequilibriumflow parameters. The observed nonequilibrium behaviorcould be described with the dual-porosity and dual-permeability models, but a unique set of soil hydraulicparameters could not be identified.

• Downward Infiltration Method : Water is supplied atthe top of a soil sample at a prescribed head (usu-ally ponding) or at a prescribed rate. Van Genuchtenparameters can be estimated by numerical inversion ofRichards’ equation. Measurements needed for the inver-sion method include: soil water tension versus time atone distance from the soil surface, the initial water con-tent, and a final steady-state water content behind thewetting front. The objective function used for parameteroptimization is constructed from two parts, one from thetransient tension versus time curve, and another fromthe steady-state water content data (Zou et al., 2001).

Field Methods

Laboratory experiments have the advantage of being com-paratively quick and precise, but they often lead to soil-physical properties that are not representative for the field.Direct in situ measurement of hydraulic and retentionproperties still provides perhaps the most reliable, andoften, the only means for determining hydraulic properties,despite their high cost and extreme time demands (Tsengand Jury, 1993). Two distinct types of field proceduresare in common use: internal drainage (ID) flux meth-ods (Section “Internal drainage method”) and infiltrationmethods. Infiltration methods can be further distinguishedin steady water application flux methods (Section “Steadyflow infiltration methods”), ponded infiltration methods(Section “Pressure ring infiltration”), tension infiltrometry(Section “Tension disc infiltration”) and infiltration fromwells or bore holes (Section “Infiltration from wells andbore holes”).

Field methods have the advantage of dealing with soil innatural conditions. However, small-scale heterogeneity in

12 SOILS

soil conditions may introduce large variation in measuredvalues (Munoz-Carpena et al., 2002). Since most field mea-surements are confined to produce a single measurement ata single field location, adequate evaluation of field hydraulicand chemical transport properties requires a large numberof measurements.

Errors in the evaluation of unsaturated hydraulic con-ductivity under field conditions may arise from a numberof sources. In the instantaneous profile experiment, mea-surements of pressure head and water content are uncer-tain owing to spatial variability, which leads to significantuncertainty by error propagation (Fluhler et al., 1976). Ten-sion disc and ring infiltrometer also have limitations; mostof them being associated with the simplifying assumptionsof the analysis used to infer soil hydraulic properties fromwater and solute flow measurements. Infiltration rates dur-ing the measurement time can be variable, both increasingand decreasing (Logsdon, 1997). Factors affecting temporalvariability of hydraulic properties during infiltration exper-iments are hydrophobicity and swelling (Roth et al., 1999;Angulo-Jaramillo et al., 2000). These limitations lead ingeneral to uncertainty, whether or not there will be majoradvances in in situ determination of K(h). In an extensivereview on published field measurement data, Jury (1985)found extremely high variation of hydraulic conductivityparameters, which he attributed partly as apparent variabil-ity, caused by fitting oversimplified functions to the data.Tseng and Jury (1993) point out that since the true physi-cal state of a soil can never be known in any field study,absolute comparisons of properties estimated from measure-ments, and thus actually occurring in the field, can never bemade. Hence, method comparisons must always be relative,and absolute statements upon the accuracy of any methodare not possible.

Internal Drainage Method

The internal drainage method, ID, or instantaneous profilemethod is regarded as a reference method to measure insitu unsaturated hydraulic properties for both homogeneousand layered soils (Hillel et al., 1972). The method wasfirst suggested by Richards et al. (1956) on the basis ofsimultaneous monitoring of water retention and flux inlaboratory soil columns. Later, the method was adapted forpractical field use (Watson, 1966). Simplified variants havebeen developed which require fewer in situ measurementsbut depend on flow approximations (Nielsen et al., 1973;Ahuja et al., 1988). Their use is mainly limited by highdemands on equipment and time.

In the ID, large rings (about 2 m in diameter) are insertedinto soil with a certain height left above ground. Withineach ring, tensiometers and TDR are installed via an accesstube. Water is ponded on the soil surface until the soil iswetted beyond the maximum depth for which the deter-minations are desired. The groundwater table should be

sufficiently below this depth to obtain maximum possibleunsaturated drainage. To minimize evaporation, temperaturefluctuation, and protect the surface from rainfall during sub-sequent drainage, the soil surface inside the rings is covered.Both θ and h are monitored for weeks. Measurements aretaken with decreasing frequency. Evaluation is performedusing instantaneous profile data analysis, which is basedon the Darcian analysis of transient soil water content andhydraulic head profiles (Watson, 1966). Zhang et al. (2003)presented an improved analysis of the data from drainageexperiments using inverse modeling, which uses nonlin-ear regression methods to estimate hydraulic parameters.All van Genuchten hydraulic parameters could be estimateduniquely when both water content and pressure head datawere used.

