Effect of Land Use Types on the Spatial Prediction of Soil Nitrogen

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1 Effect of Land Use Types on the Spatial Prediction of Soil Nitrogen Mingkai Qu Department of Resource and Environmental Information, College of Resources and Environment, Huazhong Agricultural University, Wuhan , China Weidong Li 1 and Chuanrong Zhang Department of Geography and Center for Environmental Sciences and Engineering, University of Connecticut, Storrs, Connecticut Shanqin Wang 1 Department of Resource and Environmental Information, College of Resources and Environment, Huazhong Agricultural University, Wuhan , China Abstract: Mapping the spatial distribution of soil nutrient contents from sample data has received much attention in the recent decade. Accurately mapping soil nutrients purely based on sample data, however, is difficult due to the sparsity and high cost of samples. Land use types usually influence the contents of soil nutrients at the local level and it is desirable to integrate such information into predictive mapping. The area-and-point kriging (AAPK) method, which was proposed recently, may provide an interpolation technique for such purposes. This study mapped the soil total nitrogen (TN) distribution of Hanchuan County, China, using AAPK with sample data (consisting of 402 points) and land use information. Ordinary kriging (OK) and residual kriging (RK) were compared to evaluate the performance of AAPK. Results showed that: (1) land use types had important impacts on the spatial distribution of soil TN; (2) measured data at 135 validation locations had stronger correlation with the data predicted by AAPK than by RK and OK, and the mean error and root mean square error with AAPK were lower than with RK and OK; and (3) AAPK generated smaller error variances than RK and OK did. This suggests that AAPK represents an effective method for increasing the interpolation accuracy of soil TN. It should be pointed out that some of the land use polygons used in this study are very large and complex, which might impact the effectiveness of AAPK in improving the prediction accuracy. Segmenting them into simple smaller areas might be helpful. INTRODUCTION Nitrogen (N) is an important nutrient in soil, a basic resource for maintaining the Earth s ecosystems, and a primary restrictive factor for crop production (Wu et al., 2009). To improve crop production, nitrogenous fertilizers have been widely applied 1 Corresponding authors; sqwang@mail.hzau.edu.cn; weidongwoody@gmail.com 397 GIScience & Remote Sensing, 2012, 49, No. 3, p Copyright 2012 by Bellwether Publishing, Ltd. All rights reserved.

2 398 q u e t a l. to farmlands. Often, the amount of soil total nitrogen (TN) exceeds the requirements of plant growth. High N fertilization rates generally result in low N use efficiency and high N loss (Li and Zhang, 1999). While effective use of N can improve crop yields, excessive use of nitrogenous fertilizers leads to negative impacts on surrounding environments, especially the aquatic environment (Carpenter et al., 1998; Smith et al., 2001; Lu et al., 2007). Therefore, the sustainable use of soils and protection of the environment require a better understanding of soil TN content in fields and its spatial variability. Geostatistics is a set of powerful spatial statistical techniques that has been widely used to characterize the spatial variability of soil properties and map their spatial distributions (Odeh et al., 1995; Ferguson et al., 1998; Burgess and Webster, 1980). Because the quality of mapping of soil properties affects the performance of site-specific soil management, how to more accurately map the target soil variable with limited sample data becomes an important study issue. In order to obtain more accurate results, an estimation model such as kriging is needed to combine sparse but accurate sample data with related abundant but inaccurate or qualitative information as the input data. One can thus use inexpensively measured data of auxiliary variables to improve the kriging estimation of a target variable that may be expensive to measure. The information available for mapping continuous soil attributes often includes field point sample data and related categorical maps (e.g., land use, soil type, or geological maps). Thus, the issue of combining data measured on different spatial supports (e.g., point and map unit) has been an important research topic in soil science. Residual kriging (RK) has been often used to integrate categorical information that can be used to inform the local mean of the random function (Goovaerts and Journel, 1995; Hengl et al., 2004; Liu et al., 2006; Zhang et al., 2010). In this approach, variography and kriging are conducted only on the stationary residuals (i.e., differences between point measurements and their means in different mapping units), and the final estimates are composed of kriged residual results and local means. By taking into account the variation components of soil (or land use) type effect and residual, some improvement in kriging interpolation accuracy can be expected. However, because RK proceeds in two steps it cannot guarantee that the final map of kriging estimates will honor the areal data: the average of the interpolated values within each area typically does not equal the areal datum. Recently, a new kriging method called area-and-point kriging (AAPK) emerged for combining areal and point data in geostatistical interpolation (Liu and Journel, 2009; Goovaerts, 2010). This method allows combination of both point and areal data through use of area-toarea, area-to-point, and point-to-point covariances in the kriging system. It ensures the coherence of the prediction so that the average of interpolated values within each mapping unit is equal to the original areal datum. Moreover, this approach capitalizes on the availability of GIS to discretize polygons of irregular shape and size and the knowledge of the point-support variogram model that can be inferred directly from point measurements, thereby eliminating the need for a deconvolution procedure (Goovaerts, 2008). Testing case studies demonstrated that AAPK generally has higher prediction accuracy than ordinary and traditional residual kriging based on the assumption that the local mean is constant within each mapping unit and the AAPK variance is a more accurate indicator of the magnitude of prediction errors (Goovaerts, 2010).

