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Published in Agron. J. 95:1121-1131 (2003).
© American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA

SITE-SPECIFIC MANAGEMENT

Creating Spatially Contiguous Yield Classes for Site-Specific Management

J. L. Ping and A. Dobermann*

Dep. of Agron. and Hortic., Univ. of Nebraska, P.O. Box 830915, Lincoln, NE 68583-0915

* Corresponding author (adobermann2{at}unl.edu).

Received for publication January 21, 2003.

   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Annual yield maps are spatially fragmented because of random variation caused by crop management as well as measurement errors. Two approaches for creating maps of spatially contiguous yield classes were evaluated at two irrigated sites. In the first approach, prior-classification interpolation (PCI), grid size was increased from 4, 8, 16, and 32 to 64 m by kriging interpolation before cluster analysis used for mapping yield classes. Choosing a coarse resolution (>16 m) for yield interpolation before spatial classification resulted in maps that did not accurately depict yield patterns, significant decline of the yield variance accounted for, and loss of resolution in areas of sharp yield transitions caused by irrigation or near the field borders. In the second approach, postclassification filtering (PCF), cluster analysis of mean relative yield was conducted on the smallest grid size (4 m), and the classification results were postprocessed using a spatial filtering algorithm with window sizes that were equivalent to the 8-, 16-, 32-, and 64-m grid sizes used in PCI. This procedure removed erroneous map fragmentation and created maps of contiguous yield classes while preserving the class means and general yield patterns at high spatial resolution. Window sizes for spatial filtering of yield maps should be in the 30- to 60-m range. Landscape pattern metrics may offer new potential for assessing mapping techniques as well as comparing agricultural production fields with regard to ranking their relative opportunities for site-specific crop management.

Abbreviations: AI, aggregation index • CONTAG, contagion index • CV, coefficient of variation • FUZ, nonhierarchical fuzzy-k-means cluster analysis • Kw, weighted Kappa coefficient • MCA, mean core area per patch • PCF, postclassification filtering • PCI, prior-classification interpolation • PD, patch density • RVc, average relative yield variance • RVj, proportion of yield variability in one year accounted for by the classification • SPLIT, splitting index • SSCM, site-specific crop management • TCA, total core area • WAR, hierarchical cluster analysis using Ward's method


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
VARIABLE-RATE PRESCRIPTIONS of production inputs for site-specific crop management (SSCM) are often based on algorithms that include a yield goal (or crop demand for nutrients and water) as well as one or more other variables such as soil properties, water availability, or previous crop. Where spatial and temporal variation in crop demand for nutrients and water is not taken into account, SSCM may not provide benefits over uniform field management (Ferguson et al., 2002). Both preplant fertilizer recommendation algorithms (Shapiro et al., 2001) as well as in-season N management methods based on detecting crop N status at critical growth stages (Schroeder et al., 2000) may require spatially varying yield goals to sufficiently increase yield and/or N use efficiency over existing, uniform N management techniques (Dobermann and Cassman, 2002).

No generally accepted procedures have been developed for creating yield goal maps for SSCM. Setting a realistic yield goal must take into account the climatic–genetic geographic yield potential—the maximum yield that can be reached by a crop in given environments (Evans, 1993)—as well as the actual site yield performance measured in the form of yield maps for a period of several years. Using plausible physiological and agronomic assumptions, crop simulation models can be used to estimate the yield potential based on long-term climatic records (Dobermann et al., 2003a). Actual yield can approach this ideal under field conditions as the precision of management minimizes all abiotic and biotic stresses other than temperature and solar radiation. However, knowing the recent yield history is important for setting a realistic yield goal and gradually increasing it over time to close the gap between actual and potential yield. If a multiyear sequence of yield maps has been obtained, it can be classified to delineate areas with different relative yield and yield stability within a field (Blackmore, 2000). In combination with information about the average yield potential, this can form the basis for mapping a yield goal for a particular cropping season.

In a previous study (Dobermann et al., 2003b), we have compared yield classification procedures with regard to how they account for spatio-temporal yield variability in production fields. This study showed that (i) cluster analysis techniques were superior to defining yield classes empirically, (ii) using univariate cluster analysis of mean relative yield provided more consistent results than multivariate yield classification based on individual years of yield data, and (iii) irrespective of the method chosen, yield classification based on small grid cells resulted in spatially fragmented yield classes. Random yield variability is due to uncertainties associated with the yield-mapping process as well as those due to true yield variability from year to year. Yield mapping using grain flow sensors is affected by errors associated with georeferencing, yield monitor operation, combine movement, grain flow, and data processing (Blackmore and Marshall, 1996; Blackmore and Moore, 1999; Beal and Tian, 2001; Arslan and Colvin, 2002). For most cells on a map, such errors are different from year to year. In addition, true short-distance yield variability, which is related to crop management, occurs and also varies from year to year. The latter may include specific events that often occur in small patches in certain years, such as poor crop establishment, nonuniform fertilizer application, herbicide damage, lodging, or pest damage.

Yield goal maps for SSCM should therefore display larger, spatially contiguous areas that reflect major and consistent differences in attainable yield, exclude noise introduced by annual factors and measurement, and accommodate field equipment. Most yield-mapping procedures, however, do not involve algorithms for forming yield classes that would be spatially contiguous. Methods such as spatially constrained multivariate classification (Oliver and Webster, 1989) or spatial smoothing of fuzzy membership values (Lark, 1998) have been proposed to achieve this, but they are not widely used yet. Spatial fragmentation in maps of yield classes may also depend on the grid cell size chosen. Increasing the grid size before or after the classification may create larger and more contiguous yield classes but requires understanding of the relationships between grid size, yield variability accounted for, and spatial map fragmentation.

The objective of this paper was to evaluate two approaches for creating spatially contiguous yield class maps. In the first approach, PCI, yield data were interpolated before cluster analysis across a range of grid cell sizes. In the second approach, PCF, cluster analysis was conducted on the smallest cell size, but the classification result was postprocessed using a spatial filtering algorithm with increasing window size, thereby forming larger map units.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Study Sites and Yield Data Collection
Details of the sites and data collected were provided elsewhere (Dobermann et al., 2003b) so that only a brief description will be given here. Yield monitor data were obtained from two production fields in Nebraska from 1996 through 2001. Field A was located near Clay Center, NE (40°30'24'' N, 98°5'5'' W), and the crop sequence from 1996 to 2001 was maize (Zea mays L.)–soybean [Glycine max. (L.) Merr.]–maize–maize–soybean–maize. The total field area was 62.7 ha, including a circular center-pivot–irrigated area (53.5 ha), three corner areas with partial furrow irrigation (6.9 ha), and a nonirrigated area (2.3 ha) in the southwest corner. Field B was located near Cairo, NE (40°58'43.5'' N, 98°35'36.5'' W). Continuous maize was grown from 1996 to 2001, except for soybean grown in the south half in 2000. The total field area was 62 ha, all under furrow irrigation, with furrows in west–east direction.

Maize was planted at 0.76-m row spacing from mid- to late April at a density of 7.4 to 7.7 plants m-2. Soybean planting was mostly done in mid-May, using seed drop rates of 35 to 40 seeds m-2. In each field, two to four different maize hybrids or soybean varieties were grown in each year in different parts of the field. Both crops were fully irrigated (except for nonirrigated pivot corners at Site A), and nutrients were applied based on routine soil-testing and standard recommendations. Grain yields were measured from 1996 to 2001 using eight-row combines equipped with DGPS receivers and Ag Leader PF 3000 yield monitors (Ag Leader Technol., Ames, IA). Yield monitors were calibrated following standard procedures, and logging intervals ranged from 1 to 2 s. Due to yield monitor problems, the 1999 data were discarded for Site A.

Figure 1 shows the general flowchart of yield data processing used at both sites. Raw data obtained from the yield monitor were adjusted using a grain flow delay of 12 s, and erroneous records were filtered out (Dobermann et al., 2003b). Depending on the site and year, the cleaning algorithm removed between 10 and 20% of the original yield monitor records. To eliminate yield variation caused by different crops or cultivars, each data point was normalized by dividing it by the average of the corresponding cultivar for a given field and year. The resulting final yields were the relative percentage yield and indicate how the yield at each point differs relative to the mean of the whole field.



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  		Fig. 1. General flowchart of yield data processing. PCI, prior-classification interpolation; PCF, postclassification filtering.

 
Spatial Yield Classification Procedures
Two algorithms for creating yield class maps were compared. In the first procedure, PCI, relative yields measured in each year were interpolated to square grid sizes ranging from 4 m (16-m2 cells), 8 m (64 m2), 16 m (256 m2), and 32 m (1024 m2) to 64 m (4096 m2 using ordinary block kriging and the global variogram option in VESPER (Minasny et al., 2002). The resulting interpolated yield maps were averaged across years to create a map of the mean relative yield for each site, which was then used for cluster analysis to map yield classes.

