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Soil Science Society of America Journal 66:276-283 (2002)
© 2002 Soil Science Society of America

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

Evaluating the Potential for Site-Specific Phosphorus Applications Without High-Density Soil Sampling

John P. Schmidt*,a, Randal K. Taylorb and George A. Millikenc

a Dep. of Agronomy, Kansas State Univ., Manhattan, KS 66506
b Dep. of Biological & Agricultural Engineering, Kansas State Univ., Manhattan, KS 66506
c Dep. of Statistics, Kansas State Univ., Manhattan, KS 66506

* Corresponding author (schmidt{at}ksu.edu)


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Because of the costs of additional soil sampling and analyses, high-density soil sampling is a major obstacle for producers when deciding whether to variably apply P fertilizer. Our objective was to develop an approach to evaluate the potential for site-specific P applications prior to high-density soil sampling. Soil samples (40–167) were collected from eight fields ranging in size from 40 to 170 ha. The soil P test frequency distribution (DT) was determined for each field using all the samples and assuming lognormally distributed soil P values. Sets (500) of random samples (n = 5, 10, 20, 30, and 50) were selected from all the samples for each of eight fields. With each sample set, the soil P test frequency distribution (Dx) was estimated. A deviation index (Udev) represented the amount that Dx deviated from DT. The generated populations of Udev were then used to evaluate the probability of exceeding any random Udev as a function of n, providing a measure of success in estimating DT. A P application based on the mean soil P test was compared with a P application based on DT, providing a measure of potential for a site-specific P application. The P application based on the mean soil P test deviated from the P application based on DT by 11.7, 9.4, and 5.1 kg P2O5 ha-1 for Fields A, B, and C, respectively, representing the average deviation for the entire field. Larger values represent greater potential return to a site-specific P application. The Udev that was obtained with 99% probability (n = 50) was used as the criterion from which to compare the success of using smaller sample sizes for estimating DT. To achieve the same success in estimating DT with 70, 80, and 90% probability, 18 to 26, 23 to 31, and 33 to 39 soil samples were required for Fields A, B, and C, respectively. This approach provides decision makers a practical tool for estimating DT prior to high-density soil sampling, with an estimate of the corresponding risk associated with different sample sizes.

Abbreviations: Dx, estimate of the soil P test frequency distribution based on simulations • DT, estimate of the soil P test population frequency distribution based on all soil samples • OM, organic matter • Udev, deviation index • Pdev, average summed deviation from the ideal P recommendation


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
THE SUCCESS of site-specific nutrient management will depend on the ability to fertilize areas that respond with increased yield and to avoid areas that are unresponsive to fertilizer applications (Sawyer, 1994). Typically, this means developing a prescription map for site-specific fertilization, which usually requires a relatively high density of soil sampling to quantify the spatial dependency of soil test values. Franzen and Peck (1995) suggested that one soil sample per 0.45 ha was required to develop a reliable map of soil P and K for variable rate fertilization. By contrast, producers who apply a uniform fertilizer application (traditional approach) may use only one soil sample per 16 ha to develop a nutrient recommendation.

High-density soil sampling is a major obstacle for producers when deciding whether to implement site-specific nutrient management. Costs associated with soil sampling and analyses for developing an accurate variable nutrient recommendation are much greater than required for a uniform recommendation. Soil analyses costs may range from $6 to $15 per sample, and increasing the number of soil samples linearly increases analyses costs. A decision to implement site-specific nutrient management, without prior knowledge of soil test variability, presupposes a return on the additional soil sampling, analyses, and variable application costs. Given the considerable costs, a means to assess the probability for success is essential to improved decision making for variable nutrient applications.

Identifying soil test variability for improved nutrient management has been a matter of research, and accordingly, producer interests for many years (Lindsley and Bauer, 1929; McIntyre, 1967; Nielsen and Bouma, 1985; Franzen and Peck, 1995). Recently soil test variability has been studied in relation to site-specific management using new technologies such as global positioning systems and geographic information systems (Borges and Mallarino, 1997; Sadler et al., 1998). Studies similar to these have focused on identifying the spatial variability, or spatial pattern and scale of variability, of field characteristics that can be managed more effectively on a scale smaller than the entire field.

