Topographic Mapping



Figure 1: SAR diagram: Electromagnetic waves are transmitted and received perpendicular to the antenna, so an aircraft that flies for 100km simulates a 100km-long antenna (red jet trail) because it constantly emits and re-receives microwaves (blue lines) that travel perpendicular to its flight path.

Image credit: VM MAK

Figure 2: InSAR diagram: Rays S1 and S2 experience a phase shift relative to each other due to a difference in round trip distance. Their sum is recorded by the sensor after they bounce back. S'1 and S'2 (taken on the next pass, from a slightly different angle) experience a different phase shift dependent on the baseline and the terrain. If the baseline is known, the terrain can be determined by the phase shift not accounted for by baseline distance. 
Image credit: What-When-How

Radar instruments bounce microwaves off the surface of the Earth as the instrument is flown on an airplane or satellite. By measuring the time it takes the beam to reflect back to the sensor, the instrument can tell how far away the target is. Knowing the GPS coordinates and altitude of the aircraft or spacecraft, the beam angle, and the beam return time, the average elevation of the targeted area can be measured. This is called radar altimetry, and it usually makes use of synthetic aperture radar (SAR). SAR uses the flight path of the aircraft or satellite to simulate a long antenna (Figure 1). Electromagnetic waves are transmitted and received perpendicular to the antenna (see Wikipedia's radio antenna page for details) so an aircraft that flies for 100km simulates a 100km-long antenna because it constantly emits and re-receives microwaves that travel perpendicular to its flight path. Interferometric synthetic aperture radar (InSAR) can be used to measure the more detailed topography within the targeted area. When a satellite passes over the same point on Earth periodically (generally every few days or weeks), it is never at the exact same location. This difference in location can be known to within centimeters and is called the baseline. As shown in Figure 2, the beam is made up of many diverging rays, which interfere with each other upon return to the sensor due to differences in path length. The sensor will receive a return signal that is the sum of these interference signals. This signal will be different depending on the satellite's distance from the target. Because the baseline is known, this differences in phase between two passes can be subtracted (assuming flat ground) so that any remaining difference is due to topography (Figure 2). After mapping the topography, computer programs can again subtract out the resulting interference pattern. Any further phase discrepancies from the expected signal are then due to changes in topography between viewings, which is why InSAR has applications for many important studies involving small surface changes.


Radar microwaves are not absorbed by clouds, so they are great for mapping topography all over the Earth's surface, even in cloudy areas. Cassini used radar altimetry to create a topographic map of Saturn's moon Titan, where a thick blanket of haze prevents visible light penetration and prevents LIDAR or photogrammetric mapping. Radar mapping is also much less expensive than LIDAR because radar beams have a much higher divergence than lasers, so a wide swath can be mapped very quickly, and radar can be flown on satellites. It is more difficult to obtain high-resolution LIDAR data from a satellite because of atmospheric interference and the large ground distance between laser pulses due to the high speed, whereas SAR can map a continuous (and wide) swath. InSAR can be used to map topography as well as changes in topography at very high resolutions and is a great tool for studying ground movements due to earthquakes, inflation of volcanic domes before an eruption, and subsidence due to water and oil extraction or mine collapse. Radar altimetry has been used to map the ocean floor. For example, the radar altimeter on Geosat was able to measure the satellite's distance above the water to within centimeters. Cryosat-2 and Jason-1 have also been used for ocean-surface radar altimetry. Knowing the altitude of the satellite at any given time, this data can be used to measure the height of a bulge of water or the depth of a "valley." Bulges occur due to the gravitational attraction of massive oceanic plateaus, volcanoes, seamounts, and spreading ridges pulling water in from the sides. Valleys occur over low-density areas such as porous oil reserves.