What model describes the shape of the Earth using mean sea level as a reference?

The geoid is the model that accurately represents the Earth's shape by accounting for variations in gravitational pull and topography, using mean sea level as its reference surface. It provides a more precise depiction of the Earth's physical form than simple geometric shapes like a sphere or spheroid because it reflects the irregularities of the Earth's gravitational field caused by factors such as mountains and oceanic trenches.

Mean sea level is crucial because it serves as a baseline for measuring elevations and depths on the Earth's surface. As a result, the geoid represents a theoretical surface where the force of gravity is computed to be constant. This makes it essential for various applications in GIS, such as determining heights and the representation of elevation data in a spatial context.

In contrast, while the spheroid and sphere are simplifications of the Earth’s shape, they do not account for the uneven distribution of mass or variations in gravity, and thus do not give a true representation of sea level or the Earth’s surface. A datum serves as the reference point for measurements but does not specifically describe the Earth’s shape. Therefore, the geoid is the most accurate model for defining the Earth with respect to mean sea level.