ArcUser Online

July - September 2003
Search ArcUser:

## Mean Sea Level, GPS, and the GeoidContinued...

### ELLIPSOID DEM

The ELLIPSOID DEM depicts the earth as an ellipsoid. Although distances from the surface of an ellipsoid to the earth's center along each latitude are identical, each latitude has its own unique value increasing from each pole toward the equator. To look at this ellipsoid earth from yet another perspective—its physical shape characterized by the distance of any point on the surface to the center of the earth's mass—a grid was generated using the WGS84 datum definition. Each grid cell value represents the distance in meters from the surface to the earth's center of mass. A complex combination of trigonometric functions was applied to create the representation of the ellipsoid. Then the DEM representing the earth's current relief was added to the ellipsoid raster.

 The map shows distances to the earth's center of mass. The areas highlighted in red represent mountains that are the farthest from the center of mass on the earth and are the areas of the lowest gravitational pull on the earth's surface.

The difference between the major and minor axes of the WGS84 ellipsoid is 42,770 meters. The difference between the length of the radius at the equator and one of the poles is 21,385 meters—only 0.33 percent of the radius. The "flattening" of the earth is, geometrically speaking, relatively insignificant but in terms of geography, it has a tremendous impact.

### If the Earth Stood Still

What would happen if the earth stopped spinning and the centrifugal effect ceased to force oceans to accumulate around the equator? It appears that the world's ocean would split into two polar oceans and leave the equatorial area totally dry. To model this hypothesis, a value of 6,371,146 meters—the distance from the earth's center indicates the approximate elevation of the sea level on the reference ellipsoid—was specified to separate water from land. For this "what if" simulation, the elevation of the sea level was based on the assumption that the volume of ocean water would be about the same as it is today.

### Melting Glaciers

 This map illustrates what would happen if all the glaciers melted. The cell values of this orthometric surface grid are related to MSL.

Returning to a geoid representation of the earth, one more simulation models an earth where all the glaciers have melted. This simulation might predict a future that is only a few hundred years distant if the large glaciers of Antarctica and Greenland, which currently cover approximately 10 percent of all land, melted as a result of global warming. If all the water in these glaciers were released, the MSL would rise about 80 meters above its current level.

### Conclusion

GIS makes it possible to explore the effects of different conceptualizations of the earth's shape and model a variety of global conditions.

### Acknowledgments

The author would like to thank his colleagues—Melita Kennedy, Lenny Kneller, Corey LaMar, and Marcelo Villacres—for their significant contributions to this article.