3.1. Overall evolution of the ice field

Information on the ice conditions was obtained from routine ice charts of the Finnish Institute of Marine Research as well as from ZIP-97 ice surveys. At the beginning of March, the basin was almost totally ice-covered, and the size of the drift-ice field was 180 km in the north-south direction and up to 120 km in the east-west direction. The ice had been packed more toward the east and north coasts by the prevailing westerly winds. The thickness of the coastal fast ice was 0.4−0.8 m, and in the north the undeformed ice in the drift-ice field was 0.2−0.5 m thick. Several deformation events had occurred during the winter, so the amount of ridged ice was large. During a northerly storm from 15 to 18 March, the ice on the eastern side of the basin was compact and weakly moving southward, while further out there was a sharp shear line with more loose ice drifting much faster in the west.

Wind data were available at the Finnish Meteorological Institute for the lighthouse stations Kemi 1 and Marjaniemi and were averaged for a representative wind field (Fig. 2). The weather was windy and the ice conditions changed much in the basin. The wind speed was usually >5m^S−1, with strong winds (>15m^S−¹) occurring on the 9th, 12th, 14th and 19th. From 5 to 13 March, southerly and southwesterly winds drove the ice northeastwards, opening a wide lead in the south and forming new ridges off the Finnish coast in the north. Two major ridging events occurred on 12 and 14 March. Then the wind direction turned northerly, and the ice moved back southwards, opening a flaw lead at the northern fast-ice boundary. Due to the cold weather, the lead froze over, and at the end of the experiment the basin was fully ice-covered again.

Fig. 2.

The wind velocity in zip-97 shown as a vector time series. the vectors are averages of the wind at the lighthouses marjaniemi (at the base) and kemil (70 km north).

The path of the drifter array is shown in Figure 3. Between 7 and 12 March the southwesterly winds forced the array to the northeast, with compression occurring toward the fast-ice boundary. The ice motion was directed to the right from the wind, as expected, but was also affected by the basin geometry. Then the northerly wind drove drifters D557 and D559 south, while only small changes occurred in the behaviour of the other drifters. A large shear strain therefore resulted in the array. In fact there were at least two marked shear lines in the coastal boundary zone: one within the drifter array about 30 km from the fast-ice boundary, and the other 10 km further out.

Fig. 3.

The gps drifter trajectories, 5−23 march 1997. the drifter labels are shown at the beginning of each track.

The raw 10 mm data were used for the first look analysis. For further analyses, the gaps were filled by linear interpolation, and the time series were low-pass filtered with the filter transition band of 6−8 cpd (cycles per day) using the Kaiser filter. The cut-off band was chosen to make the noise level lower than the signal and to ensure that sudden shifts created by the GPS system were sufficiently smooth. The GPS noise is not necessarily Gaussian, which may affect the features of the filtered time series. There are no significant tides in the Baltic Sea; inertial oscillations are often found, but they are not fully resolved by the present filter. The filtered records were resampled at 2 h intervals to make the Nyqvist frequency equal to the filter cut-off. This low-pass filtering with cut-off reduced the noise level to 10 m.

Unfortunately, a serious outlier problem was found. In seven cases, remarkably rapid displacements, on the order of 1 km per 10 mm, were recorded, but they are considered questionable. A careful examination showed that the most likely explanation is the following. Occasionally, GPS errors may become quite large in recording sequential shifting positions, i.e. there is inertia in the system to determine whether a drifter has been displaced or not. Such rapid shifts have not previously been reported from this basin. Distributed over a 4 h filtering period, a 1 km displacement averages to 42 m which is the standard deviation for the positioning of a fixed position.

3.2. Ice drift

The equation of motion of drift is written (e.g. Reference Leppäranta and LeppärantaLeppäranta, 1998):

where p is ice density, h is ice thickness, u is ice velocity, t is time, / is the Coriolis parameter, k is the unit vector vertically upward, a is ice stress, τ_a and τ_w are the tangential stresses of air and water on ice, g is the acceleration due to gravity, and ξ is the sea-surface elevation. The governing terms in the dynamics of the thin Baltic Sea ice are the internal friction of the ice and the air and water stresses. A natural inertial timescale becomes t1 ∼ τa/(ρhu), where u is the ice-velocity scale. For u ∼ 0.1 m s"₁, we have TI ∼ 10₃ s.

