spatial variability of soil properties at different scales...

Ž .Catena 33 1998 139–153

Spatial variability of soil properties at differentscales within three terraces of the Henares River

ž /Spain

A. Saldana ), A. Stein, J.A. Zinck˜ITC International Institute for Aerospace SurÕey and Earth Sciences, P.O. Box 6, 7500 AA Enschede,

Netherlands

Received 26 September 1997; revised 27 August 1998; accepted 27 August 1998

Abstract

This paper applies statistical and geostatistical procedures to a soil chronosequence on theŽ .terraces of the Henares River NE Madrid to analyse the spatial distribution of several soil

properties and use the contribution of geostatistics to establishing a landscape evolution model ofthe area. Particle-size distribution, pH, calcium carbonate and organic carbon were analysed.Statistical procedures focus on analysing differences between terraces. Geostatistical proceduresidentify short- and medium-range variations within individual terraces at different scales. Standardtransitive variogram models describe the properties of the younger terrace, whereas the linearintransitive model fits the majority of variograms of the older terrace. The analysis confirms andquantifies the decrease in variability of soil properties from young to old deposits, showing thus anincrement of soil homogenisation with time. Ageing of the terraces causes the variables to shownontransitive variogram models with unbounded variances within the observation range. q 1998Elsevier Science B.V. All rights reserved.

Keywords: Chronosequence; Spatial variability; Variogram; Soil homogenisation; Spatial sampling

1. Introduction

Ž .Spatial variation in soil has been recognised for many years Burrough, 1993 . Auseful distinction is that between random and systematic variation. Systematic variationis a gradual or marked change in soil properties as a function of landforms, geomorphic

) Corresponding author. Zaragoza 5, 28804 Alcala de Henares, Madrid, Spain. E-mail: [email protected]´

0341-8162r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved.Ž .PII: S0341-8162 98 00090-3

( )A. Saldana et al.rCatena 33 1998 139–153˜140

Ž .elements, soil-forming factors andror soil management Jenny, 1941 . Random varia-tions entail either differences in soil properties which cannot be explained in terms ofknown soil-forming factors, recognisable at a reasonable sampling density, or measure-ment errors at the scale of the study. Few attempts have been made so far to differentiate

Žbetween systematic and random soil variations in chronosequences Harrison et al.,.1990 .

The soils of the Henares River terraces are arranged in a topo-chronosequence. Theyhave been studied along transects to establish relationships between terrace surfaces andsoil properties, and to understand the evolution of the valley during the Pliocene and

Ž .Quaternary see, e.g., Ibanez et al., 1990, 1994 . However, few soil chronosequence´˜studies were based on sufficient data points within terraces and at different depths toenable the degree and nature of soil variability within and between seemingly homoge-neous land areas to be determined.

On a soil map, variation is displayed using geomorphic and soil knowledge, mainly interms of systematic variation. Map units often contain information on the degree andnature of spatial variation, but the areal proportion occupied by each taxum is not alwaysprecisely determined. Moreover, the patterns of soil distribution and the scale at whichthe soil components are mapped may not be compatible.

In this paper, statistical methods were used to describe quantitatively the variation insoil properties within and between map units. The coefficient of variation and the t-test,for instance, help distinguish variation between units. Geostatistics, based on the theoryof regionalized variables, provides a basis for quantifying the spatial relation amongsample values within map units. It also allows to predict values at unvisited locations by

Ž .kriging and to design rational sampling schemes Webster, 1985 . However, uncriticaluse of geostatistics in soil survey has several drawbacks. The large number of datarequired to estimate a variogram and the assumptions regarding stationarity of thevariation, necessary to measure spatial variation from a single set of observationsŽ .Journel and Huijbregts, 1978 , restrict the application of the variogram to small sections

Ž .of landscape Agbu and Olsen, 1990 . Selection of the appropriate variogram model isstill largely done interactively, which may introduce some subjectivity in the process.Interpolation of data yields maps of single properties at one depth, whereas a real soilbody on the landscape integrates many soil properties at several depths. In spite of theselimitations, a combination of geostatistics with soil classification could improve the soilsurvey method and, in particular, determine the observation density needed to properly

