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Published in Soil Sci. Soc. Am. J. 69:427-442 (2005).
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

Division S-4—Soil Fertility & Plant Nutrition

Mapping Soil pH

Accuracy of Common Soil Sampling Strategies and Estimation Techniques

S. M. Broudera,*, B. S. Hofmanna and D. K. Morrisb

a Agronomy Dep., Purdue Univ., 915 W. State Street, West Lafayette, IN, 47907
b Biological and Agricultural Engineering Dep., 123 E.B. Doran Bldg., Louisiana State University, Baton Rouge, LA 70803

* Corresponding author (sbrouder{at}purdue.edu)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
The theoretical profitability of variable rate (VR) lime management has driven adoption of intensive soil sampling strategies used with complex statistical techniques without demonstration of approach efficacy. Our objective was to compare the accuracy of spatially continuous pH and lime requirement (LR) maps derived from commercially used approaches to sampling and LR prediction at unsampled locations. We evaluated point (P) sampling on 0.1-, 0.4-, and 1.0-ha grids and area composite (AC) sampling by 1-ha grids, soil type (ST), and whole field (WF). Inverse distance (ID) weighting and ordinary kriging were applied to water pH and LR data from 11 fields. Modeling of semivariance identified range parameters of ≤100 m. For intensive P sampling (0.1- or 0.4-ha grids), kriging was occasionally more accurate than ID weighting but mean absolute error (MAE) differences were small (≤0.01 pH units and ≤0.13 Mg lime ha–1), suggesting little practical consequence to prediction method selection. One-hectare point data were too sparse to produce variograms and applying ID weighting to these data found only small advantages over WF compositing. Lime use was either unaltered or minimally reduced (10%) by 1-ha P as compared with WF compositing. When compared with WF composites, map prediction efficiencies (PEs) based on mean square error (MSE) analysis ranged from 7 to 51, –13 to 40, and –6 to 54% for ST compositing, 1- and 0.4-ha P sampling, respectively. These results suggest ST compositing remains viable and cost-effect for pH management, especially where ancillary information exists to verify distinct soil series boundaries.

Abbreviations: AC, area composite • CP, center point • CV, coefficient of variation • DPAC, Davis Purdue Agricultural Center • ID, inverse distance • IQR, interquartile range • LR, lime requirement • MAE, mean absolute error • MSE, mean square error • NEPAC, Northeast Purdue Agricultural Center • P, point • PA, precision agriculture • PE, prediction efficiency • SMP, Shoemaker-McLean-Pratt • ST, soil type • TF, true farm • VR, variable rate • WF, whole field


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
THE NEGATIVE IMPACTS of soil acidity and the qualitative value of liming acid soils to enhance agricultural productivity have been well documented (for reviews see Adams, 1984; Ulrich and Sumner, 1991; Black, 1993). Over-liming of agricultural soils is also known to reduce potential soil productivity through a variety of complex, pH-dependent processes ranging from restricted nutrient availability (e.g., Marschner, 1995, p. 641–657; Olness, 1999) to increased disease pressure (Huber and Wilhelm, 1988; Kurtzweil et al., 2002) or weed pressure (Childs et al., 1997). Since the profitability potential for precision agriculture (PA) and VR input management is anticipated to increase if profitability penalties follow both under and overapplication, VR lime application has been repeatedly identified as an expected benefit of PA (Pierce and Nowak, 1999; Bongiovanni and Lowenberg-DeBoer, 2000). Furthermore, within field variability in soil pH and LR has long been understood to be a common feature of commercial fields (Linsley and Bauer, 1929; Cline 1944; Peck and Melsted, 1973). Consequently, theoretical benefits coupled with aggressive commercialization of the enabling technologies have resulted in implementation of soil testing and VR lime application strategies that have not yet passed rigorous scientific evaluation.

Studies providing convincing support of VR lime management are few in number and tend not to be comprehensive in nature. For the benefits of PA and VR applications to accrue, the management objective must be (i) measurable, (ii) treatable, and (iii) result in a quantifiable gain in productivity or production efficiency (Pierce and Nowak, 1999). In comparative assessments of soil fertility parameters for PA, coefficients of variation (CV) of soil pH tend to be relatively low (<20%) when compared with CVs for available P and K (>30%) (Cambardella and Karlen, 1999; Chang et al., 1999; Geypens et al., 1999; Kravchenko et al., 1999; Wollenhaupt et al., 1997). In reviewing PA management potentials for different inputs, Wollenhaupt et al. (1997) state that soil properties with low CVs tend to require less intensive soil sampling schemes, implying that the spatial structure of soil pH should be easier to determine with fewer soil samples than other soil properties, including P and K. However, for soil acidity, the CV is for the log transformation of the management objective, [H+], and large differences in LR may accompany small changes in soil pH. Indeed, some of the studies cited above as well as the summary within McBratney and Pringle (1999) indicate soil pH may have one of the shortest spatial ranges of the soil properties typically tested by producers. This suggests that more not fewer samples may be required to accurately characterize pH and LR spatial structure, especially when grid or other systematic soil sampling strategies are used.

