Soil Science Society of America Journal 63:1740-1747 (1999)
© 1999 Soil Science Society of America
DIVISION S-4-SOIL FERTILITY & PLANT NUTRITION
Phosphorous and Potassium Fertilizer Recommendation Variability for Two Mid-Atlantic Coastal Plain Fields
C.M. Anderson-Cooka,
M.M. Alleyb,
Robert Noblea and
R. Khoslab
a Dep. of Statistics (0439), Virginia Polytechnic Inst. and State Univ., Blacksburg, VA 24061 USA
b Dep. of Crop and Soil Environmental Sciences (0404), Virginia Polytechnic Inst. and State Univ., Blacksburg, VA 24061 USA
candcook{at}vt.edu
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ABSTRACT
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Fertilizer recommendations for variable rate treatments developed from grid soil sampling protocols are unproven for mid-Atlantic Coastal Plain soils. The objectives of this study were to compare soil test results for P and K fertilizer recommendations for two fields utilizing two grid sampling sizes (0.33 ha and 0.83 ha), sampling by soil type, and standard composite sampling. The study location contained alluvial soils ranging from a loamy sand to a silt loam. The two fields totaled approximately 21 ha and were sampled on grids 18.5 by 30.4 m. Samples consisted of composites of eight cores to a 20-cm depth that were analyzed for Mehlich I extractable P and K. Two statistical models were developed for comparing the extractable P and K data and the resulting fertilizer recommendations. The first model, following a precision farming approach, implies sources of variation are systematic and attributable to narrow geographic locations. The second model, associated with composite sampling, utilizes less specific patterns of variability. Comparisons showed that the smaller grid (0.33 ha) produced more precise estimates of extractable K in only one field (with 67% of tested locations receiving appropriate fertilizer rates), with no improvement for extractable P in either field. Both grid-sampling systems improved estimate precision for extractable P and K (with a smaller average misapplication rate) compared with a whole-field composite. The composite-by-soil-type approach was superior to the whole-field composite for estimating extractable P and K with a lower average misapplication and higher percentage receiving appropriate fertilizer rates. The composite-by-soil approach produced the most precise fertilizer recommendations for small systematic variation and required fewer laboratory measurements. It approached the grids-sampling system precision of fertilizer recommendations for large in-field variation. Only when strong trends in extractable P and K exist would grid sampling be recommended over the composite-by-soil-type sampling approach.
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INTRODUCTION
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PRECISION AGRICULTURE USING the global positioning system (GPS), grid soil sampling, and variable rate fertilizer application is becoming more widely utilized, while the relative effectiveness of this strategy for determining fertilizer recommendations is unproven. In this paper we consider different methods for determining K and P fertilizer recommendations and use a model to explain some of the success and shortcomings of a variety of strategies. Fertilizer recommendations using a precision agriculture approach, with samples on 0.33- or 0.83-ha grids, is compared to more traditional approaches of a single recommendation based on a global composite, or a composite-by-soil-type represented in the field. Sawyer (1994) noted that "field research indicates ... that positive economic return to variable rate application technology does not always occur."
We present individual results for the fields considered, as well as some general principles about identifying situations where precision agriculture approaches will likely outperform the traditional approaches of composites, or vice versa.
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Theory
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To provide a more formal context to describe the nature of plant-available P and K variability in the field, we present general random effects models that incorporate the different sampling schemes to allow for more direct comparison between methods. Fertilizer recommendations are based on a two-phase process: In the first stage, plant-available K and P measurements (hereafter referred to as y) are taken according to either the precision farming approach on various sized grids or by using composites across sections of the field. The second stage takes the actual measurements of plant-available K and P and converts them to fertilizer recommendations (hereafter referred to as z) in 11.2–22.4-kg ha-1 increments based on calibration curves from previous research (Donohue and Heckendorn, 1994). This conversion process involves transforming y to z using a step function with a small number of recommendation levels (11.2–22.4-kg ha-1 measurements). This conversion masks much of the variation in the actual measurements and also provides a buffer to make small variations in the actual measurements of plant-available K and P less critical.