An extreme is the free-drift case. The internal friction and advection are neglected and then the stationary solution of the free-drift velocity u_F is (e.g. Reference Leppäranta and LeppärantaLeppäranta, 1998):

where u_Fa is the wind-driven free-drift velocity and u_w is the water velocity beneath the surface boundary layer. The former part is obtained by contraction (wind factor a) and rotation (clockwise deviation angle 6). In the Baltic Sea free-drift conditions, α ≈ 2.5% and θ α 30° (Reference Leppäranta and OmstedtLeppäranta and Omstedt, 1990). For moderate and strong winds, the wind-driven contribution dominates in the Baltic, u_f ≈ u_Fa.

With plastic internal ice friction, the one-dimensional solution is (Reference Hibler and UntersteinerHibler, 1986):

where p* is the compressive strength of the ice, l is the wind fetch, ρ_w is water density and c_w is the ice-water drag coefficient. Thus the ice fails as soon as τ_al > p*h. In the present case under westerly wind the ice generally moved when the wind speed was >10 ms⁻¹ (τ_a > 0.2 Nm⁻²), and with l ≈ 100 km and h ≈ 0.5 m we have p ≈ 4 × 10⁴ N m⁻² which is close to the value of 3 × 10⁴ N m⁻² observed earlier in the same basin (Reference Leppäranta, Sun and HaapalaLeppäranta and others, 1998). Thus a natural length scale is l ∼ P* tyr_a which is about 40 km for the present maximum wind speed of 15 m s"¹.

In the coastal zone of the drifting ice pack, the free-drift model is usable for offshore winds, but becomes seriously biased when the wind has an onshore component (Reference Leppäranta and LeppärantaLeppäranta, 1998). In the coastal zone, the wind-factor level is an indication of how strongly the internal friction of the ice is resisting the motion. The result for an onshore (within ±30°) wind direction agrees with Equation (3) and ends up with a motionless condition where the wind stress can no longer overcome the yield strength of the ice (Reference Leppäranta and HiblerLeppäranta and Hibler, 1985). If the wind has an onshore component but is directed onshore <60°, there is an adjustment of the ice-thickness distribution so that a shear flow develops parallel to the fast-ice boundary. The ice velocity is u|| = α*u_a, where a* is a coefficient (0 < a* < a) depending on the shear strength of the ice and wind direction.

For the present data, the ice velocities were obtained from the positions by first-order differencing. Assuming that the position error is white noise with a sampling interval At and variance a\ the variance spectrum of a velocity component is

where w is frequency. The observed ice-velocity spectra were quite flat for frequencies of >2 cpd and hit the noise level at 5–10 cpd frequencies. Consequently the filtered data (6−8 cpd transition band) were used for further kinematics analysis. The total standard deviation is which is 94 mm s"¹ in the raw data (At = 10 min) or 3.9 mm s _–1 in the filtered data.

From zero to 2 cpd the velocity spectra were red. Closer to the fast-ice boundary, the red portion became weaker. Ice speeds of >0.05 m s"¹ were observed only four times, on 7, 13−14, 17 and 22 March, even though the wind speed was usually >5 m s"¹. These events lasted about half a day each. The first and second cases were connected with ridging events under southwesterly winds, while the third case occurred during the northerly storm.

The northerly wind caused a slight offshore component in the ice drift in the north, but further south the direction of the coastline turned toward the wind direction. The coast provided a barrier for the drift ice, so the velocity did not approach the free drift, but there was a long shear line further out, beyond which the free-drift state appeared. The ice resistance was consequently dominated by its compressive strength, and a good estimate for the shear strength of the ice was not obtained. Over the next 3 days, the freely drifting ice continued south and cracks appeared in the compact coastal zone.

The time series of the drifter D559 velocity is shown in Figure 4. The ice velocity was usually very low, well below 0.01ms−¹, which in fact is zero within the given accuracy. The movement took place in short pulses of not more than 12 h. The only exception started in the evening of 14 March, when the velocity peaked sharply at 0.5 m s"¹ and the spin-down lasted >1 day. Such high speeds are occasionally observed in the Baltic under very strong winds. Also shown are a few outliers resulting from GPS errors as discussed above. The velocity outcome in the drifters was well correlated, but closer to the fast-ice boundary the levels were lower. The maximum speed was about 0.05 m s"¹ for drifters D556 and D558 and 0.1 m s"¹ for drifter D540.

Fig. 4.

Observed velocity time series of drifter d559. the raw 10 win data are presented as crosses; the circled points are classified as outliers due to the gps errors. the straight line equal to 0.01 cm s–1 shows a conservative uncertainty limit

It is clear that the drift velocity was different from the free-drift case (Fig. 5). With increasing wind speed, however, the ice speed approached the free-drift level. This is expected for a plastic system where drag forces scale with squared velocities but the internal friction is strain-rate (or coastal-velocity) independent. In the other drifters, there was a similar tendency but not so strong as for drifter D559. For lower wind speed, the ice speed was close to the measurement noise level. Also, with increasing wind speed the angle between the ice and wind velocities converged toward 40−45° while the free-drift value was 30° in the Baltic. This difference is due to the geometry in the dynamics of the ice field, favouring the main axis of the basin, because the width of the basin is only about twice the length scale l ∼ p*h/τ_a of compact Baltic drift ice.

Fig. 5.

Based on drifter d559 are shown: (a) the wind factor equal to the ratio of ice speed to wind speed, the dashed line illustrating the theoretical free-drift value; and (b) deviation angle (clockwise angle from wind vector to ice-velocity vector). free-drift value is about 20° for wind speed >10m s–1.

3.3. Ice deformation

Deformation of the ice field is obtained from the velocity gradient:

where ϵ is the strain-rate tensor, ω is the vorticity, and u and v are the × and y components of the ice-velocity vector u (e.g. Reference Hibler, Weeks, Kovacs and AckleyHibler and others, 1974; Reference Leppäranta and LeppärantaLeppäranta, 1998). Strain rate has two principal axes with values _ϵ1 and £₂, ϵ₁ > ϵ², and furthermore their sum equals the divergence of the flow and their difference gives twice the maximum rate of shear in the deformation. The filtered velocities were used to estimate the deformation, and the standard deviation became approximately 2σ/(iδt) ≈ 1.0 × 10−3 h−1 , where i = 20 km is the size of the measurement array.

The area of the drifter array decreased significantly during the experiment (Fig. 6). In the beginning it was 310 km², and it decreased to 200 km² on 17 March before starting to increase again. Since the initial ice compactness was about 1.0, this means that the ice thickness must have increased by 50% within the area of the array.

Fig. 6.

Evolution of the drifter array area during the period of the experiment.

The time series of the principal-axis presentation of the strain rate illustrates the physical deformation of the drifter array (Fig. 7). Half of the time, the deformation level was close to the measurement noise level. It is seen that often the strain was nearly uniaxial. In two cases there was a biaxial strain period of about half a day: (1) 13 March, 1800 h to 14 March, 0800 h, and (2) 16 March, 1000−1800 h. The uniaxial strain equals convergence and also twice the maximum shear strain. In the biaxial cases, the signs of the principal-axis values were opposite, which gives smaller convergence and larger shear. Whether contraction or dilatation, there was a dominant direction, although this varied over different cases. The direction comes from the wind and coastline orientation. Also it is seen that major deformation events lasted about half a day, as was also the case for the motion events. The reason for this is not known, but the forcing and the evolution of ice strength lie in the background.

Fig. 7.

Principal-axis presentation of the strain-rate tensor at 2 h time intervals based on the filtered data. north is up. the notation 10/15 means 10 march 1997,1500 h utc. solid lines mark dilatation, and dashed lines mark contraction.

From 7 to 9 March, there were more-or-less onshore convergence cases, with ridge formation being observed. On 14 March, there was substantial deformation in both principal-axis directions, with contraction along one axis and dilatation along the other. The contraction axis was again onshore and resulted in the second ridging episode during the experiment. When the wind shifted north after 13 March, deformation was at first weak. Subsequently, on 18 March, nearly uniaxial dilatationtook place. The ice opened up, with cracking parallel to the coastline; the northerly wind tends to open the ice since, via the Coriolis effect, the ice drifts 20−30° to the right of the wind direction.

The directions of the principal axes were mainly northeast and northwest. That is, the geometry of the whole basin rather than the direction of the local fast-ice boundary determined them. The length scale of deformation being comparable to the size of the basin, the geometry plays a major role. Like the strain rate, vorticity was also very low except for short intensive periods (Fig. 8). There was a negative tendency from 9−10 March with a peak of −0.1 ° h⁻¹. The vorticity was close to zero at this time, but otherwise peaked at 0.2° h⁻¹ late on 11 March. The magnitude of vorticity appears to be much less than the rate of shear in the present data, which is likely due to the direction of the forcing with respect to the coastline orientation.

Fig. 8.

The time series of the deformation of the drifter array based on the filtered data: (a) principal strain rates ϵ1 > ϵ2, (b) divergence (solid line) and maximum rate of shear (dashed line); ( c) direction of the first principal axis; and(d)vorticity.

Compared with results from the central basin of the Bay of Bothnia (Reference LeppärantaLeppäranta, 1981), the main differences are that the proportion of (nearly) uniaxial strain cases is larger and that the level of large deformation rates is larger (2% h⁻¹ compared to <1%h −1 in the central basin). Both these features can be explained by the presence of the coastline, which limits the deformation possibilities and which introduces large spatial changes for the plastic ice flow at the fixed boundary.