In the second procedure, PCF, cluster analysis of mean relative yield was conducted first on the 4-m maps of mean relative yield, and larger map units were then created by applying image-processing techniques with window sizes that were equivalent to the grid sizes of 8, 16, 32, and 64 m used in PCI (Fig. 1). That process involved a sequence of applying FOCAL ANALYSIS, CLUMP, and ELIMINATE functions in ERDAS Imagine 8.5 (Leica Geosystems, Atlanta, GA) to the original 4- by 4-m yield classes maps. Focal analysis is a smoothing process, which uses a moving window to replace the value of a cell ( = center point of a moving window) based on a set of surrounding cells. We used window medians to replace the center point from the neighbors of 3 by 3, 5 by 5, 9 by 9, and 17 by 17 cells, which simulated the corresponding 4-, 8-, 16-, 32-, and 64-m grid sizes used in the PCI approach. Next, in clumping analysis, each cell was assigned to contiguous groups, and the resulting images were then processed through the ELIMINATE function, which removes small clumps by replacing the values of pixels in these clumps with the value of nearby larger clumps. The software applies a focal majority filter on the input file in an iterative fashion so that the data values of large clumps overwrite those of small clumps. With each iteration, the one-pixel-width outer edge of the small clump is replaced with values from the surrounding larger clumps. The iteration continues until all of the small clumps have been completely removed. The final clumps are then recoded using the Original Value attribute so that the output values of the remaining clumps are in the same range as the values in the original file (Erdas, 1999). The clump units defined in this study were 64, 256, 1024, and 4096 m2, corresponding to the series of different neighborhood sizes used in the focal analysis to match the different cell sizes in the PCI procedure.

Cluster analysis of mean relative yield in both PCI and PCF was conducted using Ward's minimum variance method (SAS Inst., 1999) or nonhierarchical fuzzy-k-means clustering (De Gruijter and McBratney, 1988). Ward's method (WAR) agglomerates clusters in a hierarchy of all of the individual objects until a single cluster contains all entities in which the within-cluster sum of squares for each given cluster number is minimized over all partitions obtainable by merging two clusters from the previous generation (Johnson and Wichern, 1998; SAS Inst., 1999). Fuzzy-k-means clustering (FUZ) is an extension of the normal, crisp k-means clustering method to account for uncertainties associated with class boundaries and the class membership. The iterative procedure minimizes the within-class sum of square errors, but each object (or cell in a map) is assigned a continuous class membership value in all classes rather than a single class membership value of 1 or 0 used in the normal k-means clustering method (De Gruijter and McBratney, 1988). Fuzzy-k-means clustering was conducted using the FuzME program (Minasny and McBratney, 2002), with Mahalanobis distance and a fuzzy exponent of 1.2 as standard settings. Each cell was assigned to a single yield category based on the highest fuzzy membership value at this particular location.

Evaluation of Classification Methods
To compare the effectiveness of the different classification methods in explaining the yield variance in each year j, we used the complement of the relative variance, denoted as RVj (Webster and Oliver, 1990):

[1]
where s2W is the within-class variance and s2T is the total variance, both estimated by postclassification analysis of variance (ANOVA) for a particular year j. Similar to the R2 value of a regression, RVj is a measure of the proportion of variance accounted for by the classification. A perfect classification would result in zero within-class variance and a RVj of 1. For each yield classification method, one-way ANOVA was conducted for each individual yield year based on the assigned yield class membership values. An RVj value was then computed for each individual yield map year, and an average value (RVc) was computed as the mean of all RVj values across years. An ideal yield classification method would have an RVc close to 1 and a small range of the RVj among individual years. An ANOVA of the RVc values was conducted to test for differences among classification methods. Other criteria used were differentiation among classes in terms of mean class yields and within-class coefficients of variation (CVs).

On a cell-by-cell basis, the spatial agreement between categorical maps of yield classes created by PCI or PCF was evaluated using the weighted Kappa index of agreement for categorical data (Kw), which was defined by Cohen (1968) as

[2]
where pij represents the number of observations that have been classified as belonging to class i by the first classification method and to class j by the second classification method and wij (i = 1, 2, ..., k; j = 1, 2, ..., k) is the Fleiss–Cohen weight. The wij was defined by Fleiss and Cohen (1973) as

[3]
where Ci, Cj, Cc, and C1 are the scores of class i, j, c, and 1, respectively. The wij is restricted to 0 <= wij < 1, with wii = 1 and wij = wji. The Kw ranges from 0 to 1, with 1 as perfect map agreement.

