Project 1: Plotting Coordinates and Projections

[Pages:6]Project 1: Plotting Coordinates and Projections

Diana Jo Lau

____________________________________________________________________________________

Project 1: Plotting Coordinates and Projections

Diana Jo Lau

Figure 1 Map of the United States (highlighted) (PennState Online Geospatial Education Program)

Figure 2 Map of Florida in (highlighted) (PennState Online Geospatial Education Program)

Project 1: Plotting Coordinates and Projections

Diana Jo Lau

____________________________________________________________________________________

To represent my hometown near Three Lakes, FL, I utilized the Interactive Album of Map Projections in . The Transverse Mercator projection was used to generate the maps in Figure 1 and 2.

Map projection classification:

Class: Cylindrical Point of Secancy: Tangent Aspect: Transverse Distortion Property: Conformal (Snyder, 1987)

Figure 1 shows the map of the United States highlighted. the limits in decimal degrees are the following: 50.0 North, 25.0 South, -125.0 West, and -60.0 East. The map shows distorted ellipses different along latitude 30.0 North. Ellipses appear uniform along the approximate latitudes of 45.0 North and 15.0 North.

Figure 2 shows a zoom-in of the state of my hometown in Three Lakes, FL. the limits in decimal degrees are the following: 31.5 North, 24.0 South, -88.0 West, and -78 East. The map shows distortion patterns to be similar at approximate latitudes of 25.0 North and 30.0 North.

The distortion property both maps is conformality. Conformality distortion distortion ellipses to be the same size, this type of projection preserves the fidelity of angle measurements from the globe to the plane (DiBiase, 2012).

Geographic Coordinates

The place name shown on the map above represents the location of my hometown. The geographic coordinates of my home town are:

Latitude: 25? 38' 31" N, Longitude: 80? 23' 54" W

The geographic coordinate system (GCS) uses longitude and latitude to define a location on the Earth's surface, this coordinate system uses a graticule which is formed by lines intersected in an spherical surface. Longitude and latitude can be expressed in degrees, minutes and seconds or in decimal degrees. The latitude is represented with lines parallel to the equator, the line across the equator is the zero (0) latitude or the origin; latitude ranges from 90 degrees in the North Pole to -90 in the South Pole. The longitude is represented with lines across the parallels, these lines are called meridians; zero (0) longitude or the origin is called the prime meridian. The latitude and longitude origin is located at the intersection of the Gulf of Guinea in the west coast of Africa and Great Britain in the north (DiBiase, 2012).

A degree of longitude at the equator represents approximately 111 kilometers. The GCS stands out at the equator because of its rotation; this coordinate system is represented by an ellipsoid or spheroid. When using the GCS it is important to specify which spheroid is being used, because the same location might have small different coordinates based on different spheroids, therefore, a misalignment of features on the map could occur (Price, 2012).

Project 1: Plotting Coordinates and Projections

Diana Jo Lau

____________________________________________________________________________________

Why are latitude and longitude coordinates expressed in degrees rather than distance units? Latitude and longitude coordinates are expressed in degrees because the geographic coordinate system measures angles in a spherical surface, these angles are represented with a graticule in a sphere.

Are latitude and longitude coordinates projected? Latitude and longitude coordinates are unprojected. In contrast with other coordinate systems the geographic coordinate system is represented in a spherical surface rather than in a flat surface.

How does a horizontal datum come into play in the geographic coordinate system? The horizontal datum in a geographic coordinate system changes when the representative shape of the Earth (e.g. ellipsoid, geoid) changes throughout the surface. Therefore, a geographic datum transformation is required to obtain the correct coordinates (ESRI, n.d.). The two most common horizontal datums used in North America are the North American Datum of 1927 or NAD27 is based on clarke 1866 spheriod, and the north American Datum of 1983 or NAD83 is based on the GRS_1980 spheriod. A common horizontal datum for satellite data is the World Geodetic Survey of 1984 or WGS84. The coordinates from a specific location can vary in hundreds of meters between NAD27 and NAD 83, therefore it is required to convert all the features into one datum to avoid alignment problems. The proper word to refer to a datum conversion is transformation (Price, 2012).

