INTEGRAL - Methodology

   



Main Tasks

The changes of a glacier's shape and of its surface structures are usually of such a magnitude that they require map revision almost as frequently as do the heavily populated areas, where civic activities rapidly change the surface of the earth (Blachut & Müller 1966).


Rapid glacier changes, the lack of reliable basic control, and frequently disappointing quality of reference models represent a significant obstacle to operational monitoring of large glacial complexes, detailed and equivalent modelling of glacier dynamics and assessing main trends in the status of land ice resources from remote sensing surveys. The factual knowledge about the regional and seasonal specifics of glacial dynamics is very limited, integral estimations of glacier changes at continental level are very few in number, and "…the representation of land-ice processes in global climate models remains rudimentary. In particular, we are lacking information on the most important maritime glacier areas" (IPCC 2001).

The main task of the INTEGRAL project is to promote an advanced observation technology based on the complementary use of satellite interferometry and altimetry for generating and upgrading morphological and rheological models of the largest European tidewater glaciers and iintegral estimations of glacier activity and changes at the continental scale. In the proposed research, main emphasis is put on the methodological set-up, algorithmic design, and the development of program tools for the efficient fusion of INSAR models with altimetry data and its practical applications aimed at

  • detailed topokinetic studies and modelling of structural morphology, rheology, and alterations of large ice caps and domes in the European Arctic Sector;
  • detecting spatial changes of European ice coasts and appraising relevant glaciomarine interactions along maritime margins of ice domes and calving fronts of tidewater glaciers;
  • measurement and variational analysis of rheological and mass-balance characteristics of several big alpine glaciers associated with the hydropower production;
  • integral evaluation, interpretation and inventorying of glacier changes at the pan-European scale, intercomparison, verification and representation of results in the form of value-added INSAR products and image maps;
  • arguing an advanced concept for the long-term satellite monitoring of large European glacial complexes, assessing and forecasting main tendencies in the state of land ice resources and related socio-economic impacts in response to climate change.

The underlying concept of the project is to compensate the lack of reliable basic, especially vertical, control and accurate reference topographic models (GCPs, DEMs), which are needed for precise interferometric modelling of large European glacial complexes, with satellite altimetry, both radar and lidar, and to apply

  • single-pass altimetry data of glacier topography to the reliable interpretation, geocoding and upgrading single SAR interferometric and radargrammetric models, and adjusting INSAR blocks;
  • multi-pass / multi-source altimetry data on glacier changes to referencing, calibrating and interpreting differential / multitemporal INSAR and radargrammetric models,

thus, updating the information content and enhancing the accuracy, integrity, durability, and versatility of glacier interferometric / image models, both available and subsequent.

The research is considered as a preparatory stage for the upcoming ESA CryoSat mission. Besides, we want to support the ongoing national and international research activities devoted to the preparation and fulfillment of the International Polar Year 2007-2009 with appropriate services and value-added products derived from spaceborne interferometric and altimetric data. Satellite remote sensing data obtained by post-operational, operational and upcoming systems such as ERS, ENVISAT and CRYOSAT will be received from the European Space Agency under the CryoSat AO contract No. 2611 "Supplementing interferometric glacier models with altimetry data" (SIGMA, PI - A.Sharov) and from other AO projects. ICESAT-GLAS lidar altimetry data will be obtained from the NSIDC User Services (Data Pool) and/or from the EOS Data Gateway under the agreement with the ICESat/GLAS Science Team.


Data Gaps

It is obvious that the European ice coasts standing at the forefront of glaciomarine interactions represent the most varied elements of the arctic coastline, which grow shorter under current environmental settings. The most retreat of ice coasts amounting to several hundred meters across the shore each year was detected at fronts of calving tidewater glaciers. This retreat is presumably related with the dominance of ice-loss processes at glacier fronts including sublimation, melting, marine abrasion and calving over the influx of glacier ice to calving faces. The rate of retreat dL/dt can be defined as a negative difference between the mean ice speed at the glacier front u and the rate of frontal ablation uc , i.e.

dL/dt = u - uc

where L is the glacier length, t is time interval, and uc is sometimes called a mean calving speed because the effect of both melting and sublimation is small compared with that of calving of icebergs (Hanson et al. 2000).

Mass-balance estimates are available only for few glaciers, and we still do not know whether the increased ablation mainly affects the current retreat of most European tidewater glaciers or the decelerated ice flow has a guiding influence on their retreat. Hence, both variables in the right part of the Eq.1 are considered as principal unknowns in environmental forcing related to climatic changes.

Calving speed increases with water depth, temperature and longitudinal strain rate, and the ice-coast sensitivity to a change in one or more of these factors depends primarily on the position of the glacier face with respect to the sea level, the ice thickness and the configuration of the glacier bed. The information about the heights of ice coasts given in available topographic maps and hydrographic charts is extremely scarce, obsolete and inaccurate. In the close vicinity of calving ice shores, bathymetric marks are not available, bathymetric contours are broken within 1 km offshore and the possible water depths at ice walls and fronts are usually unknown. Hence, only few data on ice thickness at glacier fronts can be derived from available maps. There is very little factual knowledge on ice flow velocities at glacier fronts, and the rate of change in ice flow is practically unidentified. The total ice discharge through maritime glacier fronts on a continental scale remains largely uncertain.

Ice divides separating adjacent drainage basins on large ice masses set up the spatial limits and boundary conditions for the rheological image modelling of individual outlet glaciers. As soon as the individual drainage basin is identified, one can determine simple glacier morphometric quantities such as length, area, highest positions, etc., and predefine ice flow directions. General morphometric characteristics of glaciation in FJL and NZ derived from aerial surveys in the 1950-s (Vinogradov et al. 1965, Varnakova et al. 1978) are not very reliable at present. Some recent morphometric studies related with the identification of major divides and drainage basins in FJL using spaceborne image data were published in (Dowdeswell et al. 1999). The exact location of other ice divides still remains uncertain. At the moment of writing this paper we had no reliable data on temporal changes in the structure and location of ice-divides systems on large ice masses in the Barents Sea region. In the view of drastic variations in glacial borders, any evidence for the structural instability in glacial morphology might lead to a number of interesting hypotheses (Sharov 1997).


Techniques for Glacier Monitoring

Two different methodological variants of regional glacier monitoring depending on the availability of reliable up-to-date cartographic materials covering the glacial area will be developed and tested:

  • Retrospective (background) monitoring is based mostly on the comparison of available maps and published geographic data, and usually does not require additional data and substantial (extensive) glaciological surveys. Methodologically, this is the simplest variant of monitoring, which can be performed wholly in the lab with minimum efforts and at lowest expenses. Excluding pure historical tasks, this approach requires homogeneous mutidate cartographic materials for the whole study region. In general, the technological scheme of this approach can be represented as "first mapping, then monitoring (change detection)".

  • Prospective (foreground) monitoring is applied under the lack of reliable (comparable) maps from different years and foresees the performance of new glaciological surveys and the acquisition of modern image data. This approach is quite laborious, since it requires much fieldwork and data processing / modelling. The advantage of this variant is that it provides up-to-date novel results at hand and better suits for change detection, modelling and, especially, forecast in the glacier environment with poor cartographic knowledge. In such glacier regions , this variant aids in deciding on the revision of available standard map series. The map revision begins after the monitoring is performed and the technological scheme looks like "first monitoring (change detection and forecast), then mapping".

In the INTEGRAL project, the majority of glacier monitoring will be performed on the prospective basis because the history of explorations was typically short, available maps were usually obsolete and typical rates of changes were unknown. The prospective approach will be realised using four principal groups of methods:

  • Methods of data acquisition / processing including terrestrial, airborne and spaceborne surveys based on
    • geodetic-topographic-glaciological measurements in situ, e.g. tacheometry, DGPS, laser scanning etc.;
    • conventional photo- and radargrammetric image processing, both mono and stereo, shape-from-shading;
    • SAR interferometry (INSAR),
    • radar altimetry (SAR and SARIN),
    • lidar altimetry.

  • Methods of data collocation including
    • data reduction, normalisation,geometric, radiometric and spectral calibration/correction,
    • georeferencing and geocoding,
    • template matching (single point and global), surface matching, image co-registration,
    • synthesising colour composites,
    • ground controlling, using orbital data and imaging geometry,
    • different techniques for data fusion at pixel, feature and decision level.

  • Methods of cartographic representation and change mapping including
    • computer-assisted image mapping,
    • data generalisation, cartographic design, map-reading and cartometry,
    • hybrid GIS technologies and data integration in vertical databases,
    • animation, multiscale representation and transformed visualisation,
    • binary change and continuous change cartographic products, generation of a "probability of change" image,
    • multistage validation.

