Using Multivariate Geostatistics to Assess Patterns of Spatial Dependence of Apparent Soil Electrical Conductivity and Selected Soil Properties

The apparent soil electrical conductivity (ECa) was continuously recorded in three successive dates using electromagnetic induction in horizontal (ECa-H) and vertical (ECa-V) dipole modes at a 6 ha plot located in Northwestern Spain. One of the ECa data sets was used to devise an optimized sampling scheme consisting of 40 points. Soil was sampled at the 0.0–0.3 m depth, in these 40 points, and analyzed for sand, silt, and clay content; gravimetric water content; and electrical conductivity of saturated soil paste. Coefficients of correlation between ECa and gravimetric soil water content (0.685 for ECa-V and 0.649 for ECa-H) were higher than those between ECa and clay content (ranging from 0.197 to 0.495, when different ECa recording dates were taken into account). Ordinary and universal kriging have been used to assess the patterns of spatial variability of the ECa data sets recorded at successive dates and the analyzed soil properties. Ordinary and universal cokriging methods have improved the estimation of gravimetric soil water content using the data of ECa as secondary variable with respect to the use of ordinary kriging.


Introduction
The quality of soil data collection for precision agriculture has a very important influence, since it has been found that acquisition of exhaustive information in this phase supports the use of geospatial technologies for the estimation of soil spatial variability and later on assists in the determination of "management units. " However, for assessing the soil spatial variability, a large number of samples are generally needed, which considerably increases costs of sampling and analysis. Notwithstanding, the sampling process can be improved, using soil variables that can be recorded or measured quickly, which can help in enhancing the estimation of other soil properties more difficult to measure. in agricultural production and environmental conservation. Thus, these data are essential for monitoring the temporal condition of the soil and application management processes [6]. Therefore, the EC a parameter is used as an aid in precision agriculture, to promote the evaluation of the spatial variability of soil and the definition of management units. The use of geostatistics has great advantages because it allows the study of the spatial variability of soil properties. Kriging is a geostatistical method that can be used to predict the value of soil properties in unsampled locations, favouring the application of differentiated soil management in precision agriculture. Several authors have devised soil sampling schemes directed by properties that directly or indirectly influence crop yield [7][8][9][10], and the success of this approach depends on the use of variables that are quickly and easily measured, such as EC a .
Based on the above rationale, the objectives of this work were as follows: (1) to analyze the spatial dependence of successive EC a data sets, (2) to assess the spatial variability of soil texture attributes using a soil sampling scheme directed by soil EC a , and (3) to improve the estimation of the spatial variability of soil variables such as soil water content through multivariate geostatistics using EC a as secondary information.

Study Site.
The experimental field is 6 ha in surface and it is located in Castro Ribeiras de Lea (Lugo, NW Spain). Geographic coordinates are 43 ∘ 09 49 N and 7 ∘ 29 47 W, average elevation is 410 m, and mean slope is 2% (Figure 1).
The area where the field is located is considered to be representative of both the topographic patterns and the main soil type of the region "Terra Cha, " which is characterized by an extensive livestock production, on a landscape with seasonal conditions of hydromorphy, due to impeded drainage.
The crop succession of the experimental site was fallowsilage corn (Zea mays L.) under no-till farming during the The soil was classified as a Gleyic Cambisol [11], and it was developed over Tertiary-Quaternary sediments; the parent material from the Quaternary has high gravel content and it is underlain by clayey Tertiary sediments with low saturated hydraulic conductivity [12]. According to Neira Seijo [13] the soil profile of the studied field is represented by the sequence A p -B w -B tg , developed on successive sedimentary layers with heterogeneous soil particle size distribution ( Table 1). The soil texture of the fine earth (<2.00 mm) was sandy-loam at the A p horizon, sandy-clay-loam in B w horizon, and clayey in the horizon B tg and there was a general clay increase with soil depth. Moreover, the A p and B w horizons were characterized by a high content of gravel, attaining 37% and 45%, respectively. The organic matter content was rather high on the A p horizon (5.05%) contrasting with the lower contents at the underlying horizons of the soil profile. The climate of the Terra Cha region is classified as maritime temperate climate (Cfb, according to Köppen), characterized by warm summers and no dry season; average annual rainfall is as high as 930 mm. EM38-DD [14]. This device consists of two integrated EM38 units oriented in the horizontal and vertical dipole positions, providing simultaneous measurements for the two dipoles modes; in the vertical dipole mode, the primary magnetic field is thought to effectively penetrate to a depth of about 1.5 m, while in the horizontal dipole position EM38-DD is thought to be effective for a shallower soil depth estimated at about 0.75 m [14].

