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Comparison of Kriging Interpolation Precision With Different Soil Sampling Intervals For Precision A


TECHNICAL ARTICLE

Comparison of Kriging Interpolation Precision With Different Soil Sampling Intervals for Precision Agriculture
Liu Guo-Shun,1 Jiang Hou-Long,1 Liu Shu-Duan,2

Wang Xin-Zhong,1,3 Yang Xia-Meng,1 Hu Hong-Chao,4 Liu Qing-Hua,4 Xie De-Ping,4 Gu Jian-Guo,5 and Li Yan-Tao5
Paz Gonzalez, 2003; Iqbal et al., 2005). To date, the nutrient management recommendations for agriculture in central China are not typically speci?c for large regions. Because of the high variability of soil nutrient levels, uniform fertilizer application is likely to lead to excessive fertilization in some areas and inadequate fertilization in other areas (Wibawa et al., 1993; Ferguson et al., 2002). Consequently, the spatial variability of the yield and the quality of the crop are increased. Variable-rate fertilizer application is only possible if the spatial variation in nutrient status across a ?eld is precisely known (Ndiay and Yost, 1989; Cahn et al., 1994). Variability-rate application strategies that improve nutrient use ef?ciency may increase farm pro?ts and greatly reduce the harmful environmental effects associated with fertilizer loss (Inman et al., 2005). Appropriate management processes and information, as well as corresponding decisions, vary among different environments. The variation in soil nutrient supply may be most signi?cant within a large ?eld or among many small ?elds within a landscape. In any case, both spatial and temporal variations must be characterized. Several knowledge-intensive and site-speci?c nutrient management approaches to address the variability of soil properties have been proposed. Geostatistics has been widely used in soil science. It has become an important tool in characterizing the spatial variability of soil properties (Goovaerts, 1997; Zhang and McGrath, 2004; Mabit et al., 2008; Wang et al., 2010). It provides a set of statistical tools for the description of spatial pattern, for quantitative modeling of spatial continuity, and for spatial prediction (Goovaerts, 1998). Geostatistical techniques that incorporate spatial information into predictions can improve estimation and enhance map quality (Mueller and Pierce, 2003). Notably, semivariogram and kriging play a principal role in this ?eld (Cambardella and Karlen, 1999). The aim of geostatistics is to use point information to estimate spatial variability. Kriging is a linear geostatistical interpolation technique that provides the best linear and unbiased estimator for quantities that vary in space. The estimates are calculated as weighted sums of the adjacent sampled concentrations. Weighting is assigned according to either deterministic or statistical criteria. Various signi?cant factors, including the nature of soil variability (Sadler et al., 1998), the intensity of sampling, and the method of interpolation, affect interpolation accuracy. Soil sampling uses point information to estimate the soil fertility level at locations where samples were not taken. To make precise estimates, the sampling points have to be taken at intervals. Sampling interval is conceptually simple. However, the selection of an appropriate sample design and grid size (point intensity) to ensure that the estimate is suf?ciently precise and within the budget range is often dif?cult. The accuracy of kriging interpolation also depends on the sample pattern and sample spacing (Laslett, 1994; Wollenhaupt et al., 1994; Gotway et al., 1996). More intense soil sampling should result in a more accurate depiction of the distribution of soil nutrients within a ?eld. Nevertheless, a compromise between sampling intensity and cost must be reached. In geostatistics, soil properties are
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Abstract: The analysis and interpretation of the spatial variability of
soil properties are keystones in site-speci?c management. Soil sampling interval is typically used in establishing management zones for sitespeci?c application of nutrients. Sampling intensity is an important factor that can potentially limit the accuracy of the management zone. The objectives of this study were (i) to quantify the spatial variability of soil properties across tobacco plantation ?elds, (ii) to select the reasonable sampling interval for eight soil variables to minimize cost and maximize evaluation accuracy, and (iii) to provide a theoretical basis for setting a reasonable sampling interval in precision agriculture. Soil samples were collected at approximately 20 m at 0- to 20-cm depth. The coordinates of each of the 111 points were recorded using global positioning system. Using a geographic information system software platform, the soil sampling points from the primary scheme were regularly deleted to create comparative schemes. The geostatistical method was used to produce distribution maps of the soil nutrients. Seven sampling points were randomly selected. The interpolation of the values of the seven soil points was compared under three sampling intervals with their actual measurements. The interpolation errors of soil organic matter and available copper were lowest in the 60-m sampling interval. In the 20-m sampling interval, alkaline hydrolyzable N, available phosphorus, available potassium, available iron, and available zinc had the least errors of interpolation. Available manganese had the least interpolation error at the 40-m sampling interval. Overall, the sampling ef?ciency could be further improved. The method can be applied in a practical and costeffective manner to facilitate soil sampling. Key words: Interpolation precision, precision agriculture, sampling interval, kriging. (Soil Sci 2010;175: 00Y00)