Unrelated to evaluating spatial variability of soil test values, there has also been past interest in estimating mean soil test values and the corresponding population distribution. Parkin et al. (1988) illustrated that the frequency distributions for many physical, chemical, and microbiological soil properties are skewed to the right and are better approximated by the lognormal frequency distribution, as compared with the normal (Gaussian) probability density function. The information provided in a frequency distribution for soil test values, for example, soil P, has not been exploited in the decision-making process for site-specific nutrient management.

Regardless of whether soil test values are spatially correlated, the frequency distribution of soil test values is an inherent characteristic of the population. The frequency distribution represents all possible soil test values in a given field, and consequently, the potential for site-specific nutrient management. If the variability in soil test values is small, then the additional costs associated with site-specific nutrient applications may be unwarranted. If the frequency distribution for the soil test population could be accurately estimated without high-density soil sampling, then producers could avoid the costs of high-density soil sampling and associated analyses costs for fields that may have little potential for variable nutrient management. Currently, a common approach to site-specific nutrient management is to begin with high-density soil sampling and analyses without any regard for potential for site-specific nutrient management. Collecting fewer samples initially, and then assessing the potential for site-specific nutrient applications would be a more prudent approach for the decision-making process in implementing site-specific nutrient management.

Our objective was to provide an approach to improve the decision-making process for the producer considering the merits of site-specific nutrient applications. We present a method to estimate soil P test variability without high-density soil sampling, providing a measure of the potential for site-specific P applications.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Soil samples were collected from eight fields in south central and northeastern Kansas (Table 1). One sample (one core, 5-cm i.d., 0- to 15-cm depth) per 0.3 ha (square unit) was collected at the center of each unit for Fields A, B, D, and F (field size ~53 ha). One soil sample (5–8 cores within a 5-m radius, 2.5-cm i.d., 0- to 15-cm depth) was collected every 0.3 to 1 ha in the other four fields (Fields C, E, G, H; field size ranging from 40–170 ha). All soil samples were air-dried, sieved to pass a 2-mm screen, then analyzed for extractable P (Bray P-1; Frank et al., 1998); organic matter (OM) content (modified Walkley-Black using heat of dilution; Combs and Nathan, 1998); pH (1:1 soil/water; Watson and Brown, 1998); and extractable K (Warncke and Brown, 1998). The number of soil samples (n) from each field ranged from 40 to 167 (Table 2). These fields were planted annually to a row crop, usually either corn (Zea mays L.), soybean [Glycine max (L.) Merr.], or grain sorghum [Sorghum bicolor (L.) Moench]. Previous P fertilizer applications were broadcast and tillage practices included chisel plowing annually. Selected soil characteristics are provided in Table 2. Descriptive statistics in Table 2 were determined using Microsoft Excel (Microsoft Corp., Redman, WA).


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  		Table 1. General field and soil descriptions.

 

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  		Table 2. Selected soil characteristics for each field and descriptive statistics for soil P test.

 
Frequency distributions were constructed to represent the number of observations in a 5 mg P kg-1 increment. Each data set was evaluated using the Kolmogorov D test statistic (SAS Institute, 1998) to determine whether the data were lognormally or normally distributed. Assuming lognormally distributed soil P test values, the estimate of the mean (m) was calculated using Eq. [1] (Method 3 from Parkin et al., 1988):

[1]
where,

[2]

[3]

[4]

The estimate of the variance (s2) was calculated using Eq. [5] (Method 3 from Parkin et al., 1988) assuming lognormally distributed soil P test values:

[5]
where, µ, {sigma}2, and {Psi} are defined in Eq. [2], [3], and [4], respectively. Parkin et al. (1988) indicated that Method 3 (uniformly minimum variance unbiased estimator, UMVUE) had outperformed the method of moments and the maximum likelihood methods for estimating both mean and variance for lognormal distributions, regardless of the skewness of the distribution.

We generated 500 hypothetical soil P test frequency distributions using Monte Carlo simulations, randomly selecting 5, 10, 20, 30, and 50 soil samples (500 times each) from the entire sample set (with replacement) for each field (<50 were selected from Fields G and H). The m and s2 (for 500 simulations) were used to generate a hypothetical frequency distribution, assuming a lognormal function (Microsoft Excel, Microsoft Corp., Redman, WA). These 500 simulated frequency distributions represented the population of frequency distributions for each sample size; in other words, they represented all possible combinations of samples given a specific n.

Statistical methods to compare estimates of the soil P test frequency distribution (Dx) with the population frequency distribution (DT) were not available in the literature. The most detailed information available (all the samples) was used to characterize DT for each field, using m and s2 (Eq. [1] and [5]). The amount that each Dx deviated from DT was determined using Eq. [6]:

[6]
where, Udev equals deviation index (unitless measure of deviation from DT); k equals number of P test increments, increment width is 5 mg P kg-1; Xi equals observations (%) for a specific P test increment for a hypothetical frequency distribution (n = 5, 10, 20, 30, and 50), Dx; and Ti equals observations (%) for a specific P test increment for DT. A population of Udev for each n was generated using the 500 simulated frequency distributions. These populations were then used to evaluate the probability of exceeding a random value, Udev, as a function of n.

We assumed that an ideal P recommendation is one in which P fertilizer is applied for every area of the field according to the current P recommendation model for corn (Table 3; Kansas State University, 1994). This P recommendation is a function of only soil test P and does not depend on yield goal. The ideal P recommendation is essentially the soil P test population frequency distribution (DT) converted to a P recommendation. The deviation of a uniform P application, based on the mean P test value, from the ideal P application was determined by Eq. [7]:

[7]
where, Pdev equals the average summed deviation from the ideal P recommendation (kg P2O5 ha-1); k equals the number of P test increments; Xi equals observations (%) for P test increment i from DT; Preci equals P recommendation (kg P2O5 ha-1) for P test increment i from DT; and PrecM equals P recommendation (kg P2O5 ha-1) for the mean P test. The Pdev represents the potential for site-specific P management, and larger values represent greater potential than smaller values.


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  		Table 3. Observed and estimated soil P test frequency distributions for eight fields in Kansas and average summed deviation from the ideal P recommendation (Pdev), as determined from Eq. [7].

 

   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY
 REFERENCES
 
Soil Phosphorus Test Frequency Distribution
The observed frequency distributions for soil P from Fields A, B, and C are depicted in Fig. 1 . Visually, the frequency distributions for Fields A and B do not appear to have the bell-shaped frequency distribution that is attributed to a normal (Gaussian) probability density function. Estimating the distribution for these two fields, based on the assumptions for a normal probability distribution (closed circles in Fig. 1), underestimates the frequency of observations for P values near the population mean and overestimates the frequency of observations for small P values. An assumption of a normal probability distribution for Fields A and B is especially inappropriate for values less than zero. However, when the values on the x-axis are transformed using a lognormal scale, the shape of the observed frequency distribution visually conforms to a bell shape (Fig. 2) . With the estimated frequency distributions (n = 166, 160, or 82) for ln (P) overlaid on the same graph, the visual evidence supporting the premise that soil P test frequency distributions are lognormal is reinforced.



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  		Fig. 1. The observed and estimated soil P test frequency distributions for Fields A, B, and C, n = 166, 160, and 82, respectively. The estimated frequency distribution was determined using the assumption for a normal probability distribution.

 


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  		Fig. 2. The observed and estimated soil ln (P) test frequency distributions for Fields A, B, and C, n = 166, 160, and 82, respectively. The estimated frequency distribution was determined using the assumption of a normal probability distribution for ln (P).

 
The Kolmogorov test statistic was used to evaluate whether the original soil test P values and ln (P) values were normally distributed. For the data from Field A, the probability of exceeding the Kolmogorov test statistic for the original P and ln (P) values was <0.01 (Table 4), rejecting H0 equal to the normal distribution for both data sets. However, the Kolmogorov test statistic for ln (P) (0.1212) was less than the test statistic for the original P values (0.2070), indicating that the frequency distribution for ln (P) was more similar to a normal distribution than the frequency distribution of the original P data. Evidence of a lognormal distribution for data from Field B was more convincing. While the null hypothesis was rejected for the original P data, the Kolmogorov test failed to reject the null hypothesis for the ln (P) data from Field B (Table 4). Similarly for the data from Field C, the Kolmogorov test statistic for ln (P) (0.1062) was less than the test statistic for the original P data (0.1278), although the null hypothesis was rejected in both instances. The Kolmogorov test statistic for the data from all eight fields was consistently lower for the ln (P) values compared with the original soil test P values (Table 4); however, the null hypothesis was rejected for ln (P) in several instances. For only one field, G, was the test for a normal frequency distribution with the original P values more favorable than the test for the ln (P) values. Parkin et al. (1988) presented considerable evidence, in the form of a short survey, that many physical, chemical, and microbiological soil properties are skewed to the right and are better approximated by a lognormal frequency distribution rather than the normal probability density function. Our results support that evidence (Table 4).


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  		Table 4. Kolmogorov test statistic for evaluating the frequency distribution of the original soil test P values and the ln (P) values for each field, H0 = normal distribution.

 
The DT (n = 166, 160, or 82 for Fields A, B, or C, respectively) represents the population of soil P test values in these fields. The frequency of observations represented by DT was not statistically different from the observed values for any fields (Table 3), based on a Chi-square test (SAS Institute, Inc., 1998). Consequently, DT represents the potential for a site-specific P application when a P recommendation is developed based on soil P test. This information can then be used to evaluate the amount of area in either field that is represented within a specific P test range.

When the estimated frequency distributions, based on an assumption of a normal distribution for ln (P) (Fig. 2), are transformed back to the original x-axis scale (substituting each estimated observation [Fig. 2] for µ in Eq. [1]), the frequency distributions are right skewed as illustrated in Fig. 3 . The implication of these apparently contrasting distributions is that within-field variability in P test may or may not warrant site-specific P management; or, that one field has a greater potential for site-specific management than the other field. The frequency distributions for the corresponding P recommendations for Fields A, B, and C are depicted in Fig. 4 (based on the current P recommendation model; Kansas State University, 1994). If this type of information were available to the producer prior to high-density soil sampling, the sampling and analyses required to create an accurate application map could be avoided for fields in which site-specific P management is unwarranted. If the producer were interested in selecting fields with the greatest potential for a site-specific P application, this information could be used to distinguish one field from another.



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  		Fig. 3. The estimated soil ln (P) test frequency distribution back-transformed using Eq. [1] (substituting each estimated observation in Fig. 2 for µ; n = 166, 160, and 82 for Fields A, B, and C, respectively).

 


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  		Fig. 4. The estimated P application frequency distribution based on the soil P test frequency distribution depicted in Fig. 3.

 
For example, a uniform P application that represents a sufficiently large area of the field to satisfy some predetermined criterion is an example of an objective method for deciding whether to implement a site-specific application. The criterion could be a uniform fertilizer application that represents 80% of the field, ±10 kg P2O5 ha-1. A producer could decide that this was sufficient to preclude investment towards a site-specific P application, or the decision maker could select some other similar criterion. Ideally, a decision to preclude a site-specific P application would be established prior to the decision to implement high-density soil sampling (with the associated costs).

Two apparent questions that are relevant when contrasting the distributions depicted in Fig. 3 and 4 are: (i) Is the P test variability sufficient to warrant the additional costs of high-density soil sampling and analyses and a subsequent site-specific P application? and (ii) Can the P test frequency distribution be estimated without collecting all the soil samples used in our examples (n = 166, 160, or 82)?

If the estimated frequency distributions depicted in Fig. 3 represent the P test populations for their respective fields, then the amount and proportion of each field represented by a specific P test are known. Although this information is insufficient to develop a spatial P recommendation map, the information is sufficient to evaluate the potential for an ideal site-specific P application. Here we have defined ideal site-specific P application as one in which the P application for every area of the field is developed using the P test for that area of the field, and P is applied using the current recommendation model (Kansas State University, 1994). If this ideal P recommendation (Fig. 4) is contrasted to a P recommendation based on the mean soil test P, the difference between these two recommendations provides a measure for the potential improvement provided by the ideal application. The ability to determine this potential depends on the ability to accurately estimate the P test population frequency distribution. To exploit this information prior to high-density soil sampling, we must estimate the frequency distribution with a relatively small sample set.

Deviation from the Ideal Phosphorus Recommendation
Current P fertilizer recommendations are usually determined based on a mean P test. Traditionally, this mean value has been estimated using the mean of several subsamples from within a field or estimated from the test value determined using a composited soil sample.

The mean soil test P for Field A was 19.5 mg kg-1 (Eq. [1]). The corresponding P recommendation would be 25 kg P2O5 ha-1 (Table 3; Kansas State University, 1994). If a producer followed the traditional management approach, applying P uniformly, this rate would be applied to the entire field. By comparison, a P recommendation for Field A based on DT would result in: 1% of the field receiving 66 kg P2O5 ha-1, 15% of the field receiving 49 kg P2O5 ha-1, 26% of the field receiving 36 kg P2O5 ha-1, only 22% of the field receiving the uniform recommendation of 25 kg P2O5 ha-1, 15% of the field receiving 18 kg P2O5 ha-1, and the remaining portions (22%) of the field receiving <12 kg P2O5 ha-1 (Table 3). A uniform P application would provide more or less than the correct P rate to the entire field, except for those areas of the field represented by the mean P test. Comparing the ideal P recommendation to the mean (uniform) P recommendation using Pdev (Eq. [7]) indicated that a uniform P application would deviate from the ideal P recommendation by an average of 11.7 kg P2O5 ha-1. The Pdev represents the potential improvement in using an ideal P application compared with a uniform P application.

By comparison, the mean soil test P for Field B was 41.5 mg kg-1 (Eq. [1]). A corresponding uniform P recommendation (Table 3; Kansas State University, 1994) for this field would result in the entire field receiving 3 kg P2O5 ha-1. Although this amount is probably too small to warrant the cost of any application (probably no fertilizer P would be applied), spatial variability in soil P test might warrant a site-specific P application for this field. Using Eq. [7] to estimate the potential for a site-specific P application resulted in a Pdev of 9.4 kg P2O5 ha-1 (Table 3).

The mean soil P test for Field C was 12.6 mg kg-1, and the corresponding Pdev was 5.1 kg P2O5 ha-1 (Table 3). The potential for a site-specific P application for Field C is less than the potentials for Fields A and B. Because the soil P test values for 50% of Field C are between 11 and 15 mg P kg-1, a uniform P application would deviate less from an ideal P recommendation compared with uniform applications for Fields A and B.

If Pdev were known prior to high-density soil sampling, these fields could be prioritized in order of potential return as a result of site-specific P applications. The Pdev for Fields A, B, and C were 11.7, 9.4, and 5.1 kg P2O5 ha-1, respectively, representing decreasing potential for site-specific P applications and representing the range of Pdev for the fields evaluated in this study (Table 3). However, without high-density soil sampling, a method to assess this potential is currently not available to decision makers.

Frequency Distributions from Simulated Random Sampling
The P test frequency distribution, DT, will not be known prior to high-density soil sampling. Consequently, any estimate of the distribution will have some associated error. The success in estimating this distribution can be evaluated as the probability of obtaining a specific threshold. For example, a specific threshold could be represented as a 90% probability of obtaining a value that is within two units of the population mean. Frequency distributions for soil P test were generated with simulated random sampling. A deviation index (Udev) was calculated for each frequency distribution, Dx, and then the populations of Udev were used to evaluate the probability of success in estimating DT.

Frequency distributions for Udev (n = 5, 20, and 50 only) in increments of two units are depicted in Fig. 5 . Two concepts are illustrated in this graph. First, as the number of samples increased from 5 to 50, the populations' mean and variance decreased. With n = 5, the frequency of observations for any increment never exceeded 10, and the shape of the distribution was flat and very broad. As the number of samples increased to n = 20, the peak frequency of observations reached 20, and the shape of the distribution was taller and narrower. With the largest number of samples, the peak frequency of observations was 34, and the shape of the distribution was taller and much narrower compared with the distribution observed for n = 5. These distributions represent the populations of Udev (Eq. [6]) for 500 simulated random samples. Second, as the sample size increased, the ability to estimate the soil P test population in each field increased in accuracy and precision, an indication that Udev performed well as an indicator for estimating DT from the population of Dx. (The distributions for n = 10 and 30 were omitted to avoid a cluttered figure.)



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  		Fig. 5. Deviation Index (Udev) frequency distributions for simulated random samples from Field A. Distributions shown for n = 5, 20, and 50 only.

 
The probability of success for each sample size can be compared with the same success level for any other sample size. The smaller mean Udev with increasing sample size, as illustrated in Fig. 5, is an indication of greater success at estimating the P test frequency distribution, DT. For the data from Field A, there was a 99% probability of obtaining a Udev <11 with 50 soil samples (Fig. 6) . If this threshold were used as the criterion from which to make other comparisons, only 33 samples would correspond to 90% probability, 23 samples to 80% probability, and 18 samples to 70% probability for obtaining the same threshold of success. Routinely in Kansas, 50 soil samples are used to determine a site-specific P application for a 50-ha field. In this example, a decision maker could collect almost half as many samples with a 80% probability of estimating DT within the accuracy assured for 50 samples and 99% probability.



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  		Fig. 6. Deviation Index (Udev) as a function of sample size. Each line represents the probability with which you would expect to obtain a Udev less than that represented by the line.

 
The numbers of samples required to achieve the same level of success for Field B were slightly greater than those required for Field A, although Udev for the simulated random samples were generally less for Field B (Fig. 6). Using the criterion, 99% probability for 50 samples (Udev = 5.8), sample sizes to achieve the same success level for 90, 80, and 70% probabilities were 39, 31, and 26, respectively. Although Udev (n = 5) values for Field B were generally smaller than results for Field A (n = 5), the improvement with increasing sample size did not increase (decreasing Udev) as rapidly for Field B (Fig. 6).

Results from Field C indicated that sample size to achieve the same success as the 99% probability level, n = 50, was intermediate to the sample sizes required for Fields A and B. As many as 37, 29, and 24 samples were required with 90, 80, and 70% probabilities of achieving similar success as achieved at the 99% probability level (Fig. 6).

The same exercise was completed for the remaining fields with similar outcomes (Table 5).


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  		Table 5. The number of samples required from each field to obtain the same Udev at 90, 80, and 70% probability as obtained at 99% probability.

 
Soil P test variability within a field can be evaluated prior to high-density soil sampling with a reasonable probability of success. Based on the results from this study, a sample size between 18 and 26 would provide a 70% probability of achieving the same success as estimating the soil P test frequency distribution, DT, with 50 samples and a 99% probability of success. To achieve the same success with 80% probability would require between 22 to 31 samples, and achieving success with 90% probability would require between 28 and 39 samples. With an estimated soil P test frequency distribution, Dx, the decision maker could then calculate a Pdev (Eq. [7]) and use this value to prioritize fields that would most likely provide a return to site-specific P applications. Comparing Pdev for Fields A, B, and C indicated that Field A had the greatest potential (Pdev = 11.7 kg P2O5 ha-1), whereas Field C had the smallest Pdev (5.1 kg P2O5 ha-1). These results suggest that Field A has greater opportunity to benefit from a site-specific P application than Field C, which is simply a consequence of the difference between a P recommendation based on the mean soil test P and a P recommendation based on DT.


   SUMMARY
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
REFERENCES
 
A common approach to variable P management is to partition a field into smaller units (sometimes called grids) (Franzen and Peck, 1995). An individual recommendation is usually developed for each unit based on the soil P test in that unit or on an interpolated estimate of the soil P test for each unit. If we assume that a lognormal population distribution best represents the population of soil P test from a field, we can estimate the frequency distribution for the soil P test population when the mean and variance is known. A method was presented here to determine fields that have the greatest potential for improving a uniform P application with a spatially variable P application, with an estimate of the probability of success. This provides producers or decision makers a practical tool, and an estimate of success rate, for estimating the potential for a site-specific P application. Consequently, decision makers can make a decision prior to high-density soil sampling and base that decision on the level of risk with which they are comfortable.

This approach includes estimating the soil P test frequency distribution using estimates of the mean and variance from fewer than 50 samples (50 was considered high density). The probability of successfully estimating the P test frequency distribution will depend on the number of samples, increasing with larger sample sizes. This probability represents the risk a decision maker is willing to accept. Our examples represent fields in south central and northeastern Kansas, and results from other geographic regions may differ from these results. The next step is to calculate the Pdev for each field (Eq. [7]). A greater Pdev corresponds with greater potential for a site-specific P application. A decision to variably apply P would then require the collection of additional samples to completely characterize the spatial variability of soil P test. A decision not to variably apply P would avoid the additional costs of characterizing the spatial variability and the subsequent variable application. Using this approach to determine the potential for a site-specific P application will help decision makers avoid the costs of additional samples for those fields in which a site-specific P recommendation deviates minimally from a uniform recommendation. Producers can distinguish fields with varying potential (Pdev) for a site-specific P application using fewer samples than required for high-density sampling and prioritize those fields for which a site-specific P application is most appropriate.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Kansas Agric. Exp. Stn. Contribution no. 01-238-J.

Received for publication December 4, 2000.


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




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The SCI Journals Agronomy Journal Crop Science
Journal of Natural Resources
and Life Sciences Education		 Vadose Zone Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome