Introduction

The routine availability of imagery from polar orbiting meteorological satellites over Arctic sea ice made possible the first large-scale studies of the patterns of open water or leads and thin ice. Studies have focused on the geometrical shapes of the patterns, their lengths and widths, their formation and disappearance, and ultimately the identification of specific mechanisms of lead formation.

Researchers have investigated the formation of and changes to lead patterns on a variety of spatial and temporal scales. Reference Marko and ThomsonMarko and Thomson (1977) focused on the large scale (hundreds of km) rectilinear or diamond-shaped patterns formed by networks of intersecting leads in the ice and concluded that these features were a result of semi-brittle failure of the ice cover during relatively rapid strain rates due to wind forcing. Reference SobczakSobczak (1977) mapped the distribution of leads and basin-scale ice movement over the Beaufort Sea and found that the passing of atmospheric pressure systems developed various sea-ice patterns which depended on the rate of movement of the systems and the intensity of the pressure gradients. Recently Reference Barry, Miles, Cianflone, Scharfen and SchnellBarry and others (1989) found that in some cases lead orientations could change noticeably within 24 h while in other cases the leads exhibited substantial persistence of orientation. They show that periods of persistence occurred when ice concentration was high and ice velocities low, suggesting the influence of internal ice stresses. Reference SteffenSteffen (1987) noted that the distribution of fractures in ice is a measure of the capacity of the ice cover to sustain deformation through convergence and shear. Thus one might expect that quantitative measurements of lead pattern changes might provide information about the stress state and mechanical properties of the ice (Reference ErlingssonErlingsson, 1988, 1989, 1991; Reference PritchardPritchard, 1988).

We present results from a case study of lead pattern change and movement in the Beaufort Sea during a period of southwesterly to southerly winds. A time series of AVHRR images during 31 March to 14 April 1991 was combined with digitized sea-level pressure fields to determine the influence that the wind forcing had on the lead patterns. This was during the period of the LEADEX pilot experiment. Changes in the lead patterns are seen as a horizontal movement of the leads or as the appearance or disappearance of certain geometric lead configurations such as the large diamond-shaped patterns. These larger-scale diamond-shaped lead patterns were seen to maintain their shapes and spacings for periods of three to four weeks. We describe the meteorological conditions present during the study period, and relate the meteorological forcing to the behavior of the lead patterns. We note that the atmospheric forcing changes direction and magnitude on scales of days to a week. Finally, we discuss the presence of smaller-scale lead patterns within the larger diamond-shaped patterns and the implications of this phenomenon to the scale invariant nature of the features seen in ice fields.

Lead Pattern Changes

Digital AVHRR imagery were collected once and sometimes twice per day over the Beaufort Sea (most often at 1300-1400h GMT). The images were navigated and remapped to a common grid. Sea-level pressure analyses were obtained every 6 h from the Anchorage Weather Service Forecast Office to track the movement of significant weather features such as fronts. Digitized sea-level pressure fields obtained from the National Meteorological Center were used to calculate surface wind fields using a 30% reduction in speed and a 20° rotation in direction. The wind fields were then remapped to the same grid as the satellite images.

From satellite imagery the Beaufort Sea could be divided spatially into two distinct lead pattern regimes. These regimes were initially separated by a long lead running diagonally from southwest to northeast across the Beaufort Sea (Fig. 1). This lead appeared to be the result of a persistent southwesterly flow over the Beaufort Sea which compacted the ice located south of this line against the eastern boundary of the Beaufort Sea, formed by Banks, Melville and the Queen Elizabeth Islands, but allowed ice motion on the north side of this lead.

North of the diagonal lead the dominant lead configuration was the diamond-shaped pattern discussed by Marco and Thomson (1977). These large curvilinear and rectilinear lead patterns (Reference ErlingssonErlingsson, 1991) with spacings in the order of 150 km were formed by two intersecting sets of leads. In general, acute angles of intersection were in the range 20-40°. Within the large-scale (150 km) diamond-shaped patterns there were also smaller-scale (10 s km) diamond-shaped features whose directions were similar to the orientations of the larger-scale lead pattern. South of the diagonal lead the large-scale lead patterns were curved and oriented in a north-south direction apparently due to the no-slip boundary between the coastline and the open ice pack.

