water content effect on soil salinity prediction: a geostatistical study using cokriging

Water Content Effect on Soil Salinity Prediction:A Geostatistical Study Using Cokriging

Peter J. Vaughan,* Scott M. Lesch, Dennis L. Corwin, and David G. Cone

ABSTRACTA geostatistical analysis of soil salinity in an agricultural area in the

San Joaquin Valley included measurements of electrical conductivity ofsoil paste extract (EC,) and water content of soil samples supplementedby surface measurements of apparent electrical conductivity (EMH).Prediction of soil salinity at unsampled points by cokriging log,(ECc)and EMH is worthwhile because EMH measurements are quicker thansoil sampling. This work studies how patterns of loge(ECe) predictedby cokriging with EMH are influenced by variation in gravimetricwater content (W). The data are mean EMH = 1.00 ± 0.13 dS m"1

for 2378 locations, mean loge(ECe) = 1.40 ± 0.29 dS m"1, and meangravimetric W = 0.260 ± 0.003, both averaged for four samples from0.3-m intervals to 1.2-m depth for 315 locations. The coefficient ofdetermination (R2) for EMH vs. loge(£Ce) increased with depth from0.05 to 0.54 whereas the R1 for EMH vs. W decreased from 0.48 to0.28. A gray-scale EMa map contained nine out of 56 quarter-sectionboundaries coinciding with step variations in EMH. The /-statistics fordifferences in mean W were six of nine significant at 0.001 and nineof nine at 0.05, but mean loge(ECe) had only two of nine at 0.05,implying that W caused EMH steps. Water-affected EMH unpairedprediction of ECe at depth by cokriging, because near-surface varia-tions in W masked ECe. Two subareas were defined, one where manage-ment factors, such as irrigation, controlled EMH, causing steps, andone where near-surface W varied less, making cokriging predictionsmore reliable.

ASESSMENT OF SOIL SALiNiZATiON in irrigated agricul-ture is important for evaluation of the long term

sustainability of agricultural production. Several mea-surement techniques requiring varying amounts of efforthave been developed in support of salinization assess-ment. Soil sampling and subsequent analysis of samplesis time consuming but provides the most accurate andreliable data for estimation of ECe (Rhoades et al.,1989a). The four-electrode Wenner array method pro-vides on-site estimation of electrical conductivity byinjecting current directly into the ground and measuringthe voltage between two passive electrodes. Direct cur-rent methods such as the Wenner array rely on effectiveelectrical contact between the electrodes and the soil. Indry soils, an effective electrical contact can be difficultto establish and an alternative technique utilizing a nonin-trusive EM method may be preferable (Rhoades andCorwin, 1981). Both the Wenner array and the EMmethods result hi an estimation of apparent electricalconductivity at the surface that is likely to be a compli-cated average of variable electrical conductivity in thesubsurface. Given the high degree of nonuniqueness inthe problem of inverting the results of a set of surface

P.J. Vaughan, S.M. Lesch, and D.L. Corwin, USDA-ARS, U.S. SalinityLab., 4500 Glenwood Dr., Riverside, CA 92501; and D.G.Cone, Broad-view Water District, P.O. Box 95, Firebaugh, CA 93622. Contributionfrom the USDA-ARS, U.S. Salinity Lab. Received 23 May 1994. "Corre-sponding author ([email protected]).

Published in Soil Sci. Soc. Am. J. 59:1146-1156 (1995).

measurements to obtain a subsurface electrical conductiv-ity distribution, the obvious choice is a simplified modelinvolving a small number of horizontal layers of infiniteextent. Under the assumption of a horizontally layeredelectrical conductivity structure, Rhoades and Corwin(1981) used regression analysis to calibrate EM measure-ments with independent measurements of electrical con-ductivity as a function of depth. An independent measure-ment might be ECe of a soil sample or an in situmeasurement of ECa using a salinity probe (Rhoades andvan Schilfgaarde, 1976). Rhoades and Corwin (1981)obtained empirical equations relating ECa at variousdepths to a linear combination of EM measurements ofdifferent types taken at a single site, an approach thatwas later improved on (Corwin and Rhoades, 1982,1983). Further refinement in the prediction of ECa fromEM measurements was accomplished by a more rigorousstatistical analysis (Rhoades et al., 1989b).

Calibration of EM measurements for prediction ofECe by regression techniques have considered soil tex-ture, water content, and soil temperature as influentialvariables (McKenzie et al., 1989; Slavich and Petterson,1990). A strong correlation between soil water contentand EM measurements was obtained for a wide rangeof soil textures in a field area in southern Ontario (Kacha-noski et al., 1988). But an assessment of soil salinity inPakistan, utilizing EM measurements and a calibrationprovided by Rhoades et al. (1990), concluded that watercontent was not necessarily a critical factor (Hendrickxet al., 1992).

Spatial variation of soil salinity was mapped by mea-suring ECe for samples taken at a relatively small numberof sites; then, by regression analysis, log(ECe) was pre-dicted on a much denser array of EM measurement sites(Lesch et al., 1992b). The mapped prediction of soilsalinity from regression equations contained some dis-crepancies when compared with a map exclusively drawnfrom a dense array of ECe measurements. Spatial autocor-relation of the residuals would suggest use of geostatisti-cal techniques. When residuals from multiple linear re-gression models are spatially uncorrelated, however,multiple linear regression techniques can be implementedmore efficiently man cokriging to accomplish the sameobjective (Lesch et al., 1995b). The observed lack ofspatial autocorrelation of the residuals implied that theerrors were not due to variability in soil physical proper-ties (Lesch et al., 1992b).

