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Soil Science Society of America Journal 65:1547-1558 (2001)
© 2001 Soil Science Society of America

DIVISION S-8 - NUTRIENT MANAGEMENT & SOIL & PLANT ANALYSIS

Map Quality for Site-Specific Fertility Management

T. G. Mueller*,a, F. J. Pierceb, O. Schabenbergerc and D. D. Warncked

a Dep. of Agronomy, Univ. of Kentucky N-122 Ag. Science North, Lexington, KY 40546-0091
b Center for Precision Agricultural Systems, Washington State Univ., Irrigated Agricultural Research and Extension Center, 24106 N. Bunn Road, Prosser, WA 99350-8694
c Dep. of Statistics, Virginia Polytechnic Institute and State Univ., 211 Hutcheson Hall, Blacksburg, VA 24061-0439
d Dep. of Crop and Soil Science, Michigan State Univ., E. Lansing, MI 48824-1325

* Corresponding author (mueller{at}pop.uky.edu)


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
The quality of soil fertility maps affects the efficacy of site-specific soil fertility management (SSFM). The purpose of this study was to evaluate how different soil sampling approaches and grid interpolation schemes affect map quality. A field in south central Michigan was soil sampled using several strategies including grid-point (30- and 100-m regular grids), grid cell (100-m cells), and a simulated soil map unit sampling. Soil fertility [pH, P, K, Ca, Mg, and cation-exchange capacity (CEC)] data were predicted using ordinary kriging, inverse distance weighted (IDW), and nearest neighbor (NN) interpolations for the various data sets. Each resulting map was validated against an independent data (n = 62) set to evaluate map quality. While soil properties were spatially structured, kriging predictions were marginal (prediction efficiencies <=48%) at high sample densities and poor at lower densities (i.e., 61- and 100-m grids; prediction efficiencies <21%). The average optimal distance exponent at each scale of measurement was 1.5. The performance of kriging relative to IDW methods (with a distance exponent of 1.5) improved with increasing sampling intensity (i.e., IDW was superior to kriging for 100% of cases with the 100-m grid, 79% of the cases with the 61.5-m grid scale, and 67% of the cases with the 30-m grid). Practically, there was little difference between these interpolation methods. Grid sampling with a 100-m grid, grid cell sampling, and simulated soil map unit sampling yielded similar prediction efficiencies to those for the field average approach, all of which were generally poor.

Abbreviations: A30, prediction for the field average approach for 30.5-m grid data set • A100, prediction for the field average approach for 100-m grid data set • CEC, cation-exchange capacity • CV, coefficient of variance • GFULL, full data set • G30, 30-m grid data set • G61a, G61b, G61c, G61d, 61-m grid data set (a total of four • a,b,c,d) • G100, 100-m grid data set • Gchck, check data set • Gcomb, combination of G30 and G100 grid data set • IDW, inverse distance weighted • NN, nearest neighbor • MSE, mean square error • RMSE, root mean square error • RSV, relative structural variability • SSFM, site-specific fertility management • VRT, variable rate technologies


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
MAPS ARE FUNDAMENTAL to SSFM because they represent either the spatial state of a condition of interest, the prescription of inputs needed to manage a particular condition site-specifically, or a record of inputs or outputs (Pierce and Nowak, 1999). In his review of variable rate technology (VRT), Sawyer (1994) concluded that the success of VRT depends to a large extent on the quality of fertility management maps. Although methods exist for measuring map quality, in general, maps used in SSFM are rarely examined for quality (Sawyer, 1994; Pierce and Nowak, 1999). Thus, poor map quality may explain why results of some SSFM agronomic and economic studies have produced mixed or negative results (Wibawa et al., 1993; Wollenhaupt and Bucholz, 1993; Snyder et al., 1996; Lowenberg-Deboer and Swinton, 1997). Map quality consists of two components, map precision and map accuracy. The former is a measure of residual variability in map prediction, whereas the latter measures the closeness to the true conditions. Map quality is quantified as the mean square error (MSE) of residuals (predicted - measured) obtained with an independent validation data set.