T

he spatial variability of soil physical properties within or among agricultural ?elds is inherent in nature because of geologic and pedological soil-forming factors. However, some variability may be induced by tillage and other soil management practices (Goovaerts, 1998; Quine and Zhang, 2002). Soil can exhibit marked spatial variability at both the macroscale and microscale levels because of the interaction of these factors across spatial and temporal scales (Brejda et al., 2000; Vieira and

1 Tobacco College Agronomy Department of Henan Agricultural University, National Tobacco Cultivation, and Physiology and Biochemistry Research Center, Zhengzhou, China. Mr. Liu Guo-Shun is corresponding author. E-mail: liugsh1851@163.com 2 Nanyang Tobacco Company of Henan Province, Nanyang, China. 3 Technology Center of Tobacco Leaf, Dali Tobacco Company, Dali, Yunnan, China. 4 Pingdingshan Tobacco Company, Pingdingshan, China. 5 Jia County Branch of Henan Tobacco Company, Jia County, China. Received February 28, 2010. Accepted for publication June 21, 2010. Copyright * 2010 by Lippincott Williams & Wilkins ISSN: 0038-075X DOI: 10.1097/SS.0b013e3181ee2915

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usually sampled on a speci?c grid or pattern that presumably represents the unsampled neighborhood. The sample design and intensity are important factors that affect the accuracy of the assessment (Foody, 2002). If the data seem to be highly continuous in space, the points closer to those estimated receive higher weights compared with those more distant (Cressie, 1990). The ?eld-speci?c characteristics of the spatial variability of soil properties and the level of soil fertility ultimately determine the required sampling intensity and scienti?c sampling method (Skidmore, 2002). Soil samples are usually collected on grids using geostatistical techniques. The sampling design is important when the objectives are to interpolate in an optimal fashion and to compute the distribution maps for soil properties. An optimal sampling scheme should provide the maximum estimation precision with the least sample cost. The number of soil samples needed to represent the variability of the ?eld has been a matter of discussion since at least the 1920s (Lindsley and Bauer, 1929). The need for sampling to describe ?eld variability has always been considered to have an economic basis (Peck, 1990). The increased income from reduced input and increased yield must offset not only the costs of characterizing the soil variability, but also the technology required for variable application. Several reports have examined the in?uence of sampling schemes on the estimation precision of soil properties. Pettitt and McBratney (1993) studied several sampling designs for estimating variance components using the restricted maximum likelihood method. Ferreyra et al. (2002) and Zhu and Stein (2006) used spatial simulated annealing to optimize the sampling schemes for minimal kriging variance and to reduce the cost. Brus et al. (2006) applied the fuzzy k-means cluster algorithm to optimize the number and spatial distribution of sampling points. The algorithm variance quadtree method was applied to design the sampling scheme of soil bulk electrical conductivity in a coastal saline ?eld (Li, 2007). Other studies have described the impact of sampling interval size on the precision of estimates. Hammond (1993) recommended the use of a grid size of approximately 60 ? 60 m and suggested that subdivisions of 120 ? 120 m or larger are inappropriate. Wollenhaupt et al. (1994) recommended the use of grids no larger than 60 ? 60 m and suggested that certain ?elds might need smaller grids. Franzen and Peck (1995) reported that a 66 ? 66Ym grid size is better than a 100 ? 100Ym one. Mallarino et al. (1997) reported that cells larger than 0.8 ha usually do not represent P and K levels appropriately. Wu et al. (2004) indicated that the reasonable interval sizes of available N, available phospho-

