Geoderma 213 (2014) 600–607

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Geoderma

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Geostatistical monitoring of soil salinity in Uzbekistan byrepeated EMI survey s

A. Akramkhanov a,1,⁎, D.J. Brus b, D.J.J. Walvoort b

a Khorezm Rural Advisory Support Service (KRASS), H. Alimjan str. 14, 220100 Urgench, Uzbekistanb Alterra, Wageningen University and Research Centre, PO Box 32, 6700 AA Wageningen, The Netherlands

⁎ Corresponding author. Tel.: +998 62 2262119; fax: +E-mail addresses: api001@yahoo.com (A. Akramkhano

1 Formerly at Center for Development Research (ZEF), UStr. 3, 53113 Bonn, Germany

0016-7061/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.geoderma.2013.07.033

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 May 2012Received in revised form 13 June 2013Accepted 31 July 2013Available online 31 August 2013

Keywords:Geostatistical simulationCalibrationProbabilityCritical thresholdTemporal trendCotton farming

Soil salinization in the lower reaches of Amudarya is a constant threat. High seepage losses in irrigationwater de-livery network and deteriorated drainage network result in rising groundwater tables. The shallow groundwatertable contributes to salinization of the rooting zone which is tackled by leaching at the end or beginning of thevegetation season. However, there is growing concern that the efficiency of the leaching with application ofhigh amounts of water is low, and besides that the leaching effects are not long-lasting. To monitor local soil sa-linity an efficient strategy is developed, using electromagnetic induction (EMI) meter measurements. The mon-itoring strategy is applied and evaluated in a case study in Uzbekistan. The study area of 80 ha was surveyed in2008–2011, at the end of the vegetation season (October–November), with the EMI in vertical dipole mode. Inaddition, at 142 calibration locations (including 28 revisited) both EMI was recorded and the soil was sampledto determine electrical conductivity (ECe) in laboratory. Log-transformed values of EMI and ECe were used tofit a simple linear regression model. Maps of ECe at the four time points were obtained by simulating multiplemaps of log(EMI) using the ordinary krigingmodel. Besides, multiple vectors of regression coefficients were sim-ulated, which were used to transform the simulated log(EMI) maps. Finally, simulated maps of regression resid-uals were added to the transformed log(EMI) fields, and backtransformed. Besides maps with predicted ECe thesimulations were used to derivemaps of the probability that ECe exceeds the critical threshold of 8 dSm−1, and amap of the predicted linear temporal trend in ECe. The results show that in 2008–2011 most of the area was notsaline, with only several spots reaching a predicted ECe of 6 dSm−1. The probabilities that ECe exceeds the criticalthreshold of 8 dSm−1were small, and the predicted percentage of the areawhere ECe exceeds this thresholdwasvery small. Atmost places a slight positive linear trend in ECewas predicted, but this predicted local trendwasnotsignificant at most places. Two areas of concern could be distinguished. First, spots occur displaying pronouncedfluctuations in salinity from year to year with peaks close to the critical threshold, suggesting that these areasmight be prone to soil salinization over short periods of time. Second, in the central part of the area a gradualbuild-up of soil salinity was seen, which calls for interventions to halt or reverse the build-up.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Soil salinization in the lower reaches of the Amudarya River is a con-stant threat. Khorezm is one of the downstream regions in Uzbekistanwheremoderate and high soil salinity levels affect 50–60% of the irrigat-ed area (SIC–ICWC, 2004). Although the area has been known to haveirrigation since ancient times (Tolstov, 1948), it has been furtherdeveloped for irrigation until 1980s and is currently heavily dissectedwith irrigation canals and drains. However, only 11% of the complexnetwork of irrigation canals was lined by 1997 (Vodproject, 1999),which is one of the main reasons of high seepage losses in irrigationcanals, contributing to a shallow groundwater table. On average, annualwater allocation for the Khorezm region amounts to 4.5 km3 to irrigate

998 62 2243347.v), dick.brus@wur.nl (D.J. Brus).niversity of Bonn, Walter-Flex-

ghts reserved.

about 270,000 ha land (SIC–ICWC, 2004). At the field level, flood andfurrow irrigation practices also cause the rise of groundwater table.

The shallow groundwater table ranging from 0.9 to 1.4 m duringirrigation period (Ibrakhimov et al., 2011) contributes to the salinizationof the rooting zone, which is tackled by leaching at the end or beginningof the vegetation season. However, there is growing concern that the ef-ficiency of the leaching with application of high amounts of water is low,and besides that the leaching effects are not long-lasting (Forkutsa et al.,2009). With the deteriorated drainage network and growing uncertaintyin water supply due to the changing environment, the efficiency ofcurrent irrigation practices and leaching activities needs to be evaluated.

