An Exercise In Precision Agriculture

Module 5, Exercise 1
State Plane Coordinate Conversion


        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 onto a flat plane or 2 dimensional view. In Kentucky and Ohio, a Lambert Conformal Conic projection is used as the basis of the State Plane Coordinate systems whereas Indiana uses the Transverse Mercator projection.. The nature of this projection and the associated mathematics are detailed in 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 Module is to understand and convert GPS point data from WGS 84 and project the data into a State Plane coordinate system for several fields located in Indiana, Kentucky and Ohio.

Map Projections

    Map projections are viewed as a mathematical operation in which latitude and longitude are transformed into Cartesian coordinates (x,y).  Map projections allows longitude and latitude coordinates to be projected from a 3-dimensional position on the earth's surface to a a plane or 2-dimensional surface (paper).  Several projections and coordinates systems exist that are defined differently, with each preserving shape, area, distance, and direction differently.  The State Plane Coordinate System (SPCS) is a widely used coordinate system, not a map projection, within the United States.  The conversion is necessary  to perform dimensional analysis such as area calculations.  The conversion allows GPS data to be projected onto a 2-dimensional plane (paper) and permits dimensional analysis such as area and length calculations.  GPS or WGS84 data is unable to provide correct dimensional calculations due to the nature of the data in degrees longitude and latitude.

    Before discussing SPSC, it is appropriate to talk briefly about datums and their function.  While map projections systematically transform a position on the globe onto a plane, a datum functions as a reference system to describe the shape and size of the earth.   A datum is a smoothed mathematical surface of the earth's mean, sea- level surface.  The earth is not a sphere but an oblate ellipsoid of revolution, also called an oblate spheroid.  The geoid defines the shape of the earth if all measurements were measured at sea-level.  A datum is necessary for the GPS system to model the earth's surface and calculate the position of GPS satellites and ultimately determine ones position on earth using GPS.  Horizontal datums consist of latitude and longitude of a point, azimuth of a line from that point, and two radii to describe the shape of the oblated sphere which best represents the earth.  Three datums exist which are frequently associated with GPS use: North American Datum of 1927 or know as NAD 27, NAD 83, and World Geodetic System of 1984 or WGS84WGS84 is the one most associated with the use of GPS data and was developed by the US Military in 1984 (basis of GPS receivers calculations).  NAD 27 is based on the Clarke Spheroid of 1866 while  NAD 83 is based on the GRS 80 derived ellipsoid.  The radii used of the Clarke and GRS80 spheroids are presented in Table 1.  An important note is that NAD 27 coordinates are in feet while NAD 83 is based on meters.

    The SPCS was devised by the US Coast and Geodetic Survey in 1933 to establish a common coordinate system across the US.  It provides a greater degree of accuracy for area and distance calculations than other projections and coordinates systems.  Many Agricultural GIS and mapping packages use this coordinate system and will be the emphasis of this exercise.  However, the SPCS varies from state to state by dividing each into zones depending on whether the state is oriented more North-South or East-West.  The orientation dictates the map projection, Lambert Conformal Conic or Transverse Mercator, applied to the state.  Lambert Conformal Conic Projection is the most widely used projection and is the basis of state plane coordinate system for states with a greater East-West than North-South distances.  The Transverse Mercator Projection is an ordinary Mercator projection turned through a 90o angle to coincide with the central meridian. This projection is used for state plane coordinate systems in states with greater North/South than East-West directions.  Table 2 presents the projection used along with the number of zones for each state.  Table 3 provides the necessary State Plane parameters and origins for each zone in Indiana, Kentucky and Ohio based on the 1927 North American Datum (NAD 27).  These parameters are necessary to transform from WGS84 into the SPCS.