  • Methods of change detection / analysis, including automatic, semi-automatic and manual techniques for
    • map- or image differencing, DEM or SM differencing,
    • gradient-based approaches (GRAZ) and correlation techniques,
    • coherence analysis, post-classification comparison and change vector analysis,
    • proxy (indirect) methods using indicators of changes, e.g. geomorphological, rheological etc.,
    • statistical and regression analysis, parametric (numerical) modelling, topological and prospective modelling.

Irrespectively of methodological variants, glacier changes will be detected and measured by comparing historical maps and charts with later surveys and modern image data resulting from remote sensing. Changes will be expressed in linear terms, as advance or retreat measured at right-angles to the glacier border; in areal terms, as the extent of ice gained or lost from a glacial area; in volumetric terms, as the quantity of ice added to, or lost from, the glacier, and in fluxometric terms, as de- or acceleration of ice influx to the tidewater glacier front. Volumetric studies are easy to advocate, but difficult to realise, and, in most cases, glacier changes will be based on linear or areal measurements. It is worth noting that the extent of glacier surficial and marginal changes is relatively small when compared to the relief energy and to the area covered by the glacier itself, which might bring about additional difficulties in change mapping / documentation. A novel stereoorthoimage technique will be devised and tested for the representation and measurement of surficial changes of test glaciers.

Basic principles for the joint interpretation of glacier rheology and determining the areas of extreme glacier changes in stereophotogrammetric, radargrammetric, altimetric and interferometric models will be designed and tested. The estimation of long-term glacier changes should be performed in the geo-coded cartographic products, such as topographic and / or rheological maps, both available and newly generated. The importance of identical geometry and comparable contents of multitemporal cartographic products to be used is underlined. It was agreed that all new cartographic products would be generated at scales and cartographic projections typical of national topographic maps.


Glacier Interferometry: Initial Remarks

Repeat-pass synthetic aperture radar interferometry (INSAR) offers a hypersensitive instrument for monitoring glacier dynamics, surveying short-term ice velocities and their long-term variations, measuring ice flux and studying mass imbalance of prominent ice sheets and relatively small valley glaciers (Goldstein et al. 1993, Joughin et al. 1999). Rheological interpretation of INSAR records, which convolve intricately the information on glacier motion, topography and surficial changes, is not always obvious, however, and geometric processing of glacier interferograms is by no means straightforward. The knotty problem of distinguishing between the impacts of ice surface topography and surface displacement on the interferometric phase is conventionally solved by means of differential interferometry (DINSAR) requiring the use of several location-coincident interferograms and necessitating additional reference data, both topographic and rheological.

In classical 2-pass DINSAR approach, the removal of topographic component and manifestation of the motion phase is based on differencing between the original (real) SAR interferogram of a glacier containing both topographic and motion phases and the reference interferogram without motion fringes, which is synthesized from available elevation model (DEM) of the same glacier. Rapid elevation changes and insufficient quality of available DEMs - a problem frequently encountered in glacier studies - is the principal limitation to such approach (Gray et al. 2001).

Alternatively, in 3- or 4-pass DINSAR approach, two real interferograms can be differenced to cancel the topographic phase and to extract the differential motion term under the assumption that glacier topography remains unchanged between INSAR surveys. In order to derive the absolute motion from the single differential interferogram one must assume that either the glacier velocity or the relation between ice-velocity gradients remains constant over the time span covered by both interferograms. Although applicable to rheological modelling in the accumulation area of large ice domes, the assumptions of steady topography and stationary motion have often proved to be incorrect in fast moving and rapidly evolving glacial areas (Nagler et al. 2002).

Furthermore, differential interferometric processing of SAR imagery is exceptionally intolerant of any imperfections in data acquisition and processing, and becomes frequently impossible because of rough topography, rapid changes, incoherent motion, and significant phase noise at glacier margins (Forster et al. 1999). Apart from the acquisition of comparable INSAR pairs, which is not an easy matter at the first place, the algorithmic complexity, computational load and processing errors, mostly at the stage of interferometric phase unwrapping, detecting and resolving the line-of-sight motion, and geocoding, bring about further obstacles disappointing those who like to get rapid access to results.