Electrical conduction in soil is caused by ionic conduc-tion in soil water coupled with conduction through thesoil solids. The conductivity will be sensitive to variationsin the salinity of the soil water as measured by ECe and

Abbreviations: ECe, electrical conductivity of soil paste extract; ECa,soil electrical conductivity; EM, electromagnetic induction; W, gravimetricwater content; BWD, Broadview Water District; GPS, global positioningsystem.

1146

VAUGHAN ET AL.: WATER CONTENT EFFECT ON SOIL SALINITY PREDICTION 1147

W. We examined these two contributions to apparentelectrical conductivity measured at the ground surfacein a field area of 2350 ha containing four soil texturemap units. Also, considering the laboratory data obtainedfor both variables along with soil maps and informationregarding management practices such as irrigation sched-uling and cropping, a rationalization of the pattern ofapparent electrical conductivity as measured by the EM-38 instrument (Geonics Inc., Mississauga, ON) is pre-sented1.

In this study, data were analyzed either as a single,complete set covering the entire area or by subdividingthe data by quarter section. No attempt was made tosubdivide the data by soil unit because the main intentof this study was a discussion of the relative correlationof measured W and log(ECe) with EM measurements.

MATERIALS AND METHODSA comprehensive field study of soil salinity was conducted

within the BWD in the San Joaquin Valley of California inMay and June 1991. The field area studied consisted of 37quarter sections (65-ha squares). A quarter section is the normalmanagement unit for agriculture in the BWD. Generally, asingle crop is grown within a quarter section, but occasionallya quarter section is split, with different crops growing indifferent parts. Each part, in this case, would be considereda management unit. Quarter sections are bounded by dirt roadsor drainage ditches. The term section refers to a surveyedsquare consisting of four quarter sections. Sections in the fieldarea are numbered according to section numbers appearing ontwo U.S. Geological Survey, 7.5-min quadrangle maps calledBroadview Farms and Firebaugh. Two basic soil types occurin this field area (Fig. la), the Lillis series (very fine,montmorillonitic, thermic Entic Chromoxererts) and the Ceriniseries (fine-loamy, mixed (calcareous), thermic Typic Tor-rifluvents). These units were mapped and described by theSoil Conservation Service during the period 1990 to 1992when the remapping of soils in the BWD and surroundingareas occurred.

Various crops are grown in the BWD and cropping ofindividual quarter sections may change from season to season.In September 1991, the land-use distribution for crops was:54% cotton (Gossypium hirsutum L.), 27% fallow, 8% tomato[Lycopersicon lycopersicum (L.) Karsten], 6% seed alfalfa(Medicago saliva L.), 4% melon (Cucumis melo L.), and 1%oat (Avena sativa L.) hay. These five crops grew during thesummer growing season, which may start as early as Marchand runs through September. In most years, winter wheat(Triticum aestivum L.) is also grown in a few quarter sections.The summer crops were already growing in the cropped quartersections when the measurements discussed here were made.

During the summer growing season of 1991, irrigated quar-ter sections received, on average, 0.35 m (depth) of irrigationwater. Amounts of irrigation water varied from 0.04 toO. 55 m.Nine quarter sections were not irrigated. Complete tile drainagesystems were installed in at least 26 of the 37 quarter sections.Due to lack of documentation, there is uncertainty regardingthe existence and extent of tile drainage in some of the otherquarter sections. The density of tile drainage varies from 12to 134 m ha"1. All tile drainage systems in the BWD areoperated by sump pumps.

The data given above on crops, irrigation, and tile drainageare elements of a body of data collectively referred to hereas management factors. Other management factors includetillage and soil treatments such as mulching. Managementfactors are approximately constant within a management unit.

Sampling and Chemical AnalysesEight locations in each quarter section were designated as

sites for taking soil samples. The EM-38 instrument was oper-ated in both horizontal dipole (EMH) and vertical dipole (EMV)modes at heights of 0.1 and 0.5 m above the ground surfacefor a total of four readings per site (Lesch et al., 1992a). Foreach quarter section, EM readings were taken at the eight soilsampling sites in addition to 56 other sites located roughly ona 100 by 100 m grid (Lesch et al., 1992a). The instrumentwas operated in the low induction number range for whichthe voltage in the receiver coil is out of phase and is directlyproportional to the apparent electrical conductivity (Keller andFrischknecht, 1966). Under these conditions, the electricalconductivity of a hypothetical infinite half space (apparentconductivity) was digitally recorded directly from the instru-ment for each of the four readings.

Locations of the EM measurement sites were determinedby GPS equipment. As much as possible, the readings weredifferentially corrected using readings obtained from an addi-tional GPS receiver at a fixed location with known geographiccoordinates. Differential correction requires data from foursatellites in the GPS system but sometimes fewer than foursatellites were visible and operating. In such cases, differentialcorrection was not possible. However, the scatter in the locationdata was substantially reduced because the fields were furrowedand movement of measuring equipment through the fieldsoccurred along straight lines constrained by the furrows. Mea-surement locations were repositioned based on simple averag-ing of the coordinate direction lying perpendicular to the beds.

