Dynamic–Thermodynamic Sea Ice Model: Ridging and Its ...123userdocs.s3-website-eu-west-1.amazonaws.com/d/0c/31/... · Arctic. Rigor et al. (2002) described the action of this mechanism

Dynamic–Thermodynamic Sea Ice Model: Ridging and Its Application to ClimateStudy and Navigation

SERGEY V. SHOUTILIN

Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan, and Arctic and Antarctic Research Institute,St. Petersburg, Russia

ALEXANDER P. MAKSHTAS

International Arctic Research Center, University of Alaska, Fairbanks, Fairbanks, Alaska, and Arctic and Antarctic Research Institute,St. Petersburg, Russia

MOTOYOSHI IKEDA

Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan, and International Arctic Research Center,University of Alaska, Fairbanks, Fairbanks, Alaska

ALEXEY V. MARCHENKO

Seoul National University, Seoul, South Korea

ROMAN V. BEKRYAEV

Arctic and Antarctic Research Institute, St. Petersburg, Russia

(Manuscript received 28 May 2004, in final form 22 March 2005)

ABSTRACT

A dynamic–thermodynamic sea ice model with the ocean mixed layer forced by atmospheric data is usedto investigate spatial and long-term variability of the sea ice cover in the Arctic basin. The model satisfac-torily reproduces the averaged main characteristics of the sea ice and its extent in the Arctic Basin, as wellas its decrease in the early 1990s. Employment of the average ridge shape for describing the ridging allowsthe authors to suggest that it occurs in winter and varies from year to year by a factor of 2, depending onan atmospheric circulation pattern. Production and horizontal movement of ridges are the focus in thispaper, as they show the importance of interannual variability of the Arctic ice cover. The observed thinningin the 1990s is a result of reduction in ridge formation on the Pacific side during the cyclonic phase of theArctic Oscillation. The model yields a partial recovery of sea ice cover in the last few years of the twentiethcentury. In addition to the sea ice cover and average thickness compared with satellite data, the ridgeamount is verified with observations taken in the vicinity of the Russian coast. The model results are usefulto estimate long-term variability of the probability of ridge-free navigation in different parts of the ArcticOcean, including the Northern Sea Route area.

1. Introduction

Recent reports of the decrease in sea ice extent (e.g.,Parkinson et al. 1999) and thickness (Rothrock et al.1999) during the early 1990s in the Arctic basin stimu-late attempts to explain this remarkable change in the

Arctic climate system. One of the useful ways to un-derstand the reasons for climate changes is to use anumerical model that reproduces observed environ-mental characteristics and examines the possiblemechanisms responsible for such changes. Explanationof these changes, however, depends crucially on themodel and the external forcing used for investigation.Many authors (e.g., Maslanik et al. 2000) explain thedecrease in sea ice cover in the eastern part of theArctic Ocean during the last three decades as a conse-quence of increased open water and thin ice, primarily

Corresponding author address: Motoyoshi Ikeda, GraduateSchool of Environmental Earth Science, Hokkaido UniversityNishi-5 Kita-10 Kita-ku, Sapporo 060-0810, Japan.E-mail: [email protected]

3840 J O U R N A L O F C L I M A T E VOLUME 18

© 2005 American Meteorological Society

JCLI3484

forced by surface wind. The sensitivity studies (Zhanget al. 2000; Makshtas et al. 2003) support the ice volumeincrease before 1987, as well as the decrease afterward,which may be attributed to the change in ice drift, prin-cipally driven by wind forcing and deformed internallyby ice dynamic processes. Prevailing divergent driftleads to a decrease of ice concentration. As a result, thesurface albedo decreases, solar radiation absorption atthe surface and in the oceanic mixed layer increasesand, finally, lateral and bottom melting increases.Hilmer and Lemke (2000), on the other hand, concludethat most of the thinning can be attributed to changes inthe surface-level air temperature rather than to those inthe atmospheric circulation. In summary, the change inArctic ice cover was referenced to the Arctic Oscilla-tion/North Atlantic Oscillation (AO/NAO) through iceadvection and air temperature (Zhang et al. 1998), anda cyclonic frequency over the central Arctic (Maslaniket al. 1996).

Rothrock et al. (1999) discussed the possible thermo-dynamic processes that could produce the observedthinning, such as an increase in oceanic heat flux, pole-ward atmospheric heat transport, and the consequentincrease in incoming longwave radiation, or an increasein down-welling shortwave radiation. Serreze et al.(2003) attributed the anomaly in ice extent and area,received from satellite data, to ice advection away fromthe coast by anomalously warm southern wind, follow-ing ice divergence and rapid melting. This was due tocyclones and high summer temperatures over the entireArctic. Rigor et al. (2002) described the action of thismechanism during the positive phase of the winter AO,as well as Ikeda et al. (2003), based on meteorologicaldata and radiation observations from the North Poledrifting stations.