Ž .describe soil units, as suggested by several authors. Stein et al. 1988 appliedŽ .co -kriging to existing soil map delineations to improve the accuracy of prediction ofland qualities at minimal effort and costs. Prior landscape stratification, based on thecorrelation of soil types with major landforms and geological features, was used toestablish the soil map units. Water-table classes based on ground-water table measures

Ž .were also considered in the analysis. Goovaerts and Journel 1995 used indicatorkriging and the Markov–Bayes algorithm to establish the probability of copper andcobalt deficiencies in soils. They showed that the use of soil map information improvesthe delineation of deficiency areas, particularly where the sampling is sparse. On the

Ž .other hand, Voltz et al. 1997 proposed a method combining soil classification andŽ .three interpolation methods kriging, inverse squared distance and nearest neighbour to

( )A. Saldana et al.rCatena 33 1998 139–153˜ 141

map soil properties at regional scale with acceptable precision. Sample information froma reference area and soil observations distributed over the region were also used. Theyfound that estimates from soil classification combined with kriging were the mostprecise.

Determining the number and location of the field observations is difficult in flatalluvial systems, where the inherent spatial variation of soil properties is not easily

Ž .predicted from soil–landform relationships Di et al., 1989 . Alluvial soils are often veryvariable, both laterally and with depth, because changes in both dimensions can resultfrom differences in parent material and depositional processes.

This paper shows results obtained from the geostatistical analysis of soil propertieswithin the terraces generated by Quaternary evolution of the Henares River incision.Stationarity is assumed provided the similar nature, origin of the parent material andpedogenesis of the terraces. The study examines sampling at different spatial scales to

Ž .establish 1 differences among three selected terraces of lower, medium and upperŽ .Pleistocene age and 2 short- and medium-range variations occurring within the

terraces.

2. Material and methods

2.1. Study area characteristics

The study area is in the provinces of Madrid and Guadalajara, between 40830X N andX X X Ž .40850 N and 3810 W and 3830 W Fig. 1 , 40 km NE of Madrid, on the southern slope

of the Ayllon mountain range. The altitude varies from 600 to 900 m above sea level.´The climate is continental Mediterranean, with hot dry summers and cold wet winters.

Fig. 1. Location of the three sample areas in the Henares River valley and structure of the 3-level samplingscheme applied to each terrace.


ŽThe annual mean temperature is 148C and the annual mean rainfall is 400 mm IMN,.1992 . The soil moisture regime is xeric and the soil temperature regime is mesic

Ž .USDA, 1994 . Past climate fluctuations, tectonic movements and lithologic-structuralcontrols have influenced the development of the Henares River valley, resulting in atypical asymmetric valley of central Spain. As many as 20 terraces and a series ofincised glacis-terraces of Pleistocene age have been identified along the right and leftbanks of the river, respectively. The granulometric and petrographic composition of theterraces is very similar throughout, with quartzite, quartz and limestone pebbles within a

Ž .sandy matrix. Calcareous pebbles are absent from the higher terraces ITGE, 1990 . Theages of the terraces probably range from late Pliocene to upper Pleistocene and

Ž .Holocene Gallardo et al., 1987 . Three terraces of lower, middle and upper Pleistoceneage were selected for description and sampling. The soil types developed on them

Ž .include Inceptisols and Alfisols USDA, 1994 . Calcixerollic, Fluventic and TypicXerochrepts are found on the lower and younger terrace. Haploxeralfs, Rhodoxeralfs andPalexeralfs, with Calcic, Petrocalcic, Vertic and Typic subgroups, dominate the middleand higher terraces. The land is mainly used for rainfed agriculture, in particular wheat,barley and sunflowers. Irrigated sunflower and maize are produced on the floodplain andlower terraces. Natural vegetation occurs only in marginal areas with poor agriculturalproductivity; it is mainly the degradation stage of the original climax forest formation.

