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

A potential model intended to be a general purpose model for the condensed phases of water is presented. TIP4P/2005 is a rigid four site model which consists of three fixed point charges and one Lennard-Jones center. The parametrization has been based on a fit of the temperature of maximum density (indirectly estimated from the melting point of hexagonal ice), the stability of several ice polymorphs and other commonly used target quantities. The calculated properties include a variety of thermodynamic properties of the liquid and solid phases, the phase diagram involving condensed phases, properties at melting and vaporization, dielectric constant, pair distribution function, and self-diffusion coefficient. These properties cover a temperature range from 123to573K and pressures up to 40000bar. The model gives an impressive performance for this variety of properties and thermodynamic conditions. For example, it gives excellent predictions for the densities at 1bar with a maximum density at 278K and an aver...

http://cacharro.quim.ucm.es/publicaciones/JCP_123_234505_2005.pdf

A general purpose model for the condensed phases of water: TIP4P/2005

The term "tipping point" commonly refers to a critical threshold at which a tiny perturbation can qualitatively alter the state or development of a system. Here we introduce the term "tipping element" to describe large-scale components of the Earth system that may pass a tipping point. We critically evaluate potential policy-relevant tipping elements in the climate system under anthropogenic forcing, drawing on the pertinent literature and a recent international workshop to compile a short list, and we assess where their tipping points lie. An expert elicitation is used to help rank their sensitivity to global warming and the uncertainty about the underlying physical mechanisms. Then we explain how, in principle, early warning systems could be established to detect the proximity of some tipping points.

/pdf/tipping-elements-in-the-earth-s-climate-system-3h0whqwzeb.pdf

Tipping elements in the Earth's climate system

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.

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

The use of SAR interferometry is often impeded by decorrelation from thermal noise, temporal change, and baseline geometry. Power spectra of interferograms are typically the sum of a narrow-band component combined with broad-band noise. We describe a new adaptive filtering algorithm that dramatically lowers phase noise, improving both measurement accuracy and phase unwrapping, while demonstrating graceful degradation in regions of pure noise. The performance of the filter is demonstrated with SAR data from the ERS satellites over the Jakobshavns glacier of Greenland.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/1998GL900033

Radar interferogram filtering for geophysical applications

Satellite radar interferometry (SRI) provides a sensitive means of monitoring the flow velocities and grounding-line positions of ice streams, which are indicators of response of the ice sheets to climatic change or internal instability. The detection limit is about 1.5 millimeters for vertical motions and about 4 millimeters for horizontal motions in the radar beam direction. The grounding line, detected by tidal motions where the ice goes afloat, can be mapped at a resolution of ∼0.5 kilometer. The SRI velocities and grounding line of the Rutford Ice Stream, Antarctica, agree fairly well with earlier ground-based data. The combined use of SRI and other satellite methods is expected to provide data that will enhance the understanding of ice stream mechanics and help make possible the prediction of ice sheet behavior.

https://science.sciencemag.org/content/sci/262/5139/1525.full.pdf

Satellite Radar Interferometry for Monitoring Ice Sheet Motion: Application to an Antarctic Ice Stream

Based on observations of the 1982–1983 surge of Variegated Glacier, Alaska, a model of the surge mechanism is developed in terms of a transition from the normal tunnel configuration of the basal water conduit system to a linked cavity configuration that tends to restrict the flow of water, resulting in increased basal water pressures that cause rapid basal sliding. The linked cavity system consists of basal cavities formed by ice-bedrock separation (cavitation), ∼1 m high and ∼10 m in horizontal dimensions, widely scattered over the glacier bed, and hydraulically linked by narrow connections where separation is minimal (separation gap ≲ 0.1 m). The narrow connections, called orifices, control the water flow through the conduit system; by throttling the flow through the large cavities, the orifices keep the water flux transmitted by the basal water system at normal levels even though the total cavity cross-sectional area (∼200 m^2) is much larger than that of a tunnel system (∼10 m^2). A physical model of the linked cavity system is formulated in terms of the dimensions of the “typical” cavity and orifice and the numbers of these across the glacier width. The model concentrates on the detailed configuration of the typical orifice and its response to basal water pressure and basal sliding, which determines the water flux carried by the system under given conditions. Configurations are worked out for two idealized orifice types, step orifices that form in the lee of downglacier-facing bedrock steps, and wave orifices that form on the lee slopes of quasisinusoidal bedrock waves and are similar to transverse “N channels.” The orifice configurations are obtained from the results of solutions of the basal-sliding-with-separation problem for an ice mass constituting of linear half-space of linear rheology, with nonlinearity introduced by making the viscosity stress-dependent on an intuitive basis. Modification of the orifice shapes by melting of the ice roof due to viscous heat dissipation in the flow of water through the orifices is treated in detail under the assumption of local heat transfer, which guarantees that the heating effects are not underestimated. This treatment brings to light a melting-stability parameter Ξ that provides a measure of the influence of viscous heating on orifice cavitation, similar but distinct for step and wave orifices. Orifice shapes and the amounts of roof meltback are determined by Ξ. When Ξ ≳ 1, so that the system is “viscous-heating-dominated,” the orifices are unstable against rapid growth in response to a modest increase in water pressure or in orifice size over their steady state values. This growth instability is somewhat similar to the jokulhlaup-type instability of tunnels, which are likewise heating-dominated. When Ξ ≲ 1, the orifices are stable against perturbations of modest to even large size. Stabilization is promoted by high sliding velocity ν, expressed in terms of a ν^(−½) and ν^(−1) dependence of Ξ for step and wave cavities. The relationships between basal water pressure and water flux transmitted by linked cavity models of step and wave orifice type are calculated for an empirical relation between water pressure and sliding velocity and for a particular, reasonable choice of system parameters. In all cases the flux is an increasing function of the water pressure, in contrast to the inverse flux-versus-pressure relation for tunnels. In consequence, a linked cavity system can exist stably as a system of many interconnected conduits distributed across the glacier bed, in contrast to a tunnel system, which must condense to one or at most a few main tunnels. The linked cavity model gives basal water pressures much higher than the tunnel model at water fluxes ≳1 m^(3/s) if the bed roughness features that generate the orifices have step heights or wave amplitudes less than about 0.1 m. The calculated basal water pressure of the particular linked cavity models evaluated is about 2 to 5 bars below ice overburden pressure for water fluxes in the range from about 2 to 20 m^(3/s), which matches reasonably the observed conditions in Variegated Glacier in surge; in contrast, the calculated water pressure for a single-tunnel model is about 14 to 17 bars below overburden over the same flux range. The contrast in water pressures for the two types of basal conduit system furnishes the basis for a surge mechanism involving transition from a tunnel system at low pressure to a linked cavity system at high pressure. The parameter Ξ is about 0.2 for the linked cavity models evaluated, meaning that they are stable but that a modest change in system parameters could produce instability. Unstable orifice growth results in the generation of tunnel segments, which may connect up in a cooperative fashion, leading to conversion of the linked cavity system to a tunnel system, with large decrease in water pressure and sliding velocity. This is what probably happens in surge termination. Glaciers for which Ξ ≲ 1 can go into surge, while those for which Ξ ≳ 1 cannot. Because Ξ varies as α^(3/2) (where α is surface slope), low values of Ξ are more probable for glaciers of low slope, and because slope correlates inversely with glacier length in general, the model predicts a direct correlation between glacier length and probability of surging; such a correlation is observed (Clarke et al., 1986). Because Ξ varies inversely with the basal shear stress τ, the increase of τ that takes place in the reservoir area in the buildup between surges causes a decrease in Ξ there, which, by reducing Ξ below the critical value ∼1, can allow surge initiation and the start of a new surge cycle. Transition to a linked cavity system without tunnels should occur spontaneously at low enough water flux, in agreement with observed surge initiation in winter.

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Glacier surge mechanism based on linked cavity configuration of the basal water conduit system

The hundredfold speedup in glacier motion in a surge of the kind the kind that took place in Variegated Glacier in 1982-1983 is caused by the buildup of high water pressure in the basal passageway system, which is made possible by a fundamental and pervasive change in the geometry and water-transport characteristics of this system. The behavior of the glacier in surge has many remarkable features, which can provide clues to a detailed theory of the surging process. The surge mechanism is akin to a proposed mechanism of overthrust faulting.

Glacier surge mechanism: 1982-1983 surge of variegated glacier, alaska.

Boreholes drilled to the bottom of ice stream B in the West Antarctic Ice Sheet reveal that the base of the ice stream is at the melting point and the basal water pressure is within about 1.6 bars of the ice overburden pressure. These conditions allow the rapid ice streaming motion to occur by basal sliding or by shear deformation of unconsolidated sediments that underlie the ice in a layer at least 2 meters thick. The mechanics of ice streaming plays a role in the response of the ice sheet to climatic change.

Physical Conditions at the Base of a Fast Moving Antarctic Ice Stream

Contrary to what has recently been assumed in modeling the proposed deforming bed mechanism for the rapid motion of Antarctic ice streams, the rheology of water saturated till is probably highly nonlinear, according to information from soil mechanics and preliminary experiments on till from the base of Ice Stream B. The equivalent flow law exponent n is probably as high as ∼100, and the nonlinearities of the shear stress and effective pressure dependences are closely linked. The high nonlinearity has important consequences for the deforming bed mechanism. A flow system operating by this mechanism can be unstable as a result of feedback from the generation of basal water by shear heating of basal till. The short-term feedback effect is analyzed for a perturbation in a model ice stream in which the basal meltwater is transported through a distributed system of narrow gap-conduits at the ice-till interface. Although the analysis is approximate and some of the system parameters are poorly known, the results suggest that the deforming bed mechanism is unstable for n > ∼ 20. The apparent lack of such an instability in the currently active ice streams implies that their motion is controlled not by the deforming bed mechanism but by some other as yet unidentified mechanism.

/pdf/rheological-nonlinearity-and-flow-instability-in-the-4b96tewyrl.pdf

Barclay Kamb

Papers

Satellite Radar Interferometry for Monitoring Ice Sheet Motion: Application to an Antarctic Ice Stream

Glacier surge mechanism based on linked cavity configuration of the basal water conduit system

Glacier surge mechanism: 1982-1983 surge of variegated glacier, alaska.

Physical Conditions at the Base of a Fast Moving Antarctic Ice Stream

Rheological nonlinearity and flow instability in the deforming bed mechanism of ice stream motion