From observations and model results, some authorsfound the shift of thick ice cover from regions wheremost submarine observations were made in response tochanges in the AO (Holloway and Sou 2002). Based onthe comparison of the two, they have concluded thatthe decrease of sea ice volume in the Arctic Ocean wassmaller than previously estimated and demonstratedthat the submarine data from the 1990s lead to an over-estimation in ice thickness trend. They have attributedthis to undersampling and shown that the changes inthe Arctic sea ice thickness distribution had a dominantmode of variability related to the shift of sea ice be-tween the central Arctic bBasin and peripheral regions.This feature could not be captured by the submarinesurveys.

Unfortunately, there is no common opinion aboutthe interannual variability of sea ice thickness in theArctic basin because the authors analyzed different

datasets, mainly from submarine cruises sparsely dis-persed in season, year, and region. The changes in icethickness varied regionally (Rothrock et al. 2003;Hilmer and Lemke 2000). The observations indicatethat ice draft in the western Arctic and a large part ofthe central Arctic basin remarkably declined since thelate 1980s, while the North Pole had only little change(Winsor 2001; Maslanik et al. 1999). On the other hand,model results (Makshtas et al. 2003; Polyakov andJohnson 2000; Rothrock et al. 2003) demonstrate icethickness reduction of 0.5–1 m within a few years as acommon feature.

The ice cover variability spreads over a wide range oftime scales from a couple of years (Laxon et al. 2003) todecadal–multidecadal (Polyakov et al. 2003; Polyakovand Johnson 2000). The diverse estimations of ice thin-ning could be attributed to small-scale spatial variabil-ity of the ice cover. Once the submarine survey datahave been taken for two subsequent years at the samegeographical location, a temporal change may reflectspatial variability in a drifting ice cover. This possibilitywas demonstrated for 1995 and 1996 by the drill holedata for two consecutive years (Haas and Eicken 2001).

In previous papers (Makshtas et al. 2002, 2003), wesuggested that the observed decrease of sea ice cover inthe early 1990s was the result of the reduction of ridgingfor dynamic reasons, namely intensification of atmo-spheric cyclonic circulation above the Arctic basin(Polyakov and Johnson 2000). Furthermore, NationalCenters for Environmental Prediction–National Centerfor Atmospheric Research (NCEP–NCAR) reanalysisforcing (Kalnay et al. 1996) extended to 2002 allows usto examine whether sea ice partially recovered at theend of the twentieth century in the Arctic Ocean, atleast in the Canadian Arctic. This is supported by theresults of Tucker et al. (2001), Winsor (2001) and Roth-rock et al. (2003). This recovery may also be attributedto intensification of ridging processes due to changes inatmospheric circulation from cyclonic to anticyclonicperiods (Makshtas et al. 2003).

In this paper, we focus on ridges, which are essentialfor total ice volume estimation. Ridges and hummocksare two of the main features of ice-covered seas, storingan essential part of the ice mass. During summer, whenexisting leads and thin level ice allow ships to maneuvermuch easier, the ridges remain as obstacles for naviga-tion. We use a dynamic–thermodynamic model forcedby atmospheric data in 1948–2003 for calculations ofthe spatiotemporal variability of level ice thickness andridge concentration. Additionally, the present model isassumed to maintain the average ridge shape based onobservations in order to describe the ridging and toestimate the long-term variation of the probability of

15 SEPTEMBER 2005 S H O U T I L I N E T A L . 3841

ridge-free navigation in different parts of the ArcticOcean, including the Northern Sea Route area.

2. Model

Sea ice cover is simulated in the large-scale dynamic–thermodynamic model (Makshtas et al. 2003). Themodel ice consists of relative areas of level or unde-formed ice (thickness hi; area Ni), which undergoesthermodynamic growth and melting; ridged ice (areaNh) with fixed effective thickness hh � 12 m; and leads(area N0). The main equations of the model are themomentum equation, which includes a parameteriza-tion of internal ice stress in the framework of a cavitat-ing fluid (Flato and Hibler 1992); the steady heat con-duction equation; and the nonstationary mass balanceequation. This last equation is

�m

�t� div�um� � f � 0, �1�

where m � hiNi � hhNh and u is the ice drift velocity.Here,

f � Ni��hi

�t �T� hi��Ni

�t �T� hh��Nh

�t �T� Nh��hh

�t �T

�2�

is a function describing thermodynamic growth or melt-ing of level ice (first term on the right-hand side of theequation), lateral melting of level ice (second term) andthe ridged ice in the leads (third term), and melting atthe upper and lower surfaces of the ridges (last term).

The model describes the growth and melting of levelice with a zero-dimensional thermodynamic sea icemodel, similar to that of Semtner (1976). We describethe energy fluxes between the atmospheric surfacelayer and sea ice surface following Jordan et al. (1999).The longwave radiation balance follows the parameter-ization of Konig-Langlo and Augstein (1994) takenfrom observations at the polar latitudes, and the short-wave radiation balance contains Shine’s parameteriza-tion (Shine 1984). The stratification of the atmosphericsurface boundary layer is taken into account during thecalculation of turbulent sensible and latent heat fluxeswith functional dependence for highly stable stratifica-tion from Holtslag and de Bruin (1988). Following An-dreas (1996), a windless heat exchange coefficient wasincluded for estimation of the turbulent sensible heatflux. This enables us to more correctly describe theenergy exchange between the snow–ice surface and at-mosphere during winter conditions when strong stablestratification often occurs. We model the heat processes

in the leads following Ebert and Curry (1993). To cal-culate the redistribution of lateral heat fluxes betweenridged and level ice, we use an algorithm proposed byDoronin (1969). We describe the bottom and surfacemelting of ridges following Thorndike et al. (1975, theirTable 1).