In studies that address measurement feasibility and map development, failure to evaluate map accuracy, the consistency between predicted and observed attribute values for any given location within the mapped region, is a recurring limitation. The accuracy of the map reflects both the suitability of the spatial intensity of sample collection strategy as well as the method used to predict the soil test values of all unsampled locations. Most studies document only that spatial variation in soil pH exists within typical farm management units with some providing characterization of spatial structure attributes by semivariance analysis. To date, few studies have examined the development of VR LR maps, and reports have tended not to include any true validation of the accuracy of the input map. For example, Borgelt et al. (1994) used intensive soil sampling patterns and kriging applied to semivariogram or variogram analysis to demonstrate that WF application of lime would result in an overapplication in 9 to 12% of a field and an underapplication in 37 to 41%. The authors acknowledge that simple documentation of over and underapplication does not equate to economic justification for the practice because it does not account for the production penalties associated with failing to manage this variability. However, they also did not quantify how much more accurate their VR map was at unsampled locations when compared with the uniform application map. Pierce and Warncke (2000) did attempt to evaluate the relative accuracy of LR maps drawn from the application of ID squared (power weight 2 or P = 2) interpolation of samples collected from 30.5-, 61-, and 91.5-m grids. They found no predictable relationship between measured and estimated LR at any sampling intensity although they acknowledge that results may be confounded with temporal variability. The limitations of this study are that map accuracy was assessed only in two very small areas (1-ha units), and the number of sample points for comparisons between predicted and measured LR were limited (nine points). Furthermore, too few details on the sampling methodologies (cores/composite, collection area per composite) were provided. Bianchini and Mallarino (2002) also examined soil sampling schemes for LR mapping and suggested that zone sampling may provide as much useful information as intensive (0.1 ha) point sampling, but a comparative analysis of map accuracy was not presented. The degree of improvement in map accuracy by intensification of sampling strategies is critical to any analysis of the value of the activity and no useful assessment of a VR activity can proceed without this information. Indeed, the only economic analysis showing profitability of VR lime application presumes that LR maps generated by coarse grids (e.g., 1-ha CP samples) were meaningful and accurate (Bongiovanni et al., 2000).

A review of comparative studies of interpolation methods applied to soil properties demonstrates that while method choice can significantly influence map accuracy, the a priori determination of which method is most suitable to apply to a given dataset is difficult to make and the practical consequences difficult to discern. Laslett et al. (1987) evaluated numerous methods for mapping soil pH and, based on prediction sums of squares, concluded both IDP=2 and isotropic kriging performed well for water and CaCl2 pH. In the past decade, several studies have compared kriging to ID for mapping other soil properties (NO3–N and organic matter, Gotway et al., 1996; P and K, Wollenhaupt et al., 1994; Kravchenko and Bullock, 1999) and have found either no difference in predictive accuracy between methods or a slight tendency for kriging to be more robust for multiple datasets than ID when no consideration is given to the selection of the ID weighting power. For soil pH, Mueller et al. (2001) present the most complete examination of the impacts of both soil sampling densities and interpolation techniques on map quality. They concluded that the commercially used 100-m grid was grossly inadequate for predicting within-field variation in soil pH but more intensive soil sampling (still within commercial constraints) appeared to offer little improvement, and the method of interpolation (ID, kriging or nearest neighbor analysis) had little impact on the outcome. While the Mueller et al. (2001) study presents some solid evidence to challenge the efficacy of practices that are becoming common in soil acidity and fertility management, the universality of these results require demonstration across other WF management units with different soil attributes. Furthermore, while this study addressed the accuracy of soil pH maps, it again did not address the accuracy of the LR map developed from the separate measurement of buffer pH. The Shoemaker-McLean-Pratt (SMP) buffer method was designed for soils with large LRs and significant reserves of exchangeable Al (Shoemaker et al., 1961) and is the recommended method for most soils in the north central region of the USA (Brown, 1998). Since the optimal LR is not a direct function of the water pH measurement, the accuracy of the soil pH map is not necessarily reflective of the accuracy of the LR map.

At present there is no consensus regarding best or most robust approaches to mapping LR and recommendations to producers remain extremely vague. Recent technical bulletins have supported the use of regular grid sampling approaches for the management of non-mobile nutrients and lime. Frequently they endorse a 1-ha or larger grid unit sampling strategy as more informative than WF, ST or other large area or zones collection strategies (Rehm et al., 2001), even though studies consistently show that spatial variability within a 1-ha unit can be comparable with that of the whole field. Other than stressing the importance of collecting multiple core samples, current recommendations offer little guidance on area over which the composite should be collected (the whole grid unit or cell versus at a georeferenced location within the grid) and on the best approach to interpolation. Many commercially available software packages offer map development by kriging and ID. For ID, exponent values of 2, 3, or 4 have been the most commonly used in agricultural studies (Kravchenko et al., 1999) and ID (P = 2 or 4) is a common default option (e.g., Hohl and Mayo, 1997, p. 347–373; Site-Specific Technology Development Group, Inc., 1999). Clearly, there remains a need to enhance the existing documentation on the relative effectiveness of such coarse grid sampling strategies and to provide a comparative assessment of pH and LR map accuracy to WF management using the variety of predictive strategies that are common in the commercial sector.

The objective of this study was to compare the accuracy of spatially continuous pH and LR maps derived from commercially used approaches to sampling and prediction of LR at unsampled locations. Specific objectives were (i) to characterize within field variability in soil pH and LR for typical production agriculture management units in the eastern cornbelt and (ii) to assess the accuracy of maps developed from commonly used, systematic soil sampling strategies and interpolation techniques, especially when compared with more traditional approaches including LR map development from composite sampling of whole fields or major soil map units within fields.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
The locations for this study were two of Purdue University's regional research centers, the Northeast Purdue Agricultural Center (NEPAC) near Fort Wayne, IN, and the Davis Purdue Agricultural Center (DPAC) near Muncie, IN. At NEPAC, seven contiguous fields were sampled in 1991 on a 30 x 30 m square (0.1-ha) grid with samples collected from the georeferenced CP (sampling strategy CP0.1ha; Table 1). Individual fields were roughly rectangular in shape, ranging in size from 6.3 to 8.4 ha for a total farm size of 50 ha. At DPAC, two fields, D and F, were also sampled on a 30 x 30 m square grid (Spring 2000). The DPAC contiguous fields R and V were sampled in 1998 at a 0.2-ha grid density using a stratified, systematic unaligned strategy (Wollenhaupt et al., 1997) to select the within grid point sample location (sampling strategy P0.2ha). At each sample collection point (all fields and locations), a 10- to 15-core composite was collected (0.2-m sample depth) from a roughly 7.5-m2 sample area. Samples were analyzed by a commercial laboratory for pH and LR (SMP single buffer method [pHSMP]) according to recommended soil testing procedures for the region (Brown, 1998).


