The elevation of the surface of the ocean and freshwater bodies on land holds key information on many important processes of the Earth System. The elevation of the ocean surface, called ocean surface topography, has been measured by conventional nadirlooking radar altimeter for the past two decades. The data collected have been used for the study of large-scale circulation and sea level change. However, the spatial resolution of the observations has limited the study to scales larger than about 200 km, leaving the smaller scales containing substantial kinetic energy of ocean circulation that is responsible for the flux of heat, dissolved gas and nutrients between the upper and the deep ocean. This flux is important to the understanding of the ocean's role in regulatingfuture climate change.The elevation of the water bodies on land is a key parameter required for the computation of storage and discharge of freshwater in rivers, lakes, and wetlands. Globally, the spatial and temporal variability of water storage and discharge is poorly known due to the lack of well-sampled observations. In situ networks measuring river flows are declining worldwide due to economic and political reasons. Conventional altimeter observations suffers from the complexity of multiple peaks caused by the reflections from water, vegetation canopy and rough topography, resulting in much less valid data over land than over the ocean. Another major limitation is the large inter track distance preventing good coverage of rivers and other water bodies.This document provides descriptions of a new measurement technique using radar interferometry to obtain wide-swath measurement of water elevation at high resolution over both the ocean and land. Making this type of measurement, which addresses the shortcomings of conventional altimetry in both oceanographic and hydrologic applications, is the objective of a mission concept called Surface Water and Ocean Topography (SWOT), which was recommended by the National Research Council's first decadal survey of NASA's Earth science program. This document provides wide-ranging examples of research opportunities in oceanography and land hydrology that would be enabled by the new type of measurement. Additional applications in many other branches of Earth System science ranging from ocean bathymetry to sea ice dynamics are also discussed. Many of the technical issues in making the measurement are discussed as well. Also presented is a preliminary design of the SWOT Mission concept, which is being jointly developed by NASA and CNES, with contributions from the Canadian Space Agency.