Apparent Soil Electrical Conductivity Measurements and
To complete continuous record of the apparent soil electrical conductivity in horizontal dipole (EC a -H, mS m −1 ) and in vertical dipole (EC a -V, mS m −1 ) (Figures 2(a) and 3), the EM38-DD was installed in a car built with plastic materials (Figure 2(b)). In addition, GPS RTK was used for georeferencing the recorded measures.
The reference measurements of EC a -H and EC a -V were performed on 23/6/2008 at 1859 sampling points following the scheme presented in Figure 2(a). The soil sampling scheme was devised using the software tool ESAP-RSSD (response surface sampling design), based on a multiple linear regression model [7,9]. This software aims to optimize the position of new sampling points considering apparent soil electrical conductivity (EC a ) measured with horizontal (EC a -H) and vertical dipoles (EC a -V) (Figure 2  addition continuous measurements of EC a -H and EC a -V were previously taken in the experimental field on 14/3/2008 and 3/4/2008, as shown in Figure 3. Note, however, that the schemes of the continuously recorded EC a data sets taken in the three successive dates were different as shown in Figures 2(a), 3(a), and 3(b).
In the 40 points selected during the EC a campaign of 23/6/2008, soil samples were taken at the 0.0-0.3 m depth with a manual soil probe. Soil texture, soil water content, and electrical conductivity of saturated paste extracts were determined using standard methods. Soil texture (clay, silt, and sand, in g kg −1 ) was determined by the sieve-pipette method, following Camargo et al. [15]; in this method a mixture of sodium hydroxide and sodium hexametaphosphate was used as chemical dispersant. The gravimetric soil water content ( , %) was obtained after weighing the mass of the wet and dry sample, according to Camargo et al. [15]. To determine the electrical conductivity of soil saturated extracts (EC e ), a mixture of soil and distilled water of 1 : 1 was prepared as proposed by USDA [16]; electrical conductivity measurements were performed using a conductivity meter ORION Model 122.

Statistical and Geostatistical Analysis.
All the values were statistically analyzed using SPSS package 11.5 at 5% level of SNK (Student-Newman-Keuls) method ANOVA. The test of normality Kolmogorov-Smirnov was used to test the normality of data with probability of error 1% ( < 0.01). The correlation was calculated with the correlation coefficient of Pearson.
The analysis of the spatial variability of soil physical properties was conducted using the experimental variogram; the fitting of variogram model was performed using the method described by Vieira [17], based on cross-validation. Initial analysis showed that the variogram of any studied properties showed a trend, so the universal kriging was used in these cases, in which the residual variogram is required [18]. For those variables that showed no trend, ordinary kriging was used. The degree of spatial dependence (SD) was determined according to the following: where 0 is nugget effect and ( 0 + 1 ) is the sill ( 0 + 1 ) according to Cambardella et al. [19], which is considered as high (SD ≤ 25%), moderate (SD = 25-75%), and low (SD ≥ 75%). Cross-variogram was used to study the spatial correlation between soil variables; when there was a trend in some of these variables, universal cokriging was used [18], instead of ordinary cokriging. The software used to perform ordinary kriging, universal kriging, and universal cokriging was Gstat [20]. In cokriging the covariance matrix must be positive and definite [18,[21][22][23]. The use of cokriging was used only for a couple of attributes that showed correlation coefficient values (| |) greater than 0.5.