Errors in K values obtained during the early stagesof drainage are primarily due to errors in determiningthe hydraulic gradient, while at later times, errors inwater content measurement are more serious. Using typicalmeasurement errors, the calculated uncertainty of K in themoist range is in the order of 40%, and in the dry rangeup to more than 100% (Fluhler et al., 1976). The failureof even one tensiometer, which is not uncommon in thefield, will significantly affect the calculation of hydraulicproperties. Because θ and h determination is needed overa long period of time, the ID is time- and equipment-intensive, and thus costly, especially if several sites mustbe monitored to estimate spatial variability.

Steady Flow Infiltration MethodsInfiltration rates effectively integrate properties of theporous media underneath the infiltrometer, including theinfluence of local-scale heterogeneity, different soil struc-ture, and textural irregularities, preferential pathways, lay-ering, and anisotropy. Hence, infiltration rates provide agood way for estimating the effective near-saturated soilhydraulic properties (Mertens et al., 2002). Steady flux isachieved either by uniform application of water by sprin-kler or trickler, or by creating a low permeability crust atthe soil surface (Hillel and Gardner, 1970). Measurementstaken under steady-state flow conditions are easier and lessprone to errors (porous cup equilibration of tensiometers)than those taken under transient conditions. It is also pos-sible to repeat pressure head, water content, and flow ratemeasurements at steady-state, whereas for transient con-ditions, the entire experiment must be repeated. However,considerable effort and time are required for the steady fluxmethod to be of practical use in the field. The crust method,while accurate, cannot be used when the soil is wet and themethod can be very costly to run, since up to 100 days maybe required to complete the measurement of K(h) over therequired potential range. In all steady flow methods onlywetting is considered.

Recent innovations in steady flow infiltration methodsinclude inverse estimation of soil hydraulic parameters in

DETERMINING SOIL HYDRAULIC PROPERTIES 13

combination with multipurpose probes that couple TDR andtensiometry used under constant flux infiltration (Gee andWard, 1999). Si and Kachanoski (2000) used multipurposeTDR probes coupled with a series of constant-rate infiltra-tion experiments to estimate the effective one-dimensionalfield-average hydraulic properties K(θ ) and θ(h). The TDRprobes are installed vertically to measure the rate of changeof local soil water storage (q) along the probe duringconstant-rate water application. The values of q are equalto local soil water flux, and assuming unit gradient, are setequal to K at the steady-state θ and h measured at longtimes. The measured values of K , θ and h from differ-ent water application rates are combined to obtain averagehydraulic functions.

• Line Source Method : Zhang et al. (2000a,b) estimatedhydraulic properties by means of multipurpose TDRprobes and existing quasi-analytical, steady-state solu-tions for infiltration from a surface line source. Theyinstalled 50 nests of multipurpose TDR probes witha between-nest spacing of 0.15 m, indicating the highcosts connected with this method. Inverse proceduresare used to estimate the inverse macroscopic capillarylength scale, α, and Ks, from h, θ , and conservativeionic tracer travel time (T ). Measurements of only h

or only T will not give unique estimates of α and Ks.Combining measurements of θ with h and/or T givesunique estimates of α and Ks.

• Point Source Method : Al-Jabri et al. (2002) used amuch simpler approach: The hydraulic properties weredetermined by applying three discharge rates higherthan the infiltration rate. This produces circular satu-rated areas at the soil surface beneath each emitter thatreach constant size depending on the irrigation rate. Theradius, r , of the areas is measured. The method requiredonly two days to collect data. Once steady-state occurs,Wooding’s (1986) solution can be applied. Ks is yieldedgraphically as the intercept of a plot of discharge rateversus 1/r . The mean Ks found were larger than withtension discs. Error sources are different radii for thesame infiltration rate, and noncircular areas. The methoddoes not offer a high level of control, but is very cheap.A single supply tube can allow for application of thepoint source method to multiple locations. Evaluationof the setup and procedure with natural field condi-tions, such as tillage practices is required for furtherestablishment.

