Estimating the saturated hydraulic conductivity in a...

Soil & Tillage Research 77 (2004) 189–202

Estimating the saturated hydraulic conductivity in a spatiallyvariable soil with different permeameters: a stochastic

Kozeny–Carman relation

Carlos M. Regaladoa,∗, Rafael Muñoz-Carpenaba Dep. Suelos y Riegos, Instituto Canario Investigaciones Agrarias (ICIA), Apdo. 60 La Laguna, 38200 Tenerife, Spain

b TREC-IFAS, Agricultural and Biological Engineering Department, University of Florida,18905 SW 280 St., Homestead, FL 33031-3314, USA

Received 6 July 2003; received in revised form 21 November 2003; accepted 15 December 2003

Abstract

The spatial variability of the saturated hydraulic conductivity (Ks) of a greenhouse banana plantation volcanic soil wasinvestigated with three different permeameters: (a) the Philip-Dunne field permeameter, an easy to implement and low costdevice; (b) the Guelph field permeameter; (c) the constant head laboratory permeameter.Ks was measured on a 14×5 array of2.5 m×5 m rectangles at 0.15 m depth using the above three methods. Ks differences obtained with the different permeametersare explained in terms of flow dimensionality and elementary volume explored by the three methods. A sinusoidal spatialvariation ofKs was coincident with the underlying alignment of banana plants on the field. This was explained in terms of soildisturbances, such as soil compaction, originated by management practices and tillage. Soil salinity showed some coincidencein space with the hydraulic conductivity, because of the irrigation system distribution, but a causal relationship between thetwo is however difficult to support. To discard the possibility of an artefact, the original 70 point mesh was doubled byintercalation of a second 14× 5 grid, such that the laboratoryKs was finally determined on a 140 points 2.5 m× 2.5 m squaregrid. Far from diluting such anisotropy this was further strengthened after inclusion of the new 70 points. The porosity (φ)determined on the same laboratory cores shows a similar sigmoid trend, thus pointing towards a plausible explanation for suchvariability. A power-law relationship was found between saturated hydraulic conductivity and porosity,Ksαφ

n (r2 = 0.38),as stated by the Kozeny–Carman relation. A statistical reformulation of the Kozeny–Carman relation is proposed that bothimproved its predictability potential and allows comparisons between different representative volumes, orKs data sets withdifferent origin. Although the two-field methods: Guelph and Philip-Dunne, also follow a similar alignment trend, this is notso evident, suggesting that additional factors affectKs measured in the field. Finally, geostatistical techniques such as crosscorrelograms estimation are used to further investigate this spatial dependence.© 2004 Elsevier B.V. All rights reserved.

Keywords:Saturated hydraulic conductivity; Philip-Dunne permeameter; Canary Islands; Modified Kozeny–Carman; Banana plant; Stochasticmodel

∗ Corresponding author. Tel.:+34-922-476343;fax: +34-922-476303.E-mail addresses:[email protected] (C.M. Regalado),[email protected] (R. Muñoz-Carpena).

1. Introduction

The spatial dependence of the saturated hydraulicconductivity (Ks) has been often investigated (Cressie,1993; Bosch and West, 1998; Moustafa, 2000).

0167-1987/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.still.2003.12.008

190 C.M. Regalado, R. Muñoz-Carpena / Soil & Tillage Research 77 (2004) 189–202

Geostatistical tools have been used with this pur-pose (Cressie, 1993), and have helped researchers inthe study of the large variability thatKs often ex-hibits in soils (Warrick and Nielsen, 1980; Jury et al.,1991). Additionally, and since the hydraulic conduc-tivity is necessary for predictive hydrological models(Vachaud et al., 1988; Braud et al., 1995; Moustafa,2000), its spatial distribution is often required. How-ever the direct determination ofKs requires mucheffort and is time consuming, because many measure-ments are required to represent the intrinsic variation.Thus indirect methods, based on other more easilymeasurable soil properties (such as porosity or tex-ture), are sometimes preferred (Ahuja et al., 1989).With this purpose in mind either empirically or phys-ically based relationships have been developed topredictKs. Among these there is the Kozeny–Carmanequation (Carman, 1937), a power-law that relatesKsto porosity (φ):

Ks = Aφn (1)

whereA is a proportionality constant andn is a fittingparameter. In an attempt to improve the predictionsof the above model, some modifications ofEq. (1)have been proposed which replaceφ with the effec-tive porosity,φe, calculated as the saturated water con-tent minus the water content at 33 kPa matric potential(Ahuja et al., 1984, 1989). Other investigators haveused parameters of the Brooks–Corey or fractal mod-els to replace the exponentn or the proportionalityconstant,A in Eq. (1) by measured water retentionparameters (Rawls et al., 1993, 1998; Timlin et al.,1999). Additionally, relation may also include the spe-cific surface area,Se (m2 m−3), such that (Petersenet al., 1996):

Ks ∝ φnS−2e (2)

However, the above indirect methods do not alwayslead to reliable results (Kutilek and Nielsen, 1994),thus researchers have resorted to direct measurementsof Ks. Several laboratory (Klute and Dirksen, 1986)and field direct methods (Amoozegar and Warrick,1986; Ankeny, 1992; Elrick and Reynolds, 1992) havebeen proposed to measure this soil hydraulic property.Laboratory methods are based on a simple applicationof Darcy’s law in one dimension. In some cases, thesehave the disadvantage of introducing artefacts becauseof soil disturbance (e.g. compaction) and also that the

soil is inhibited from other dominant hydraulic effectspresent in the field (capillary effects, other dimen-sional components, etc.). An example of this methodis the constant head laboratory permeameter (LP)(Klute and Dirksen, 1986), selected for this work. Bycontrast, field methods deal with the soil in naturalconditions and therefore small scale heterogeneities(structure, texture, flora, fauna, soil composition, etc.)may contribute to the above one-dimensional flow. Itis thus expected that these field effects will affect thevalue and spatial distribution ofKs, but to what extendthis is the case is not well understood. The Guelph(GP) (Reynolds et al., 1983) and Philip-Dunne (PD)(Philip, 1993; Gómez et al., 2001; Muñoz-Carpenaet al., 2002) permeameters will be selected in thiswork as field methods.