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  		Table 1. Area descriptions, primary soil sampling system and soil map units of the experimental fields at the Purdue University Northeast Purdue Agricultural Center (NEPAC) and Davis Purdue Agricultural Center (DPAC) farms.

 
University recommendations were used to select the soil-specific input rates for lime for each point sample location. The fertility management guidelines common to Michigan, Ohio, and Indiana (Tri-State Recommendations, Vitosh et al., 1995) recommend correcting soil pH with lime when water pH values fall 0.2 units below optimum. A pH of 6.0 to 6.5 is considered desirable for the mineral soils used in this study, and therefore a lime application would be recommended for soils of pH ≤ 5.8. Input rates for lime to correct soil pH to 6.5 are calculated as

[1]
assuming 0.2-m incorporation of agricultural limestone (90% neutralizing value).

Univariate statistics were calculated for pH and LR for the CP0.1ha/P0.2ha datasets from each field. Semivariance analysis was used to characterize soil pH and LR spatial autocorrelation. For this analysis, datasets from contiguous fields (Fields R and V at DPAC and all NEPAC fields) were considered together because available farm records either showed identical management for recent history or were too incomplete to identify substantive management differences among fields. Furthermore, many of the fields were relatively small (≤7 ha) and thus semivariance analyses were expected to be dominated by edge effects. Semivariance for a specific distance interval was calculated as

[2]
where h is a specific distance class for pairs of observations, zi is the measured sample value at Point i, zi+h is the measured sample value at Point i + h, and N(h) is the total number of sample couples for h (Isaaks and Srivastava, 1989, p. 40–66). Spherical, exponential, linear, linear to sill and gaussian isotropic models were tested for goodness-of-fit to the variogram (GS+ Software, Robertson, 1998). Selection among these models and of the specific model parameter values themselves were based on minimizing the reduced sums of squares.

Both ordinary block kriging and ID were used to estimate pH and LR at unsampled locations. Cross validation was performed to evaluate predictive accuracy. Each measured point in a given sample set was individually removed from the set and its value estimated via kriging from all remaining observations (Isaaks and Srivastava, 1989, p. 40–66). For a given dataset, the relationship between values estimated by cross validation (independent variable) and actual values (dependent variable) was characterized with regression analysis.

To assess both the impact of sampling density as well as interpolation method (kriging or ID), data subsets representing point sample densities of 0.4 and 1.0 ha were extracted and used to predict pH and LR for the remaining observations in the original data sets. For the 0.4-ha sample density, a 64 x 64 m grid was superimposed over the original sample collection pattern and 1 of the 4 points within the expanded cell was randomly selected to represent the point sample for the new grid unit (sampling strategy P0.4ha). For DPAC R and V, where the densest sampling was P0.2ha, between 2 and 4 points occurred within the simulated 64-m grid. The same process was followed for simulating a 1.0-ha sample collection strategy but, instead of randomly selecting a point within the 100 x 100 m grid, the point sample location closest to the center of the grid cell was selected (sampling strategy CP1ha). Semivariance analysis with kriging and ID were then applied as described above to develop pH and LR maps for each field. In the case of the CP1ha datasets, pH, and LR maps were also developed by disregarding all neighboring values and simply assuming the center point (CP) observation of a given grid unit represented all unknown locations within that grid (No Smooth. CP1ha).

The relative success of a given sampling density and estimation method was examined by evaluating the difference between estimated and known values. For the CP0.1ha and P0.2ha sampling densities, estimated values were strictly those derived from cross-validation. For P0.4ha and CP1.0ha collection strategies, cross-validation estimates were made for all sample points within the collection strategy subset. Remaining sample points from a given field were treated as an independent dataset for a jackknife approach to validation of the method. Statistical comparisons of slopes and intercepts of regression relationships between predicted and actual values derived from cross-validation versus jackknife validation and comparisons of means and variances indicated no consistent, systematic, or significant differences between the two populations of predicted values. Cross-validation and jackknife datasets were then combined so that each original sample location in the CP0.1ha/P0.2ha datasets had an estimated value for all simulated sampling densities and estimation methods examined. Differences between actual and predicted values were calculated and univariate statistics of these residuals were used to assess which method(s) produced the distribution of errors with center, spread, and skewness values closest to zero. To evaluate the bias and spread of the estimation methods, the MAE and MSE were calculated as

[3]

[4]
where n is the number of observations and r is the residual (true – estimated) value for an individual observation. Analysis of variance (SAS Proc. GLM; SAS Institute, 1992) was used to determine the effects of sampling density and estimation method on MAE, MSE, and the interquartile range (IQR) of the residuals.

All point collection strategies (CP0.1ha, P0.2ha, P0.4ha, and CP1ha) were then compared with AC sampling on a 1.0-ha grid (AC1ha) or whole field basis for the relative success of predicting the pH and LR at each original point location. Mean pH, pHSMP, and LR were calculated for the 1.0-ha cells. For individual whole fields two separate estimates for whole-field composite values were developed. The first value was the calculated mean from all collected observations within the field boundary (ACWhole Field or ACWF) while the second value was either measured in a true composite sample made of soil from the sample location subset used in simulated CP1ha collection strategy described above (equivalent weight of air-dry soil from each sample) or the calculated mean of the samples in the CP1ha subset. The latter approach was used for the NEPAC fields, as archived soil samples were not available from this location. This second set of pH and LR represents a composite approach that more closely approximates true commercial practices in that soil was collected from only 10 to 20 locations within a field (designated ACTrue Farm or ACTF). In all cases where composite pH values were calculated and not measured directly, individual values were back-transformed to [H+] before averaging.

