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Case Study: Precision Agriculture


A working draft of resources and reports from an NSF-sponsored project intended to strengthen the role of mathematics in Advanced Technological Education (ATE) programs. Intended as a resource for ATE faculty and members of the mathematical community. Comments are welcome by e-mail to the project directors: Susan L. Forman or Lynn A. Steen.


Computer tools such as spreadsheets and technology such as Global Positioning Systems (GPS) have begun to transform agriculture to a precision, high-performance industry where data are used to minimize costs and optimize yields. Farmers use tractor-mounted GPS receivers to record location both when they take soil chemistry readings and when they apply fertilizer and herbicides. In precision agriculture, these GPS data are then combined with other data such as pH, moisture content, weed density, and crop yield in a computer spreadsheet or a Geographic Information System (GIS). Careful use of such data, combined with comparison information from other farms and earlier years, enables farmers to minimize waste and optimize yield. The investment required of farmers for GPS receivers and associated computer equipment is about $20,000 which is cost effective for farmers who use it for 1000 acres or more.

Examples of Use

Data gathered from a tractor-mounted GPS system can be used to create a map of a farm (in either vector or raster form) that is linked by means of a GIS program to a database containing spatial or thematic information. This information can then be used to create thematic maps for soil type, pH, potash, organic matter, weeds, and yield.

Using data on yield gathered either from previous years or from databanks of information on similar farms, the GIS system can be used to prepare "prescription maps" of fields that indicate how much fertilizer, herbicide, and water is needed in each small patch of land. Additional soil analysis combined with market information about predicted crop prices can help farmers make wise decisions about crop rotation and planting schedules. Regular use of such systems can optimize crop yield and minimize costs, thus increasing the chance of profit for the farm.

Supporting Mathematics

To use GPS information most effectively, farmers must combine this satellite information with data collected on the ground, and then convert these coordinated data into topical (or thematic) maps that display the variation of yield, moisture, soil pH, and other relevant factors. This task--to convert discrete data into continuous maps--is the opposite of what is normally taught in mathematics courses. Instead of calculating data points from formulas, GPS provides the data points and farmers determine the graphs that most accurately represent the data. This technique, called "surface analysis," involves construction of topographic maps from isolated data points. Depending on the goal (crop yield, moisture conservation), there are many possible algorithms that can be used for this process.

Because farmers need GPS data that are more accurate than the normal range of 50-100 meters provided by standard receivers, they rely on supplementary data from ground-based stations that transmit estimates of the current error from satellite signals in that region. By combining this information with that of the GPS satellites--using the error as a new unknown and adding data from a fourth satellite--the tractor-based GPS receivers can calculate position to within approximatley 8-10 meters.

Sophisticated use of GPS and GIS data also requires some information, however tentative, on market conditions for various possible crops. With these data, optimization tools such as linear programming can be used to help decide how much of which crop to plant on which field in order to maximize the likelihood of profit.

Projects and People

The ATE-supported Precision Agriculture Education Network (PrAEN) centered at Hawkeye Community College in Iowa is developing a school curriculum to support this new quantitatively-oriented approach to agriculture. Most of this curriculum is mathematical: These quantitative themes support applications in agriculture, horticulture, natural resources, and animal science.

Programs and People:

Precision Agriculture and Food Technology (Iowa). Contact Information: Project e-mail; Project Director: Terry Brase.

Precision Farming National Project (Georgia)

Precision Agriculture Education Network (PrAEN)

AgInnovator OnLine News.

Trimble Precision Agriculture


The Precision Farming Primer by Joe Berry.

Feder, Barnaby F. "From Amber Waves of Data." New York Times, (May 4, 1998) C1,C4.

Committee on Assessing Crop Yield. Precision Agriculture in the 21st Century : Geospatial and Information Technologies in Crop Management. Washington, DC: National Academy Press, 1998.


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Supported by the Advanced Technological Educaiton (ATE) program at the National Science Foundation. Opinions and information on this site are those of the authors and do not represent the views of either the ATE program or the National Science Foundation.

Copyright © 1999.   Last Updated: October 12, 1999.   Comments to: Susan L. Forman or Lynn A. Steen.