For the precision farming approach where sampling is done on a predesignated grid size, measurements of K or P take the following form
 | (1) |
This model involves nested factors, where some observations are randomized within a particular combination of other factors. For more details on nested models, review an advanced experimental design text such as Box et al. (1978) or Winer et al. (1991). The terms Ri, Cj, and RCij represent row and column main effects and the row-by-column interaction based on the location of the points. These terms are treated as random effects in the statistical model. This implies that the differences between row and column locations are not of particular interest individually but are considered primarily to obtain information about general patterns of differences within the field that might generalize to other fields. Hence, location terms are all assumed to contribute their own variance components (
2R, 2C, and 2RC, respectively) to the individual observations, yijkl. The term 
k(ij) is associated with the sample location within a particular grid location, specified by a particular row and column, while the term 
l(ijk) is associated with a particular soil core within each sample at a given location. Indeed, recent work shows that significant differences can be found when samples were obtained on a 0.305 by 0.305 m (1 x 1 ft.) grid (Raun et al., 1998). These terms are also assumed to contribute variance components, 2samp and 2, to each observation. Hence, each observation, yijkl represents a measurement associated with a particular soil core (subscript "l") within a particular sample (subscript "k") at a given grid location specified by subscripts "i" and "j".
Generally with precision farming, observations yijkl are not observed directly because of the prohibitive cost of laboratory work; instead an average over 6–8 observations at a given sample location is taken. This value can be represented by 
ijki·, where the bar above y indicates that an average has been taken, and the dot indicates over which subscript the average was taken. In addition, the subscript k generally only takes one value because only one sample is taken within any grid location. However, since this study considered multiple grids for a given field, an estimate of the variance within the sampling grids is possible.
Interest with this model is two-fold. First, we wish to determine if the effects Ri, Cj, and RCij contribute meaningfully to the model. This would imply there are significant differences between grid locations and hence sampling at these points gives useful information about the different fertilizer requirements at various field locations. Second, estimating the variance components 2R, 2C, 2RC, 2samp, and 2 can give important information about the relative size of the contribution of these components and can suggest an efficient sampling scheme to obtain the most accurate fertilizer recommendations. For example, if 2R, the variance component associated with the rows of the field, is larger than 2C, then a more efficient sampling scheme would place an increased emphasis on sampling the different rows rather than different columns to detect the major sources of field variation.
A different model is required for composite sampling schemes, since there is no intrinsic row and column built into the model. In this case, each K or P observation has the form
 | (2) |
The term Loci identifies a particular location within a field or soil type and contributes variance component 2Loc to each observation. The nested term l(i), with variance component 2, denotes the particular soil core at a particular location. Generally, only a single observation is taken at each location, so the subscript "l" serves just to remind us of the additional variation contributed from the core. Again, the actual observations, yil, are not observed; the overall average of all the observations, ··, is the single measure that is obtained per field (for a global composite sample) or per soil type (for a composite by soil sampling scheme).
Once ijk· or ·· have been obtained and laboratory analysis completed, the fertilizer recommendations are calculated by converting the plant-available K and P values into kg ha-1 fertilizer application rate zij or z··.
The form of this model implies a different set of assumptions of associations between field measurements than the model in Eq. [1]. In this case, a simpler model that acknowledges differences between locations is used, but has no geometric orientation for specifying components of location as specific sources of variation. This suggests that variability in different locations does not come from easily assignable sources and hence is just dealt with in very general terms. The two models make for good comparisons between the potential theories underlying the various sampling schemes: the precision farming models imply that sources of variation are attributable to narrow geographic locations in a predictable way, while the global-composite and composite-by-soil-type approaches suggest less specific patterns are identifiable.
The objectives of this study were to compare soil test results for P and K and fertilizer recommendations for two fields utilizing two grid sampling sizes (0.33 ha and 0.83 ha), sampling by soil type, and standard-composite sampling.
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Materials and methods
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The study location is in the Virginia Coastal Plain and has alluvial soils ranging from Bojac 1A and 2A (coarse-loamy, mixed, thermic, Hapludults) to Wickham 3A and 4A (fine-loamy, mixed, thermic, Ultic Hapludalfs) (Order I Soil Survey, NRCS staff, 1998). Ranges in productivity and fertilizer needs are associated with available water-holding capacity and soil texture (Simpson et al., 1993).