Pressure Ring InfiltrationRing infiltrometers are probably the most widely useddevice for measuring field infiltration rates (Wu et al.,1997). The technique is useful in the estimation of the insitu field-saturated hydraulic conductivity, Kfs, and matrixflux potential �m. Water is supplied to the soil surfaceat a positive pressure head h0 either by a Mariotte bottle

allowing a wide range of h0, or by a small capillary tubealso acting as a measuring burette. Water can be infiltratedat a constant or at a continuous falling head. A double ringinfiltrometer can be used to minimize lateral flow duringthe experiment. Infiltration from the outer ring before andduring the measurement should guarantee one-dimensionaldownward flow from the inner ring. The analysis isperformed only with infiltration from the inner ring, andis essentially the same as for single ring infiltrometers.

Various techniques based on either transient or steady-state water flow approaches have been used to infer soilhydraulic properties from ponded ring infiltration tests(Angulo-Jaramillo et al., 2000). Basically the flow froma ring infiltrometer set at a positive pressure head h0 iscontrolled by Kfs which accounts for the gravity effect andby �m, the matrix flux potential for saturated conditions,which is defined as

�m =∫ 0

hu

K(u) du (8)

Constant head conditions have traditionally been used,because constant head devices are easy to maintain exper-imentally and because the analysis is relatively simple(Mertens et al., 2002). It is possible to show (Elrick andReynolds, 1992) that the steady-state flow rate out of aring infiltrometer is given by

q0∞ = Kfs

(1 + H

πrdG

)+ �m

πrdG, (9)

where G is a shape parameter, and rd is the radius of thering. Applying successively to the same ring two positivehydraulic heads H1 and H2 allows solving simultaneouslythe resulting two equations for Kfs and �m. In highlyheterogeneous and low permeable soils, the method cancause a large percentage of invalid (i.e. negative) andunrealistic Kfs and �m. Here the one-dimensional steady-state saturated flow analysis can be replaced by a transientanalysis using nonlinear least-squares inversion procedures.

Another possibility to analyze infiltration experiments isto use falling head methods, where a ring is inserted aknown distance into the soil, and attached to a mariottereservoir. Infiltration from the ring is allowed to come tosteady-state under a constant ponded head, after whichthe head is allowed to fall and the head is measuredas a function of time (Parkin et al., 1999). A numericalinversion procedure is used to calculate the soil hydraulicproperties. Measurements of early-time infiltration underboth constant and falling head can better characterize thehydraulic properties of low permeability media.

Advances have been made in using ring infiltrometersand TDR to measure hydraulic properties in unsaturatedsoils (Parkin et al., 1995). Estimates for hydraulic conduc-tivity can be achieved for heads greater than –60 cm, which

14 SOILS

is the range with most effect on ponded infiltration. How-ever, generally ponded infiltration measurements are notsensitive for estimating unsaturated soil hydraulic conduc-tivity (Bagarello et al., 2000).

Tension Disc Infiltration

A tension disc infiltrometer (TI) is a constant head infil-trometer that can operate at either a positive or a negativehead and thus it can be used for determination of both satu-rated and unsaturated hydraulic properties. TI have becomevery popular devices for the in situ estimation of soil sur-face hydraulic properties (Angulo-Jaramillo et al., 2000).Because of their portability, disc and ring infiltrometers areuseful instruments to investigate statistical distributions ofhydraulic conductivities. While ponded infiltration is usedto determine the saturated hydraulic conductivity, tensioninfiltrometry also provides an opportunity to estimate unsat-urated hydraulic properties. TI associated with conservativetracers was also used for inferring parameters describingthe water-borne transport of chemicals and other param-eters such as mobile/immobile water content fraction orexchange coefficient (Clothier et al., 1992; Jaynes et al.,1995). A number of challenges still remain unresolved forboth theory and practice for tension disc infiltrometers.They include questions on how to consider and charac-terize saturated-unsaturated preferential flow or preferentialtransport processes, and the problem of contact resistancebetween the tension disc membrane and the soil.

