Topographic Maps and Digital Elevation Models

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Chapter 6 Topographic Maps and Digital Elevaton Models 99 96" 95" 94" 93" 92" 91" 90" W 48°N -rt-+--++--+---4+--+--t-r-~ 5,400,000 mN 5,300,000 mN -+-+-+--+1--+--++--+-+-+ 5,200,000 mN +-+--+---++--1--++--+-+-+ 5,100,000 mN lambert Equal Area Projection A. FIGURE 6.7 A. UTM-grid zones in North America. Each zone is 6° of latitude wide. The zones are numbered counting west to east from the International Date Line. At the middle of each zone is the central meridian used to set up the eastwest 1000-meter UTM grid lines. B. Example showing two parts of the UTM grid for zone 15 (black lines). The lines of latitude and longitude are in red. The grid system counts meters north of the equator and east or west of the central meridian, which is arbitrarily set to 500,000 meters. The lines on the two grids are parallel near the equator but not at higher latitudes because most latitude and longitude lines are projected as curves, whereas UTM lines are drawn as straight lines on this projection. The point in the shaded area is located in Figure 6.6. +-+-+--I-I--+---+t----+---+--+ 5,000,000 mN 44°N -~:t:t=:=+t==t:=:tt:=~:::t:4,900,000 mN ! I II w E o ,8 I~ w Eo .........~r'--, ;-, I I ' ! , w J.J ~ 'w E E E E 8 8 § g 8 8 8' g\ 1.0 (0 I'-- co, 10 o /8 " +-+--++---++--+---j-+---1-+-+-+- 400,000 mN -+-+---1-j---+I---+---++--H--+--+- 300,000 mN 2°N --=l:::t=ti=:tt:=::j::=~=t:t=::j:::t 200,000 mN -+-+---1-+--++---+---++--H--+--+- 100,000 mN 91" 90" W Because the Earth is round, even small areas (like the shaded one in Fig. 6.5B) represent curved surfaces that must be shown on flat maps. This requires a projection of the three-dimensional curved surfaces onto a two-dimensional sheet of paper. Many ways have been developed to accomplish this-names such as "Mercator projection" or "polyconic projection" may be familiar to you-but all unavoidably result in some sort of distortion and create certain difficulties. Universal Transverse Mercator (UTM) System A second widely used global coordinate grid is the UTM system. Its set-up may seem somewhat complex, but the UTM system produces a handy grid of I-km squares on many maps. This makes it easy to determine accurate grid coordinates from paper maps and to determine distances between points. Most global positioning system (GPS) units allow you to switch between latitude-longitude and UTM coordinates. The UTM system divides the 360° range of longitude into 60 north-south zones, each 6° wide. Figure 6.7A shows these zonc:s in North America. The zones are numbered from west to east, beginning at the International Date Line. The zone number is given in fine print in the lower left corner of USGS quadrangle maps. Each zone is divided into a grid with its origin at the intersection of the equator and its own central meridian, as shown for zone IS in Figure 6.7B (e.g., 93° W is the central meridian between 90° to 96°). A metric grid, with lines intersecting at right angles, is developed from this origin on a transverse-Mercator-type map projection. Lines running east-west count the number of meters from the equator. North-south lines measure the number of meters from their zone's central meridian, which is arbitrarily set to a value of 500,000 m to avoid coordinates with negative numbers (study Fig.6.7B). Features are located by their UTM coordinates. UTM coordinates are given by distinctive numbers (e.g., 49 44°00, 49 45) along the margins of USGS maps (Fig. 6.6). The numbers give the distance in meters from the zone origin. In Figure 6.6, for example, 49 43°00 mN describes an east-west line 4,943,000 m (4943 km) north of the equator. The east-west line I km (1000 m) to the north is 49 44°00 mN. The larger "44" makes it easier to count the I-km increments. The complete UTM coordinate is given as: north-south coordinate (northings), east-west coordinate (eastings), zone number, and hemisphere (north or south). Because some give the east-west coordinates first and the northsouth coordinates second, it is essential to label your UTM coordinate numbers with "mN" (meters north) and "mE" (meters east). Figure 6.6 gives a worked example determining UTM coordinates.
