# OBJECTIVES MATERIALS BACKGROUND. Maps and Mapping. Key Terms. Common units and conversions. Introduction. Page 1 of 10

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2 Latitude/Longitude Geographical coordinates in latitude and longitude are angular measurements given with respect to an arbitrarily selected origin at the intersection of the equator and the Prime Meridian, which was standardized by the International Meridian Conference of 1884 when a line passing through Greenwich Observatory in England was adopted as the zero-longitude reference line. Latitude ranges from 90 degrees north or south of the equator while longitude ranges from 180 degrees east or west of the Prime Meridian. To precisely locate points on the earth's surface, degrees longitude and latitude have been subdivided into minutes (') and seconds (") of arc. There are 60 minutes in each degree. Each minute is divided into 60 seconds. Seconds can be further divided into tenths, hundredths, or even thousandths. At any point on earth, the ground distance covered by one degree of latitude is about 111 km. The ground distance covered by one degree of longitude at the equator is also about 111 km, but decreases until it becomes zero at the poles. Latitude and longitude is the basis for USGS map tiling that is, the edges of maps follow lines of equal latitude and longitude. Universal Transverse Mercator (UTM) The UTM coordinate system is included on most USGS topographic maps. This grid-based coordinate system divides the earth into 60 pole-to-pole zones, each 6 degrees of longitude wide, starting at 180 W (the International Date Line), and increasing east. Each zone is divided by its hemisphere into N or S. For the coterminous United States, California falls into zones 10N and 11N. A false origin for each zone is established. In the northern hemisphere, this false origin is at the equator beyond the westerly limit of each zone. In the southern hemisphere, the zero northing is at the South Pole. This numbering scheme allows all coordinates to be given in positive northings and eastings, a location s distance in meters from the false origin. The central meridian for each zone is given the value of 500,000 meters. State Plane Coordinate System (SPCS) SPCS divides the United States into a number of smaller zones following state and county boundaries. Each state contains one or more zones that use a simple Cartesian coordinate system, thus reducing map projection distortion because such issues are minimal for fairly small regions. Outside a specific state plane zone, accuracy rapidly declines, thus the system is not useful across zone boundaries. Most state plane zones are based on either a Transverse Mercator projection or a Lambert conformal conic projection depending upon the shape of the state and its zones. States that are elongated in the east-west direction typically use the Lambert conformal conic projection because it maintains accuracy along an east-west axis. Zones that are elongated in the north-south direction use the Transverse Mercator projection because it is better at maintaining accuracy along a north-south axis. SPCS coordinates are given in meters or feet north and east of the false origin, which is arbitrarily defined beyond the southwesternmost point of each zone. Page 2 of 10

4 Look for the symbol that marks the current Four Corners monument at the bottom of the map. (Hint: Follow the state boundary lines to find the square marker symbol). Click on the first button on the TerraGo toolbar. Read the information in the dialog box that appears which provides instructions on displaying coordinates. Zoom into the Four Corners monument location. Position your mouse cursor over the marker as precisely as possible, then single click on the marker symbol to freeze the coordinate display on the bottom right. a. What are the lat/lon coordinates of the marker as it appears on the map? The Four Corners monument was intended to be established at 37 N, W. You will locate this point on the USGS Yellow Rock Point East Quadrangle using the TerraGo toolbar. Click on the second button in the toolbar, with an icon of arrow superimposed on a globe. A window should appear that will enable you to input search coordinates. b. What is the current datum and projection setting? What is the coordinate system and unit? Click on the arrow on the bottom right of this window Click on Set Projection Parameters in the drop down menu. In the window that appears, click on the Predefined tab and scroll through the list of coordinate systems to find NAD83 (NSRS2007). Select this projection and click OK. The Locate window should update to the selected coordinate system. Page 4 of 10

5 c. First, convert the coordinates for the monument s intended location from degrees minutes seconds (DMS) to decimal degrees (DD). Example: Leave the degree, the first number, unchanged: 20 Multiply the minutes by 1/60 to convert it to degrees: 10 * (1/60) = Multiply the seconds by 1/60 to convert it to minutes. Then multiply by 1/60 again to convert it to degrees: 15 * (1/60) * (1/60) = Sum all three numbers: = Show your work: What are the coordinates in DD? Enter the coordinates in the Locate window. d. Does the coordinate you entered coincide with the marker for the monument printed on the map? Following the above procedure for setting projection parameters, change the coordinate system to SPCS and then UTM. e. What are the coordinates for the intended monument location in SPCS and UTM Zone 12N? Be sure to include units. SPCS: UTM: Part 3. Measuring error a. According to the National Geodetic Survey datasheet, the Four Corners monument is currently located at N, W in reference to NAD 83(2007). Convert this coordinate to DD, record it here, and enter the coordinate into the Locate window. Page 5 of 10