Soil samples were taken on a grid throughout the two fields with a total approximate area of 21 ha. Mehlich I extractable P and K were determined on each sample (Donohue and Heckendorn, 1994). The first field, with relatively less variability for both P (standard deviation [s.d.] across the field of 4.4 mg kg-1) and K (s.d. of 15.7 mg kg-1), consisted of 133 samples (seven rows 18.5 m apart with 19 samples at 30.4-m intervals). The second field with considerably greater differences in fertilizer needs (s.d. for P of 15.9 mg kg-1 and for K of 41.3 mg kg-1) contained 280 samples (14 rows 18.5 m apart with 20 samples at 30.4-m intervals). The size of the grid reflects the standard width of the application equipment and a realistic length of field where fertilizer adjustments between sites could be performed during normal application. Plots of the extractable K and P soil measurements for each of the fields are given in Fig. 1 and 2 . The details of these particular fields are not of primary interest, but instead serve to illustrate some of the ideas behind the comparison between methods. Field 1 values for extractable K and P are relatively consistent with smaller overall variations than Field 2, which has a distinct decreasing trend along the rows for P and a less predictable pattern for K. Details of soil sampling as well as extractable P and K levels by field and by soil type within the field are given in Table 1
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Table 1 Average Mehlich I extractable P and K levels for Fields 1 and 2 by field and by soil type within each field
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Sampling for the precision farming 0.83-ha grid used every fifth row and third column. The 0.33-ha grids were sampled from every third row and second column. The global composite was calculated by sampling 20 locations from each field (mimicking the approach suggested by Peterson and Calvin [1996]). The composite-by-soil-type calculations were obtained by taking 20 observations for well-represented soils and 10 observations for more scarce soil types (2A in Field 1 and 4A in Field 2). Table 2
summarizes the minimum, maximum, and average values obtained for each sampling scheme.
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Table 2 Minimum, maximum, and average soil tests for Mehlich I extractable P and K from Fields 1 and 2, using different methods of sampling
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A second study compared variation at the core level to variation at the sample level. The study involved four soil core measurements and one sample measurement at each of four locations within both the Bojac and Wickham soil types. It measured the relative size of variance components between samples (2samp) and between soil cores (2). The estimation of 2 gives a measure of the microvariation levels that exist in the field. This was required in order that the composite and composite-by-soil-type values could be accurately measured. Since these observations were actually based on composites of eight soil cores per location, a variance inflation factor was introduced to compensate for the increased precision of measurement from the soil core composite at each location. The variance inflation factor was determined in the second study. Since many samples for each strategy would have been possible, 200 samples for each sampling scheme from each field were simulated with the results presented as an average across all observed samples for a particular scheme.
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Results and discussion
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Using the models presented in Eq. [1] and [2], the importance of various factors to explain differences in extractable P and K values can be assessed. For the precision farming approach, both one-way and two-way analyses of variance with random effects assess the importance of the general location effects as well as a breakdown of differences by row and column.
The 0.83-ha grids divided Field 1 into two rows and seven locations within rows, and Field 2 into three rows and seven locations within rows. For the 0.33-ha grids, Fields 1 and 2 were divided into 30 (3 x 10 rows) and 50 (5 x 10 rows) locations. A highly significant difference in locations was identified for extractable P and attributed to only column differences in both Fields 1 and 2, for both the 0.33-ha and 0.83-ha grids. Extractable P data plotted in Fig. 2 shows that there are some undulations in the levels of extractable P that change across the rows.
The variance components give information about the relative size of the contributions to the measurements yijki·. For the 0.83-ha grids the estimates of 2C and 2samp are 28.1 and 4.0 for Field 1 and 36.3 and 2.4 for Field 2, respectively. Units for all of the variance estimates are (mg kg-1)2. As expected, differences between columns are larger on Field 2 where more dramatic changes are observed. Variation explained by different grid locations is 7–15 times as large as the within-grid location variability. For the 0.33-ha grids, estimates of 2C and 2samp are 29.1 and 1.9 for Field 1 and 36.7 and 0.3 for Field 2, respectively. The relatively small increase in 2C between the two grid sizes suggests that there is little advantage to increasing the sampling rate from once every 0.83 ha to once every 0.33 ha.
Similar results were obtained for extractable K for both the 0.33-ha and 0.83-ha grids in both fields. However, in Field 2 differences in location were attributable to not only the column effect, but also row-by-column interaction. The pattern of extractable K plotted in Fig. 1 does not follow the simple change between columns that is characteristic of extractable P in both fields and extractable K in Field 1. In Field 2 there are distinct patches of increase and decrease that depend on both row and column location, characteristic of row-and-column interactions. Hence our model in Eq. [1] formalizes patterns that have been observed in Fig. 1 and 2.