UTM Coordinates

The UTM coordinates (NAD83 or NAD27) of my hometown are:

Easting: 560395.455 meters, Northing: 2836169.659 meters, Zone & Hemisphere: 17 N

The Universal Transverse Mercator (UTM) coordinate system is based on the Transverse Mercator projection that does not cover polar areas (latitudes higher than 84? N and 80?S are excluded). The UTM coordinate system is divides the world map into 60 zones, each zone span 6? of longitude where 1? of longitude is about 111 km in length (DiBiase, 2012).

The UTM reference ellipsoid is GRS 80 in North America. The unit of measurement is in meters (m). The origin of longitude and latitude is at the central meridian and the equator, respectively. The false northing is 0, for the southern hemisphere a false northing of 10,000,000 m is used. A false easting of 500,000 m is used for the central meridian of each zone, southern and northern zones (see Figure 3). The scale factor at the central meridian is 0.9996 in a given zone. the variation reaches 1 part in 1,000 from true scale at the Equator. The lines of true scale are approximately parallel to and approximately 180 km east and west of the central meridian (Snyder, 1987)

Figure 3 Easting and Northing coordinates of the origin of a UTM grid zone ()

Project 1: Plotting Coordinates and Projections

Diana Jo Lau

____________________________________________________________________________________

Why are eastings and northings expressed in meters rather than degrees? The UTM coordinates are expressed in meters because they are represented in a flat surface rather than a spherical surface.

Are UTM coordinates projected? If so, according to what map projections(s)? Yes, UTM coordinates are projected. The map projection is the Transverse Mercator; the Transverse Mercator is a cylindrical projection that shows a conformal distortion property which minimizes distortion by using standard lines.

How does a horizontal datum come into play in the UTM coordinate system? The horizontal datum in a UTM coordinate system changes when the location in UTM coordinates changes.

National or Regional Coordinates

The State Plane coordinates (NAD83 or NAD27) of my hometown are:

Easting: 260416.069 meters, Northing:145087.180 meters, Zone: 0901

State Plane Coordinates (SPC) refer locations on the earth in a flat area. This coordinate system is expressed in eastings and northings. The SPC system is divided into 124 zones that covers the 50 states of the United States. Compared to the UTM coordinate system, the SPC is better used for small areas because distortion is minimized (DiBiase, 2012).

The maximum error rate is 1 per 10,000 (DiBiase, 2012).

How are eastings and northings determined? Each SPC zone has a specified relative to an origin. The SPC zone origins are positioned south; northings and eastings values at the origin are not in 0,0; the origin depends on the map projection used and it coincides with its central meridian. The origin eastings varies from 200,000 to 8,000,000 m East (DiBiase, 2012).

Why are eastings and northings expressed in meters rather than degrees? SPC are expressed with eastings and northings in meters instead of degrees because the coordinate system is represented in a flat surface rather than a spherical.

Are SPC coordinates projected? If so, according to what map projections(s)? State Plane Coordinates are projected. The most common map projections in SPC are the Transverse Mercator and Lambert Conic Conformal. Transverse Mercator projection represent better the "Tall" zones like the state of Florida. Lambert Conic Conformal projection represent better the "Wide" zones like the state of Pennsylvania (DiBiase, 2007). Except for zone 1, in Alaska, the oblique Mercator projection is used (Anderson and Mikhail, 1998).

How does a horizontal datum come into play in to SPC coordinates? Horizontal datum in SPC changes when the ellipsoid changes. This is because the SPC system is based on a georeferenced plan coordinate. The SPC system tied with NAD 27 uses the U.S. survey foot as the basic unit and is referred

Project 1: Plotting Coordinates and Projections

Diana Jo Lau

____________________________________________________________________________________

to SPCS 27. When the SPC system uses NAD 83 as it recently, the system is expressed in meters (Anderson and Mikhail, 1998).

