Ice‐floe collisions interpreted from acceleration data during LIMEX ‘89

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Ice‐floe collisionsinterpreted fromacceleration data duringLIMEX ‘89R.F. McKenna a & G.B. Crocker ba Institute for Marine Dynamics , NationalResearch Council of Canada , P.O. Box 12093,Station A, St John's, Newfoundland, A1B 3T5b Centre for Cold Ocean ResourcesEngineering (C‐CORE) , Memorial University ofNewfoundland , St John's, Newfoundland, A1B3X5Published online: 19 Nov 2010.

To cite this article: R.F. McKenna & G.B. Crocker (1992) Ice‐floe collisionsinterpreted from acceleration data during LIMEX ‘89, Atmosphere-Ocean, 30:2,246-269, DOI: 10.1080/07055900.1992.9649440

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Ice-Floe Collisions InterpretedFrom Acceleration Data During

LIMEX '89

R.F. McKennaInstitute for Marine Dynamics

National Research Council of CanadaP.O. Box 12093, Station A

St John's, Newfoundland A1B 3T5

and

G.B. CrockerCentre for Cold Ocean Resources Engineering (C-CORE)

Memorial University of NewfoundlandSt John's, Newfoundland A1B 3X5

[Original manuscript received 23 September 1991; in revised form 28 November 1991]

ABSTRACT Wave-induced ice motions measured during the Labrador Ice Margin Experiment(LIMEX '89) were interpreted to determine the cause and the frequency of collisions betweenfloes. The LIMEX acceleration data were acquired with an optimal resolution near thepredominant wave frequency and did not contain information above 0.5 Hz. It was thereforepossible to establish the frequency of collisions, but not the magnitude of the events. Eventswere defined by any contact between floes in a wave cycle, and the distribution of timesbetween events indicates that floes are more likely to collide in adjacent wave cycles than ifthe events were independent. Periods of continuous and intermittent collisions were relatedto the wave characteristics, and the frequency of events increased with a decrease in airtemperature and an increase in local wind speed. Contrary to expectations, there was nota positive relation between collision frequency and wave amplitude.

RÉSUMÉ On analyse les mouvements des glaces induits par les vagues, mesurés durantLIMEX '89, pour déterminer la cause et la fréquence des collisions entre les floes. Lesdonnées d'accélération de LIMEX furent acquises avec une résolution optimale près de lafréquence d'onde prédominante et ne contenaient pas d'information au-dessus de 0,5 Hz. Ila donc été possible d'établir la fréquence des collisions mais non la force des événements;un événement étant un ou plusieurs contacts entre les floes dans un cycle de vagues. Ladistribution des périodes entre les événements indique qu'il est plus que possible que les floesse frapperont dans des cycles de vague adjacents que si les événements étaient indépendants.On a associé les cas de collisions continuelles et intermittantes aux caractères des vagues;la fréquence des événements a augmenté avec une baisse de la température de l'air et une

ATMOSPHERE-OCEAN 30 (2) 1992, 246-269 O7O5-590O/92/0OO0-0246SO1.25/0© Canadian Meteorological and Océanographie Society

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Ice-Floe Collisions Interpreted From Acceleration Data During LIMEX '89 / 247

augmentation locale de la vitesse du vent. Contrairement aux prévisions, aucune associationpositive n'a été observée entre la fréquence des collisions et l'amplitude des vagues.

1 IntroductionThe ice floes encountered during the Labrador Ice Margin Experiment (LIMEX)in March and April 1989 were small by most standards; most floes were less than15 m across and were approximately 1 m thick. Collisions between the floes are ofinterest because they influence the lateral deterioration of the floes and contribute towave attenuation within the ice-pack, particularly when there is continuous contactbetween adjacent floes within each wave cycle. On a broader scale, collisionsbetween floes have a role in determining ambient noise levels beneath the ice andin the drift of the pack-ice, but neither of these is pursued in the present work. Thewave-induced motions and the contact between floes are also of importance, forexample, in predicting the dispersal of an oil slick in this environment.

Several features of the marginal ice zone environment are expected to influencethe nature and frequency of collisions between floes. The present analysis concen-trates on the characteristics of the wave field, ambient temperature and local winds.A characteristic feature of small floes is that they tend to follow the motion of thesea surface and are therefore prone to collide on a regular basis according to thewave cycle, in contrast to floes that are larger relative to the wavelength, whichhave more damped motions.

In McKenna and Crocker (1990), the influence of wave amplitude on the relativespeed between floes at the point of contact was investigated. Only direct collisionsin the direction of wave propagation were considered. The contact was assumed tobe inelastic and ceased when the floes drifted apart. Such a situation is likely tocause the largest collision energies for small floes relative to the wavelength (e.g.10-m floes with a 10-s wave period), but contact with other neighbouring floesis probable when floes are not circular or are offset. Furthermore, collisions aremore likely when different wave frequencies and directions are superimposed. Forseveral periods during the LIMEX '89 experiment, the air temperature droppedwell below freezing and ice was formed between the floes, occasionally filling theentire space. This meant that there was continuous energy transfer between floes,with each wave cycle, until the ice melted with the heat of the day.