rus, and available potassium are 64 ? 51 m, 32 ? 76 m, and 32 ? 25 m, respectively. Wang et al. (2005) found that the interpolation errors of total N, available N, and available phosphorus increased along with the size of the sampling grids. However, those of potassium and other micronutrients exhibited an opposing trend. The distribution of soil sampling points had a direct effect on the interpolation results. Because of economic and time considerations, producers and consultants usually tend to minimize the number of soil samples collected. But additional soil sampling results in a more accurate estimation. On the other hand, additional sampling uses additional resources and time. The objectives of this study were (i) to quantify the spatial variability of soil properties across tobacco plantation ?elds under three sampling intervals, (ii) to select the reasonable sampling interval for the eight soil variables while minimizing the cost and maximizing the evaluation accuracy, and (iii) to provide a theoretical basis for setting a reasonable sampling interval in precision agriculture.

MATERIALS AND METHODS
The ?eld used in this study is located southwest of Jia County (34-04?36?N, 113-05?04?E) in Henan Province in Central China. In this region, most of the ?elds have been managed with a 10-year tobacco rotation. Soil samples were collected after the tobacco harvest and before fertilization. A total of 111 samples were collected from the upper 20-cm layer on an approximately 20-m grid using a global positioning system unit. The coordinates of the sample locations (X, Y) are shown in Fig. 1. The landform is complex with the dominant surface textures of the soil ranging from sandy to medium clay loam. The soil is slightly alkaline (pH , 7.9). Irrigation is poor. The site is characterized by a warm-temperate continental monsoon climate, with an average annual temperature of 14.6-C and mean annual precipitation of about 680 mm. The soil samples were placed into plastic bags, air-dried, ground to pass through a 2-mm sieve, and analyzed for soil physicochemical properties. Organic matter (OM) content was measured using the wet oxidation method of Walkley and Black (Nelson and Sommers, 1982). Alkaline hydrolyzable N (AN) was measured using the alkaline hydrolysis diffusion method (Bao, 2005). Available phosphorus (AP) was determined by the Olsen extraction method using alkaline sodium bicarbonate as the extractant in a 20:1 ratio (Olsen et al., 1954). Available potassium (AK) was measured using extraction with the

FIG. 1. Soil sample distribution under three grids (20 m, 40 m, 60 m) in the 4-ha area.

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Comparison of Kriging Interpolation Precision

ammonium acetate extraction method (Richards, 1954). Available Fe, Cu, Mn, and Zn were extracted using diethylenetriamine pentaacetic acid (Lindsay and Norvell, 1978) and analyzed using inductively coupled plasmaYatomic emission spectroscopy. Descriptive statistics, including mean, S.D., minimum, median, maximum, coef?cient of variation (CV), skewness, and kurtosis, were calculated for each variable with SPSS-13.0. The distributions of these variables were tested for normality using Kolmogorov-Smirnov statistics. Semivariance calculation and semivariogram function model ?tting were performed using the geostastistical software ArcGIS for Windows. The data of the selected points must be deleted in the process of kriging interpolation. Then the interpolation results were evaluated by comparing the data of selected points from kriging with those of the measured values. The values of the seven points were deleted from the data set, and the remaining values were used for interpolation by performing the interpolation algorithm at different intervals (20 m, 40 m, and 60 m, respectively). The interpolation values of the seven soil points under the three intervals were then compared with the actual measurements. A total of 104 points was used for kriging in the 20-m grid. Twenty-seven sampling points were selected for the kriging in the 40-m grid by removing every other row and deleting every other rank in the actual sample ?gure. Fourteen soil points were used for the kriging of the 60-m grid. The points were chosen by deleting every after two rows and removing every after two ranks in the actual sample ?gure (Fig. 1). To evaluate the accuracy of the estimates, the performance of each interpolation under different intervals was assessed by comparing the deviation of estimates from the measured data through cross-validation (Webster and Oliver, 2001.). The comparison results of the performance among the three intervals were obtained using the following statistics: mean error (ME), mean square error (MSE), average standardized error (ASE), root mean square error (RMSE), and root mean square standardized error (RMSSE). The ME was used to determine the degree of bias in the estimates; MSE provided a measure of the size of the MSE; ASE was used to identify the degree of ASE; RMSE provided a measure of the error size that it is sensitive to outliers; and RMSSE was used to determine the degree of RMSSE. The ?ve error statistics of predictions were used in the cross-validation analysis. The equations are as follows (Johnston et al., 2001): ME ? 1 N ~ ?Z?xi ?jZ?xi ?? ? N i?1 ?1? ?2?

