Topographic Map
Interpretation

TECHNIQUE NUMBER 5

DIRECTION

X,Y axes

The last independent measurement we can make on a topographic map is that of direction. (Direction is not really independent - we can give changes in location to indicate direction, but that is unwieldy.) Direction is an interesting variable because it can be either unidirectional or bidirectional. For example: does US 191 west of Bozeman, MT, run from east to west or west to east? Answer: either one is correct - the road is bidirectional. Does the Gallatin River on the same quadrangle run north-south or south-north? Answer: from south to north - water flows downhill. When making orientation measurements, be sure to specify whether it is uni- or bidirectional. To indicate this to a reader, the mode of presentation differs (below).

To measure direction, you need two things: a straight line segment and a datum. The straight line segment is the feature that you need to determine orientation; the datum is True North. By convention, all directions are given in terms of variance from True North. We have several choices for datums on our map. Each of the coordinate systems we have used for location purposes is somehow related to a north-south axis.

The most accurate north-south datum is the latitude/longitude grid system. The sides of the map are each aligned north-south, as are the grid tics along the margins and in the body of the map.

NOTE:

• These lines are aligned north-south, but they are not parallel! Why?
• __________________________________________________
• [If you don't believe me, measure the distances across the top and bottom of a map.]

Also potentially accurate are the blue marginal UTM grid tics. Although these grid lines are only north-south in the center of a gore, the magnetic declination diagram usually shows the deviation of the UTM grid from True North at the center of the map. The correction to true north is therefore a simple addition or subtraction. The least accurate of the coordinate systems for direction is, of course, the Township and Range system. A glance at the right edge of the Bozeman quad will show you that the grid is not aligned with true north; examination of individual section lines will reveal individual deviations of up to 10 degrees from true. Try not to use the T/R grid for calculation of orientation!

To measure the direction of a straight line segment, you need to extend it, with a soft, sharp pencil, to the nearest grid line. The line segment must be long enough to cross your protractor. If your line segment is close to the margin of the map and nearly perpendicular to it, then extend it to that line. If your line segment is in the center of the map, or nearly parallel to the map margin, lightly connect the appropriate grid tics, marginal or central, with a thin pencil line to define your datum.

NOTE:

• A little effort spent on accuracy here will be reflected in a real improvement in the accuracy of your measurement.

The measurement itself can be made easily with a protractor once the lines have been established. Your measurements should be made to the nearest degree, at the most accurate. Keep in mind the effect of both the allowable inaccuracy on the map and the judgement process you went through in defining your initial line segment.

One of the most important aspects of directional data is its presentation. The most commonly used form of presentation is the compass rose diagram. There are two variants of this diagram - the full rose and the half rose, usually the north half. The full rose diagram is used for the plotting of unidirectional data and the half rose for bidirectional data.

NOTE:

• For comparison, two different bidirectional data sets can be plotted on opposing halves of a rose diagram. Be sure to clearly differentiate them, as with different colors or patterns!

To generate a compass rose diagram you must first have a data set. There is no fixed number of data points, but a workable minimum is 25. The more data you have, the better the resolution of subtle trends. Your data should be in the form of a table, divided into increments on the basis of orientation. Each increment is usually 5, 10, 15, 30, or 45 degrees. Which should you use? Mathematically, the optimum number of increments can be estimated by using the formula I = 8(log₁₀n) + 2, where I indicates the number of increments and n is the number of data points. For 40 data points, for example, log₁₀n = 1.6, thus the optimum number of increments is (8 * 1.6) + 2, equals 14.8, or 15. If we are plotting data only in the northern hemisphere (on a half rose), the optimum size for each increment would be 180 degrees/15 = 12 degrees. Twelve degrees would be an awkward number, as it does not divide evenly into 90, a compass quadrant, so we would use either 10 or 15. A table is provided to allow you to chose an appropriate number and size of increments.

NOTE:

• The table can be used for any histograms, not just compass rose diagrams.

There are two axes on compass rose graph paper; direction and distance. The distance from the origin of the graph can (and often does) represent frequency - the number of measurements within an increment. It can also represent magnitude - the sum of measurements falling within an increment. Once the data table has been generated, the number (or sum of values) of measurements falling in each class can be determined. This number can be plotted radially outward from the center of the compass rose graph paper.

Example: The unidirectional data from the table below are plotted on the compass rose graph paper at right.

Increment	Frequency
0-30	12
30-60	18
60-90	6
90-120	1
120-150	0
150-180	0
180-210	0
210-240	1
240-270	0
270-300	3
300-330	7
330-360	11

EXERCISE: On the graph paper at right, plot the frequency of directions of straight-line segments of streams and creeks (not canals!) on the Bozeman MT quadrangle.  Explain the observed distribution and discuss the difficulty of this process. Note that there are no radial lines inside the unit ring, 10° radials from 1 to 5 units, 5° radials from 5 to ten units, 2° radials from 10 to 20, and 1° radials beyond that. NOTE: You must make some decisions as to the length of a "straight-line segment".  State your assumptions!