Comparison

The geographic coordinate system (GCS) is based on a spherical surface and locations are expressed in latitude and longitude, unlike UTM coordinates and SPC systems are based on a flat surface and locations are expressed with northings and eastings in meters. Since, the geographic coordinate system is based on a spherical surface, it is not projected; in contrast the UTM and SPC are projected coordinates and both system divide the earth into zones with the exception of the Poles. The main difference between UTM and SPC is that the UTM coordinate system divides the Earth grid into 60 zones, and the SPC system divides a certain region into zones, for example, the United States is divided into 124 zones that cover the 50 states only if using SPC.

When SPC zones are of irregular shape, a combination of Lambert Conic Conformal and Transverse Mercator projection is used in such zone; for example, Florida has an upside down L shape, the largest area is projected using Transverse Mercator and the widest area is projected using Lambert conic (Snyder, 1987). One of the major disadvantages of using GCS is the difficulty of calculating distances and areas. Compared to UTM and SPC systems its coordinate system is easier to calculate distances and areas because they use cartesian coordinates or northings and eastings in length units. The greatest advantage of SPC system compared to UTM, is that the SPC provides better accurate measurement and shape preservation of the zone. The UTM is better used when dealing with larger areas. Also, the UTM projects zones around the world except the poles, unlike the SPC is only used in certain areas of the globe, mostly in the United States (DiBiase, 2012).

Why are some coordinates projected and others not? When the coordinate system is based on a spherical surface like the Geographic Coordinate System, the coordinates are not projected. If the coordinate system is based on a flat surface, that is when the spherical surface is projected through a flat area then this type of coordinate system has to be projected; for example the UTM and SPC.

What geometric property is preserved in the projected coordinate systems? In UTM and SPC, conformality is preserved.

Explain the difference between NAD83 and NAD27. Why are different horizontal datums in use? The NAD 83 is based on the Geodetic Reference System of 1980 and the NAD 27 was based on the Clarke Ellipsoid of 1866. The datum point of the NAD 27 was measured in a single point in Kansas, while the NAD 83 does not have a datum point, it is represented as a geocentric reference system. The United States has officially adopted the NAD 83. The NAD 83 minimized distortions from the coordinate systems currently in use (Indiana Geographic Information Council, 2001).

Sources

Anderson, J.M., & Mikhail, E. (1998). Surveying: Theory and Practice. (7th ed. International edition). Taipei, Taiwan.

DiBiase, D. and others (2012). The Nature of Geographic Data. The Pennsylvania State University. Retrieved February 15, 2013 from

ESRI (n.d.). Coordinate systems, map projections, and geographic (datum) transformations. Retrieved January 30, 2013, from

Indiana Geographic Information Council (2001). Standards and Recommendations - Projections, Datum, Coordinate Systems, and Units of Measure Standards. Retrieved January 30, 2013, from

(n.d.). MapTools: Tools for plotting GPS coordinates. Retrieved February 115, 2013, from

Project 1: Plotting Coordinates and Projections

Diana Jo Lau

____________________________________________________________________________________

National Geodetic Survey (n.d.) NADCON - North American Datum Conversion Utility. Retrieved January 29, 2013, from

National Geodetic Survey (2004a). SPC Utilities. Retrieved January 29, 2013, from

National Geodetic Survey (2004b). UTM Utilities. Retrieved January 29, 2013, from

Penn State Online Geospatial Education Program (n.d.). Interactive Album of Map Projections. Retrieved February 15, 2013, from

Price, M. (2012). Mastering ArcGIS. (5th ed.) New York, NY: The McGraw-Hill Companies, Inc.

Snyder, J. P. (1987). Map Projections - A Working Manual. U.S. Geological Survey Professional Paper 1935. 48-64.

United States Geological Survey (2006a). Geographic Names Information System. Retrieved July 7, 2010, from

This document is published in fulfillment of an assignment by a student enrolled in an educational offering of The Pennsylvania State University. The student, named above, retains all rights to the document and responsibility for its accuracy and originality.

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