which should be approximately zero. The RMSE and ASE reveal the precision of prediction. Their values should be as small as possible. The RMSSE compares the error variance with the kriging variance. The RMSSE should be approximately 1. If the RMSE equals ASE, then all errors are of the same smallness. If ASE 9 RMSE, or RMSSE G 1, the model-predicted values are larger than the actual values (Tang and Yang, 2006).

RESULTS AND DISCUSSION Descriptive Statistics
A summary of the statistics of the soil parameters is shown in Table 1. The descriptive statistics of soil data suggest that the data are all normally distributed (according to KolmogorovSmirnov test, P 9 0.05; Table 1). The CV for each of the soil variables was signi?cantly varied. The greatest variation was observed in AP (43.85%), whereas the least variation was found in ACu (13.49%). Similar results were reported by Wei et al. (2009). Variations in organic matter and ACu were low (CV G15%), whereas all other soil variables exhibited moderate variation (CV 15%Y50%); these results were in accordance with the guidelines for determining the variability of soil properties (Warrick, 1998). Several researchers (Cambardella et al., 1994; Gupta et al., 1997) have shown coef?cients of variation ranging from 30% to 55% for P and from 19% to 43% for K. Yasrebi et al. (2008) also reported a medium variation for AFe and AMn and a low variation for ACu. The descriptive statistics of the soil properties within the seven selected points (Fig. 1) are as follows. According to the maximum-to-minimum ratios, AMn had the highest variability, followed by AP. For AN, point A had the greatest value, whereas the remaining points were average. All soil properties were moderate at point B. All soil variables had moderate content and large variability in the study area.

Geostatistical Analysis
To identify the possible spatial structure of different soil variables, semivariograms were calculated. The best model that describes these spatial structures was identi?ed. The result of the geostatistical analysis is shown in Table 2. This analysis ?tted several spatial distribution models, exhibiting different spatial dependence levels for the soil variables. The coef?cient of determination (R2) of all variables, except for AZn and OM, was greater than 0.94, indicating good ?ts. All soil variables were modeled satisfactorily with spherical models. Ruth and Lennartz ¨ (2008) also found that all soil properties can best be described using spherical models. All variables except for AZn (strongly spatially dependent) were moderately spatially dependent, with the nugget-sill ratios ranging from 31.76% to 49.99%. Wang et al. (2009) found that most of the soil properties in the studied area were classed as moderately spatially dependent. The ranges of spatial dependences exhibited a large variation (from 34.30 m for AZn to 376.30 m for AMn; as shown in Table 2). Knowledge of the range of in?uence for various soil variables allows for the construction of independent data sets that can be used for classical statistical analysis. This can be used in determining where to resample in the design of future ?eld experiments to avoid spatial dependence. There are large differences among ranges of different soil properties. Yasrebi et al. (2008) found that most soil properties have a variable range between 49.5 m and 181.94 m. Liu et al. (2008) examined a 100-m sampling grid in Central China for site-speci?c fertilizer management and found that all soil variables had a variable range between 274 m and 1,066 m.
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MSE ?

1 N Z?xi ?jZ?xi ? ? ~ N i?1 R?i? s???????????? 1 N ~ R?i? ASE ? N i?1

?3?

? s??????????? 1 N ? ~ ?Z?xi ?jZ?xi ?2 ? RMSE ? N i?1 s????????????( ? 1 N Z?xi ? ~ Z?xi ?j RMSSE ? N i?1 R?i?

?4?
2

g

?5?

? where Z?xi ? is the predicted value, Z(xi) is the observed value, N is the number of values, and R is SE for location i. The criteria for cross-validation were as follows. The ME and MSE indicate the degree of bias in the model prediction,
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TABLE 1. Descriptive Statistics of Soil Chemical Properties (n = 111) in the Study Field Variables OM, g kgj1 AN, mg kgj1 AP, mg kgj1 AK, mg kgj1 AFe, mg kgj1 AMn, mg kgj1 ACu, mg kgj1 AZn, mg kgj1
?