Various landscape pattern metrics were computed for the resulting categorical yield class maps in both fields to assess their spatial fragmentation (McGarigal, 2002). These metrics assume that a landscape (= field in our study) is composed of a mosaic of patches (j = 1, 2, ...n), which belong to different patch types (= yield classes, i = 1, 2, ...m). Patch sizes and shapes may vary. Spatial pattern metrics can be defined at three levels (patch, class, or landscape metrics), and many of them are highly redundant. Several landscape-level (whole-field level) metrics were included in this study and computed using FRAGSTATS (McGarigal and Marks, 1995).

Patch density (PD, no. ha-1) equals the number of patches in the whole field (N) divided by the total field area (A, ha):

[4]

Total core area (TCA, ha) is the sum of the core areas of all patches found within a given field:

[5]
where acij is the core area (ha) of the jth patch in the ith class, based on the specified edge depth (6 m). The core area represents the interior area of patches that has a certain edge buffer zone eliminated. For calculating core area metrics, we used a non-core-area edge depth of 6 m, which is equivalent to the swath width of the combine used for yield mapping. The TCA may range from 0 (no core area, field is fragmented into numerous small patches) to approaching the total area of the field in situations where the classification leads to few very large patches with narrow edges. The mean core area per patch (MCA, ha) equals the TCA divided by the total number of patches (N).

The contagion index (CONTAG) is a measure of both the dispersion and intermixing of patch types in a map (O'Neill et al., 1988; Li and Reynolds, 1993):

[6]
where Pi = proportion of the field occupied by patch type (yield class) i, gik = number of adjacencies (joins) between pixels of patch types i and k, and m = number of patch types present. The CONTAG is a measure of the tendency of patch types to be spatially aggregated and measures the extent to which cells of similar class are aggregated. It approaches 0 when all patch types are maximally disaggregated (every cell is a different yield class) and interspersed. It approaches 100 when the landscape consists of a single patch.

The splitting index (SPLIT) characterizes the subdivision of a landscape independently of its size (Jaeger, 2000) and is related to PD, patch clumpiness, and patch distribution. The SPLIT equals the total landscape area (A) squared divided by the sum of patch areas (aij) squared, summed across all patches in the landscape:

[7]

SPLIT is a measure of subdivision, i.e., the degree to which a patch type is broken up into separate patches (fragments), irrespective of the shape or spatial arrangement of those patches. It ranges from 1 to the maximum number of cells in the landscape squared and increases as the landscape is increasingly subdivided into smaller patches.

The aggregation index (AI) equals the number of like adjacencies involving the corresponding class, divided by the maximum possible number of like adjacencies involving the corresponding class. The AI is given by

[8]
where gii is the number of like adjacencies between pixels of patch class i and max_gii is the maximum number of like adjacencies between pixels of patch classes. The AI ranges from 0 to 100.


   RESULTS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Maps of Yield Classes
Aggregating yields by increasing the interpolated grid sizes from 4 m (16 m2) to 64 m (4096 m2) affected the frequency distributions of yield although means and medians remained mostly unchanged (Table 1). Smoothing of the frequency distributions, expressed by decreasing maximum yield, increasing minimum yield, and a decrease in standard deviation and CV, was small if cell length ranged from 4 to 32 m. Skewness only decreased when cell length changed from 4 to 8 m. However, increasing the cell length from 32 to 64 m caused larger differences in yield statistics. The minimum relative yield changed from 0.43 to 0.62 at Site A and 0.22 to 0.60 at Site B. Corresponding CVs decreased from 11.5 to 9.2% at Site A and 12.2 to 7.7% at Site B.


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  		Table 1. Effect of interpolation to different square grid sizes on descriptive statistics of mean relative yield at Sites A (Clay Center, NE) and B (Cairo, NE).

 
Figure 2 shows the changes in yield class maps created by hierarchical cluster analysis of mean relative yield as a function of increasing grid size before classification (PCI-WAR) or increasing window size used for spatial filtering of yield classes following the cluster analysis (WAR-PCF). Results for fuzzy-k-mean classification are not shown because the maps were similar to those obtained with WAR. The original map of yield classes using 4- by 4-m cells was very fragmented at Site A where the center-pivot irrigation also caused narrow yield transitions from irrigated to rainfed areas found in the pivot corners. At Site B, yield zones were larger, less contaminated by cells with different class membership (speckles), and arranged in a northwest–southeast trend, following the changes in elevation in the same direction (data not shown).