Comparison of the estimations of the hydraulicconductivity with different methods on a spatial basishas been poorly investigated in the past (Reynoldsand Zebchuk, 1996), and particularly in relation to theeffect of agricultural practices on theKs distribution.Comparisons of laboratory and fieldKs methods interms of spatial variability are also rare. In additionstudies on the spatial variability of the hydraulic prop-erties of highly micro-aggregated soils, as those ofvolcanic origin, are scarce (Romano, 1993; Ciollaroand Romano, 1995; Zhuang et al., 2000). The inten-tion of this paper is thus two-fold. Firstly the spatialdistribution ofKs in a drip-irrigated volcanic soil ba-nana plantation in the Canary Islands, is comparedusing the above three permeameters. In particular weshall concentrate on the performance of the PD inpredicting theKs spatial variability (since this is aneasy to implement and low cost but poorly studiedpermeameter). Secondly, the predictive capability un-der field conditions of the Kozeny–Carman relation,which usually makes use of laboratory determina-tions is investigated. Modified versions of (1) are alsoinvestigated, in order to improve its predictabilitypotential and allow for comparison between the dif-ferent permeameters. By comparing such a relationwith the laboratory and field permeameterKs, con-clusions are drawn about what soil properties maybe determining the spatial structure of the saturatedhydraulic conductivity in the field. Conclusions arealso drawn about the consequences of soil tillage andmanagement practices on the spatial distribution ofthe soil hydraulic properties of a banana plantation.

C.M. Regalado, R. Muñoz-Carpena / Soil & Tillage Research 77 (2004) 189–202 191

2. Materials and methods

2.1. Soil physical–chemical properties

Vertical undisturbed soil cores were collected at0.15 m soil depth (top of the core) in stainless steelrings using a centred hammer driven sampler. The coredimensions were 0.056 m internal diameter and 0.04 mhigh. Water contents in the laboratory for porosity es-timation were determined gravimetrically. Field watercontents for the PD measurements (see below) wereobtained with a Trase Time Domain Reflectometry(TDR) equipment (Soilmoisture Equipment Corp.) us-ing a 0.06 m long three guide probe. A TDR soil spe-cific calibration was carried out since this soil divergessignificantly from Topp’s equation (Regalado et al.,2003).

Water retention curves (WRC) were determined bymeans of Tempe cells on 10 steps of pressure up to90 kPa suction (ψ) and Richards pressure plates forthese additional pressure steps: 100, 500 and 1500 kPa.For the description of the retention characteristic, themodel ofBrooks and Corey (1964)was used:

Θ = θ − θr

θs − θr=

(ψ

ψa

)−λforψ > ψa

1 forψ ≤ ψa

(3)

whereλ is the pore-size distribution index—a param-eter related to the width of the pore-size distribution;θ, θs andθr are the volumetric, saturated and residualwater contents, respectively.Θ is known as the effec-tive saturation;ψa (L) is the matric potential at the airentry point. Model (3) was fit to the water retentiondata with the help of the SHYPFIT program (Durner,1995).

For the determination of the specific surface,Se,the soil was first sieved to 2 mm, dried in vacuum toconstant weight with di-phosphorus pentaoxide andfinally saturated by adsorption in a sulphuric acidatmosphere (Newman, 1983). We chose this methodinstead of others more widely used, such as theethyleneglycol method, because it is well known thatthe latter overestimates the specific surface in thesesoils (Fernandez-Caldas et al., 1982; Gonzales-Batistaet al., 1982).

Na-Amberlite IR-120 (500�m mesh) cation ex-change resins were used as dispersing agent for soil

texture determination (Bartoli et al., 1991) in air-driedsamples. Particle-size distribution was determined bythe Bouyoucos densimeter method (Gee and Bauder,1986).

Clay mineralogy was determined by X-ray diffrac-tion in randomly oriented specimens and oriented sam-ples with glycerol and heat treatments (Philips PW1720) (Whittig and Allardice, 1986).

2.2. Field experimental work

A 850 m2 (33.3 m × 25.5 m) greenhouse drip-irrigated banana plantation was selected for sam-pling and measuring. This was selected because itis representative of the agricultural practices car-ried out in the Canary Islands on exportation crops(mainly bananas and tomatoes). The plot is terracedwith an average soil effective depth of 0.85 m overbasaltic fractured rock. The soil has volcanic ori-gin, clay loam texture (36± 6% clay, 21± 2%silt, 43 ± 7% sand) and exhibits andic proper-ties (bulk density< 0.9 g cm−3, Al0 + 1/2 Fe0 >

2%, phosphate retention> 85%). The soil maybe classified as an Andisol (Armas-Espinel et al.,2003). The andic character translates into a stablemicro-aggregation and unusual values of soil bulkdensity (0.87±0.08 g cm−3), porosity (66.42±2.42%)and specific surface area (200± 17 m2 g−1). A rect-angular regular grid (2.5 m × 5 m) was laid out onthe plot surface yielding 70 grid intersection points(Fig. 1). A regular grid was chosen since this repre-sents a more efficient sampling scheme (Webster andOliver, 1990). TheKs measurement and sampling pro-tocol is described elsewhere (Muñoz-Carpena et al.,2002).

2.3. Laboratory and field permeameters

Laboratory measurements ofKs were made on arecirculating constant head permeameter on undis-turbed soil cores saturated with calcium sulphate fol-lowing the procedure described byKlute and Dirksen(1986).