Wind and ocean current stresses on sea ice are de-termined following Brown (1981) and McPhee (1979),respectively. The cavitating fluid model produces thehigher ice drift velocities, as they may lead to overesti-mation of the ridging, suggested by Kreyscher et al.(2000). It is noted also in the same paper that mostdifficulties and differences occur in the coastal regions.In our model, we introduce a coastal sublayer with 200-km width along the coast where an additional viscosityterm is added in the momentum equation with a no-slipboundary condition. In the innovative paper by Flatoand Hibler (1992), they compared different schemesand mentioned that the cavitating fluid reproduced arealistic circulation under smoothed (monthly aver-aged) wind forcing. In our case, we use the daily windfield averaged from the 4-times per day SLP field. Inspite of these studies, the question of rheology is im-portant but not so evident. Makshtas et al. (2003) usedall available data for the validation of the results andshowed a good agreement with these data. The com-parison was made on lead and ridge concentration, heatfluxes, and ice area and volume fluxes through FramStrait.

Because the total area occupied by the leads, levelice, and ridges in each cell cannot exceed the cell area,we set the relation

N0 � Ni � Nh � 1. �3�

Following the large particle method (Belotserkovskii1984), we integrate Eq. (1) in three steps. In the first(Eulerian) step, values within the cell, as a whole, areestimated under the assumption of solid-body move-ment. In the second (Lagrange) step, after applying thecorrection of ice drift velocities from a cavitating fluid,the exchange of properties between cells is calculatedunder the assumption that properties (leads, level ice,and ridge areas, as well as level ice and ridge volumes)are carried across cell boundaries by the drift velocitycomponent normal to the cell boundary. We calculatethe exchange of area, which shifts from one cell to theother and brings forth the aforementioned properties.After calculating the exchange across all cell bound-aries, the new level ice and ridge volume and area in thecell are calculated.

Finally, in the last step, all ice cover parameters areredistributed in the initial grid. The new level ice thick-


ness in the cell is calculated by dividing the new levelice volume by its area. When the total of leads, level ice,and ridge areas in the cell satisfies Condition (3), nocorrection is applied. If the total ridge and level ice arearemains less than that of the cell, we simply increase thelead area. When ice convergence takes place and addi-tional areas of the level ice and ridges come into the cellfrom the surrounding cells, the new total area of levelice and ridges exceeds the cell area. Then, we supposethat ridging occzurs and apply the simple condition thattotal area of level ice and ridges is equal to the cell area,while the new level ice thickness and total ice volume(level ice and ridges) are conserved during the ridgingprocess.

Nif � Nh

f � 1 �4a�

Nihi � Nhhh � Nifhi � Nh

f hh. �4b�

In this context, ridging means that level ice area de-creases due to the transformation of the excessive levelice area (and volume) to the ridges, whereas the ridgearea (and volume) increases. The final new values Nf

i

and Nfh are calculated from the following equations,

which are easily obtained from conditions (4a) and(4b):

Nif � �Nihi � �Nh � I �hh��hi � hh� �4d�

Nhf � 1 � Ni

f. �4c�

The model is driven using daily 2-m air temperatureand relative humidity, atmospheric surface pressure, to-tal cloudiness amount, monthly mean solid precipita-tion, and dynamic height of the ocean surface. Hori-zontal and temporal resolutions are at 50 km by 24 h,respectively. With this model, we can calculate the spa-tial distributions of the level sea ice thickness and area,ridges and leads areas, snow depth, turbulent sensible(H) and latent (LE) heat fluxes, longwave (R) andshortwave (F) radiation balances at the upper surfacefor each kind of ice cover, temperature in leads and inthe upper ocean, and heat flux from the oceanic mixedlayer to the ice bottom.

For future consideration, it needs to be emphasizedthat the simplest rectangular shape of ridges with afixed height of 12 m was used in the model. The modelreproduces the volume of ridged ice in each cell only.For estimating the number of ridges in a unit area, wemust use typical values for the cross-sectional area andlength of a single ridge. We calculate the cross-sectionalarea of a typical ridge profile using data concerninggeometrical parameters of cross sections from Burdenand Timco (1995), as they analyzed data from morethan 250 measurement sites. The generalization of their

results gives a mean value of ridge cross-sectional areaof about 190 m2, with variations from 100 to 250 m2.Following this estimation, we use the value of 180 m2 inour calculations.

The data concerning ridge extent are much moresparse. Hibler and Ackley (1973) described the difficul-ties of its estimation due to technical problems, as wellas subjective judgment about the definition of heightcutoff, which must be applied to obtain ridge lengthdistributions. Based on available aerial photographsand field observations (Hibler and Ackley 1973), it issuggested that the mean ridge length increases slightlywith height (sail height) and may be of an order of 2 kmfor 2.5–3.0-m ridge height and 1 km for 1–1.2-m ridgeheight. From their Figs. A1 and A2, constructed for thenorthern part of the Beaufort Sea, we use, in thepresent model, the value of 1 km for a typical ridgelength.