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  		Fig. 2. Maps of yield classes at Sites A (Clay Center, left) and B (Cairo, right) as affected by aggregation method (PCI: prior-classification interpolation; PCF: postclassification filtering) and cell size used for interpolation in PCI or windows size used for PCF (4–64 m). All maps shown are for hierarchical cluster analysis using Ward's method. Light colors show high-yielding areas; dark colors show low-yielding areas with high yield variability among years. At Site A, the circle indicates the center-pivot–irrigated area.

 
In general, as the grid size (PCI) or window size (PCF) increased, the maps became less speckled, and larger, more spatially contiguous map units were formed. This process was consistent for the PCF method, which also resulted in smoother polygons because the base map resolution of 4 by 4 m was preserved. In contrast, aggregating to larger cell size before cluster analysis resulted in inconsistent changes in the yield classification results, and the resulting map unit shapes appeared more unrealistic, particularly at the 64- by 64-m cell size.

The choice of the spatial aggregation method (PCI or PCF) affected the spatial agreement between the categorical maps of yield classes. Kappa coefficients generally indicated better agreement among maps created by PCF than those with PCI at different cell sizes (Table 2). For the cell sizes compared, the majority of Kw values were >0.9 with the PCF method compared with mostly <0.9 with PCI. Map disagreement was generally largest between the 16- and the 32-m cell length maps, particularly for the WAR method. The smallest Kw (0.59–0.78) was observed for the PCI-WAR method at Site A. Comparing the 8-, 16-, and 32-m maps with the 4-m maps, both WAR and FUZ clustering methods followed by PCF resulted in high Kw of 0.89 to 0.98 (Table 2).


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  		Table 2. Weighted Kappa coefficients (Kw) describing the spatial agreement among categorical maps of six yield classes at Sites A and B generated by hierarchical (WAR) and nonhierarchical (FUZ) clustering techniques and two spatial smoothing methods. All Kw values were significant at p < 0.0001.

 
Yield Variability Accounted For
There were no significant differences in terms of the RVc accounted for between the WAR and FUZ classification methods (Fig. 3) , suggesting that either one could be used for yield classification conducted on mean relative yields. Slightly higher RVc was observed for PCF compared with PCI used as spatial aggregation methods. Across all grid or windows sizes, the RVc accounted for was 57% for PCI and 61% for PCF.



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  		Fig. 3. Effect of different spatial aggregation techniques on the average yield variance (RVc, %/100) accounted for by the classification at Sites A (a and b, Clay Center) and B (c and d, Cairo). Left (a, c): Mean relative yield was first interpolated to maps of different grid cell size and then classified using hierarchical cluster analysis (WAR) or fuzzy-k-means clustering (FUZ). Right (b, d): Mean relative yield was interpolated to 4- by 4-m grid cell size and classified using WAR or FUZ, and the resulting yield classes were then spatially filtered using different window sizes ranging from 8 to 64 m.

 
Cell size affected the RVc, and this effect differed between the PCI and PCF spatial aggregation methods. In general, RVc decreased as cell sizes, increased but the difference was smaller with PCF than with PCI (Fig. 3), suggesting that the PCI procedure was more sensitive to changes in grid sizes than PCF was to changes in the smoothing window size. The influence of cell size on RVc was linear over the range of cell sizes tested, with nearly identical slopes and intercepts for the FUZ and WAR classification methods (Fig. 3). However, at both sites, and with both classification methods, slopes in the PCI procedure were more negative than those in the PCF aggregation method. A consistent and statistically significant decrease of RVc occurred at both sites using PCI (Fig. 3), particularly when grid size was increased to 64 m. To maintain a high RVc of more than 0.60 while aggregating the cells, maximum allowable grid size was about 16 m with PCI compared with 32-m window size with PCF. In another words, PCF allowed the use of larger aggregation sizes while keeping higher RVc. Within both aggregation methods, RVc was more affected by cell size at Site B than at Site A (Fig. 3) because narrower yield class transition zones existed at Site B (Fig. 2), which were mainly related to changes in topography. Consequently, using large cell sizes at Site B would compromise more yield classes and cause larger classification errors than at Site A.

Increasing cell sizes had little effect on mean relative yields of the resulting yield classes but increased the within-class CV values and altered the proportional field area occupied by each class (Table 3). These effects were most pronounced for increasing the grid size in PCI (data not shown), whereas changes were small for increasing window sizes in PCF, particularly in the range of 4 to 32 m. Average within-class CV was 5.1, 5.2, 5.4, 5.9, and 6.8% at Site A and 11.4, 14.6, 17.8, 19.3, and 26.0% at Site B when window size increased in the order of 4, 8, 16, 32, and 64 m, respectively. Mean relative yields in high-yield classes (5 and 6) were stable but increased in the low-yield classes (Table 3). This trend was similar to the influence of aggregating the cell area before the cluster analysis (Table 1) although quite different classification algorithms were involved. Site B was affected more by the smoothing process than Site A, but the largest differences in CV at Site B mainly occurred in the lowest-yielding classes (1 and 2), which together accounted for only 2% of the total field area. Using a 64-m smoothing window in PCF decreased the area of the lowest relative yield class (1) at Site B to less than 0.1% of the total area. At both sites, however, the 32-m window size used with PCF resulted in class distributions that were similar to the ones obtained from the original 4-m cells.


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  		Table 3. Effect of postclassification filtering (PCF) with different square window size on the mean relative yield, standard deviation (SD), coefficient of variation (CV), and the proportional area (percentage of whole field) of yield classes. Values are shown for hierarchical cluster analysis using the Ward method.

 
Spatial Fragmentation of Yield Classes Maps
Landscape pattern metrics reflected differences in the maps of yield classes among sites, spatial aggregation methods, and the cell sizes used (Fig. 4) . The number of patches per unit area (PD) decreased sharply when grid size (PCI) or window size (PCF) increased from 4 to 16 m and then approached a near-constant value of 0.3 to 0.5 patches ha-1 at both sites even though the initial PD was much higher at Site A than at Site B (Fig. 4). The decline in PD with increasing cell size was described by a power function and differed little between the PCI and PCF methods.



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  		Fig. 4. Effect of increasing grid cell size used in prior-classification interpolation (PCI, left) or window size used in postclassification filtering (PCF, right) on selected landscape pattern metrics describing the categorical maps of yield classes at Sites A and B. Landscape metrics shown are patch density (PD), the total core area per field (TCA), the mean core area per patch (MCA), the contagion index (CONTAG), and the splitting index (SPLIT). All values refer to hierarchical cluster analysis using the Ward method.

 
The MCA is a potentially important criterion for selecting a classification method for yield classification because it indicates the area within a patch that can be reliably assigned to a certain yield class and, therefore, managed according to the specifications of the available agricultural equipment. For example, equipment with large swath width is likely to require patches with a large core area so that application rates can be varied reliably from patch to patch or within a patch. In general, larger MCA values for yield goal maps would facilitate site-specific management better than small ones. The MCA increased linearly with increasing cell sizes in the range of 4 to 64 m at both sites (Fig. 4). When cell sizes were equal or less than 8 m, the average MCA was less than 0.25 ha per patch, and numerous small patches remained that were unlikely to represent true variation in attainable yield because they were caused by random yield variation in individual yield years. However, the MCA increased to about 1.5 ha per patch when cell size was 32 m. The slope of the relationship between MCA and cell size differed between sites for PCI but was similar for the PCF procedure, indicating that the latter might result in more consistent changes in MCA across different sites, despite different structure of yield variability.

In a precision-farming context, a large TCA is desirable because it reduces the proportion of transitional (edge) zones, for which membership to a certain yield class is less certain, which could cause site-specific treatment to be less successful. The TCA increased nonlinearly with increasing cell size for both PCI and PCF methods (Fig. 4). At both sites, large changes in TCA occurred when cell size increased from 4 to 32 m, with relatively little further change by increasing it to 64 m. Although both fields had similar total area, PCF resulted in consistently larger TCA at Site B than at Site A, whereas these site differences were masked by using PCI with grid sizes larger than 4 m. At Site A, the center-pivot irrigation caused more narrow transitions from irrigated to rainfed areas (Fig. 2), thereby decreasing the manageable TCA in absolute terms compared with Site B.