Soil samples were taken in furrows at 0.3-m depth intervalsto a maximum depth of 1.2 m with an auger. Each sample,of length 0.3 m, was mixed prior to any measurements. Mea-surements made on each mixed sample include: (i) ECe of thesoil paste extract; (ii) W; and (iii) determination of the saturationpercentage (water content of the saturated soil paste). Gravimet-ric water content was calculated from the mass lost after dryingat 105°C for 24 h divided by the dry mass. The depths ofsamples are given as the midpoint of the depth range for thatsample. For example, the soil sample from the top 0.3-m depthrange is considered to represent the 0.15-m depth.

Geostatistical AnalysisA geostatistical analysis of the data was performed to attempt

to determine soil salinity, as measured by log(ECe), at unsam-pled points by kriging and cokriging. Semivariograms werecalculated for log(ECe), the apparent electrical conductivity(EM), and W. The semivariance y(h), representing spatialautocorrelation of a variable, M, is a function of the spacing,h, between pairs of points:

1 N(h)

1 The use of brand names in this report is for identification purposesonly and does not constitute endorsement by the USDA.

[1]where the sum runs across all pairs (i,j) that lie within aspecified tolerance of a central value, h (Isaaks and Srivastava,1989). Cross-correlation between variables was calculated us-ing the cross-variogram, yuv:

1148 SOIL SCI. SOC. AM. J., VOL. 59, JULY-AUGUST 1995

Lillis Clay, very fine

Lillis Clay, fineCerini Clay Loam

I Cerini Clay Loam, saline

Fig. 1. (a) Soil map of the study area in the Broadview Water District digitized from a preliminary map provided by the Soil ConservationService, (b) Gray-scale map of apparent electrical conductivity (EMn) normalized to zero mean and unit variance. Measurements were madeon a roughly 100 by 100 m grid. Squares in the grid are shaded based on measured values at enclosed points. Some squares, shown in white,enclosed no point.

(M, - Uj)(vi - [2]

where M and v represent correlated variables. For cross-variograms and semivariograms used for cokriging, the datawere normalized to zero mean and unit variance prior tothe calculation of y(h). Data were not normalized prior tocomputation of the semivariogram used for ordinary kriging.

Estimation of the measured variables at unsampled pointson a square 100 by 100 m grid was accomplished by ordinaryblock kriging (Journel and Huijbregts, 1978). The estimationfacilitated representation of the variables in map form byproviding a higher resolution coverage. For variables that arecross-correlated an alternative technique is cokriging, wheremeasurements of both variables together form the basis forestimation of one of the variables (Deutsch and Journel, 1992;

Isaaks and Srivastava, 1989; Yates and Warrick, 1987; Vauclinet al., 1983; Journel and Huijbregts, 1978). The equationsdenning the cokriging algorithm can be found in any of thesereferences.

Cokriging provides an estimate of a primary random functionbased on a combined set of samples of the primary functionand one or more auxiliary, cross-correlated random function.Cokriging is most useful in situations where one function issampled more intensively than the other (Yates and Warrick,1987). In this case, the less-sampled function can be estimatedat a point density equivalent to that of the more intensivelysampled function. Cokriging requires the computation of semi-variograms and cross-variograms for a pair of variables toprepare models of spatial autocorrelation and cross-correlationstructure. Parameters for the semivariogram model may needto be adjusted to maintain a reasonable fit and simultaneously


provide a linear model of coregionalization, |Y</(A)| <V[Y'iCOYi/COl] where i and j refer to the primary and auxiliaryfunctions (Isaaks and Srivastava, 1989; Yates and Warrick,1987). The type of cokriging discussed here, standardizedordinary cokriging, was accomplished utilizing the single non-bias condition that the sum of the weights for both data setscombined was unity (Deutsch and Journel, 1992). Cokrigingmay be done with multiple auxiliary variables, but the modelingof all required semivariograms and cross-variograms renderssuch an approach too tedious for most practical considerations(Leschet al., 1995a).

RESULTS AND DISCUSSIONFigure Ib is a map of the field area showing normalized

variance of the apparent electrical conductivity measuredwith the EM-38 in the horizontal dipole mode and located0.1 m above the ground surface (EMH). The values ofEMn and EMv are highly correlated both in the presentdata set (R2 > 0.93) and in a study of a quarter sectionin the adjacent Westlands Water District near Coalinga,CA(Leschetal., 1995b). Theoretical predictions indicatethat EMV samples a lower depth range than EMH. Thevalue of EMH was consistently lower than EMv (averageEMH/EMV = 0.62 + 0.01 dS m"1) indicating increasingelectrical conductivity with depth, as found by Lesch etal. (1992a) by regression analysis on the same data set.The high value of R2 for EMH vs. EMV suggests thatlittle will be gained by treating EMH and EMv separately.Thus, we will deal exclusively with EMH data.

