Thursday, September 9, 2010

Bathymetric Maps and Hypsographic Curves

Bathymetric maps are maps that represent underwater depths (in oceans, seas, or lakes) at specific coordinates as topographic maps show elevation at specific locations on the Earth's surface.  Most bathymetric maps show isobaths (lines of equal depths) as contours for the body of water.  This gives a person an idea of how the basin of the body of water is shaped. 

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. 

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