Mean 17.19 74.97 7.39 161.40 8.56 7.37 0.93 1.79

S.D. 2.40 14.31 3.24 30.84 1.71 2.48 0.13 0.65

Minimum 11.25 45.66 2.02 104.68 5.12 3.46 0.72 0.57

Median 16.85 71.25 6.94 159.31 8.64 6.74 0.92 1.68

Maximum 22.78 110.27 14.23 239.43 12.42 14.50 1.25 3.31

CV, % 13.95 19.09 43.85 19.10 20.00 33.69 13.49 36.51

Skewness 0.38 0.63 0.69 0.60 0.14 0.74 0.40 0.77

Kurtosis j0.07 0.01 j0.20 j0.15 j0.21 j0.17 j0.31 j0.03

K-S test? 0.33 0.12 0.16 0.17 0.71 0.11 0.82 0.13

K-S test: Kolmogorov-Smirnov test was used to test the signi?cance level of normality; all variables were normally distributed (P 9 0.05). OM: organic matter.

Interpolation Results Analysis for the 20-m Interval
The interpolation errors from seven selected sample points arranged in a 20-m interval are shown in Table 3. The results of kriging indicated that OM was overestimated on four points (B, D, E, and F) and underestimated on three points (A, C, and G); the greatest/largest and the smallest prediction errors were found at points E and G, respectively. Organic matter content had a minimum error of average (EA), whereas the OM of the seven points was overestimated. For all soil properties, the largest interpolation error was AMn on point F (116.52%). This is mainly because the AMn content of the point was signi?cantly lower than those of the surrounding points. Consequently, the krigingpredicted values were magni?ed by the weighting process. The results of cross-validation are shown in Table 3. The ME was always nearly equal to the MSE, ASE was slightly equal to RMSE, and the values of RMSSE were always close to 1. Ultimately, kriging was shown to be accurate for most soil variables (AN, AP, AK, AFe, and AZn) by the ?ve statistical criteria given in the 20-m interval.

diction. The results indicate that the precision of the prediction in the 20-m sampling interval was better than 40 m. The mean interpolation error for AN at the seven points was less than 0.64%, whereas the largest error was AMn at point F (141.24%) primarily because of the observation that the AMn content of the point was signi?cantly lower than those of the surrounding points. Consequently, the kriging-predicted values were magni?ed by the weighting process. The results of cross-validation indicate that the interpolation results in the 40-m sampling interval were worse than those from the 20-m sampling interval. For AZn, the absolute values of ME and MSE were slightly greater than zero, whereas the absolute value of RMSE was remarkably close to and less than that of ASE; AZn was underestimated in the 40-m sampling grid.

Interpolation Results Analysis for the 60-m Interval
Based on the accuracy of estimates obtained from the crossvalidation procedures and the errors of kriging, the results for the 60-m sampling interval are shown Table 5. The errors of interpolation on speci?c sampling points were larger than those for the 20-m and 40-m sampling intervals. The largest error was AP, which was as great as 146.91% at point F. The interpolation error of point G was zero for AP and AK; at the same point, the error of AFe was only 0.03%. The absolute values of ME, RMSE, ASE, and MSE of ACu were very close to zero, and

Interpolation Results Analysis for the 40-m Interval
Errors of kriging and the results of cross-validation from the seven points arranged in the 40-m interval are shown in Table 4. These data may be more useful in comparing the errors of pre-

TABLE 2. Characteristic of Calculated Semivariograms for All Soil Properties in Study Area Variable OM AN AP AK AFe AMn ACu AZn
? ?

