An Exercise In Precision Agriculture
Module
1, Part 2
Area Determination
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An Exercise In Precision Agriculture Module
1, Part 2 |
The global positioning system (GPS) has been adopted by many U.S. grain producers as a method for referencing geographic and agronomic data in a geographic information system (GIS) database. GPS fixes take the format of latitude, longitude and elevation using a WGS84 datum. A datum is a reference for physical parameters such as the shape of the earth. To utilize the GPS data the coordinates must be projected to a flat plane. Map projections and the associated mathematics were discussed in Module 1 and are detailed in the book Map Projections—A Working Manual, authored by the U.S. Geological Survey as Professional Paper 1395. Once the projected coordinates are obtained, points, lines and polygons can be quantified. These geometric entities form the basis of a GIS database. A more descriptive definition for GIS is that it is a relational database where properties are assigned to point, line and polygon entities in space. The objective of this exercise is for the student to understand and manipulate GPS point data to define a polygon, and then by using the projected data in State Plane Coordinate system from various fields around Indiana, Kentucky and Ohio, to determine the projected area of the polygon.
Area Determination
As one might suspect, calculus can be used to estimate the area of the enclosed polygon defined by the set of GPS coordinates. Simply stated, the area of any real region is defined as,
(1)
Using Green’s Theorem, the area of smooth simple closed curve C is defined as,
(2)
Similarly we can right,
(3)
Combining both relationships the area is determined to be,
(4)
The line integral can be evaluated using the following discrete approximation,
(5)
Procedures
Field boundary traverses of fields from Indiana, Kentucky and Ohio will be used to calculate the projected area of these fields. A downloadable Microsoft Excel file is provided containing the necessary data to complete this assignment. The Area.xls contains boundary coordinate data already converted into state plane coordinates. This data will then be used to calculate the area in acres for each particular field. The first step involves downloading a self-extracting Microsoft Excel file. Once downloaded and extracted, follow the exercise steps to determine the area of each field.
1) Downloading the Excel File
To download the file, click on the button at the bottom of this page. When downloading the "AREA.xls " file, the following message box will appear:
make sure the 'Save this program to disk' dialogue box is checked and press the 'OK' button. Next, another message box will prompt you to select the directory to download this application file into:
Find the appropriate directory or create a new directory to download the applications file into and then click 'SAVE.' Once completing this step, use your "Windows Explorer" to navigate to this application file. After locating it, double click on the file icon to run the application. The application will extract the necessary Excel file named 'AREA.xls' which can now be used for this assignment. It is suggested to save this file under a new name in case something wrong would occur.
2) Exercise Steps
The AREA.xls file contains several sheets. The boundary data is contained on the second sheet labeled Raw Data - WGS84. It was obtained using an ATV with a DGPS receiver and laptop computer. The boundary of the field was traced by a rider operating the ATV with DGPS fixes recorded every 1 second. Note that the first and last records contain the same point in order to close the polygon representing the field boundary. Start this exercise by performing the following steps.
