Topographic Map
Interpretation

TECHNIQUE NUMBER 1

LOCATION

X and Y axes

Location is determined by reference to one or more of the grids on the margin of the map. Two of these grids (UTM and latitude-longitude) are designed for global use, the others (state and township-range) are more appropriate to regional use. Your choice of grid depends on availability and your purpose. Note: the exercises discussed below refer to the Bozeman, MT 15' (1:62,500 nominal scale) topographic map, accessible here and printable from your browser.

Latitude-longitude. The position of a point on the surface of a sphere can be uniquely described by two variables, the distance around the sphere from a designated starting point (longitude), and the distance above (or below) the equatorial plane (latitude). The distances can be defined for a sphere of given radius in linear units (for example, kilometers), but is most easily defined for a sphere of any radius by using angular units (degrees, minutes, and seconds).

There is a logical starting point for latitude - the Equatorial plane. This plane is midway between the rotational poles (at 90^o N and S) and perpendicular to the rotational axis which joins them. The starting point for longitude is not quite as logical: note that 0^o N(S), 0^o W(E) is located in the Gulf of Guinea (find it on a map or globe!) Actually, although the origin of the grid is located there, the 0^o longitude meridian is defined on the basis of the Royal Observatory in Greenwich, England.

A problem with this world-circling system is that the lines of longitude (meridians) converge towards the poles, therefore a degree of longitude (separating two meridians) is of different lengths at different latitudes. At the equator, one degree of longitude is about 111 km. (The same is true for one degree of latitude at any longitude.) At 45^o N (just south of Bozeman, MT) one degree of longitude is about 78.5 km. In general, assuming a spherical earth, the length of a degree of longitude can be determined as:

111 km x sin(90^o - latitude)

For example, @ 45^o N:

• 111 km x sin(90 - 45) =
• 111 km x sin(45^o) =
• 111 km x 0.707 = 78.5 km

Unless applied by very precise measuring techniques, this method does not enable you to find your position on a map. The usual method is to interpolate your position within one of the rectangles (2.5' per side on a 7.5' quad, 5' per side on a 15' quad) defined by the map margins and the lat/long tics. For example: On the Bozeman, MT 15' quadrangle, the intersection of US 191 and US 10 (the intersecting dashed red roads in town) falls within the NE rectangle. The length of 5' of latitude at this scale is 15.0 cm on the downloaded map (actually14.73 cm on the original); the intersection is 12.7 cm below the top margin, or 2.3 cm N of 45°40'; 15.3% of the way from 45^o40' to 45^o45'N latitude. 15.3% of 5'= 0.765'= 45.9" ("seconds"). The latitude of the intersection, therefore, is 45^o40'45.9"N. The longitude is found in the same way.

NOTES:

• Drawing extremely faint, thin lines between grid tics, using a sharp, soft pencil, may help to define the rectangles, thus making measurement easier!
• Working in base 60 is nearly impossible without a calculator!
• Your measurements MUST be as precise as possible in order not to end up in someone's backyard by mistake!!!

UTM Grid. The UTM grid, like the latitude-longitude grid, is designed for use all over the globe. The UTM grid, however, is square throughout its coverage. If that sounds impossible on a globe, it is! The UTM grid consists of gores which, like longitude, taper towards the poles. Within the gores lie the squares, which therefore run north-south at the center of the gores and diverge from that to either sides. At the sides of the gores there are partial squares (messy!) If you are within a gore, however, location of a point is quite easy.

(This grid is used on a global scale by the military, who use it to define artillery and other targets. A computer has little trouble crossing gore boundaries in computation! It is also recommended for use by the U.S. Geological Survey "to the maximum extent feasible".)

Locations on the UTM grid are given in terms of "eastings" and "northings". The origin of the grid in any gore (or "zone") is at the center of the zone (easting = 500,000m, by definition), on the Equator (northing = 0m, by definition). The UTM coordinates therefore tell you how far east or west you are from the center of a zone and how far north of the equator.