Postclassification filtering with increasing window size caused a continuous, nonlinear increase in CONTAG at both sites, with CONTAG approaching values of about 55 at Site A and 70 at Site B with window sizes of either 32 or 64 m. Large yield class patches following a general northwest to southeast trend probably caused the high CONTAG at Site B while more interlaced and lateral shapes of patches with narrow transitions from irrigated to rainfed zones were seen at Site A (Fig. 2), resulting in a lower CONTAG. Unlike PCF, using the PCI method for aggregating the yield data resulted in inconsistent changes in CONTAG with grid size and less obvious site differences (Fig. 4).

The SPLIT also revealed differences among sites and mapping methods with regard to spatial fragmentation of a field. At Site B, initial spatial fragmentation was less than at Site A, and SPLIT changed little, from 4.8 to 3.9, as the window size used in PCF increased from 4 to 64 m (Fig. 4). At Site A, however, increasing window size in PCF gradually decreased SPLIT to levels similar to those at Site B, reflecting the noise-filtering process that occurred during formation of spatially contiguous yield classes. Using PCI spatial aggregation instead of PCF did not result in a gradual change in SPLIT with increasing grid size. At Site A, SPLIT dropped abruptly from 15 at 4-m grid size to 4.2 at 8-m grid size, with no significant change thereafter. Changes in AI with increasing cell size were similar to those observed for TCA, i.e., a gradual nonlinear increase with AI remaining consistently higher at Site A than at Site B for the PCF method but not for PCI. The AI increased from 80.1 to 93.7 at Site A or 87.3 to 95.6 at Site B as window size used in PCF changed from 4 to 32 m (Table 4).


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  		Table 4. Summary of the effects of postclassification filtering (PCF) after hierarchical cluster analysis (WAR) on the maps of relative mean yield classes. Data are shown for the original map of yield classes (4- by 4-m grid) and two levels of spatial filtering using 32- by 32- and 64- by 64-m window sizes.

 

   DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
In many precision-farming studies, square grid cell sizes used to create interpolated yield maps were in the 10- to 50-m range (Lark and Stafford, 1998; Juerschik et al., 1999; Taylor et al., 2001). However, in our study, choosing a coarse resolution (>16 m) for yield interpolation before spatial classification (PCI) resulted in more biased aggregated data sets (Table 1), maps that did not accurately depict yield patterns (Fig. 2), significant decline of RVc (Fig. 3), loss of resolution around sharp yield transitions, and poorer agreement with the original map (Table 2). The PCI method was sensitive to changes in cell size, and agreement between WAR and FUZ classification methods was more erratic than with the PCF procedure. Errors with PCI can be severe if a grid size that is too large is used for interpolation. For example, using a kriging grid size of 64 by 64 m increased the estimated values near the field edges by combining areas with higher yield with poor-yielding areas near the edges, which mainly represented end rows (headlands) or zones with insufficient irrigation.

In contrast, applying image-processing techniques such as the PCF algorithm to small-cell maps of yield classes created by hierarchical or fuzzy-k-means clustering of mean relative yields greatly improved the quality of the final yield class maps. At both sites, this procedure allowed forming large finite map elements but with little loss of the spatio-temporal yield variability accounted for (Table 4). The PCF procedure mainly removed map unit contamination due to erroneous data while preserving the class means (Table 3), a high RVc (Fig. 3), and the general yield patterns (Fig. 2), including retaining high spatial agreement with the original 4-m maps (Table 2). Moreover, when spatial aggregation was done with PCF after classification, results did not depend on whether WAR or FUZ methods were used for cluster analysis, which reduces the risk for errors due to the choice of a classification method. Unlike the PCI method, PCF maintained a small grid size (here: 4 by 4 m), allowing display of more detail in maps of yield classes, particularly near thin transition zones within a field and near the field boundaries.

What is an optimal window size for applying PCF to maps of yield classes? Using RVc (Fig. 3), the resulting maps (Fig. 2), and various landscape metrics (Fig. 4 and Table 4) as criteria, the results of our study suggest that the smoothing window size should be in a range of about 30 to 60 m, depending on how much loss in RVc is acceptable and how large the desired yield zones should be. In our case, the 32-m window size provided a good compromise. At Site A, the original map of six yield classes accounted for 60.5% of the yield variability observed but was composed of 837 patches, with an average patch size of just 0.07 ha. A revised map of six relative yield classes based on PCF with 32-m window size accounted for 59.5% of the yield variability, even though the number of patches was reduced to 32, with a mean patch size of 1.96 ha. At Site B, the original map accounted for 67% of the yield variability and had 441 patches, with a mean patch size of 0.14 ha, whereas the revised PCF map accounted for 61%, with only 30 patches and an average size of 2.07 ha per patch. At both sites, the TCA increased to about 73 to 80% of the whole field. Doubling the window size further to 64 m had relatively little effect on further decreasing spatial fragmentation but caused a significant decline in RVc (Table 4).