For the estimation of sensitivity of simulation resultsto the chosen ridge thickness, a case study was madeagainst the control experiment with a ridge thickness of9 m. The deviations of the averaged ice thickness fromthe standard case do not exceed�10% during all cy-clonic and anticyclonic periods. The open water areachanges by 5%–10% in winter and 15% in summer,even taking into account the changes in lateral melting.

3. Spatiotemporal variability of sea ice in theArctic Ocean

In previous papers (Makshtas et al. 2002, 2003), weinvestigated spatiotemporal variability of sea ice coverin the Arctic basin during 1959–97 and its sensitivity toexternal forcing. The comparison of modeled sea icecover with available data showed a reasonable agree-ment in the ice extent; the spatial distributions of levelice thickness; areas of leads, level ice, and ridges; andthe ice flux through Fram Strait (Makshtas et al. 2003).It was found that atmospheric dynamics and relatedridging processes determine the main changes in thecharacteristics of sea ice cover, while an increase insurface air temperature during the investigated periodcauses only 20% of the ice thickness decrease in theCanada Basin. The smaller changes in ice volume occurafter 1993. NCEP reanalysis data from 1948 up to 2003give a possibility to investigate changes in Arctic sea icecover for a longer period.

a. Response of modeled sea ice to changes inatmospheric circulation

The model has satisfactorily reproduced the mainfeatures of the Arctic ice cover as well as its seasonal


and interannual variability, including the thinning of iceduring the 1990s and the decreasing trend in the iceextent within the last three decades (Makshtas et al.2003). Model simulations show the contrast in sea icevariations between the eastern and western parts of theArctic, found by X. Zhang et al. (2003). The redistri-bution of sea ice in the Arctic during the positive AO islower than the normal thickness in the East SiberianSea and higher in the Beaufort Sea and Canadian Ar-chipelago (Zhang et al. 2000; Holloway and Sou 2002).

The results are compared with Johannessen et al.(1999). The comparison is not straightforward becausewe divide sea ice into ridged ice and level ice, in con-trast to the division into multiyear (MY) and first-year(FY) ice in their study. The modeled sea ice shows anegative trend of total ice volume in September from1978 to 2003 at 31% (12.6% decade�1) and a total icearea decrease of 5.26% (2.1% decade�1), as compa-rable to Parkinson et al. (1999). At the end of winter (inApril), the ice also has negative trends of total volumeat 18% (7.1% decade�1) and ice area at 2.1% (0.85%decade�1). The annual mean ice thickness averagedover the whole region decreases during this period aswell at 13% decade�1, along with 17% decade�1 inSeptember and 9% decade�1 in April. We assume thatsea ice, which has survived (outlived) the previous sum-mer melting will become MY during the next winter.We then estimate the area of MY ice and also FY fromthe difference between total ice area and MY area. TheMY area decreases since 1978 by 4.66% (1.86% de-cade�1), and FY decreases by 7.5% (3% decade�1).These values are half of those estimated by Johannes-sen et al. (1999), and it can be noted that our estimateof the MY area (4.7 � 106 km2) is comparable withtheir value.

Figure 1 presents spatial distributions of level icethickness and the number of ridges per unit area. Thelatter values were recalculated from the model resultswith the use of the available data concerning the geom-etry of ridges, described in section 2. The first two av-eraging periods (1984–88 and 1989–93) were chosen asperiods with dominant anticyclonic and cyclonic circu-lations of polar atmosphere (Proshutinsky and Johnson1997). The last averaging period (1999–2001) was cho-sen as the nearest one to the present. Here, and alsolater, we refer to cycles from Proshutinsky and Johnson(1997), who described the two circulation regimes ofwind.

Figure 1 also shows a partial recovery of level icethickness in the Canadian region in 1999–2001, espe-cially noticeable in May, with a seasonal maximum inthe ice thickness. It corresponds to the change in atmo-spheric circulation from cyclonic to anticyclonic after

1996 (Polyakov and Johnson 2000). In the Eurasianregion, a small decrease in level ice thickness can berecognized. The most remarkable feature is the tempo-ral variability of ridged ice. In 1989–93 the ridge num-ber decreased in comparison to that in 1984–88 by morethan 50%, especially in the central part of the Canadianregion. In 1999–2001, the number of ridges was almostthe same as that during 1984–88 and was even larger inthe northeastern part of the Beaufort Sea, which wasalso pointed out by Kwok (2002). The present resultssupport the conclusion of Rothrock et al. (2003) in re-lation to the absence of evidence that the decline of seaice thickness through 1996 should be extrapolated as aprediction of its future behavior.

The yearly averaged ice volume systematically growsin the Arctic Ocean (Figs. 1 and 2), especially in theCanadian region, during the periods with anticycloniccirculation (Makshtas et al. 2003), but the prevailingcyclonic regime leads to a shrink of ice cover, as notedby Walsh et al. (1996). Cyclonic circulation results inreducing MY concentration along with increasing thefractional coverage of FY in the central Arctic duringwinter. The model also shows that periods with theanticyclonic circulation in the atmosphere lead to a de-crease in ridging intensity in the Canada Basin, adja-cent parts of the central Arctic, and marginal seas. Thisdecrease causes, on average, the thinning of sea ice inthe early 1990s, when cyclonic circulation in the polaratmosphere was well developed.

The supporting evidence of the increasing ridge num-ber in the last few years of the twentieth century canalso be found in the data, reproduced in Laxon et al.(2003, their Fig. 3a). They showed, along with contin-ued thinning of the Arctic ice cover beyond 1998, anincrease in the mean winter ice thickness in 1997 and1998 and the subsequent decrease in 1999 and 2000.The reversal of Arctic circulation in 1997 might lead toa thickening of Arctic ice pack during the late 1990s(Zhang et al. 2000; Rothrock et al. 2003). Transitionfrom a negative anomaly in the Arctic in 1995 to a largepositive one in 1996 was reproduced by model simula-tions (Fichefet et al. 2003).

b. Contrast in sea ice variability

Since sea ice variability has various patterns for dif-ferent parts of the Arctic Ocean, it may be useful todivide it into two regions for characterizing the large-scale features of the change in ice cover. The east–westArctic anomaly pattern (EWAAP) as a response ofArctic sea ice to the North Atlantic Oscillation wasdescribed by Zhang et al. (2000; X. Zhang et al. 2003).Their model shows a reduction of thick ice in the east-ern Arctic and an increase in the western Arctic, and


total ice volume over the whole Arctic decreased dur-ing 1989–96. A different regional contrast in sea icevariability is connected with AO, which shows a de-crease of sea ice area and volume over the eastern Arc-tic, whereas ice volume increases without any essentialchange of ice area in the western Arctic.

In contrast to the division to the western and easternArctic along meridian 0°–180° (Zhang et al. 2000), wedivide the Arctic area into two regions by meridians140°E and 40°W across the North Pole (Fig. 4). Thefirst region (Region 1) extends from the Lincoln Sea tothe New Siberian Islands and from Greenland to Nor-way’s coast. It covers the Greenland, Barents, Kara,and Laptev Seas and has an open boundary to the At-lantic Ocean. This region is exposed to the AO and/or

NAO along with an inflow of Atlantic water and, as aresult, has weaker ice cover characterized by strongseasonal and interannual variability. Region 2 is situ-ated from the Canadian coast to the East Siberianand Chukchi Seas. This region is characterized bythicker ice. The strongest ice remains in the BeaufortGyre, while it shifts and changes its size in response toAO. In contrast, the division into western and easternArctic leads to the inclusion of areas adjacent to theAtlantic Ocean in both regions, and hence, both regionsundergo the common influence of the AO and/orNAO.

To examine the tolerance of this choice, we use oursimulation results for April and September to representthe end of winter and summer seasons, respectively. We

FIG. 1. Spatial distributions of level sea ice thickness HL (m) and ridges NR (number per km2) in May and Sep. (top row) Meanvalues of parameters averaged for 1984–88; (second row) the differences between values of corresponding parameters averagedfor 1989–93 and 1984–88 and (third row) the differences between 1999–2001 and 1984–88.


calculate the correlation coefficients (Table 1) betweentotal ice volume (V) and area (S) over the entire ArcticOcean for each month (left column) and the main char-acteristics of ice cover within the chosen regions andthe whole Arctic (R1, R2, and A in column titles).These characteristics for the regions include the totalice area and volume (S and V), level ice area and vol-ume (Si and Vi), and only the area of ridges (Sr) becausethe correlation for ridge area and volume are the sameowing to fixed ridge thickness in the model. Bold valuesshow important correlations.

Table 1 testifies to a highly positive correlation inApril between total ice cover area in the Arctic andboth total ice area (0.98) and level ice area (0.91) inRegion 1. An area of ice cover during wintertime isstrongly dependent on the position of the ice edge inthe Barents and Greenland Seas, while the coastalboundaries along the Canadian and Siberian coastsform the upper limit on spreading ice cover. Hence,only low correlations of total ice area in the Arctic withareas of all ice gradations in Region 2 exist along withthe low correlation with ridge area in Region 1 due toweak ridging. At the same time, a high correlation ex-ists in April between total ice volume and ridge area(0.90) as well as total ice volumes (0.92), but a negativecorrelation (�0.89) exists with the level ice area in Re-gion 2, in compensation to ridging processes by the icegrowth in newly formed leads.

During summertime, there is no lower limit, and totalice area is positively correlated with total area of bothregions and depends on level ice area (row three), as aresult of low ridging production compensated by fastmelting. Again, there is a high positive correlation forSeptember between the total ice volume in the Arcticand total ice (0.92) and ridge volume (0.92) in Region 2,as well as between the total ice area in the Arctic andlevel ice area in Region 1. The last three columns testifythat total ice volume in the whole Arctic Ocean is wellcorrelated to the ridge areas for both seasons (0.96),although the total ice area is correlated (0.84) to thelevel ice area for summer months only.

FIG. 2. Time series of ice volume in the whole Arctic and inRegions 1 and 2 in (a) Apr and (b) Sep (see text of paper forexplanation). (c) The annual mean and Apr and Sep monthlymeans of the ridge volume in the Arctic Ocean.

TABLE 1. Correlation between the total ice area and volume over the entire Arctic Ocean (S and V in left column) for Apr and Sep,and the main characteristics of ice cover within the chosen regions and the whole Arctic (R1, R2, and A in column headers). Thecharacteristics for these regions include (in column headers): total ice area and volume (S and V ), level ice area and volume (Si andVi), and only the area of ridges (Sr), because the correlation for ridge area and volume are the same due to ridge thickness being fixedin the model. Bold values show the highest and most important correlations, also discussed in main the text.

SR1 VR1 SiR1 ViR1 SrR1 SR2 VR2 SiR2 ViR2 SrR2 SiA ViA SrA

Sapr 0.98 0.45 0.91 0.53 0.30 �0.06 0.43 �0.47 �0.09 0.44 0.29 0.32 0.48Vapr 0.46 0.64 0.29 0.61 0.55 0.23 0.92 �0.89 0.00 0.90 �0.61 0.44 0.96Ssep 0.64 0.49 0.64 0.57 0.37 0.59 0.40 0.40 0.55 0.29 0.84 0.74 0.38Vsep 0.33 0.47 0.28 0.46 0.42 0.35 0.92 �0.23 0.48 0.90 0.02 0.63 0.96


In summary, total ice volume in the Arctic is con-nected to total volume in Region 2, which is character-ized by the heaviest ice cover, and stays in close con-nection to the ridge volume in this region. This is evi-dence of the role of ridges as a storage of ice mass. Thisremark is supported by the suggestion that the mostimportant change of ridging processes occurs in Region2 as a result of intensification, spread or weakening, andshift of the Beaufort Gyre in response to changes in theAO index. These variations in spatial distribution ofridging zones and changes in ridging intensity should beresponsible for long-term variability of the Arctic icecover along with the advective displacement of thethick ice area from one region to the other, driven bychanges in atmospheric circulation (Zhang et al. 2000).

c. Variability of the total ice volume and role of theridges

Annual mean ice thickness has an average of 2.3 mfor the period of simulation with a range of variation of0.8 m, in which values are close to the results of Flato(1995), J. Zhang et al. (2003), and Arfeuille et al.(2000). Since 1988, these variations stay within 0.5 m.Other models (Polyakov and Johnson 2000; Hilmer andLemke 2000; Holloway and Sou 2002) demonstrategreater ice thickness but similar ranges of variation.

Mean ice thickness in April in the Arctic Ocean hasan average of 3.05 m (4.06 and 2.12 for Regions 1 and2, respectively) over the simulation period. April meanice thickness and volume reach their maxima during1964–66 (3.51 m and 29143 km3, respectively) andminima in 1990 (2.59 m and 21029 km3) as well as an-nual mean ice volume, in agreement with results ofFichefet et al. (2003) and in contrast to local maximaonly, at times of the others models (Dumas et al. 2003,Polyakov and Johnson 2000).

Annual mean ice volume has an average of 20 270km3 and scale of interannual variability of 40% of thisvalue, whereas variations of total ice volume in Aprildo not exceed 30% of the mean. The decrease of annualmean ice volume in the model between 1984–88 (21 166km3) and 1989–93 (17 311 km3) is 17%, but since 1996the volume begins to rise and increases by 7% before1999–2001. These values of total ice volume over theArctic are close to those of the model estimation byZhang et al. (2000; X. Zhang et al. 2003), but the rangeof its change is twice as large in their simulation. Roth-rock et al. (2003) noted that the ice thickness during themid-1990s was thinner by 1.4 m than the 3.5-m maxi-mum in 1966 (a decrease of 40%), and there was a localmaximum value of 3.0 m in 1987, whereas the mean icethickness over 50 years is 2.9 m.

The wind field, which is responsible for sea ice mo-tion, was stronger in 1979–88 than in 1989–96. As an-other possible cause, the 1979–88 anomaly of the geo-strophic wind field (differences between the means of1979–88 and 1979–96) was cyclonic, whereas the 1989–96 anomaly field (likewise, between 1989–96 and 1979–96) was anticyclonic (Zhang et al. 2000). Holloway andSou (2002) estimated a decrease in total ice volume intheir model simulation from 1987 to 1997 varying be-tween 16% and 25% in response to wind forcing data.

Total ice volume in April demonstrates the same be-havior (Fig. 2a), but the extreme values are less signifi-cant than the annual mean due to averaging for theentire month, while the ice reaches maximum thicknessat the end of April. The mean thickness of level ice forthe Arctic in April is 1.97 m, with a maximum value of2.24 m in 1964 and a minimum of 1.80 m in 2000. Themean level ice thickness in Region 1 is 1.56 m and 2.47m in Region 2. This is explained by the fact that in theBeaufort Gyre sea ice stays long enough to remainclose to the thermodynamical equilibrium, but in Re-gion 1, the sea ice has a much shorter residence time.