To locate yourself by the UTM grid, first find what zone you are in. The zone designation is given in the lower left corner of the map margin. Next, locate the approximate coordinates of the NW or SE corner of the map. The grid coordinates are followed by an "N" or "E", are given in thousands of meters, and are marked with a light blue tic. (On more recent maps, a faint line grid crisscrosses the map, connecting these tics.) Notice that the kilometer coordinates are given around the perimeter of the map, except where they would obstruct some other information. To locate a certain spot, simply connect the grid marks surrounding the spot, read off the coordinates of the SW corner of the square you have outlined, and determine the location within the square as a percentage of the square. On a given map, you would normally use only the bold digits, given easting first, then northing, to designate a spot within a kilometer. This is termed a "four-digit" coordinate. A six-digit coordinate would identify a spot within 100 meters, and an eight-digit coordinate within 10 m. To all practical purposes, this is as close as you can get, as it approaches the map standards of accuracy.

For example: on the Bozeman, MT 15' quadrangle (within grid Zone 12), we can locate the intersection of US 191 and US 10  using the UTM grid.

1. Outline the UTM grid square around the spot (carefully and LIGHTLY!)  Note that 111^oW is the center of grid Zone 12, thus the ⁵00 tic is on the east (right margin, and is oriented along the map edge.  Usually the UTM grid is misaligned with the Lat/Long grid.
2. Locate the coordinates of the SW corner of the square. Easting ⁴96000m E, Northing ⁵⁰58000m N. This number locates the intersection within one kilometer, and can be abbreviated (on a known map) as 9658. If the highway intersection was closest to the SE corner of the grid, it would be more accurate to estimate its location as 9659.
3. Locate the point within the kilometer grid. At this scale (1:62,500), 16 mm on the map equals one kilometer on the ground. The intersection is 7 mm east of the grid line, or 438m, and 3.8 mm north, or 238 m. The six-digit location would thus be 964582 (rounded to the nearest 100 m). Similarly, the eight-digit location would be 96445824 (rounded to the nearest 10 m). You could determine a ten-digit location, but the accuracy would be spurious - it would exceed the accuracy of the map.

NOTE:

• This, like all other measurement techniques, will only work if you are painstakingly accurate in your measurements. Keep your pencils sharp, use a light touch, and use an accurate scale. A triangle helps project perpendiculars.

State Grid. The state grid is used exactly like the UTM grid, except that 1) the starting coordinates are given in the SW and NE corners of the map, 2) the coordinates are usually in feet, not meters, 3) the spacing in 10,000 feet, and 4) the tics are black, not blue.

US Public Lands System - also known as Township and Range. The township and range grid is shown on many maps by an overlay of red lines, with red numbers and letters in the margins. To locate an area, you must first determine the township and range from the margins. Each township (about 6 miles square, or 36 square miles) is outlined in a slightly heavier red. The township and range system is defined with reference to Baselines, which run east-west, and Principal Meridians, which run north-south. There are a number of these across the country, so if you must locate a spot in a nationally unique fashion, you must designate the baseline and principal meridian. Like the UTM grid, however, if you are within a map sheet or county, the larger designations are unnecessary. The townships (numbered in red) in turn are subdivided into 36 sections, each about 1 mile square or 1 square mile.

Sections, in turn, are subdivided into ¼ sections, which in turn can be quartered, and so on. Because a township is normally 6 miles square, a section is 1 mile square, or 640 acres, a 1/4 section is 160 acres, a ¼ ¼ section is 40 acres, and so on. These numbers should be familiar to those of you with an agricultural background, as most farms and some ranches are in units of 40 acres. For example: On the Bozeman, MT 15' quadrangle, the largest building at Montana State College (1953 map!) is located in the NE¼ of the NW¼ of section 13, Township 2 south (T2S), Range 5 east (R5E): NE¼ NW¼ sec13 T2S R5E. EXERCISE: What is the township/range location of the Fowler School (SW of Bozeman)? ____________________________________

NOTE:

• This method seems easy, and is, but it is deceptive for two reasons. First, there are many areas not covered by the township and range system. This is true for the eastern United States and especially Louisiana, where similar red markings outline very different land ownership patterns! Second, it is inaccurate due to surveying error in most areas. On the Bozeman quadrangle, sight along the N-S section lines. The irregularities imply sections which are not square. Be careful if you are using these lines to estimate the scale of a fragment of a map!

Location Accuracy. However tempting it may be to assume that a topographic map is perfectly accurate, you must realize that it is merely a picture of the earth's surface. This picture has been generated through photogrammetric techniques, which have finite limits. For most common maps (those at scales of 1:20,000 or smaller), the limits of map accuracy are +0.02 inches "for well-defined points". There are no standards of accuracy for points which are not well-defined, such as the edge of a stand of trees or a gentle break in slope.