3 l a n d u s e t y p e s a n d s o i l n i t r o g e n 399 In China s Jianghan Plain, the major crops are rice and wheat, which are cultivated under different land use regimes. While wheat grows only in dry farmlands, rice requires ample water to flood the fields. So rice fields are also called water farmlands. These two different land use types usually cause differences in many soil properties such as the contents of soil nitrogen and organic matter. In this paper, we used AAPK to map the spatial distribution of soil TN contents in Hanchuan County, China through the integration of both soil sample data and information on land use type. The objectives are to: (1) investigate the effect of land use types on soil TN contents; (2) explore the capability of AAPK in improving the mapping accuracy of the spatial distribution of soil TN with land use type data as auxiliary information; and (3) compare the performance of AAPK, RK, and ordinary kriging (OK) in soil TN predictive mapping. The ultimate objective is to suggest a more appropriate soil nutrient mapping method for precision farming and environmental management. Study Area and Land Use METHODS AND MATERIALS The study was conducted in Hanchuan County, an agricultural region in central China. The study area is located in the Jianghan Plain of central Hubei Province, bounded by the longitudes and East, and the latitudes and North, with an area of 1659 km 2. It belongs to the northern subtropical monsoonal climate zone, with a temperate-humid climate throughout the year and four distinct seasons. The average annual temperature is 16.1 C and the mean annual precipitation is approximately 1198 mm. The land use data were collected from the county s local agricultural department. In this region, the major land use types are paddy fields and dry farmlands. We further edited the land use map and simply classified the land use into four types (or categories) paddy fields, dry farmlands, water bodies, and other land use types. The spatial distribution of the land use types is shown in Figure 1. Paddy fields (i.e., rice farmlands) and dry farmlands use very different forms of cultivation, which usually have strong impacts on soil properties. Other land use types include all locations without tillage, such as woodlands, wild lands, and village and town areas. Water bodies include rivers, lakes, and ponds. This land use type was first separated as a GIS layer and then overlaid on the kriged maps of soil TN, so it was not considered in the interpolation processes of soil TN by different kriging methods. Paddy fields are the dominant land use type of the county, which is one of the most developed cropproducing bases in Hubei Province. Soil Sampling and Lab Analysis In present study, the topsoil sampling points consist of prediction points (n = 402) and validation points (n = 135). Among the 402 prediction samples, 215 samples were taken from paddy fields, 130 samples from dry farmlands, and the remaining samples were taken from other land use types (Table 1). The validation samples contain all of the three land use groups presented in the prediction samples, although they were collected with consideration of randomness and homogeneity in the area. All samples

4 400 q u e t a l. Fig. 1. Soil sample locations and distribution of land use types. were taken in fall after harvest and before the next cropping season in order to avoid the effect of fertilization during crop cultivation. When sampling, soils were collected in the top layers (0 15 cm), 6 8 points at each site over an area of approximately 0.01 ha, and then mixed and divided into parts of 1 2 kg each, which were delivered to a laboratory for analysis. Sample locations were recorded using a hand-held global position system (GPS). All samples were air-dried at room temperature (20 22 C). After stones or other debris were removed, samples were then sieved to ensure the soil particles were less than 2 mm in diameter. Portions of each sample (about 100 g) were ground in an agate grinder and sieved through mm mesh. TN was determined using the Kjeldahl method with H 2 SO 4 + H 2 O 2 digestion (Kim, 2005). Variogram and Ordinary Kriging Geostatistics provides the methods to predict values at unsampled locations from values at sampled locations by taking into account the spatial correlation of sampled points. It can minimize the variance of estimation errors and investigation costs (Ferguson et al., 1998; Saito et al., 2005). The variogram the spatial measure for kriging is an effective tool for evaluating spatial variability (Boyer et al., 1991; Cahn

