Sea Ice Displacement Measured by ERS-1 SAR Interferometry

Abstract

1. Introduction

After the launch of ERS-1 in 1991 satelliteborne SAR (Synthetic Aperture Radar) imagery is routinely used for sea ice investigations. The advantages of SAR imagery for sea ice mapping are weather independency and high spatial resolution, and the use has so far focused on ice classification from individual images and large-scale ice kinematics from consecutive images. However, with InSAR (SAR interferometry) new measurement tools are provided for research in sea ice mechanics.

The InSAR technique has turned out to be very valuable for the utilization of satellite SARs. At least two SAR images over the same area, acquired from slightly different sensor positions, can be combined into an interferogram which contains geophysical information. It has been shown (e.g. Graham 1974, Zebker and Goldstein 1986, Li and Goldstein 1990) that, for a stable surface, the phase of the interferogram is related to the large-scale topography. For an unstable surface, relative surface displacements also affect the phase, and therefore multiple SAR images may be used to detect surface changes over large areas. The resolution of the ERS SAR interferograms is approx. 1-2 m for topography and 1 mm for relative displacements. The extreme sensitivity of this technology, combined with its high resolution and broad coverage makes it useful for extensive and accurate measurements of various geophysical parameters, including heaving and buckling in fault zones, displacements caused by seismic events (Gabriel et al. 1989, Massonnet et al. 1993, Rignot and Zyl 1993) and glacier movements (Goldstein et al. 1993).

Consequently, InSAR has a large potential in sea ice mechanics investigations to map ridge topography and small deformations. A particular area where this technique may become valuable is the topography of grounded ridges and the stability of the sea ice in the fast ice zone (fast ice is defined as in WMO No.5 1989, i.e. the fast ice is attached to something, here it means shore-fast ice). Fast ice is nearly stationary and may experience discontinuous slips or small continuous deformations. The displacements may be up to meter-size which is below the resolution of normal SAR imagery. Because of the scale and accuracy requirements, there is not much earlier data on this subject. The required accuracy is possible to obtain with precise geodetic ground survey methods but at the cost of poor spatial coverage. In this study ERS-1 SAR interferograms and intensity images have been studied from the northern part of the Bay of Bothnia, Baltic Sea. The images were acquired during the BEERS-92 (Baltic Experiment for ERS-1 1992) program (Leppäranta et al. 1993, Thompson et al. 1993, Ulander 1994). An earlier, more technical, study of this dataset can be found in (Dammert and Hagberg 1994).

2. SAR image data set

The winter of 1992 was exceptionally mild in the Baltic Sea area. The air temperature was almost all the time above the long-term average, and only the northernmost basin, the Bay of Bothnia became ice covered, see Fig. 1. The maximum ice extent occurred on 21 February with a coverage of only 15 % of the Baltic Sea area while the long-term average is 45 %. The drift ice field in the Bay of Bothnia showed large variations. In March there was not much net change in the ice volume but the ice was packed by the winds into the east and north sides of the basin.

Figure 1. Ice chart 29 March 1992 for the Bay of Bothnia (SMHI 1992).
The SAR images cover a 50x50 km large area at the north part of the basin.

The present study period is 24-30 March. At that time there was only ice in the northernmost 100 km of Bay of Bothnia. Fig. 1 shows an ice chart from 29 March which accurately represents the whole study period. Half of the ice cover was fast ice with a thickness of 30-55 cm. The drift ice patch was nearly triangular with an area of approx. 3000-4000 km2 and with a thickness of 30-50 cm. At the boundary of fast ice and drift ice, a 5 - 10 km wide lead with new ice formation opened during the study period. The core of the drift ice patch was compact and heavily ridged while at the ice edge there was a 10-20 km wide thinner and more open zone. The weather was cold (air temperature below 0° C), the winds were varying, and the drift ice moved mainly south. To analyze the case, we have collected weather data and sea water level data from the nearby Swedish and Finnish stations. Logs of the Swedish icebreakers which were in the area at the time have also been available (courtesy of the Swedish Navigational Board).

Table 1 Weather conditions at Storöhamn, 65°44'N 23°06'E in late March 1992 according to SMHI.

1 At 9 hrs.

2 From 6 hrs to 6 hrs next day.

This study includes three ERS-1 SAR images obtained on 24, 27 and 30 March 1992, the overflight time was 0948 GMT. The images originate from the BEERS-92 experiment, and normal intensity images over ice from that period have been examined in detail by (Ulander 1994). Since the weather was cold, any snow on the ice was probably cold and dry and thus interfered very little with the radar wave. As a result the interferometric coherence over the ice was relatively high for the InSAR pairs. A 50x50 km2 area from northern Bay of Bothnia, south of the city Kalix, has been extracted from the SAR data for this study.