Results and Discussion
Statistical analysis of the data ( Table 2) indicates that there is great variation between samples, in accordance with low (CV ≤ 12%) and middle (CV = 12-60%) variation coefficient values, by classification of Warrick and Nielsen [24]. It is verified that the apparent electrical conductivity of the soil (EC a ) measurement with the horizontal dipole (EC a -H) has lower CV than the measurements with the vertical dipole (EC a -V). This fact can be explained because the vertical dipole mode explores a larger volume of soil than the horizontal dipole, and there is greater heterogeneity in those variables that affect the EC a values, mainly clay content, organic material, water content in the soil, porosity, salinity, and so forth [2][3][4][5].
Only data EC a -V and EC a -H sampling in 23/6/2008 did not show differentiation by the average test (ANOVA) between the different sampling dates.  The values of the electrical conductivity of the saturation paste extract of the soil (EC e ) are higher than the values of EC a -V and EC a -H; this fact is because EC e is a parameter that depends on the content of anions and cations in the soil solution; the water content is homogeneous in all samples, because the sample is saturated with water, and the soil apparent electric conductivity values measured with the equipment EM38-DD (EC a -V and EC a -H) are very influenced by the soil water content [2,3,5]; and the water content in the soil is variable along the field. EC a -V and EC a -H measured on several sampling dates (14/3/2008, 3/4/2008, and 23/6/2008) showed lognormal distribution (Table 2). Other attributes studied showed normal frequency distribution (EC e , clay, silt, sand, and soil water content).
In the geostatistical analysis, lognormal transformation was used for properties that showed lognormal distribution.
The highest values of coefficient of correlation between EC a variables and clay and silt content are on the first measurement date (14/3/2008); on this date the soil moisture is lower coincided with data of precipitation and evapotranspiration (Table 3). Grandjean et al. [25] describe that soil with moisture lower is ideal for characterization of soil bulk density and of soil texture, using measurements of electrical conductivity.
The coefficient of correlation between EC a -V 23/6/2008 × ( = 0.685) and EC a -H 23/6/2008 × ( = 0.648) was moderately positive (0.5 ≤ < 0.8), confirming the correlation between the values of EC a -V and EC a -H and the water content in soil, because according to Grandjean et al. [25], under wet conditions, electrical conductivity measurements are dominated by the effect of water content, which tends to hide the influence of the other factors.
The values of log EC a -V are affected by the groundwater level, so the variogram follows the trend in the ground water level ( Figure 4). As can be seen on standardized variograms with the value of the sample variance, data from EC a -V measurement on 14/3/2008 and 3/4/2008 present a trend, following the same pattern of the digital elevation map of the area (Figure 1(b)). Analyzing standardized variograms for log EC a -H data can be seen that only shows trend for the variogram of 14/3/2008 and 3/4/2008, but not for the variogram of 23/6/2008; on this date the water table was probably located below the depth of soil investigated with the horizontal dipole mode.
Corwin and Lesch [4] found higher values of correlation between data from log EC a -V and log EC a -H and electrical conductivity of the saturation extract (EC e ) and clay content, but lower than those found for log EC a -V and log EC a -H and the water content in soil. Martínez and Vanderlinden [26] described a higher correlation between EC a and water content in loamy soils, while in clay soils the correlation was lower. The correlation coefficients for EC e , silt, and clay with the log EC a -H are greater than with the log-EC a -V.
In order to improve the correlation between the values of EC a -V and EC a -H with clay content, soil water content should be as homogeneous as possible within the study area, better if 6 The Scientific World Journal its value is closer to field capacity and unlike the water table is as low as possible, so the best time to take measurements under these conditions would be in the autumn, when there was heavy rainfall, although under these conditions the water table probably would not have ascended enough to be close to the surface.