The electrical conductivity of soil should be moreaccurately predicted by a volumetric rather than gravi-metric expression. But, conversion to volumetric watercontent requires knowledge of the soil bulk density. Alimited sampling for soil bulk density was conducted inthe BWD in 1993 when 98 samples were collected at0.3-m depth. This limited sampling did not have sufficientcoverage of the area to warrant use of the bulk densitydata to convert gravimetric to volumetric water content.

Figure Ib was produced by overlaying a square 100by 100 m grid on the EMn data points. Each square inthe grid was then filled in from a gray scale accordingto the value at the enclosed data point. Squares enclosingno data point remained white. In the few cases wheremore than one data point was enclosed, the geographicinformation system that was used to prepare this mapselected one of the data values arbitrarily. Figure la isa soil map of the same area digitized from a larger mapprovided by the Soil Conservation Service. A north-northeast-trending low value of EMH runs from the north-east corner down toward the southwest corner of thecentral portion of the field area (Fig. Ib). The EMHvalue is also low in an area near the southeast corner.These two lows occur in the same general areas as theCerini clay loam soil. In an area of the map betweenthe two low values of EMn just described, there isevidence of quarter-section control of EMn~ The mapof quarter-section outlines (Fig. 2) can be compared withthe EMH map (Fig. Ib) to note significant step variationsin EMH occurring at some of the boundaries. This local-ized pattern of step variations in EMH conforming toquarter-section boundaries is most reasonably explained

|N

8-2

8-4

/4-1

4-3

9-1

9-3

16-1

16-3

4-2

4-4

9-2

9-4

16-2

16-4

3-1

3-3

10-1

10-3

15-1

15-3

3-2

3-4

10-2

10-4

15-2

15-4

11-3

14-1

14-3

11-4

14-2

14-4

1 km

13-1 13-2

13-4 18-3 18-4

Fig. 2. Quarter-section identification map.

by differences in management practices between adjacentquarter sections. An inference that may be drawn fromvisual inspection of the raw EMn data is that both soiltexture and management practices appear significant indetermining EMH in the BWD. Also, the relative impor-tance of soil texture or management factors appearsvariable across the area.

The apparent electrical conductivity measured at thesurface (EMH) is likely to be correlated with severalphysical variables Including salinity of the soil water,water content, and properties such as clay content thatare determined by soil texture (Lesch et al., 1992b).Mean gravimetric water content was obtained by averag-ing across the four sampling depths. The ECe value forthe same set of samples was log transformed and thenaveraged. These results were normalized to zero meanand unit variance and plotted with normalized EMH (Fig.3). There is roughly the same coefficient of determinationbetween each of these physical variables and EMu [R2 =0.48 for log(ECe) and R2 = 0.55 for W] indicating thatboth variables influence the pattern of apparent electricalconductivity in the BWD. Correlation between depth-averaged Wand log(ECe) is low (R2 = 0.1).

For both W and log(ECe), the relative contributionsof samples from different depths to the EMn measurementwas studied by calculating the coefficient of determinationfor each of the four sampling depths (Fig. 4). The coeffi-cient of determination for EMH vs. log(ECe) increasessignificantly with increasing depth (R2 = 0.05-0.54)whereas the correlation of W with EMH decreases withdepth (R2 = 0.48-0.28). For the BWD, measurementsof EMH will be most useful for predicting the watercontent near the surface (0-0.6 m) and the salinity atgreater depths (0.6-1.2 m).

Kriging ResultsOrdinary kriging of log(ECe) for the samples taken

from 1.06-m depth was accomplished by computing andmodeling the semivariogram. Then, using the modelingresults, a block kriging algorithm computed the interpola-tion of log(ECe) onto a square grid with a 100-m cellsize. An exponential model of the semivariogram witha 1-km range provided useful fits for all of the varioustypes of data being modeled. This model is given by

Y(/0 = Co + Cc [1 - exp(- hla)] [3]where h is the lag distance, Co represents the nuggeteffect, Cc is a structural component, and a is the range.


bR = 0.55

>loge(ECe)

*'**

-4 -3 -2 -1 0

a™Fig. 3. Scattergrams of normalized apparent electrical conductivity measured at the soil surface (EMH) vs. normalized log-transformed electrical

conductivity of the soil paste extract (ECe) and water content, both averaged across four sampling depths.

The nugget was estimated by the intersection of the fittedexponential model with the semivariance axis at zerolag because very closely spaced data were not availablefor an independent estimate. The map of the kriged resultfor log(ECe), shown in Fig. 5, has both similarities anddifferences when compared with the raw EMH data (Fig.Ib). A broad similarity is the correspondence of a lowvalue in EMH with a low log(ECe) in the areas whereCerini clay loam is the soil. Also the highest values ofboth log(ECe) and EMH occur in the same areas. Adifference is the lack of sharp variations in log(ECe) atquarter-section boundaries when compared with EMn.Since this latter effect may simply be due to smoothingcaused by a 500-m kriging radius, which is substantiallylarger than the 100-m spacing for the raw EMn data,the kriging calculation was applied to the raw EMH data

0.6-

0.5-

0.4-

0.3-

0.2-

0.1

Water Content

loge(ECe)