The Guelph permeameter is a constant head wellpermeameter (Reynolds et al., 1983, 1985) consist-ing on a mariotte bottle that maintains a constantwater level inside a hole augered in the soil. Thesimultaneous approach for solving the Richard’s


Fig. 1. Sampling points and plant distribution of the experimental plot.

based steady-state equation (Philip, 1985; Elrick andReynolds, 1992)

2πH2i Ks + Ciπa

2Ks + 2πHiφm = CiQi (4)

requires at least two different water heads in the samewell. In Eq. (4) φm (m2 s−1) is the matric flux po-tential,Qi (m3 s−1) the steady-state flow rate into thesoil, when the steady depth of water in the well isHi (m), a (m) the well radius, andCi is a dimen-sionless proportionality constant dependent onHi/a.The augered wells used in this study were 0.06 m indiameter, with 0.05 and 0.1 m constant water levels(Hi), andC1 = 0.8, C2 = 1.2 (double-head method).The double-head method may yield negativeKs val-ues due to non-attainment of the steady-state, exper-imental error, soil profile discontinuity (Elrick et al.,1989; Elrick and Reynolds, 1992) and ill-conditioningof the simultaneous equations inKs andα∗ = Ks//φm(Philip, 1985). To get around negativeKs values, asingle-head procedure has been proposed, whereby asite estimatedα∗ is introduced to avoid the need ofa second ponded head (Elrick et al., 1989). The pa-rameterα∗ may be either obtained from soil texturalcharacteristics, from the meanα∗ values of all positiveKs values or by an optimisation procedure (Mertens

et al., 2002). Alternatively,Vieira et al. (1988), haveproposed to recompute the anomalousKs values (i.e.φm < 0, α∗ < 1 m−1, α∗ > 100 m−1) arising fromthe double-head method, making use of the conduc-tivity values obtained from the Laplace solution,KL(which neglects the capillarity forces in the soil) andthe “correct”Ks values,K∗

s, via the empirical relationK∗

s = βKγL. The fitting parametersβ and γ are ob-

tained from the log–log plot ofK∗s versusKL.

The Philip-Dunne permeameter consists of a tubeof internal radiusri = 0.018 m, vertically inserted toa certain depth into a soil borehole with zero gap, andthen filled with water up to a heighth0 = 0.30 m attime t = 0. During infiltration, the times when thepipe is half full (tmed ath = h0/2) and empty (tmax ath = 0) are recorded, along with soil moisture at thebeginning (θ0) and at the end of the test (θ1). To obtainthe value ofKs with the PD, thePhilip (1993)analysismakes use of a simplification whereby the disk-shapedwater supply surface is replaced by a spherical waterfront of equal area, i.e. of radiusr0 = ri/2. If R = R(t)

is the soil wetted bulb radius from the water supply attime t, then the following differential equation holds

π2R(R− r0)

8r0Ks

dR

dt= ψf + h0 + π2/8

�θ− R3 − r30

3r20(5)


subjected to the initial conditionR(0) = r0, whereψf (=α∗−1) is the suction at the wetting front and�θ=θ1−θ0. Eq. (5)may be integrated to give the tem-poral variations of the wetted radius and water depth(Philip, 1993). Making use of the two-measured times,tmed andtmax and the increment in soil moisture con-tent,�θ, the values ofKs andψf can be computed(De Haro et al., 1998; Appendix A inMuñoz-Carpenaet al., 2002).

2.4. Statistics

Standard statistics was carried out withSYSTAT 10(SPSS Inc., 2000)and spatial statistics was performedwith VARIOWIN 2.21 (Pannatier, 1996).

3. Results and discussion

3.1. Statistical results

The saturated hydraulic conductivity was approxi-mately described by a log-normal probability distri-bution for the three permeameters (Muñoz-Carpenaet al., 2002). Probability plots showed surface area,porosity and theα∗ parameter to be also closelylog-normally distributed (results not shown). Meanvalues ofKs for the different methods are summarisedin Table 1. The LP-Ks (27.90 × 10−4 cm s−1) is

Table 1MeanKs values(cm s−1)±standard deviation (S.D.) for the labo-ratory, Philip-Dunne and Guelph permeameters, with the two-head,Laplace, Vieira and 0.05, 0.10 m one-head methods

Permeameter Method MeanKs ±S.D. (×104)

Guelph (GP) Two-head 12.07± 8.74Laplace 10.24± 5.04Vieira 6.72± 2.61One-head (0.10 m) 7.77± 4.24One-head (0.05 m) 5.24± 2.86One-head (0.10 m,α∗ = 0.12)

5.94 ± 3.36

One-head (0.10 m,α∗ = 0.36)

8.42 ± 4.77

Laboratory (LP) Klute and Dirksen(1986)

27.90± 2.82

Philip-Dunne (PD) De Haro et al. (1998) 87.30± 4.95

placed in between the PD and GP. Differences be-tween field and laboratory methods are well knownin the literature (see also discussion below). ThePD gives the highest values (8.73 × 10−3 cm s−1)while the Guelph permeameter shows a decreas-ing trend from the two-head (12.07 × 10−4 cm s−1),Laplace (10.24 × 10−4 cm s−1), 0.10 m one-head(7.77 × 10−4 cm s−1), Vieira (6.72 × 10−4 cm s−1)and 0.05 m one-head (5.24× 10−4 cm s−1) methods.For the one-head method we used the meanα∗ =0.22 cm−1 value obtained from the Vieira analysis.This value forα∗ is placed betweenα∗ = 0.12 cm−1,proposed for structured clay loamy soils and un-structured sands, andα∗ = 0.36 cm−1 for highlystructured soils and coarse sands, and it is thus con-sistent with the expectedα∗ deducible from texturalsoil characteristics (Elrick et al., 1989). The errorsinvolved by choosing either of these two extremeα∗values are though small (cf. row 4 with 6 and 7 inTable 1).

3.2. Spatial distribution of Ks

Fig. 2 depicts the contour plots of the spatial dis-tribution of Ks obtained with the three permeameters:LP, GP and PD. It can be seen that the LP-Ks followsa spatial trend that resembles the alignment of ba-nana plants (compare withFig. 1). Field Ks exhibitsa subtler aligned disposition, which is also smoothedout because of edge effects that render some highKsvalues. Many factors may be responsible for these dif-ferences. Flow dimensionality and the representativeelementary volume are considered here as the twomost relevant.