Landscape pattern metrics may provide useful information about differences in the shapes and spatial structure of yield classes among sites. In the SSCM context, patches can be viewed as finite management elements, which are assumed to be different from adjacent patches. Differences among neighboring patches can be large (abrupt change from a high to a low class level) or more gradual (from one class level to the next), which is likely to affect management decisions. Depending on the data source, cell size chosen, and the classification method, a field can be composed of few larger patches (or zones) or many small patches with varying patch core area, contrast, and connectivity. Core area metrics are of particular relevance for evaluating SSCM options. In ecology, buffer or edge zones represent transition habitats between two distinctively different patches (McGarigal and Marks, 1995). In the SSCM sense, we can think of them as class boundaries that are uncertain due to the errors associated with the measurement and mapping process. Consequently, within a patch, cell membership in a yield class represented by the patch becomes more certain with increasing distance from such user-defined edge buffers. The patch core area is most likely to respond to management decisions that are based on the yield classification because it can be thought of as a relatively stable area in terms of yield potential. For example, while a patch may be large enough to be distinguished from neighboring patches, its core area may not be large enough to justify a separate yield goal or different management because swath widths or the travel distance per application rate change of the application equipment used may exceed the patch core area.

Indices such as TCA, CONTAG, SPLIT, and AI showed differences between the two sites studied, and this may reflect the inherent differences between these two sites in terms of the spatial structure of yield variation (Fig. 2), which was mainly affected by crop irrigation (Site A) and elevation (Site B). It remains to be seen whether these indices have potential for comparing fields with regard to opportunities for SSCM. Pringle et al. (2003) proposed an "Opportunity Index" for identifying fields with the greatest overall potential for SSCM, which they calculated from the magnitude and spatial structure of yield variation in a single-year continuous yield map, including defining empirical "thresholds" for both. Compared with this, landscape pattern metrics as used in our study were easier to compute and referred to categorical maps of mean yields over time, which may be more suitable for making management decisions. Like most indices, however, landscape pattern metrics have many limitations because they depend on user-defined data formats, scales, and other settings and their interpretation is constrained by lack of proper theoretical understanding of metric behavior (McGarigal, 2002).


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
Yield goal is one variable in many equations used for making management decisions. Yield zones should be delineated as larger, spatially contiguous areas within a field, which mainly represent the measurable, stable site yield potential, not random yield variation caused by measurement error or specific, unrepeated crop management events. Inputs can then be applied at variable rates according to both differences among and within yield zones because more continuous spatial soil variation exists within larger patches of yield classes that were formed from historical yield map records.

Postclassification spatial filtering of maps of yield categories established by cluster analysis removed map fragmentation, thereby creating maps of yield classes that were composed of contiguous map units. The original map resolution was maintained, and little loss of the yield variance accounted for occurred. In contrast, interpolating yield maps to a coarse grid size before the classification lead to erroneous maps of yield classes and significant losses of information. Depending on the nature of yield variation, how much loss of information is acceptable, and how large the desired yield zones should be, window sizes for spatial filtering of yield maps should be in the 30- to 60-m range. Landscape pattern metrics may offer interesting potential for assessing mapping techniques as well as comparing agricultural production fields with regard to ranking their relative opportunities for SSCM.

The procedures evaluated in our studies with irrigated crops are currently not implemented in most commercially available farm management software. More research should be conducted to assess similar yield class mapping procedures in other environments, identify the most useful landscape metrics for different SSCM purposes, and understand their interpretation.


   ACKNOWLEDGMENTS
 
We thank Lyle VonSpreckelsen (V6 Farms, Clay Center, NE) and Arnie Hinkson (Hinkson Land Tech, Wood River, NE) for providing the yield monitor data used in this study. Funding for this research was provided through the USDA-CSREES/NASA program on Application of Geospatial and Precision Technologies (AGPT, Grant no. 2001-52103-11303) and the U.S. Department of Energy (i) EPSCoR program, Grant no. DE-FG-02-00ER45827 and (ii) Office of Science, Biological and Environmental Research Program (BER), Grant no. DE-FG03-00ER62996.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Contribution of the Nebraska Agric. Exp. Stn. Sci. J. Ser. Paper no. 14008.


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




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