The variance components for extractable K, 2C and 2samp are 5.0 and 14.1 (0.83 ha) and 7.8 and 11.4 (0.33 ha) in Field 1, respectively. In Field 2, because there is an interaction effect as well, 2C, 2RC, and 2samp are 56.7, 35.6, and 173.1 (0.83 ha) and 82.0, 47.8, and 134.9 (0.33 ha), respectively. The relative improvement in precision of estimates seems to increase more from 0.83 ha to 0.33 ha in Field 2 than in Field 1, suggesting that there may be additional advantage to the smaller grid in Field 2 where there is more dramatic and rapid undulation of observed extractable K values.
A significant difference between locations here means that the grids are giving a more precise representation of the values of extractable soil P than just taking a single measure across each of the entire fields. We would expect that this would translate into more precise fertilizer recommendations for the precision farming approach. When differences between soil types are measured with the one-way analysis of variance there are highly significant differences between soil types for both extractable soil P and K in each field. Table 3
summarizes the results obtained, with the second column showing the estimated size of the variance contribution from different soil types and the third column summarizing the remaining component attributable to different locations within a soil. The extremely small significance levels indicate that soil type is very important in explaining differences in extractable P and K in each of the fields. This suggestion that a composite-by-soil-type approach should give better results than a single composite for the entire field, since soil type is identifying and extracting known substantial contributors to the variability of the K and P measurements.
However, since these analyses examine only the values of plant-available P and K, without incorporating the translation of individual measurements to fertilizer recommendations, they should be helpful to understanding the variance component structure, but not a good assessment of different fertilizer application strategies. To compare precision farming with composite approaches, the second phase of the process, namely the conversation to application rates using the calibration curves with 11.2–22.4-kg ha-1 increments, must be incorporated. To illustrate why this is necessary, consider the situation where there are significant differences between locations indicated by the individual measures ijki·, but all of the measures yield the same fertilizer recommendation. In this case, the composite will also suggest a constant application rate and the two methods will perform equally well, despite the real differences in nutrient availability between locations. Hence the broad classes of fertilizer application rates make some of the observed variation in nutrient availability between locations unimportant in the final assessment of strategies. If the variation of a particular location or composite is small relative to the class boundaries of the fertilizer application rates, estimated fertilizer rates will be stable for most of the grids overlaid on the field.
Now that we have some understanding of the variation within the fields, we examine the different fertilizer recommendations afforded 0.83- and 0.33-ha precision farming grids compared to the composite and composite-by-soil-type approaches. The results are given in Tables 4–7
for each value of P and K for each field. We use the 133 (7 x 19 rows) and 280 (14 x 20 rows) measurements from each of the fields as our baseline in the first row of each table to assess how well each of the strategies predicts the correct fertilizer recommendation. The number of samples and laboratory measures give an assessment of the relative cost of the different methods: Collecting more samples at different locations in the fields is time-intensive, and having many laboratory measurements taken is cost-intensive. The "total fertilizer" column gives a summary of the average amount of fertilizer that would be recommended for application for each of the different methods. The "average miss" column is the average of the absolute values of overfertilization or underfertilization at each of the 18.5 by 30.4 m grid locations. The "maximum misses" column shows largest underfertilization rate, denoted by the negative extreme of the range, and the largest overfertilization rate. The last three columns show the percentage of locations that were underfertilized by at least 22 kg ha-1, fertilized to within 11.2 kg ha-1 of the true value, and underfertilized by at least 22 kg ha-1, respectively. These columns allow a balanced assessment of the methods on a variety of criteria that would be influential in choosing the best fertilizer recommendation strategy. Data plotted in Fig. 3
show the optimal fertilizer application rates suggested by the 18.5 by 30.4 m grids for extractable K. Figure 4
gives a visual summary of each of the four fertilizer application strategies.