During tension disc infiltration, a reservoir tower pro-vides the water supply, and a bubble tower with a moveableair-entry tube imposes the pressure head ho of the water atthe cloth base. For measurements under tension, intimatehydraulic contact between the soil surface and the sourceof water is essential. This is generally achieved by pouringat the surface a layer of sand that should be made as thinas possible. The contact sand can introduce flow impedanceeffects at the high infiltration rates associated with pondedconditions. The same is true for the porous membrane ofthe infiltrometer (Mohanty et al., 1998). For every imposedvalue ho, the cumulative infiltration, I(t), is recorded eitherby noting the water level drop in the reservoir tower orby using pressure transducers (e.g. Ankeny et al., 1988).Additionally, initial and final water content are determined.Water flow from a tension infiltrometer disk to the underly-ing soil follows a three-dimensional flow process. Varioustechniques have been developed to infer hydraulic prop-erties from measurements of either transient flow rates,or steady ones, that emanate from a disc (Wang et al.,1998). The methods of analysis of cumulative infiltrationare based either on quasi-analytical solutions or on inverseparameter estimation techniques, depending on whether thesoil profile is homogeneous or not (Angulo-Jaramillo et al.,2000). Vandervaere et al. (2000) found for 7 largely differ-ent soils that the lateral capillary flow (S2) dominates the

gravity flow (K) during a disk infiltrometer experiment.Thus hydraulic conductivity must be considered as a vari-able playing a minor role, and hence difficult to determineaccurately. Although performing infiltration experiments atthe same location for several tensions can affect infiltra-tion rates, TI causes relatively little disturbance of thesoil macrostructure. Still the tension disc method yieldedlower Ks values under high-permeability conditions rela-tive to other methods, because the ring may be too smallto adequately sample cracking clay loam soil (Reynoldset al., 2000).

• Steady-State Analytical Solutions Wooding’s equation(1986) equation is at the heart of most of these analyses.It approximates the steady infiltration rate, q0∞ from adisc as

q0∞ = K0 + 4�0

πrd(10)

where �0 is the matrix flux potential for unsaturatedconditions defined by

�0 =∫ θ0

θn

D(u) du =∫ h0

hn

K(u) du, θ0 ≥ θn, hn ≤ h0

(11)

In these equations, K0 is the hydraulic conductivity atthe imposed pressure head h0, and D(u) is the capillarydiffusivity [L2T−1]. The subscript 0 refers to the conditionimposed at the supply surface of the disc, and the subscriptn denotes the antecedent condition prevailing in the soilbefore the infiltration takes place. Early-time infiltrationdata can be used to estimate the sorptivity (White andSully, 1987) and, consequently, the matrix flux potential.Equation (10) can be solved for K0 and �0 by using eithermultiple radii (MR)(at the same value h0) or multiple head(for a given disc radius) procedures. Drawback of theMR method lies in the fact that the two (or more) diskexperiments must be performed at different locations, whichintroduces complications from the short-distance spatialvariability of soil properties (Wang et al., 1998).

Large variations or discrepancies are reported in the liter-ature when comparing Wooding’s method results with othermethods. One possible source of error is its limitations forrelatively small disk sizes. Several studies have shown thatWooding’s approach will overestimate the soil hydraulicconductivity if steady-state infiltration is not reached. Dis-crepancies between tension infiltrometer and other methodsin practice, however, are caused probably more by vari-ability within each method such as soil heterogeneity orsimplification of the hydraulic conductivity function to anexponential expression, than by inherent limitations of thesteady-state solutions (Wang et al., 1998).• Transient State: Quasi-analytical Solutions Restrictions

in the use of Wooding’s equation, together with the factthat much useful information is lost by ignoring the

DETERMINING SOIL HYDRAULIC PROPERTIES 15

transient stage and large time savings can be achieved(Logsdon, 1997) have strengthened the need for atransient three-directional infiltration equation for discinfiltrometers. The most recent expressions (Warrick,1992; Haverkamp et al., 1994; Zhang, 1998) have incommon the following two-term form of the cumulativeinfiltration equation:

I (t) = C1

√t + C2t (12)

but they differ by the expressions of the coefficients C1

and C2. Haverkamp et al. (1994), for example, posed thefollowing physically based expressions valid for times notapproaching steady-state:

C1 = S0

C2 = Kn + 1

3(2 − β)(K0 − Kn) + γ

rd(θ0 − θn)S0

2 (13)

where β is a parameter depending on the capillary diffusiv-ity function. It lies in the interval [0, 1], and γ is a constantapproximately equal to 0.75.