6 Use the third button on the TerraGo Toolbar to measure the length of any discrepancy between the marker s current location and its intended location. (In the next lab Land Navigation, you will learn how to use the Pythagorean Theorem to calculate the Euclidean distance between two points. For now, you will approximate the distance using this digital tool.) b. Is the actual marker misplaced from its intended location? If so, how far away is it in feet? In meters? Describe the marker s directional location in relation to its intended location. c. News articles publicized that the marker was misplaced by 2.5 miles east. Is this correct? Compute their accuracy. A way to compute the percent accuracy, given an estimate E (reported displacement) and an observation V (actual displacement) is: V E A V Example: Suppose the measured distance is 2650 and the observed value is 2686, then: A = [ /2686] x 100 (Note the use of absolute values ) = [1 (36/2686)] x 100 = 98.65% Show your work: The accuracy is % d. According to the NGS, the Four Corners Monument is exactly in the right place. Read the following article on the controversy at and summarize why monuments rule. Page 6 of 10

7 Part 4. Map interpolation To complete this portion of the lab, you will need to print out the attached map which displays a portion of a USGS quad for the Four Corners region. Or click HERE to download it. Although using GeoPDFs simplify the coordinate reading process, map interpolation is an important skill to acquire so that coordinates can be read without the use of a computer. Reading lat/lon coordinates is straightforward if a location falls on the lines of latitude and longitude printed on the map. However, if the place of interest lies somewhere between the graticule lines, the task becomes more difficult. Reading Latitude/Longitude Coordinates We will use a proportional method and paper strip technique to determine the geographic coordinates for three locations on the attached topomap. Map interpolation requires a graticule as a starting point. First, we will determine the parallels and meridians that enclose this map. The attached map is bounded: Longitude W and W (an interval of 5 = 300 ) Latitude N and 37 N (an interval of 2.5 = 150 ) As mentioned above, the distance covered by a degree of longitude varies by latitude because the meridians converge at the poles. On the attached map, at latitude 37 N the length of a degree of longitude is meters. The length of a degree of latitude is 110, meters (approximately 111 km). a. Recall that there are 60 minutes in a degree. What is the length of one minute of longitude at 37 N? Using the lengths of degree given above, the Total Longitude Distance covered by this map can be calculated as meters. The Total Latitude Distance covered by this map is meters (110, m divided by 60, multiplied by 2.5). (If these lengths were unknown, one could use the graphic scale on the bottom of the map to make these measurements.) Locate Point 1 on the map. You will use the paper edge technique to measure the straight-line distance between Point 1 and the southern boundary of the map, which we will call the Partial Latitude Distance. Step I. Lay a straight-edged piece of paper on the map so that the edge of the paper touches both points and extends past them. Step II. Make tick marks on the edge of the paper at each point. Page 7 of 10

8 Step III. The earth distance is determined by checking the measurement against the graphic bar scale. If the measured distance exceeds the length of the graphic scale, several partial measurements should be combined. Step IV. The partial distance is in direct proportion to the total distance, and will be used to set up a ratio. Partial Distance Total Distance x arcseconds Example: Suppose we determine the partial latitude distance is meters. Taken as a proportion of the known total latitude distance and arc seconds then: 4160 x " 4624 * x = 150 * 4160 use cross multiplication to solve for x x = Convert seconds to minutes by dividing by 60. The integer quotient will provide the minutes, while the remainder will be the seconds: /60 = Now add this number to the southern latitude coordinate that bounds the map, and this will be the latitude of Point N = N b. Repeat the above paper strip technique to measure the partial longitude distance. Then use this number to set up a proportional ratio to find the longitude of this point. Partial Longitude Distance: Longitude coordinate: Page 8 of 10

9 c. Repeat the paper strip and proportional method to find the coordinates of Point 2. Latitude: Longitude: Reading UTM Coordinates UTM coordinates are easily interpreted if a point falls on gridlines; however, when the point of interest lies between the lines, some interpolation is required. Again, reading coordinates is simpler in UTM and SPCS because we can use the provided tick marks and map scales to compute distances. To measure a coordinate: 1. First find the nearest grid lines to the south and west of your point of interest. 2. Next, measure the distance from those grid lines to the point using the paper edge trick, then use the graphic scale to determine this distance on the ground. 3. Add the gridline values to the measured distance. (Note: UTM lines are aligned with grid north instead of true north. It would be helpful to align corresponding tick marks at the top and bottom of the map to superimpose a grid and read coordinates.) d. Interpolate the UTM coordinates for Point 3 on the attached map. Northing: Easting: Page 9 of 10

10 e. Interpolate the UTM coordinates for Point 4 on the attached map. Northing: Easting: RELATED LINKS Dr. Map article that appeared in ACSM Bulletin. April NGS Four Corners Marker Datasheet. NGS National Spatial Reference System REVIEW 1. What are the intervals and units of the three coordinate systems that appear on your quadrangle map? How are they symbolized? 2. How are the UTM and SPCS reference systems similar? 3. How are UTM zones divided? What type of projection does it use? Conformal or equivalent? This lab was developed by Susan Tran UCSB Geography September 2009 Page 10 of 10

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