BAE 599
Topics in Agricultural Engineering: Precision Agriculture

Spring Semester 2007

 Educational Module 9 Exercise: Variable-Rate Fertilizer Recommendations


The Cooperative Extension Service does not currently publish variable-rate lime and fertilizer recommendations for Kentucky.  However, variable-rate lime and fertilizer application services are being provided to many Kentucky producers.  If we assume that ARG-1 2002-2003 Lime and Fertilizer Recommendations are appropriate (the best available information) to guide producers in the development of variable-rate prescriptions, how should these recommendations be implemented in a GIS environment?  In simple terms, how can we generate equations that continuously map soil test values to application rates?

The basis of the AGR-1 recommendations are described at the beginning of the publication as follows:

"Additions of a nutrient as a fertilizer are recommended based on a soil test result only when a crop yield or economic response has been measured for that crop under Kentucky soil-climatic conditions.

Many field studies have been conducted by the Kentucky Agricultural Experiment Station under Kentucky farm conditions to determine the extent of any need for nutrients (primary, secondary, and micro). Yield and soil test data from these studies serve as guidelines in establishing recommendations in this publication.

Recommendations contained in this publication are based on soil test values obtained from testing methods used in laboratories operated as part of the Kentucky Agricultural Experiment Station. Recommendations for phosphate, potash, and zinc are based upon extraction by Mehlich III extract. Buffer pH is determined by a modification of the SMP (Shoemaker, McLean, and Pratt) method. The Mehlich III and SMP methods are described in Bulletin 190, Procedures Used by State Soil Testing Laboratories in the Southern Region of the United States, Southern Cooperative Series, November 1984. A detailed description of the soil test procedures used in the UK Soils Testing Laboratory will be published in the UK Agronomy Department's Agronomy Notes during 2000.

The recommendations should not be used for soil test results obtained by other testing methods. Recommended rates are based on assumed average climatic and management conditions and average yields. Rates should be adjusted upward or downward to reflect anticipated deviations from these average conditions.

The rates recommended are for production of the crop to be grown each year and will not increase soil test values for P and K rapidly. Using these recommended rates would likely take four years or longer of annual fertilization to result in an appreciably higher test level for P and K."

            The objective of this exercise is to use data from AGR-1 and software applications such as Excel and MatLab to generate a set of equations that map soil fertility test results to application rates for soil amendments.  Specifically, you are to develop a set of equations capable of generating application prescriptions for phosphate and potash fertilizers along with a prescription for the application of agricultural lime. Further in this exercise we will extend these relationships to an actual field situation, specifically Field 41 at the Worth and Dee Ellis Farm in Shelby County, Kentucky.  For comparison purposes you will be required to generate a shape file for use in variable-rate application.  This file should contain fields that specify application rates for agricultural lime (lb/ac).  The fertility management polygon has been developed (1-acre grid) and can be downloaded below.  This will form the basis for the development of the application shape file.  In addition to generating the variable-rate application shape file you should do a comparison of variable-rate versus "field-average" management using AGR-1 recommendations.  The comparison should include specification of the total quantities of lime and fertilizer to be applied under either approach.  

Project Requirements

  1. Visit the web site to view ARG-1 2004-2005 Lime and Fertilizer Recommendations publication. A copy will provided for completing this assignment.
  2. Using Excel, and the "regression" command, generate a "response surface" that describes desired lime application rates as a function of both soil water pH and buffer pH.  Assume the target pH to be 6.4.  The use of regression Excel will be demonstrated in class.
  3. Generate a plot of your response surface to confirm that your function is continuous over the range of values of soil water pH and buffer pH within AGR-1.
  4. The necessary data for this exercise is to be found in the Microsoft Excel spreadsheet that may be downloaded using the hot button below.  Other data needed are corn price ($3.10/bushel), VRA fertilizer application costs of $8.50 per acre and the corn yield response function: Yield = 24 + 4.1 K – 0.018 TK –0.0055 K2 where K = potash applied and T=Test value of potassium.  Note that MPP = 4.1 -0.018 T –0.011 K.  Develop a complete worksheet incorporating the appropriate formulas for relevant calculations and answer the questions below.  
  5. Please submit a hardcopy of your recommendation functions for phosphorus, potash and agricultural lime.  Along with hardcopies of the plots provide complete listings of equations along with a definition of the variables.  Also, provide answers to the following questions.
  6. Download and expand the shape files for Field 41 as demonstrated in class.  Using these shape files generate a project in ArcView named Field 41.
  7. Open ArcGIS and bring the shape file into the Field 41 project.  You should be able to view the table and see the recommended application rates.  Using the new file generate and print application maps for agricultural lime.  Be certain to change the key to reflect varying levels of application.
  8. Using the Excel version of the edited ".dbf" file determine the total quantities of agricultural lime to be applied in Field 41 under both field-average and variable-rate management approaches.  Please note that one field contains the area of each polygon.
  9. For this project you will be require to submit hard-copies of the application rate maps, and your answers to the questions below.  Also, e-mail the instructor a copy of the Excel spreadsheet used to determine the application rates and total quantities of lime to be applied using the variable-rate application approach.


  1. How applicable are your lime fertilizer recommendations for variable-rate application in Kentucky?
  2. How might you modify these recommendations based on you knowledge soil fertility management?
  3. How should we conduct field experiments to assess the profitability of you variable-rate recommendations?
  4. How does the total quantity of applied agricultural lime differ between the variable-rate versus field-average management approaches?
  5. Is it appropriate to use a one-acre sampling grid for specification of variable-rate application prescriptions?
  6. If you were to redefine the fertility management grid, what changes would you make?

Additional Information

            The soil sample results from Field 41 at Worth and Dee Ellis Farms in Shelby County, Kentucky are zipped and included below.  This data was obtained by grid sampling the field and submitting the samples to Regulatory Services at the University of Kentucky.  Mehlich III extraction methods were used to arrive at the soil test values for P and K.  Assume this year’s crop will be corn, and the preceding crop was wheat followed by double-cropped soybeans.  The management grid is composed of 1.0-acre cells.  Assume that each sample corresponds to a single complete cell.  Agricultural lime will be used to adjust the soil pH.  Agricultural lime is valued at $13.00 per ton.  Please show all work used to arrive at the total cost of inputs under either scenario.  Save your fertility recommendations in shape file format so that we can use them later in ArcGIS to generate profit maps.

Click on the file name to download the self-extracting executable file:

Excel File - Ag Lime

Field 41 Fertility Regions - Shape File

Field 41 Aerial Photo - DOQQ

State Roads - Tiger File

Excel Solution