This is a map of the "geoid" in the vicinity of Hawai'i. If the Earth were all water, or at least if you cut a bunch of canals through the continents so that water could flow freely between the oceans, the geoid would be the surface of that water. This imaginary body of water (the geoid) reacts to the force of gravity, which is not constant everywhere on Earth. Where the force of gravity is stronger more water will be attracted and flow into the area making the geoid height higher. Areas with lower gravity will be the places that give up this water and there the geoid height will be lower. In Hawai'i, however, there is no need to have an imaginary surface of water because we're surrounded by the Pacific Ocean. Does this mean that the ocean is not "flat" in the vicinity of Hawai'i? Yes! The excess of dense mantle material provided by the upwelling hotspot means that the force of gravity is higher centered over the hotspot. The ocean surface is actually tilted upwards toward the big island of Hawai'i. The units are in meters, meaning that off the north coast of the big island the geoid is about 22 meters higher than the reference level. You couldn't actually see this tilting of the ocean surface with your eyes because it is very gradual and would be masked by waves. However, in the steepest parts of this geoid anomaly, if you use celestial navigation (which also relies on gravity to tell you the relationship between the stars and "down"), you can be off by up to 1 km. (Data courtesy H. Haack).
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