The first step in SSFM is to assess spatial variability in soil fertility. A number of sampling approaches have been used such as grid-soil sampling and area-based procedures including grid cell sampling and zone or directed sampling. Grid soil sampling for soil fertility has been popular but commercial applications have generally relied on coarse sampling grids (regular grids with 100-m spacing or more) and simple interpolation procedures (primarily inverse distance to some power) to minimize costs. Soil fertility condition maps and fertility management maps can be created from grid data using a number of geostatistical, mathematical interpolation, and graphical procedures (Isaaks and Srivastava, 1989; Goovaerts, 1997; Wollenhaupt et al., 1997; Burroughs and McDonnell, 1998). Thus, for a given spatial data set, different procedures will produce maps of varying quality. For example, the optimal distance exponent for the IDW interpolation procedure may depend upon the coefficient of variation (CV; Gotway et al., 1996). It is also clear that the geometry and intensity of the sampling design greatly affect map quality (Wollenhaupt et al., 1994). At this time, there is no consensus on which grid design and data analysis approach are best suited for SSFM. A grid-sampling approach that leads to an accurate condition map depends on many factors but ultimately on the spatial structure of soil properties (Flatman and Yfantis, 1996; Sadler et al., 1998) including the range of spatial correlation (Mohamed et al., 1996).

Concerns over cost and performance of grid sampling have renewed interest in area sampling schemes which are inherently more economical and more in line with traditional soil fertility sampling guidelines. While grid-sampling and interpolation approaches have limitations, a shift from grid-sampling to area-sampling approaches may or may not improve map accuracy. Zone or directed sampling (Pocknee et al., 1996) is a method where soil samples are composited from areas or regions delineated as having similar yield potential or fertility status. In grid cell sampling, composite samples are obtained within rectangular gridded areas. Grid cell sampling has found limited use, in part because of reports that grid point sampling more accurately described soil properties than did grid cell sampling (Wollenhaupt et al., 1994). In general, area based sampling schemes depend to some extent on the investigator's ability to classify the study region into areas homogenous with respect to yield or soil fertility status. The concern is that proven guidelines for delineating fertility management zones within fields have not yet been established. The accuracy of maps derived from area-sampling schemes has not been reported.

Regardless of the sampling approach, all methods for assessing soil variability are prone to certain errors including errors associated with soil sampling, laboratory analysis, interpolation, and map preparation. The difficulties in providing recommendations to practitioners are compounded by the fact that there is no agreement on how to best assess map quality (Wollenhaupt et al., 1994; Franzen and Peck, 1995; Gotway et al., 1996).

The purpose of this study was to evaluate how different soil sampling approaches and grid-interpolation schemes affect map quality. For this study, a field was subjected to several soil sampling strategies including grid point sampling at several grid spacings, grid cell sampling, and directed soil map unit sampling. Soil fertility and fertilizer recommendation data were interpolated using ordinary kriging, a range of IDW methods, and NN analyses for each of the sampling schemes. The resulting prediction maps were tested against an independent validation data set.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
This study was conducted within a 20.4-ha field (42°57'54'' N, 84°43'38'' W) in Clinton County, Michigan, 6 km south of Fowler (Fig. 1) . The field had been in a corn (Zea mays L.)–soybean [Glycine max L. (Merr.)] rotation for 22 yr and contains a number of soil map units (Table 1; Fig. 1), most of which were formed from glacial till and are somewhat poorly drained. Historical fertility management was based on the Tri-state fertilizer recommendation (Vitosh et al., 1995) using a target pH of 6.8.



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  		Fig. 1. A digital orthophotograph overlaid by the 30.5-m grid data set (G30, black squares), the 100-m grid data set (G100, at the intersections of the straight black dashed lines), the check data set (Gchk, white circles) and NRCS soil types (CaA represents Capac loam with 0 to 4% slope; MeA represents Metamora–Capac sandy loam with 0 to 4% slope; MoB represents Morley Loam with 2 to 6% slope; and WbA represents Wasepi sandy loam with 2 to 6% slope). The solid white lines represent the soil types boundaries. Some of the grass water ways in the field (dashed white lines) and the boundaries of the NRCS soil map units were used to define directed sampling zones (DS 1-11). The dashed black lines also indicate the boundaries of the Gcell based sampling.