Total ice volume for September in the present simu-lation is more fickle, and the amplitude of variationexceeds 50% of its mean value of 14 346 km3. The high-est volume of 17 962 km3 was reached in 1966, and thelowest of 9530 km3 in 1990 (Fig. 2b). The mean icethickness over the period of simulation is 3.04 m, beingslightly above Rothrock’s value (Rothrock et al. 2003).The maximum value of 3.77 m was in 1980 and theminimum of 2.16 m was in 1992. The higher values ofmean thickness in summer are explained by melting ofthe thin ice fraction.

The present model shows the current gradual de-crease since 2000 in total ice volume in April and Sep-tember in Region 2 and a small increase in Region 1. Asa result, it also shows the stepwise reduction of ice vol-ume over the whole Arctic in September, when it isaccompanied by open water expansion and ice extentdecrease. This fact was also noted by Serreze et al.(2003) from analyses of satellite observations in Sep-tember 2002 when the Arctic sea ice extent and areawere at their lowest since 1978. However, these pro-cesses in Regions 1 and 2 are partially compensated byeach other, without any essential change over the Arc-tic in April (Figs. 2a and 2b), as ice volume increases inRegion 1 along with a decrease in Region 2.

The annual mean ridge volume varied from 13 680km3 in 1980 to 6974 km3 in 1992 and had an averagevalue of about 10 682 km3 over 56 years (Fig. 2c). Thereare local maxima in 1988 (13 486 km3) and 1966 (13 498km3). Thus, the amplitude of variation in the modeledridge volume is larger than 50% of the average ridge


volume. The areal percentage of ridges in total ice vol-ume in April is 46%, on average, within the range from53% in 1981 to 37% in 1992. Hence, it contributes tothe mean ice thickness by 1.45 m. These estimations areclose to those by the model of J. Zhang et al. (2003)with assimilations of ice motion observations for the1990s. Ridges occupy about 67% of total ice volume inSeptember because ice extent decreases and, hence,level ice volume and area decrease more substantiallyduring the summer months than ridge volume. Therange of ridge volume variation is also larger in Sep-tember. The present results show that the role of icedeformation is very important for the mass balance ofthe Arctic ice cover.

d. Ridge production

The model in this paper allowed us to estimate theridge production rate. An annual ridge production overthe Arctic has an average of about 5950 km3 yr�1 andvaries from year to year by 20% of the mean amount.Maximum annual production occurs in 1987 (7229km3), whereas the minimum of 4840 km3 occurs in2003 (Fig. 3a). The annual and seasonal ridging produc-tion over the Arctic falls stepwise after 1999 and

reaches the minimum over the whole period in 2003(Fig. 3b). Total winter production from November toApril (mean value of 4629 km3 over 56 years) is 3.5times more than the summer production from May toOctober (mean value of 1324 km3) and occupies about77% of the annual amount. Minimal winter ridge pro-duction occurred in 2003 (3905 km3 season�1), whilethe maximal value was reached in 1980 (5390 km3 sea-son�1).

Figure 3c demonstrates the mean annual cycle of to-tal ice volume and ridge volume over the Arctic Oceanalong with the mean monthly ridge production. Totalice volume reaches the maximum value of 25 170 km3 inApril and has a minimum of 14 345 km3 in September,whereas ridge volume has a maximum of 12 150 km3 inJune and minimum of 9490 km3 in October. This annualcycle is explained by the fact that before June, ice staysadequately compact in the Arctic basin and ridging con-tinues, but before October the amount of leads existssufficiently, which reduces ridging.

The monthly volume of the ridging divided by themonthly mean level ice thickness gives us the value oflevel ice area involved in ridging and, hence, allowsestimations on the convergence of the level ice. As the

FIG. 3. (a) Annual ridge production (km3 yr�1) and over the Arctic and two chosen regions. (b) Annual (km3 yr�1) and seasonal ridgeproduction (km3 season�1) over the Arctic. (c) Annual cycle averaged for 1948–2003 of total ice volume, (left scale) ridge volume, and(right scale) monthly ridge production. (d) Annual cycle of ice extent and (left scale) level ice area, and monthly values of (right scale)the level ice area that is transformed into the ridged sea ice area (RSA).


next step, we will estimate the convergence over theentire region.

Only a small percentage of the level ice volume isinvolved in the ridging processes during each month.This amount varies between 0.2% and 7.4% and has anaverage of 2.2% for August when monthly ridge pro-duction is minimal (156 km3 month�1), whereas thehighest value of about 6%–10% is typical for January(708 km3 month�1) and December (Fig. 3c). Mean-while, the monthly ridge production reaches only thevalue of 6%–7% of ridge volume for the same month inthe winter season, but only 1.5%–3% in summer. As aresult, the summer seasonal production (May to Octo-ber) reaches, on average, about 30% of the winter pro-duction (November to April) and gives rise to only 23%of the annual production. During each year about 4.5 �106 km2 of level ice undergoes ridging over the ArcticOcean or, in other words, about 50% of the initial levelice area from October to November (9.5 � 106 km2).Meanwhile in winter, about 36% (3.5 � 106 km2) of thisarea transforms into ridges, yet only 0.96 � 106 km2

during summer.Another estimation of the ridge production (m) is

done by calculating the ridge volume (m3) formed perunit area (m2, km2, or area of cell) over a chosen timeinterval. The average annual ridge production overthe Arctic is about 0.81 m, while Region 2 gives morethan 63% of this amount. The ridge production reaches0.61 m in winter and 0.21 m in summer.

