Similar to bathymetric maps, hypsographic curves show a relationship between the Earth's surface and water depth (or elevation). However, unlike bathymetric maps, a hypsographic curve shows a relationship between elevation or underwater depth and the amount of Earth's surface covered. For example, if a hypsographic curve existed for a lake of interest, and one wanted to know what the surface area of the lake would be if the water level dropped to a specific depth, say 10 feet, the curve could be used.
In class, we created a hypsographic curve from a given bathymetric map of a lake ranging from 0-11 feet in depth. Using a square cutout of the scale (representing 10,000 square meters) and precise cutouts of the lake following each depth contour, the area at each depth was determined through a weight-area relationship (0.103 grams = 10,000 square meters). Next, the hypsographic curve was created in Excel by plotting the areas on the x-axis versus the depths (in reverse order with 0 meters at the top of the graph) on the y-axis. The resulting curve is shown below in Figure 1.
Another useful curve shows lake volume as a function of water depth. This sort of graph can easily be created from a hypsographic curve. First, the change in depth between two data points (surface to 1 meter down, for example) must be determined. Then the recorded surface areas at the two points can be averaged and multipled by the change in depth, resulting in a volume in cubic meters. The midpoints for each change in depth are the plotted on the y-axis in reverse order versus the volumes on the x-axis. The volume vs. depth graph for the bathymetric map given in class is shown below in Figure 2.
Using the volume graph, one can also determine the total volume of a body of water. To do so, the total volumes at each depth range from surface to the deepest point are added together. This is a very easy calculation is the data is set up in Excel. The total volume of the lake used in class was found to be 820,728 cubic meters.