 

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  		Table 1. Map symbols, soil or soil complex name, NRCS soil taxonomic classification (Soil Conservation Service, 1978), drainage class, and area occupied in the field.

 
Soil samples were obtained in the spring of 1997 from the field using three sampling designs: a 30.5-m regular grid (G30), a 100-m regular grid (G100), 1-ha cell composite samples (Gcell; Fig. 1). A check data set (Gchk; n = 62) was obtained by sampling a 61-m unaligned grid augmented by additional random samples. At each of the grid and check points, five soil subsamples (one at the grid point and four within a 1.5-m radius) were obtained using a 2.5-cm diam. core to a depth of 20 cm and composited. The Gcell samples were taken by compositing 2.5 by 20 cm soil cores obtained from nine sample locations spaced at regular intervals within each 100-m grid cell. Any points falling in grass waterways were offset into the field.

Soils were dried under forced air at 35°C for 3 d and ground to pass a 2-mm sieve. Standard soil analyses were conducted by the Michigan State University Soil and Plant Nutrient Laboratory using recommended chemical soil test procedures for the north central region (Brown, 1998). Analyses included pH (1:1 soil/water mixture), buffer pH [bpH; Shoemaker-Mc-Lean-Pratt (SMP) buffer], P (Bray P-1 extractable), K, Ca, and Mg (1 M NH4OAc extractable). Cation exchange capacity was calculated by cation summation. Lime recommendations (Lrec), P fertilizer recommendations (Prec), and K fertilizer recommendations (Krec) were calculated using the Tri-state fertilizer recommendations (Vitosh et al., 1995) for corn with a uniform yield goal of 11.3 Mg ha1.

To more completely assess how different sampling schemes and estimation procedures affected map quality, additional data sets were derived from the original sampled data sets including the combination of the G30 and G100 (Gcomb), four separate 61-m grids (G61a, G61b, G61c, G61d), and a soil map unit sampling consisting of average values by soil map unit (Table 2). The full data set (GFULL) (301 sample locations) consisted of all samples except the 1-ha cell samples, yielding an average sampling intensity of 14.8 samples ha-1 and sufficient samples at small lag distances needed to accurately describe the spatial structure via the semivariogram. Normal probability plots with 95% confidence intervals were used to assess normality (Friendly, 1991) and contour maps of semivariogram surfaces were used to determine the severity of anisotropy (Isaaks and Srivastava, 1989; Goovaerts, 1997). For the GFULL, G30, G61a-d, G100, and Gcomb grid data sets, empirical semivariograms were calculated using Variowin (Pannatier, 1996) and omnidirectional and directional models (depending on the semivariogram surface analysis) were fit to the empirical semivariograms. Using Surfer (Golden Software, Golden, CO), we interpolated 4 by 4 m grids by ordinary point kriging (Isaaks and Srivastava, 1989; Goovaerts, 1997) each data set based on the modeled semivariograms, using IDW with distance exponents from 0.1 to 5.0 in 0.1 increments, and NN. The kriging search radius was limited to the distance at which the semivariogram behavior was stable and a maximum of 24 points were used. For IDW interpolation, all points were used for predictions. For log-normally distributed data, log-normal ordinary point kriging was employed and back transformations were conducted as described in Kravchenko and Bullock (1999). Predictions for the field average approach were calculated as the means of the G30 and G100 data sets and are referred to as A30 and A100. For a comparison of the kriging and IDW techniques, see Gotway et al. (1996).


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  		Table 2. Semivariogram parameters for soil properties (exponential models) for the FULL data set.

 
Semivariogram models were described with three parameters. The range of the spatial correlation measures the distance beyond which two observations are spatially uncorrelated. The nugget represents measurement error and unobserved microscale variability. For second-order stationary spatial processes, the sill represents the constant variance of the observations. In models with a nugget effect, the partial sill represents the difference between the sill and the nugget effect. Isaak and Srivastava (1989), Cressie (1993), and Goovaerts (1997) provide a more thorough discussion of these semivariogram parameters. We have defined the relative structural variability (RSV) as the ratio of the partial sill to the sill (Robertson et al., 1993). The RSV indicates that proportion of the variability that is spatially structured. Variables with small range and RSV values are expected to produce maps of low quality.

