Scaling properties of sea ice deformation duringwinter and summer

Jennifer Hutchings, Petra Heil and Andrew Roberts

Abstract

We investigate sea ice deformation observed with ice drifting buoy arraysduring two field campaigns. Ice Station POLarstern [ISPOL], deployed inthe western Weddell Sea during November 2004 to January 2005, includeda study of small-scale (sub-synoptic) variability in sea ice velocity anddeformation using an array of 24 buoys. Upon deployment the ISPOL buoyarray measured 70 km in both zonal and meridional extent, and consistedof sub-arrays that resolved sea ice deformation on scales from 10 to 70 km.The Sea Ice Experiment: Dynamic Nature of the Arctic (SEDNA) used twonested arrays of six buoys each as a backbone for the experiment, that weredeployed in late March 2007. The two arrays were circular with diameter140 km and 20 km. ISPOL and SEDNA provide insight into the scalingproperties of sea ice deformation over scales of 10 to 200 km during earlyastral summer and late boreal winter.

Time series and spectral analysis of divergence and shear for sub-arrayswithin the ISPOL and SEDNA arrays revealed that deformation did notvary smoothly over length scales of 10 to 40 km. This indicates variability ofinternal ice stress on the scale of 10 km. Across the ISPOL array divergencevaried, and did not show a distinct coherence length scale. The SEDNAarray displayed low values for coherence between divergence at 20 and 140 kmscales, with the coherence reducing as the season progressed towards summer.

The ISPOL and SEDNA arrays were split into sets of sub-arrays with varyinglength scales. We find that variance of divergence decreases as the length scaleincreases. The mean divergence for each length scale set follows a log-linearscaling relationship with length scale. This is an independent verificationof a previous result of Marsan et al. (2004) (referred to as M04 from hereon). This scaling is indicative of a fractal process. Deformation occurs atlinear features (cracks, leads and ridges) in the ice pack, that are distributedwith scales that range from meter to hundreds of kilometers in length. Themagnitude of deformation at these linear features varies by two orders ofmagnitude across scales. We demonstrate that the deformation at all thesescales is important in the mass balance of sea ice. Which has importantimplications for the design of sea ice deformation monitoring systems.

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Figure 1: TheISPOL arraywas deployed ina region of over90% ice cover,straddling thecontinental shelfand slope. Thearray containeda shear zone(region A) aswell as on theshelf that werepredominantlytidally driven(B and C).The equilateraltriangle designcan be split intosets of strainarrays of varyinglength scale from50 km (yellow)to 10 km (blue).

SEDNA: Boreal Winter, Beaufort Sea

Figure 2: APLIS 2007 was deployed on a multi-year ice floe within a packof mixed ice age. Two hexagons of GPS ice drifters defined a set of nestedstrain arrays with approximate length scale 140 km (white), 70 km (yellow),20 km (green) and 10 km (blue). Black vectors are ice velocity and red linesare discontinuities in the velocity field, estimated as Thomas (2008).

The colour codes used for buoy arrays of varying size magnitudes in figures 1 and 2 isused throughout this poster to identify data from particular buoy arrays.

AcknowledgmentsSEDNA is funded by the National Science Foundation, ARC0612527. Itis a collaborative effort between IARC, CRREL, U. Delaware and variousEuropean collaborators. The U.S. Navy’s Arctic Submarine Laboratoryprovided access to APLIS07, supporting camp construction. Many thanksto Fred Karig and the APL team who ran APLIS07. Many thanks to PatMcKeown, ’Andy’ Anderson and Randy Ray who deployed the SEDNA strainarray. The International Arctic Buoy Program archives the SEDNA buoydata presented here.

The ISPOL buoy array was a collaborative effort between IARC, AAD,AWI and FIMR. Many thanks to Christian Haas and Jouko Launiainen whocontributed buoys. Many thanks also to the captain and crew of the RVPolarstern, Adrienne Tivy, Tony Worby, Sasha Willmes, and Carl Hoffmanwho ensured the field campaign was a success. The IARC ISPOL buoydeployments were funded by JAMSTEC. The AAD component was funded byAustralian Antarctic Science grants #742, #2559 and #2678; and supportedby the Australian Government’s Cooperative Research Centre Programthrough the Antarctic Climate and Ecosystems Cooperative Research Centre.

Wavelet software was provided by C. Torrence and G. Compo, and is availableat URL: http://paos.colorado.edu/research/wavelets/. ESA is thanked forproviding Envisat ASAR data ( c!ESA (2004)). RADARSat imagery was pro-vided by the Canadian Space Agency, and analysis performed by M. Thomas,C. Khambhatmettu and C. Geiger.‘

Weddell Sea

Figure 4: There were two distinct re-gions in the ISPOL array. Region B (seefigure 1c) was dominated by shear alongthe continental shelf break. The rest ofthe array diverged in concert with thetides. See Hutchings et al. (2009) formore details.