Fig. 2 shows the 27 March SAR image. It is possible to distinguish the Swedish coast, fast ice in the archipelago, and the lead at the fast ice edge. In the fast ice zone the strength of radar backscatter is related to the degree of deformation of the ice. In the inner archipelago the ice is smooth and undeformed while in the outer archipelago ice ridges have formed earlier in the ice season. The straight lines are ship channels. The image clearly tells how the character of the ice which is adjacent to the fast ice zone becomes rougher as the zone expands towards the south. This is expected as deeper ridges are needed for grounding points which stabilize the ice between. The signature from the lead shows the special features of new ice being formed.

Figure 2. ERS-1 SAR image on 27 March 1992 over the study area. © ESA 1992.

3. Background on SAR interferometry

The basic idea of the SAR interferometry is that the backscattered signals are correlated, both in amplitude and phase, within a small angle interval seen from a resolution cell. An interferogram is produced by multiplication of two complex SAR images (either one is conjugated), pixel by pixel, and the phase is extracted. The geometry of a spaceborne repeat-pass SAR system is shown in Fig. 3. For two images, the phase difference is , where is the radar wavelength and and are the distances to the object. It can be accurately measured from the interferogram (Fig. 4). The formula for the interferometric phase, in the repeat-pass case, is after correction for the phase difference for the flat earth

(1)

where the geometrical parameters are defined in Fig. 3, represents a small movement between the image acquisitions, and is the phase noise due to speckle decorrelation, changes of scatterers and thermal noise. Finally, we have the general 2 ambiguity associated with all phase measurements. Note that the term disappears in single-pass InSAR systems. From Eq. (1) we see that measurements of both surface elevations and small displacements are possible from a repeat-pass interferogram. However, it is impossible to discriminate between the two in one interferogram. The temporal surface movement, , is measured in the look direction and can be either horizontal or vertical or a combination of both. The sensitivity for the surface topography increases with the baseline while the sensitivity for surface movements is independent for all baselines.

Depending on the application, single-pass InSAR systems will be good for producing topography maps and repeat-pass InSAR systems with a small baseline will be good for displacement maps. In our case, we have repeat-pass images from ERS-1 with a relatively small baseline, i.e. low sensitivity for ice topography and good for displacement maps. The particular ERS-1 parameters are R = 785 km, = 5.7 cm and = 20-26°.

Figure 3. The geometry of a spaceborne repeat-pass SAR system.

4. Interferograms

Two interferograms have been produced over the study area. The first is formed by the image pair 27 and 30 March (see Fig. 4), and the second formed from the image pair 24 to 30 March. Thus there were three and six days, respectively, between the passes. The interferometric baselines were 145 m for the first case and 65 m for the second. The weather conditions during the period of these cases are given in Table 1. From one interferogram only, it is impossible to know whether the phase shift originates from the surface topography or from the relative surface movements.

Over land the fringes mainly show topography and over the ice mainly temporal surface movements. The coherence over land is mainly related to volume and temporal decorrelation while over the ice, the coherence is more related to temporal decorrelation, e.g. water flooding on the ice. However, over land it is possible to discern the Kalix river valley, another valley north of the river, a small crest south of the river and several other hills.

The sea area contains the fast ice zone, drift ice, and open water (see Figs.1 and 2). In the illustrated interferogram, see Fig. 4, the lead containing new ice appears as a noisy region. The coherence was lost since the surface changed completely on the cm-scale between the two passes. In the interferogram there are also noisy regions with low coherence in the estuary of the Kalix river and in the river channel itself. This is possibly due to flooding of the ice after the snowfall in 28-30 March. However, most of the fast ice has a high coherence, thus a good visibility of the interferometric phase fringes. The discontinuities in the interferograms show slip lines in deformation of the fast ice zone. The smoother transitions are due to ice topography and deformation, but the interferogram structure suggests that a significant part must be due to horizontal displacements. The outermost fast ice has the highest deformation activity.

Figure 4. The interferogram over 27 and 30 March 1992. Red to red means 65 meters in height or 28 mm in movements. © ESA and Chalmers University of Technology 1992.

