Johan Jacob Mohr

Three-dimensional glacial flow and surface elevation measured with radar interferometry

Outlet glaciers—which serve to drain ice from ice sheets—seem to be dynamically less stable in North Greenland than in South Greenland. Storstrømmen, a large outlet glacier in northeastern Greenland which surged between 1978 and 1984 (ref. 2), has been well studied. In general, neither glacier surge mechanisms nor the geographical distribution of the surges are well known. Conventional satellite radar interferometry can provide large-scale topography models with high resolution, and can measure the radar line-of-sight component of ice-flow vectors, but cannot map full vector flow fields. Here we present an interferometry method that combines observations from descending and ascending satellite orbits which, assuming ice flow parallel to the topographic surface, allows us to use the differing view angles to estimate full three-dimensional surface flow patterns. The accuracy of our technique is confirmed by the good agreement between our radar-based flow model and in situ Global Positioning System (GPS) reference data at Storstrømmen. Radar measurements such as these, made regularly and at high spatial density, have the potential to substantially enhance our understanding of glacier dynamics and ice-sheet flow, as well as improve the accuracy of glacier mass-balance estimates.

Geometric calibration of ERS satellite SAR images

Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed and calibrated by using the European Space Agency (ESA) transponders at Flevoland. The resulting accuracy of the slant range images corresponds to 10 m horizontally on the ground. The results are verified by using runway intersections and corner reflectors surveyed with differential GPS techniques. Based on a seven-year ERS-1 and a four-year ERS-2 time series, the long term stability is found to be sufficient to allow a single calibration covering the entire mission period. A descending and an ascending orbit tandem pair of the ESA calibration site on Flevoland, suitable for calibration of ERS SAR processors, is described to allow other researchers to geometrically calibrate their processing systems.

Three-dimensional surface velocities of Storstrømmen glacier, Greenland, derived from radar interferometry and ice-sounding radar measurements

Non-steady-state vertical velocities of up to 5 m y-1 exceed the vertical surface-parallel-flow components over much of the ablation area of Storstrommen, a large outlet glacier from the East Greenland ice sheet. Neglecting a contribution to the vertical velocity of this magnitude, results in substantial errors (up to 20%) also on the south north component of horizontal velocities derived by satellite synthetic aperture radar interferometry (InSAR) measurements. In many glacier environments the steady-state vertical velocity component required to balance the annual ablation rate is 5 to 10 m y-1 or more. This indicates that the surface parallel flow assumption may be problematic also for glaciers in steady state. Here we derive the three-dimensional surface velocity distribution of Storstrommen by using the principle of mass conservation to combine InSAR measurements from ascending and descending satellite tracks with airborne ice-sounding radar measurement of ice thickness. The results are compared to InSAR velocities previously derived by using the assumption of surface parallel flow, and to velocities obtained by Inin-situ GPS measurements. The velocities derived by using the principle of mass conservation are in better agreement with the GPS-velocities than the previously calculated velocities derived with the assumption of surface parallel flow.

Accuracy of three-dimensional glacier surface velocities derived from radar interferometry and ice-sounding radar measurements

We present a method for analyzing the errors involved in measuring three-dimensional glacier velocities with interferometric radar. We address the surface-parallel flow assumption and an augmented approach with a flux-divergence (FD) term. The errors in an interferometric ERS-1/-2 satellite radar dataset with ascending- and descending-orbit data covering Storstrommen glacier, northeast Greenland, are assessed. The FD error assessment is carried out on airborne 60 MHz ice-sounding radar data from the same area. A simple model of an interferometric radar system is developed and analyzed. The error sources considered include phase noise, atmospheric distortions, baseline calibration errors, a dry snow layer, and the stationary-flow assumption used in differential interferometry. The additional error sources in the analysis of FD errors are noise, bias and unknown variations of the ice thickness, and approximations of the ice-flow model. The example glacier is now building up following a surge. The analysis shows that in the case study presented the errors are small enough to justify the use of both the estimated surface-parallel flow term of the vertical velocity and the estimated FD term of the vertical velocity.