Fig. 1. AVHRR image (3 km resolution) for 1300h GMT, 1 April 1991. The image shows a long lead (arrow) running diagonally southwest to northeast across the Beaufort Sea with large-scale diamond-shaped lead structures north of this line and arch-shaped lead structures running basically northward from the coast and merging with the diamond-shaped features to the north. Surface winds (in kt) are also plotted on the image using the standard meteorological convention.

Fig. 2. Sea-level pressure map for 1800 h GMT, 6 April 1991. This pattern was typical of the flow regime over the Beaufort Sea during the period 31 March-6 April. Winds were generally southwesterly.

Fig. 3. Sea-level pressure map for 0000 h GMT, 8 April 1991 showing a strong frontal system across the Beaufort Sea. Prefrontal winds were from the south and post-frontal winds from the west creating a strong wind shear at the front.

Fig. 4. AVHRR image (3 km resolution) for 1300 h GMT, 9 April 1991 showing changes that have occurred in the lead patterns since 1 April. Several more slip lines (arrows) can be seen to the south of the original long diagonal lead.

The period can be divided into several wind-forcing regimes. Prior to 7 April the time series of surface geostrophic winds showed that winds were nearly parallel to the long diagonal lead (Fig. 2). A weak frontal system moved across the Beaufort on 5 April with winds behind the front having a slightly more westerly than southwesterly component. Then on 7 April a strong cold front moved across the Beaufort Sea (Fig. 3) with strong southerly prefrontal winds and winds from the west behind the front. After this frontal passage several additional long leads appeared to the south of the original diagonal lead, positioned at an angle of about 30° to the original lead (Fig. 4). With westerly winds behind the frontal system continuing on 8 and 9 April these new leads partially closed. We conjecture that the stresses induced by westerly winds prior to the passage of the frontal system were large enough to have exceeded the yield strength of the existing ice cover, giving rise to the lead system. Next there was divergence with southerly winds opening up the pattern followed by shearing deformation with westerly winds. From 10-14 April a low over the Chukchi Sea and a high over the southeastern Beaufort Sea resulted in an extended period of strong southerly winds during which these leads reopened and a large coastal lead formed along the Alaska coast (Fig. 5).

Fig. 5. AVHRR image (3km resolution) for 1300 h GMT, 12 April 1991 showing the large coastal lead that has opened up along the north coast of Alaska due to the prolonged period of strong southerly winds over the Beaufort Sea.

Ice Velocities

In this section we analyze the lead motions and changes that took place in the lead patterns during the above meteorological regimes. Day-to-day lead motion images were generated on a Macintosh Ilfx image-processing workstation by first inverting the look-up table (i.e. making a negative) of the first image. This image was then combined with the image for the following day using a logical AND operation. The result was an image in which the leads for the first day were white and the leads for the second day were black. Quantitative measurements of the lead motions could then be obtained from this composite image.

An Argument for the Fractal Nature of Ice

An interesting issue for sea ice is the near scale-invariant (or fractal) nature of the crack patterns seen in satellite imagery. Examples of this can be seen in Figure 8. The large-scale diamond-shaped patterns have a spacing of about 150 km and acute breaking angles of approximately 30°. The smaller-scale lead patterns have spacings of tens of km with similar breaking angles.

Consider the one-dimensional case of the sea-ice momentum balance in the x direction, with a frictional drag term dependent on the ice velocity, u_i , an external wind stress, T_a, and the compressional stress σ,

Fig. 6. Lead motion composite image (1 km resolution ) for the period 31 March-5 April 1991. White leads are for 31 March and black leads for 5 April 1991.

Fig. 7. Lead motion composite image (1 km resolution) for the period 5-9 April 1991. White leads are for 5 April and black leads for 9 April 1991.

Fig. 8. AVHRR image (1km resolution) for 1300h GMT, 1 April 1991 showing that within the larger-scale (≈150 km) lead features are smaller-scale (≈10-20 km) lead structures of similar shape and with similar breaking angles (≈30°).

