Precision Agriculture

, Volume 10, Issue 4, pp 356–369 | Cite as

A variable-rate decision support tool



Profitable precision or variable application of inputs depends on many factors; however, the inherent variability in a soil and or crop property and the relative responsiveness of yield to fertilizer inputs at different soil concentration levels are the most important factors in influencing economic gain. Generally, the greater is the spatial variation in the property influencing the input rate, the greater is the potential economic return from precision application compared to uniform application of an input. Based on a quantitative assessment of the spatial variation in soil properties that influence rates of input, a variable-rate decision support tool (VRDST) was developed to: (1) assess the potential profitability of variable-rate compared to uniform application and (2) identify the economic optimal uniform application rate if this is selected. The VRDST was evaluated using spatially distributed soil data from selected fields in North Carolina. Net return from variable-rate application and the economically optimal uniform rates are illustrated. Varying fertilizer cost, crop price and sampling costs greatly influenced net return from variable-rate application.


Variable application Decision support Economic return 


Quantifying nutrient requirements by soil analysis depends on careful sampling and analytical methods calibrated for the representative crops and soil in a specific region. Levels of sufficiency are commonly used in soil testing, where a high concentration for a soil property represents 90–100% sufficiency in supplying adequate plant nutrients from the soil. Sufficiency levels decrease as the nutrient concentration declines. Knowing the relationship between soil concentration levels and crop nutrient response is essential for providing accurate nutrient recommendations.

Two common methods of soil sample collection are: (1) composite sampling of whole or parts of fields to provide an ‘average’ soil concentration value or (2) sampling to describe the spatial variation in such values. The value of a soil property from a composite sample represents the average over the sampling unit. Although composite sampling to obtain the field average of a soil property is commonly used, site-specific nutrient management requires the spatial distribution of soil information. The most accurate means of describing the spatial distribution in soil properties is to sample on an intensive grid across a field (Hergert et al. 1997). However, in most cases this approach is too expensive and time consuming. Decreasing grid size increases the number of samples to be collected, and associated sampling and analysis costs, but improves the probability of describing the true variation accurately. Alternatively, soil survey information, yield monitor data and other spatial data can be used to establish management zones within which to target soil sampling. This can reduce costs of obtaining spatially variable soil data (Havlin et al. 2005). The additional costs of acquiring spatial soil information by grid sampling should be potentially recoverable either by using less input or by increasing yield.

Interpretations of soil data have generally assumed that the values are normally distributed (Fig. 1). Most soil data are log normally distributed, where >50% of the soil values are less than the mean (Parkin et al. 1988; Hergert et al. 1997). When this occurs, uniform nutrient recommendation is underestimated because the mean of a composite sample would be greater than the most frequent value. Therefore, the uniform nutrient application rate from a composite sample will generally be less than that determined from spatially distributed values. This becomes economically important when the mode of the soil values is substantially less than the mean (Fig. 1). In this situation underestimation of the soil nutrient content would have a substantial impact on yield resulting in a lower economic return.
Fig. 1

Mean and mode values for the normal and log normal distributions in soil data (Havlin et al. 2005)

Several factors affect the potential economic return from the application of nutrients or lime. These include the variation in soil values across the field, crop yield response at different nutrient levels, fertilizer or lime costs, crop value and the cost of acquiring spatial soil data (Lowenberg-DeBoer and Swinton 1997). Although many factors influence the decision to apply nutrients either uniformly or by variable application, in general the greater is the spatial variation in soil values, the greater is the potential of an economic return from variable application compared to uniform application. Ultimately, it is the relative responsiveness of yield to applied nutrients that determines whether or not the potential economic return to variable-rate fertilizer application is realized. In addition to the potential economic return from variable-rate application, the accuracy of estimating the optimal uniform nutrient application rate is enhanced by using spatial soil information.