0 0.2 0.4—i—0.6

—l—0.8 1.2

Depth (m)Fig. 4. Coefficient of determination (R2) for plots of apparent electrical

conductivity measured at the soil surface (EMH) vs. log-transformedelectrical conductivity of the soil paste extract (EC,) and EMHvs. gravimetric water content (W) is itself plotted against depth.Correlation between EMH and near-surface log(ECe) is near zerobut increases with depth, whereas for W the correlation decreaseswith depth.

using a 500-m kriging radius. The resulting map exhibitedsmoother transitions but a pattern following quarter-section boundaries persisted in the area of sections 11-3,11-4, 14-1, 14-2, 14-3, 14-4, 15-3, and 15-4 (data notshown). Kriged maps of both log(ECe) and water contentfailed to exhibit this pattern. However, based on previouswork (Rhoades and Corwin, 1981; Corwin and Rhoades,1982, 1983; Lesch et al., 1992b; Lesch et al., 1995b)there is strong evidence for correlation between log(ECe)and EMn. Less work has been done on the correlationbetween water content and EMH but there is considerableevidence that a correlation exists because recommenda-tions for salinity survey methods specify that water con-tent should be uniform (Kachanoski et al., 1988; Leschet al., 1992b). Given these known correlations and thecomputed coefficients of determination for the BWDdata set (Fig. 3), the explanation for differences in thelocalized patterns of log(ECe) compared with EMH andwater content compared with EMH may lie in the differ-ence in sampling density rather than a lack of correlation.We chose a set of specific subareas within the BWD fordetailed examination of the actual data in areas wheresharp discontinuities in the mapped values of EMH occur.

Explanations of Mismatch betweenSurface-Measured and Soil-Paste-Measured

Electrical ConductivityA specific area of mismatch between maps of EMH

and the kriged log(ECe) data occurs in quarter section4-3. An east-west trending boundary in quarter section4-3 separates a rectangular area of low EMH in thenorthern portion from an area of much higher EMH inthe southern portion of 4-3 (Fig. Ib). By contrast,log(ECe) has a relatively high value forming a north-south trending band along the western half of 4-3 (Fig.5). Quarter section 4-3 took no irrigation deliveries dur-ing the period of 1991 before the field measurementswere made. Thus, irrigation management was not a factorcausing the east-west trending, split pattern in EMH.


Fig. 5. Gray-scale map of the kriging estimate of log-transformed electrical conductivity of the soil paste extract (EC.) determined from samplestaken at 1.06-m depth. Semivariogram was modeled using an exponential with an effective range of 1 km. Lows in the kriged result generallycorrespond to areas of clay loam soil texture (Fig. la).

But cropping of the field was split along an east-westtrending line, with winter wheat grown in the northernportion while the southern portion remained fallow. Thesix sampling points in the northern portion of the fieldwere located in the portion where wheat was grown andthe other six sampling points were in the fallow area.Within the positional constraint afforded by the soil sam-pling locations, the location of this east-west trendingline is the same as the location of the abrupt change inEMH between northern and southern areas of the quartersection. Table 1 provides median values of water contentat four depths for each portion of quarter section 4-3.In the depth range 0 to 0.75 m, the range in which watercontent has high variability causing a high sensitivity ofEMH to water content, the median water content inthe northern portion was significantly lower than in thesouthern portion. Thus, variation of water content re-sulted in a pattern that matches the general pattern ofEMH but variation of log(ECe) does not. The winterwheat had matured and was harvested shortly beforethe field measurements were made on 22 Apr. 1991.Evidently, growth of the wheat depleted the soil waterrelative to that of the adjacent fallow area, causing bothlower values of water content in the soil samples andlower values of EMH.

Management factors also appear to predominate in thearea of quarter section 14-2 and its four nearest neighbors(Fig. Ib). No irrigation water was delivered to 14-2during the period of 1991 prior to the EMH measure-ments. Deliveries of irrigation water to all four of thequarter sections that border 14-2 occurred between Janu-ary and April 1991. These deliveries are called preirriga-

Table 1. Median water content for samples from six sites in eachsubarea.

Water contentSubarea 0.15 m 0.46m 0.76m 1.06m

-kgkg-NorthSouth

0.1980.307

0.2450.351

0.3050.344

0.3850.335

tions, meaning that water is applied before a crop isplanted. In the depth range of 0 to 0.9 m, the medianwater content for 14-2 was lower than in any of thebordering quarter sections (Table 2). This low watercontent may be attributed to the lack of any preirrigation.In general, water content does not correlate particularlywell with either the amount of irrigation water appliedor the elapsed time between preirrigation and the dateof the measurements. While the largest irrigation oc-curred in quarter section 14-4, which has the highestaverage water content for all depths, a scatter plot ofirrigation amount vs. water content for the four borderingquarter sections gave R2 = 0.42 (not shown). This sug-gests that influence by other management factors, asoutlined above, may also be affecting water content.

The explanation of irrigation management is even lesseffective in rationalizing the sharp variations in EMHbetween quarter section 11-3 and its neighbors to theeast and south. In 11-3, the median water content at the0.3-m depth is 0.185, which is lower than either thecorresponding water content of 11-4 (0.242) or 14-1(0.219 for all points). Thus, quarter section 11-3 haslower water content and lower average EMH, but asubstantially larger amount of irrigation water was ap-plied to this quarter section than to either 14-1 or 11-4(Table 2). Some factor other than simple amount of

Table 2. Median water content for various quarter-sections.Median water content

IDt

14-213-114-414-111-411-315-415-3

0.15 m

0.2200.3160.2980.2840.3190.2270.3190.148

0.46m

————— kg kg0.2250.3030.3370.2950.2820.2600.2710.154

0.76m-i

0.2660.2840.3280.2820.2830.2780.2720.181

1.06m

0.3120.2810.2980.2760.3060.2900.3060.193

Irrigationamount!

m00.160.2150.0730.0650.12800

t Quarter-section identification number.$ Total depth of water applied during 5 mo prior to sampling.


irrigation water applied caused lower water content inquarter section 11-3.

Very low water content occurred at all depths in quartersection 15-3 compared with 15-4 (Table 2). This contrastin water content is correlated with a step increase inEMH going from 15-3 to 15-4. Neither quarter section hadbeen preirrigated, implying that the observed variation inwater content is also due to some factor other thanirrigation. Another step variation in EMH across a quar-ter-section boundary occurs between 18-3 and 13-4. Themedian water content at the 0.15-m depth in 18-3 is0.229, whereas median water content is 0.192 in 13-4at the same depth. This variation in water content isparticularly difficult to explain by irrigation managementsince quarter section 13-4 had been preirrigated whereas18-3 had not. However, there is a contact between clayloam and clay that lies close to this quarter-section bound-ary and the occurrence of a step variation in water contentmay be explained by the difference in soil texture (Fig.la).

Further evidence of the relative significance of watercontent and log(ECe) in explaining the differences inmeasured EMH occurring at quarter-section boundariescan be judged by comparing maps of posted data for the

a: water content

two variables at a representative boundary. The posteddata were superimposed on a gray-scale map of normal-ized EMH, which indicates the step variation in EMHoccurring at the boundary between quarter sections 14-2and 11-4 (Fig. 6a and 6b). All eight measurements ofW in the upper quarter section (11-4) are higher thanthe highest measurement in quarter section 14-2 (Fig.6a). In contrast, there is considerable overlap of thelog(ECe) data, which varies between 1.63 and 3.08 in11-4 and between 0.66 and 2.53 in 14-2. There is clearlyan increase hi the mean value of log(ECe) going from14-2 to 11-4, suggesting some correlation between EMnand log(ECe), but the change in W is more definitive andis clearly associated with the quarter-section boundary.Similar results, for this kind of comparison, were ob-tained at the other nine quarter-section boundaries, indi-cating that near-surface water content rather thanlog(ECe) is a better predictor of EMH in areas exhibitingstep variations in EMH at the boundaries. The mainevidence that these nine boundaries are associated withstep variations in EMn is drawn from examination ofFig. Ib, but to provide some quantification, the meanEMn values were computed for all quarter sections.Using those means, the nine designated step boundaries

b: logfECJ 200m

Fig. 6. (a) Gray-scale map of apparent electrical conductivity measured at the soil surface (EMH) in quarter section 11-4 (top) and 14-2 withsuperimposed posting of water content at 0.15-m depth for samples taken at eight locations in each. Gray scale was recalculated to maximizecontrast; it is uncalibrated. (b) Same gray-scale map with superimposed posting of log-transformed electrical conductivity of the soil pasteextract (ECC) at 1.06-m depth (dS m"1).


showed a mean, absolute value step of 0.52 ± 0.19whereas the other 47 boundaries exhibited a mean, abso-lute value step of 0.18 ± 0.14. The observations ofsteps in EMH were statistically analyzed by a series ofMests conducted for each of the nine boundaries (Table3). The hypothesis being tested in each case was: Isthere a significant difference in the mean of W valuesbetween the two quarter sections on either side of eachboundary having a step variation in £MH? The samehypothesis was also tested for log(ECe) values. In sixout of nine cases, the f-statistic for W was significant atthe 0.001 level. Two of the other cases were significantat a 0.01 level, the last case at a 0.05 level. But, forlog(ECe) none of the results were significant at a 0.01level and only two out of nine cases were significant ata 0.05 level. Also, for log(ECe), three out of nine caseshad negative values because the means for log(ECe) werenegatively correlated with EMH.

These results demonstrate that the identified step varia-tions in EMH are caused by variations in W rather thanlog(ECe). The origin of these step variations in watercontent may be correlated with variations in irrigationamount but this cannot be the explanation of all ninecases. Three of the nine boundaries that were studied(4-2/3-1, 13-4/18-3, and 16-3/16-4) lie close to contactsbetween clay loam soil and clay (Fig. la). In these threecases the quarter section that is predominantly clay loamhad significantly lower water content. Thus, water con-tent in these three cases was probably controlled by soiltexture rather than management factors. Another sharpEMu boundary occurring within a single quarter section(4-3) was also a boundary between higher and loweraverage values of water content. This latter case cannotbe explained by a contact of soil textures and was proba-bly the result of wheat growing in the northern portionwhile the southern portion was fallow. Of the remainingsix quarter-section boundaries, irrigation may explainobserved variation in water content in four cases. Theother two cases must be due to some other managementfactor.