3.3. Flow dimensionality

Flow dimensionality may be a source of differ-ence among permeameters. Horizontal saturated hy-draulic conductivity,Ksh, determinations on a subsetof 10 cores showed significant differences betweenKsh and Ks (meanKsh = 0.02275 cm s−1 and meanKs = 0.00093 cm s−1). Laboratory measurements aremainly prevented from other than one-dimensionalflow components. Thus the faster horizontal wa-ter flow component may counteract high verticalKs values in those permeameters that explore thethree space dimensions, i.e. field permeameters, and


Fig. 2. Contour plots of the spatial distribution of porosity andKs as determined by the LP, GP and PD.x–y-axes labels denote distance(m). The grey scale representsKs (cm s−1) or porosity (cm3 cm−3) values.

therefore smooth out spatialKs differences.Basak(1972)found that the hydraulic conductivity of kaoli-nite was greater in the horizontal than in the radialdirection. X-ray diffraction shows that the dominantmineralogical phases of the studied soil are allo-phane and halloysite and a minor phase of illite.Halloysite consists of elementary layers of kaolin-ite and water. Hence the anisotropic orientation ofkaolinite may explain the large horizontal conductiv-ity (Basak, 1972), and thus the differences betweenpermeameters. Although the Philip-Dunne perme-ameter assumes a three-dimensional spherical flow,this is a simplification made for mathematical con-venience (see above). The “true” flow is initiallyone-dimensional and approaches three dimensionalityonly whenh0 − h = 4�θ0r0 (Philip, 1993). Such ini-tial disk-shape one-dimensionality may be reinforcedbecause of the orientation of clay particles, and thusyield large PD-Ks values.

3.4. Representative elementary volume

The different volume explored by the three perme-ameters: 2× 10−3 m3 for the PD and 4× 10−3 m3 forthe GP versus 1×10−4 m3 for the LP (Muñoz-Carpenaet al., 2002), may be also an important factor that ex-plainsKs differences, since a larger volume averagesover more heterogeneities, and this results in a lowervariability in the field methods. This agrees with thevalues obtained for the coefficient of variability, whichis highest for the LP (101%), followed by the PD(56%) and GP (56 and 38% for the single-head andVieira Ks, respectively).

3.5. Other factors: permeameter assumptions, fieldheterogeneity, initial water content

Even taking these considerations into account com-parison between different methods is difficult because


of underlying assumptions, different response of thepermeameter to soil conditions, etc. (Bouma, 1983).Additionally, field specific heterogeneities (flora,fauna, etc.) may also maskKs differences withina close neighbourhood. Although soil initial watercontent,θi, was not monitored prior to the GP mea-surements, no correlation was observed betweenθiand PD-Ks, contrary toReynolds and Zebchuk (1996)who found that antecedent water content was slightlycorrelated with GP-Ks. It is the increment in watercontent before and after the test has been performed,and not the antecedent water content, what is relatedto the PD-Ks (seeEq. (5)). Assuming that both PD-Ksand GP-Ks are somehow related, the same would beexpected for the Guelph permeameter.

Some low suction values at the wetting front werecoincident with large porosities, but with no clear spa-tial structure (results not shown). This may be due tothe large uncertainty implicit in the estimation ofα∗(Mertens et al., 2002).

3.6. Banana plants versus Ks

Several hypotheses may be explored in order to ex-plain the coincidence of banana plants and LP-Ks.First, the banana root system (exploring the top 0.30 mof the soil) may affect the surrounding soil physicalproperties. In fact the annual selection of shoots fromthe mother banana plant yields a spatial “rotation” ofplants. This may explain that the matching of plantsand LP-Ks is not perfect.

Secondly, localised drip fertigation may modify thehydraulic conductivity of the soil in the neighbour-hood of plants. For exampleDorel et al. (2000), foundthat surface desiccation of an Andosol planted withbananas, led to a significant soil shrinkage that af-fected its hydraulic properties. The accumulation ofsalts around the wetting bulb may also exert chemi-cal effects upon the soil constituents, which result inalteration of its hydraulic properties (Bresler et al.,1984 and references therein). However, the magni-tude of this effect depends not only upon the saltsource but also upon the nature of the soil materials.Armas-Espinel et al. (2003)found that lowKs in vol-canic soils was associated with high(Na+Mg)/Ca ra-tios and low electrical conductivity (EC) values, whichthey attributed to an increase in swelling pressure. Ad-ditionally, excess sodium in low salinity conditions

will decrease hydraulic conductivity through disper-sion of fine clay materials.Fig. 3 shows the surfaceplot of LP-Ks, EC and exchangeable sodium percent-age (ESP) of the soil saturation extract. It can beobserved an almost exact matching between EC andESP and certain coincidence of LP-Ks and the salin-ity status. A cross correlogram analysis (seeSection3.9) shows that EC–ESP correlation is high 0.773 (co-varianceσ = 7.96 × 10−2). According toEmerson(1977), soil swelling pressure raises with increasingESP and decreasing EC. Therefore a swelling mech-anism seems unlikely to explain the spatial distri-bution of Ks, since high values of ESP would becounterbalanced by high salinity conditions (Wagenetand Bresler, 1983) (Fig. 3). Salinisation and sodifi-cation, induced by irrigation with low quality watersand intensive fertilisation, is frequent in cultivatedsoils from the Canary Islands—mean CE in this soilis 4.70 dS m−1. Also, physical properties of clayeysoils can be strongly affected by amorphous materi-als and oxy-hydroxides of iron and aluminium. Suchandic materials induce strong aggregation and im-part favourable structural properties such as reducedswelling (El-Swaify, 1975). It is suggested that thespatial coincidence of soil salinity with the hydraulicconductivity, is an artefact of the irrigation system dis-tribution. This is also in agreement withBresler et al.(1984)who found that soil salinity only accounted for10–15% of the spatial variability ofKs in two selectedagricultural fields.

Finally field management practices and tillage mayintroduce soil disturbances, such as soil compaction,and this by turn may affectKs. Dorel et al. (2000)showed that soil hydraulic conductivity was drasti-cally reduced in the compacted layers of a mechanisedbanana plantation, and that soil tillage increased themeanKs. Also Moustafa (2000)found that the spatialdependence ofKs was correlated with the agriculturalpractices of field soils in Egypt.

3.7. Ks versus porosity

From the above discussion it follows that both het-erogeneous desiccation and compaction may be re-sponsible for the spatial distribution ofKs, probablybecause these affect soil structure.Dorel et al. (2000)showed that the hydraulic effects of both mechanisa-tion and desiccation on an Andosol banana plantation


Fig. 3. Surface plots of the laboratoryKs, electrical conductivity (EC) and exchangeable sodium percentage (ESP) of the soil saturationextract.


were due to changes in soil porosity. The hypothesisof soil compaction would be also consistent with thepreferential horizontal orientation of clays in this soil(see above), since compacted clays will be more ori-ented than non-compacted clays (Al-Tabaa and Wood,1987). Basak (1972)found that the vertical hydraulicconductivity of kaolinite was more sensitive to the voidratio (volume of voids/volume of solid) than the radialhydraulic conductivity. Thus LP-Ks will be more sen-sitive to differences in soil compaction than the fieldmethods.

The Kozeny–Carman relation (1) was first tested asa plausible explanatory model for the distribution ofKs, since alsoFig. 2 already points in this direction.Porosity values, obtained on the same cores that LP-Kswere determined, show a power-law relationship ofthe form:Ks = 5× 10−33φ16.27 (r2 = 0.38) as statedin (1). There exists the possibility that such a corre-lation between LP-Ks andφ may be biased becausesoil cores were placed inside the lab-permeameter ingroups of 10 consecutive samples. In order to dis-card such an artefact, a second 70 grid point meshwas intercalated in between the first one, such thatthe laboratoryKs and porosity were finally determinedon a 2.5 m× 2.5 m square grid. Additionally, in sucha square grid the maximum distance between neigh-bour sampling points is maximised. Thus unrepresen-tation and redundancy of some areas is minimised(Webster and Oliver, 1990). The order of introductionof the new soil cores in the LP was randomised to

Fig. 4. Contour plots of the spatial distribution of measured vs. estimated LP-Ks as predicted by relationKs = 5 × 10−33φ16.268. Whitecrosses correspond to sampling points. The grey scale representsKs values (cm s−1). x–y-axes labels denote distance (m).

further discard a possible bias in theKs determination.Far from diluting such anisotropy, this was furtherstrengthened, thus suggesting a plausible origin for thespatial distribution of the laboratory conductivity data(Fig. 4).

Comparison of measured and predictedKs figuresshows that in general predictedKs differences havebeen smoothed out. High LP-Ks values on the left edgehave been almost erased and some of the LP-Ks “hotspots” in the plants middle lines have also disappeared.All this indicates that not only porosity but also someother factors may affect the value ofKs.

In an attempt to look for such factors responsi-ble for theKs spatial dependence, we tried a modi-fied Kozeny–Carman relation proposed byAhuja et al.(1984), whereφ is replaced by the effective porosity,φe is calculated as the saturated water content minusthe water content at 33 kPa matric potential. Addition-ally, the relation

Ks ∝ φ3−λe (6)

where the exponentn in (1) has been replaced by theλ parameter of the Brooks–Corey model (3), was alsoinvestigated. A linear relation in the log–log space wasfound betweenKs versusφe (r2 = 0.36), thus con-firming the model ofAhuja et al. (1984). However formodel (6) we did not find a simple law of proportion-ality Ks versusφ3−λ

e , but an exponential dependence,although with large data dispersion (r2 = 0.25). Thisresult suggests the possibility of a relation of the form


(Rawls et al., 1993; Timlin et al., 1999)

Ks = B(λ,ψa)φn (7)

By plotting B, calculated asKs/φn for fix n = 2.5,againstλ or ψa, we identified a possible functionaldependence of this parameter on the air entry po-tential index. Such dependence is highly non-linear,Bαexp(ψa), although very scattered,r2 = 0.16(Regalado and Muñoz-Carpena, 2001). Furthermore,considering the coefficientB either a function ofψaalone or a combination ofλ andψa in (7), did notsignificantly improved the predictions ofKs versusφe.

3.8. A stochastic Kozeny–Carman relation

In this and previous studies (Messing and Jarvis,1990; Timlin et al., 1999; Zhuang et al., 2000) the fit-ting results obtained with the Kozeny–Carman equa-tions (1) and (2) are usually poor. In order to improveits predictability potential, the modified versions (6)and (7) have been proposed, although still the scat-tering is remarkable (Ahuja et al., 1984, 1989). TheKozeny–Carman relation assumes a deterministicpoint-to-point relationship betweenKs and some soilphysical property, such as porosity or surface area.However this hypothesis may not be valid if for ex-ample physical properties are determined on samplesclose to, but from a different location whereKs hasbeen measured, or if the volume that such properties(e.g. surface area) refer to differs significantly fromthe representativeKs volume, and thus averagingSe over the wholeKs volume may not be realistic.This may also explain the lack of accuracy of theabove expressions. Hence a statistical reformulationof the Kozeny–Carman equation would be desirable,whereby pairs of observation frequencies replacepoint-to-point correlations. The following stochasticform of (2) is thus proposed

P(Ks) ∝ A · ℵ(φ, µ1, σ1)pℵ(Se, µ2, σ2)

q (8)

whereP(Ks) is the cumulative frequency ofKs; ℵ(·)the normal cumulative distribution function (CDF)of porosity and surface area, respectively, with shapeparametersµi, σi; A, p, q are the fitting parameters.Normal CDFs were first fitted to the cumulative fre-quencies ofφ andSe. Obtained parametersµi andσiare 0.662, 0.026 (r2 = 0.996) and 172.50, 15.24 (r2 =

Fig. 5. Agreement between experimental laboratory constant headKs data and the proposed stochastic Kozeny–Carman equation (8).

0.998), respectively. These were then substituted into(8) and a least square fitting procedure was used toestimate the parametersA = 1.065,p = 0.434 andq = 0.552 from the cumulative frequencies of LP-Ks(r2 = 0.999) (Fig. 5).

The same procedure followed above for the lab-oratory Ks data may be pursued with the fielddeterminations. As already discussed, a statistical rep-resentation of the Kozeny–Carman equation (1), doesnot preclude a point-to-point relationship between thefitted variables, and thus the porosity data obtained inthe laboratory cores may be used to predict the fre-quency of Guelph and Philip-Dunne measurements.The following statistical form of (1) was investigated

P(Ks) = A · ℵ(φ, µ, σ)p (9)

whereP(Ks) is the cumulative frequency ofKs andAis a fitting proportionality constant. Good fit was ob-tained with the PD data (µ = 0.662,σ = 0.026,A =0.994, p = 0.992, r2 (observed versus predicted) =0.987), but a poorer regression (cf.Fig. 6a and b)was achieved with the GP measurements (µ =0.643, σ = 0.009, A = 0.966, p = 0.956,r2 (observed versus predicted) = 0.966), thus indicat-ing that either the Guelph method is more sensitive toerrors in the porosity estimates or it is more affectedby other soil properties not considered in (9) (Fig. 6).The values of the constantA and the powerp in (9)are very close to unity, thus field frequencies may


Fig. 6. Agreement between experimental data and the proposed stochastic Kozeny–Carman equation (9) for the field Guelph, GP-Ks (a)and Philip-Dunne, PD-Ks (b) permeameter data sets.

be estimated from porosity values without additionalfitting. Furthermore the shape parameters of the PDdistribution are the same than the ones obtained forthe porosity CDF (see above), indicating that bothfollow a similar trend of occurrence even though apoint-to-point relationship may not be established.

3.9. Geostatistical analysis

Geostatistics is the name proposed for a methodof spatial analysis that makes predictions from asample data, whose relative spatial locations areknown. In geostatistics it is required that the expec-tation of a random measurement made at locationx, is constant. This hypothesis is known as the sta-tionarity assumption, and it is often overlooked byresearchers who proceed directly to applying geosta-tistical tools. By comparing the median versus thesquared inter-quartile range (a measure of the dataspreading independent of symmetry) for different datatransformations, one may find a suitable symmetris-ing and variance stabilising transformation (Cressieand Horton, 1987). The log-transformation was foundto satisfy both criteria, i.e. (1) it made the data sym-metric, and (2) it straightened out the data such thatvariation is no longer a function of location (Regaladoand Muñoz-Carpena, 2001).

In order to quantify spatial correlations betweenvariables, we assessed the correlation between ad-jacent log-transformed porosity and LP-Ks observa-tions. The plot of the estimated correlation coefficient

Fig. 7. Directional experimental cross correlograms of log-porosityvs. log-LP-Ks. (a) Horizontal (west-east) direction; (b) vertical(south-north) direction. Numbers on empty circles indicate numberof pair comparisons used to compute the correlation coefficient.


of log-porosity versus log-LP-Ks as a function of theseparation distance, the so called experimental crosscorrelogram, is shown inFig. 7. Directional correl-ograms in both the horizontal (west-east) direction(Fig. 7a) and vertical (south-north) direction (Fig. 7b)are plotted. It may be observed that although hori-zontal correlation decreases up to 22.5 m, beyond thisan increasing correlation tendency may be observedwith the separation distance (an effect previously re-ferred to as the lag effect). The same occurs in thevertical direction for separation distances greater than15 m. However in general correlation is greater atshorter distances, while large-range correlations aresupported by a smaller number of pair comparisons(cf. numbers shown in graph).

4. Summary and conclusions

The saturated hydraulic conductivity is often re-quired for hydrological studies and it is either labora-tory or field measured, or it is deduced from other moreeasily measurable physical soil properties. However,not very often its spatial structure is investigated bycomparing different estimation methods. Significantdifferences observed betweenKs measurements maybe partly explained in terms of flow dimensionalityand representative elementary volumes, and may beworsened because preferential flow in the horizontalcomponent, originated by orientation of clay particlesin this soil. The results shown in this paper indicate thatalthough soil (effective) porosity may be an underlyingprocess determiningKs distribution, field effects maysmooth out this dependence such that this is no longerdetectable. We may thus conclude that the spatial vari-ability of Ks is not an easily distinguishable result ofsoil porosity or water retention characteristics. This isalso affected by other components of the soil (e.g. claycontent, degree of aggregation), especially under fieldconditions, or by the experimental design (e.g. mea-surement technique). All these factors are difficult todetect if comparisons between different permeametersare not performed orKs measurements are restrictedto laboratory determinations. This may also limit thefield applicability of indirectKs estimation methodsof the kind of the Kozeny–Carman model, which usu-ally makes use of laboratory determinations, thus ne-glecting other field factors more relevant to the soil in

natural conditions. A modified Kozeny–Carman equa-tion defined in statistical terms may overcome theselimitations, allowing comparisons between differentrepresentative volumes orKs data sets with differentorigin. This is also a rather convenient reformulation,amenable for stochastic modelling or Monte-Carlosimulations of the spatial variability of hydraulicproperties, whereby locally defined parameter valuesare replaced by probability distribution functions ofparameters (Braud et al., 1995; Vachaud et al., 1988),and thus this deserves further investigation.

Processes promoting soil degradation as surfacedesiccation and soil compaction, induced by tillageand localised irrigation, may be responsible for theanisotropy ofKs. Soil salinity showed some coinci-dence in space with the hydraulic conductivity, be-cause of the irrigation system distribution, but a causalrelationship between the two is discarded, since highvalues of exchangeable sodium are counterbalancedby high salinity conditions and andic materials thatimpart favourable structural properties, such as re-duced swelling. This had not been detected if detailedinformation about soil mineralogy and chemical prop-erties had not been available, and we had thus arrivedto erroneous conclusions about the origin of the spa-tial distribution of Ks. Such considerations of bothspatial dependence and measuring technique shouldvery much be taken into account in future studiesintending to make use of a single (mean) effectivevalue of the saturated hydraulic conductivity.

Acknowledgements

This work has been supported by the FloridaAgricultural Experiment Station Journal Series No.R-09021, a Project Grant and Postdoctoral Fellow-ship from the Spanish INIA-National R & D Program(Project SC99-024-C2-1) and the European UnionCOST Action 622. The authors would like to thankDr. J. Jawitz from the Soil and Water Department,University of Florida, for his careful reading andrevision of the manuscript.