The initial geostatistical data analysis showed that the physical properties of the soil (clay, silt, sand, and gravimetric water content) showed no trend, then being possible the estimate of the variable using the original data with ordinary kriging. Moreover, EC e data and apparent electrical conductivity of the soil (EC a -V and EC a -H) on several sampling dates show trend in Figure 3; the semivariance value is not stabilized around variance value of data, and the universal kriging was used to construct the maps of spatial variability of these variables.
The fitted variogram parameters (Table 5) show that the spherical model was the fitted model to the properties under study, according to Cambardella et al. [19], Goovaerts [18], Vieira [17], and Siqueira et al. [27] describing this model; it is usually best fitted to the properties of soil and plant. All attributes had low values of nugget effect ( 0 ). Range values (a) varied from 40.00 m (log EC a -H Residual 3/4/2008 ) to 130.00 m (clay, silt, and soil water content). The degree of spatial dependence between samples was high (SD ≤ 25.00%) across the study, the exception being log EC a -H Residual 14/3/2008 which presented a moderate degree of spatial dependence (SD = 31.67%).
The spatial variability maps obtained with universal kriging ( Figure 5) show that there is a similarity between the maps EC a -V (Figures 5(a), 5(c), and 5(e)) and EC a -H ( Figures  5(b), 5(d), and 5(f)) on several sampling dates, with further differentiation of maps of EC a -V and EC a -H on the measured data on 23/6/2008 (Figures 5(e) and 5(f)) when the water table level was lower.
It is observed that the maps of EC a -V and EC a -H ( Figure 5) and the map of the water content in soil (Figure 6(e)) obtained with ordinary kriging (Figure 6(e)) look similar, following the same pattern of digital elevation model (Figure 1(b)).
The map of the electrical conductivity of the saturation extract (EC e , Figure 6(a)) shows inverse behaviour to maps EC a -V and EC a -H ( Figure 5). Moreover, the map of spatial variability of clay content in the study area (Figure 6(b)) shows no similarity to maps EC a -V and EC a -H ( Figure 5); this fact is also repeated with silt ( Figure 6(c)) and sand ( Figure 6(d)). Table 6 presents the fitting parameters cross-variogram between × EC a -V ( = 0.685) and × EC a -H ( = 0.648). The cross-variograms were fitted to a spherical model with the same range compared to single variograms to obtain a linear model coregionalization ( Table 6).
The spatial variability maps constructed using ordinary and universal cokriging (Figure 7) demonstrate that the use of the soil apparent electrical conductivity measured by electromagnetic induction (EC a -V and EC a -H) on 23/6/2008 was a secondary variable that improves the estimation of the soil water content using cokriging. This improvement in the estimation of can be observed in Table 7, where it showed an increase in the value of the correlation coefficient between the measured and the estimated values from cross-validation using ordinary cokriging with log-EC a -V (0.746) and with log-EC a -H (0.756) as secondary variables with respect to use of ordinary kriging (0.637). Moreover, in the case of the soil water content map obtained with ordinary cokriging using as secondary data EC a -H (Figure 7(b)) is less smooth than the map obtained with ordinary kriging (Figure 6(e)).

Conclusions
When taking into account all the soil properties studied, EC a and gravimetric soil water content measured at the same date, that is, 23/6/2008, showed the highest coefficients of correlation Table 4. Moreover, EC a showed higher coefficients of correlation to clay and silt content than to silt content, and the strength of the correlation was higher for the first EC a recording date, that is, 14/3/2008, when the soil moisture was lower. Thus, coefficient of correlation of EC a with silt and clay content showed a trend to increase the soil moisture decreased; this result suggests the usefulness of recording EC a on successive dates with different soil water contents.
The spatial patterns of spatial variability of the logarithmic values of apparent soil electrical conductivity (EC a ) and the electrical conductivity of the soil saturated paste (EC e ) were modeled by universal kriging, whereas those of sand, clay, silt, and gravimetric water content were modeled by ordinary kriging. The use of cokriging with EC a data as secondary variable improved the estimation of the gravimetric soil water content with respect to the use of kriging.       Ciência e Tecnologia do Estado de Pernambuco (Brazil)) and they also thank CNPq for the scholarship DCR-Regional Scientific Development awarded to the first author. Also thanks are given to FAPEMA, MA, Brazil, for funding the publication of this paper. The authors would like to thank two anonymous reviewers for the comments that undoubtedly improved the quality of this paper.