Controls on the Basal Water Pressure in Subglacial Channels Near the Margin of the Greenland Ice Sheet

Assuming a channelized drainage system in steady state, we investigate the influence of enhanced surface melting on the water pressure in subglacial channels, compared to that of changes in conduit geometry, ice rheology and catchment variations. The analysis is carried out for a specific part of the western Greenland ice-sheet margin between 668 N and 66830 0 N using new high-resolution digital elevation models of the subglacial topography and the ice-sheet surface, based on an airborne ice-penetrating radar survey in 2003 and satellite repeat-track interferometric synthetic aperture radar analysis of European Remote-sensing Satellite 1 and 2 (ERS-1/-2) imagery, respectively. The water pressure is calculated up-glacier along a likely subglacial channel at distances of 1, 5 and 9 km from the outlet at the ice margin, using a modified version of Rothlisbergers equation. Our results show that for the margin of the western Greenland ice sheet, the water pressure in subglacial channels is not sensitive to realistic variations in catchment size and mean surface water input compared to small changes in conduit geometry and ice rheology.

Coherent lidar modulated with frequency stepped pulse trains for unambiguous high duty cycle range and velocity sensing in the atmosphere

Range unambiguous high duty cycle coherent lidars can be constructed based on frequency stepped pulse train modulation, even continuously emitting systems could be envisioned. Such systems are suitable for velocity sensing of dispersed targets, like the atmosphere, at fast acquisition rates. The lightwave synthesized frequency sweeper is a suitable generator yielding fast pulse repetition rates and stable equidistant frequency steps. Theoretical range resolution profiles of modulated lidars are presented.

An Error Prediction Framework for Interferometric SAR Data

Three of the major error sources in interferometric synthetic aperture radar measurements of terrain elevation and displacement are baseline errors, atmospheric path length errors, and phase unwrapping errors. In many processing schemes, these errors are calibrated out by using ground control points (GCPs) (or an external digital elevation model). In this paper, a simple framework for the prediction of error standard deviation is outlined and investigated. Inputs are GCP position, a priori GCP accuracy, baseline calibration method along with a closed-form model for the covariance of atmospheric path length disturbances, and a model for phase unwrapping errors. The procedure can be implemented as a stand-alone add-on to standard interferometric processors. It is validated by using a set of single-frame interferograms acquired over Rome, Italy, and a double difference data set over Flevoland, The Netherlands.

A Tunable Closed-Form Model for the Structure Function of Tropospheric Delay

Several interferometric synthetic aperture radar applications could benefit from the availability of a closed-form model for the second-order statistics of atmospheric delay. Due to the variability of the latter, it would also be desirable for the model to be tunable to some acquisition-specific information, describing the atmospheric state. In this letter, a closed-form expression for the zenith delay structure function of tropospheric propagation delay is derived from a two-regime power spectral density function reported in the literature. The power at a specific spatial frequency is used as a free model parameter, which may be tuned to available measurements or, in the absence of these, to atmospheric statistics. The latter approach is used to compare the derived model with previously published results.

Mapping of a hydrological ice-sheet drainage basin on the West Greenland ice-sheet margin from ERS-1/-2 SAR interferometry, ice-radar measurement and modelling

Abstract The hydrological ice-sheet basin draining into the Tasersiaq lake, West Greenland (66°13’ N, 50°30’W), was delineated, first using standard digital elevation models (DEMs) for ice-sheet surface and bedrock, and subsequently using a new high-resolution dataset, with a surface DEM derived from repeat-track interferometric synthetic aperture radar (SAR) and a bedrock topography derived from an airborne 60 MHz ice-penetrating radar. The extent of the delineation was calculated from a water-pressure potential as a function of the ice-sheet surface and bedrock elevations and a hydraulic factor k describing the relative importance of the potential of the ice overburden pressure compared to the bedrock topography. Themeltwater run-off for the basin delineations was modelled with an energy-balance model calibrated with observed ice-sheet ablation and compared to a 25 year time series of measured basin run-off. The standard DEMs were found to be inadequate for delineation purposes, whereas delineations from high-resolution data were found to be very sensitive to changes in k in a non-linear way, causing a factor 5 change of basin area, corresponding to a doubling of the modelled runoff. The 50% standard deviation of the measured basin run-off could thus be explained by small year-to-year variations of the k-factor.

Remote sensing: Searching for new islands in sea ice

Tobias Island, discovered in 1993 by the German research vessel RV Polarstern, is a system of low-lying banks and shoals hidden in sea ice 70 km off the northeastern coast of Greenland. Here we use satellite radar interferometry and airborne laser scanning to show that this island is 2 km long and 35 m high — much larger than was originally reported. We have also been able to pinpoint the exact location of a stable area where a new group of small islands may be hidden. This demonstrates that satellite radar interferometry is an effective tool for finding ice-covered islands as well as for mapping them.