References

Ahuja, L.R., Naney, J.W., Green, R.E., Nielsen, D.R., 1984.Macroporosity to characterize spatial variability of hydraulic


conductivity and effects of land management. Soil Sci. Soc.Am. J. 48, 699–702.

Ahuja, L.R., Cassel, D.K., Bruce, R.R., Barnes, B.B., 1989.Evaluation of spatial distribution of hydraulic conductivity usingeffective porosity. Soil Sci. 148, 404–411.

Al-Tabaa, A., Wood, D.M., 1987. Some measurements of thepermeability of kaolin. Géotechnique 37, 499–503.

Amoozegar, A., Warrick, A.W., 1986. Hydraulic conductivity ofsaturated soils: field methods. In: Klute, A. (Ed.), Methods ofSoil Analysis. Part 1. Physical and Mineralogical Methods, 2nded. Agron. Monogr. 9. ASA, Madison, WI, pp. 735–770.

Ankeny, M.D., 1992. Methods and theory for unconfinedinfiltration measurements. In: Topp, G.C., Reynolds, W.D.,Green, R.E. (Eds.), Advances in Measurements of Soil PhysicalProperties: Bringing Theory into Practice. SSSA Spec. Publ.30. SSSA, Madison, WI, pp. 123–141.

Armas-Espinel, S., Hernández-Moreno, J.M., Muñoz-Carpena,R., Regalado, C.M., 2003. Physical properties of “sorriba”-cultivated volcanic soils from Tenerife in relation to andicdiagnostic parameters. Geoderma 117, 297–311.

Bartoli, F., Burtin, G., Herbillon, A., 1991. Disaggregation and claydispersion of Oxisols: Na resin, a recommended methodology.Geoderma 49, 301–307.

Basak, P., 1972. Soil structure and its effects on hydraulicconductivity. Soil Sci. 114, 417–422.

Bosch, D.D., West, L.T., 1998. Hydraulic conductivity variabilityfor two sandy soils. Soil Sci. Soc. Am. J. 62, 90–98.

Bouma, J., 1983. Use of soil survey data to select measurementtechniques for hydraulic conductivity. Agric. Water Manage. 6,177–190.

Braud, I., Dantas-Antonino, A.C., Vauclin, M., 1995. A stochasticapproach to studying the influence of the spatial variabilityof soil hydraulic properties on surface fluxes. J. Hydrol. 165,283–310.

Bresler, E.G., Dagan, G., Wagenet, R.J., Laufer, A., 1984.Statistical analysis of salinity and texture effects on spatialvariability of soil hydraulic conductivity. Soil Sci. Soc. Am. J.48, 16–25.

Brooks, R.H., Corey, A.T., 1964. Hydraulic Properties of PorousMedia. Hydrology Paper 3. Colorado State University, FortCollins, CO, pp. 1–27.

Carman, P.C., 1937. Fluid flow through granular beds. Trans. Inst.Chem. Eng. 15, 150–166.

Ciollaro, G., Romano, N., 1995. Spatial variability of the hydraulicproperties of a volcanic soil. Geoderma 65, 263–282.

Cressie, N.A.C., 1993. Applications of geostatistics. In: Statisticsfor Spatial Data. Wiley Series in Probability and MathematicalStatistics. Wiley, New York, pp. 211–276.

Cressie, N.A.C., Horton, R., 1987. A robust-resistant spatialanalysis of soil water infiltration. Water Resour. Res. 23, 911–917.

De Haro, J.M., Vanderlinden, K., Gómez, J.A., Giráldez, J.V., 1998.Medida de la conductividad hidráulica saturada. In: González,A., Orihuela, D.L., Romero, E., Garrido, R. (Eds.), Progresosen la Investigación de la Zona No Saturada, Collectanea, vol.11. Universidad de Huelva, Spain, pp. 9–20.

Dorel, M., Roger-Estrade, J., Manichon, H., Delvaux, B., 2000.Porosity and soil water properties of Caribbean volcanic ashsoils. Soil Use Manage. 16, 133–140.

Durner, W., 1995. SHYPFIT 0.24, User’s Manual. ResearchReport 95.1. Department of Hydrology, University of Bayreuth,Germany.

Elrick, D.E., Reynolds, W.D., 1992. Infiltration from constant-headwell permeameters and infiltrometers. In: Topp, G.C., Reynolds,W.D., Green, R.E. (Eds.), Advances in Measurements of SoilPhysical Properties: Bringing Theory into Practice. SSSA Spec.Publ. 30. SSSA, Madison, WI, pp. 1–24.

Elrick, D.E., Reynolds, W.D., Tan, K.A., 1989. Hydraulicconductivity measurements in the unsaturated zone usingimproved well analyses. Ground Water Monit. Rev. 9, 184–193.

El-Swaify, S.A., 1975. Changes in the physical properties of soilclays due to precipitated aluminium and iron hydroxides. I.Swelling and aggregate stability after drying. Soil Sci. Soc.Am. Proc. 39, 1056–1063.

Emerson, W.W., 1977. Physical properties and soil structure.In: Russel, J.S., Greacen, E.L. (Eds.), Soil Factors inCrops Production in a Semiarid Environment. University ofQueensland Press, St. Lucia, Qld, pp. 78–104.

Fernandez-Caldas, E., Tejedor-Salguero, M.L., Quantin, P., 1982.Suelos de regiones volcánicas. Tenerife, Islas Canarias.Colección Viera y Clavijo. IV. Secretariado de publicacionesde la Universidad de La Laguna, CSIC (in Spanish).

Gee, G.W., Bauder, J.W., 1986. Particle-size analysis. In: Klute,A. (Ed.), Methods of Soil Analysis. Part 1. Physical andMineralogical Methods, 2nd ed. Agronomy 9. ASA/SSSA,Madison, WI, pp. 383–411.

Gómez, J.A., Giráldez, J.V., Fereres, E., 2001. Analysis ofinfiltration and runoff in an Olive Orchard under no-till. SoilSci. Soc. Am. J. 65, 291–299.