To simulate pH and LR maps developed by collecting composite soil samples by STs, discrete zones were delineated for different soil map units identified in the published or order soil survey (scale 1:15840). A given map unit was itself divided into multiple zones if it was spatially discontinuous. Thus, at DPAC where all fields are dominated by three map units (Table 1), the actual numbers of soil-type zones were 9, 5, 6, and 7 for Fields D, F, R, and V, respectively. All CP0.1ha/P0.2ha values within a given zone were averaged to obtain the simulated pH or LR value (strategy designated ACSoil Type or ACST). At NEPAC, the field locations were not georeferenced during sample collection and the exact location of field boundaries relative to the published soil survey is somewhat unclear. Therefore, these data were not used to simulate ACST.

The ACTF strategy was used as the basis for quantifying improvements in mapping accuracy or PE resulting from alternative approaches. A one-sample t test was used to determine if the mean of ACTF residuals deviated from 0. For a given field, a two-sample t test was used to determine if the mean of the residuals from an alternate strategy differed from the mean of the ACTF residual. The equality of the variances of the residual populations from ACTF and the alternate strategy were evaluated with Levine's test. Gotway et al. (1996) quantified the improvement in PE of an alternative mapping strategy when compared to the original approach as

[5]
where MSEOrig and MSEAlt are for deviations of observed from estimated values following the original and alternative strategies, respectively. The PEs for all strategies relative to ACST were also calculated.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Soils at DPAC are in the Blount–Pewamo (fine, illitic, mesic Aeric Ochraqualfs and fine, mixed, mesic Typic Argiaquolls, respectively) association characterized by somewhat poorly to very poorly drained medium textured and moderately fine textured soils (Neely, 1987) (Table 2). Moderately well drained Glynwood (fine, illitic, mesic Aquic Hapludalfs) soils are minor in this association. At NEPAC, Fields 1 and 2 are in the Boyers–Kalamazoo (coarse-loamy, mixed mesic Typic Hapludalfs, fine-loamy, mixed, mesic Typic Hapludalfs, respectively) association characterized by well to somewhat poorly drained soils formed in outwash on terraces, moraines, and bottomland. All other NEPAC fields are in the Morely–Rawson (fine, illitic, mesic, Typic Halpludalfs and fine-loamy, mixed, mesic Typic Hapludalfs, respectively) or Morely–Glynwood association (Ruesch, 1990). The Morley–Rawson association is characterized by nearly level to steep, well to moderately well drained soils formed on glacial till and in loamy outwash over glacial till. The Morley–Glynwood association soils are gently to steeply sloping, well to moderately well drained and formed in glacial till. At both locations, soil surveys (scale 1:15840) indicate individual fields have substantial within-field variability in soil map units suggesting substantial within field variability in related soil chemical properties. Furthermore, as is typical of the region, both farms have a history of manure application, which is likely to introduce more small-scale variability in soil test values.


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  		Table 2. Univariate statistics for soil pH and lime requirement (LR) to correct pH to 6.5 for the Northeast Purdue Agricultural Center (NEPAC) and Davis Purdue Agricultural Center (DPAC) field management units described in Table 1.

 
For each of the 11 study fields, calculated whole-field average pHs indicate that a WF AC sampling might not have identified a need for lime. Arithmetic means ranged from 6.26 to 6.66 while logarithmic means were from 0.15 to 0.30 pH units lower (Table 2). In soil pH studies that have simulated AC sampling by averaging values from an over-sample dataset it is often not clear how the mean was computed. Because arithmetic pH means can be significantly higher than means computed from [H+] (e.g., Mahaman, 1993), it has long been recommended that arithmetic means be used only when the range in pH is narrow (Ball and Williams, 1968). In our study, the pH values that were directly measured in the ACTF composite for DPAC D, F, R, and V were 6.1, 5.9, 6.0, and 5.9, respectively, values that were closer to the back-transformed mean [H+] than to the mean pH (Table 2). However, regardless of how we determined WF mean pH, the individual field values all exceeded 5.8, the recommended critical value for identifying lime need for soils used in this study (Vitosh et al., 1995). Reviews of crop response to lime suggest maximum yields for corn (Zea mays L.) and soybean (Glycine max L.) in the midwestern USA are attained at pHs of approximately 6.6 but yield depressions associated with lowering pH to 6.0 are considered minimal (<1.5 and <10% for corn and soybean, respectively) (Mengel et al., 1987; McLean and Brown, 1984). Therefore, for the purposes of these analyses, we assumed a notable productivity response to lime would only occur at pH < 6 (specifically 5.8).

Within-field variation in pH was substantial, however, and all fields contained areas where lime application would be recommended to optimize crop productivity as well as areas where soil pH neared or exceeded neutrality and lime application would be considered not only unnecessary but also potentially undesirable (Table 2). For a given field, the percentage of observations with pH ≤ 5.8 ranged from 0 to 21. As soil pH levels decrease from 6.0 to 5.5 yield reductions can be anticipated to increase marginally for corn (3%) but more dramatically for soybean (20%; McLean and Brown, 1984). Thus, many of the study fields represent management units where it would be theoretically logical to consider VR lime. A majority of the fields had over a quarter of the sample points requiring <1.0 Mg ha–1 of agricultural limestone while >4 Mg ha–1 were required for another quarter of the sample locations.