5. Topographic effects

Nevertheless, it is likely that some topographic effects also exist. As an example, a part of the area marked '2' belongs to a heavy long ridge in the fast ice zone (see Figs. 2 and 4). Assuming that the phase shift over the ridge originates just from the ridge topography, it is possible to measure a ridge height. A part of the ridge, sitting on some breakers, was selected. Fig. 5 shows profiles across the ridge (from the level ice north of the ridge to the level ice south of the ridge) in both interferograms. The phase shift interpreted as an ice ridge height is displayed on the left-hand sides of the diagrams, while the phase shift interpreted as a temporal movement is displayed at the right-hand sides. The level ice at the north part of the ridge is set as a reference.

The measured heights are not unlikely, but the measured phase shifts are more likely related to small displacements. Unfortunately, there is no ground truth available but the ridge was probably grounded and its height can therefore be several meters. Other ridges were measured during BEERS-92 (Ulander and Carlström 1993) but those do not appear in the interferograms. Measurements from interferogram 24/30 March give a 10 m height which is large. However, such ridge heights were not reported from BEERS-92 reconnaissance flights from the northwest Bay of Bothnia region. Moreover, the difference of two height determinations may be due to a small shift or change of the surface topography of the grounded ridge.

(a) (b)

Figure 5. A phase difference profile across a ridge interpreted for the surface topography (left ordinate) and relative movement (right ordinate):
(a) Interferogram 27/30 March 1992, (b) Interferogram 24/30 March 1992.

6. Small Displacements

The interferograms give a good overall view of the ice deformation with slip lines shown exactly and also continuous zones mixed with the topography.

Vertical ice movements are related to sea level changes or to local mechanical ice deformation, e.g. ridge formation. Small horizontal shifts result as a response of the ice to stresses which are below the plastic yield limit. Horizontal shifts can be examined by the quasi-static approximation (Hibler 1986, for Baltic applications see Leppäranta 1981)

(2)

where is the plane stress tensor, and are the tangential stresses of air and water on ice, is the ice density, h is the ice thickness, g is the gravity acceleration and is the sea level elevation. For the air and water stresses, quadratic drag laws are employed. Horizontal shifts may thus be caused by winds, currents, and sea level tilt. Once the external forcing is given, the strain is obtained from the rheology formula

(3)

where stands for the material properties of the ice. Pack ice rheology is complicated and includes elastic, viscous, and plastic regimes. When the ice really starts to move (more than approx. 1 cm/s) the flow is plastic. But when the forcing is low, the ice is stationary or nearly stationary and the displacements are elastic strains or viscous creeps within meters or so. The transition of when and how the (nearly) stationary ice starts to move is largely open for observational data. With InSAR maps it is possible to control the "nearly stationary state". Because of the lack and difficulties in other observational techniques this new information is very valuable.

The stretching or compression of the ice in the two cases, elastic rheology and linear viscous rheology, is determined by the the two cases' rheology formulas. The elastic case with rheology , where the constant E is approx. 109 N/m2, and the linear viscous case with rheology , where the constant is approx. 1012 - 1015 kg/(ms).

Examine now a particular ice patch in the interferograms between two icebreaker tracks and marked with '1'. They have fractured the ice sheet and made it possible for the narrow area in between to move differently compared to the surrounding ice. The most southern part of this narrow ice patch between the tracks has moved approximately 19 cm (projected in the radar look direction) relative to the north part of it. The ice patch divided by the two icebreaker tracks is clearly distinguished by the interferometric fringes. Assuming that this patch is flat, the interferometric fringes are totally induced by a motion between image acquisitions. As the movement direction is projected in the look direction, we will try to determine if it is vertical or horizontal and try to determine the factor(s) behind the movements. The northern part of the patch seems to be stable and attached with the surrounding ice while the southern part has moved. The southern part could have moved up or down, it could have been stretched or compressed or a mix of the two movements.

Vertical movements of the southern part of the ice patch may be caused by changes in sea level. The phase shift along the patch interpreted as a vertical movement is compared with the actual Kalix sea level. Comparing measurements from the interferogram 27/30 March and the sea level, the sea level has sunk 27 cm while the patch has sunk 18 cm from the interferogram. Moreover, for the 24/30 March case the interferogram suggests a movement of 18 cm while the Kalix sea level has barely changed. Thus the phase shift cannot be explained by the sea level changes and it is then assumed to be due to horizontal motion.

Assuming that the movement is horizontal, both interferograms suggest a compression of 94 cm of the ice patch. The conclusion from the measurements is that the movement must have occurred between 27 and 30 March. The compression results either from the easterly wind on 28 March, either wind stresses directly or from boundary forces of the drift ice patch south of the fast ice edge. Then it is remarkable that the northernly wind could not extend the patch. Hence, the compression was not fully elastic and as the the tensile strength is small, the shear strength has been significant to prevent an opening.