5 l a n d u s e t y p e s a n d s o i l n i t r o g e n 401 Table 1. Soil TN Content (g kg 1 ) Statistics a for Different Land Use Types Land use type N Range Minimum Maximum Mean SD Skew Kurt CV Total Paddy field Dry farmland Other land use type a SD = standard deviation; skew = skewness; kurt = kurtosis; CV = coefficient of variation (%). et al., 1994). A variogram describes the spatial autocorrelation structure of a continuous variable and provides some insight into possible factors that affect data distribution (Webster and Oliver, 1990). Spatial patterns of soil attributes following intrinsic stationarity can be described using the following experimental variogram: N( h) 1 γˆ ( h) = [ z( x (1) 2N( h) i ) ( x i + h) ] 2 i = 1 where N(h) is the number of data pairs separated by distance h, and z(x i ) and z(x i + h) are the measured values for regionalized variables Z(x) at the locations of x i and x i + h, respectively. In this study, no apparent anisotropy was found for any studied variable through experimental variograms. So all experimental variograms were in the isotropic form, and were fitted using basic mathematical models, such as the spherical and exponential models, for kriging interpolation. Ordinary kriging (OK) was chosen to create the spatial distribution map of soil TN contents, with the maximum search radius being set to the autocorrelation range of the corresponding variable. OK is expressed as a linearly weighted average of observations in the neighborhood of the unsampled location x 0 : n ỹ( x 0 ) = λ i y( x i ) i = 1 where ỹ( x 0 ) is the predicted value at location x 0, y(x i ) is the measured value for soil property at position x i, and λ i is the weight of the corresponding datum, obtained from the ordinary kriging system with the constraint n λ i = 1. Here n is the number of i = 1 sample data in the neighborhood. The interpolated grid had a resolution of 400 m 400 m. Readers may refer to Goovaerts (1997) for a more technical description of kriging and the variogram. Residual Kriging The spatial variability of the TN data is partially caused by the complex distribution of land use types in the study region, which increases the uncertainty of TN prediction. To reduce this uncertainty, in residual kriging (RK) we divided the TN content z(x kj ) of every sample into two parts the mean value within the land use type to which the sample belongs and the corresponding residual r(x kj ): (2)

6 402 q u e t a l. z( x kj ) = mt ( k ) + r( x kj ) (3) where x kj is the location of the sample z(x kj ) and t k is the land use type that x kj belongs to. Therefore, the variance σ z 2 of original of z(xkj ) can be given as the sum of the two components σ s 2 between different land use types and σr 2 within a land use type: σ z = σ s + σ r which shows the influence of land use types on spatial variability of TN and its variation within a land use type, respectively (Liu et al., 2006). Then, the residual r(x kj ) can be treated as a new stationary regionalized variable to be used in spatial interpolation using RK. In this study, the residual data were interpolated using OK and the variogram model of residual data. Area-And-Point Kriging In order to incorporate data with different spatial supports, 2 both point and area data must be considered simultaneously in the kriging system. In this study, point data refer to soil TN sampling data and area data refer to the mean TN contents of sample points within a specific land use type area (map unit). The arithmetic of area-and-point kriging is described in the following (Liu, 2007; Liu and Journel, 2009; Goovaerts, 2010). Consider the problem of estimating the value of a continuous attribute z at any location u within a study area A. The information available consists of a set of point data collected at n discrete locations u α {z(u α ); α = 1,..., n}, supplemented by a set of K areal data {z(v k ); k = 1,..., K} recorded for mapping units v k of various sizes and shapes. Both point and areal data can be simultaneously incorporated into the prediction using the area-and-point kriging (AAPK) estimator, defined as (4) n( u) z AAPK ( u) = λ α ( u)z( u α ) + α = 1 n( u) + K λ k ( u)z( v k ) k = n( u) + 1 (5) where n(u) and K are the number of the surrounding point and areal data, respectively. Point observations are typically selected based on their distance to the interpolation node u while areal data are chosen according to adjacency rules; for example, all polygons adjacent to the polygon including u are used in the estimation. The kriging weights are the solution of the following ordinary kriging system n( u) + k λ j ( u)cx ( i, x j ) + μ( u) = Cx ( i, u), i = 1,, n( u) + K j = 1 n( u) + k λ j ( u) = 1 j = 1 (6) 2 Spatial support here refers to the area represented by a datum, which may be a point, block, pixel, or polygon.

7 l a n d u s e t y p e s a n d s o i l n i t r o g e n 403 where μ(u) is the Lagrange multiplier, x i = u i if i n(u) and x i = v i otherwise. The quantity C( x i, x j ) represents a point-to-point, point-to-block, or block-to-block covariance depending on the indices i and j. As in traditional block kriging, the block-to-point covariance is approximated by the average of the point support covariance C(h) computed between the location u and a set of P k points discretizing the block v k. A similar procedure is used for the block-to-block covariance C( v k, v k ' ) = Cov{ z( v k ), z( v k' )} and involves averaging C(h) computed between any two points that discretize the blocks v k and v k'. The prediction variance associated with the AAPK estimator is computed as 2 σ AAPK n( u) n( u) + K ( u) = C( 0) λ α ( u)c( u α, u) λ k ( u)c ( v k, u) μ( u) α = 1 Interpolation Method Evaluation k = n( u) + 1 Kriging prediction variance can provide information concerning the confidence associated with the kriging estimates, and interpreting such maps is an important step toward quantifying reliability in spatial estimation (Olea, 1999). The larger the prediction variance, the lower is the reliability of the estimate. In this study, we compared the reliability in TN estimation by the methods of AAPK, RK, and OK based on maps of prediction variance. We also compared the Pearson s correlation coefficient (r) between the predicted and measured values of the 135 validation samples as well as the mean error (ME) and root mean square error (RMSE) for the three methods. The ME and RMSE are calculated by the following equations: (7) ME = N { zx ( N i ) z ( x i )} i = 1 (8) RMSE = N zx ( N { i ) z ( x i )} 2 i = 1 where N is the number of validation points, and z*(x i ) and z(x i ) are the measured and predicted values of the validation points, respectively. The ME provides a measure of bias, and the RMSE provides a measure of accuracy. Greater r and lower ME and RMSE values indicate higher prediction accuracy. In this study, Software version 2.1 of S-GeMS (Remy et al., 2009) was used to perform all of the geostatistical computations. Statistical analyses were conducted in SPSS 13.0 for Windows (SPSS, Chicago). Statistics of Soil TN Data RESULTS AND DISCUSSION The descriptive statistics for sampled TN contents are given in Table 1. The mean TN contents of all samples is 1.46 g kg 1. Among the 402 samples, the lowest and (9)

8 404 q u e t a l. Fig. 2. Histograms of (A) original soil TN data and (B) residuals after removing the mean values for each land use type. highest TN contents are 0.31 and 3.04 g kg 1, respectively. The coefficient of variation (CV) of all samples is 37.14%. When all samples are classified into three land use groups, their average TN contents in descending order are 1.62 g kg 1 for paddy fields, 1.38 g kg 1 for dry farmlands and 1.25 g kg 1 for the other land use type. This means that land use types indeed affect the contents of soil TN. Among the CV values of the three land use types, those associated with other land use type and paddy fields are the highest (41.80%) and lowest (33.82%), respectively. Both the original TN content data and the residual data (i.e., after the mean values for different land use types are removed from sample data) fit approximately to normal distributions (Fig. 2). The TN contents are found to be correlated with land use types. Such a characteristic is consistent with the previous studies (Wang et al., 2009). In general, paddy fields have higher TN contents as a result of more mineral and organic matter input and slow decomposition of organic matter, whereas dry farmlands have lower TN contents because of less fertilizer input, fast organic matter decomposition, and not being regarded as the primary land use type for agricultural production in this county. This result implies that categorical land use information should be a valuable input in kriging interpolation to improve spatial prediction accuracy. Spatial Prediction of Soil TN The variogram provides a description of the spatial autocorrelation structure of the variable under study and some insights into possible processes affecting the spatial distribution of the variable (Paz González et al., 2001). Experimental variograms and fitted models for original TN content data and the residual data are presented in Figure 3. The parameters indicate that the experimental variogram of the original TN data (for use in OK and AAPK) is well fitted by an exponential model, and that of the residuals (for use in RK) is a good fit to a spherical model. Because of the removal

9 l a n d u s e t y p e s a n d s o i l n i t r o g e n 405 Fig. 3. Experimental variograms of (A) original data and (B) residuals for soil TN with fitted models.