Lag,? m 22.90 17.89 23.00 25.12 20.20 19.10 19.92 17.03

Model? S S S S S S S S

Co§ 1.81 105.60 3.91 435.00 1.80 4.66 0.01 0.06

Co + C 5.86 232.90 12.31 1179.10 3.59 9.32 0.02 0.44

Nugget,|| % 30.87 45.34 31.76 36.89 49.99 49.99 49.71 13.61

Spatial class? M M M M M M M S

Range, m 56.50 112.60 124.90 312.40 233.20 376.30 89.30 34.30

R2 0.875 0.996 0.996 0.947 0.980 0.990 0.985 0.646

RSS 4.73Ej01 5.39E+01 1.43Ej01 6.21E+03 3.05Ej02 2.33Ej01 6.68Ej07 1.05Ej02

Lag: lag interval. S: spherical models. § Co: nugget variance; C: structural variance. || Nugget %: Co/(Co + C) ? 100. ? M: moderate spatial dependence (nugget between 25% and 75%); S: strong spatial dependence (nugget, G25%). RSS: reduced sums of squares.

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TABLE 3. Error of Prediction and the Results of Cross-Validation From the Seven Points Arranged in the 20-m Sampling Interval Point A B C D E F G EA ME RMSE ASE MSE RMSSE OM, % 4.48 j4.07 10.07 j6.34 j13.13 j12.84 3.00 j1.99 j0.008 2.091 2.195 j0.003 0.952 AN, % 13.73 j0.04 j3.84 10.78 j2.55 j22.60 j11.94 j1.49 j0.010 11.840 12.380 0.001 0.959 AP, % j20.08 7.58 j24.12 10.00 j4.66 6.65 j51.39 j8.49 j0.007 2.301 2.506 0.001 0.921 AK, % j2.80 9.24 5.62 j15.06 j11.58 j9.42 j5.72 j3.71 j0.049 24.700 23.000 0.000 1.070 ACu, % j4.55 j4.22 19.48 j6.51 j14.89 j18.16 j17.39 j4.31 0.001 0.111 0.115 0.005 0.970 AFe, % j0.21 j5.11 19.18 j2.25 j4.40 j57.70 j24.51 j5.62 0.003 1.334 1.492 0.001 0.901 AMn, % j11.83 j54.22 34.96 j15.93 j15.24 j116.52 j10.21 j13.43 j0.003 2.229 2.335 0.000 0.959 AZn, % j11.14 j2.68 5.24 j17.12 35.03 j46.01 2.25 0.31 j0.005 0.657 0.656 j0.008 1.003

RMSE G ASE, RMSSE G 1. Consequently, ACu provided better interpolation results. The ACu was slightly overestimated at this sampling interval. The interpolation result of AZn was better as well, and it was overestimated by kriging.

Comparison of Interpolation Error for the Three Sampling Intervals
The EM and the EA of interpolation of the eight soil properties at all seven points are shown in Table 6. When the size of the sampling interval increased, the absolute value of EM and the EA of OM decreased. The overestimate was gradually reduced until it was underestimated. The absolute value of the interpolation error was gradually reduced too. For AP, the opposite trend was observed. The size of the sampling interval increased, along with the two types of error. Other soil variables exhibited a similar trend. Compared with the CV the interpo, lation error was signi?cantly related to CV.

Comparison of Maps of Ordinary Kriging Under the Three Sampling Intervals
The amount of variability and the spatial patterns for each sampling procedure were studied by observing the soil test in-

terpretation classes. The spatial distribution maps of all variables under the different sampling intervals in the selected study site are shown in Fig. 2 (20-m interval, 40-m interval, 60-m interval). All soil properties had a similar distribution with the different sampling intervals (Fig. 2). As the sampling density increased, the patches of spatial distribution of the soil properties became increasingly evident. The accuracy of interpolation also continuously improved. The interpolated map of OM for the three intervals showed strong positional similarities, with high contents in the southwest and middle of the ?eld and low contents distributed in the east, south, west, and middle parts of the ?eld (Fig. 2). The planting distribution used by the farmer may explain this observation. Different planting patterns, crops, and types and quantities of fertilizer likely affected the distribution of OM. For AK, the interpolation of the surrounding area of point A was satisfactory under the three sampling intervals. Smaller interpolation errors were found in the midwest part of the study area with the 40-m sampling interval. The minimum interpolation error was observed in the eastern and southern parts of the area with the 20-m sampling interval. Potassium fertilizer was not typically used in the study area. From the perspective of the producer, underapplication of potassium fertilizer usually resulted in greater economic risks than its overapplication in a