However, considering the distributed forces over the ice patch, we have the following estimates of the forces. The wind force was at most about 0.1 N/m2 (wind speed 7 m/s), similar magnitude would result from a water current at 15 cm/s which is possible to have there. The sea surface tilt is here less than 10-6 and the force then smaller than 10-2 N/m2. Thus the magnitude of the force F was 0.1 N/m2 and at most than 0.2 N/m2. For the maximum forcing estimate 0.2 N/m2 the elastic compression would be 5 cm, much less than observed. The linear viscous creep is another possibility, that is 15 m for = 1012 kg/(ms) and 1.5 cm for = 1015 kg/(ms). The latter viscosity, a typical glacier value (e.g. Paterson 1995), is too large. The former which is too small has been used in viscous-plastic sea ice models (Hibler 1986). Although it has been questioned whether this sea ice viscosity represents real physics, the magnitude of the movement would be close to the present compression. The values are summarized in Table 2.

Table 2 Forces and relative movements for the ice patch, over the time period 27-30 March. Interferogram measurement is 0.94 m.

Type of force	Wind	Water currents	Sea surface tilt
Maximum force estimate (N/m2)	0.2	0.2	0.01
Elastic compression (m)	0.05-0.09	0.05-0.09	0.003-0.005
Linear viscous compression (m):
kg/(ms)	15	15	0.8
kg/(ms)	0.015	0.015	0.0008

For the case of boundary forces, quite similar results would follow. Because of the lack of a time history it is not possible here to distinguish between elastic and viscous changes with certainty. The elastic case would require a breakage at a weak point but the deformation is quite smooth for such interpretation. Icebreakers may actually push the ice. It is known that icebreaker Ymer visited the Axelsvik, south of Kalix on the morning of March 27. But again one must note the smooth deformation pattern rather than a push from a track.

Similar data over sea ice fields does not exist to our knowledge. It is a tough measurement problem to map distances over sea ice fields very accurately. In spite of the uncertainties, an upper bound is certainly found for the wind forcing effect and the upper bound is quite small. Since the patch is around 16 km long, such measurements with cm accuracy over such large distances are rather unique.

7. Conclusions

A case study of using SAR interferometry in sea ice mechanics investigations has been made using the BEERS (Baltic Experiment for ERS-1) data from winter 1992. InSAR is particularly useful to examine small deformations in the nearly stationary fast ice zone. Unfortunately, there is an ambiguity between surface topography and relative motion as well as another ambiguity in the movement direction.

Vertical topography maps are most useful to examine ice ridges but the ice must then be stationary which necessiates a very good control of the ice field; a potential is here to use the system for topography of grounded ridges. For ERS the resolution is too large to image the height of the floating Baltic ridges but an airborne InSAR system may work well for that. Large grounded ridges may well be 10 m high, 40 m or more wide and several hundred meters long.

In the present case the ice was nearly stationary under the low forcing conditions and thus indicating a significant shear strength. The analysis has shown that fast ice can be affected by many different phenomena and that interferometric SAR can provide insight into these effects providing complementary in situ data. Independent of the ambiguity, bounds can be set to horizontal shifts which means that it is possible to analyze cases when the pack ice is nearly stationary. This transition from stationary to moving state is one major problem in mechanics of sea ice fields for which almost no data exist. A model which could simulate the case maybe does not yet exist.

This study has shown that there is additional information in the interferograms compared to the intensity images. Interferograms with a shorter time lag would certainly be more interesting and will to some extent solve the ambiguities. Interferograms from both ascending and descending orbits will also help solve the ambiguities. A system without the time lag, for example an airborne system with two antennas, would make it possible to produce unambiguous maps of the ice ridge heights in real time. One proposed application would be to follow and measure the stress by the ice on lighthouses during the winter.

8. Acknowledgments

We would like to acknowledge Dr. Lars Ulander and Jan Hagberg for their valuable comments. The meteorological data is provided with courtesy of Bertil Håkansson, the Swedish Meteorological and Hydrological Institute (SMHI), and the icebreaker logs with courtesy of the Swedish Navigational. The first and third authors are supported by the National Space Board under the project "Microwave remote sensing of sea ice". The work of the second author is supported by the Academy of Finland, project "Modelling the long term variability of the Baltic Sea" .

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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry