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Published online 23 May 2006
Published in Soil Sci Soc Am J 70:1200-1209 (2006)
DOI: 10.2136/sssaj2005.0126
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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Nutrient Management & Soil & Plant Analysis

Interpolating Soil Properties Using Kriging Combined with Categorical Information of Soil Maps

Ten-Lin Liua, Kai-Wei Juangb and Dar-Yuan Leea,*

a Graduate Institute of Agric. Chemistry, National Taiwan Univ., 106 Taipei, Taiwan, R.O.C.
b Dep. of Post-Modern Agriculture, MingDao Univ., 523 Pitou, Changhua, Taiwan, R.O.C

* Corresponding author (dylee{at}ccms.ntu.edu.tw)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Kriging interpolation is frequently used for mapping soil properties in the analysis and interpretation of spatial variation of soil. Mapping quality could affect the performance of site-specific management. Soil map–delineation in existing soil maps showing abrupt changes at the boundaries between different soil types can provide valuable categorical information for interpreting variation in soil properties. In this study, map units were used to group sampled observations, and the variation in soil properties was separated into two parts: (i) between soil types (i.e., soil type effect) and (ii) within each soil type (i.e., residual). A kriging model combined with soil map–delineation, taking into account the variation components of soil type effect and residual, was proposed. A comparison of performance of kriging combined with soil map–delineation (KSMD) and ordinary kriging (OK) was performed to assess the feasibility of KSMD for improving the interpolation of soil properties. Real data of soil properties (sand, silt, and clay contents; pH; and Mehlich-3 Ca and P) in a field of midwestern Taiwan were used for illustration. The analysis of variance table revealed that the contribution of soil types is a significant source of the spatial variation of soil. The spatial variation components of soil type effect and residual were thus determined for KSMD. When comparing KSMD and OK, the mean errors of KSMD and OK estimations were similar. However, decreases in estimation of imprecision for KSMD relative to OK (DIP %) for the 127 validation locations for sand, silt, and clay contents; pH; and Mehlich-3 Ca and P were 34, 40, 48, 20, 42, and 3%, respectively. These results suggested that the proposed KSMD method could use the information of soil map–delineation to increase precision of the interpolation of soil properties.

Abbreviations: DIP %, decrease of estimation imprecision of KSMD relative to OK • IP, imprecision • KSMD, kriging combined with soil map–delineation • ME, mean error • OK, ordinary kriging • RMSE, root mean squared error


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
THERE are complex spatial changes in a field scale, even for the same soil type. While showing the different types of soil properties in a region, a detailed soil map includes the mutual spatial variation between soil types and the variability within each soil type (Oberthür et al., 1999). A satisfied interpolation for soil property mapping should involve these two components of spatial variation. Thus, within-stratum interpolation, called stratified kriging, was proposed, with resulting kriging performed separately for each soil type (Stein et al., 1988). A similar procedure of integrating a soil map with kriging was used by Boucneau et al. (1998). However, numerous observations in each soil type for calculating a stratum-specific variogram are needed in stratified kriging. This requirement is not generally available in a field-scaled survey. The performance of kriging interpolation is thus restricted by the number of samples observed and the location configuration. Mueller et al. (2001) suggested that the larger the number of soil samples, the more accurate the kriging maps of soil properties. Kriging interpolation is frequently used for mapping soil properties for the analysis and interpretation of spatial variation. The quality of the mapping soil properties affects the performance of soil site-specific management. Insufficiently intensive sampling wastes time and money because it cannot provide the level of accuracy and precision needed for successful site-specific management (Mueller et al., 2004). However, the cost of intensive soil sample collection and analysis quickly exceeds any benefits from site-specific management (Kravchenko, 2003).

The objective of using kriging is to obtain the desired quality of mapping at reasonable sampling costs. A compromise is to combine a few exact measurements with numerous but moderately accurate measurements. One can thus use cheap-to-measure auxiliary variables to improve the kriging estimation of an expensive target variable. Odeh et al. (1994) used dense observations of landform attributes derived from digital elevation models to estimate soil properties with sparsely located observations. Knotters et al. (1995) used soil electrical conductivity measurements as the auxiliary variable to improve the interpolation of the depth to soft layers like peat and unripe clay. Juang and Lee (1998) used numerous observations of heavy metal contents in topsoil as auxiliary variables for spatial interpolation of heavy metal contents in subsoil. Triantafilis et al. (2001a) used apparent soil electrical conductivity as an ancillary variable for estimating clay contents. The most frequently used kriging approaches with auxiliary information for interpolation are cokriging (Ersahin, 2003; Wu et al., 2003), kriging with external drift (Bourennane et al., 2000; Snepvangers et al., 2003), and regression-kriging (Hengl et al., 2004). The general discussions of cokring, kriging with external drift, and regression-kriging used for soil property interpolation have been proposed in many studies (Odeh et al., 1995; Triantafilis et al., 2001b; Mueller and Pierce, 2003; Baxter and Oliver, 2005). Recently, kriging with categorical auxiliary information generated from rapid tests and existing soil survey reports was also proposed (Oberthür et al., 1999; Carré and Girard, 2002).