Prediction Errors and Efficiencies
Cross-validation with replacement (Isaaks and Srivastava, 1989) and cross-validation with an independent validation data set referred to as "jackknife analysts" by Deutsch and Journel (1998) were applied to interpolations to obtain the MSE as a measure of map quality. The MSE is the sum of accuracy (bias2) and precision and is defined as

(1)
where {nu}i is the difference between predicted value and observed value at location si, i = 1, ..., nv, and nv is the number of values in the check data set. Bias is defined by

(2)
and precision (the variance of the residuals) as

(3)
where represents the mean of the residuals. An accurate map will have no bias. Relative accuracy can be used to assess the severity of bias and is calculated as

(4)

The root mean squared error (RMSE) is the square root of the MSE. Prediction efficiency, referred to as goodness-of-prediction by Gotway et al. (1996), is calculated as

(5)

Positive prediction efficiencies can be interpreted as the percent reduction in MSE compared to the field average approach (e.g., A30). A kriging prediction efficiency of 15%, for example, indicates that compared with the field average approach, kriging reduced the MSE by 15%. The RMSE and prediction efficiencies are scaled measures of measures of map quality. We used the RMSE and prediction efficiency to compare map quality for the interpolations of different variables across different scales of sampling. The distance exponent for IDW interpolation that yielded the lowest RMSE was considered the optimal IDW method.

To quantify map quality for each variable, sampling scheme, and interpolation method, the differences between the predicted surface and the Gchk data points were calculated and used to determine RMSE and prediction efficiency. Since the validation points did not always coincide with the 4 by 4 m predicted grid locations, bilinear interpolation was used to estimate the predicted value at each Gchk grid location. The additional uncertainty introduced by this interpolation was negligible as determined by kriging at the exact locations of the Gchk data set and comparing the residual errors. Because a single value is assigned to each soil management unit, to each cell, and to the entire field, residuals for the SMU, Gcell, A30, and A100 predictions were calculated as the difference between the validation points and the measured value for the area containing that point.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Field average values for pH and P were optimal, K was high, and Ca and Mg were adequate. According to the Tri-state fertilizer recommendations (Vitosh et al., 1995), this field would require 2.9 Mg ha-1 of lime and 73 kg ha-1 of P2O5; however, only 43% of pH values were low or slightly low and 52% of P values were slightly low (Fig. 2) . Preliminary analysis suggested that this field might benefit from SSFM particularly with grid soil sampling. A soil map unit sampling approach was not promising because the data related poorly to soil type.



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  		Fig. 2. Soil fertility values for the 30-m grid (G30) data set overlain by NRCS soil types (CaA represents Capac loam with 0 to 4% slope; MeA represents Metamora-Capac sandy loam with 0 to 4% slope; MoB represents Morley Loam with 2 to 6% slope; and WbA represents Wasepi sandy loam with 2 to 6% slope).

 
All soil fertility properties showed spatial dependence when the GFULL data set was analyzed (Table 1). Ranges of spatial correlation were between 59 and 134 m and most of the variables had RSV values >81% except K (54%). These geostatistical parameters are generally in line with what others have reported (McBratney and Pringle, 1997; Cambardella and Karlen, 1999).

Semivariograms for two of the variables (pH and Ca) reached a plateau, then continued to increase (Fig. 3) . This behavior was not because of large-scale drift but rather because of high levels of Ca in a small area in the southeastern region of the field where dredged material from stony creek had been deposited (Fig. 2). This was confirmed when the points in this region were removed from the data sets and the semivariograms no longer increased after the plateau. Since the high testing area occupies only a small part of the field and involves relatively few sample points, ordinary kriging was appropriate using the complete datasets while limiting the search radius to the distance over which the semivariogram exhibited second-order stationary behavior (the distance to which pH and Ca were modeled in Fig. 3).