2.2. Statistics and geostatistics

2.2.1. Variogram estimationStatistics, such as minimum, maximum, mean, median, standard deviation and

coefficient of variation summarise the data. Graphs of the cumulative relative variancefor increasing distances show the distances at which important increases in variance

Ž .occur. To analyse the spatial variability between observation points horizontal andŽ . Žobservations depth vertical , use was made of geostatistical methods Journel and

.Huijbregts, 1978; Cressie, 1991 . Each soil variable that is measured is associated withŽ . Ž .its observation location x. For the ith variable, denoted as z x , the variogram g h isi i

the expected squared difference as a function of the distance h or lag between twolocations, defined by:

1 2g h s E Z x yZ xqh ,Ž . Ž . Ž .i i i2

where x and xqh are two locations, separated by a distance h, at which theregionalized variable is measured, and E denotes the mathematical expectation.

w Ž .xUse of the variogram for interpolation requires E Z x to be constant in the areaiŽ .and that the g h do not depend upon x, according to the so-called intrinsic hypothesis.iŽ . Ž . Ž . Ž . Ž .To estimate g h using n observations of Z x with values z x , z x , . . . , z x ,i i i 1 i 2 i n

Ž .the expectation E is replaced by the average value and a sample variogram g h isˆ i

computed by:Ž .N hi1 2

g h s z x yz x qh ,Ž . Ž .ˆ Ž .Ž .Ýi i j i j2 N hŽ .i js1


Ž . Ž .where z x and z x qh form a pair of points separated by a distance h of whichi j i jŽ .there are N h . Commonly, pairs of observations are grouped into a limited number ofi

Ž .distance classes to ensure that N h is sufficiently large. Each class contains pairs withi

approximately the same distance. The sample variogram was estimated using theŽ .programme SPATANAL Stein, 1993 .

2.2.2. Model fittingThe parameters of a variogram contain the spatial information required for prediction;

Ž .they are estimated for distances h and sample variogram values g h . A variogram is aˆ i

mathematical function that must be able to characterise three important parameters: thenugget variance, the sill variance and the range. The nugget is the positive intercept ofthe variogram with the ordinate and represents unexplained spatially dependent variationor purely random variance. Transitive variograms reach a sill value at which they levelout, at a distance known as the range of spatial dependence. Common transitive models

Ž . Žare the spherical, exponential, Gaussian, hole effect or wave and pure nugget Cressie,.1991 . Continuous, gradually varying attributes are often described by a Gaussian

Ž .variogram. Attributes with abrupt boundaries at discrete and regular spacings the rangeare described by the linear model with a sill. The spherical model describes variablessimilar to the previous ones when the distance between abrupt changes is not clearlydefined. Attributes characterised by abrupt changes at all distances are described by theexponential model. The hole effect model reflects repetition in the data related to theperiodicity of parent material deposition and consequently to the repetition of landformsequences in space. The pure nugget model indicates that there is no spatial dependenceat the scale of investigation. In contrast, a common nontransitive model is the linear one,

Žwhich is suitable to describe attributes varying at all scales Journel and Huijbregts,.1978; Burrough, 1983, 1987; Oliver, 1987 .

Model fitting is required for interpolation procedures and is a previous step to thecreation of soil property maps. Model selection was based on a combination of the R2,

Žor unadjusted coefficient of determination, of a weighted nonlinear regression values.close to 1 indicate a good fit , and interactive interpretation of the sample variogram

values. For example, both the hole effect and the Gaussian models yielded a similar R2

value for the pH at depth d in sample area A , but the experimental variogram did not2 1

show any evidence of periodicity. Therefore, the Gaussian model was selected. Allparameters were estimated by a weighted nonlinear regression procedure using the

Ž .Statistical Analysis System SAS, 1985 .

2.3. Spatial sampling at different scales

A previous knowledge of soil properties and variation relationships with landscapefeatures and statistical sampling can be used to collect spatial information. The collected

Ž . Ž .data z x , . . . , z x , including their sampling locations x , . . . , x , can bei i1 i i n i1 i nŽ .summarised by the sampling design for the ith variable S s z , x , distinguishingi i i

between the variable-specific part of the design and the location-specific part. For thelocation-specific part, random sampling, grid sampling or any other sampling procedure


can be applied. The final sampling design SsjS is the collection of the individuali

sampling designs. The density of observations depends on the variation: a very variableproperty may need to be collected with a greater density than one that is less variable.The sampling density for the random design and for the grid sampling is governed by

Ž .criteria such as the standard deviation of the observations z x .i

Sampling is complicated by the fact that the data are spatially dependent, usually withan unknown degree of spatial dependence, hence the need to cover several scales ofspatial resolution for several variables in a single sample design. van Groenigen and

Ž . Ž . Ž .Stein 1998 distinguish between 1 designs for estimating spatial dependence, 2designs for even spacing of data throughout the area using previous observations and

Ž .ancillary information such as irregular boundaries of the area, and 3 designs foroptimising spatial interpolation. These designs might be totally different even for asingle variable. The design for estimating spatial dependence leads to a clustering ofobservation locations in an area, whereas this is generally avoided when an even coverof samples or a design for optimising spatial interpolation is applied. All theseconsiderations therefore produce a sampling scheme that has to serve several objectives,several variables and an unknown relation between a variable and its observationlocations.

