Slope and Gradients
Topographic maps permit measurement of the slope, defined as the change in vertical distance divided by the horizontal distance (rise over run). For example, to calculate the slope of a hill that has a vertical rise of 80 feet and a horizontal run of 800 feet:
slope = 80 ft / 800 ft = 0.1
Note that the units of measurement (in feet) cancel each other out; thus, the calculated slope is dimensionless. To calculate the slope in degrees you would take arctangent of rise over the run and convert radians to degrees.
gradient = difference in elevation (ft) / horizontal distance (mi)
gradient = 64 ft / 1.8 mi
gradient = 35 ft/mi
Stream and river gradients may be calculated in a similar fashion; however, map distances must be measured along stream channels, rather than as a straight line.
Relief
Relief refers to the difference between the highest and lowest point in a given area. Relief can be expressed either numerically (e.g. a mountain has 865 ft of relief above the valley floor), or in a relative sense (e.g. a plain would have low relief while a mountain range would have high relief).
Topographic Profiles
To better visualize topography, it is often advantageous to construct a topographic profile, which presents a “side-view,” or cross-section, of the Earth’s surface.
Construction of a topographic profile is not difficult if the following guidelines are followed:
Place a strip of paper along a selected profile line (Figures 1-9A and 1-9B).
Mark on the paper the exact location where each index contour line, hill crest, and valley crosses the profile line. Label each mark with its elevation (Figure 19B). For very steep topography, where contour lines are very close together (e.g., a steep cliff), you may decide to only label the base of steep cliff and its top elevation before continuing to label the index contours.
Make a vertical grid on graph paper. The horizontal axis should show units of horizontal distance along the profile line and be the same length as your profile line. The vertical axis should show elevation units ranging from the lowest to highest points on your profile line.
Place the paper strip above the vertical grid and project each marked topographic feature downward to its proper elevation (Figure 1-9C).
Connect all the points on the grid with a smooth line, which is consistent with topographic trends. The result is a silhouette of the topography along the profile line (Figure 1-9C).
Figure 1-9A-C: Constructing a topographic profile.
Map Symbols
In the lower right corner of most U.S. Geological Survey (USGS) topographic maps, a legend is given that shows a few of the important symbols used on the map. The USGS has adopted standardized map symbols and color-coding to represent physiographic, cultural, and survey features shown on the map. A complete list of these symbols can be found at: pubs.usgs.gov/gip/TopographicMapSymbols/topomapsymbols.pdf In this portion of the lab, we will be creating two topographic profiles for two transects (A to A’ and B to B’) in the Icicle Creek-Leavenworth area. However, instead of constructing our topographic profiles by hand, as discussed above, we will be using this template and the Icicle Creek Topographic Map. Horizontal distance and elevation data will be inputted into this excel spreadsheet template and the topographic profiles will be constructed using the excel graphing program. Further instructions are included in the template file. If you do not have Excel, you can access the template through your Google Drive using Google Sheets.
Remember, a topographic profile presents a “side-view”, or cross-section of the earth’s surface. This area represents a spectacular landscape created by the actions of glaciers, rivers, and mass wasting processes (landsliding). Use the map and your cross section to answer questions 16 to 22. Upload your Cross Sections here. Please up load an excel, PDF or a screen shot jpeg of your cross-section. Some spread sheet programs are not compatible and we cannot read or grade them.
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