Fig. 9. (a) Results of a simulation for an onshore wind of 10ms⁻¹ and other standard parameters as in Reference Overland and PeaseOverland and Pease (1988). The panel gives the daily ice compactness and thickness for day 1 through day 7. (b) The offshore stress balance shows a shift from a wind stress/water stress balance to a wind stress/internal ice-stress divergence balance near the point of 1.0 compactness, (c) Similar to Figure 9a except the wind speed was reduced from 10ms^−l to 5 m s⁻¹from day 3 to day 4. Note that the ice does not continue to thicken in the nearshore zone (<20km) after the reduction in wind. In this region the ice strength gradient which developed to balance an onshore wind of 10 ms⁻¹is greater than the internal ice stress divergence necessary to balance a 5ms⁻¹ wind.

(1)

We consider a hardening plastic rheology, that the y stresses are such that the one-dimensional case is valid and that there is a coastal wall at x = 0. A hardening plastic is one in which the strength can increase with state variables such as ice thickness. A one-dimensional case implies that there is a confining stress in the y direction such that its gradient is zero. Reference HiblerHibler (1986) investigated the case with a constant wind blowing toward shore and a uniform ice strength, P'; all the deformation is at the coastline and integration of Equation (1) gives

(2)

For the offshore region the stress is below the yield criteria of -P*.

A second case is the solution for Equation (1) in which P' is proportional to h² for a hardening plastic and quadratic dependence for friction (Reference Overland and PeaseOverland and Pease, 1988); the ice thickness is h. Figure 9a shows the growth of the coastal rubble zone and a ridging front for their model after one through seven days for an onshore wind of 10 ms⁻¹. The entire ice field landward of the ridging front is yielding with stress gradient based on the spatial gradient of ice strength balancing the wind stress (Fig. 9b). If the wind is reduced to 5ms⁻¹ after day 4 (Fig. 9c) the strength gradient in the nearshore region is greater than the wind stress and the ice will be motionless landward of 25 km. In the case of Reference HiblerHibler (1986) P* is a constant with deformation only at the coastline σ(x = 0) = −P*. In the second case we had ∂σ/∂x∼ constant with σ∼−P*∼h ².

A way to look at the condition for the stress gradient remaining nearly constant is to consider the space scale over which the stress will vary. Large strength gradients can be maintained over large distances (hundreds of km) while on short length scales (~1 km), the yield criteria is quickly reached for modest values of strength. Thus we can build up a picture of an ice field composed of multiple scales. On the smallest deformation scale we have a stress gradient at the yield point where the absolute magnitude of the stress is small but the local gradient of stress is large. At larger scales, stress from the smaller interactions accumulates. Collectively, these regions require a larger ice stress to deform because of the greater horizontal distances involved. In certain strong ice strength regions, built from previous storms, the strength gradient is steeper than that required to balance the applied wind stress load; i.e. the icefield is below the yield point. Thus we have a fractal-like model where the ice is not ridged at one location as in the first case presented but is yielding on all length scales to form the composite picture (Fig. 8). That the distribution of the depth of ice keels per km follows a negative exponential (Reference Wadhams and DavyWadhams and Davy, 1986), adds further support.

Summary

By analyzing the motion of sea ice in the Beaufort Sea during a southwesterly to southerly wind regime we have been able to corroborate the theoretical results of Erlingsson concerning the breaking angles of ice forced by a wind field. We note that time-dependent winds can change a given icefield from being under shearing stress with leads at an acute angle to the wind direction to a non-cohesive opening pattern with the leads at 90° to the wind direction and then back to shearing. We have noted that a constant stress gradient can consist of a gradient of weaker (thinner) ice over short distances or stronger ice over greater distances. Both features must exist simultaneously to have the scale-invariant lead features seen in the 1-5 April 1991 case.

Acknowledgements

This research was supported by Office of Naval Research (ONR) contract N00014-91-C-0056 with Science Applications International Corporation (B.A.W.) and N00014-92-F-0013 with PMEL (J.E.O.). This paper is contribution No. 1365 from NOAA Pacific Marine Environmental Laboratory.