In spite of all these difficulties, DINSAR has made it possible to derive ice surface velocity fields without the expense of in-situ measurements in hundreds of cases, making the interpretation of glaciological processes through remotely-sensed observations more tractable. Existing studies have e.g. used DINSAR observations to monitoring ice sheet motion (Goldstein et al. 1993, Rignot et al. 1997), identify glacial surges and observe the effects of surge on icefields (Joughin et al. 1996), and quantify the surface flow evolution over time of Arctic surges (Luckman et al. 2002, Murray et al. 2003), see Fig. 1, (at the left) shows the progressive velocity increase from September 1991 to January 1994 and (at the right) it represents the progressive velocity decrease from January 1994 to October 1997, with a temporary possible velocity increase between December 1995 and May 1996. The start point at 0 km represents the furthest extent of the glacier front.

Processing of dual-azimuth data (i.e. from ascending and descending modes) has made it possible to map the three-dimensional surface flow of glaciers under the assumption of flow parallel to the glacier surface (Mohr et al. 1998, Joughin et al. 1998).



Fig. 1. Time series of velocity from DINSAR along a longitudinal profile of Monacobreen, a surging glacier in Svalbard, adapted from Luckman et al. 2002, Murray et al. 2003.

Some time ago, we started experiments related with the direct determination of glacier dynamic quantities from interferometric phase gradients that does not involve complex process artifices and does not require additional topographic reference models (Sharov et al. 2002). The INTEGRAL project foresees the continuation of our studies devoted to the simplified rheological and morphological modelling of large European maritime glaciers and assessing glaciomarine interactions along European ice coasts in single ERS-1/2 SAR interferograms. Geometric processing and rheological interpretation of 20-look INSAR data will be supported with the additional spaceborne single-pass altimetry data obtained from the ICESAT-GLAS and CryoSat-SIRAL sensors. The major tasks of INSARIN data processing are related with

  • interferometric analysis of the fast-ice deformation and interpretation of glaciomarine interactions along European ice coasts,
  • measuring horizontal velocities, strain rate and calving ice flux at fronts of large tidewater glaciers,
  • determining the position of ice divides and identifying main drainage basins on the largest European ice caps,
  • interferometric modelling of glacier rheology and integral estimation of glacial changes in the Barents Sea region.

Ice Coasts and Ice Divides in SAR Interferograms

The representation of ice coasts and ice divides in high-quality INSAR products is mainly determined by

  • the type of INSAR product (amplitude, coherence, fringe or phase gradient image),
  • INSAR spatial and temporal baseline,
  • glacier topography, surface state and motion,
  • effects of temporal and geometric decorrelation.

The proper selection of interferometric pairs allows the effects of temporal and geometric decorrelation to be kept small (Sharov et al. 2002). All 24 ERS-1/2 interferometric pairs used in our study were obtained in October - March 1994-1996 under steady and cold weather conditions with suitable spatial baselines of 0 - 200 m and temporal intervals of 1 or 3 days between SAR data takes. The INSAR products generated from this data set are free of unfavourable effects due to high winds, heavy clouds, precipitation and melting at the glacier surface.

In our interferograms, all time-stable areas are reproduced with a typical mean coherence value of 0.6 - 0.7, and the interpretation of coherence images, which represent the coefficient of complex correlation between subsequent SAR scenes in shades of grey (Fig. 2, a), does not bring about essential difficulties. Fig. 2 shows, for example, 20-look interferometric pictures of the northern margin of Tindall Ice Dome on Wilczek Land, FJL with several large outlet glaciers flowing into Austrian Channel (South and North Karo glaciers) and Vanderbilt Straight (Milky, Basin 2, and Impetuous glaciers). Glacierized and ice-free coastlines even of small islets, e.g. Gage Island (GI) in Vanderbilt Straight, are well detectable and inland borders of outlet glaciers can be reliably delineated. The lowest mean coherence value of about 0.47 was observed in frontal areas of very fast moving glaciers like South Karo Glacier, the leftmost in Fig. 2, a - d.



Fig. 2. 20-look INSAR products of Wilczek Land, FJL: coherence image (a), fringe image (Bn = 129 m, b) and phase gradient image (c) of 09/10.10.95, fringe image of 17/18.12.95 (Bn = -43 m, d)

A thin dark line separating areas of high coherence on the fast ice and inland can be frequently observed in winter coherence images along coastlines, both precipitous and low-lying. At active glacier fronts, the line becomes interrupted and blurred or even vanishes. At steady coasts, its width usually does not exceed several pixels and we suppose that this effect might be explained by the influence of layover and shadowing in SAR imagery. The line looks similarly to crevasses in sea-ice floes and its interpretation as a coastal fissure in the fast ice, at least locally, may not be excluded.

Highly accelerated ice motion, excessive strain rates and rough surface with numerous crevasses lead to rapid changes in backscattering properties near the glacier face, and the fringe image of glacier exteriors is characterized by low contrast, high local fringe rates and significant phase noise / aliasing (Fig. 2, b, d). Frequently, the direct interferometric analysis of such areas becomes impossible even in tandem INSAR pairs taken in winter (Sharov et al. 2003).

In contrast to calving faces, where the horizontal velocity of ice and the surface roughness attain frequently their maximum, at a symmetric divide on a horizontal bed, the shear stress and horizontal velocity of ice are zero, but the longitudinal stress is high, particularly in the upper layers (Paterson 1994). Sometimes, major ice divides on large ice caps can be detected as bright stripes with darker surroundings in amplitude and coherence images taken in late winter (May - June) or late summer (late August - early October) (Dowdeswell et al. 1999, Sharov 1997). The width of these stripes varies from 150 m to 1000 meters depending on surface topography, and their origin might be related with melting and refreezing processes, which mostly take place along ice divides because of the low sun elevation. In winter, INSAR products are characterised with homogeneously higher backscattering and coherence values at glacial tops, and the recognition of ice divides becomes more difficult.

At best, the identification of ice divides and drainage basins can be performed in a phase gradient image or topogram, which is calculated from the original fringe image φ(x,y) by using the method of finite (central) differences as (Sharov et al. 2003)


On traversing the divide, the value of the phase gradient clearly changes from negative to positive values. The shift values Δx (in range) and Δy (in azimuth) are equal 1 pixel usually, but, in general, can be manipulated separately in azimuth and range direction within the interval from 0 to several pixels. The increase in the shift value enhances the contrast of elongate crests on ice caps, but amplifies the phase noise and coarsens the spatial resolution of the topogram. The use of SAR interferograms with longer spatial baselines should be preferred in this concern.

Typical topogram showing a complicated system of ice divides in the northern part of Tindall Ice Cap is given in Fig. 2, c. Since each original interferogram of a living glacier contains both topographic and motion phases, the resultant topogram reproduces the glacier surface topography together with the motion component. This is why the ice divides identified in the topogram are referred to as ice-flow divides.


INSAR Representation of the Fast Sea Ice Attached to Glacier Fronts

The area of consolidated fast sea ice covering straights of arctic archipelagos for most of the year is often reproduced with quite good coherence and demonstrates good visibility of interferential fringes. Apart from tidal effects, the fast coast ice attached to any active glacier front undergoes the powerful action caused by the glacier motion.

In winter fringe images, the fast-ice displacement / deformation forced by the glacier flow manifests itself as a zone of concentric hemi-elliptical fringes converging at the tips of the glacier front. Such interferential features called "outflows" are permanently found at fronts of nearly all tidewater outlet glaciers oriented along the SAR cross-track direction (R); the latter is marked with an arrow in all figures. Outflows have been detected at both open ice shores and in glacial fjords, but we did not observe these features at glacier-free coasts. The lateral extent of outflows may reach 10 kilometers and more. Often albeit not always, the local coherence within outflows is somewhat lower and the phase noise is higher than outside (Fig. 2, d). This fact might be related with the deformation and lower thickness of sea ice in the area of outflows.

It is believed that the thickness of fast-ice floes and their resistance to stress can influence the shape and the extent of outflow, but not the total number of interferometric fringes within it. Fig. 2, d) shows, for example, the larger extent and the lower rate of motion fringes at the front of Impetuous Glacier, flowing into Vanderbilt Straight with typical ice thickness of 80 to 100 cm, than those at Karo Glaciers terminating in Austrian Channel with commonly thinner (40 - 50 cm) ice . The rate of fast ice displacement / deformation decreases with the distance from the glacier front and increases in the vicinity of natural obstacles such as shoals, other islands, etc. The amount of fast ice displacement usually increases from zero at the tips of the glacier front to its maximum in the mid point at the glacier snout (Fig. 2, c).

Fig. 3, a) represents the outflow with somewhat distorted shape located at the front of Shokal′skogo Tidewater Glacier. For the sake of reference Fig. 3, b) provides an amplitude image reproducing the rough surface of glacier front by light tones while the homogeneous area of nearly stationary fast ice nearby appears dark. Note the absence of interferometric fringes on the fast ice surface along the glacier-free coastline to the north and to the southwest from the glacier front.



Fig. 3. Fringe image (a) and amplitude image (b) of Shokal′skogo TWG, north NZ, 5/6.03.96

The general origin of outflows is believed to be related primarily to the horizontal displacement of the coastal ice forced by glacial flow because of

  1. prevailing orientation of outflows along the SAR cross-track direction and the inverse interferometric contrast in outflows observed at outlet glaciers flowing in opposite directions, i.e. toward or away from the sensor;
  2. enlarged lateral extension of outflows and the increased number of interferential fringes within on SAR interferograms with longer temporal baselines;
  3. consequent character of outflows in multitemporal interferograms and similarity of phase-gradient patterns over flat glacier margins and outflows;
  4. no evidence for specific geophysical effects, e.g. tides, currents glacial winds, icings etc., that might control the occurrence and outline of outflows;
  5. available analogies in the area of interferometric control and fringe projection, c.f. (Muramutsu et al. 2003).

It is quite clear that vast plane floes of young coastal ice with a very small elevation above sea level (10 - 30 cm) represent an ideal surface for the interferometric analysis of small horizontal motions close to ice coasts and their driving forces. There is no need for topographic reference in this case (Still, there is a necessity for the compensation of tidal effects), and the length of spatial baseline becomes a less critical issue. This factor makes it possible to accurately measure frontal glacier velocities in single SAR interferograms.


Glacier Altimetry

Valuable additional information on the sea ice freeboard and roughness in the areas of permanent outflows can be derived from the ICESat-GLAS L1B & L2 lidar altimetry data taken over the study areas in March, October and November 2003. Preliminary interpretation of multitemporal GLA06 altimetry products showed that the ice surface roughness in outflows was mostly greater than that of surrounding ice floes. Fig. 4 shows several typical fragments from the ICESat GLA06 altimetry products representing the sea ice surface roughness and freeboard versus horizontal location in the outflow orthogonal to the Impetuous Glacier front for 12 March (a, b) and 31 October 2004 (c, d). Both dates correspond to the first quarter of the moon (neap tide). The altimetry data were not corrected for local tidal effects. All transects begin at the ice coast, which is not represented due to scaling problems, and terminate in the middle of Vanderbilt Straight. Several concurrent thermal-infrared images obtained from NOAA and ERS-2 satellites were involved in the interpretation of altimetry products. All ICESat altimetric transects were co-registered to available topographic maps 1:200,000.

The ICESat profile of 31.10.03 in Fig. 4, a) demonstrates the presence of moderate deformation in the young fast-sea-ice cover within the outflow. The sea ice thickness growths through time and the sea-ice deformation features within the outflows become especially noticeable in late winter (Fig. 4, c). Careful analysis of a dozen multitemporal altimetry transects showed that, within outflows, the sea ice surface was usually 0.3 - 0.6 m lower than the mean level outside (Fig. 4, b, d). We suppose that the decreased sea ice thickness in outflows is directly related with the glacial forcing, but still don't understand what that is.



Fig. 4. Sea ice roughness and freeboard close to the Impetuous Glacier Front from ICESat parallel altimetric transects of October 31 (a, b) and March 12, 2004 (c, d).

Besides, the lidar altimetry data taken in early winter 2003 will be applied to measuring the present heights of ice coasts and ice divides in the NZ test site, as well as to studying glacier elevation changes in the ablation area and their relation to changes in the accumulation area. The comparison of 10 altimetric transects with the hypsometric profiles derived from topographic maps corroborates the general retreat of ice coasts and shows that some calving faces have become 10 to 40 m higher with respect to the sea level. This can be explained by rapid disintegration of thinner frontal parts of tidewater glaciers with corresponding increase of the subaerial part of glacier face. Typical hypsometric profiles of Petersen Glacier in north NZ derived from the topographic map and ICESat altimetry data are given in Fig. 5 There is a hypothesis on the surging character of this glacier.



Fig. 5. Hypsometric profiles AB of Petersen Glacier from topographic map 1:200,000 (1950-s, green) and ICESat altimetry data (09.11.03, blue)


Joint Processing of INSAR and Altimetry Data

Up to now, the terrestrial coverage of study glaciers by the ICESat GLAS data remains rather sparse and altimetric heights can be defined only for some "tie" points on ice coasts and ice divides at widely spaced intervals of several kilometres. In order to define the unknown heights between tie points, we will co-register all available altimetric transects with corresponding interferometric models using the rigorous point-by-point transformation and the ERS-SAR sensor model implemented in the RSG 4.1 software. The co-registration accuracy is characterized with the r.m.s. error of ca. ± 1.2 pixel. Afterwards, the relative height differences between the target and tie points Δh will be determined simply by counting the number of interferometric fringes K enclosed between those points with its subsequent multiplication on the value of height ambiguity h2π as

Δh = K · h2π ≈ 0.5K · λ · H · Bn-1 · tan Θ

where H ≈ 785 km is the height of the satellite above the reference body and Bn is the normal component of the interferometric spatial baseline.

In the case of active ice coasts, some additional correction is needed to compensate the influence of glacier flow on the height measurement. This can be done, e.g. by subtracting the number k of interferometric fringes within the corresponding outflow from the real value K. Apart from measuring glacier heights, which are needed for rheological modelling, such an approach mitigates some local problems related with the procedure of interferometric phase unwrapping at ice cliffs and provides high accuracy of geocoding and change detection at glacier fronts.

An original INSAR composite image of the northern part of Main Ice Sheet consisting of an amplitude image (inland) and fringe image (offshore) with several altimetric transects overlaid is given in Fig. 6, a. Digits 1 through 5 denote Inostrantseva, Pavlova, Vera, Bunge and Petersen glaciers respectively. Straight boundary separating the fast sea ice from drift ice is well detectable in the left upper corner. Fig. 6, b represents one of ICESat altimetric transects (blue) across the Main Ice Divide (CD in Fig. 6, a) together with the phase profile (green) from corresponding fringe image.



Fig. 6. INSAR composite showing active ice coasts and major ice divides of Main Ice Sheet in north NZ with altimetric transects (cyan) overlaid (a); altimetric and phase profiles CD across the Main Ice Divide (b).

There are no pronounced summits on the altimetric transect near major ice divide, and the divide region appears very flat and broad; its width exceeds 6 km. By contrast, there is a distinct maximum on the phase profile, and, in fringe image, the ice divide area is relatively narrow. We suggest that this could be a result of non-zero surface velocity components, which become noticeable at distances of only 1-2 kilometres from the ice crest. Given 7-year time difference between the data sets, the local phase maximum in the interferometric profile coincides well (within 500 m) with the highest position (564.1 m) in the divide area on the altimetric transect, c.f. Zwally et al. 2002. The effect of radar penetration on the location of ice divides in INSAR products has yet to be studied.


Some Additional Thoughts about Rheological Modelling

The detailed and equivalent rheological models that reliably describe the distribution and variations of frontal glacier velocities and stresses are essential for better understanding the evolution of ice coasts, monitoring glaciomarine interactions and adequate forecasting of possible alterations in the glacier extent. Available 2- or 3-D numerical models of glacier flow involving complex equations and numerous variables such as ice temperature, thickness, deformation, bottom melting, etc. are perplexed, cumbersome and error-prone, especially, if applied in the glacier environment different from original applications. The polar idea of the present study is to utilize the simplest image models derived from spaceborne INSAR data, which relate the quantities observed in interferometric products with real rheological unknowns on a pixel-by-pixel basis at both local and regional scales.

The scope of rheological modelling can be defined in accordance with the graphical scheme presented in (Oerlemans 2001) and reproduced in Fig. 7. The modelling process consists of several consequent steps involving forward and inverse interrelations. The present research is mostly focussed on "inverse problems", i.e. we shall concentrate on ice-flow modelling from "geometric" observations and shall try deducing climate change from glacier fluctuations, both geometric and fluxometric. In our case, the sequence of modelling operations should look as follows

  • estimating the evolution of glacier geometry G(t),
  • determining the geometry of glacier bed and surroundings,
  • ice flow modelling,
  • measuring mass-(im)balance,
  • studying meteorological conditions,
  • deducing climate change and other environmental trends,
  • forecasting potential glacier changes / scenarios.



Fig. 7. General flow chart of glacier modelling (after Oerlemans 2001)


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