The difficulty arises from how to incorporate all these factors to enhance the decision-making process because of interactions between the concentrations of nutrients in the soil and the crop’s response to different levels of added fertilizer. Computer decision aids have the potential to incorporate several factors: crop, prices, yield responses, nutrient sources and producer preferences in a process that provides answers to complicated questions (Larson 2005; Hoffman 1991). Several papers have described the use of these aids to address decisions concerning precision agriculture applications. For example, Attanandana (2007) used a decision aid to assist farmers in selecting the best approach to soil sampling and the use of site-specific technologies for P and K. This aid focused on the costs of soil sampling, but it did not address potential yield responses to sampling strategies. Comis (1999) used a decision aid to help grower’s select optimum fertilizer rates based solely on soil property values. The problem with both of these approaches is that they did not include yield response as a component of the decision process. The purpose of this project was to incorporate the potential yield response to fertilizer or lime into a decision tool to assist growers in assessing the potential profitability of variable-rate compared to uniform application, and if uniform application is preferred to identify the economically optimal uniform application rate.

Materials and methods

General VRDST description

The Variable Rate Decision Support Tool (VRDST) was developed to address variable versus uniform application decisions with phosphorus (P), potassium (K) and lime for corn, soybean, wheat and cotton production. Future versions will include additional crops. The program is based on the relationships between: (1) soil concentration values and recommended P, K or lime rates required for optimal yields, (2) soil test pH, P and K values and percentage sufficiency in crop yield and (3) yield increase from the use of either a uniform or variable-rate fertilizer application based on the difference between percentage sufficiency of the nutrient at the recommended fertilizer rate and that of the nutrient when no fertilizer is applied. Figure 2 illustrates these relationships for P on corn in North Carolina (Hardy et al. 2003).
Fig. 2

Soil P calibration data used for determining relative yield response to applied P. Each line represents a quadratic response to P at a specific soil value (adapted from Hardy et al. 2003)

The general theory behind determining the nutrient status of the soil is whether the values represent a level of sufficiency relative to that needed to obtain the potential maximum yield (Dahnke and Olson 1990). Thus, for a given soil test pH, P or K value if the rate of an applied nutrient is less than that required to achieve the level of sufficiency, the result will be a reduction from maximum potential yield. The best method for determining yield response to applied fertilizer and the amount of fertilizer sufficient for maximum yield has been to use the average yield response obtained from a large number of research trials done under different climate conditions on soil with different nutrient concentrations. The data from these trials were then collated by soil type or series to develop recommendations for that specific soil that cover the entire range of soil pH, P or K values. The equations used to determine fertilizer rates were based on these trials and represent the best estimate of the probability of obtaining a given yield response.

The VRDST uses this approach and these same functions to determine the yield response to added fertilizer. Once the spatial distribution in soil P, K and pH has been measured, the appropriate function to determine relative yield response (sufficiency level) to added nutrients or lime is identified either for the field as a whole or for each cell or zone within the field (Fig. 2). Relative yield response functions for each soil test value were derived from the extensive database covering many locations and years used for determining P, K and lime recommendations in North Carolina (Hardy et al. 2003). These data and resulting recommendations are described in Hardy et al. (2003). These studies describe the quadratic equations that were fitted to the relationship between increasing nutrient rates and the relative yields observed at sites with specific nutrient concentrations. Among the various mathematical functions examined, the quadratic provided the best fit between the nutrient rates and relative yield across all soil test values. The VRDST uses the soil pH, P or K value to calculate the recommended fertilizer or lime rate based on the recommendation equations in Hardy et al. (2003) and then uses the appropriate relative yield function to determine the percentage sufficiency of the nutrient to attain the maximum yield that results from the use of that fertilizer rate.

Once the percentage sufficiency to attain maximum yield has been determined, the VRDST calculates the potential yield response to an applied nutrient or to lime using Eq. 1.
$$ {\text{Yield response to applied nutrient }}\left( {{\text{kg}}\,{\text{ha}}^{ - 1} } \right)\, = \,{\text{YG}}\left( {\% S_{\text{F }} \, - \,\% S_{0} } \right), $$
where YG is the yield goal (kg ha−1), %SF is the % sufficiency to attain maximum yield calculated for a given nutrient rate (kg ha−1) and %S0 is the % sufficiency to attain maximum yield with no nutrient applied (0 kg ha−1).

Once the potential yield response has been determined, net return to input application is calculated based on user supplied nutrient costs, grain prices, and sampling and application costs by taking the gross return (yield response × grain price) minus the nutrient, sampling and application costs. In the case of a variable-rate application the net return is calculated for each grid cell or zone. These net returns from each cell or zone are then summed to determine the net return for the field.

To determine the economically optimal input rate from the spatial distribution of soil values compared to a composite soil test value, net returns are determined using increasing increments of fertilizer or lime rates applied to each grid cell or zone, and subsequently compared to the whole field optimal input rate determined from the composite or field average soil value.

Specific VRDST function

The VRDST was developed using Visual Basic for Applications within Microsoft Excel (Microsoft Corp., Seattle, WA). This approach allows users to input spatial soil data from several sources and provides a simple framework for displaying output to meet user needs.

Recognizing the diversity in soil sampling methods, the VRDST allows the user to assign an area to each soil sample, which will vary depending on whether zone or grid sampling are used. Users can either use geographic information software (GIS), such as ArcGIS (ESRI, Redlands, CA), to determine and assign an area to the sample or, if it is on a uniform grid, they can assign the area (ha) to the soil sample within the model. This allows the user to take advantage of his knowledge of the field and its spatial patterns to provide the most accurate method of assigning an area to a sample.

Once each sample has been assigned to an area, the model separates samples into six categories based on sufficiency levels of the relevant nutrients for a given crop. In North Carolina (NC) these categories are assigned to nutrient indices: very low (0–12), low (13–25), medium (26–37), high (38–50), very high (51–62) and excessive (>62). For pH the categories are: very low (<5.0), low (5.0–5.3), medium (5.4–5.7), high (5.8–6.1), very high (6.1–6.5) and excessive (>6.5). The advantages of these categories are that they reflect the significant range for determining the effect of an input on yield and the range of uncertainty in the assignment of nutrient concentrations to areas of the field. They also simplify the interpretation of fertilizer and yield comparisons.

Applying the VRDST

The program starts automatically once the spreadsheet containing the VRDST has been opened. After a screen describing the VRDST appears, the user identifies the soil data file with soil property values for each sample and the sample area. If the area for each soil sample has not been defined previously, the user can enter the sampling grid size. The user then identifies the column with the required soil property, i.e. P, K or pH, and, if desired, the sample areas. At present, only one soil property can be analyzed at a time, but as growers often apply only one nutrient at a time variably this is not a problem. The model is designed to assist in determining which nutrient should be applied variably.

The key inputs for model operation are: (1) soil type (mineral, mineral-organic or organic), (2) soil property (P, K or pH), (3) crop, (4) crop value, (5) expected crop yield, (6) fertilizer analysis, (7) fertilizer cost, (8) soil sampling cost and (9) cost of both uniform and variable-rate application (Fig. 3). Soil type, soil property, crop and expected yield are used to identify the set of equations that the model uses to determine yield response to different rates of input and ultimately the expected yield gain from added fertilizer or lime. Crop value, fertilizer analysis, fertilizer cost, soil sampling cost and cost of uniform and variable-rate applications are used to calculate the cost of soil sampling and applied inputs for both uniform and variable rate strategies, and the economic return from the yield gained under both strategies.
Fig. 3

Input screen showing data entered by the user and options for comparing variable to uniform application, or to determine the optimal uniform rate

Once the input information has been entered, the user has two options. The first is to calculate and view the partial economic returns between uniform and variable application. This option produces a display screen where the output field is divided into the six nutrient or pH categories described earlier. It gives the area in each category, the amount of fertilizer or lime to be applied, the expected yield, and the differences in input and yield between uniform or variable application. The economic returns from the expected yield increase, the costs for fertilizer application and soil sampling, and finally the gain (or loss) from both approaches are also given, together with the economic differences between the two fertilizer application strategies.

The second option allows the user to determine the economically optimal uniform application rate. This recognizes that given the changes in crop and fertilizer price, the maximum rate of fertilizer indicated by the soil database might not be the most cost effective rate. Given the capability of the model to determine yield response to added fertilizer this option uses an optimizing function to determine the economically optimal rate of fertilizer to apply. This option provides a graph of the level of economic return from each increase in fertilizer applied and an inset showing the economically optimal rate.

The output from the model can be printed according to the users’ requirements and made available to the grower, the consultant or the fertilizer supplier. The procedures described above can be applied sequentially to different nutrients, crops and application scenarios. The model is being developed to enable variable-rate applications of two nutrients applied as a blended fertilizer to be determined and to allow users to use their own site-specific yield response functions.

Results and discussion

Demonstration of the VRDST: case studies

To demonstrate the utility of the VRDST in identifying the effect of spatial variation in soil on economic return and the robustness of the decision aid across different locations, two fields were selected with different patterns of spatial variation. The first field is in Duplin Co. (34.7186°N, −77.7897°W). The main soil series are Croatan Muck (Terric Haplosaprists), Muckalee Loam (Terric Haplolsaprists) and Leon Sand (Aeric Alaquods). This field is typical of eastern NC where changes in nutrient content are often associated with changes from organic to mineral soil. This 30 ha field was in a corn-wheat-soybean rotation. Soil samples were collected on a 0.4-ha grid in spring 2004 and analyzed by the North Carolina Department of Agriculture & Consumer Services (NCDA & CS) laboratory. Nutrient concentrations in NC are reported using an index system that allows the solution concentration to be adjusted for different soil types. The P indices range from 7 to 64 (mean = 29; mode = 28), and K indices range from 30 to 107 (mean = 56; mode = 55) (Fig. 4). Yield potential at this site is high with an average corn yield of 9.35 t ha−1, soybean yield of 3.23 t ha−1 and wheat yield of 3.62 t ha−1.
Fig. 4

Soil P and K values at two sites in North Carolina shown according to the index categories representing very low, low, medium, high, very high and excessive concentrations

The second field is in Rowan Co. (35.679883°N, −80.400075°W). The main soil series are Hiwassee clay loam (Typic Kanhapludults) and Enon fine sandy loam (Ultic Hapludalfs). This field is typical of the Piedmont region where nutrient concentrations are often associated with topography and eroded sites within the field. This 18 ha field was in a corn-wheat-soybean-soybean rotation. Soil samples were collected on a 0.4-ha grid and analyzed by NCDA & CS. Phosphorus indices range from 10 to 64, but are highly skewed (mean = 23; mode = 18) (Fig. 4). Potassium indices range from 28 to 100, but are more normally distributed (mean = 63; mode = 66). Soil pH is between 5.9 and 7.5 (mean = 6.6; mode = 6.4). Due to the eroded nature of this site, yield potential is lower with average corn, soybean and wheat yields of 6.90, 2.82, and 3.09 t ha−1, respectively.

At both sites nutrient application strategies indicated by VRDST were assessed by two sensitivity analyses. The first examined the impact of changes in crop value and fertilizer price on the difference in partial profit between variable-rate and uniform application. This analysis highlighted the conditions where growers might consider using a variable-rate strategy to address the spatial variation in nutrient concentrations in a field. The second sensitivity analysis examined the impact on changes in crop value, expected yield and fertilizer price on the economically optimal rate of fertilizer to apply. The aim of this analysis was to determine the effect of these factors on fertilizer rates.

A comparison of variable and uniform rate strategies

Figure 5 illustrates the VRDST output for the Duplin Co. farm with corn at $196 t−1, diammonium phosphate (18-46-0) at $990 t−1, a yield goal of 9.35 t ha−1, and soil sampling and application costs of $29.64 ha−1. The uniform application rate based on the field average soil values is 43.8 kg P2O5 ha−1, which would increase yield by 46.8 t for the field or by 1.29 t ha−1. Variable P application (VRT) resulting in an average application rate of 50.5 kg P2O5 ha−1 would increase total yield by 1.59 t ha−1. The results indicate a partial return of $19.56 ha−1 for VRT compared to uniform P application.
Fig. 5

Example output screen capture that compares the economic advantage between variable and uniform application of P at the Duplin Co. site

The VRDST also calculates the economically optimal uniform P rate determined from the spatial distribution of soil P, where it is similar to that in Fig. 6. In this case the optimal uniform P rate is about 49 kg P2O5 ha−1, whereas the uniform P rate based on a composite field average soil value is 44 kg P2O5 ha−1.
Fig. 6