Soil salinity is traditionally determined in the laboratory on the basisof total dissolved solids in soil samples. Such analysis is time-consumingand costly, so that in general only a low sampling density can be afforded.For estimating the mean soil salinity in an area this needs not be a prob-lem. However for mapping soil salinity, so that we know where the soilsalinity exceeds critical levels, a much higher sampling density is re-quired. For this aim electromagnetic induction (EMI) instruments have

Table 1Annual average temperature and precipitation for the years of investigation.

Temperature, °C Precipitation, mm

Year Mean Min Max Mean Min Max

2008 11.7 8.1 14.7 78 47 1252009 14.2 14.0 14.6 68 43 1062010 14.1 13.6 15.1 69 58 802011 15.0 13.6 17.9 86a 86a 86a

a Limited data.

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been developed (Rhoades and Corwin, 1981). This EMI-technique hasbeen tested in Khorezm, and has been proven to be suitable for theassessment of soil salinity (Akramkhanov et al., 2010).

Mapping soil salinity with the use of EMI instruments, coupled withdata logger and GPS, therefore is potentially advantageous, as the highdensity of EMI-readings can reveal local anomalies. However, theEMI-readings should be treated as proxies of soil salinity, and must becalibrated against direct measurements of soil salinity, as can beobtained, for instance by measurements of the electrical conductivity.This introduces uncertainty about the soil salinity at the sensed loca-tions. Apart from this, uncertainty is introduced by spatial interpolationof the EMI-readings to obtain full coverage maps of soil salinity ofthe study area. Uncertainty in the covariate maps obtained by spatialinterpolation is commonly ignored in digital soil mapping studies, lead-ing to underestimation of the uncertainty about the soil property.

Often interest is not only in the current salinity status of the soil, butalso in whether this salinity increases, or decreases due to measures.This can be done by repeating the EMI surveys several times. The tempo-ral trend in soil salinity will not be the same everywhere, but can varysubstantially in space due to local conditions. To anticipate this spatiallyvarying temporal trend, we might want to map the temporal trend ofsoil salinity. An important question, central in this paper, is how to obtainmaps of the local trend of soil salinity from repeated EMI surveys. Besides,an important question is how to quantify the reliability of this map, inorder to determine where significant time trends of soil salinity occur.

This leads to the following research objective: to develop an efficientstrategy formonitoring local soil salinity using electromagnetic induction

Fig. 1. Study area (2000 × 400 m) showing transect tracks where EMImeasurementswere maalong the southern edge of the sampling area.

measurements, and to apply and evaluate this strategy in a real-worldcase study in Uzbekistan.

2. Materials and methods

2.1. Study site description and data collection

Khorezm province is located in Uzbekistan in the upper delta plainof the Amudarya River. The province is part of alluvial lowlands withfaint relief; elevations range from 77 to 132 m, with a slight inclinationto thewest. Annual average temperature and precipitation for the yearsof investigation are presented in Table 1. Soils are formed under theinfluence of water from the meandering Amudarya River. The currentlandscape is much altered by man, harnessing the river water, and cul-tivating the land into 270,000 haof irrigated land.Most soils in Khorezmare silt loams (USDA soil texture classification), which together withsandy loams and loams constitute 80% of all soils (Sommer et al.,2010). Agriculture is the major sector in Khorezm providing around40% of employment. Major crops grown in the area are cotton, winterwheat, and rice.

The study area is a farm of 80 ha, part of a regional Cotton ResearchStation (Fig. 1). In 2008, 2009, 2010, and 2011, at the end of the vegeta-tion season (October–November), soil salinity was surveyed withthe electromagnetic induction (EMI) meter (EM38, Geonics Limited,Canada) in vertical dipole mode, sensing depth up to 1.5 m with thehighest sensitivity depth at 0.4 m. The EMI device was coupled withGPS (average accuracy from 3 to 5 m) so that we obtained continuousgeo-referenced EMI-readings along transects (Fig. 1).

At 142 locations (including 28 revisited) both EMIwas recorded, andthe soil was sampled down to 1.5 m at 30 cm increments (Fig. 2). Thesecalibration locations were selected on the basis of the EM38 readings atthe times the calibration samples were collected. Locations were select-ed such that the expected range of EMI-values was covered as good aspossible. These soil samples, separately from each depth, were used todetermine electrical conductivity (ECe) in the laboratory with the helpof a portable conductivity meter (HI98311, Hanna Instruments, USA),and values were averaged for each location. These calibration datawere collected at eight dates during the period March 2008–March

de in 2009. Note, irrigation canal passes along the northern edge and drainage canal passes

Fig. 2. Soil sampling locations to calibrate EMI-readings.

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2011. In the statistical analysis a threshold of 8 dSm−1 was used, sincethe yields of cotton and winter wheat, drastically decline above thisthreshold.

2.2. Statistical methods

An important aspect of this study is to quantify the reliability of theseries of maps of ECe, and of the map of the temporal trend in ECe,accounting for uncertainty in the regression model for ECe and uncer-tainty in the EMI-values at the nodes of a fine grid. A straightforwardmethod to achieve this is geostatistical simulation. Geostatistical simu-lation can be easily integrated with regression analysis in order tostudy the propagation of errors in the regression predictions of ECe inthe maps with interpolated ECe (Heuvelink, 1998; Heuvelink et al.,

EM38-survey 2008

Variogram of log(EM)

Simulated fields of log(EM)

Calibration data

Regression model for log(ECe)

β0, β1 + var. and covarresiduals

Simula-tions of

β0 and β1

Variogram of residuals

OLS

EM38-survey 2009

Variogram of log(EM)

Simulated fields of log(EM)

EM38-survey 2010

Variogram of log(EM)

Simulated fields of log(EM)

ˆ ˆ

ˆ ˆ

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Variogram of log(EM)

Simulated fields of log(EM)

Simulated fields of regres-sion residuals

2008

Simulated fields of regres-sion residuals

2009

Simulated fields of regres-sion residuals

2010

Simulated fields of regres-sion residuals

2011

Fig. 3. Flowchart of the si

1989). Also, with geostatistical simulation a transformation of the targetvariable (ECe) can easily be handled.

The statistical mapping procedure is shown in Fig. 3, and will bedescribed in detail now. First, the EMI-readings along the transects in2008, 2009, 2010 and 2011 were log-transformed. We log-transformedthe EMI data as the untransformed data showed positive skew, whichdisappeared largely by the log transformation. This is important as inthe simulation described hereafter, we assumed that the EMI data werenormally distributed. These log-transformed measurements were usedto fit an ordinary kriging model for each year separately. Variogramswere estimated by the method-of-moments. These models were usedto simulate for each year 1000 maps of log(EMI) by sequential Gaussiansimulation (Goovaerts, 1997). For both variogram estimation and condi-tional geostatistical simulation we used the add-on R package gstat(Pebesma, 2004).

Maps of pre-dicted ECe, prob-

ability ECe>8, temporal trend

Simulated fields of log(ECe) 2008

Simulated fields of log(ECe) 2009

Simulated fields of log(ECe) 2010

Simulated fields of log(ECe) 2011

mulation procedure.

Table 2Summary statistics for the collected data.

Year N Mean SD Min Max Skewness Skewnessafter logtransformation

Survey dataEMI 2008 16,068 50 23 12 203 1.9 0.1EMI 2009 10,584 67 30 19 225 1.1 −0.1EMI 2010 8270 68 37 14 305 2.2 0.3EMI 2011 14,755 52 22 12 182 1.3 0.0

Calibration dataEMI 2008–2011 142 69 35 6 196 1.4 −0.6ECe 2008–2011 142 3.2 2.0 0.6 10.9 1.4 −0.1

SD—standard deviation; EMI (mSm−1); ECe (dSm−1).

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Second, a linear regression model for log(ECe) with log(EMI) as asingle predictor was fitted by ordinary least squares, leading to esti-mates of the two regression coefficients and their variance-covariancematrix (Draper and Smith, 1998). The log transformation of ECe slightlyimproved the model. A single model was fitted on all calibration datacollected at eight different times. It appeared that time-specific modelswere not significantly better than the single time-invariant model. Theestimated regression coefficients and their variance–covariance matrixwere used to simulate 1000 vectors of regression coefficients (interceptand slope), assuming a bivariate normal distribution. These simulatedregression coefficients were used to transform the simulated fieldsof log(EMI) into fields of expected log(ECe), by multiplication with asimulated slope and adding a simulated intercept.

Finally, fields of simulated regression residuals, obtained by se-quential Gaussian simulation, were added to these fields of expectedlog(ECe). To simulate these fields with regression residuals, theresiduals at the calibration locations were used to compute an ex-perimental variogram for each of the eight dates at which calibrationdata were collected. These date-specific experimental variogramswere then pooled, i.e. for each distance class (lag) averages across theeight dates of the semivariances were computed, using the numbersof pairs of points as weights. A model was fitted to this pooled experi-mental variogram. This fitted variogram was then used to simulate foreach year 1000 maps of regression residuals, assuming temporal inde-pendence of the regression residuals. After adding the fields with simu-lated regression residuals to the fields with expected log(ECe), theresulting fields were backtransformed by exponentiation.

y = 0.76x - 2.12 R² = 0.44

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 1.0 2.0

log(

EC

e), d

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Fig. 4. Scatter plot and fitted regression line for t

These simulations were finally used to derive for each year: i) a mapof the predicted ECe; ii) a map of the probability that ECe exceeds thecritical threshold of 8 dSm−1; iii) amap of the predicted linear temporaltrend in ECe. The first map was simply obtained by computing for eachsimulation node the average of the 1000 simulated ECe-values. The sec-ond map was obtained by counting for each simulation node the num-ber of simulated ECe-values N8 dSm−1, and dividing by 1000. The thirdmap was obtained by ordinary least squares fitting of a straight line ateach simulation node, using the simulated ECe as response variableand the year as predictor. For each simulation node this is repeated1000 times, resulting into 1000 fitted linear time trends per simulationnode. The average of the 1000 fitted linear trends was used as a predic-tion of the linear trend. Its standard error was obtained by the standarddeviation of the 1000 fitted trends.

3. Results

3.1. Descriptive statistics

Table 2 presents the summary statistics of the EMI surveys andof thecalibration data (EMI and ECe). Themean EMI-values in the survey datarange from 50 to 52 mSm−1 during 2008 and 2011 to 67–68 mSm−1 in2009–2010, respectively. There is a considerable range between theminimum and maximum EMI-values, particularly in the year 2010,with a range of 291 mSm−1.

EMI-values in the calibration data, with an average of 69 mSm−1,

are similar to EMI-values in the survey data. The mean value of ECe3.2 dSm−1 indicates a slight soil salinity level.

Both EMI and ECe measurements showed moderate to strong skew;after log-transformation skewness was close to 0 (Table 2).

3.2. Regression model for log(ECe)

Fig. 4 shows the results of the regression analysis. The residual vari-ancewas 0.195. The percentage of variation accounted for was 44%. Thispercentage was lower compared to other studies reported in the litera-ture. This could be due to the narrow salinity ranges in the calibrationdata (Akramkhanov et al., 2010), as well as the fact that in flat irrigatedlands, irrigation and soil management can dominate intrinsic soil char-acteristics, (Akramkhanov et al., 2008; Hendrickx et al., 1992). Note thatthe residual variance is accounted for in the simulation procedure. A

3.0 4.0 5.0 6.0

), mSm-1

he relation between log(EMI) and log(ECe).

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60.675 60.680 60.685 60.690 60.695

20082009

20102011

ECe (dSm−1)

2

3

4

5

6

Fig. 5. Map of predicted ECe for the years 2008–2011.

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large residual variance will lead to a large variation in simulated ECe-values, reflecting our uncertainty about soil salinity.

3.3. Geostatistical simulation

The experimental variogramof the regression residuals, pooled acrossthe eight dates, showed some spatial structure. An exponential with nug-getmodel (Webster andOliver, 2001)wasfitted to this pooled variogramwith a nugget of 0.087 (dS2 m−2), partial sill of 0.078 (dS2 m−2), anda distance parameter of 0.00052 decimal degrees, which correspondswith approximately 120 m.

Geostatistical simulation showed that in 2008–2011most of the areawas not saline, with only several spots reaching a predicted ECe of6 dSm−1 (Fig. 5). In 2008 spots with relatively high predicted ECe-values were located in the western part of the study area, and eastof the center. The same spots were more pronounced and grew in sizeduring 2009–2010. During the last survey in year 2011 the predictedECe-values were mainly low, with less pronounced areas due to smallerspatial variation, rarely exceeding 4 dSm−1.

The location-specific probabilities that ECe exceeded 8 dSm−1 weresmall with a maximum of about 25% (Fig. 6). For the years 2008 and

2011 the exceedance probabilities were smaller than for the years 2009and 2010, which is in accordance with the results for the predicted ECe.

