An ice drift series from the Fram Strait January-March 1992 based on ERS-1 SAR data REINERT KORSNES Korsnes, R. 1994: An ice drift series from the Fram Strait January-March 1992 based on ERS-1 SAR data. Polar Research 13. 55-58. A time series of ERS-1 SAR images is used to estimate ice drift in the Fram Strait January-March 1992 (the ERS-1 mission first ice phase). The images all cover the same area. The sampling interval is three days. The paper shows examples of estimation of ice drift and divergence from this image time series. Divergence is an important quantity in order to cstimate ice production and hence mixing of the ocean water masses. A reference configuration of ice points is defined for each image. These ice points are identified in the successive image giving a set of point pairs. These point pairs are input for statistical analysis. Upward looking sonars (ULS) and current meters are moored below the scene. A combination of the SAR derived dynamics and the ULS derived ice thickness series will give opportunities to estimate ice mass flux into the Greenland Sea, and t o improve ice classification algorithms. R . Korsnes, Norsk Polarinsritutt. P . 0. Box 5072, N-0501 Oslo, N o r w a y . Introduction This paper gives results from work demonstrating modes as in the Taylor-like expansion: T,,.,*(x) = 9 + A ( x - 9 + E (1) . . the feasibility of using ERS-1 SAR imagery data where and to estimate temporal variations of ice velocities in the East Greenland ice stream. This ice stream represents about 95 percent of all the ice that are mean points of a reference configuration of corresponding ice points at times f , and f2 respectively. A is a matrix. is an leaves the Arctic Ocean (Vinje & Finnekba 1986) and is therefore an important climatic parameter. A time series of ERS-1 SAR images covering the same area of 100 x 100 square kilometres and spatial resolution of about 30 metres is used to estimate ice drift in the Fram Strait January- March 1992. Fig. 1 shows the spatial outline for this image time series. The sampling interval is three days. Analysis method Let X, denote the set of all ice particles at time f in the actual region including the frame of obser- vation Z, that also may depend on the time t . We may regard Z, and X, as subsets of the plane R2 (X,, Z, C R2). We want a sensible probabilistic and physical interpretation of the transformation the times I, and 1,. A first approach may be to represent T,,,,, by the shift, stretch and rotation Tl,,t, which maps corresponding ice points between Fig. 1 . Spatial coverage of ERS-1 S A R image time series used to estimate ice drift in the Fram Strait January-March 1992 (satellite mission first ice phase). 56 R . Korsnes error or model failure term. Rothrock & Stern (1992) obtained the invariants uorticity , diuer- gence and shear by interpreting the terms of the matrix A as the partial derivatives of a velocity field (a direct use of Equation 1). Their work is based on SEASAT SAR images 19 July-7 Octo- ber, 1978. Loshchilov et al. (1980) made similar approaches twelve years earlier using SLAR (the author was shown during a stay at the Arctic and Antarctic Research Institute, AARI, in St. Petersburg, June 1992). The vector b = 9 - reflects ice drift. The transformation A maps a unit circle into an elipsis with axes of length ui(A) = {Ai(A7A}1/2, i = 1,2, where Ai(A7A) are the eigenvalues with the cor- responding eigenvectors ei of the symmetric, posi- tive semidefinite, matrix ATA. We assume A1 3 h2. ui(A) are in the literature called singular ualues of the matrix A (cf. e.g. Ciarlet 1988, Chapter 3). We can interprete ul(A)u2(A) as the increase of area between the image sample times. Let A = C U (2) be the (unique) polar factorization of (the invert- ible) matrix A where C is a rotation and U is a positive definite matrix (note: we can assume determinant (A) > 0). U reflects deformation given by its eigenvalues ui,i = 1,2, and direction el of the eigenvector e l . The measure for approximation in this paper is the common method of least square. A reference configuration {xi} of ice points is defined for each image. Each ice point xi, is in the successive image Table 1: Estimates of three days ice drift in the East-Greenland ice stream January-March 1992 based on ERS-1 SAR data (satellite mission first ice phase). Each 3 days period is labeled by its start date. = means analysis performed by eye due to too little common ice in image pair. Blank means missing data. Angles are given relative to north (positive clockwise). @ESA (1992). Drift (b) Deformation (U) Mean Date velocity Length Dir 8, (1992) (m/s) (km) (deg) 01 0 2 (deg) 01.09 .24 61 221 1.00 1 .00 102 01.12 =.35 -90 -200 01.15 z.35 =90 -200 01.18 .18 46 200 1.15 .79 112 01.21 .14 36 181 1.01 .91 - 33 01.24 .14 38 194 1.01 .99 - 43 