Recall that TOPEX/Poseidon orbits the Earth at an altitude of 1300 km. The altimeter sends several thousand radar pulses towards the ocean each second then measures the time for the pulse to return to the spacecraft. Not only does the computer have to match the right transmitted pulse with the right received pulse, but it has to compute the time of transit properly. An error in time of only a microsecond would mean an error of tens of centimeters.
To get the height of the satellite above the ocean, the time for the pulse to return has to be converted to range using the speed of light. However, the speed of light is constant only in a vacuum. The radar pulse travels through the atmosphere twice, where it is refracted by air molecules, water vapor, free electrons, and is partially scattered by surface waves. The size of these errors add up to more than 3 meters. However, all of them can be measured or modeled.
Finally, the precise location of the satellite needs to be known, since the sea-level is the difference between the satellite location above the center of the Earth and the height of the satellite above the ocean. If the satellite location were only good to 1 meter, then the sea-level measurement would only be good to 1 meter.
But, how accurate is the image on the previous slide? The accuracy is amazing, considering all of these problems listed above: about 2 to 3 cm (1 in). Thatís about the diameter of a quarter. We know this because we can compare sea-level measured by T/P with sea-level measured at the ocean surface with tide gauges.