Vandervaere et al. (2000) proposed several new methodsfor the analysis of tension disk infiltrometer tests and thedetermination of sorptivity and hydraulic conductivity. Thesingle test method uses one disk radius and one value ofpressure head. The multiradii method uses two or more diskradii and one value of pressure head. The multiple sorptivitymethods use one or multiple disk radii and two or morevalues of pressure head. Method appropriateness was shownto be highly dependent on the ratio of K and S. A goodexperimental strategy consists of choosing the method ofanalysis on the basis of the dominant flow: vertical capillaryflow, vertical gravity flow, or lateral capillary flow.

• Transient State: Inverse Estimation An alternative todirect estimates of soil hydraulic properties is the use ofinverse methods when in situ conditions differ stronglyfrom assumptions required for the use of semianalyti-cal solutions of the flow equation, that is, nonuniformwater content distribution, and multilayered soils. Froman analysis of numerically generated data, Simunek andvan Genuchten (1996) concluded that the cumulativeinfiltration curve by itself does not contain enough infor-mation to provide a unique inverse solution. Schwartzand Evett (2002) reported that inverse optimizations,which included in the objective function both, waterretention and cumulative infiltration, led to excellent fitsof this data for high initial volumetric water content.Simunek and van Genuchten (1997) put forward thatthe best practical scenario is to estimate the hydraulicparameters from the cumulative infiltration curve mea-sured at several consecutive tensions applied to the soilsurface, in conjunction with the knowledge of the initialand final water content.

Infiltration from Wells and Bore Holes

Tension disc and ring infiltrometers are constrained tothe near-surface and are easily impacted by microtopogra-phy. These limitations can be partly overcome by infiltra-tion from bore holes with or without cone penetrometers.Combinations of TDR and permeameters with cone pen-etrometer technology show promise for minimally intrusive,cost-effective measurements of K(h) and θ(h) to greaterdepths (Gee and Ward, 1999).

Guelph Permeameter(GP) The Guelph Permeame-ter (GP) is a constant head well permeameter consisting ofa mariotte bottle that maintains a constant water level insidea hole augered into unsaturated soil. Flow from this perme-ameter is assumed to reach steady-state after a transientstate during which the soil saturated bulb and the wettingzone increase in size by migrating quasi-spherically fromthe infiltration surface. At steady-state, the saturated bulbremains essentially constant in size, while the wetting frontcontinues to increase (Reynolds et al., 1985). The analysisrequires measurements from two different water levels inthe same well. Munoz-Carpena et al. (2002) provided meth-ods for inverse optimization for parameter identification.They found that GP gives lower Ks estimates comparedto other methods. A multiplying factor of 2 to 3 has beenproposed to account for air entrapment in the field soil.

Cone Permeameter The cone permeameter is fittedinto a hole, where a soil core of smaller diameter wasremoved with a sampler. Water is injected into the soilthrough a screen, and the progress of the wetting front ismeasured with two tensiometer rings positioned above thescreen. Tests are conducted with two sequentially appliedpressure heads of different magnitudes. After the supplyvalve is closed, tensiometers monitor the redistribution ofwater in the soil profile. It is possible to evaluate wettingonly, or wetting and drying simultaneously, via analysisof different parts of the experiment, that is, during waterapplication and during redistribution. Cumulative inflowand pressure head readings are analyzed with inverseoptimization. Final moisture content information improvesestimates of unknown hydraulic parameters (Gribb, 1996).Soil densification caused by pushing the cone permeameterto the testing depth resulted in lower values of θs and Ks

(Kodesova et al., 1999).

Use of Tensiometer Response to Measure SoilHydraulic Conductivity

The use of a ceramic cup tensiometer to measure soilhydraulic conductivity was proposed as early as 1937 byRichards et al. (1937). Recently, Hayashi et al. (1997)developed a method to determine the hydraulic conductivityof unsaturated soils from the response of a tensiometer to anartificially induced perturbation of pressure. The response

16 SOILS

time of tensiometers is controlled by soil hydraulic con-ductivity when the flow resistance of the porous cup issufficiently small. Advantages are the fast procedure (1 h)and the use of readily available equipment. Tests must berepeated over time to determine the in situ relationshipbetween matric potential and hydraulic conductivity. Theestimated conductivity is sensitive to the disturbance of thesoil in close proximity to the porous cup. It is also sen-sitive to changes in the matric potential during a responsetest. Timlin and Pachepsky (1998) also developed a methodto determine unsaturated hydraulic conductivity using ten-siometers. They measured water flux into a tensiometerafter a suction is applied to its inside. The reduced pressurein the tensiometer causes water to flow into the tensiome-ter from the soil leading to a decrease of the volume ofair, and subsequently pressure increases. The unsaturatedconductivity parameters are determined by using a two-dimensional finite element soil model coupled with inverseoptimization. Shortcomings of the method are clogging ofthe tensiometer pores by fine soil material, which leads toa change of conductivity of the ceramic cup over time, andpossible poor contact between tensiometer and soil.

