There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Cationminus signpi Interaction.

Synthetic aperture radar interferometry is an imaging technique for measuring the topography of a surface, its changes over time, and other changes in the detailed characteristic of the surface. By exploiting the phase of the coherent radar signal, interferometry has transformed radar remote sensing from a largely interpretive science to a quantitative tool, with applications in cartography, geodesy, land cover characterization, and natural hazards. This paper reviews the techniques of interferometry, systems and limitations, and applications in a rapidly growing area of science and engineering.

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Synthetic aperture radar interferometry

In this paper, we provide a review of the different approaches used for target decomposition theory in radar polarimetry. We classify three main types of theorem; those based on the Mueller matrix and Stokes vector, those using an eigenvector analysis of the covariance or coherency matrix, and those employing coherent decomposition of the scattering matrix. We unify the formulation of these different approaches using transformation theory and an eigenvector analysis. We show how special forms of these decompositions apply for the important case of backscatter from terrain with generic symmetries.

A review of target decomposition theorems in radar polarimetry

Geophysical applications of radar interferometry to measure changes in the Earth's surface have exploded in the early 1990s. This new geodetic technique calculates the interference pattern caused by the difference in phase between two images acquired by a spaceborne synthetic aperture radar at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide an unsurpassed spatial sampling density (∼100 pixels km−2), a competitive precision (∼1 cm), and a useful observation cadence (1 pass month−1). They record movements in the crust, perturbations in the atmosphere, dielectric modifications in the soil, and relief in the topography. They are also sensitive to technical effects, such as relative variations in the radar's trajectory or variations in its frequency standard. We describe how all these phenomena contribute to an interferogram. Then a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS-2, JERS-1, and RADARSAT. The next chapter suggests some guidelines for interpreting an interferogram as a geophysical measurement: respecting the limits of the technique, assessing its uncertainty, recognizing artifacts, and discriminating different types of signal. We then review the geophysical applications published to date, most of which study deformation related to earthquakes, volcanoes, and glaciers using ERS-1 data. We also show examples of monitoring natural hazards and environmental alterations related to landslides, subsidence, and agriculture. In addition, we consider subtler geophysical signals such as postseismic relaxation, tidal loading of coastal areas, and interseismic strain accumulation. We conclude with our perspectives on the future of radar interferometry. The objective of the review is for the reader to develop the physical understanding necessary to calculate an interferogram and the geophysical intuition necessary to interpret it.

/pdf/radar-interferometry-and-its-application-to-changes-in-the-2xi2itqotn.pdf

Radar interferometry and its application to changes in the Earth's surface

C-band synthetic aperture radar (SAR) imagery from the European Space Agency's ERS-1 satellite reveals the basic zonation of the surface of the Greenland Ice Sheet. The zones have backscatter signatures related to the structure of the snowpack, which varies with the balance of accumulation and melt at various elevations. The boundaries of zones can be accurately located with the use of this high-resolution imagery. The images also reveal a large flow feature in northeast Greenland that is similar to ice streams in Antarctica and may play a major role in the discharge of ice from the ice sheet.

https://science.sciencemag.org/content/sci/262/5139/1530.full.pdf

Greenland Ice Sheet Surface Properties and Ice Dynamics from ERS-1 SAR Imagery

[1] RADARSAT data from the 1997 Antarctic Mapping Mission are used interferometrically to solve for the 3-dimensional surface ice motion in the interior of the West Antarctic Ice Sheet (WAIS). An area of ∼125 km2 in a tributary of the Kamb Ice Stream slumped vertically downwards by up to ∼50 cm between September 26 and October 18, 1997. Areas in the Bindschadler Ice Stream also exhibited comparable upward and downward surface displacements. As the uplift and subsidence features correspond to sites at which the basal water apparently experiences a hydraulic potential well, we suggest transient movement of pockets of subglacial water as the most likely cause for the vertical surface displacements. These results, and related lidar observations, imply that imaging the change in ice surface elevation can help reveal the key role of water in the difficult-to-observe subglacial environment, and its important influence on ice dynamics.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004GL021387

Evidence for subglacial water transport in the West Antarctic Ice Sheet through three‐dimensional satellite radar interferometry

Early 1960's reconnaissance satellite images are compared to more recent image and map data in an inter- annual and seasonal study of West Central Greenland margin fluctuations. From 1962 to 1992, ice sheet margins to the north and south of Jakobshavn Glacier retreated despite a decline in average summer temperatures. The retreat may be reversing along the southern flank of the ice stream where regional mass balance estimates are positive. From 1950 to fluctuated -2.5 km around its annual mean position. The total calving flux during the summer is more than six times that during winter. We identified that summer melting and the break-up of sea ice and icebergs in the fjord are important in controlling the rate of iceberg production. If correct, calving rates may be expected to increase should climate become warmer in the near future.

/pdf/jakobshavn-glacier-west-greenland-30-years-of-spaceborne-wjja7yutxc.pdf

Jakobshavn Glacier, west Greenland: 30 years of spaceborne observations

The University of Kansas developed a coherent radar depth sounder during the 1980s. This system was originally developed for glacial ice-thickness measurements in the Antarctic. During the field tests in the Antarctic and Greenland, we found the system performance to be less than optimum. The field tests in Greenland were performed in 1993, as a part of the NASA Program for Arctic Climate Assessment (PARCA). We redesigned and rebuilt this system to improve the performance. The radar uses pulse compression and coherent signal processing to obtain high sensitivity and fine along-track resolution. It operates at a center frequency of 150 MHz with a radio frequency bandwidth of about 17 MHz, which gives a range resolution of about 5 m in ice. We have been operating it from a NASA P-3 aircraft for collecting ice-thickness data in conjunction with laser surface-elevation measurements over the Greenland ice sheet during the last 4 years. We have demonstrated that this radar can measure the thickness of more than 3 km of cold ice and can obtain ice-thickness information over outlet glaciers and ice margins. In this paper we provide a brief survey of radar sounding of glacial ice, followed by a description of the system and subsystem design and performance. We also show sample results from the field experiments over the Greenland ice sheet and its outlet glacicrs.

/pdf/an-improved-coherent-radar-depth-sounder-48jy7c4h5p.pdf

Kenneth C. Jezek

Papers

Greenland Ice Sheet Surface Properties and Ice Dynamics from ERS-1 SAR Imagery

Evidence for subglacial water transport in the West Antarctic Ice Sheet through three‐dimensional satellite radar interferometry

Jakobshavn Glacier, west Greenland: 30 years of spaceborne observations

An improved coherent radar depth sounder

Radarsat Antarctic Mapping Project digital elevation model version 2