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Table 4 Potassium fertilizer recommendations, sample numbers, and number of laboratory measures for various sampling approaches in Field 1
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Table 5 Potassium fertilizer recommendations, sample numbers, and number of laboratory measures for various sampling approaches in Field 2
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Table 6 Phosphorous fertilizer recommendations, sample numbers, and number of laboratory measures for various sampling approaches in Field 1
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Table 7 Phosphorous fertilizer recommendations, sample numbers, and number of laboratory measures for various sampling approaches in Field 2
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Fig. 4 Potassium fertilizer recommendations for Field 1 for 0.83-ha grids, 0.33-ha grids, global-field composite, and composite by soil type
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Examining the results for K (Tables 4 and 5) we see that the amount of K fertilizer suggested by each of the methods does not vary by more than 68 kg K total in Field 1 and 114 kg K in Field 2. The composite over the entire field is clearly the least desirable option for both fields because it has by far the highest amount of fertilizer required while the average miss is considerably higher than any of the other three options. In addition, the percentage within ±11.2 kg ha-1 is much lower. In Field 1, where there does not appear to be a dramatic trend across the field, the composite-by-soil-type method does best with the smallest average miss, the smallest range of maximum misses, and the largest percentage within ±11.2 kg ha-1. In Field 2, the precision farming approach on 0.33-ha grids fares best with the smallest average miss and largest percentage within ±11.2 kg ha-1, but both the 0.83- and 0.33-ha grids had larger maximum case misses than the composite-by-soil-type method. Therefore, in cases where there are wide fluctuations between response values, the precision farming approaches generally do better at tracking those changes. However, if these approaches do not track the changes well at a particular location, the fertilizer recommendations can be extreme.
Examining the results for P (Tables 6 and 7), we again see relatively small differences between P fertilizer application totals (less than 45 kg P across all of the strategies). The 0.33-ha grid sampling approach does best in both fields for the smallest average miss and largest percentage within ±11.2 kg ha-1, with the 0.83-ha grid second in both categories. However, in Field 2 with the stronger linear trend across the field, the column labeled "maximum misses" for the precision farming grid sampling shows that sometimes this strategy does not perform well.
We find some useful general results from this study for these particular fields. First, strong undulations and variations in the observed values of extractable K or P in a field make the precision farming approach more advantageous. However, even in situations where the average miss is low, there may be locations in the field where fertilizer is grossly underapplied or overapplied. The composite-by-soil-type approach does best in fields with relatively little systematic variation across the field, but is a consistent performer in all situations with a competitive average miss and percentage within ±11.2 kg ha-1, and moderate maximum misses even in the presence of rapidly fluctuating response values. Given the reduction in laboratory measurements and the simplicity of fertilizer applications with the composite-by-soil-type approach, this fertilizer application strategy has considerable advantages. Only when strong trends are known to exist in a field would it not be a recommended choice. The total fertilizer recommended by a particular strategy is not one of the most influential factors to be considered, since across the different patterns of variation and sampling methods there was relatively little difference in total cost contributed by this aspect. The maximum difference in total fertilizer from the average recommended by all five strategies was only 3–12%.
It should be noted that, as suggested earlier, data analysis without taking into account the translation to fertilizer application could be quite misleading. Some of the results were predicted by the initial analysis, such as the improved performance of the 0.33-ha grid for extractable K in Field 2 due to the increase in the variation explained with the finer grid. However, the near-parity of performance of the global composite approach and the precision farming methods for extractable P in Field 2 is somewhat unexpected considering the highly significant differences between locations.
This study helps to understand the influence of the location of the average extractable soil K or P level relative to fertilizer recommendation values. For example, consider the entire field composite for extractable P in Field 2, where the average extractable value across all 280 values is 14.8 mg kg-1. The transition between fertilizer recommendation levels is 15 mg kg-1 (Donohue and Heckendorn, 1994), which means that if the average for the field is just less than 15 mg kg-1 the fertilizer recommendation is 67 kg ha-1; if the average is just over 15 mg kg-1, the recommendation is 44.8 kg ha-1. The data in Table 7 show a lack of symmetry in the percentage underfertilized and overfertilized (30% versus 12%). Soil test data presented in Fig. 5
shows a possible distribution for the averages and how the location of the transitions between fertilizer recommendations influences the proportion correctly classified. The distribution of possible average values that can be obtained from the sampling in this field is centered at 14.8 and frequently for a single observed sample the average will be slightly larger than 15, giving a lower fertilizer recommendation than is actually required.