TABLE 4. Error of Prediction and the Results of Cross-Validation From the Seven Points Arranged in the 40-m Sampling Interval Point A B C D E F G EA ME RMSE ASE MSE RMSSE OM, % 6.56 5.59 15.60 j13.03 j18.42 j14.71 5.76 j0.64 0.019 2.265 2.049 0.009 1.089 AN, % 19.41 3.52 j6.50 8.25 j3.00 j32.54 j20.05 j3.21 j0.017 13.910 14.270 j0.002 0.983 AP, % j11.15 j8.19 j113.17 j1.12 6.61 3.38 j54.45 j15.63 j0.059 2.726 2.630 j0.017 1.032 AK, % j15.64 4.12 9.41 j26.16 j24.00 j7.94 j7.78 j8.69 0.556 26.700 22.820 0.015 1.153 ACu, % j1.75 1.10 21.90 j7.75 j10.82 j22.78 j30.49 j4.39 0.003 0.097 0.107 0.027 0.921 AFe, % 3.37 j2.09 18.97 j1.04 3.86 j62.66 j39.66 j5.33 0.077 1.422 1.598 0.046 0.897 AMn, % j16.74 j58.47 35.78 j25.78 j13.64 j141.24 j20.21 j18.96 0.004 2.377 2.346 0.002 1.017 AZn, % 0.18 4.70 11.30 j11.01 42.36 j25.94 j11.41 6.45 0.028 0.581 0.577 0.047 1.005

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TABLE 5. Error of Prediction and the Results of Cross-Validation From the Seven Points Arranged in the 60-m Sampling Interval Point A B C D E F G EA ME RMSE ASE MSE RMSSE OM, % j6.97 j8.96 j9.57 8.65 13.06 11.40 j6.34 j0.64 0.03 1.78 1.90 0.00 0.96 AN, % j16.06 j2.81 j4.91 j20.79 2.15 29.03 2.14 j3.21 j0.93 17.00 15.60 j0.06 1.10 AP, % 5.10 j30.54 14.71 j106.57 j74.95 j146.91 0.00 j15.63 j0.30 2.55 2.42 j0.07 0.94 AK, % 4.74 j21.90 j4.92 10.52 12.63 5.33 0.00 j8.69 j5.53 22.79 22.79 j0.13 0.92 ACu, % 5.78 j3.99 j37.36 6.87 20.05 13.20 j0.20 j4.39 0.00 0.08 0.09 0.01 0.91 AFe, % j0.36 j1.75 j48.47 j9.62 j7.23 23.97 j0.03 j5.33 0.01 0.66 0.93 0.01 0.73 AMn, % 11.15 26.73 j75.07 4.86 6.84 59.43 13.26 j18.96 0.21 3.13 2.95 0.07 1.06 AZn, % 4.24 3.09 j0.60 17.40 j59.37 24.28 10.22 6.45 0.01 0.74 0.79 0.01 0.93

tobacco ?eld. However, less potassium fertilizer was used with other crops. Thus, the distribution of AK content decreased from south to north. Soil parent materials may be another main cause of the varied distribution. The effectiveness of manganese was distinctly related to soil OM. The Mn levels were in?uenced by soil pH in the study area (Jiang et al., 2010). The maps of AMn exhibited greater similarity to those of OM under these three sampling intervals, with a low value in the northern part of the ?eld and a high value in the southern part of the ?eld (Fig. 2). The lowest interpolation error of AMn was found with the 40-m sampling interval, followed by the 20-m sampling interval, whereas the highest was observed with the 60-m sampling interval. The results of crossvalidation of the remaining soil properties indicated that a reasonable sampling interval of AN, AP, and AFe in the site was 20 m, whereas that for ACu was 60 m. From the analytical results of kriging, the interpolation error of all soil properties did not increase with the size of the sampling interval. Therefore, a greater sampling density does not always result in lesser interpolation error in precision agriculture. The results obtained are similar to those of Webster and Oliver (1992), Dungan (2002), and Ortiz and Deutsch (2002). Consequently, to determine the optimal size of the soil sampling interval, the spatial autocorrelation, trend effect, and anisotropy combined with practical conditions must be further analyzed. Numerous studies (Beckie, 1996; Gotway et al., 1996; SkLien and Bloschl, 2006) clearly illustrated that sampling intensity can ¨ in?uence the distribution and shape of areas that represent different soil properties within a ?eld.