_ of Selected Areas to EstimateSoil-Paste-Measured Electrical ConductivityThe argument given above suggests that parts of the

BWD are areas in which the management factors involv-ing entire, or portions of, quarter sections are important

Table 3. Comparison of means for EMH and two variables.

(statistics

Boundaryt Water content loge(EC«)16-3:16-413-1:14-218-3:13-414-1:14-214-2:14-43-1:4-215-3:15-411-4:14-211-4:11-3

3.62**7.49***2.77*7.14***9.21***5.34***

13.91***14.18***4.51**

-0.38NS- 0.46 NS

1.79 NS- 0.64 NS

0.45 NS0.75 NS0.43 NS2.37*2.79*

*, **, *** Significant atO.05,0.01, andO.OOl probability levels, respectively;NS = not significant.

t Boundary between quarter sections in which means were calculated.

in determining the measured EMH. This can be crudelyjudged by examining the quarter-section boundaries. Ifthere are step changes in EMn occurring in a consistentmanner along the length of a boundary and that boundarydoes not coincide with a change in soil texture, thenmanagement factors such as irrigation, tillage, tile drain-age, or cropping may be influencing water content inone or both of the quarter sections on either side of theboundary. For the purpose of comparison, two areas werechosen for further study. One of these is characteristic ofa zone judged to be influenced by management factorson the basis of step changes in EMH occurring at quarter-section boundaries (Section 14). The other section doesnot appear to be influenced by management factors (Sec-tion 3). Section 3 was not irrigated in 1991 prior totaking the EMH measurements and has a median watercontent of 0.137, compared with 0.220 for Section 14.For each section, scattergrams of the normalizedlog(ECe) and W plotted against normalized EMH werefitted by linear equations. Section 14 has R2 = 0.59 forwater content at 0.15-m depth and R2 = 0.44 for log(ECe)at 1.06-m depth. The situation is almost the reverse inSection 3, where R2 = 0.43 for water content and R2 =0.54 for log(ECe) at the same depths. There are approxi-mately 32 points in each section, so these numbers areless certain than the R2 values for the entire area, butthe qualitative result, the reversal of relative importanceof water content at shallow depths and log(ECe) at 1.06m, is reasonably certain. This comparison of Sections3 and 14 indicates that the relative importance of Wand log(ECe) in controlling patterns of EMH is spatiallyvariable as well as varying with depth.

Cokriging is most useful when the auxiliary functionis sampled at higher density than the primary function(Yates and Warrick, 1987). This is the case for our dataset but, as pointed out above, there are really two primaryrandom functions that may be cokriged with the auxiliaryfunction. The correlation between each of these primaryrandom functions and the auxiliary function is itselfspatially variable, such that areas may be delineated inwhich the auxiliary function will have greater utility inthe estimation of one primary variable as opposed to theother. A method is required to distinguish areas in whicheach type of primary variable can best be estimated.One obvious choice is computation of the coefficient ofdetermination for each variable within some set of arealsubunits. In practical terms, this is somewhat suspectbecause individual quarter sections generally contain onlyeight points. Instead, areas lacking obvious, visual evi-dence of management factors controlling water contentwere chosen for cokriging to estimate log(ECe).

As a first step in the presentation of cokriging results,Fig. 7 is a gray-scale map of the estimation of log(ECe)at 1.06-m depth obtained by cokriging log(ECe) withEMH. Two semivariograms for the primary and second-ary variables are included in Fig. 7 along with the cross-variogram. These three variograms were approximatedby an exponential model (Eq. [3]) including a nuggeteffect. The model curves do not match the data in eachindividual variogram particularly well, but instead, rep-resent a compromise required by the constraint of a


0 400 800 1200 1600lag distance (m)

400 800 1200 1600

lag distance (m)400 800 1200 1600

lag distance (m)

Fig. 7. Gray-scale map of the cokriging estimate of log-transformed electrical conductivity of the soil paste extract (EC,) at depth using apparentelectrical conductivity measured at the soil surface (EMH) as the auxiliary data. Semivariograms for log(ECc) and EMH were modeled usingEq. [3] but the evident lack of fit is due to constraints by the linear model of coregionalization.

linear model of coregionalization (Isaaks and Srivastava,1989). Certain areas of the map in Fig. 7 are characterizedby a pattern of step variations at quarter-section bound-aries. These patterns are clearly caused by step variationsin EMH because there are no such step variations whenlog(ECe) is kriged by itself (Fig. 5). For example, aridge of relatively high log(ECe) values trends norththrough quarter sections 14-4, 14-2, and then 11-4 (Fig.5). But in Fig. 7 this same set of quarter sections hashigh log(ECe) in 14-4, low log(ECe) in 14-2, and a highvalue again in 11-4. The low value in the cokrigedestimate of log(ECe) in 14-2 must be due to low valuesin EMH, which were caused by water content variations(compare Fig. Ib and 6). Therefore, the operation ofcokriging log(ECe) with EMH across the entire studyarea resulted in a map containing patterns that are artifactsrepresenting water content rather than log(ECe) varia-tions. From such a map, one might make the erroneousconclusion that salinity variations in parts of the BWDare the result of management practices.