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  		Fig. 3. Omnidirectional (omni) and directional experimental semivariograms and omnidirectional semivariogram models for the combination(Gcomb) data set. The directions indicate the anisotropic axis.

 
The two most common procedures for assessing map quality are cross-validation with replacement and cross-validation with an independent validation data set. We found that estimates of spatial uncertainty were substantially larger for cross-validation with replacement than cross-validation with an independent validation data set (Fig. 4) . Cross-validation with an independent data set directly estimates the spatial uncertainty, as validation points are located randomly throughout the field. For cross-validation with replacement of regular grids, the point to be estimated and the four nearest neighbors are separated by a minimum of one-grid increment so this procedure does not reflect the prediction problem of interest. Therefore, cross-validation with replacement does not adequately assess the prediction errors between grid points. Therefore, for all subsequent map quality assessments we used cross-validation with an independent validation data set.



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  		Fig. 4. Predicted vs. measured for P and K for cross-validation with replacement and with an independent validation data set.

 
Maps developed from kriging will have prediction errors because of the spatial variability of the mapped property, the adequacy with which the semivariogram model represents the spatial structure, and the sampling design. While the fit of the exponential model to the experimental semivariograms for the Gcomb was satisfactory (Fig. 3), plots of predicted versus measured for the Gcomb (Fig. 5) show considerable deviation from the 1:1 line and low prediction efficiencies (<=48%). Predictions of soil K were especially poor. Additionally, the bias values for soil K were especially large, as indicated by the large relative accuracy values, suggesting that kriging malfunctioned for this variable.



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  		Fig. 5. Predicted vs. measured for the 100-m grid (G100) data set.

 
There are a number of considerations in geostatistical analysis including normality, anisotropy, and semivariogram model selection. While normality is not a requirement for developing the semivariogram or kriging, the classical linear kriging predictor is not the best predictor if the spatial process is not Gaussian (Cressie, 1993). Two of the variables exhibited lognormal behavior (P and K). Although transformations to normality slightly reduced the RMSE for ordinary kriging in the case of K, there was little difference in plots of predicted versus measured values. Some of the variables exhibited slightly anisotropic behavior (Fig. 3), the condition by which the spatial dependence depends on direction, not just distance. However, choosing directional semivariogram models did not significantly impact prediction errors or plots of predicted versus measured. Exponential models had the best overall fit (indicator goodness-of-fit; Pannatier, 1996) to the experimental semivariograms. While in some cases, spherical models had better fits, the kriged interpolations did not necessarily have lower RMSE values and the plots of predicted versus measured were minimally impacted.

Sampling design (geometry and intensity) affected the semivariogram and map accuracy depending on the soil fertility parameter. The GFULL data set yielded a stable estimate of the semivariogram (Fig. 6) , especially short-range variability (smallest lag class for the GFULL data set was 7.2 m with 104 pairs). Removing the 62 validation points from the Gfull data set to create the Gcomb data set did not greatly affect the semivariogram parameters, as sufficient short distance lags remained in the Gcomb (smallest lag class for Gcomb was 9.2 m with 34 pairs). The G30 did not contain a sufficient number of data points at short lag distances (smallest lag class was 36.6 m) to adequately model the nugget effect, although sill estimates for the G30 were comparable to those obtained with the GFULL and Gcomb data sets. The semivariograms from the four G61 were the same, and like the semivariograms for the G100, bore little resemblance to the semivariograms for the GFULL data set because at low sampling densities, the ability to discern spatial structure is lost. Therefore, only the Gcomb grid sufficiently modeled the semivariogram for soil fertility and fertilizer recommendations for this field. For a few variables, specifically pH and soil test K, the semivariograms modeled from the G30 were reasonably close to the GFULL data set.



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  		Fig. 6. Omnidirectional empirical semivariograms and fitted exponential semivariogram models for pH, P, and K using the full (FULL), combination (Gcomb), 30.5-m grid (G30), 61-m grid (G61), and 100-m grid (G100) data sets. The lag distance at which semivariogram models were cutoff was used as the search radius for ordinary kriging.