This study provides a theoretical basis for the practice of precision agriculture. For agricultural production, examining the distribution and abundance and shortage situation of all nutrients is not necessary, with the exception of the restrictive fertilizer of the crop. Therefore, the restrictive nutrient must be closely considered by the producer when determining the sampling interval. For example, AN and AK are highly important factors that affect the quality of ?ue-cured tobacco (Liu, 2003). Thus, we collected soil samples at the 20-m interval in the studied ?eld. Further studies will be conducted to determine the reasonable intervals for cost-effective soil sampling in accordance with spatial autocorrelation, trend effect, and anisotropy effect of soil properties.

CONCLUSIONS
The PingDingShan Tobacco Plantation in China was selected as the area of study. Geostatistics combined with geographical information system was used to investigate the reasonable sampling interval of eight soil variables using 111 top soil samples. The conclusions are as follow: (1) Generally, the kriging interpolation error decreased with the size of sampling interval for most of the soil properties. However, for certain sites or nutrients, the interpolation error decreased as the sampling interval within a certain range increased. Therefore, growers may ?rst investigate the distribution of soil properties and spatial autocorrelation to determine the size of the sampling interval and then analyze soil potential and other site-speci?c production limitations

TABLE 6. The Mean of Error of Interpolation and the Error of Mean in the Seven Points Items EM Grid scale 20 m 40 m 60 m 20 m 40 m 60 m OM,? % j18.83 j12.65 1.28 j1.99 j0.64 0.15 AN, % j16.45 j30.90 j11.25 j1.49 j3.21 j0.06 AP, % j76.03 j178.08 j339.16 j8.49 j15.63 j37.62 AK, % j29.73 j67.98 6.41 j3.71 j8.69 1.26 ACu, % j46.23 j50.58 4.34 j4.31 j4.39 0.66 AFe, % j75.01 j79.25 j43.50 j5.62 j5.33 j6.90 AMn, % j188.99 j240.31 47.20 j13.43 j18.96 9.59 AZn, % j34.43 10.18 j0.75 0.31 6.45 j0.19

EA

Negative: overestimate; positive: underestimate. EM, the mean of error of interpolation; EA, the error of average.

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FIG. 2. Distribution maps of soil OM, AN, AP, AK, AFe, ACu, AZn, and AMn by kriging interpolation under the three sampling intervals (20 m, 40 m, 60 m). * 2010 Lippincott Williams & Wilkins www.soilsci.com

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FIG. 2. (Continued)

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FIG. 2. (Continued)

after soil test levels are corrected or eliminated as a production limitation. (2) The CV of soil properties is high, whereas the appropriate sampling interval is small, and vice versa. Therefore, the spatial variability of soil properties must be considered when setting their reasonable sampling interval. (3) In this region, the interpolation errors for OM and ACu increased from the 60-m to the 20-m sampling interval, revealing that the best sampling interval was 60 m. The AN, AP, AK, AFe, and AZn had the smallest kriging errors in the 20-m sampling interval. For AMn, the least interpolation error was shown in the 40-m sampling interval. The variability of soil properties not only exists in the spatial dimension, but also in the temporal dimension. Because of time constraints, the temporal variability or stability of these variables was not taken into account. Therefore, further research must be conducted to de?ne reasonable sampling intervals according to the spatial variability and temporal variability of
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soil attributes. In agricultural production, obtaining the distribution maps to guide nutrient fertilization by intensive sampling and nutrient analysis is not economical. Therefore, the potential success of soil sampling depends on estimation precision based on the CV spatial variability, and autocorrelation, trend effect, , and anisotropy effect of soil properties. ACKNOWLEDGMENTS The authors thank Gu Shao-Long and Qian Hua for help with ?eld sampling. Financial support for this work was provided by the National Tobacco Monopoly Bureau and Key Laboratory on Cultivation of Tobacco Industry and the Pingdingshan Tobacco Company. REFERENCES
Bao, S. D. 2005. Agricultural and Chemistry Analysis of Soil [In Chinese]. Agriculture Press, Beijing, China.

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