In this study, a multi-scale sampling grid was used to quantify and model the spatialvariability of soil properties. For such a grid, s grid meshes d , js1, . . . ,s, are decidedj

upon in advance, and sampling grids SŽ1., . . . , SŽ s. are defined such that for i- j theaverage distance between points in SŽ i. is less than that in SŽ j.. A multi-level grid hassome advantages over a single grid as single observations may belong to more than onelevel of the design. For example, each design may be concentrated around a single point,that is the centre of all of the designs SŽ i.. This enables the spatial dependence of thedata to be analysed at different spatial scales and a comparison between the scales isthen easy to determine. This provides a compromise where there are variables withdifferent spatial behaviour and when different research objectives are pursued. In such ascheme, there is some clustering and, at the same time, the area is fairly evenly coveredwith observations.

Ž .Three areas of 540 m=540 m were sampled Fig. 1 . Sample area A was located on1Ž . Ž .a low Pleistocene terrace T-29 , A on a middle Pleistocene terrace T-25 and A on a2 3Ž . Ž .high Pleistocene terrace T-15 , with terrace labelling according to ITGE 1990 . Three

Žsampling intervals were selected and the observations arranged in a nested scheme Fig..1 with:

Ø 10 m intervals, to sample the short-range variation at the intra-polypedon scale,giving 49 observations on a square grid of 7 by 7 points;

Ø 30 m intervals, to sample the medium-range variation, giving observations on asquare grid of 7 by 7 points, with the innermost nine locations coinciding with thelocations on the 10-m-interval grid. A distance of 30 m was considered appropriate todescribe the transverse structure of alluvial systems, e.g., variation from the levee to the

Ž .basin. It corresponds to the sampling distances used by Campbell 1978 and Weitz et al.Ž .1993 ;

Ø 90 m intervals, to sample medium-range variation, giving 49 observations on asquare grid of 7 by 7 points, with the innermost nine locations coinciding with the


locations on the 30-m-interval grid. This interval is appropriate for terrace fragments oflimited flat areas, as higher terraces have been strongly dissected by erosion.

The total number of observations was 129, as there was some overlap in the centrallocations. At each observation point, samples were taken at three standard depths:

Ž . Ž . Ž .0.1–0.2 m d , 0.4–0.5 m d and 0.9–1.0 m d . Variables measured in all areas1 2 3Ž .included sand, silt, clay, calcium carbonate and soil reaction pH . Organic carbon was

determined in all areas at d and in A also at the other depths. Particle-size distribution1 1

was determined by the Bouyoucos method, organic carbon by the Walkley–Blackmethod, calcium carbonate with the Bernard calcimeter, and pH with a pH meter in1:2.5 soil–water mixtures.

A test was developed to investigate the significance of the differences in mean valuesŽ .between strata when the observations of a regionalized variable are spatially related.

Suppose p strata are investigated, from every stratum it is known that the spatialŽ .dependency structure is given by the variograms g r for rG0, is1, . . . , p. As ani

estimator for the mean and the variance within the ith stratum we have:

1X Gy1 yn im s ,ˆ i X y11 G 1n i n

where the matrix G contains values of the variogram in the ith stratum; G depends oni i

the variable under study. The variance of the mean is equal to:

y1 1Var m s s .Ž .ˆ i X y1 g1 G 1 in i n

The null hypothesis H that no differences exist between the different strata and the0

alternative hypothesis H can be formulated as:1

H :m sm s . . . sm0 1 2 p

H : at least one m differs from the other mX s, i/ j.1 j i

When the spatial structure is known, this hypothesis is tested with the test statistic:2p

g m̂Ý i ip ž /is12Ts g m y ,ˆÝ pi i

is1 gÝ iis1

which has under H a x 2-distribution with py1 df. Of course, in practical studies, the0

spatial structure has to be estimated from the data. As the test value will only slightly2 Ž .change, the same x -distribution can be used Stein et al., 1988 .

Ž .The variogram parameters were used in the program OPTIM Stein, 1996 thatdetermines the best sampling interval to obtain estimates at a given level of precision foreach soil property, i.e., the necessary sampling spacing to arrive at a preset krigingvariance s 2. For square grids, the highest kriging variance occurs at the centre of four0

grid points. Moreover, the kriging variance is independent from actual observations.OPTIM uses an iterative optimisation procedure. It needs the size of the area, d , as thea

Ž .upper limit for grid spacing d , as well as a minimum grid spacing, d , initially setM m


equal to 0. It then starts with a grid mesh d s1r2 d , yielding a maximum kriging1 a

variance s 2. If s 2 )s 2 then the second grid mesh d equals 1r2 d , d is fixed at1 1 0 2 1 m

zero, and d changes to d . If, on the other hand, s 2 Fs 2, mesh d is set equal toM 1 1 0 2Ž .1r2 d qd , d to d , and d remains unchanged. Next, a grid mesh d is1 a m 1 M 3

determined, yielding new values for d and d in a similar way as d . Iteration stopsm M 22 Ž y4 .when s is determined to a sufficient level of precision e.g., 10 , yielding an0

optimal grid spacing d . Values of s 2 below the size of the nugget effect can neveropt 0

be reached, even with a very small grid mesh. Inversely, values of s 2 above the sill0

value are always reached, even if a single measurement point is used.

3. Results and discussion

3.1. Summary statistics and tests for significance

Table 1 shows summary statistics of sand, silt, clay, calcium carbonate, organiccarbon and pH for the three sample areas at the different sampling depths. The variablessand, CaCO and pH decrease with the age of the terrace presumably as a consequence3

of weathering and leaching. On the contrary, the clay content increases both in depthand from the lower to the higher terraces as a result of clay illuviation and weathering,

Table 1Summary statistics of soil properties for the sample areas

Ž . Ž . Ž .Variable Depth A Ns129 A Ns129 A Ns891 2 3

m s CV m s CV m S CV

Sand% d 35 6 16 31 3 11 25 5 191

d 31 8 24 27 4 16 22 6 252

d 31 5 47 – – – 26 6 213

Silt% d 42 5 11 41 4 9 41 4 101

d 43 6 15 37 6 16 33 5 162

d 45 10 22 – – – 26 5 193

Clay% d 22 3 14 28 4 13 34 6 171

d 27 4 15 36 6 17 45 6 142

d 24 7 28 – – – 48 5 113

pH d 8 0.3 4 6.9 0.3 4 6.7 0.4 61

d 8.2 0.2 2 7.4 0.4 5 7.2 0.3 42

d 8.3 0.2 2 – – – 8.2 0.3 43

CaCO % d 7 6 80 0 0 0 1 173 1

d 14 11 73 1 1 171 0.1 1 5502

d 24 6 25 – – – 7 5 783

O.C.% d 0.7 0.1 14 0.5 0.1 20 0.6 0.1 171

d 0.4 0.2 50 – – – – – –2

d 0.21 0.15 70 – – – – – –3

NsNumber of data for each depth; msmean; ssstandard deviation; CVscoefficient of variation.A , A , A are the sample areas in terraces T-29, T-25 and T-15, respectively.1 2 3

d s10–20 cm depth; d s40–50 cm depth; d s90–100 cm depth.1 2 3


Table 22 Ž .Statistics of the x -test for soil properties at different depths significance at -0.05 level in bold face

Variable Depthbd d d1 2 3

Sand% 607 609 142000Silt% 11.3 1850 1750Clay% 38 625 3320pH 0.01 0.02 4.81

aCaCO % – 485 85303

O.C.% 0.0002 – –

aCalculation considering A and A .1 3bCalculation considering A and A .1 3

whereas the silt content increases with depth in the younger terrace and decreases in theolder one. The clay distribution in the three terraces correlates with the presence of Bwhorizons in A and Bt horizons in A and A at d and sometimes d depth. The1 2 3 3 2

organic carbon of d shows little variation because of similar soil management practices.1

The variation of the properties within terraces is generally small: the CV values are lessŽ .than 50% for texture, pH and organic carbon. There are large CV values up to 550%

for CaCO at d either because of uneven decalcification or local recalcification in the3 2

upper parts of the cambic and argillic horizons. The presencerabsence and concentrationof CaCO are very variable at short-distances, even within individual pedons.3

Differences between terraces are significant for most variables as shown by the testsŽ .at 0.95 confidence level Table 2 . The only nonsignificant differences are for sand and

Table 3Ž .Distance in metres to largest cumulative relative variance for soil properties at different depths

Depth Variable A A A1 2 3

d Sand% 30 10 901

Silt% 10 90 90Clay% 10 30 90pH 10 90 90CaCO % 10 – 903

O.C.% 30 90 90d Sand% 30 30 902

Silt% 30 90 90Clay% 90 30 90pH 30 30 90CaCO % 30 90 903

O.C.% 10 – –d Sand% 30 – 903

Silt% 30 – 90Clay% 30 – 90pH 90 – 90CaCO % 90 – 903

O.C.% 10 – –


Table 4Ž .Best fitting variogram models and ranges in brackets for selected soil properties

Area Depth Sand% Silt% Clay% pH CaCO % O. C.%3

Ž . Ž . Ž . Ž . Ž . Ž .A d Hole 27 Gauss 66 Sph 76 Hole 27 Sph 65 Sph 931 1Ž . Ž . Ž . Ž . Ž .d Sph 131 Sph 84 Exp 71 Gauss 55 Hole 23 Nugget2

d Nugget Nugget Nugget Nugget Nugget Nugget3Ž . Ž .A d Nugget Hole 26 Nugget Sph 161 – Linear2 1

Ž .d Nugget Linear Nugget Exp 50 – –2Ž .A d Nugget Linear Linear Sph 100 – Linear3 1

d Linear Linear Linear Linear Power –2

d Linear Linear Linear Power Linear –3

Sph: spherical; Exp: exponential; Gauss: Gaussian.

organic carbon at d , and for pH at d in all areas as it is strongly influenced by the1 1

homogenisation effect of land management.The distance at which the highest cumulative relative variance occurs is an inherent

feature of each soil property, but is also controlled to a certain extent by the samplinginterval. For example, the distance at which this occurs might be 15 or 20 m, but the

Ž .latter were not used as sampling distances in this study Table 3 . The effect of depth isbest illustrated within terrace A . At d , four variables show the greatest variation at a1 1

distance of 10 m and the other two at 30 m. At d , four variables show the most2

variation at 30 m, whereas for organic carbon and clay this occurs at 10 and 90 m,respectively. At d , the particle size components show the largest variance at 30 m, pH3

and CaCO at 90 m and organic carbon at 10 m. There is little change in the distance of3

maximum variance within terrace A , with the largest variance mainly at 30 and 90 m at2

both d and d . For terrace A , the maximum variance occurs at 90-m distance for all1 2 3

soil properties and at all depths. Thus, in this respect, terrace A is intermediate between2

terraces A and A . The analysis of the sampling interval indicates that the degree of1 3

variation in the soil decreases from the lower to the higher terraces.

Fig. 2. Depth to the gravel layer in terrace A , showing large irregularities.1


3.2. Spatial Õariation

Table 4 displays the best fitting models and ranges of the variograms within thedifferent sample areas. In A , the youngest terrace, the spatial behaviour of the selected1

soil properties is rather diverse and almost all common transitive models could be fittedat depths d and d . At d , however, all the variograms were pure nugget effect, which1 2 3

reflects the absence of spatial correlation at the sampling scale arising from largepoint-to-point variation at short distances. This is probably related to the irregularity of

Ž .the underlying gravel layer Fig. 2 . Within A , the oldest terrace, the most common3

Ž . Ž . Ž .Fig. 3. Variograms and interpolated maps for CaCO % in area A : a depth d ; b depth d ; c depth d . As3 1 1 2 3Žthe model fitting the latter is nugget hence the structure of the variation is not revealed at the scale of

.sampling , it is not possible to create a map.