Figure 3: Divergence and MaximumShear Strain rate estimated from drift ofbuoys around ISPOL array perimeter.

Three ways of looking at spatial scaling

Is there a decorrelation length scale?

Figure 6: We calculate the correlationcoe!cient between time series of to-tal deformation (divergence + maximumshear strain rate) for pairs of buoys subarrays shown in figure 2B. This is plot-ted above against the distance betweensub-array centroids in each pair. Allpossible permutations of sub-array pairsare plotted.

Figure 5: Net divergence of the ISPOLarray was highly heterogeneous on the10km scale, with no discernible pattern.Net shear, on the other hand, decreaseduniformally across the continental shelfbreak.

Note the large variance in correlation coefficient that appears to increase asdistance decreases. We did not find any changes in these coherence resultswhen we considered cross-correlations between triangles only within or onlyacross the shear zone in the ISPOL array.

Can small scale deformation be predicted given larger scale measurements?

We consider the correlation of divergence time-series between a large triangleand smaller triangle embedded inside the larger triangle. The full range of tri-angles we can use to calculate divergence are illustrated in figure 1, colouredblue, green, red, orange and yellow. There are 4, non-overlapping, 30km scaletriangles, each containing 6 20km triangles. The 40km triangle contains 1120km triangles and 1 30km triangle ... and so on. Table 1 contains the meanand standard deviation of correlation between time series of total deformationfor all possible combinations of small triangles embedded in a larger triangle.

Table 1: Note there is asweet spot in the ratio be-tween large and small tri-angles at which point thereis maximum correlation be-tween deformation time se-ries.

Is there a relationship between spatial scale and deformation magnitude?

Figure 7: Distribution of to-tal strain rate for sub-arraysof length scale set rangingfrom 10 km (blue) to 50 km(yellow). Right panel is thecumulative probability den-sity function.

Figure 8: We find a log-linear scaling relationshipwith exponent H=-0.21,similar to M04. Ourrelationship for variancedoes not match M04’sresults however.

Beaufort Sea

Figure 9: Time series of divergence(top) and maximum shear strain rate(bottom) for the 20 km hexagon (green)and 140 km hexagon (black) buoy ar-rays shown in figure 2.

We consider the time period March 24 to April 14 2007, when all the GPSstations illustrated in figure 2 were reporting. This is late winter, when theice pack is close to it’s maximum volume and we expect ice pack deformationto be correlated over larger distances than a looser late summer ice pack.

Two ways of looking at spatial scaling

Can small scale deformation be predicted given larger scale measurements?

We consider the correlation of divergence time-series between a large buoyarrays and smaller arrays embedded inside the larger array. The full rangeof buoy arrays we can use to calculate divergence are illustrated in figure 2,coloured blue, green, yellow and white. There are 6, non-overlapping, 10 kmscale triangles (blue) , contained by a 20 km hexagon (green). These arecontained within a 140 km hexagon (white). The 140 km hexagon also contains6 70 km triangles (yellow). Table 1 contains the mean and standard deviationof correlation between time series of total deformation for combinations ofsmall arrays embedded in a larger array.

Table 2: Note the correlation between largearrays (70 or 140 km) and the small arrays(10 km) they contain is low.

Is there a relationship between spatial scale and deformation magnitude?

The figures showing relationship between deformation rate (divergence plusmaximum shear strain rate) and length scale for SEDNA and ISPOL wherecreated using the same methodology as M04. M04 used RGPS ice deformationdata, covering the western Arctic, and have recently extended their analysisto 7 winters (Stern & Lindsay 2009, SL09). Our analysis differs in that weconsider a time series of deformation rather than a spatial series.

Figure 10: Divergencedemonstrates a log-linearscaling relationship withexponent H=-0.26. Therelationship for maximumshear strain rate is close tozero.

SL09 indicate that we might expect higher exponent values in the southernBeaufort, where deformation rate is greater, than central Arctic. Hence ourdivergence estimate appears to be reasonable. Shear strain rate needs to belooked at a little more carefully.

Is there temporal evolution in coherence between large

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Figure 11: Wavelet spectra of divergence time series (fig. 9) for small, 20km hexagon(bottom right) and large, 140km hexagon (bottom left). The coherence between these twois shown at top. 95% significance levels are solid line, and the cone of influence is shownwith bold solid line.