    As mentioned, GPS point data is provided in WGS84.  Two sets of equations exist that transform this data into the SPCS since both the Lambert Conformal Conic and Transverse Mercator projections are used depending upon the state orientation.  The  intent of this assignment is to not fully explain all the equations but to understand that they exist and how they can be used to transform WGS84 positions into the SPCS.   Table 4 provides the various equations necessary for the transformation.  Notice that several equations exist for each of the Lambert Conformal Conic and Transverse Mercator projections.   By knowing the standard parallels, origin, ellipsoid parameters and point to be transformed, one can simply plug these initial variables into the equations to calculate x and y coordinates in the SPCS.  It should be noted that longitude and latitude must be degrees and not in degree/minute/second.  If the latter exists, a conversion must be performed to convert from minute and seconds to degrees (1 degree = 60 minutes; 1 minute = 60 seconds).

Procedures

    Field boundary traverses of crop fields from Indiana, Kentucky and Ohio field will be used to transform from WGS84 to State Plane Coordinates.   A downloadable Microsoft Excel file is provided containing the necessary data and conversion equations to complete this assignment.  The St_plane.xls contains the WGS84 DGPS boundary points along with a table containing text and equations for projecting the DGPS points into the appropriate State Plane Coordinate System zone.  Start by downloading the Excel file containing the DGPS data for several fields from the three states.  Once the Excel file has been extracted fill in the provided tables to convert the DGPS data into State Plane coordinates.

1) Downloading the Excel File

To download the file, click on the button at the bottom of this page.  When downloading the "St_plane.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 (State Plane Conversion.exe).  After locating it, double click on the file icon to run the application.  The application will extract the necessary Excel file named 'St_plane.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 St_plane.xls file contains the equations and data required to complete this assignment.  The first two sheets contain the parameters for each of the projections.  The Raw Data WGS84 is provided on the next six sheets and labeled according to state and particular zone.  There are two boundaries from each state with each boundary being obtained from a different zone.  For example, KYN represents data collected from the Kentucky North State Plane zone.  The remaining sheets provide prefabricated tables for each boundary from a particular zone to calculate the State Plane Coordinates for each field boundary.  Equations will be entered on these pages to calculate the x and y coordinates.  

Below are several steps outlining what is needed to complete this assignment.  Before starting, look over the first two sheets labeled 'Lambert Conformal Relationships' and 'Transverse Mercator'.  These two pages contain the necessary variables and their equations for each of the projections.  Equations can be viewed by clicking on a variable's particular cell.  The raw WGS84 data is contained on separate sheets and in degrees longitude and latitude.  The page following each of these data sheets is provided to perform the transformation into the SPCS.  Several variables must be calculated for each data point before using the x and y equations for the projections to determine the new location in meters.  Each table has been labeled with the required variables to calculate.  Equations from Table 4 must be entered to calculate these variables and the new coordinates.  Some equations have been entered for the first point due to their complexity and time to type in.  These must be copied and pasted for the rest of the points.  

  1. Plot the latitude and longitude coordinate pairs in Microsoft Excel using the Chart Wizard to confirm that indeed an enclosed polygon exists (remember that longitude and latitude are in degrees).
  2. On the appropriate labeled sheets ( i.e. KYN SPCS for Kentucky North), transform the WGS84-GPS coordinates to the correct State Plane Coordinate System using the proper projection and the NAD27 datum.  Equations are provided on the first sheet labeled Projection Relationships.  Table headings have already been provided to help keep data organized.
  3. Convert the calculated  Easting and Northing coordinates from meters to feet (1 meter = 3.281 feet).
  4. Again, plot the coordinate pairs in Microsoft Excel to confirm that a polygon exists.
  5. Print out a hardcopy of the original boundary and the newly projected boundary in SPCS for comparison and contrast.

Questions and Answers

  1. Compare and contrast the shape of both polygons constructed from the WGS84-GPS and NAD27-Kentucky North State Plane coordinate pairs. Why are these shapes similar or different in appearance, and which set of coordinates will yield an estimate of the area of the field.

   Click on the file name to download the self extracting executable file:  St_plane.xls
(Feb 4, 2000 - All the boundary data has not been collected, only a KY north field is provided)

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