# Ellipsoid geoid relationship with god

### 1-Mean Sea Level, GPS, and the Geoid

infinity mercy of God, this thesis would not have seen the light of day. To God .. Figure The relationship between orthometric height, ellipsoidal Figure The relationship among the quasigeoid, the geoid and the. The shape of the ellipsoid was calculated based on the hypothetical the two heights—the difference between the ellipsoid and geoid—is the geoid height (N). Finally I am grateful to the Almighty God, for the provision of the necessary spiritual .. Figure Relationship between geoid and reference ellipsoid.

The Earth is not a true sphere, it is an ellipsoid, as Earth is slightly wider than it is tall. Although other models exist, the ellipsoid is the best fit to Earth's true shape. Geoid Like the ellipsoid, the geoid is a model of the Earth's surface. According to the University of Oklahoma, "the geoid is a representation of the surface of the earth that it would assume, if the sea covered the earth. Dynamic effects, such as waves and tides, are excluded in the geoid model.

Sciencing Video Vault Topographic Elevation Topographic elevation also known as "topographic height" is a more accurate model of the earth than either the geoid or the ellipsoid.

Topographers measure the Earth's height using either satellite or aerial photography.

### Ellipsoids | The Nature of Geographic Information

This model's elevation values are calculated relative to the average sea level in various places across the planet. Key Differences Unlike the geoid, the ellipsoid assumes that Earth's surface is smooth. Additionally, it assumes that the planet is completely homogeneous.

If this were true, Earth could have no mountains or trenches. Further, the mean sea level would coincide with the ellipsoid surface. Geodesists once believed that the sea was in balance with the earth's gravity and formed a perfectly regular figure. MSL is usually described as a tidal datum that is the arithmetic mean of hourly water elevations observed over a specific year cycle.

This definition averages out tidal highs and lows caused by the changing effects of the gravitational forces from the moon and sun. MSL is defined as the zero elevation for a local area. The zero surface referenced by elevation is called a vertical datum. Unfortunately for mapmakers, sea level is not a simple surface. 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.

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. The MSL surface is in a state of gravitational equilibrium. It can be regarded as extending under the continents and is a close approximation of the geoid. By definition, the geoid describes the irregular shape of the earth and is the true zero surface for measuring elevations. 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.

Previously, there was no way to accurately measure the geoid so it was roughly approximated by MSL. 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. Differing Measurements GPS has transformed how altitude at any spot is measured. GPS uses an ellipsoid coordinate system for both its horizontal and vertical datums.

This data was represented in the Earth Geodetic Model EGM96which is also referred to as the spherical harmonic model of the earth's gravitational potential. Conceptually, this precisely calculated ellipsoid, called an oblate ellipsoid of revolution, was intended to replicate the MSL as the main geodetic reference or vertical datum.

If this ellipsoid vertical datum is used, height above the ellipsoid will not be the same as MSL and direct elevation readings for most locations will be embarrassingly off. This is caused, in part, because the GPS definition of altitude does not refer to MSL, but rather to a gravitational surface called the reference ellipsoid.

Because the reference ellipsoid was intended to closely approximate the MSL, it was surprising when the two figures differed greatly. These measurements have demonstrated that neither human error nor GPS inaccuracies are responsible for the sometimes substantial discrepancies between ellipsoid and MSL measurements.

## 14. Ellipsoids

In fact, the three-dimensional surface created by the earth's sea level is not geometrically correct, and its significant irregularities could not be mathematically calculated; this explains the difference between the ellipsoid-based GPS elevation readings and elevations shown on accurate topographic maps. A brief examination of elevation readings for Esri headquarters in Redlands, California, demonstrates these differences.

The campus elevation is shown on topographic quadrangle maps and high-resolution digital elevation models DEMs for the area as approximately meters above MSL.