100 Part III Maps and Images A. R4E B. Correction line }Tier 3S (T3S) \Correction line SE)4, NW)4, Sec. 16, T3S, R4E NW)4 NW)4 FIGURE 6.8 U.S. Public Land Survey subdivision, illustrated by successively smaller areas. A. Example of a baseline and principal meridian in the western United States. The area to which they apply is shaded. B. From a starting point at the intersection of a principal meridian and a baseline, 6-milewide tier and range bands subdivide land into 36-square-mile townships. C. Townships are subdivided into 36 I-square-mile sections. D. Sections can be divided into halves, quarters, eighths, or other fractions. R5E 24 T2S ~ G 29 31 32 33 34 35 36 3 ?- /( 6 5 4 3 2 1 6 lE V 12 7 8 9 10 11 12 7 , -fa 18 17 16 15 14 13 18 T3S R4E ~ 24 19 20 21 I~~ 24 19 A C. Wyoming R3E Base Colorado South Dakota Nebraska line Kansas T3S 1""- 25 30 29 28 27 26 § ;::::-.. I~ 31 32 33 34 35 36 31 tt- -?..> :q 6 5 ~ 3 2 1 F --¥ H 0 T4S u.s. Public Land Survey System The U.S. Public Land Survey System was designed to efficiently describe areas of land in most states outside of the original 13 colonies. This system, commonly called the Township-Range system, was started in 1785, when the old Northwest Tenitory (Lake Superior region) was opened to homesteading. It has been widely used for ordinary and legal land descriptions in the western two-thirds of the United States ever since. The method subdivides land into 6- X 6-mile squares called townships; these are further subdivided into 1- X I-mile squares called sections. D. E~ The starting point for subdivision is the intersection of selected latitude and longitude lines. The starting latitude is the baseline, and the starting longitude is the principal meridian. Baselines and principal meridians are established for a number of areas in the United States; an example is shown in Figure 6.8A. Lines drawn 6 miles apart and parallel to the baseline form east-west rows called tiers. North-south lines parallel to the principal meridian and 6 miles apart form northsouth columns called ranges (Fig. 6.8B). The squares formed by the intersection of tiers and ranges are called townships. Each township is approximately 6 miles square and has an area of about 36 square miles. Political townships, usually named after the largest town within the area at the time they were designated (for example, Baraboo Township, Wisconsin), may or may not coincide with Public Land Survey townships. Tiers and ranges are numbered by reference to the baseline and principal meridian (Fig. 6.8B). The first tier north of the baseline is Tier 1 North (abbreviated TIN); one in the fifth tier to the north is T5N, and so forth. Ranges are numbered to the east of the principal meridian (for example, R5E) and to the west (R2W). A Public Land Survey township (like the shaded one in Fig. 6.8B) is located using tier-range coordinates: T3S, R4E. NOTE: Tier is always written first, range second. Because lines of longitude (meridians) converge toward the poles, it is impossible to maintain squares that are 6 miles on a side. Thus, a correction is made at every fourth tier line (labeled correction line on Fig. 6.8B), and new range lines 6 miles apart are established. The cOlTection restores townships immediately north of the line to their proper size. Each 6-mile-square township is subdivided into thirty-six, 1- X I-mile squares, called sections, which are numbered in a specific sequence (Fig. 6.8C). Each section consists of 640 acres. A section is subdivided into halves, quarters, eighths, sixteenths, and so on (Fig. 6.8D). A sixteenth of a section is 40 acres. Points are located according to the smallest subdivision required. In Figure 6.8D, the star is located, to the nearest 40 acres, in the SE )4, NW )4, Sec. 16, T3S, R4E. Locations are always written from the smallest unit to the largest, and tier is written before range. Section numbers and tier and range values are written in red on USGS topographic maps (see Fig. 6.6). Map Scale The scale of a map is essential because it tells the user the size of the area represented and the distance between various points. Three types of scales are in common use: ratio, graphic, and verbal scales. A ratio or fractional scale, shown at the bottom of Figure 6.9, is the ratio between a distance on a map and the actual distance on the ground. The ratio
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