Rottier (1991) developed a model for predicting collision frequencies under var-ious wave conditions and floe dimensions in an effort to simulate floe collisionsin marginal ice zones. Based on observations in Fram Strait and the Barents Sea,three types of collisions were characterized: (i) a collision that is caused by a di-rect hit, (ii) compression of broken ice pieces or newly grown ice in the interstitialspaces, and (iii) shear between adjacent floes transverse to the direction of wavepropagation. The more irregular the floe sizes and shapes are, the more likely thattype (iii) interactions will occur. Collisions may not fall uniquely into one of theseclasses, but are likely to have varying contributions from each. Because it was not

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248 / R.F. McKenna and G.B. Crocker

possible to isolate the different types of collisions in our data, the term "collision"is used to refer to any contact between adjacent floes during a wave cycle.

Even though the interpretation of floe collisions from the motion package datawas not the primary goal of the LIMEX '89 experiment, the evidence of collisionsin the data provides an opportunity to investigate the behaviour of small floes undermoderate wave conditions. The ice motion records are interpreted to estimate thenature and number of collisions that occurred during the measurement period.

2 Measurement of ice accelerations: Motion packagesSix instruments for measuring ice motion were constructed for the LIMEX '89experiment. These are subsequently referred to as "motion packages". Each consistsof three accelerometers mounted in orthogonal directions, a gyro measuring tilt, anda compass, allowing for the measurement of all of the translational and rotationalmotions of the floes. The accelerometers were Sundstrand QA-700 proof masstype and the gyro was a Humphrey VG-24 model, with pitch and roll measuredusing potentiometers. Rotation in the horizontal plane was determined using Endeco869 solid state flux gate compasses. The motion packages were optimized formeasuring lower frequencies, and the analogue signal was passed through a 0.5-Hzanti-aliasing filter. With digital storage at a premium, the data were logged at 4 Hzin blocks of 215 s and filtered digitally using a low-pass finite impulse responsefunction filter. The data were then resampled at 1.33 Hz and recorded in blocks of200 s.

The ice motion packages were deployed during phase II of the LIMEX '89 experi-ment conducted from the MV Terra Nordica between 15 March and 4 April 1989.Six experiments were conducted with the motion packages, with varying numbersof the packages operating simultaneously. The packages were not fastened to theice, but a good bond was achieved since the ice was deformed by the weight ofthe instrument. The packages were positioned by visual means, as near as possibleto the centre of mass of each floe, and there was no evidence that there was anysliding of the packages on the ice surface in the time series used in the presentstudy.

The first few deployments were made to coincide with overflights where syntheticaperture radar imaging was recorded. Subsequent deployments were dedicated towave/ice interaction studies, and the last of these, termed experiment 6 (2 April1989), forms the basis for the present study. The total period of the deploymentduring experiment 6 was approximately 20 h. Deployment times and floe charac-teristics are listed in Table 1.

Because of the memory limitations of the data acquisition system and a desire toextend the period over which data were acquired, a special strategy was used forsampling. Data for the six channels were recorded at a sampling rate of 1.33 Hz (atime increment of 0.75 s) for a 30-min period each hour, resulting in a discontin-uous series of 2430 record sampling periods. For the most part, ice motions wereconsistent over these time-scales and each time series was long enough to obtaingood estimates of the wave spectra. Following the experiment, digital means wereused to correct and calibrate the data. Translational accelerations were resolved

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TABLE 1. Details of motion package deployments

PackageNumber

3

5

6

DeploymentTime(UTC)

21002 April

22152 April

22002 April

RecoveryTime(UTC)

16403 April

16153 April

16003 April

Thickness(m)

1.13

0.89

0.89

Floe

Dimensions(mxm)

28X25

13X 11

20 x 15

into N-S and E-W components in the horizontal plane, and into a vertical or heavecomponent. Tilt angles were also resolved to N-S and E-W components. The datawere analysed using a right-handed coordinate system; therefore positive accelera-tions and ice surface gradients are oriented north and west. The physical resolutionand the frequency response of the measurements were better than the resolutionsimposed by the initial digitization of the analogue signal and by the low-pass fil-tering. Therefore the latter controlled the quality of the data. The resolution of theaccelerations was about 0.001 m s~2, the pitch and roll angles were recorded to±0.01° and compass bearings were resolved to ±0.3°.

The motion packages gave accurate measurements of wave-induced motions,but did not provide much information on the high-frequency response due to floecollisions. Fortunately, although it was not possible to achieve detail on the signatureof the collisions, there was generally sufficient detail to establish whether collisionshad actually occurred, except for very low sea states.

It should be noted that the motion sensor packages record the motions of the icefloes, not of the sea surface. In the following discussions, it is assumed that the twoare the same. This will be true only if the Response Amplitude Operators (RAOs)of the floes are unity for all motions. Although this is not always true for largeirregular bodies such as ice floes, the low-pass filter effect of the ice-pack results inwave spectra with very little of the high-frequency energy normally present on thesea surface. Theoretical analyses by Masson and LeBlond (1989) and Rottier (1991)have shown that for most of the ice, wave and water depth conditions encounteredduring experiment 6, all of the RAOs would be very close to unity. Also, the floesselected for package deployments were chosen primarily for their symmetry, andthe packages were placed as close as possible to the floe centres.

3 Ice and environmental conditionsThe present experiment was part of a series conducted from the MV Terra Nordicabetween 16 March and 4 April 1989. On 2 April, the vessel was drifting with thepack-ice, 200 km northeast of the eastern coast of Newfoundland, in a water depthof approximately 300 m as shown in Fig. 1. This is near the edge of the continentalshelf over the Funk Island Bank. At that time, the outer extent of the pack-ice wasapproximately 120 km offshore of this location, placing the experiment well within

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51

47

Edge ofContinental

Shelf

Experiment \

MaximumIce Extent!

Maximum;;!.̂Ice Extent

56 54 52

Longitude (W)

Fig. 1 Map of experiment location.

50 48

the pack-ice. The pack-ice cover was by no means continuous within this area andthere is evidence of locally generated, high-frequency waves for brief periods inthe data.

The initial and final positions of the floes on which the motion packages weredeployed are shown in Fig. 2. Drift was consistently toward the southeast overthe 20-h period spanning 2-3 April 1989. Although a significant distortion of theice-pack in this area over the measurement period occurred, this was not welldocumented by remote imaging and cannot be used to account conclusively for icecollisions. However, the degree of consolidation of the ice-pack varied considerably,and the distortion of the triangle formed by the positions of the packages does notnecessarily imply that the pack should have been any more or less consolidated.Total displacements of the packages over the period ranged from 22 to 36 km,resulting in an average displacement rate of 0.45 m s"1.

The package positions shown in Fig. 2 were not measured at the same time,nevertheless, small temporal errors do not alter the following conclusions. Refer-enced to the initial package positions Xi(iJ,k = 1 , 2 coordinates in the plane ofthe ice; where a sum is made over repeated indices), the strain was calculatedfrom the package displacements £/, using

(1)

where a linear estimate of the displacement gradients was made from the data. Theaverage strain ey/2 experienced by the ice in this area was about 0.8, which means

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Ice-Floe Collisions Interpreted From Acceleration Data During LEMEX '89 / 251

50

49.9

49.8

v•? 49.7

49.6

49.5

49.4

UMEX 89 ICE MOTION : Experiment 6

initial package positionsfinal package positions

Package (Julian day hourmin)

(92 22:00) 6 I

5 (92 22:15)

l 3 (92 21:00)

5' (93 16:15)

K(93 16:00) 6'x

•3' (93 16:40)

51 50.8 50.6 50.4 50.2

Longitude (W)

Fig. 2 Initial and final positions of the ice motion packages for the experiment 6 deployment.

that on this scale the ice-pack diverged by about 80% based on the initial packagepositions. The equivalent shear strain (ey-ßy)1/2 (where ey = ey- — 8^6^/2) was 0.7,which is of the same order as ey/2, indicating that there was a combination ofdeformation modes. Furthermore, there was a significant rotational component tothe motion. It is unwise to make any strong conclusions from these indices sincethe ice concentration was highly variable and, for any given half-hour period, thepackage may have been in a congested ice region. But the data suggest that floecollisions in the marginal ice zone do not require a strongly converging ice fieldover a scale of 5 to 10 km for these ice conditions.

In general, the floes were small, thin and in a state of deterioration. As with mostice in the Labrador marginal ice zone, the ice was formed in an active environment.Thin sections of sample ice cores revealed that the crystal structure near the surfacewas a mixture of frazil ice, snow ice and columnar ice. Below the first 40 cm or so,it was mostly columnar but still retained evidence of an active deformation history.Some of the floes were rafted and thus were greater than 2 m thick, althoughit is not believed that such rafted floes formed a significant proportion of theice-covered area. Floes tended to be approximately circular in shape because offrequent collisions, and floe sizes ranged from 4 to 30 m as documented by Winsoret al. (1990) during the experiment. The floes had a mean diameter of 9.5 m, andthe average ice thickness was 1.0 m.

The range in the floe dimensions encountered was not large. Except for brokenice pieces between floes, most of the floes were about the same size and thickness.Although one of the floes on which a motion package was located did fracture

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10 m/s

00:00 12:00

April 2

00:00 00:00 (UTC)

April 3

Fig. 3 Measured winds (15-m height, 10-min average) and wind speed at the MV Terra Nordica for2-3 April 1989.

during a previous deployment, there was otherwise little evidence of this. It ispresumed that these floes had reached a stable size with regard to flexure and wouldnot tend to fracture again until melting had further decreased their thickness.

The floes that the packages were placed on were not radically different from theirneighbours in size or shape, except they had flat surfaces, had little or no visibleridging and were not rafted. In most respects, they can be considered representativeof the floes in that area at that time.

The air temperature varied from —15 to about +5°C between 16 March and4 April, which is significant since it caused considerable growth and melting ofthe ice between the floes. New ice was observed each morning between floes. Thethickness of this ice, which appeared to have formed under continuous deformation,varied from a few centimetres to about 20 cm. There was often evidence of brashice that had been broken up from the continuous contact mixed with the newerice. The air temperature was 0°C at the time of the deployment of the motionpackages on 2 April and decreased to —4°C at 1000 UTC (just after sunrise) on 3April. The significance of such ice on collisions during the deployment is uncertainsince ice conditions were not surveyed continuously over the measurement period.Nevertheless, an air temperature of —4°C is not believed to be sufficient to causesignificant ice growth between floes and should not be considered as a likely causeof collisions in this case.

The local wind was recorded from the deck of the MV Terra Nordica at aheight of about 15 m above sea level. The wind was sampled in 5-s bursts eachminute and averaged. Winds at 30-min intervals were obtained by averaging 10 ofthese values about the required time. The wind vectors and the corresponding windspeeds are shown in Fig. 3; wind speeds ranged from 4 to 18 m s"1. Predominantsoutherly winds for the day preceding the deployment of the motion packages were

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Ice-Floe Collisions Interpreted From Acceleration Data During LEVDEX '89 / 253

TABLE 2. Wave characteristics determined from motion package displacements: significant wave height,Hs, mean zero-crossing wave period, T, and mean compass direction, <)>, from which thewaves were incident

Time(UTC)

2130-22002230-23002330-00000030-01000130-02000230-03000330-04000430-05000530-06000630-07000730-08000830-09000930-10001030-11001130-12001230-13001330-14001430-15001530-16001630-1700

Hs(m)

0.280.280.320.360.350.360.300.330.350.330.300.300.310.270.330.260.280.260.250.27

Package 3

T(s)

10.09.89.79.79.89.510.09.79.89.910.810.911.411.512.011.711.911.811.711.6

<t>O136129138122132153140161145157171204203176168163153151172181

H,(m)

0.320.340.370.380.380.350.320.340.320.260.280.260.220.240.220.250.220.28

Package 5

T(s)

9.99.89.79.69.59.79.59.710.210.711.111.211.311.611.711.711.811.6

4»o184182188195199181168145161177192213216222215249190187

Hs(m)

0.300.310.280.330.290.290.280.300.260.230.210.170.180.200.180.240.280.20

Package 6

T(s)

10.210.110.310.09.610.210.210.510.811.211.411.811.911.912.311.911.611.9

<t>O

124143132148131140160159169171176177171148132175179177

responsible for the initial swell at the ship, which was attenuated by 3 April whenthe wind veered to the west and northwest.

4 Acceleration and displacement time seriesAcceleration, tilt and compass data were recorded for a 30-min period each hourfor the duration of experiment 6. Displacements of the packages were calculatedfrom the accelerations by filtering out frequencies less than about 0.05 Hz, thenintegrating twice with respect to time. Ice motion characteristics for each half-hourperiod were described by 2292 data points in each of the three translations and thetwo surface slopes corresponding to the north and west directions. The analysis ofthe data follows the approach of Longuet-Higgins et al. (1963) and Wadhams et al.(1986) for which details are given in the Appendix. Power spectra were computedin 512-point segments, which were overlapped by 256 points and processed usinga Hanning window.

The attributes of the motion of the three motion packages are shown in Table2. Details on the calculation of the significant wave height Hs, the mean zero-crossing wave period T and the direction from which the waves are travelling <|)(clockwise from true north) are given in the Appendix. Three indices of directionwere calculated: the average direction weighted by the energy in the heave spectrum,the direction for the frequency where the heave energy was at a maximum, and thedirection for the frequency corresponding to the wave period T. All were in close

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agreement and the first, the average direction, is given in Table 2 since it had theleast variability. Wave directions calculated from the horizontal accelerations andthe surface slopes agreed to within a few degrees in all cases. Any difficultiescaused by the circular distribution of directions when calculating the first momentof the wave direction with respect to the heave spectrum were avoided by using astepwise rotation of axes.

Similar patterns over time are evident for the three packages. Initially, significantwave heights were above 0.3 m and decreased over the deployment period. At thesame time, the dominant wave period increased from about 10 to 12 s. The transitionwas earliest for package 6, and latest for package 3. It is worth remembering thatthese are the characteristics of waves that have propagated through the ice-pack;they are not just the cause, but are to some extent, the result of floe collisions. Anestimate of the wave propagation speed showed that the waves passing package3 would reach package 5 in less than half an hour. There is a change in wavedirection for package 3 at about 0800 UTC on 3 April but, overall, the average wavedirection was fairly constant. Further discussion of wave characteristics is left tothe discussion associated with Fig. 12.

Angular spread (see Appendix) varied between 40 and 60° for all three packages,with no trend observed during the course of the deployment. This index can varybetween 0° (oriented) and 90° (scattered), and tends to increase while waves areattenuated in the marginal ice zone (Wadhams et al., 1986).

5 Characterization of collisionsAs noted earlier, the acceleration data were filtered to optimize data storage andemphasize the frequencies related to the wave period rather than the high-frequencycycles encountered during collisions. The data had a frequency response that wasonly sufficient to identify deviations from regular floe motion, but not enough tocharacterize the signature of the collisions. It became clear from examining theacceleration traces that it would be impossible to identify the collision types, e.g.direct hit, buffered hit and shear, only that something out of the ordinary hadoccurred.

In identifying collisions from the measured ice motions, the first thing to noteis that, as they were configured for the present experiment, the response of themotion packages to sinusoidal forcing at 0.1 Hz is continuous. Furthermore, thereare periods during the present experiment in which there are no discontinuitiesin the acceleration records. Based on the theoretical response of floes calculatedby Masson and LeBlond (1989) and Rottier (1991), a 10- to 20-m diameter by1-m thick floe in 10-s waves follows the water particle motion. If discontinuitiesappear in the accelerations, they are most likely caused by contact with adjacentfloes or by the response of the package to higher frequency wave excitation. For5-s waves, the wavelength and floe size are of the same order and the floe motionmay not concur with the wave motion. The surge RAO will be less than unity andresonance in heave is unlikely for these floes at this and any other wave period.The ice motion is potentially out of phase with the waves, leading to conditionsthat allow collisions with any adjacent floes.

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Practically, the following guidelines were used to help identify wave cycles inwhich contact between floes occurred:

1) Discontinuities appeared in the horizontal acceleration, but not in the verticalor heave component. If discontinuities are found in the heave cycle also, thisdoes not necessarily exclude the possibility of contact since wave-induced floemotions that are not resolved in the data may be a cause of collisions.

2) Repeated discontinuities at a given point in successive wave cycles were ob-served. These were typically near the point of maximum or minimum horizontalacceleration and correspond to the minimum or maximum horizontal displace-ments of the floe.

As expected, most of the evidence for collisions was found in the horizontalaccelerations. The tilt measurements did not show much evidence of inter-floecontact. Although one would expect some compass response to contact since thefloes are free to rotate, the response time and accuracy of the compass data wereinsufficient and few collisions were noted.

The time series can be divided into two fundamental segments that were evidentin the data from all three of the motion packages. The first period began at 2230UTC 2 April (1900 LT 2 April) and lasted until about 0800 UTC on 3 April. Therewas a significant swell, westerly winds, and falling air temperatures with the onsetof darkness. The time series show collisions that were sometimes regular with thewave cycle, but mostly intermittent.

Wave amplitudes were smaller between 0800 and 1600 UTC on 3 April. Duringthis interval, temperatures were at their lowest (—4°C) and the winds were veeringto the northwest. Because of the small swell amplitudes, there is less resolution inthe accelerations and less certainty that variations in the translational componentsin the horizontal plane were due to ice processes rather than due to noise and todigitization errors. It is more likely, however, that frequent, if not continuous, con-tact occurred between floes. An example from this period is given by the horizontalacceleration trace shown in Fig. 4. The accelerations are distinctly skewed and themotion is likely due to repeated collisions at a given point in the wave cycle. Itis possible, but less likely, that this was caused by the locking of adjacent floessuch that the net motion was that of an oddly shaped body for which the motionwas not measured at the centre of mass. Whatever the cause, such contacts are stillconsidered as collision events.

The transition between the initial period of intermittent events and the latterperiod proved to be interesting. Continuous events were observed at about 0740UTC on 3 April as shown in Fig. 5. The N-S horizontal component of the powerspectrum for the half-hour period in which this record originated is shown in Fig.6; considerable energy is found in the frequency range centred on 0.27 Hz. Theenergy at this frequency was not found in the corresponding heave spectrum. Inspite of the lack of resolution in the data at these frequencies, Fig. 6 is significant inthat it indicates the quantity of energy in these events. The discontinuous nature ofthe heave component of the acceleration is interesting since heave was continuous

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20 40 60 80 100 120 140 160 180

Fig. 4 Translational accelerations from motion package 6 between 1157:14 and 1200:37 UTC on 3April 1989.

during most of the collision events recorded at other times. A further explanationof these features can possibly be concluded from subsequent events.

A higher frequency component was present in the acceleration data for package5 subsequent to 1030 UTC on 3 April. This was not sufficient to influence the meanzero-crossing wave period but nevertheless made the identification of collisionsdifficult. Because the RAOs for the floes at this wave period are not unity and thereis poor frequency resolution in the data, it is difficult to make definite conclusionsregarding the latter portion of the record for package 5. Although concurrent wavedata were absent during the bulk of the experiment, Eid et al. (1991) analyseddirectional Waverider buoy data measured in a small area of open water not far fromthe location of package 5 between 1200 and 1330 UTC on 3 April. A significanthigh-frequency component with a 4- to 5-s period was found in the wave spectrum.This period coincided with the strongest winds recorded during the deployment andindicates that local wind may have been a factor in the observed ice motion. Theeffect of wind on floe collisions potentially results from these locally generated

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0.1

0.05

0

-0.05

-0.1

VnA/VM

20 40 60 80 100 120 140 160 180

Fig. 5 Translation^ accelerations from motion package 5 between 0737:00 and 0740:22 UTC on 3April 1989.

waves and also from the differential drag on neighbouring floes, which will bringthem into contact.

Not much more can be established from the data for the latter period, following0800 UTC on 3 April, except that the contact between floes was probably continuoussave for brief periods near the end of the record. There is a correlation betweenthe decrease in temperature and the decrease in the wave amplitude, but thesechanges also follow a change in the wind. Whether there was more ice in theinter-floe spaces causing increased wave attenuation, or whether a decrease in thewave amplitude allowed ice to form, can probably be answered by assuming thatthe process was interactive. There is no information available to confirm that theice-pack was actually converging in the immediate neighbourhood of the floes onwhich the motion packages were located, a process that could have explained theincreased contact.

The remaining discussion will focus on the earlier period when intermittentcollisions took place. A portion of the acceleration records for package 5 is given

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10- '

0.4 0.5 0.6 0.7

Fig. 6 Power spectrum of N-S horizontal accelerations from motion package 5 between 0730 and 0800UTC on 3 April 1989.

in Fig. 7, which suggests that there were four cycles where contact with adjacentfloes was made and possibly another cycle thereafter. Figure 8 shows the powerspectrum of acceleration for the N-S translations of the 30-min data segment fromwhich this trace was taken. Comparison with the spectrum shown in Fig. 6, wherecontinuous collisions took place, shows decreased energy in the frequency rangebetween 0.2 and 0.35 Hz. Note that the sampling frequency is 1.33 Hz and thepredominant wave frequency is 0.10 Hz.

There did not appear to be an increase in collision frequency with increasing waveamplitude; in fact, the opposite was observed in a number of cases. Judging fromFig. 9, it would be difficult to argue that larger wave amplitudes were necessarilythe cause of collisions. An interesting feature observed at some other times was theapparent correspondence between irregularities in the heave cycle and collisionsindicated in the horizontal accelerations.

When the individual components of the accelerations are displayed as functionsof time (e.g. Figs 4, 5 and 7), collisions appear to occur most often at the stationaryvalues of horizontal acceleration, in other words, where the horizontal displacementsare minimum or maximum. This makes sense intuitively, but the important thingis not the absolute motion, but the relative motion of adjacent floes. A simplifiedanalysis for linear waves showed that the maximum relative velocity between floesin the direction of wave propagation occurred close to the inflection or zero-crossingpoints in the vertical acceleration and displacement trace (McKenna and Crocker,

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«I

vU

as-

0.1

0.05

0

-0.05

-0.1

0.1

0.05

0

•0.05W

60 80 100 120

Time (s)

140 160 180

Fig. 7 Translation^ accelerations from motion package 5 between 2237:00 and 2240:22 UTC on 2 April1989. Periods in which the contact between floes was identified are indicated by the arrows.

1990; for 10-m diameter floes in 10-s waves). The inflection points in the verticalacceleration correspond to the stationary points of the horizontal accelerations; thusthere appears to be consistency.

Another method of displaying the data was used in an attempt to verify at whatpoint in the cycle the events occurred. Several cycles of floe accelerations in thevertical plane are shown in each of the two examples of Fig. 10. The trace onthe left in Fig. 10 shows about 3 | cycles in which a single event is evident inthe horizontal acceleration. In the other sequence, several smooth wave cycles arefollowed by vertical cycles in which horizontal motion is impeded. Although thisrepresentation holds promise for gaining insight on the place where the events occurduring the cycle, it is not a very efficient technique overall.

6 Distribution of collisionsConsidering the tedious procedure of identifying individual collisions manually, au-tomated schemes were investigated. Logical candidates for representative measures

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26o / R.F. McKenna and G.B. Crocker

10-1

0.1 0.2 0.3 0.4 0.5 0.6 0.710-8

Fig. 8 Power spectrum of N-S horizontal accelerations from motion package 5 between 2230 and 2300UTC on 2 April 1989.

included an acceleration magnitude and some index of texture or local smooth-ness of the trace. Because the accelerations were heavily filtered, neither techniqueproved feasible. The overall shape of the cycle of one of the horizontal compo-nents, with some confirmation from the other component, was deemed to be themost reliable measure of collision. One way of implementing this scheme numer-ically would be to use zero crossings to define cycles, or half cycles, and thenevaluate the variance of the data about a regular cycle, but at 10 to 13 data pointsper wave cycle there is no guarantee of success. It was finally decided to identifythe events visually and to record them manually, an event being evidence of anycontract with an adjacent floe during a single wave cycle. Multiple events within awave cycle were therefore ignored.

Cycles in which collisions were deemed to have occurred were identified as 1and the others as 0. The scheme was actually implemented in a semi-automatedfashion by displaying 100-s segments (about 10 wave cycles) on the screen at atime, and simultaneously using single keystrokes of 0/1 to input the information foreach wave cycle. Though the method was not foolproof, repetition of the procedureon the same datasets at different times gave the same average numbers of collisionsand the same distributions described in the next section.

The periodicities of the wave cycle and the corresponding collision events en-courage the use of the above discrete measure for their description. Each 30-mintime series was reduced to an equivalent one of the form, 011000101110101where 0 and 1 represent wave cycles where no contact and contact occur, re-

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20 40 60 80 100 120 140 160 180

Fig. 9 Translational accelerations from motion package 6 between 0250:30 and 0253:52 UTC on 3 April1989. Periods in which the contact between floes was identified are indicated by the arrows.

spectively. There is also the question of the time for each wave cycle, but this wasfairly consistent within each 30-min period; thus one need only consider the singledominant wave period T given in Table 2. The question remains: How does onecategorise the equivalent distribution?

Average behaviour can be characterized by the proportion of wave cycles forwhich events occurred; call this p. This is a useful statistic since, if an averagecollision energy is known, then the rate of energy lost from the collisions can beestimated. The average separation time between events expressed in terms of wavecycles is 1/p, and in terms of real time is T/p (= I/A, in Eq. (2)), where T is thewave period. The statistic p was calculated for all of the 30-min data segments andthe results are given in Table 3. This is instructive since there is a clear increasein the frequency of collisions over the period of the experiment. Package 3 hadthe least number of collisions, whereas package 6 had the most during the initialseriod. The most violent collisions were experienced by package 5 between 0730uid 1000 UTC on 3 April. As discussed in the last section, collisions are not reportedluring the latter portion of the record for package 5.

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-0.1 0.1

Horiz. Acceleration (m/s?) Horiz. Acceleration (m/s?)

Fig. 10 Examples of floe acceleration cycles in the vertical plane.

It is interesting to speculate on what actually causes the floes to make contactduring one cycle, and not the next. In other words, are the collision events inde-pendent and completely random, or are there physical conditions that might causethe floes to collide more at certain times? Note that this is not a comparison overseveral hours where wave, ice, wind and temperature conditions are likely to bedifferent. Only the data within a given half-hour segment are considered.

Random point processes in time can be represented using the Poisson distribu-tion, in which the events are assumed to be independent. In its standard form thisdistribution is used to estimate the probability of a certain number of events occur-ring within a given time interval. An equivalent form is to express the distributionof time T between events as the exponential

fT(i) = X,exp(—Xx) (2)

where I/A, is the average separation time. This ties in with results from the exper-iments by noting that the average separation time can be estimated by T/p, wherethe wave period T and the fraction of cycles in which collisions occurred p aresummarized in Tables 2 and 3. If the time between events in normalized by theperiod T, the Poisson parameter X is equivalent to the collision frequency p.

If the floe collisions are independent events, then the distribution of times be-tween them is random and the probability of collisions taking place in successivecycles is not large. Floe spacing is believed to be a major contributor to collisionsand will not vary substantially between adjacent cycles. It is expected, therefore,that more collisions occur in adjacent cycles than would be predicted by assum-ing that the collisions are independent events. The data were analysed with this inmind, while recognizing the limitations imposed by the choice of discrete events.

The distribution of times between recorded collision events, normalized withrespect to the wave period, is shown in Fig. 11 for motion package 3 at variou^stages during the deployment. Frequencies were normalized to sum to unity foJ

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TABLE 3. Collision frequencies for 2 and 3 April 1989

Tim**1 llllC

(GMT)

2130-22002230-23002330-00000030-01000130-02000230-03000330-04000430-05000530-06000630-07000730-08000830-09000930-10001030-11001130-12001230-13001330-14001430-15001530-16001630-1700

Proportion of Wave Cycles p in Which

Package 3

0.510.460.400.350.570.380.380.380.370.310.600.770.840.830.950.970.991.000.990.97

Events Occurred

Package 5

0.550.450.380.480.410.580.630.931.001.00

__-__-__

Package 6

0.470.620.630.630.640.800.490.890.840.960.870.940.830.880.840.910.600.69

The dash indicates that an interpretation of collisions was notpossible.

comparison with the Poisson distribution. In these cases, it appears that there aremore measured events in adjacent wave cycles (separation = 1 cycle) than predictedby the Poisson process, particularly since the number of collisions increases overthe deployment period. This was true to a varying degree, for each of the packages,for each of the 30-min measurement periods, and it is suggested that the wavecycles in which collisions occur are not entirely independent.

Note that the collision process might be expressed equivalently using the bino-mial distribution; however, the Poisson process is attractive because of the easewith which the distribution of times between events can be represented. The for-malism is also useful because it does not assume a discrete wave cycle. When oneevent or perhaps several can be distinguished within a wave cycle, the precisetime between events can be recorded and a continuous distribution of separationtimes can be estimated.

7 DiscussionIt is clear that both atmospheric and wave processes have an effect on the relativemotions of adjacent floes. Figure 12 documents the air temperature at the icesurface, the wind speed at the MV Terra Nordica, the motion characteristics of thepackages and the relative collision frequencies over the deployment period. Theiignificant wave height Hs and period T were calculated from the moments of theleave spectrum, and are also given in Table 2. The wave direction <(> is the compass

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c

I

oz

0.5

3cr

oz

OZ

Fig.

Package 3 0030-0100 GMT April 3. 1989

0.5

Pockage 3 0430-0500 GMT April 3, 1989

0 —

0.5

0 —-L

1

Package 3 0830-0900 GMT April 3, 1989

0.5

Package 3 1230-1300 GMT April 3, 1989

1 82 3 4 5 6 7

Separation (wave cycles)

11 Distribution of times in wave cycles between collisions for motion package 3 as it changeover the deployment period. The solid line denotes the Poission distribution with the parameteI/A, equal to the relative collision frequency p.

direction from which the waves were coming and was calculated by taking the firsmoment with respect to the energy in the heave spectrum. The collision frequency fis the relative proportion of wave cycles in which events were identified. All of th<wave characteristics are based on 30 min of data, and the winds and temperature:are 10-min and 200-s averages, respectively.

Motion package 3 was on the largest of the three floes (Table 1) and the closes!to the ice edge (Figs 1 and 2). The latter distinction may be relevant since tha

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13

12

11

10

g

0.5

C L

,x />4Pockage 3Package 5Pockage 6

00:00 06:00 12:00 18:00

Time (GMT)

12 The relation between wind speed, air temperature, significant wave height Hs, wave period T,wave direction <)> and relative collision frequency p between 2200 UTC on 2 April and 1640UTC on 3 April 1989. The wave direction is the true compass bearing from which the wavesare incident.

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waves were coming primarily from the southeast and would reach this packagefirst. Over time, there is a decrease in wave height and an increase in wave period;this could be due to a change in the incident wave spectrum entering the ice-pack orto changes in ice conditions that contributed to wave energy attenuation. Since thecollision frequency increased over time, it is also possible that collisions may havecontributed to wave attenuation. Unfortunately, the spatial distribution of the icemotion measurements was insufficient to assess overall attenuation with distancefrom the ice edge. Also evident in Fig. 12 is the coincidence of the increase in pwith the change in the wave direction at motion package 3. Unfortunately no moresubstantiating evidence for this link exists.

From Fig. 12, both air temperature and wind speed appear to be related to p, buta physical basis for the relation cannot be established from these data. As discussedin Section 5, wind may influence floe collisions directly through differential driftor indirectly through locally generated waves. A link between low air temperaturesand the compression of new ice between the floes has been observed, although thetemperatures measured during this deployment did not drop below —4°C and newice growth was minimal. At this stage, it is worth considering both wind and airtemperature as potential sources for increased wave-induced collisions.

8 ConclusionsAt the outset, it was hoped that the acceleration data from LIMEX '89 wouldprovide information on the nature and energy involved in the floe collisions. Un-fortunately, it proved difficult to establish the energy content because the data wereonly resolved for frequencies below 0.5 Hz. Nevertheless, valuable informationwas obtained regarding the frequency of collisions, which is an important compo-nent for estimating wave attenuation and floe deterioration. Collision events weredefined by the evidence of any contact between floes during a wave cycle.

Several features of the wave-induced collisions between the floes were observed.First, since the floes were small relative to the wavelength, the collisions wereclosely related to the wave cycle. There were periods during the experiment whenevents were intermittent and times when inter-floe contact was virtually continuous.For the most part, the events were not large and the heave cycle was not alteredsubstantially, but there were periods when collisions were more violent, as shownin Fig. 5. By comparing the distribution of times between events to that of a Pois-son process, recorded events were generally more frequent in adjacent cycles thanindependent events would suggest. This is consistent with the idea that local iceconditions have a significant influence on the collisions. The local ice concentra-tion is certainly an important factor in wave-induced collisions, but this was notdocumented continuously during the experiment.

Overall, an increase in the number of collision events coincided with decreasingwave heights and increasing wave periods calculated from the motions of the icefloes. The pattern suggests that collisions may have caused the changes in thewave characteristics measured from the floe motions, but it is also possible thatother factors caused the wave attenuation, and the relation may be coincidental!

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There is not sufficient supporting evidence to confirm the relation. Wave directiondetermined from the motions of the floes was fairly constant during the deployment,although a change in the wave direction at motion package 3 midway throughthe experiment coincided with a change from intermittent to continuous events.The increase in the frequency of collisions also coincided with a decrease in airtemperature and an increase in local wind speed. During 2 and 3 April 1989,temperatures were not low enough to cause significant ice growth between floes,suggesting that the link between temperature and collisions was incidental. Theincrease in local wind speed was probably more significant.

Collisions were visible in the spectra of horizontal accelerations, but this cannotbe used as an identification technique based on the present data. The directionalspectrum was not investigated in detail, but may be used as a measure of bothcause and effect for wave-induced events. We recommend making higher frequencymeasurements in subsequent experiments, allowing not just the numbers of events,but also the collision energy to be estimated. Since contact between the floes isfrequent, it is feasible to obtain characteristic signatures in the motions indicatingdirect, buffered or shear collisions. The detailed measurement of contact areas andforces is possible because of the small size of the floes in the Labrador ice margin.

AcknowledgementsThe authors thank all those involved in the logistics of the LIMEX '89 experiment.The ice motion packages were designed, built and deployed by the Centre forCold Ocean Resources Engineering (C-CORE). Construction of the motion sensorpackages was funded under an NSERC cooperative grant involving C-CORE andLavalin Inc., Halifax. The paper was written while Richard McKenna was a visitingscholar at the Scott Polar Research Institute of the University of Cambridge. BillWinsor of C-CORE performed all of the calibrations and corrections to the motionpackage data and calculated displacement time series, and Phil Rottier of Scott Polarassisted with the calculation of the wave spectra. The wind data were provided byRichard Olsen of Lavalin Inc., Halifax. The authors also thank the reviewers whose.uggestions helped to improve the quality of the paper.

Vppendix: Analysis of motion package displacements["he ice displacements measured by the motion packages were resolved into theomponents x,y,z,dz/dx and dz/dy, and assigned the designations Ç,, where

Ml of the analyses are referenced to a right-handed coordinate system in whichirection x is oriented north, v is oriented west and z is the elevation of the seaurface. If the cross spectrum between any two components of the data is />(£,, ̂ , s),îen the co-spectra are defined by

Ç,, s)}

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and the quadrature spectra by

Qij{s) = imag{/»&, Ç,, s)},

where s denotes frequency. At each frequency, the wave direction was calculatedfrom the surface slopes using

and alternately from the horizontal components of the displacements using

The compass direction from which the waves were incident is given by

<|> = 2JC - 6

Angular spread (Wadhams et al., 1986) was calculated from

which can vary between 0 and jt/2 and which, for narrow distributions, is the rmsangular spread about the mean wave direction.

The wave height and period were defined from the moments of the heave half-spectra, i.e.

Jo

yoo

mo = / Cu(s)ds

and

Jo

where s denotes frequency. Since half-spectra were used, the significant wave heightis

Hs = y2

and the mean zero-crossing wave period is

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References

EID, B.; R. OLSEN and E. DUNLAP. 1991. Investigationof ice motion and wave generated ice condi-tions during LIMEX '89. Data analysis rep.,Prepared for Bedford Inst. of Oceanography byMacLaren Plansearch Ltd.

LONGUET-HIGGINS, M.S.; D.E. CARTWRIGHT and N.D.

SMITH. 1963. Observations of directional spec-trum of sea waves using the motions of a float-ing buoy. In: Ocean Wave Spectra, Prentice-Hall, Englewood Cliffs, N.J., pp. 111-136.

MASSON, D. and P.H. LEBLOND. 1989. Spectral evolu-tion of wind-generated surface gravity waves ina dispersed ice field. J. Fluid Mech. 202: 43-81.

MCKENNA, R.F. and G.B. CROCKER. 1990. Wave en-

ergy and floe collisions in marginal ice zones.Proa, Ice Technol. Conf., University of Cam-

bridge, 18-20 September 1990, ComputationalMechanics Publ., T.K.S. Murthy, J.G. Paren,W.M. Sackinger and P. Wadhams (Eds), pp. 33-45.

ROTTIER, P.J. 1991. Wave/ice interactions in themarginal ice zone and the generation of oceannoise. Ph.D. Thesis, University of Cambridge.

WADHAMS, P.; V.A. SQUIRE, J.A. EWING and R.W. PAS-CAL. 1986. The effect of the marginal ice zoneon the directional wave spectrum of the ocean.J. Phys. Oceanogr. 6: 358-376.

WINSOR, W.D.; G.B. CROCKER, R.F. MCKENNA and C.L.

TANG. 1990. Sea ice observations during LIMEX,March-April 1989. Can. Data Rep. Hydrogr.Ocean Sci., Bedford Inst. Oceanogr., Fisheriesand Oceans Canada, No. 81, 43 pp.

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Documents

Ice‐floe collisions interpreted from acceleration data during LIMEX ‘89