![]() The surface of global undulations was calculated based on altimetric observations and very precise (up to two centimeters) measurements taken from the TOPEX/POSEIDON satellite. An ellipsoidor flattened sphereis used to represent the geometric model of the earth. ![]() GPS uses an ellipsoid coordinate system for both its horizontal and vertical datums. GPS has transformed how altitude at any spot is measured. Although for practical purposes, at the coastline the geoid and MSL surfaces are assumed to be essentially the same, at some spots the geoid can actually differ from MSL by several meters. Previously, there was no way to accurately measure the geoid so it was roughly approximated by MSL. Because the geoid surface cannot be directly observed, heights above or below the geoid surface can't be directly measured and are inferred by making gravity measurements and modeling the surface mathematically. ![]() By definition, the geoid describes the irregular shape of the earth and is the true zero surface for measuring elevations. It can be regarded as extending under the continents and is a close approximation of the geoid. The MSL surface is in a state of gravitational equilibrium. However, zero elevation as defined by Spain is not the same zero elevation defined by Canada, which is why locally defined vertical datums differ from each other. Since the sea surface conforms to the earth's gravitational field, MSL also has slight hills and valleys that are similar to the land surface but much smoother. Unfortunately for mapmakers, sea level is not a simple surface. The zero surface referenced by elevation is called a vertical datum. MSL is defined as the zero elevation for a local area. This definition averages out tidal highs and lows caused by the changing effects of the gravitational forces from the moon and sun. MSL is usually described as a tidal datum that is the arithmetic mean of hourly water elevations observed over a specific 19-year cycle. Geodesists once believed that the sea was in balance with the earth's gravity and formed a perfectly regular figure. ![]() The figure above shows the relationships between the different models and explains the reasons why the two hardly ever match spatially.įor generations, the only way to express topographic or bathymetric elevation was to relate it to sea level. The signed difference between the two heightsthe difference between the ellipsoid and geoidis the geoid height (N). The traditional, orthometric height (H) is the height above an imaginary surface called the geoid, which is determined by the earth's gravity and approximated by MSL. The GPS uses height (h) above the reference ellipsoid that approximates the earth's surface. The accuracy of GPS height measurements depends on several factors but the most crucial one is the "imperfection" of the earth's shape. ![]() Controlled by the gravitational potential of the earth, these irregularities form very gentle but massive "hills" and "valleys." This astonishing finding was made possible through the use of GPS, a technology designed by the United States Department of Defense to revolutionize navigation for the U.S. These irregularities are an order of magnitude greater than experts had predicted. However, only recently have the more substantial irregularities in the surface created by the global mean sea level (MSL) been observed. That the earth does not have a geometrically perfect shape is well established, and the geoid is used to describe the unique and irregular shape of the earth. This chance discovery led to the development of the antibiotic penicillin. When a staphylococci bacteria culture was mistakenly contaminated with a common mold, the clear area between the mold and the bacterial colony led to the conclusion that the mold, Penicillin notatum, produced a compound that inhibited the growth of bacteria. When European explorers set out to find a shortcut to India, they discovered the New World. However, even the most mathematically sophisticated geoid can only approximate the real shape of the earth.įrequently research and technology endeavors have unforeseen but positive outcomes. A significant difference exists between this mathematical model and the real object. The shape of the ellipsoid was calculated based on the hypothetical equipotential gravitational surface. \Īll mathematical drawings and images were created with GeoGebra.By Witold Fraczek, Esri Applications Prototype Lab The altitude of such a triangle can be calculated using the following formula: ![]()
0 Comments
Leave a Reply. |