Hydrographic Project

The Surface of Directed Gradient is a second derivative surface derived from topographic map of surface S(x,y,z). It identifies the point where the “slope of a topographic surface S(x,y,z) has the maximum change in its gradient of that surface occurring at its base”. This is the ‘foot of the continental slope’ in bathymetric data.

In this cross-section below of the topographic surface, S(x,y,z), the arrow indicates where this point occurs:

The SDG identifies where the gradient of the surface S(x,y,z) has the maximum change, hence maximum run-off for water.

Below three figures with contour maps the area east of the Rocky Mountains made using NOAA’s ETOPO5 Data. The rectangular data grid is about 6 miles.

These three Figures are:

Figure 1 – Topographic Contour Map East of the Rocky Mountain Region, CI = 100 M, contours in red, state outlines in black. There is some slight data smoothing.

Figure 2 – Contour Map of Surface of Directed Gradient which is a second derivative surface of topographic contours from Figure 1. Contours of SDG are in blue. Closed contours indicate area of maximum run-off.

Figure 3 – is an overlay of Figure 2 over Figure 1

Please examine these maps to evaluate their potential in identifying the areas of maximum run-off and hence maximum possible erosion and flooding. Your time and opinions are much appreciated.

John O. Bennett