01.27 .33 85 205 1.01 .99 -21 01.30 .I7 44 1% 1.03 .96 124 Rotation C error E (deg) (m) Prediction -1.6 33 0.1 715 -6.3 764 6.6 214 3.2 204 7.7 24 1 02.02 .17 44 02.05 .19 49 02.08 .27 71 02.11 .09 23 02.14 .09 23 02.17 .10 25 02.20 .27 70 02.23 02.26 02.29 ~ 191 1 .00 .97 17 7.4 192 184 1.42 .68 101 -14.6 789 1% 1 .w .99 4 9.2 37 177 1.11 1 .o 131 3.5 355 184 1.49 1.01 96 7.8 1(n6 206 1.39 .62 122 - 15 1335 224 1.04 .87 49 8.6 323 03.03 03.06 03.09 .31 81 199 1.15 .82 127 9.3 80 1 03.12 03.15 03.18 .29 76 186 1.04 .88 112 8.0 285 03.21 .I7 44 180 1.01 .97 114 12.4 377 03.24 .22 56 192 1.00 1 .00 -12 9.1 39 03.27 .16 41 192 1 .00 .99 119 6.1 49 An ice drift series from the fram strait 57 Fig. 2. Development of regular grid of ice points S 1 2 March 1992. The images cover 20 X 20 square kilometre subsets of the original ERS-1 SAR scenes. Only the points with significant identification confidence are shown in the right image from 12 March. The image is received and processed at TSS. OESA (1992). identified as yi with a weight of confidence mi between 0 and 1. The estimates for A minimize the mean square prediction error: observation code based on physical insight. As such, Equation 1 gives an a d hoc description of ice drift T,1,t2 without any a priori relevance for significant data reduction. Decomposition of drift into tidal components and residual drift in principle would give results more independent on ad hoc sampling time E Z d e f c ly; - A(xi - -f) - y12mi/%i (3) In the present analysis the points yi were identified by a semi-automatic procedure based on cross correlation. The author manually checked the results. If any doubt about the value of yi the weight m, was set to 0 (otherwise 1). The reference configuration of moving ice points in this case is a regular grid of 121 points covering about 10 x 10 kilometre as illustrated in Figs. 2 and 3. The observation times t , < . . . < t , have a constant sampling interval ti + I - ti = 6t of three days. Table 1 shows the, preliminary, result from this analysis. i i Discussion The aim for the analysis of this paper is to give a the ice drift in the actual region. Time and spatial Fig. 3. Development of regular grid S 1 2 March 1992 (geo- are slightly different due to rudimentary data collection timing representative and general purpose for coded) estimated from ERS-1 SAR data, The image coverages aspects are to be considered when setting up an code (later improved). O E s A ( 1 9 2 ) . 58 R. Korsnes schemes. However, tidal estimates for the actual location are minor to the normal mean drift (cf. Schwiderski, 1980). The estimates of A and b may be sensitive to the choice of the initial reference configuration of ice points { x i } . A grid covering a small area often will reflect rigid motion of ice floes and spatial shifts of the grid will give variations of the drift term b reflecting divergence in the ice field. This approach may lead to statistical techniques on ice classification and description based on the identification of rigid sets. A final report with the present approach will include relations between grids of varying size and location in order to provide a general purpose statistical description of the ice dynamics of the region in the freezing season. Acknowledgemenfs. -The data used in this report were provided partly free of charge derived from the ERS-I satellite payload in response t o the Announcement of Opportunity for ERS-1 (A.O.), issued by the European Space Agency on 20 May, 1986. The Norwegian Polar Institute joins the ESA Programme for International Polar Ocean Research (PIPOR) as ERS-1 Experiment ICECLIMA-n8. I acknowledge the Norwegian Space Ccntrc for the oppor- tunity to work on these till now unique data sets. I specially thank staff at Tromse Satellitte Station (TSS) for good com- munication and the foresighting extra service of collecting and storing of more data than first requested. References Ciarlet, G . C. 1988: Three-dimensional elasficify, vol. 1 of Marhematical elasficify. Elsevier Science Publishers B.V., Amsterdam. Loshchilov, V. S., Voevodin, V. A . & Borisov, R . A. 1980: Pnmenenie Samoletnoi Radiolokatsionnoi Sfanfsii bokouogo obzora dla issledouanija morskin ldou (The use of SLAR for sea ice research), vol. 12 of Mezvedomfuennyi Sbornik - Issledooanie mirouogo Okeana. Leningradskyi Polytech- nicheskyi institute, Leningrad. Rothrock, D. A. & Stern, H. L. 1992: Sea Ice Deformation observed with ERS-I SAR. In Proceedings of the Firsf ERS-I Symposium: Spaceaf the Service of our Environment, Cannes, France. Schwiderski. E . W. 1980: Reviews of geophysics and space physics. On charring global ocean rides. 18(1): 243-268. Feh- ruary 1980. Vinje, T. & Finnekasa 1986: The Ice Transport through the Fram Strait. Technical Report 186. Norsk Polarinstitutt, Oslo.