Besides the maps with the location-specific probabilities we com-puted histograms of the percentage of the area where the criticalthreshold of ECe exceeded 8 dSm−1 (Fig. 7). The counts in the histo-grams are the number of simulations. So for each simulated field ofa given year the areal percentage exceeding the threshold was comput-ed, leading to 1000 areal percentages. The histograms illustrate our un-certainty about the size of the area where ECe was exceeded. Theaverage of the areal percentage across the 1000 simulations is the pre-dicted areal percentage exceeding the critical threshold (red verticalline in histogram). In 2008 the predicted percentage of the area whereECe exceeded 8 dSm−1 was 0.66% only. This percentage increasedover the years to 1.68% in 2009 and 2.48% in 2010, and then decreasedagain to 0.63% in 2011.

The map of the predicted linear trend in ECe (Fig. 8) shows that inthe largest part of the study area there was a slight positive timetrend in ECe of about 0.5 dSm−1 per year. At the same time, thehigh salinity spots in the western part of the study area and eastof the center displayed a negative time trend of up to 1.0 dSm−1

per year. These location-specific time trends were statistically not

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60.675 60.680 60.685 60.690 60.695

20082009

20102011

Prob.

0.00

0.05

0.10

0.15

0.20

0.25

Fig. 6. Map of location-specific probability that ECe exceeds 8 dSm−1.

Areal percentage where ECe > 8 dSm−1

freq

uenc

y

0

50

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200

250

300

2008

0 1 2 3 4 5 6 7

2009

0 1 2 3 4 5 6 7

2010

0 1 2 3 4 5 6 7

2011

0 1 2 3 4 5 6 7

Fig. 7. Histograms of the predicted areal percentage where ECe exceeds 8 dSm−1.

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trend

−1.0

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Fig. 8. Predicted linear trend of ECe from 2008 to 2011.

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significant at most places. At sites where the probability of a positivetrend exceeds 0.90, the positive trend is significant (α = 0.10),where it is smaller than 0.10, there is a significant negative trend(Fig. 9). As can be seen the size of the area with a significant (positiveor negative) trend is small.

In the central part of the study area an area occurswith a statisticallysignificant (probability N0.9) positive trend N0.5 dSm−1 per year. Fluc-tuations in soil salinity between the years in this area were small; thebuild-up of soil salinity seems to be more consistent here. This areaindicates that interventions might be necessary to arrest soil salinitybuild-up. Landmanagement practices in areaswhere statistically signif-icant negative trends were observed, may help to reduce soil salinitybuild-up in other, adjacent areas.

We think that the observed trends provide evidence of the effects ofcarried out management practices over the considered years. Relativelyhigh soil salinity spots in the western part and to the east of the center,exhibited stronger fluctuations from year to year compared to the otherlocations of the study site. Consequently, such areas are prone to soilsalinization over short time periods.

The observed changes in ECe can be linked to driving environmentalfactors. In 2008 and 2011 there was a considerable shortage of surfacewater, whereas in 2009 and 2010 water was abundant. According to“Amudarya” Basin Water Organization data (http://www.cawater-info.net/amudarya/index_e.htm) in 2008 and 2011 the Khorezm provincereceived only 2.4 and 2.6 km3 of water for irrigation, instead of theplanned 4.2 and 4.6 km3, respectively. This means that only 56–57% ofthe planned water demand could be supplied in 2008 and 2011 for theprovince. The interaction of reduced water supply and soil salinitybuild-up is complex. However, the water shortage in 2008 and 2011may have contributed to a lower groundwater table, and subsequentlyto a reduced build-up of salts in the soil profile.

4. Discussion and conclusions

In this paper we describe a cost-efficient, relatively simple andstraightforward strategy for local monitoring of soil salinity (ECe). The

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Fig. 9. Map of the probability of a posit

strategy requires as input repeated EMI surveys at a high spatial density,and laboratory measurements of ECe at a set of locations (calibrationdata). The core of the method is a geostatistical model for log(EMI), asimple linear regressionmodel for log(ECe) using log(EMI) as predictor,and a geostatistical model for the regression residuals. These threemodels are used to simulate multiplemaps of ECe, one series per surveyyear, from which various maps depicting quantities to describe statusand trend of soil salinity, as well as maps of the uncertainty aboutthese quantities, can be derived. We think that this monitoring strategycaptures the most important sources of uncertainty. We would like tostress here that this quantification is conditional on the fitted models.Other models will lead to other uncertainties. A model-independentquantification of uncertainty can only be obtained by independent val-idation (Chatfield, 1995). When these validation locations are selectedby probability sampling, model free estimates of validation criteriasuch as the Mean Squared Error of Prediction, can be obtained (Bruset al., 2011).

In the study area the probabilities that ECe exceeds the critical thresh-old of 8 dSm−1 were small, and the predicted percentage of the areawhere ECe exceeds this threshold was very small. At most places a slightpositive linear trend in ECe was predicted, but this predicted local trendwas not significant at most places at a confidence level of 0.90. Twoareas of concern could be distinguished in the study site. First, spotsoccur displaying pronounced temporal changes in salinity from year toyear, with peaks close to the critical threshold, suggesting that theseareas might be prone to soil salinization over short periods of time. Sec-ond, in the central part of the area a gradual build-up of soil salinity wasseen, which calls for interventions to halt or reverse the build-up.

Besides, there were some areas where a negative trend was ob-served. Such areas might be helpful in identifying management prac-tices to be applied in other areas at risk, to reduce soil salinity build-up.

In order to keep the mapping approach as simple as possible the EMIdata of the four yearswere simulated separately. So, in geostatistical sim-ulation of EMI for a given year, the EMI data of other yearswere not used,as can be done, for instance, by simulatingwith the cokrigingmodel. Thiswould require fitting a model of coregionalization. However, we do not

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expect much gain in using the EMI data of other years as covariables,due to the high spatial density of the EMI-readings.

Another simplification is that we assumed that the regression resid-uals are uncorrelated in time. This might be unrealistic. When dueto local circumstances ECe at a location in a given year is, for instance,larger than the expected ECe on the basis of the EMI-reading at thatlocation (positive regression residual), then in other years this residualmight also be positive, as the circumstances responsible for the positiveresidualmight not have changed. The reason thatwe assumed temporalindependence of regression residuals is lack of data. The calibration datadid not allow the fitting of a space–time model. Assuming uncorrelatedresiduals when in reality the residuals are correlated, leads to underes-timation of the uncertainty about the location-specific trend.

This brings us to the sampling design of the calibration data. Indesigning this calibration sample we must decide both on the numberof calibration locations (spatial sample size) and the spatial pattern.Moreover, as we are considering repeated surveys (multiple years),we must also decide on the space–time pattern (Brus and de Gruijter,2011).With this respect, an important question is whether it is efficientto resample locations, and if so howmany, all of these or a subset only?The calibration data are used for calibrating the space–time model,more specific for deciding on the structure of the relation between ECeand EMI (structure of the trend, e.g. log–log linear as in this paper),and estimation of the regression coefficients and the space–timevariogram parameters.

For calibration of the trend part of the model a spreading in EMI-space is important. We would like to have locations with small andhigh EMI-readings, and locations with intermediate EMI-readings, sothat we can decide on the structure of the relation. In practice thisimplies that preferably the calibration locations are selected shortlyafter the first EMI survey, so that these data can be used in the selectionprocess. Note that there is no reason for random selection of the calibra-tion sites as the data are not used in design-based statistical inference.In general random selection of locations for calibration is suboptimal(Brus and Heuvelink, 2007).

A simple method for spreading the calibration locations in EMI-space is to cluster the sensing locations by k-means on the basis of theEMI-reading into n clusters (n is the number of calibration locationsper year). The centroids of these clusters are used as calibration loca-tions. A similar approach, based on fuzzy k-means with extragradeswas proposed by de Gruijter et al. (2010). If we want to avoid strongspatial clustering of the calibration sites, then we can use the spatialcoordinates as (additional) classification variables in k-means cluster-ing, as proposed by Brus et al. (1999).

The calibration data are also used for calibration of the space–timevariogram of the regression residuals. We are not aware of papers onsampling design for estimating space–time variograms. For estimatingspatial variograms, Lark (2002) showed that in the optimal samplingdesign sampling locations are spatially clustered. The degree of thisclustering depends on the underlying model. A simple straightforwardmethod to account for this is to supplement several of the samplinglocations obtained by the k-means method by a few locations at shortdistance from these starting locations, so that several clusters of pointsare obtained. For estimating space–time variograms we expect thatclusters of observations in space–time are beneficial. For that reason,we recommend, for the time being, to revisit the calibration locationsat subsequent sampling times, leading to a static-synchronous design

(de Gruijter et al., 2006). This enables estimation of the time variogram.Research into optimal sampling design for calibration of space–timemodels is an interesting and relevant topic for the future.

Acknowledgments

This study was funded by the German Ministry for Education andResearch (BMBF; Project Number 0339970A).

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