Integrated Determination by Inverse Modeling

By the very nature of the unsaturated flow processes,the classic direct measurements of hydraulic propertiesremain extremely demanding with respect to experimen-tal procedures, requiring, for example, excessive equilib-rium times, small sample sizes, strictly stationary flow orpressure conditions, and perfect contact between porousmembranes and measurement sensors. At the same time,they generally yield only limited information about thehydraulic properties, for example, one point on a mois-ture retention curve. In order to come to a faster andmore integrated way to characterize hydraulic propertiesof soils, inverse simulation of transient flow processeson the laboratory and on the field scale will play thekey role in future developments of measuring techniques.The highly dynamic and strongly nonlinear water flowin the unsaturated zone is clearly too difficult to repre-sent in analytical or semiempirical approaches (Kutilekand Nielsen, 1994; Feddes, 1995). With the progress incomputer simulation, an intensive further development oftransient methods that aim on the simultaneous deter-mination of the hydraulic properties over a wide mois-ture range by inverse simulation is currently underway(Vrugt and Dane, 2005, Chapter 77, Inverse Modelingof Soil Hydraulic Properties, Volume 2). Specifically,the inclusion of the measurement instrument itself and itsinteraction with the surrounding soil environment in theinverse analysis bears a tremendous potential to improvethe precision of hydraulic properties estimates. Further-more, developments in combined instrumentation, wherecontrolled or uncontrolled water fluxes are measured

together with water content and water potential simulta-neously by the same instrument, will become more impor-tant.

Still, in the attempt to estimate soil hydraulic propertiesit appears that we are faced with an analogue to the Heisen-berg uncertainty principle: The more precise the hydraulicproperties are obtained for a point in space or an isolatedsoil sample, the less relevant this precision might be forcharacterizing the flux at the field scale. In the range wherethe process model is valid, we can now achieve an almostperfect history matching by inverse modeling of labora-tory experiments, which allows characterizing the hydraulicproperties of soil samples to an exceptional high degree ofaccuracy (Bitterlich et al., 2004). This kind of measure-ment evaluation further allows to expand the limits of ourconceptual understanding of the flow process (e.g. two-phase flow effects, hysteresis model inadequacies, dynamiceffects). However, flow and transport processes in vadosezone hydrology may be controlled by structures, which havean extent similar to the scale of the system of interest(Vogel and Roth, 2003). This means that without identi-fying these structures, our efforts on local precision arefutile. As hydraulic properties cannot be directly measuredon larger scales, we depend on proxy variables. If structureis identified at the scale of interest, it might be sufficient todetermine the hydraulic properties of the structural elementsin an approximate manner. Stochastic fusion of a variety ofmoisture-related instrumental information by noninvasivesensoring methods (electrical resistivity tomography, pas-sive microwave, ground-penetrating radar, and others) andits inverse evaluation (Yeh and Simunek, 2001) appears tobe a promising direction.

While keeping in mind that the general interest clearlyfocuses on effective large-scale properties, it must bestressed that only a thorough understanding of the under-lying point-scale processes allows to judge on appropriateways to upscale local properties. For processes of dissipa-tive nature, effective macroscale properties obtained just byaveraging will be a valid description (e.g. Schmalz et al.,2003). However, other processes must be known (and mea-sured) in spatial and/or temporal detail, because neglectingthem will lead to systematic misconceptions. For example,small changes in water content in the pressure range nearsaturation, as frequently encountered in natural soil sam-ples, indicate a secondary pore structure, which controlspreferential flow of water on the scale of interest. Neglect-ing this by fitting oversimplified models for the constitutiverelationships will lead to a systematic misconception andsystematic errors in modeling water and solute transport(Mahmood and Hubbard, 2003).