10 406 q u e t a l. of mean values, the experimental variogram of the residuals is quite different from that of the original TN data (Fig. 3). The sill and range parameters for the residuals are both smaller than those of the original TN data, because the structural variances derived from land use patterns are eliminated with the removed mean values of mapping units. The C 0 /(C 0 +C) ratio is usually used as a criterion to define the spatial autodependence of a variable. Ratio values lower than 25% and higher than 75% correspond to strong and weak spatial dependencies, respectively, while ratio values between 25% and 75% indicate moderate spatial dependence (Cambardella et al., 1994). Generally, strong spatial dependence of soil properties may be attributed to intrinsic factors and weak spatial dependence may be attributed to extrinsic factors (Cambardella et al., 1994). The C 0 /(C 0 +C) ratio of the variogram model for original TN data is 48.7%, exhibiting moderate spatial auto-dependency which may be attributed to both intrinsic factors such as other soil properties and extrinsic factors such as human activities (e.g., land use). The TN spatial distribution maps interpolated using AAPK, RK, and OK are presented in Figure 4. All maps show similar general trends, with higher TN values appearing in the northwest region and lower values mainly occurring in the mid-south region of the county. Among the three predicted distribution maps of soil TN, the AAPK- and OK-interpolated maps are obviously smoother than the RK-interpolated map. This smoothing effect is a widely known characteristic of kriging interpolation that may cause low values to be overestimated and high values to be underestimated (Lark and Webster, 2006). Although the AAPK interpolated map is smoother than others, it may more accurately display the lower or higher contents as expected on different land use types, in particular when compared with the OK-interpolated map. For example, at the top-left corner of the study area where no sample data exist, while the land use type implies a lower TN content, the AAPK-interpolated map indeed shows a lower value but the OK interpolated map indicates a higher value (see Figs. 1 and Fig. 4). The-RK interpolated map is the least smooth one among the three maps. However, it looks rather messy, and there is no guarantee that the coherence constraint is honored once the kriged residuals are added to the trend estimates. Such a constraint can only be imposed through the joint incorporation of field point data and areal map data as done in AAPK (Goovaerts, 2010). From Figure 4, it also can be seen that the differences between the general spatial patterns predicted by the three methods are relatively minor. This means that the advantages of AAPK over RK and OK are not much evident in this case study. One reason may be that the effect of land use types on soil TN contents is not sufficiently large in this case (but it can be large for the contents of some available nutrients). The other reason, we speculate, should be that some of the land use polygons are too large and complex in shape due to the spatial connection of many farmland pieces under the same land use types. 3 For this situation, segmenting a complex-shaped large land use polygon into simple-shaped small areas might be helpful to improving the effectiveness of AAPK. 3 For example, numerous pieces of rice fields divided by narrow ridges are not spatially separated by other land use types, thus forming complex-shaped large polygons. See Figure 1 for this situation.

11 l a n d u s e t y p e s a n d s o i l n i t r o g e n 407 Fig. 4. Soil TN distribution maps generated by (A) AAPK, (B) RK, and (C) OK. Variance and Accuracy Analysis The prediction variance of RK is computed as the sum of the OK variance for residuals and the variance associated with the trend model. From the kriging prediction variance maps (Fig. 5), one can find that the prediction variance of soil TN by AAPK is apparently smaller than that by RK and OK throughout the study area. The mean kriging prediction variances of TN by AAPK, RK, and OK are , , and , respectively. While the kriging variance is a measure of confidence in estimates and the sampling configuration only, and it is independent of the data values (Goovaerts, 1997), for different kriging methods a lower kriging variance may imply the kriging method can globally estimate more accurately (or with more confidence) than the kriging methods with higher kriging variance values. From this point, RK seems the worst estimator here. The correlation coefficients r, the ME values, and the RMSE values between the observed and predicted data at the 135 validation locations for the three kriging options are shown in Figure 6. The r values are 0.81, 0.67, and 0.55 for AAPK, RK, and OK, respectively. The ME and RMSE values are and 0.29 g kg 1 for AAPK, and 0.36 g kg 1 for RK, and and 0.41 g kg 1 for OK, respectively. The larger