Effect of increasing P rate on marginal return for the Duplin Co. site

The sensitivity analysis shows that the economic advantage of VRT decreases by $0.82 ha−1 for each increase of $110 t−1 in fertilizer (Fig. 7). More total fertilizer was used in the VRT application resulting in a decline in the economic advantage of VRT. The economic difference between VRT and uniform application seems relatively insensitive to fertilizer price compared to the sensitivity of economic return from VRT to corn price. For each $39.3 t−1 increase in corn price the economic difference between VRT and uniform application increases by $11.78 ha−1. The impact of crop price on net return between VRT and uniform application emphasizes the value of VRT in the yield response obtained by optimizing fertilizer distribution. Since each $ ha−1 spent on soil sampling reduces the advantage of VRT by a similar amount, this cost becomes less significant as crop prices increase. The sensitivity analysis shows that with this spatial distribution in soil P and high yield potential, the primary factor in determining the advantage of VRT is the crop price. The higher the crop price the more likely a grower will benefit from VRT.
Fig. 7

Sensitivity analysis of the economic return from variable-rate P and K applications and corn prices at the Duplin Co. site

The analysis at the Rowan Co. site, using similar inputs and a yield goal of 6.90 t ha−1, shows that the uniform application rate (based on average soil values) is 88.3 kg P2O5 ha−1 which would increase yield by 66.3 t for the field or by 3.68 t ha−1 (Fig. 8). By comparison, VRT results in an application rate of 94.4 kg P2O5 ha−1 to increase yield by 69.9 t or 3.88 t ha−1. This yield increase covers the increased cost of fertilizer and soil sampling resulting in a small economic gain from the use of VRT of $0.40 ha−1. The sensitivity analysis shows that the skewed distribution of P in this field increases the sensitivity of the economic return of VRT to increases in fertilizer cost with the economic gain from VRT decreasing by $1.46 ha−1 for each $110 t−1 increase in fertilizer cost. By comparison, the sensitivity of economic return of VRT to increases in corn price is less than that at the Duplin Co. site increasing by $7.68 ha−1 for each $39.3 t−1 increase.
Fig. 8

Sensitivity analysis of the economic return from variable-rate P and K applications and corn prices at the Rowan Co. site

Differences in the spatial distribution of soil values between sites influenced both the effects of fertilizer and crop prices on the economic return from VRT. Differences in yield goals also influenced economic return from VRT. A 0.63 t ha−1 increase in yield goal increased economic return from VRT by $3.48 ha−1.

Analysis of marginal returns from uniform or VRT applications of K also emphasize the importance of the spatial distribution in soil K (Fig. 5) and crop yield response in determining whether or not to use VRT. By comparing methods of K application most of the prices and yield levels remained the same as in the previous analysis for P except that 0-0-60 ($880 t−1) was used. Using a field average value of soil K resulted in a uniform rate of 34.7 kg K2O ha−1 which would increase yield by 1.15 t ha−1. By comparison, VRA would result in an average 39.1 kg K2O ha−1 which would increase yield by 1.32 t ha−1. The analysis shows that the economic advantage of VRA decreases by $0.84 ha−1 as fertilizer price increases by $110 t−1 and that the economic advantage decreases by $6.92 ha−1 as corn price decreases by $39.3 t−1 (Fig. 7). As in the previous analysis economic return decreases as fertilizer price increases because more fertilizer was recommended when using a variable-rate application.

At the Rowan County site (Fig. 8) the average soil K value results in a uniform application of 19.6 kg K2O ha−1 which would increase yield by 0.51 t ha−1, whereas VRT results in an average 34.8 kg K2O ha−1 and a yield increase of 0.95 t ha−1. With this spatial distribution of K the economic advantage from VRT decreases by $2.82 ha−1 as fertilizer price increases by $110 t−1 and the economic advantage decreases by $17.98 ha−1 as corn price decreases by $39.3 t−1. The variation in K at this site resulted in large differences in K applied and potential yield between uniform and VRT, which magnified the impact of fertilizer or crop prices on the economic differences between these two application strategies.