It was known that soil maps showing the spatial distribution of soil types were derived from geological and pedological knowledge and that the abrupt changes at the boundaries between different soil types were determined using expert knowledge (Soil Survey Staff, 1993). The existing soil survey reports for soil map–delineation can provide valuable information (Goovaerts and Journel, 1995; Oberthür et al., 1996, 1999). The soil map–delineation, which is a kind of categorical information showing abrupt changes at the boundaries between different soil types, can be used to group the sampled observations and to show the differentiation of soil types. Combining kriging estimation with soil type information using weighted average was thus proposed for spatial estimation of soil properties (Heuvelink and Bierkens, 1992). This combination method provided some satisfactory results in the case studies (Heuvelink and Bierkens, 1992; Voltz et al., 1997; Utset et al., 2000), but the estimation variance propagated in combination with the weighted average. An estimation method with a minimized estimation variance is desired in spatial interpolation. To minimize the estimation variance, one must develop a model that can address the sources of variance of the observed data as completely as possible. The variation of soil properties mainly depends on genesis processes and historical practices. The genesis processes cause variation on a geological scale that is used to determine soil classification. Thus, soil types indicate the variation from soil genesis processes. The alternative source of soil variation from historical practices often happens in a field scale, which can be defined within each soil type. Because the soil map delineating the boundaries of soil types is available, one can use soil map–delineation to characterize the variation components of soil properties of agronomic interest. Both components of the variation between and within soil types can be measured using the analysis of variance (ANOVA) (Oberthür et al., 1999).

In this study, based on the soil map–delineation of soil types to group the sampled observations, the variation of soil properties was separated into two parts: (i) between soil types (i.e., soil type effect) and (ii) within each soil type (i.e., residual). The variations within each soil type were pooled together and stated in a random field satisfied with stationarity. A kriging model combined with the information of soil map–delineation, taking into account the variation components of soil type effect and residual, was proposed. A study site in midwestern Taiwan, a region with four soil types on 1/25 000 scale soil maps of Taiwan farmlands, and a data set (n = 175) of soil properties within this site were used for illustration. The objectives of this study were (i) to characterize the spatial variation of soil properties based on soil map–delineation and (ii) to assess the feasibility of the derived kriging model with soil map–delineation in the spatial interpolation of soil properties.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Study Area and Soil Measurements
The alluvial plain of the Choshui River is the main paddy field in midwestern Taiwan. The study site is 19.3 ha in area on the north bank of the Choshui River. The rotation of paddy rice (Oryza sativa L.) and sugarcane (Saccharum officinarum L.) is currently being performed. According to the 1/25 000 scale soil maps of Taiwan farmlands and soil survey reports, the soils are characterized by shale and slate alluvial soils and are classified into four soil types: Chunliao (Cl), Tingfanpo (Ti), Wanhoh (Wa), and Yuliao (Yl) (Soil Survey Report of Changwhua County, 1969).

Soil samples were taken regularly on grid nodes (25 by 50 m). Because the irrigation channel dissects the southern side of the field, the intensive sampling nodes were added (25 by 25 m) for assessing the geometric and zonal anisotropic variations of soil (Goovaerts, 1997). There were 175 sampling points selected, and then the topsoils (0–15 cm) were collected. The sampling configuration is shown in Fig. 1 . Each soil sample was air dried and passed through a 2-mm sieve. Soil properties investigated in this study included sand, silt and clay contents, pH, and Mehlich-3 extractable P and Ca (Mehlich, 1984). Sand, silt, and clay contents were determined by the hydrometer method (Gee and Bauder, 1986), and soil pH was measured on the soil suspension (soil/water ratio 1:1) with the pH meter method (McLean, 1982). Phosphorus and Ca in the Mehlich-3 extracts were determined, respectively, by the methods of Murphy and Riley (1962) and atomic absorption spectroscopy.


