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The elevation of the ocean surface has been measured for over two decades from spaceborne altimeters. However, existing altimeter measurements are not adequate to characterize the dynamic variations of most inland water bodies, nor of ocean eddies at scales of less than about 100 km, notwithstanding that such eddies play a key role in ocean circulation and climate change. For terrestrial hydrology, in situ and spaceborne measurements of water surface elevation form the basis for estimates of water storage change in lakes, reservoirs, and wetlands, and of river discharge. However, storage in most inland water bodies, e.g., millions of Arctic lakes, is not readily measured using existing technologies. A solution to the needs of both surface water hydrology and physical oceanography communities is the measurement of water elevations along rivers, lakes, streams, and wetlands and over the ocean surface using swath altimetry. The proposed surface water and ocean topography (SWOT) mission will make such measurements. The core technology for SWOT is the Ka-band radar interferometer (KaRIN), which would achieve spatial resolution on the order of tens of meters and centimetric vertical precision when averaged over targets of interest. Average revisit times will depend upon latitude, with two to four revisits at low to mid latitudes and up to ten revisits at high latitudes per ~20-day orbit repeat period.