A comparison of economically optimal application rates

The VRDST enabled us to examine the impact of corn and fertilizer prices on optimal uniform application rates. At the Duplin Co. site the recommended P rate based on the average soil P was 43.8 kg P2O5 ha−1. However, the VRDST shows that at $196 t−1 for corn the economically optimal rate increases exponentially from 49 to 82 kg P2O5 ha−1 as fertilizer price decreases from $990 to $220 t−1 (Fig. 9). Reducing corn prices by $39.3 t−1 decreases the economically optimal application rate by 5.6–6.7 kg ha−1. At Rowan Co. the recommended P application rate based on an average soil P value was 88.3 kg ha−1. With a price of $196 t−1 corn, the economically optimal rate of P increased from 91 to 114 kg ha−1 as fertilizer price decreased from $990 to $220 t−1 (data not shown). A decrease in corn price of $39.3 t−1 reduced the economically optimal fertilizer rate from 4.5 to 9 kg ha−1.
Fig. 9

Sensitivity analysis of the economically optimal uniform fertilizer rate to the prices of fertilizer and corn at the Duplin Co. site

The results are similar for K (Fig. 9). At the Duplin Co. site the recommended fertilizer application rate is 35 kg K2O ha−1. At $196 t−1 for corn, the economically optimal rate of K increases from 44 to 59 kg K2O ha−1 as fertilizer K decrease from $880 to $220 t−1. Economically optimal rates of K decrease by only 2.8–3.9 kg K2O ha−1 as corn prices decline by $39.3 t−1. At the Rowan Co. site the recommended uniform rate was 19.6 kg K2O ha−1. However, at $196 t−1 corn, the economically optimal rate increased from 38 to 60 kg K2O ha−1 as K prices declined from $990 to $220 t−1 (data not shown). Economically optimal fertilizer rates declined by only 2.2–7.3 kg ha−1 when corn prices were reduced by $39.3 t−1.

These sensitivity analyses show that the key factors influencing the choice of uniform application are the prices of fertilizer and corn. The soil values have little impact on the economically optimal fertilizer rate.


Sensitivity analysis of the VRDST using two fields and two nutrients demonstrates the importance of economics in selecting fertilizer application strategies. For the decision between uniform or variable application, crop price largely determined which strategy to choose. When the spatial distribution of a soil property favored potential yield increases by increasing the application rate in areas with small values of the property, the VRDST showed that the economic advantage of variable-rate changed quickly based on crop price and to a lesser extent fertilizer price. When spatial distribution of the soil property resulted in less response for potential yield, the economic advantage of using variable-rate application was generally lower and less sensitive to changes in price.

The ability to quantify potential yield gain from variable–rate application based on the spatial distribution in soil values is essential for identifying the best management option. The VRDST shows that the main advantage of variable-rate is the improvement in yield through the proper distribution of fertilizer. In this study we used the entire soil sampling data set to determine the average soil nutrient content in the field. By doing this we assumed that we had perfect knowledge of the field nutrient level. Therefore, the mode will always be less than the mean resulting in a recommendation of more fertilizer for the variable-rate application making it mathematically impossible to explore a situation where VRT resulted in less fertilizer applied compared to uniform application. In practice growers would have less information on the true nutrient status of a field because of much sparser sampling. Therefore, it is possible to apply less fertilizer using VRT compared to uniform application. Even in situations where VRT resulted in less fertilizer applied, the yield gain from matching fertilizer application to the soil value at individual sites would still be key to deciding which application management strategy to use.

Comparisons between the two field sites with their differences in realistic yield levels showed that potential yield gains were less important when determining the optimal uniform rate. There was little difference between the two sites in how fertilizer rates responded to changes in fertilizer or crop prices. Instead, it is the price of fertilizer and to a lesser extent the crop price that determines the optimal uniform rate. When fertilizer prices are low the VRDST shows that choice of the economically optimal rate is sensitive to small price changes. Conversely, when fertilizer prices are high the optimal uniform rate becomes less sensitive to price changes and will eventually reach a point where the fertilizer price is too high relative to the crop price resulting in a recommendation of a zero fertilizer rate.

This study shows that the VRDST can successfully integrate crop response, fertilizer requirement and economics into the decision as to which fertilizer management strategy to use and ultimately help to determine economically optimal uniform rates.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Soil ScienceNorth Carolina State UniversityRaleighUSA
  2. 2.Department of Crop ScienceNorth Carolina State UniversityPlymouthUSA

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