12 408 q u e t a l. Fig. 5. Maps of prediction variances generated by (A) AAPK, (B) RK, and (C) OK. r value and the smaller ME and RMSE values for AAPK means it generates a more accurate prediction map than RK does. OK is apparently the least accurate estimator here. CONCLUSION Land use types were found to have some impacts on soil TN contents in the study area, because the mean TN content in paddy fields is apparently higher than that in dry farmlands. The recently emerged AAPK was used to interpolate soil TN so that the influence of land use types can be incorporated. Interpolated results showed that the soil TN contents were generally lower in the mid-south region and higher in the northwest region in the county. Comparison with OK and RK was also conducted to evaluate the merits of the AAPK method. The predictive map of soil TN contents by AAPK with the incorporation of land use data indicated an improvement in prediction accuracy over those by RK and OK, as represented by prediction variance, correlation coefficient, ME, and RMSE values, although the differences were not visually very significant in prediction maps of soil TN contents. It seems that the occurrence of complex-shaped large polygons of land use types impacted the effectiveness of

13 l a n d u s e t y p e s a n d s o i l n i t r o g e n 409 Fig. 6. Scatterplots between observed soil TN data and predicted data for validation using different interpolation methods: (A) AAPK; (B) RK; (C) OK.

14 410 q u e t a l. AAPK in improving prediction accuracy. Segmenting those large complex polygons into smaller simple-shaped areas might help effectively demonstrate the capability of AAPK and might be considered in further study. In general, land use types indeed have important impacts on the spatial distribution of soil TN, and incorporation of such categorical information is necessary for more accurately mapping soil properties. It is also concluded that AAPK is an effective prediction method for increasing the interpolation accuracy of soil TN through integration of both point and area data. Such a conclusion should also be applicable to other soil properties. The interpolated maps of soil TN contents may provide useful information for effective management of soil nutrients and the environment. ACKNOWLEDGMENTS Support from the National Natural Science Foundation of China under Grants and is greatly appreciated. REFERENCES Boyer, D. G., Wright, R. J., Feldhake, C. M., and D. P. Bligh, 1991, Soil Spatial Variability in Steeply Sloping Acid Soil Environment, Soil Science, 161: Burgess, T. M. and R. Webster, 1980, Optimal Interpolation and Isarithmic Mapping of Soil Properties: I. The Semivariogram and Punctual Kriging, Journal of Soil Science, 31: Cahn, M. D., Hummel, J. W., and B. H. Brouer, 1994, Spatial Analysis of Soil Fertility for Site-Specific Crop Management, Soil Science Society of American Journal, 58: Cambardella, C. A., Moorman, T. B., Nocak, J. M., Parkin, T. B., Karlen, D. L., Turco, R. F., and A. E. Konopka, 1994, Field-Scale Variability of Soil Properties in Central Iowa Soils, Soil Science Society of America Journal, 58: Carpenter, S. R., Caraco, N. F., Correll, D. L., Howarth, R. W., Sharpley, A. N., and V. H. Smith, 1998, Non-point Pollution of Surface Waters with Phosphorus and Nitrogen, Ecological Applications, 8: Ferguson, C. C., Darmendrail, D., Freier, K., Jensen, B. K., Jensen, J., Kasamas, H., Urzelai, A., and J. Vegter, 1998, Better Methods for Risk Assessment, in Risk Assessment for Contaminated Sites in Europe, Vol. 1. Scientific Basis, Nottingham, UK: LQM Press, Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation, New York, NY: Oxford University Press. Goovaerts, P., 2008, Kriging and Semivariogram Deconvolution in Presence of Irregular Geographical Units, Mathematical Geosciences, 40: Goovaerts, P., 2010, Combining Areal and Point Data in Geostatistical Interpolation: Applications to Soil Science and Medical Geography, Mathematical Geosciences, 42: Goovaerts, P. and A. G. Journel, 1995, Integrating Soil Map Information in Modeling the Spatial Variation of Continuous Soil Properties, European Journal of Soil Science, 46:

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