Visual inspection of the map of EMn (Fig. Ib) com-bined with information regarding soil texture, irrigation,and cropping resulted in the designation of a contiguoussubset of 23 quarter sections in which log(ECe) could beestimated by cokriging with EMH. Within this designatedarea, the correlation of EMH with ECe at 1.06-m depthis significantly higher than correlation of EMu and watercontent at 0.15 m (R2 = 0.60 compared with 0.44).Semivariograms for EMH and log(ECe) as well as thecross-variogram were computed for the enclosed sets ofdata points after normalization to zero mean and unit

variance. These Semivariograms were modeled usingboth spherical and exponential models, but the exponen-tial model with a range of 1 km produced the best fits,as verified by cross-validation. Some adjustment of themodel parameters was necessary for the three modelsto conform to a linear model of coregionalization. Cross-validation was then performed to determine whetherthese adjustments caused large changes in the standarddeviation of the point estimation errors. The standarddeviation increased by <1 % for the two semivariogrammodels. A more extensive cross-validation procedurewas not warranted in this study because refining themodels of Semivariograms to accommodate slightly im-proved cross-validation results is not a recommendedprocedure (Isaaks and Srivastava, 1989). Furthermore,such refinements are unlikely to significantly improvethe resulting estimates. The problem that has been dis-cussed at length regarding spatial variability of watercontent and its influence on EMH is likely to be a greatersource of error in the cokriged estimates of log(ECe).

Block cokriging of 193 log(ECe) values for the 1.06-mdepth using 100 by 100 m blocks and 1483 EMH valuesgenerated a rectangular grid of estimated values forlog(ECe). The result provides more detail (Fig. 8) thanis available by simply kriging the ECe data (Fig. 5). Themap of the cokriged estimates for 23 selected quartersections (Fig. 8) also does not exhibit artifacts of stepvariation at quarter-section boundaries (Fig. 7). Highlog(ECe) values occur hi quarter section 4-1, and areasof moderately high log(ECe) include quarter sections4-2, 8-2, 8-4, 9-1, 15-2, and the east side of 9-4 (Fig.


a• +3• +2• +1D MEANa-ia-2

8-2

S-4

4-1

9-1

9-3

16-1

16-3

4-2

4-4

9-2

9-4

16-2

16-4

3-1

3-3

10-1

10-3

15-1

3-2

3-4

10-2

10-4

15-2

Fig. 8. Gray-scale map of the cokriging estimate of log-transformedelectrical conductivity of the soil paste extract (EC,) at 1.06-m depth.The set of quarter sections was chosen based on the perception thatmanagement factors related to water content were less significantin determining apparent electrical conductivity measured at thesoil surface (EMH) than for the set not shown. Patterns of EMH inthe quarter sections not shown suggested domination of variabilityby water content rather than log(ECe), see Fig. Ib.

7). A linear trend of low log(ECe) runs between quartersections 16-3 and 3-1. This trend follows the Cerini clayloam soil unit, which has lower clay content and higherpermeability than the surrounding clays.

CONCLUSIONA fundamental objective of studies of the type de-

scribed here and elsewhere (Leschetal., 1992b,1995a,b;Rhoades and Corwin, 1981; Corwin and Rhoades, 1982,1983) is the assessment of salinization potential. Anestimate of the salinity at depths near the base of theroot zone is useful for identifying areas subject to saliniza-tion. The EMH (or EMv) measurements of apparentelectrical conductivity are made quickly and extensivecoverage of field areas is feasible.

For the BWD data set, both water content and ECeof the soil water are significant factors influencing themeasured values of EMn, but the influence of watercontent decreases with depth while the influence of ECein soil water increases. Water content is controlled byboth soil texture and management factors such as irriga-tion and cropping. In those regions where soil watercontent near the surface was highly variable due tomanagement factors, these variations tended to mask thevariability in EMn due to depth variations in ECe. Anattempt was made to rationalize those variations of EMHnot associated with soil texture contacts by analyzingthe potential of particular management factors to explainobserved soil water content. Extensive data are availablefor irrigation and some variability in soil water contentappears related to irrigation amounts, but soil textureand irrigation cannot account for all of the observedvariability. Thus, prediction of soil water content by a

combination of soil texture and management factors wasnot possible.

An alternative and less ambitious undertaking is thedesignation of particular areas as unsuitable for cokrigingEMH and log(ECe) because of the water content effect.In certain parts of the BWD study area, variations insoil water content occurred in regular patterns with stepvariations at quarter-section boundaries and, in one in-stance, a boundary between crops within a single quartersection. This pattern also appeared in the EMn data.Identification of this pattern in gray-scale maps of EMHpermitted designation of areas where water content waslikely to be dominating variability of EMH. At certainquarter-section boundaries, variation in water content wasassociated with a variation in soil texture. At other quarter-section boundaries, variations in water content are the resultof either irrigation management or some other managementfactor. Isolation of the areas in which management factorswere not significant defined a zone where cokriging ofEMH and the deepest level data for log(ECe) resulted ina map with improved resolution of log(ECe) comparedwith the map obtained by kriging of log(ECe) alone.

ACKNOWLEDGMENTSMr. Kerry Arroues of the Soil Conservation Service pro-

vided the draft soil map. Many members of the U.S. SalinityLaboratory staff contributed to the data collection operations.

water content effect on soil salinity prediction: a geostatistical study using cokriging

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