Note reducing coherence, at longer time scales (8-32 days) with time. Thisis consistent with an ice pack becoming looser and less able to support largescale coherent motion during Spring.

Case Study of lead impact on ice mass balance

Buoy array divergence was used toforce a model of lead ice growthand ridging. This provides anestimate of the impact of leadswithin the buoy array on icemass balance. An example of theestimate of ice grown in leads isshow in figure ?? for the largestSEDNA hexagon. During thestudy period, basal ice growthis estimated to be about 7.5 cm.Lead ice growth as a fraction ofthe total buoy array area variedacross the SEDNA region.

Figure 12: Time series of divergence(top), lead area (estimated from diver-gence), volume of lead ice grown, vol-ume of new ice ridge and total volumeof ice grown in leads (ridged plus level,bottom), for 140 km hexagon buoy ar-ray shown in figure 2. Ice growth ratesare taken from Maykut & Unterstiener(1971).

Figure 13: Basal plus total lead ice

growth (per m2) within each buoy ar-ray identified in figure 2, plotted againstmean length scale of the buoy array.Note that ice growth is higher and showsmore variability for the smallest set ofarrays (blue). This is consistent with lo-calisation of ice deformation at the leadscale (< 10 km). A log-linear relation-ship between ice growth and length scalehas H=-2.2.

Summary and Initial ConclusionsCan small scale deformation be predicted given larger scale measurements?

In our investigations of correlation between divergence of smaller buoyarrays contained in larger arrays we found no obvious trends with array sizeor ratio of array sizes. What is apparent, however is that correlationbetween the smallest arrays (10 " 20 km) and a larger (40 " 140 km) arraycontaining the smaller array is consistently below 0.5. This suggests lowpredictability of deformation at 10 " 20 km scales given a large scale measurement.We have not identified the reason behind this, however expect that it maybe related to the fact that lead systems (where the deformation occurs) havewidths of up to 10 km. A small 10 " 20 km array may or may not containdeforming leads that reside within the larger array. This has important im-plications for processes that are affected by the local ice thickness distributionand the presence of leads. Localised measurements of such processes shouldinclude observations of ice deformation 10 " 20 km around the measurementsite.

Is there a decorrelation length scale for deformation?

The ISPOL experiment was designed to investigate this question.

Figure 14: Least squares fit (red) in-dicates a decorrelation length scale of380 km. Note the large variability incorrelation between buoy arrays closeto each other. This variability re-duces as the arrays move further apart.Close arrays can have higher correla-tions, and we estimate the decorrelationlength scale of the most correlated arraysto be 250 km (blue line).

The

decorrelation length scale is larger than the ISPOL array.

Is there a relationship between spatial scale and deformation magnitude?

As M04 we find an inverse relationship between deformation magnitude andlength scale, with fractal scaling properties. The relationship we find issimilar to SL09, however this is surprising.

Our time step is 1 hour, and based on work by Rampal et al. (2008) wecould expect such a short time step should lead to higher exponents than weobserved. This needs to be investigated further, and may be due to differingerror characteristics (the ISPOL and SEDNA buoys have position, velocityand deformation accuracy an order of magnitude higher than both ARGOSand RGPS)

Is ice mass dependent on lead scale deformation?

Yes! High spatial variability, and localisation of the deformation at leadsand ridges means that for accurate estimates of new ice growth in leads, thedeformation at the lead scale must be resolved.

ReferencesHutchings, J.K., P. Heil, A.Steer, W.D. Hibler III, Small-scale spatial vari-ability of sea ice deformation in the western Weddell Sea during early summer.Submitted to J. Phys. Oceanogr.Hutchings, J. K. and I. G. Rigor (2008), Mechanisms explaining anomalousice conditions in the Beaufort Sea during 2006 and 2007. Submitted to J.Geophys. Res.Marsan, D., H. Stern, R. Lindsay and J. Weiss (2004), Scale dependence andlocalization of the deformation of Arctic sea ice, Phys. Rev. Lett, 93(17),178.Maykut, G. A., and N. Untersteiner (1971), Some results from a time-dependent thermodynamic model of sea ice, J. Geophys. Res..Rampal, P., J. Weiss, D. Marsan, R. Lindsay and H. Stern (2008), Scalingproperties of sea ice deformation from buoy dispersion analysis, J. Geophys.Res. (113), doi:10.1029/2007JC004143.Stern, H. L. and R. W. Lindsay (2009), Spatial scaling of Arctic sea ice de-formation, J. Geophys. Res. (114), doi:10.1029/2009JC005380.Thomas, M. V. (2008), Analysis of Large Magnitude Discontinuous Non-rigidMotion, Ph.D. Dissertation, University of Delaware.