Topographic Map
Interpretation

Once the prior ground surface has been contoured (with thin, light lines, of course), the map will have two sets of contours upon it. The difference in elevation between those contours, whether positive or negative, represents a depth, height, or thickness. This value, integrated over the area, represents volume.

To determine the area over which a given thickness, etc. is valid, simply contour the differences in elevation between the two sets of contour lines. The points where the new (map) contours deviate from the old (reconstructed, penciled) contours will be the zero contour (there is no difference in elevation). The contours on elevation change will have the same contour interval as the original map, and a value is generated wherever two contour lines cross. Connect the points of equal elevation difference and you will have generated a contour map of the volume of interest. Characterize each area between contours with the midpoint value of the two contours (for example: if the two contours indicate zero and 20 feet thickness, the area between them averages about 10 feet thick), and multiply by the area between those two contours to estimate the volume in that increment. Add the values generated from within each of the sets of contour lines (estimating the thickness within the innermost contour as that contour plus 1/4 contour interval) to arrive at the total volume.

It is difficult to evaluate error in this process because you are contouring contours. In general, the percentage uncertainty decreases with the volume of mass being estimated, from about 100% if only one contour line is generated to less than 5% if a large volume is being evaluated.