model is the linear one, indicating that the sill variance has not been reached within themaximum sampling distance of 540 m. This suggests that spatial correlation extendsbeyond the size of the current sampling scheme. The oldest terrace, therefore, has along-range spatial dependence, which results from advanced homogenisation of the soilcover during the Quaternary and correlates with the observed large distance at which the

Ž .highest variance of the selected soil properties 90 m occurs.Of particular interest is the spatial structure of CaCO , because of its somewhat3

deviant behaviour but also because of the important role it plays for soil evolution in thevalley. Figs. 3 and 4 show the variograms and interpolated maps obtained by ordinarykriging in sample areas A and A . Different variogram models provided the best fit to1 3

the same property at different depths within the same sample area. In area A , a1Ž .spherical model with a range of 65 m is obtained at d Fig. 3a , whereas periodicity1

Ž .related to the structure of the river depositional system is evident at d Fig. 3b .2

Homogenisation of calcium carbonate in the surface layer is due to farming practices.The irregular distribution of the CaCO in the gravel layer generates a pure nugget3

Ž . Ž .effect in d of A Fig. 3c . Within A , power model is observed at d Fig. 4a3 1 3 2Ž .whereas the linear model fits the variable at d Fig. 4b . The quadratic model could3

indicate a structural change of CaCO within A , resulting from the leaching of CaCO3 3 3

from the upper terrace.

Ž . Ž .Fig. 4. Variograms and interpolated maps for CaCO % in area A : a depth d ; b depth d . CaCO is3 3 2 3 3

absent in the upper part of the soils of this sample area.


Table 5Ž .Required sampling distances m to predict CaCO % with various precisions3

Ž .Precision % A , d A , d A , d1 1 1 2 3 3

5 48 -1 846 66 -1 4198 )1000 29 )1000

10 )1000 82 )1000

3.3. Effects of sampling at different scales

As a final analysis, the sampling interval required to estimate properties with aprescribed precision was investigated. Optimal grid spacings, depending on the esti-mated variograms, were determined to obtain an estimated map of CaCO with3

Ž .precisions of 5, 6, 8 and 10% Table 5 . The 5% precision can only be obtained atterrace A , depth d , by using a 48 m grid spacing. The 6% precision can be obtained at1 1

terrace A , depth d with a 66 m grid spacing and at terrace A , depth d with a 419-m1 1 3 3

grid spacing, but it cannot be obtained at terrace A , depth d , because of the large1 2

nugget effect. In the case of the terrace A , depth d , the sampling density should be1 3

increased to reveal the spatial structure and shorter range of the soil variables. The 8 and10% precisions require a grid interval of 29 and 82 m at terrace A , depth d ,1 2

respectively, and are always obtained at terrace A , depth d and at terrace A , depth1 1 3

d . Small differences in percentage, even smaller than the determination errors in the3

laboratory, have a large influence on the sampling distances: at A , depth d , a1 1

difference in precision from 6 to 8% leads to a difference in sampling distance from 66to more than 1000 m.

4. Conclusions

As a consequence of soil evolution, increasing clay translocation and calciumcarbonate leaching are evident from younger to older terraces of the Henares River. Claycontents increase with depth. A large coefficient of variation illustrates the irregulardistribution of calcium carbonate at depth mainly coinciding with Bwk or Btk horizons.

The analysis of spatial variation using variograms shows that many standard modelscould be fitted to soil properties in the area. Several types of model describe the

Ž .properties of the younger terrace T-29 , while the linear model fitted most variogramsŽ .for the older terrace T-15 . The older terrace has the largest range of spatial depen-

dence, resulting from the homogenisation of soil properties with increasing time. Thisresults in unbounded models within the range of observation. Thus, the variability of thesoil properties decreases from younger to older deposits, as soil bodies converge toincreasing homogenisation as a function of age.

Development and application of a multi-scale sampling strategy have the advantageŽthat, with a shorter data set some observations belong to more than one level, which

.means cost reduction and time saving , a compromise can be achieved between short-and long-range variation, and that various targets of spatial analysis are met.


Acknowledgements

Ž .This paper is funded by the project NAT89-0996 supported by the CICyT Spain .Ž .We are grateful to the Centro de Ciencias Medioambientales CSIC, Spain , the

Ž . Ž .Regional Government of Madrid Spain and the ITC The Netherlands for theireconomic support.

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