Figure 1
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  		Fig. 1. Soil map delineations of the study site and the sampling locations stratified into four soil types.

 
Variogram Model and Ordinary Kriging
Variogram modeling is used to show the spatial structure variation in geostatical analyses. The spatial patterns of soil properties z(xi) following the intrinsic stationarity (Goovaerts, 1997) can be described using the semivariogram model {gamma}z(h).

Formula 1[1]
where N(h) is the number of pairs separated by a lag distance h. The spatial structure of the variogram is the main factor, affecting the accuracy of the geostatistical estimation (Kravchenko, 2003). The commonly used estimation model, ordinary kriging, is expressed as a linear weighted average of observations in the neighborhood of the unsampled location xo:

Formula 2[2]
where {lambda}i is the weight obtained from the ordinary kriging system (Journel and Huijbregts, 1978; Goovaerts, 1997). The semivariograms were characterized and modeled using the software package GS+ (Gamma Design Software, 1994). Regression coefficients of the model fitting were used to select the best fitted variogram model.

Soil Map–Delineation and Soil Type Effects on the Spatial Variation
A soil map delineates different soil types and is considered categorical information. The boundaries of the soil map divide the study area into a finite number of polygons (Aj) associated with soil types. The notation of (Aj) was used to quantify the information of soil map–delineation as nominal data. Because the observations of specific soil properties are located in the same polygon, the observations are denoted with the same soil type. The categorical information of soil maps can thus be included in the interpretation of the variation of soil properties. Thus, each observation z(xkj) on one specific soil property can be expressed as

Formula 3[3]
where xkj is the sampling location of z(xkj), which is on the polygon Aj. s(Aj) is the mean value of z(xkj) over the polygon Aj, and r(xkj) is the residual. s(Aj) and r(xkj) should be independent mutually. The variation of r(xkj) should be homogeneous over all polygons. The variance {sigma}2z of z(xkj) can be shown as the sum of the two components: {sigma}2s between polygons and {sigma}2r within polygons:

Formula 4[4]
The variance {sigma}2s between polygons indicates the soil type effect on the spatial variation of soil properties. The variance {sigma}2r shows the overall variation within polygons, which is always defined homogeneously as the intrinsic stationarity is assumed. In this study, there are four soil types (Cl, Ti, Wa, and Yl) within the study area. The soil map–delineation is shown in Fig. 1. The 175 sampling locations were then categorized based on location within soil polygons. Based on the model of Eq. [3], the variance of each soil property between and within soil types was determined by using ANOVA with the software package STATISTICA for Windows v. 6.0 (StatSoft, 2001).

Kriging Combined with Soil Map–Delineation
Because the variance {sigma}2s between soil types is significant in ANOVA, the model of Eq. [3] is valid for the estimation of soil properties. The soil type effects can be shown as the term s(Aj), which is the mean value of z(xkj) over the polygon Aj. Moreover, the residual variance {sigma}2r is homogeneous and pooled over all soil types. The residual term r(xkj) thus can be stated as a stationary random field over the whole site. In this study, Eq. [3] was used for spatial interpolation of soil properties. The estimator, derived from Eq. [3], is combined with the kriging estimate r*(xol) of residual and the estimate of soil type effect s*(Al):

Formula 5[5]
This approach is similar to the regression-kriging model (Odeh et al., 1995). Instead of using regression, the soil map–delineation is used in the estimator z*(xol). The soil type estimate s*(Al), which is used as auxiliary information to improve the spatial interpolation of soil properties, is:

Formula 6[6]
where n(l) is the number of observations in the soil type l of the soil map–delineation. The residual estimate r*(xol) is obtained by using the ordinary kriging model:

Formula 7[7]
where {lambda}ij is the weight obtained from the ordinary kriging system, and n(j) is the number of observations in the soil type j. s*(Aj) is the mean of z(xij) of the soil type j stated as in Eq. [6]. The variogram of r(xkj) required for kriging estimation is calculated using the pooled residual data r(xi) over all soil types:

Formula 8[8]
where N(h) is the number of pairs separated by a lag distance of h.