It appears that in the development of measurementtechniques for hydraulic properties characterization thereis currently a threefold transition:

DETERMINING SOIL HYDRAULIC PROPERTIES 17

• There is a transition from “classic” methods, whichdepend on equilibrium, steady-state flow, or strictboundary conditions, toward generalized nonequilib-rium methods. This represents a change in paradigmfrom measurements that are based on high experimentaland low calculus requirements towards measurementswith great freedom in experimental boundary condi-tions, but high requirements with respect to sensorresponse (in particular, with respect to temporal res-olution and signal accuracy) and with respect to asophisticated and robust model inversion.

• There is also a transition from point measurement tolarge-scale measurements, based on a combination ofnew hydrogeophysical techniques that are applicable onlarge areas such as satellite-based ground-penetratingradar. The focus must be to identify the largest struc-tures in the materials on the respective scale of interestbecause these determine the system behavior. Togetherwith flow observations on large areas (drained land) andregional estimates of evapotranspiration, these observa-tions can be evaluated by inverse modeling in orderto search for the existence of effective processes andproperties on the scale of interest (Feddes et al., 1993).

• Finally, there is an increasing recognition that due tothe overwhelming complexity of natural flow processes,the idea to measure “true” and “universal” hydraulicproperties on a large scale must be replaced by object-dependent measurement methods and properties, wherethe target variable of interest (e.g. irrigation demand,mean flow to the groundwater, structure of flow fieldfor solute transport) decides upon the most appropriatemanner to evaluate the data (Abbaspour et al., 2001).

CONCLUDING REMARKS

Our knowledge of basic vadose zone flow and transportprocesses has advanced considerably over the last severaldecades. Unfortunately, the ability to determine processparameters has not kept pace with the ability to put theprocesses into numeric models. Although various field andlaboratory methods for determining unsaturated hydraulicproperties have been proposed, there remains a glaring lackof standardized procedures. Despite enormous investmentsof time and money made by soil scientists, hydrologists,and others, improvements over several decades in directmethods to measure hydraulic properties of field soils havebeen rather marginally achieved. Specialized equipment tomeasure the unsaturated hydraulic properties is generallyexpensive because of a relatively small market. Therefore,a disproportionate amount of time and money is stillbeing used to conduct routine experimental work. Thedifficulty to solve Richards’ equation for transient fluxconditions hindered for a long time the rigorous evaluationof experiments and the development of experiments that are

designed to maximize the information content with respectto the properties of interest (Vrugt and Bouten, 2001).Furthermore, not much of the knowledge gained duringthe last decade on measurement methods is being used inmanagement practices. Thus, narrowing the gap betweenthe state of the art and the state of the practice is one ofthe fundamental issues required in order to solve problemssuch as contamination of the vadose zone and groundwater.

On the positive side, experimental procedures are nowgreatly benefiting from the use of flexible inverse estimationprocedures, improved numerical models, more powerfulcomputers, and increased automation in data collectionefforts. For many years, measuring and monitoring methodshave lagged behind numerical analyses of water flow andsolute transport through the vadose zone. However, recentadvances in electronic components, renewed interest indevelopment of monitoring methods, and the infusion ofgeophysical methods into vadose zone hydrology havebegun to address this imbalance. Future developmentsin instrumental field techniques and in improved inversemodeling techniques must direct toward a point whereavailable tools will be so well adapted to the needs ofsoil physicists and vadose zone hydrologists, that theyare also easy to use in practice. Essential in that is thatinverse modeling techniques must not only be robust andthus lead to accurate results, but also must obligatorilyindicate the adequacy of the underlying model assumptionsand the uncertainty of the resulting estimates. Becauseof the increasing speed of computers, there is a rapiddevelopment in this area (e.g. Vrugt et al., 2003), and theuse of Monte Carlo based stochastic methods to estimatethe uncertainties, appears very promising.

Probably the most challenging task with respect todetermining hydraulic properties of soils is the coupling ofsoil mechanics, soil chemistry, and possibly soil biology,with soil hydraulics. Since there is an enormous sensitivityof parameters, such as the saturated hydraulic conductivity,on these factors, this is not merely an academic question.Despite the long-lasting knowledge upon the importanceof the various feedbacks (e.g. Nielsen et al., 1986), notmuch progress has been achieved in this field during thelast decades. Substantial progress will depend on the abilityof scientists to bridge the traditional disciplinary boundaries(US Department of Energy, 2001). To date, we still sufferfrom the ‘inability to integrate simultaneously the mostrelevant physical, chemical, and biological processes in aunified theoretical framework’ (Nielsen et al., 1986).

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