Define "geoid."

The geoid is defined as the equipotential surface of the Earth's gravity field that coincides with mean sea level. This means it is a hypothetical surface that reflects where water would naturally rest under the influence of gravity alone, without other factors like wind or tides. The geoid represents the shape of the Earth as influenced by its rotation and gravitational field, taking into account variations in mass distribution.

This concept is vital in geodesy as it serves as a reference surface for measuring elevations and understanding Earth's topography. It helps in determining the relationship between the mean sea level and the ellipsoidal surface used in mapping and GPS. Other options do not pertain to the geoid. For example, one option discusses the total area of the Earth's surface, which is unrelated to gravitational effects, while another focuses on temperature distribution and the atmosphere, which are not relevant to the geoid's application in geodesy and Earth measurement.