Simulation Procedures and Interpolation Comparison
To assess the feasibility of the kriging combined with soil map–delineation (KSMD), a comparison with ordinary kriging (OK) was performed by using a simulation process. A subset with 30 samples was drawn from the original 175 samples for each soil property interpolation. To ensure a homogeneous sampling density in each soil type, stratified random sampling was used to obtain the 30-sample subset. The sample number in each soil type was determined according to the ratio of the area of each soil type to the whole area. Next, to prevent the large interpolation errors from the edge of the field, the area for interpolation comparison was narrowed to exclude the 48 outer sampled locations around the field edge, and only the 127 inner sampled locations were assigned as validation locations. The 30-sample subset was used in KSMD and OK for each soil property interpolation at the 127 validation locations (Fig. 1). Finally, 1000 iterations of the previously described procedure were performed. The flow chart describing the interpolation procedures in detail is shown in Fig. 2 . Then, 1000 realizations of soil properties were generated from the interpolation simulation.


Figure 2
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  		Fig. 2. Flow chart of ordinary kriging (OK) and kriging combined with soil map–delineation (KSMD) interpolation procedures.

 
Jackknife validation as proposed by Deutsch and Journel (1998) was used to make a comparison of KSMD and OK. The validation results were summarized with mean error (ME) and root mean squared error (RMSE) to measure the mapping quality (Triantafilis et al., 2001b; Zhu et al., 2004). In this study, based on the 1000 estimated values of soil properties at each location, the ME and RMSE were derived and defined for location xo as

Formula 9[9]
and

Formula 10[10]
The ME value, with an expected value equal to 0 on an unbiased estimation, is a measure of estimation bias. The variation of estimation errors, called imprecision (IP), is expressed as the following equation and is used to measure the quality of estimation (Mueller and Pierce, 2003):

Formula 11[11]


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Soil Map–Delineation
Soil map–delineation of the four soil types is shown in Fig. 1. The choropleth map classifies soil types with abrupt boundaries separating uniform groups. Based on the sampling locations and the soil map–delineation, the data of soil properties are stratified into four groups corresponding to soil types. Although the crisp boundaries of soil types are located inaccurately in the geographical space, the boundaries separating the soil property groups with clear difference in statistical inference are most successful in improving spatial estimation, and at the same time some of these delineations are satisfactory for the expert (Brus et al., 1996). Table 1 shows the ANOVA table for testing the variance of soil properties between the four soil types. The soil map–delineation of the data of sand, silt, and clay contents; pH; and Mehlich-3 Ca were statistically significant except Mehlich-3 P. Because of the soil texture, pH and soil calcium are dominated by geological and pedological features, so the variation of their observed data is significantly related to soil map–delineation. In contrast, the soil phosphorous is usually influenced by historical practices and fertilizer applications (Mallarino, 1996). Thus, the soil map–delineation is not significant to the data of Mehlich-3 P.


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  		Table 1. Analysis of variance table for testing the significance of soil type effects on the variance of soil properties.

 
Data Characterization
Summary statistics of soil properties for the data stratified into the four soil types are listed in Table 2. Significant differences of the mean values were noted by the least significant deviation. Only the Mehlich-3 P shows a mutually nonsignificant deviation between soil types. This is consistent with the result of the ANOVA and indicates that using the soil map–delineation does not successfully improve the spatial interpolation of Mehlich-3 P. Based on the definition as per Eq. [3], the original values z(xkj) were separated into the two components: the mean value s(Aj) and the residual r(xkj). The isotropic variograms of z(xkj) and r(xkj) are shown in Fig. 3 . The spatial structures of the residuals r(xkj) were obviously different from those of the original values z(xkj). This indicates that the data of soil properties were not stationary over the whole site. The contribution of the mean values s(Aj) of the soil types (called a local trend effect) to the spatial variation of z(xkj) was sufficiently substantial to influence the kriging estimation in Eq. [2], especially for the data of sand, silt, and clay contents; pH; and Mehlich-3 Ca. It is necessary to come up with a derived method that takes into account the local trend effect (i.e., soil type effect) for spatial interpolation of the soil properties. Moreover, the variograms of z(xkj) and r(xkj) for Mehlich-3 P were much the same. This indicated that soil types were not the main sources of the spatial variation of Mehlich-3 P. This phenomenon was consistent with the ANOVA testing (Table 1) and shows that the mean values s(Aj) of Mehlich-3 P between soil types were not different significantly.


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  		Table 2. Statistics of soil properties for the 175 soil samples stratified into four soil types.

 

Figure 3
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  		Fig. 3. Variograms of the original values z(x) and the residuals r(x) for the sand, silt, and clay contents; pH; and Mehlich-3 P and Ca.

 
Assessing the Feasibility of KSMD Compared with OK
Figure 4 shows one realization of selected 30-sample values and interpolated values generated by OK and KSMD (only one realization of Mehlich-3 Ca is shown as an example). Figures 5 and 6, respectively, show the diagrams of the ME and IP values generated from the interpolation simulation using the 30-sample subset for comparison of KSMD and OK. The ME values of KSMD and OK estimations were almost clustered on the 1:1 diagonal line for each soil property (Fig. 5). This indicates that the estimation bias of KSMD for all tested soil properties was similar to that of OK. On the other hand, the IP values of KSMD and OK estimations for the tested soil properties except Mehlich-3 P were clustered under the 1:1 diagonal line (Fig. 6). This indicates that the imprecision of KSMD estimations for the tested soil properties except Mehlich-3 P was lower than that of OK estimations. The decrease of estimation imprecision of KSMD relative to OK (DIP %) for the 127 validation locations can be calculated as per the following equation to represent the extent of improvement of estimation precision of KSMD over OK:

Formula 12[12]
The DIP values for sand, silt, and clay contents; pH; and Mehlich-3 Ca and P were 34, 40, 48, 20, 42, and 3%, respectively. The positive values of DIP demonstrated that KSMD could improve the precision of estimation for the tested soil properties. The smallest DIP values of Mehlich-3 P among the tested soil properties that corresponded to the mean values of Mehlich-3 P between soil types were not different significantly. Consequently, the extent of the improvement in estimation precision over OK by using KSMD was small. This suggests that for soil properties showing significant variation between soil types, using KSMD could increase the interpolation precision compared to using OK.


Figure 4
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  		Fig. 4. Choropleth maps of one realization of (a) selected 30-sample values and interpolated values of Mehlich-3 Ca (mg g–1) generated by (b) using ordinary kriging (OK) and (c) using kriging combined with soil map-delineation (KSMD).

 

Figure 5
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  		Fig. 5. Diagrams of the mean errors (ME) of the ordinary kriging (OK) estimations and the kriging combined with soil map–delineation (KSMD) estimations of the soil properties (sand, silt, and clay contents; pH; and Mehlich-3 P Ca) using the 30-sample subset.

 

Figure 6
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  		Fig. 6. Diagrams of the imprecision (IP) of the ordinary kriging (OK) estimations and the kriging combined with soil map–delineation (KSMD) estimations of the soil properties (sand, silt, and clay contents; pH; and Mehlich-3 P and Ca) using the 30-sample subset.

 
Spatial Characterization for the Performance of KSMD
To show the precision of interpolation at specific locations, the maps of IP values obtained from the interpolation using the 30-sample subset are shown in Fig. 7 (only Mehlich-3 Ca is shown as an example). The IP maps of sand, silt, and clay contents; pH; and Mehlich-3 Ca generated by using KSMD were different from those generated by using OK in spatial distribution. The KSMD estimation provided better precision than OK at the locations with high IP values. The locations with high IP values are almost all situated in the area with a large gradient in soil properties (Fig. 7). Estimating the soil properties precisely within the regions with a large gradient could increase soil mapping quality and reduce the uncertainty of soil delineation for site-specific management.


Figure 7
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  		Fig. 7. Choropleth maps of Mehlich-3 Ca (mg g–1) (a) original data set and imprecision (IP) of estimated values on 127 validating locations by (b) using ordinary kriging (OK) and (c) using kriging combined with soil map–delineation (KSMD).

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
This study proposes a derived kriging approach with categorical ancillary information (KSMD). A comparison of KSMD and OK without the auxiliary information was performed for assessing the feasibility of KSMD. The estimation bias of KSMD is similar to that of OK. However, compared with OK, the precision of interpolation is raised by using KSMD. The soil map–delineation as an auxiliary information in the KSMD estimator can reduce the variation of estimation errors for those tested soil properties that showed significant variation between soil types (sand, silt and clay contents, pH, and Mehlich-3 Ca). The results suggested that the soil map–delineation could be used as auxiliary variables to improve the spatial interpolation of soil properties.


   ACKNOWLEDGMENTS
 
This research was sponsored by the National Science Council, Taiwan, R.O.C., under grants NSC 92-2313-B-451-002, NSC 93-2313-B-451-001, and NSC 93-2313-B-002-007.

Received for publication April 19, 2005.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 





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