legally mandated coordinate system. Universal Transversal Mercator (UTM) is widely used around the world, and thus is of great importance. All loca- tion systems and coordinate systems use a scale to reduce the size of mea- surements on the ground to map size or a comparable size in geographic information. Geographic information from one scale can be easily converted to another scale; it is much more labor-intensive to scale different maps.
Review Questions
1. What are common applications for spherical coordinate systems?
2. What is the main practical importance of coordinate systems?
3. What is the main difference between coordinate and locational sys- tems?
4. What is the transformation from x, y to x , y called when all scale factors are the same?
5. What is the difference between rectangular and polar coordinates?
6. For what purpose was Roman centuration devised?
7. What is the similarity between metes-and-bounds and the PLS in the United States?
Step 5: Calculate overall error. Assuming a linear relationship between individual errors and total error, use a root-mean-square equation and apply the law of error propagation to determine the maximum potential error.
Step 6: Document the georeferencing process. Documentation of the process and consid- erations used in determining the georeferencing are important for people working with the locality information later.
Based on: Wieczorek, J., Q. Guo, et al. (2004). The Point–Radius Method for Georeferencing Locality Descriptions and Calculating Associated Uncertainty. International Journal of Geographical Information Science, 18(8), 745–767.
TABLE 5.3. Common U.S. Surveying Measurements 1 link = 0.66 feet or 7.92 inches
1 pole or 1 rod = 16.5 feet or 25 links 1 chain = 100 links, 4 rods, or 66 feet
80 chains = 1 mile, 320 rods, 1,760 yards, or 5,280 feet
1 acre = 10 sq. chains, 160 sq. rods, 4,840 sq. yards, or 43,560 sq. feet 1 square mile = 1 section of land or 640 acres
Township = 36 sq. miles (36 mile-sq. sections)
These survey measurements are historical and archaic, but because of their legal nature these historical surveys are still valid. Current surveys generally use standard or metric measurements.
8. What is the State–Plane Coordinate System?
9. How are locational and coordinate systems used for public adminis- tration?
10. Why are 3-D coordinate systems still uncommon?
Answers
1. What are common applications for spherical coordinate systems?
Spherical coordinate systems are commonly used for satellite tracking and global models.
2. What is the main practical importance of coordinate systems?
Coordinate systems provide for the common recording of positional loca- tions against which distortions can be measured.
3. What is the main difference between coordinate and locational sys- tems?
Coordinate systems are mathematically defined based on a model of the earth’s surface and shape; location systems can be mathematically defined, but are usually created without relating them to a model of the earth’s sur- face and shape.
4. What is the transformation from x, y to x , y called when all scale factors are the same?
A constant scale transformation is called a linear transformation.
5. What is the difference between rectangular and polar coordinates?
Rectangular coordinates are orthogonal, that is, the x, y origin is defined by a right angle.
6. For what purpose was Roman centuration devised?
Colonizing and developing conquered areas.
7. What is the similarity between metes-and-bounds and the PLS in the United States?
In the areas they respectively dominate, they are legally accepted means of recording land ownership.
8. What is the State–Plane Coordinate system?
The State–Plane coordinate System was established during the 1930s in the United States to specify coordinate systems for each area. Many states have legally adopted the SPCS.
9. How are locational and coordinate systems used for public adminis- tration?
Locational and coordinate systems are used for recording locations, help- ing government/private coordination, and providing a structure for future activities.
10. Why are 3-D coordinate systems still uncommon?
The complex mathematics and lack of a common reference standard along
with the abundance of 2-D maps and GI hinder the widespread use of 3-D coordinate systems.
Chapter Readings
Caravello, G. U., & P. Michieletto. (1999). Cultural Landscape: Trace Yesterday, Pres- ence Today, Perspective Tomorrow for “Roman Centuriation” in Rural Venetian Territory. Human Ecology Review, 6(2), 45–50.
Dilke, O. A. W. (1985). Greek and Roman Maps. London: Eastern Press.
