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The path a radar pulse takes through the atmosphere is never a straight line. Radar pulses are light waves with wavelengths of several centimeters. The troposphere (and to some degree the ionosphere) distorts the path slightly by slowing the wave down, causing a "delay" in the two-way return time of the echo relative to vacuum conditions. This delay varies according to the weather: temperature, humidity and pressure all affect the echo path.

The 3-D movement of a point on the ground over a 24-hour period due to the solid Earth tide. The red curve is the vertical movement, blue is the eastwards movement, green the northwards movement.

The Earth's continents are slowly moving and jostling each other; this is called continental drift. If map coordinates from a reference frame connected to one plate are to be compared to coordinates in a frame connected to another plate, this drift needs to be taken into account. The Eurasian plate is drifting at a rate of about 2.4 cm/year towards the north-east relative to WGS84, which is a global Cartesian reference frame with its origin at the center of mass of our planet.

"Piercing an apple"
from a distance of 700 km

Article in the Journal of Geodesy: http://www.springerlink.com/content/31nkj5177t778233/

A long-term investigation into the geometric quality provided by the German Aerospace Center's (DLR) TerraSAR-X satellite has revealed it to be astonishingly accurate and stable. From an altitude of 514 km and along a sideways line-of-sight distance of about 700 km, it is able to locate a point on the ground with an accuracy of just a few centimeters - about the size of an apple. This is possible not only thanks to the stability and precision of the system itself, but also SARLab's careful correction for various Earth processes that affect the image geometry.

TerraSAR-X is a satellite carrying a SAR (synthetic aperture radar) sensor able to obtain images of the Earth's surface with a spatial resolution of about 1 metre on the ground - providing the "sharpest" radar images currently available to civilians. SARLab collected a 16-month time-series of about 80 high-resolution images from the satellite over a test site in the west of Switzerland, Torny-le-Grand. Corner reflectors, which appear as bright points in SAR images, were used as reference points; their 3-D positions were known to within about a centimeter thanks to careful D-GPS measurements.

Animation showing how TerraSAR-X sends focused pulses sideways down to Earth to collect image information. The metallic corner reflectors at the test site reflect echoes directly back to the satellite, creating bright points in the resulting images. TerraSAR-X satellite animation copyright DLR; pulse-echo animation created by A. Schubert using Google Earth and Adobe After Effects.

Although these images look nice, the image "sharpness" alone tells us nothing about the 3-dimensional "map locations" of the image pixels. That's why the images are delivered along with geometry information, such as the satellite positions during the image acquisition. This extra information allows the images obtained to be projected into a map geometry of our choosing, so we can now assign latitude/longitude/height (or Easting/Northing/height) coordinates to each pixel. But if the inherent sub-metric accuracy of TerraSAR-X is needed, there's plenty of work left to be done...

At a resolution of 1 meter, the effect of the atmosphere on the radar echoes transmitted and received (used to "focus" the images) cannot be neglected. The atmosphere slows the radar waves down and bends it like a prism bends sunlight, and this results in longer echo-return times, which translate to distance measurements that are too large by up to a few meters if left uncorrected. To compensate for this distortion, SARLab collected weather data for each acquisition day and, using it, was able to simulate the distorted path of the radar echoes through the atmosphere. This allowed them to compensate for the "slowing" effect of the atmosphere for all pixels in the images and subsequently increase their geolocation accuracy, bringing each pixel to within decimeters of its "true" position.

But not only the atmosphere "distorts" the radar measurements. The lunar ocean tides are familiar to most people, but less well known is the fact that the Earth's solid crust is also pushed and pulled on by a complex dance between the lunar pull and "Coriolis" forces generated by the Earth's revolution about its axis (solid Earth tide). These forces cause the Earth's crust not only to wobble up and down, but also horizontally, causing points on the ground to "jiggle" around by up to about 20 cm. Luckily, this effect can also be modelled quite accurately and removed from the radar images, increasing their geolocation accuracy by a few more centimeters.

If the images from the satellite-mounted radar sensor are to be used within European map coordinates, then to attain true decimeter-level accuracy a final subtle but important effect needs to be accounted for. The satellite geometry is given in terms of the global geodetic reference frame WGS84, whose origin lies at the Earth's center of mass. However, European map projections are generally defined to move with the Eurasian tectonic plate so as to remain stable over many years. As it happens, the Eurasian plate is drifting towards the north-east at a rate of about 2.4 cm/year relative to WGS84. In Switzerland, the local map coordinates and WGS84 were last "synchronized" in 1989; since then, the local Swiss frame has been drifting away from WGS84. That means that satellite images acquired in 2010 are geometrically "out of synch" by about half a meter relative to Switzerland's maps! So when projecting the satellite images into our own map coordinates as accurately as possible, this relative drift also needs to be estimated and included in the transformation.

For each image obtained over the test site, SARLab modelled and removed the distortions caused by the atmosphere and crustal movements. They were able to show that the positions of the reference points in the images could be determined with a consistency of only a few centimeters. From an along-sight distance of about 700 km, this represents a remarkable feat made possible by the combination of precision technology and geoscience.

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