In estimating soil test values at unknown locations, high CVs and deviations from normality of the sampled population are indications that prediction may be problematic. All pH data tended to be normally distributed. At NEPAC, skewness and kurtosis values were close to zero (Table 2). At DPAC, pH datasets were slightly positively skewed reflecting a greater range in values between the third quartile and the maximum. In contrast, some of the LR datasets tended to have much higher CVs when compared with pH datasets and to be more positively skewed with positive kurtosis (NEPAC 5, 6, and 7). However the degree of skewness was less than is commonly seen with other soil test data (e.g., P and K, Kravchenko et al., 1999), and LR deviations from normality were not ones that could be addressed with common default transformations available in commercial software (lognormal or square root). Therefore, raw LR data were used in all analyses.

All fields exhibited some degree of spatial autocorrelation. Anisotropic analysis revealed no strong, direction-dependent trends in the data and therefore all reported data are for isotropic variogram models. When CP0.1ha/P0.2ha pH and LR data were examined, variograms could be satisfactorily fit with either an exponential or spherical model (Fig. 1). Differences in fit between models were not large but data are reported only for the model with the lowest reduced sums of squares (Table 3). Spatial structure accounted for between 29 and 73% of the observed variation. This percentage assumes the variance at the minimum inter-sample distance represents the nugget effect. Nuggets (y-intercepts) estimated by modeling were one-tenth these values but, since no samples were collected at distances closer than 30 m, the accuracy of these modeled values cannot be confirmed. Early work in Indiana farm fields on core-to-core variability over short distances (15 cores evenly spaced over 5-m transects) reported variances ranging from 0.02 to 0.17 (Stivers, 1968) suggesting true nuggets are likely higher than our modeled values.



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  		Fig. 1. (a) Absolute and (b) standardized variograms for pH and (c) absolute and (d) standardized lime requirement (LR) based on point sampling densities of 5 (DPAC R and V) or 10 (all others) locations per hectare. Separate variograms are shown for fields that are not contiguous.

 

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  		Table 3. Parameters of the models fit to variograms for soil pH and lime requirement (LR) for contiguous field areas sampled on a 0.1- or 0.2- (DPAC R and V only) ha grid and selected results following kriging.

 
With one exception, we found range parameters (95% of the sill value for exponential models) for pH and LR were <100 m, results in agreement with Mueller et al. (2001) who examined similar soil types. While a few studies have documented much longer ranges for pH (Kravchenko et al., 1999), the majority report ranges close to 100 m or less. In a literature review of spatial scales of soil test properties, Wollenhaupt et al. (1997) report pH spatial ranges of 20 to 132 m. McBratney and Pringle (1999) used fourth root transformation to obtain an average pH variogram for variogram data from 19 different studies. The average data were best fit by an exponential model with a spatial range of 62 m that identified as spatial structure 70% of the observed variation. Standardizing variograms permits comparisons to be made not only among datasets of the same attribute but among datasets of different attributes (Rossi et al., 1992). In our study, dividing semivariances by field variances for pH and LR (Fig. 1b and 1d, respectively) illustrates the marked similarity of variograms for both pH and LR (all fields and locations) despite large differences among absolute variances (Table 3). The range parameters achieved by fitting an exponential model to pooled data from standardized variograms were approximately 100 m for both pH and LR (data not shown). Thus, our data support a general recommendation against point sampling strategies using grids >1 ha, as they will likely be too sparse to produce useful information on manageable variability in pH.

The standardized variograms for pH and LR from P0.4ha datasets exhibit the same general pattern as the standardized variograms for CP0.1ha/P0.2ha but the variogram features appear less evident (Fig. 2). For some fields, the smallest inter-sample distance (independent variable, Fig. 2) is greater than the range parameter identified through modeling the CP0.1ha/P0.2ha data (Table 3). Furthermore, only half the total distance measured in any direction can legitimately be used in variogram development as lags larger than half the maximum distance primarily compare edges (Rossi et al., 1992). In small fields or fields that are short in one dimension, there will likely be too few points in a regular grid to develop a variogram. In our study, DPAC D and F measure 220 and 190 m, respectively, in their shorter dimension (Table 1), and there were not enough data points to characterize a sill.



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  		Fig. 2. Standardized variograms for (a) pH and (b) lime requirement (LR) based on a point sampling density of 2.5 ha–1 (0.4-ha grid). Separate variograms are shown for fields that are not contiguous.

 
Following kriging, comparison of combined validation results (cross- and jackknife) for the P0.4ha dataset with cross-validation results from the denser dataset (CP0.1ha or P0.2ha) further illustrated loss of prediction accuracy with sparser sampling. When CP0.1ha/P0.2ha data were modeled, ranges (maximum–minimum values) in estimated pH and LR values (Table 3) are slightly less than observed (Table 2), but, for the regressions characterizing the observed–predicted relationship, regression coefficients and y-intercepts were not significantly different from 1 and 0, respectively (Fig. 3 and 4). The sole exception to this observation was for the LR in DPAC D where the regression coefficient of 0.77 was significantly <1 (Fig. 3b). In all cases the regression relationships were significant (r2 = 0.08–0.56). When P0.4ha data were used to model the spatial variation in pH and LR, the significant regressions (r2 = 0.1–0.34) had coefficients < 1 and y-intercepts > 0, reflecting general over- and underprediction of low and high values, respectively. At DPAC D, regressions for pH and LR were not significant.



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  		Fig. 3. Comparison of actual DPAC (a, c, and e) pH and (b, d, and f) lime requirement (LR) values with values estimated by cross validation of block kriging based on either the most dense point sampling strategy (•, 10 [CP0.1ha] or 5 [P0.2ha] points ha–1) or a sparser strategy of 2.5 points ha–1 (P0.4 ha). Estimated CP0.1ha/P0.2ha values are from cross validation while estimated P0.4 ha values represent the combination of results from cross and jackknife validation.

 


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  		Fig. 4. Comparison of actual NEPAC pH (a) and lime requirement (LR: b) values with values estimated by cross validation of block kriging based on either the most dense point sampling strategy (•, 10 points ha–1 [CP0.1ha]) or a sparser strategy of 2.5 points ha–1 (P0.4 ha). Estimated CP0.1ha values are from cross validation while estimated P0.4 ha values represent the combination of results from cross and jackknife validation.

 
While cross validation with replacement is commonly recommended for assessing map accuracy (Isaaks and Srivastava, 1989, p. 40–66), some studies have suggested this method overestimates map error. In comparing this approach to jackknife validation, Mueller et al. (2002) found that estimates of spatial uncertainty in soil test properties were substantially larger for cross validation with replacement, which they attributed to artifact that occurs when all the points to be estimated are separated from their four nearest neighbors by one grid increment, the maximum distance. However, our comparison of these validation approaches found no significant difference. For example, at DPAC RV relationships between actual and estimated pH (kriged) are virtually identical for cross and jackknife validation, as slopes, intercepts, and r2 values were not significantly different (Fig. 5). Our P0.4ha datasets are not CP and thus, unlike Mueller et al. (2001), we were not predicting results for only the maximum inter-sample distances. Furthermore, their independent dataset appears to have a smaller range of soil test values than their cross validation dataset, increasing the likelihood for comparatively better estimation with jackknife validation. The ranges of P and K values in their cross validation dataset were approximately 10 to 80 and 100 to 300 mg kg–1, respectively. The ranges for P and K values in their independent dataset were 10 to 55 and 125 to 225 mg kg–1, respectively. In our study, the cross validation and independent datasets had similar descriptive statistic attributes.



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  		Fig. 5. Comparison of actual DPAC Field R and V pH with pH estimated by either cross validation with replacement (•) or jackknife validation with independent data ({square}). Cross validation estimates were derived following block kriging pH values collected at a density of 2.5 points ha–1 (P0.4 ha).

 
In the comparison of spatial prediction methods for pH and LR, kriging occasionally outperformed ID but any advantages were slight. Kriging (CP0.1ha, P0.2ha, and P0.4ha) resulted in significantly lower MAE and MSE for both pH and LR and lower IQR for LR residuals when compared with IDP = 1 (Table 4). The magnitudes of the significant differences in MAE were 0.01 pH units and 0.13 Mg ha–1 for pH and LR, respectively. With IDP=2 or IDP=4, IQR, MAE, and MSE were not significantly different than those obtained by kriging. The significant interaction between prediction method and grid size reflect that the relatively greater advantages of kriging obtained with the densest sampling strategies (CP0.1ha/P0.2ha) were lost when sampling densities were sparser (e.g., P0.4ha). Indeed, semivariance analyses of CP1ha density failed to produce a variogram with identifiable features (nugget and range) and cross-jackknife validation results showed either no relationship or a negative relationship between observed and predicted values (data not shown). Therefore, kriging CP1ha results were not further evaluated. For the CP0.1ha, P0.2ha and CP0.4ha, a significant site by grid size interaction reflects differences in spatial ranges, field sizes and dimensions among the different locations and the associated differences in the variograms derived with the two sampling intensities (Fig. 1 vs. 2). The lack of a significant interaction for site and method main effects indicated method results were consistent among all locations even though IQRs for residuals, MAEs and MSEs varied significantly among locations.


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  		Table 4. Results of AOV of selected parameters describing the differences between actual pH and LR values and values estimated by kriging and ID (P = 1, 2, and 4) using point samples collected from a 0.1-ha (0.2 ha for DPAC RV) grid and a 0.4-ha grid applied to contiguous field areas. Least square means are reported for the interquartile range (IQR), the mean absolute error (MAE) and the mean (error)2 (MSE).

 
In 1987, Laslett et al. remarked "No one prediction method can ever out-perform all other methods on all reasonable data sets examined." For the implementation of PA, the challenge has been to determine whether these performance differences, if they exist at all, have any practical consequence to the farmer. Gotway et al. (1996) recommended kriging over ID for soil properties because they noted that the accuracy of predictions with kriging were high and unaffected by the variation in the datasets. In contrast, they noted that selection of an optimal power value for ID varied with the CV of the dataset, and ID could produce highly inaccurate predictions if this factor were ignored. They proposed that datasets with a high CV (≥25%) would be best modeled with ID if P was low (e.g., P = 1) whereas datasets with low CVs (≤25%) required higher P (e.g., P = 2 or 4) for optimal outcomes. Our CVs for pH were all below 10% while the CVs for LR were far in excess of 25%, but, when differences in ID predictive accuracy occurred due to the distance power used, higher distance powers produced the best results for both attributes (Table 4). Regardless of the special circumstances posed by evaluating CVs of log function data, our data on LR do not support this CV decision rule for ID exponent selection. It should be noted that Gotway et al. (1996) derived this interpretation primarily from datasets that were far denser than would ever be collected on a commercial field (12- to 24-m sample spacing), and their results showed prediction method had much less of an effect at sample spacings of 48 or 72 m.

In advocating kriging over simpler techniques such as ID, journal reports have also referred to the fact that semivariance analysis permits some estimation of the prediction error (Table 3), allowing uncertainty or risk concepts to be incorporated into the development of an input application map (Gotway et al., 1996; Wollenhaupt et al., 1994). While this may very well be a theoretical advantage, how this information could be used in practice has not been proposed. Finally, kriging may require a higher level of user knowledge to achieve good results, and some studies have actually found that ID produced the more accurate soil property maps at commercially feasible sample densities. Mueller et al. (2001) found that ID (P = 1.5) out-performed kriging at inter-sample distances of 30, 61, and 100 m, with the advantage increasing with increasing distances between samples. Their results are consistent with ours in that 100-m grid data did not produce variograms with any clearly defined features, and the differences between prediction methods for all sampling intensities were small. Thus, there may be little practical consequence of selecting one prediction method over another for current commercial sampling densities.

A sampling and interpretation strategy that represents an improvement over a WF composite will have a PE value that is positive and substantially greater than zero, reflecting residuals that group notably closer around a mean and median of zero. A near-zero or negative PE indicates that using an ACTF was as or more accurate than the alternate method. In our study, the ACWF tended to be more accurate than ACTF with PEs ranging from 2 to 32% and 0 to 39% for pH and LR, respectively (Fig. 6a–f and 7a–b). The largest improvements corresponded to either a significant shift of the mean residual value toward zero or a significant reduction in the variance of the residual populations. This is to be expected as the ACWF value, based on a much greater number of sample locations, was less prone to bias from an occasional, extreme value although exceptions occurred (e.g., pH for NEPAC Field 1, Fig. 7c).



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  		Fig. 6. The under- or overestimation of pH and lime requirement (LR) following map development based on area composite (AC), point (P) or centers point (CP) sampling strategies for DPAC. Composite strategies include a research whole field (AC WF, all samples averaged), a commercial or true farm whole field (AC TF, subsets of samples representing a density of 1 ha–1 averaged), and 1-ha grid (AC 1 ha, all samples averaged on a ha–1 basis). Maps developed from point data use either the CP value of a given ha to represent the whole ha without any smoothing (No. Smth CP1ha), IDP = 2 applied to CP 1-ha data, or kriging applied to P 0.2 and 0.4 ha data. Box plots show error mean (...), median (—), 25th to 75th percentiles ({square}), 10th and 90th percentiles ({vdash},{dashv}), and 5th and 95th percentiles (•). A cross ({dagger}) next to the AC TF mean absolute error (MAE) indicates µAC TF != 0 (p < 0.05). Underlined MAEs of other strategies indicates µother != µAC TF (p < 0.05). All prediction efficiencies (PE) are calculated relative to AC TF, and underlined PEs indicate {sigma}other != {sigma}TF (p < 0.05).

 


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  		Fig. 7. The under- or over-estimation of pH and lime requirement (LR) following map development based on area composite (AC), point (P) or centers point (CP) sampling strategies for NEPAC. Composite strategies include a research whole field (AC WF, all samples averaged), a commercial or true farm whole field (AC TF, subsets of samples representing a density of 1 ha–1 averaged), and 1-ha grid (AC 1 ha, all samples averaged on a ha–1 basis). Maps developed from point data use either the CP value of a given ha to represent the whole ha without any smoothing (No. Smth CP1ha), IDP=2 applied to CP 1 ha data, or kriging applied to CP 0.1 and P 0.4 ha data. Box plots show error mean (...), median (—), 25th to 75th percentiles ({square}), 10th and 90th percentiles ({vdash},{dashv}), and 5th and 95th percentiles (•). A cross ({dagger}) next to the AC TF mean absolute error (MAE) indicates µAC TF != 0 (p < 0.05). Underlined MAEs of other strategies indicates µother != µAC TF (p < 0.05). All prediction efficiencies (PE) are calculated relative to AC TF, and underlined PEs indicate {sigma}other != {sigma}TF (p < 0.05).

 
Kriging using P0.4ha data improved most PEs when compared with the ACTF strategy but improvements in PEs for a given field tended to be markedly lower than with the CP0.1ha/P0.2ha dataset (PE 20 to 74%). In some situations, there were no apparent advantages to the P0.4ha sampling intensity when compared with ACTF (e.g., LR for DPAC D and NEPAC 7, Fig. 6b and 7d, respectively). Such instances of no improvement in map accuracy with intensive sampling correspond to LR maps only and occurred in fields where mean and median pH values are relatively high (approximately 6.5, Table 2) and thus the mean and median LRs were relatively low (≤1.95 Mg ha–1, Table 2). In these fields, areas with very high LR exist but are few in number. Examination of LR univariate statistics (CV, skewness and kurtosis) had indicated that identifying these few, extreme locations could be problematic.

The pH maps developed with IDP=2 CP1ha had PEs of 13 to 40% when compared with ACTF while LR maps showed either no improvement (–13%) or improvements ranging from 5 to 34% (Fig. 6 and 7). Again, instances of comparatively little improvement in PE for LR maps tended to correspond to fields with low mean/median LR. It should be noted that while a large PE value is clearly better than a smaller value, the minimum PE value required to make quantifiable gains in input management would be a function of the VR application technology performance and economics. In our study, PEs between –20 and 20% tended to reflect situations where residual means and/or variances were not changed when compared with ACTF. Thus, without the benefit of either an evaluation the application technology performance or a full cost-benefit analysis, we suggest that improvements in PEs that are ≤20% be evaluated with caution.

Using a CP1ha sample collection strategy to directly develop a map without any weighting from neighboring values (No Smooth. CP1ha, Fig. 6 and 7) tended to be the poorest strategy. This strategy only offers an advantage over ACTF when variation across the field is pronounced but variation within individual hectares is minimal, a condition that semivariance analyses illustrated was not likely to be the case. In contrast, composite sampling by 1-ha grid units (AC1ha) improved map accuracy over ACTF on a par with the more intensive sampling strategies. The MAEs for both pH and LR for AC1ha were comparable or lower than kriging P0.4ha, and PEs tended to be better than with either ID CP1ha or kriging P0.4ha. However, while this strategy would reduce total sample numbers submitted to the soil testing laboratory when compared with the P0.4ha strategy, the cost of the labor to collect the samples would be much higher and would likely eliminate any total cost advantage.

For regions of the country where infield variation in soil map units was expected to influence soil fertility, the ACST strategy has been commonplace. In Indiana, university guides recommend collecting 15-core composites from soil map units with similar management history and areas ≤10 ha (Mengel and Hawkins, 1995). While both our ACTF and ACST strategies involve either composites or averages of composites and thus can be criticized for being better samples than would normally be collected, the relative outcome of the comparison is likely to be highly analogous to real-world sampling.

Our simulation of ACST demonstrated that it could be clearly superior to ACTF. Mean LR residuals for ACST were not different from zero. While DPAC D pH residuals were similar for ACST and ACTF, mean pH residuals in DPAC F and combined R and V were reduced when compared with ACTF (Table 5). Furthermore, ACST was as or more accurate for mapping both pH and LR than ID CP1ha (–16.5% ≤ PE ≤ 48.5%) and tended to be no less accurate than kriging P0.4ha (–24.0% ≤ PE ≤ 21.1%). These results contradict the most recent VR lime studies that conclude ACST offers little improvement over AC of whole fields (Mueller et al., 2001; Bianchini and Mallarino, 2002). Bianchini and Mallarino (2002) note that inaccuracies in soil survey maps may be the primary reason for the poor results from ACST. At DPAC, the delineations of soil series by the soil survey maps were supported by aerial photographs and more intensive surveying activities (data not shown).


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  		Table 5. The pH and LR mean error (ME) and mean absolute error (MAE) from ACST and the comparison of ACST residuals with those resulting from ACTF, IDP = 2 CP1ha, and Krig. P0.4ha. Results are shown for comparing the ME to 0 (t test for µ = 0), and the ME of zones residuals and variances to the ME of residuals and variances for the alternative strategies (µ1 = µ2 and {sigma}1 = {sigma}2, respectively). The prediction efficiency (PE) characterizes the reduction in mean square error from following the ACST. {dagger}

 
The economic advantages in VR management are realized when either less total product is used and yields are not strongly affected or the same or more product is used but the distribution is changed and yields are increased. Methodologically, there are many ways to evaluate how map information might be translated into changes in amount of product purchased. For purposes of this study, we assumed that all areas of a field would be corrected to pH 6.5, even when initial test levels were above pH 6. Kriging at either CP0.1ha/P0.2ha or P0.4ha and ACST all resulted in total LRs that closely matched the whole-field LRs based on summing the LR for all measured locations (Table 6). The ACTF strategy also accurately predicted the whole-field LR at DPAC D, but it slightly underestimated the LR at NEPAC (9.3 Mg or 0.2 Mg ha–1 = 7%). Furthermore, it overestimated the WF LR at DPAC F and RV by 7.9 Mg (1.3 Mg ha–1 = 43%) and 25.3 Mg (0.9 Mg ha–1 = 30%), respectively. Applying IDP=2 CP1ha resulted in whole field lime use that was similar to that resulting from the ACTF strategy for NEPAC, DPAC D, and DPAC F. In DPAC RV, IDP=2 CP1ha reduced lime use by 0.4 Mg ha–1 (10%) when compared with ACTF. Thus, the savings in total lime by alternatives to WF management were inconsistent and not on the order of some recent studies that have documented as much as 60% reductions in lime with VR management (Bianchini and Mallarino, 2002). Characterizing the productivity impact of lime redistribution as well as the performance of application technology were beyond the scope of this study but remain critical needs in research on VR lime profitability.


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  		Table 6. Total agricultural limestone required for contiguous field areas based on different approaches to soil sampling and using the soil sampling information to develop a lime requirement (LR) input map. Field areas are 49.3, 12.4, 5.9, and 28.8 ha for combined NEPAC fields, DPAC D, DPAC F, and combined DPAC R and V, respectively.

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The intent of this study was to provide quantitative information on soil assessment and mapping methods that are in common use by the commercial sector. With respect to point data collected on small grids (≤0.4 ha), differences in estimation methods were found to be negligible in any practical context. Data points from larger grids (≥1 ha) were too far apart to provide much information about the nature of pH and LR change between adjacent sampling locations. Our results add further weight to the current thinking that zones or directed sampling strategies are required to implement soil testing-based VR lime management as <1-ha grid sampling is too costly and ≥1-ha grid sampling is too uninformative for the cost. Where ancillary information can be used to confirm or adjust the boundaries of distinct soil series delineated by published soil surveys, this no-cost information may be a highly cost-effective way to plan sample collection for pH and lime management. Future comparative studies will likely focus on selection of best-suited ancillary information.

For soils and regions where the SMP buffer method is recommended, the accuracy of a continuous-surface LR maps may be further compromised if they represent a direct translation of a continuous pH map. In this study we illustrated the extent of map error that can occur in either pH or SMP-determined LR but we did not directly compare accuracies of the two approaches. To do so would have required the full examination of the spatial behavior of proxy measures of reserve acidity, which was beyond the scope of this study. For example, the cation exchange capacity (CEC) or the organic matter (OM) content can be used to estimate liming needs for a given soil water pH (Black, 1993; Hoeft and Peck, 2002) but the quality of the continuous-surface CEC or OM maps developed from either sparse soil test data or indirectly from other measures (e.g., classified aerial images of bare soil) needs to be rigorously examined. Implementation of on-the-go soil sensing, a potential lime-mapping alternative to directed or zones based sample collection and remote sensing analysis, will require rigorous evaluation of the component of error that is introduced when LR is determined by proxy.

Received for publication June 19, 2003.


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





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