Gonzales-Batista, A., Hernández-Moreno, J.M., Fernández-Caldas,E., Herbillón, A.J., 1982. Influence of silica content on thesurface charge characteristics of allophanic clays. Clays Miner.30, 103–110.

Jury, W.A., Gardner, W.R., Gardner, W.H., 1991. Soil Physics.Wiley, New York.

Klute, A., Dirksen, C., 1986. Hydraulic conductivity anddiffusivity: laboratory methods. In: Klute, A. (Ed.), Methodsof Soil Analysis. Part 1. Physical and Mineralogical Methods,2nd ed. Agron. Monogr. 9. ASA, Madison, WI, pp. 687–734.

Kutilek, M., Nielsen, D.R., 1994. Soil Hydrology. CREMLINGEN-Destedt: CATENA-Verlag, Catena.

Mertens, J., Jacques, D., Vanderborght, J., Feyen, J., 2002.Characterisation of the field-saturated conductivity on ahillslope: in situ single ring pressure infiltrometer measure-ments. J. Hydrol. 263, 217–229.

Messing, I., Jarvis, N.J., 1990. Seasonal variation in field-saturatedhydraulic conductivity in two swelling clay soils in Sweden. J.Foil Sci. 41, 229–237.

Moustafa, M.M., 2000. A geostatistical approach to optimize thedetermination of saturated hydraulic conductivity for large-scalesubsurface drainage design in Egypt. Agric. Water Manage. 42,291–312.

Muñoz-Carpena, R., Regalado, C.M., Álvarez-Benedı́, J., Bartoli,F., 2002. Field evaluation of the new Philip-Dunne permeameter


for measuring saturated hydraulic conductivity. Soil Sci. 167,9–24.

Newman, A.C.D., 1983. The specific surface of soils determinedby water sorption. J. Soil Sci. 34, 23–32.

Pannatier, Y., 1996. VARIOWIN: Software for Spatial DataAnalysis in 2D. Springer-Verlag, New York.

Petersen, L.W., Moldrup, P., Jacobsen, O.H., Rolston, D.E., 1996.Relations between specific surface area and soil physical andchemical properties. Soil Sci. 161, 9–21.

Philip, J.R., 1985. Approximate analysis of the boreholepermeameter in unsaturated soil. Water Resour. Res. 21, 1025–1033.

Philip, J.R., 1993. Approximate analysis of falling-head linedborehole permeameter. Water Resour. Res. 29, 3763–3768.

Rawls, W.J., Brakensiek, D.L., Logsdon, S.D., 1993. Predictingsaturated hydraulic conductivity utilizing fractal principles. Soil.Sci. Soc. Am. J. 57, 1193–1197.

Rawls, W.J., Gimenez, D., Grossman, R., 1998. Use of soiltexture, bulk density, and slope of the water retention curve topredict saturated hydraulic conductivity. Trans. ASAE 41, 983–988.

Regalado, C.M., Muñoz-Carpena, R., 2001. Field spatial variabilityof the saturated hydraulic conductivity as measured with threekinds of permeameters. ASAE Annual International Meeting,Paper Number 012147, Sacramento, California, USA.

Regalado, C.M., Muñoz-Carpena, R., Socorro, A.R., HernándezMoreno, J.M., 2003. Time domain reflectometry models as atool to understand the dielectric response of volcanic soils.Geoderma 117, 313–330.

Reynolds, W.D., Elrick, D.E., Clothier, B.E., 1985. The constanthead well permeameter: effect of unsaturated flow. Soil Sci.139, 172–192.

Reynolds, W.D., Elrick, D.E., Topp, G.C., 1983. A reexaminationof the constant head well permeameter method for measuringsaturated hydraulic conductivity above the water table. Soil Sci.136, 250–268.

Reynolds, W.D., Zebchuk, W.D., 1996. Hydraulic conductivityin a clay soil: two measurement techniques and spatialcharacterization. Soil Sci. Soc. Am. J. 60, 1679–1685.

Romano, N., 1993. Use of an inverse method and geostatisticsto estimate soil hydraulic conductivity for spatial variabilityanalysis. Geoderma 60, 169–186.

SYSTAT 10, 2000.http://www.systat.com/products/Systat/. SPSSInc.

Timlin, D.J., Ahuja, L.R., Pachepsky, Ya., Williams, R.D.,Gimenez, D., Rawls, W., 1999. Use of Brooks–Coreyparameters to improve estimates of saturated conductivity fromeffective porosity. Soil Sci. Soc. Am. J. 63, 1086–1092.

Vachaud, G., Vauclin, M., Balabanis, P., 1988. Stochastic approachof soil water flow through the use of scaling factors:measurement and simulation. Agric. Water Manage. 13, 249–261.

Vieira, S.R., Reynolds, W.D., Topp, G.C., 1988. Spatial variabilityof hydraulic properties in a highly structured clay soil. In:Proceedings of the Symposium on Validation of Flow andTransport Models for the Unsaturated Zone, Ruidoso, NM.

Wagenet, R.J., Bresler, E., 1983. Soil salinity effects on thespatial variability of hydraulic conductivity. United States-IsraelBinational Agricultural Research and Development (BARD)Fund. Final Report Project No. US-21-79, Bet Dagan, Israel.

Warrick, A.W., Nielsen, D.R., 1980. Spatial variability of soilphysical properties in the field. In: Hillel, D. (Ed.), Applicationsof Soil Physics. Academic Press, New York, pp. 319–344.

Webster, R., Oliver, M.A., 1990. Statistical Methods in Soil andLand Resource Survey. Oxford University Press, New York.

Whittig, L.D., Allardice, W.R., 1986. X-ray diffraction techniques.In: Klute, A. (Ed.), Methods of Soil Analysis. Part 1. Physicaland Mineralogical Methods, 2nd ed. Agron. Monogr. 9. ASA,Madison, WI, pp. 331–362.

Zhuang, J., Nakayama, K., Yu, G.R., Miyazaki, T., 2000. Scalingof saturated hydraulic conductivity: a comparison of models.Soil Sci. 165, 718–727.

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