Ferrar, M. J., & A. Richardson. (2003). The Roman Survey of Britain. Oxford: Hedges.
Goodchild, M. F., & J. Proctor. (1997). Scale in a Digital Geographic World. Geograph- ical and Environmental Modelling, 1(1), 5–23.
Linklater, A. (2002). Measuring America: How an Untamed Wilderness Shaped the United States and Fulfilled the Promise of Democracy. New York: Walker & Company.
Thrower, N. J. W. (1966). Original Survey and Land Subdivision. Chicago: Rand McNally.
Web Resources
NOAA’s National Geodetic Survey maintains key resources for locational and coordi- nate systems at www.ngs.noaa.gov/
The documentation of the U.S. State–Plane Coordinate System prepared by James Stem is available from NOAA at www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf Roman Centuration is described in some detail by John Peterson at www.sys.uea.ac.
uk/Research/researchareas/JWMP/AgrimensoresMapConv.pdf
The National Atlas provides an introduction to the PLSS at http://nationalatlas.gov/
articles/boundaries/a_plss.html
Detailed instructions for the Public Land Survey are contained at www.blm.gov/
cadastral/Manual/73man/id1.htm
A very thorough and well-developed introduction to the history and legalities of land surveys and information in the United States is available at www.premierdata.com/
literature/Intro%20Land%20Information.pdf
A good description of the metes-and-bounds survey system from Tennessee is avail- able at www.tngenweb.org/tnland/metes-b.htm
Detailed description and parameters for the State–Plane Coordinate System are avail- able at www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf
Resources on U.S. datum measurements and conversions are available at www.ngs.
noaa.gov/PC_PROD/pc_prod.shtml
The U.S. Forest Service and Bureau of Land Management maintain a website for information for specific PLS questions at www.geocommunicator.gov
The Information and Service System for European Coordinate Reference Systems (CRS) has a website at http://crs.bkg.bund.de/crs-eu/
Exercises
1. Use PLS Coordinates
On a topographic map of the place you’re from or one you’re familiar with in the United States, determine the location of your home, school, and other important local feature using the Public Land Survey coordinates. Townships should be given on the east and west edges of the map, ranges on the north and south.
2. EXTENDED EXERCISE: Locational and Coordinate Systems Overview
In this exercise you will interpret the impact of land subdivision systems and learn how to read coordinates from United States Geological Survey (USGS) topographic maps. This exercise also introduces you to basic topographic mapping concepts and how to recognize them.
Concepts
Topographic maps are the most general-purpose maps in circulation. They repre- sent a multitude of features and relationships that you can “read” by looking at and studying a map. Among other things, they are useful for studying general land use development.
Exercise Steps and Questions
In this step you should use an index of topographic quads for a state in the United States to find a map of your home or a place you are familiar with. The feature you look for can also be a particular place, mountaintop, radio antenna, or structure—for example, a lighthouse. It should be small enough to be located distinctly: a small building or pond is OK, but not a large lake or structure. Most of all it, it should be someplace you are familiar with. If you can’t find the 7.5 quad you need, first check to see if an older quad is available for the area. If not, choose a feature somewhere else.
Answer these questions before continuing:
1. What is the name of the place you chose?
2. What is the type of feature?
3. Why did you choose it?
4. What is the latitude and longitude of the southeast corner of the map?
5. What is the distance, in kilometers and miles, from east to west across the map?
Kilometers Miles
6. What is range of elevation in this area?
Highest Lowest Average
7. Does this map show elevation in feet or meters?
8. Do you see any consequences of land subdivision—for example, in the orientation of roads?
9. What is the name of the map you choose?
10. Find the feature you described in question 2 and locate it using the fol- lowing coordinate and land subdivision systems:
Latitude Longitude
UTM Northing UTM Easting
Township Range Section
You should use a straightedge for these measurements and interpolate the distance.
11. What is the datum of the UTM coordinates?