 
As expected from the effect of grid design on the semivariogram, the prediction of the check data set worsened with increasing grid size (Fig. 7) . The differences in prediction quality for the four G61 data sets indicates that map quality at this scale is very sensitive to the placement of the grid in the field. The prediction efficiency increased with sampling intensity (Fig. 8) but the rate of increase was scale and variable dependent. In summary, maps worsened with increasing grid increments.



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  		Fig. 7. Predicted vs. measured for ordinary kriging at each scale of measurement of pH, P, and K.

 


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  		Fig. 8. Prediction efficiency vs. sampling intensity for pH, P, and K.

 
Commercial SSFM enterprises commonly use IDW interpolation in lieu of kriging because it does not require semivariogram modeling. Like kriging, the RMSE for IDW interpolation was affected by grid increment, but was also affected by the choice of the IDW distance exponent (Fig. 9) . Generally, RMSE decreased with increasing sampling intensity except for CEC. The RMSE decreased markedly for P with an increase in sampling intensity from G61 to G30 while the RMSE for K was reduced minimally. The RMSE decreased only modestly for all variables with an increase in sampling intensity from G100 to G61. The optimal distance exponent depended on the variable and sampling intensity. The finding of Gotway et al. (1996), that the optimal distance exponent was inversely related to the CV, was confirmed for the more dense data sets. The average optimal distance exponent at each scale of measurement and each variable was calculated to be 1.5.



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  		Fig. 9. Performance of IDW, ordinary kriging, and log-normal ordinary kriging as a function of sampling scale and design.

 
The performance of kriging and IDW were scale dependent (Fig. 7, 9, and 10) . Kriging tended to improve relative to IDW as sampling intensity increased (i.e., G30 and Gcomb) and with the addition of closely spaced points (i.e., Gcomb). The prediction efficiencies were greater for IDW with a distance exponent of 1.5 than for ordinary kriging for all cases at the G100 scale, for 79% of the cases at the G61 scale, 67% of the cases at the G30 scale, and 17% of the cases at the Gcomb scale (Fig. 11) .



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  		Fig. 10. Predicted vs. measured for IDW with a distance exponent of 1.5 at each scale of measurement of pH, P, and K.

 


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  		Fig. 11. Prediction efficiency for IDW vs. prediction efficiency for ordinary kriging at each scale of measurement.

 
Most studies that have compared interpolation methods (i.e., NN, IDW or kriging) have designated one of the interpolation method superior. These include studies in soil science (Laslett et al., 1987; Hosseini et al., 1994; Gotway, 1996; Kollias, 1999; Kravchenko and Bullock, 1999), entomology (Weisz et al., 1995; Dalthorp et al., 1999), hydrology and climatology (Creutin and Obled, 1982; Tabios and Salas, 1985; Nalder and Wein, 1998), the health sciences (Wartenberg et al., 1991) and geology (Zimmerman et al., 1999; Weber and Englund, 1992). Most of the conclusions have been based on quantitative measures of map error, not on graphical plots of predicted versus measured. In our study, while there were differences between predicted and measured for kriging (Fig. 7) and IDW with a distance exponent of 1.5 (Fig. 10), the differences were of little or no practical significance because of overall poor map quality.

Kravchenko and Bullock (1999) found convincing evidence that the performance of kriging was consistently superior to IDW. Kriging yielded more accurate estimates of soil P and K than IDW for most of the 30 locations. However, the design of this study may have favored kriging. Their semivariogram models, semivariogram parameters, and the size of their kriging neighborhood were optimized for kriging predictions. Cross-validation (with replacement) errors used as optimization criteria for kriging were compared with cross-validation (with replacement errors) for IDW, which had not been similarly optimized. The IDW procedure was optimized by selecting the distance exponent (1st, 2nd, 3rd, or 4th) and search radius that minimized cross-validation with replacement errors. For a rigorous comparison of these procedures, an additional check data set would have been required. As discussed earlier, cross-validation with replacement consistently and grossly over-predicted map errors (Fig. 4). Some have caution against the use cross-validation for selecting semivariogram model parameters (Isaaks and Srivastova, 1989; Goovaerts, 1997).

Nearest neighbor interpolation performed very poorly (Fig. 9) except at intensive scales of measuring (i.e., G30) for some of the variables (i.e., pH, Ca, and Mg). For these cases, the RMSE for IDW was also minimized with large distance exponents because of the similarities between the procedures. When the RMSE for IDW was minimized with small distance exponents (i.e., K), the field average approach performed well compared with other procedures.

Semivariogram models are fit to empirical semivariogram clouds calculated for discrete lag classes by combining data pairs with similar lags to increase the stability of the empirical semivariogram (Fig. 12) . Although kriging and IDW predictions produce spatial estimates, these procedures still depend upon field average models of spatial continuity. This aspect may explain the poor performance of kriging in this study. For soil P, one of the more structured variables in this study, there is a modest amount of dispersion of the semivariogram cloud around the first lag class for soil P (Fig. 12; Gcomb), but for larger lags the dispersion is considerable. When interpolating with data sets that have an average grid intensity of the larger lags (e.g., G30, G61, and G100) kriging or IDW at these scales will yield poor predictions because the semivariogram models do not adequately represent the spatial variability. For a given variable, the dispersion of the semivariogram cloud at a lag distance equivalent to a desired grid sampling intensity may be one determinant of map quality.



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  		Fig. 12. Individual semivariogram pairs (small circles) and average semivariograms for each lag class (large circles; plotted in Fig. 2) for soil P at the combination (Gcomb) scale.

 
Alternatives to grid sampling include cell sampling and directed sampling. The Gcell approach had the highest RMSE for most variables (Fig. 7) and the lowest prediction efficiencies, confirming the results of Wollenhaupt et al. (1994). The directed sampling based on soil map unit had RMSEs that were similar to the A30 (prediction efficiencies near zero), indicating no advantage of soil map unit sampling over the field average approach for this field (Fig. 8). Ideally, directed sampling zone should relate to regions of fields that have similar soil fertility properties. For this field, the SMU approach was not a good basis for making directed sampling zones because soil map units are more often an indicator of productivity rather than fertility likely because past management practices have altered the spatial variability of soil chemical properties.

The data suggest that the use of the field average fertility values to manage this 20.4-ha field was not substantially worse than other sampling approaches especially considering the cost associated with intense grid sampling. Further, there are additional errors associated with the calculation of fertilizer recommendations and with variable rate application. The field average approach could be considered Gcell sampling with a cell size of 30.4 ha. The optimal cell size and the best sampling intensity per cell are unknown. Sensors that detect changes in the soil fertility status and other soil properties may be useful for delineating fertility management zones or for enhancing spatial estimates from grid sampling.


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
We examined map quality of soil fertility at multiple scales of measurement (Gcomb, G30, G61, G100) and with multiple prediction methods (ordinary kriging, IDW, NN, grid cell, soil map unit sampling, and field average approaches). Cross-validation with an independent data was superior to cross-validation with replacement as a basis for measuring map quality in this study. For this data set, sampling at lower intensities diminished our ability to describe spatial structure and generally increased the errors of prediction. While a common, commercial scale of grid sampling of 100 m was grossly inadequate, sampling at greater intensities only modestly improved prediction accuracy and would not justify the geometric increase in sampling costs. At the optimal distance exponent of 1.5, the accuracy of IDW interpolation generally equaled or exceeded the accuracy of kriging at each scale of measurement with the exception of the finest scale of measurement (Gcomb). This spatial variability of soil fertility in this field was not greatly suited to site-specific management. However, we would recommend the use of validation data sets in conjunction with graphical and numerical analytical methods to assess opportunities for SSFM regardless of the sampling approach used to assess site-specific fertility needs.


   ACKNOWLEDGMENTS
 
The authors gratefully acknowledge Pat Feldpausch for allowing us to conduct this experiment on his farm, Steven Law and the Clinton Co. NRCS office for help soil sampling, G. Philip Robertson and Pierre Goovaerts for thoughtful suggestions on geostatistical analyses, and Brian Long for assistance in the field.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Contribution no. 00-06-42 from the Kentucky Experiment Station, Lexington, KY.

Received for publication February 28, 2000.


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




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