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Fig. 5 Distribution of composite average relative to P fertilizer recommendation transitions for 11.2–22.4 kg ha-1 calibration categories with fractions of data correctly fertilized, overfertilized, and underfertilized
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Therefore, not only is the spread of the extractable K and P values important in determining the variability of prediction, but the proximity of the averages to changes in fertilizer recommendation levels also dramatically changes the performance of the approaches. If the fertilizer recommendations were based on a finer calibration curve, say in 5.5-kg ha-1 increments, some of the lack of symmetry would disappear but the number correctly classified would be reduced. This would be a result of the smaller range of initial values that would yield the same fertilizer recommendation. This smaller range would give more samples with recommendations that would be incorrect, but the average for any particular field would appear to be more central within the recommendation ranges. Soil test data shown in Fig. 6
illustrates this scenario for the 5.5-kg ha-1 calibrations.
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Fig. 6 Distribution of composite average relative to P fertilizer recommendation transitions for 5.5 kg ha-1 calibration categories with fractions data correctly fertilized, overfertilized and underfertilized
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Conclusions
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Soil sampling using a global position system for sample location and subsequent variable-rate fertilizer treatment does not require that samples be taken on a grid system. Our study of two fields determine that a 0.33-ha grid sampling system produced more precise estimates of Mehlich I extractable K than a 0.83-ha grid in one field, but did not improve the estimates of extractable P in either field. Both grid-sampling systems improved the precision of the extractable P and K estimates, as did the compositing-by-soil-type sampling approach, compared to whole-field composite sampling. Fertilizer recommendations associated with the various extractable P and K values showed the grid-sampling approach was only advantageous in fields with large, systematic variation in extractable P and K levels. The composite-by-soil-type sampling approach produced the most precise fertilizer recommendations when the systematic variation was small. This approach also required many fewer laboratory measurements and rivaled the grid-sampling system precision of fertilizer recommendations, even with large in-field variation. Only when strong trends in extractable P and K are known to exist in a field would the grid-sampling system be recommended over the composite-by-soil-type approach. These results are consistent with those of Wollenhaupt et al. (1994) and Franzen and Peck (1994) who found grid sampling to be advantageous on highly variable fields with trends.
The main disadvantage to the composite-by-soil-type sampling system is that soil boundaries must be accurately mapped and entered into the geographic information system prior to sample collection. Although this may present challenges when using older maps, or maps on large scales that do not adequately show small soil inclusions, the detailed soils map needs to be prepared only once for each field. The results of this study clearly indicate the composite-by-soil-type approach offers significant advantages in terms of collection of samples, cost of laboratory analysis, and improved fertilizer recommendations for certain situations. Further research with other fields in the mid-Atlantic region is justified to develop parameters for determining when the composite-by-soil-type approach or grid-sampling approaches are most suitable.Hammond 1993
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ACKNOWLEDGMENTS
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This research was supported by grants from the Foundation for Agronomic Research, United Soybean Board, Virginia Corn Board, and Virginia Small Grains Board. Appreciation is expressed to John Nicholson, Greg Hammer, David Harper, and Mark Crouch (Natural Resource Conservation Service) for the Order I soil survey of the site and to S. J. Donohue and S. E. Heckendorn for the soil sample analyses.
Received for publication October 22, 1998.
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REFERENCES
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- Donohue S.J., Heckendorn S.E. Soil test recommendations for Virginia. Blacksburg, VA: Virginia Cooperative Extension, 1994.
- Franzen D.W., Peck T.R. Field soil sampling density for variable rate fertilization. J. Prod. Agric. 1994;8:568-574.
- Hammond M.W. Cost analysis of variable fertility management of phosphorous and potassium for potato production in Central Washington. In: Robert P.C., et al. , ed. Soil-specific crop management. Madison, WI: American Society of Agronomy, 1993:213-228.
- Peterson R.G., Calvin L.D. Sampling. In: Bartels J.M., ed. Methods of soil analysis. Madison, WI: Part 3. Chemical methods. Soil Science Society of America, 1996:1-18.
- Raun W.R., Solie J.B., Johnson G.V., Stone M.L., Whitney R.W., Lees H.L., Sembiring H., Phillips S.B. Microvariability in soil test, plant nutrient, and yield parameters in Bermudagrass. Soil Sci. Soc. Am. J. 1998;62:683-690.[Abstract/Free Full Text]
- Sawyer J.E. Concepts of variable rate technology with considerations for fertilizer application. J. Prod. Agric. 1994;7:195-201.
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TOP
ABSTRACT
INTRODUCTION