At a regional scale, the level ice area, which under-goes ridging during a year, is essentially larger (2.6 �106 km2) in Region 1 in comparison to that of Region 2(1.85 � 106 km2). This difference for winter is as largeas 2.15–1.41 (� 106) km2 but smaller for summer [0.52–0.43 (� 106) km2]. Larger values of level ice area, whichtransform into the ridges in Region 1 in comparison toRegion 2, can be explained by Region 1 consisting ofmore thin ice and can more easily make this transitionthan thicker ice. Hence, more resistant ice is formed inRegion 2. Figure 3d presents the average seasonal cycleof total ice and level ice area along with the cycle ofmonthly values of level ice area transforming into theridges. This figure shows that this level ice area in-creases from September to December. This change isconnected with new ice growth over open water andincreases in young ice area and ice extent during fall.

An annual ridge production rate (m3 m�2) for thedifferent phases of the AO is represented in Fig. 4. Thedistribution of ridge production is rather nonuniformover the Arctic Ocean. It should be noted that the highridge production around the islands, comparable to theridge production in the Beaufort Gyre, is the reflectionof ridge accumulation under onshore winds. This natu-

ral effect is an essential feature of the coastal area,where the ridged ice zones and rubble fields actuallyexist. Meanwhile, this ridging around the islands is notreflected in the average ice thickness here because themodel does not reproduce grounded ice, fast ice, andice freezing to the beach. Therefore, winds with change-able direction lead to ridged ice floating away fromshore and spreading over the Arctic.

Figure 4 demonstrates that Region 1 is characterizedby low ridge production, which is usually less than0.1 m3 m�2 yr�1, whereas Region 2 has the highestvalue, reaching 0.5–0.7 m3 m�2 in the Beaufort Gyre,particularly along the Canadian coastal line. For thecentral part of region 2, a remarkable decrease of an-nual ridge production occurred after 1988 from 0.5–0.7to 0.2–0.5 m3 m�2, while Region 1 had no significantchange. Over the period from 1994 to 1998, the modelshows a slight increase in ridging, to 0.4–0.5 m3 m�2, formost of Region 2, and then another increase, to 0.5–0.9m3 m�2. It may be thought that this increase leads tothe recovery of previous thinning and future thickeningof ice cover.

4. Application of the model results to navigationin the Arctic

It is well known that a main obstacle for navigation inthe Arctic Ocean, the best trade route from Asia toEurope, is the presence of drifting and fast ice. Evennavigation along the Northern Sea Route, as being themost investigated and convenient way, is rather com-plicated and relatively unpredictable from a point ofview of voyage duration and cost, despite the existenceof powerful nuclear icebreakers and the long period ofexploration. Some suggestions are also made about apossibility to use not only the Northern Sea Route, butalso a route from Bering Strait to the entrance of theNorthwest Passage through the Canadian Archipalagofor commercial navigation in the near future. Thesesuggestions are based on some model estimations orextrapolation of the sea ice cover decrease in the early1990s, described in section 3, though the results of thepresent model calculations for 1999–2003 (Figs. 1 and5) do not confirm such optimistic expectations.

Together with data of level ice thickness and ice con-centration, the information about ridges is very impor-tant. Usually, it is presented by the number of ridgesper unit length or by relative area occupied by ridgesfrom observations (Boradachev et al. 1994). We intro-duce a new parameter: a ridge-free navigation index(RFNI). This is defined as being the probability forwhich no ridge is met per unit length, under the condi-tion of isotropic and random distribution of ridges witha fixed length:


RFNI � �1 �l

�a�2N

, �5�

where l is a characteristic length of a ridge, a is the unitlength of linear displacement, and N is ridge concen-tration.

Equation (5) is obtained through a generalization ofthe classical Buffoon problem. Despite some restric-

tions related to the peculiarities of ridge space distri-bution (Davis and Wadhams 1995), it is a useful objec-tive index for the forecasting of navigation conditionswith prognostic numerical models, which usually pro-duce relative areas of different sea ice types. RFNI al-lows conversion of data of an areal ice distribution tothe linear measures (along a ship track), useful for plan-ning of navigation.

FIG. 4. Spatial distribution of annual mean ridge production rate (m3 m�2) averaged for periods of 1984–88,1989–93, 1994–98, and 1999–2001.


Figure 5 demonstrates the spatial distribution ofRFNI during three periods. The most favorable ice con-ditions for navigation are evident during 1989–93 whenRFNI exceeded 0.1 for one-half of the Arctic Ocean.However, RFNI remained very small in the CanadianArctic, supporting the suggestion of a problematic useof the Northwest Passage in the future. The presentmodel result also shows the severe conditions, particu-larly at the beginning of the twenty-first century.

To investigate the long-term variability of sea iceconditions along the Northern Sea Route in May, themost difficult month for navigation, we choose fourpoints in the central part of the Kara, Laptev, EastSiberian, and Chukchi Seas (Fig. 6). For these points,the model results were extracted characterizing thestate of sea ice during the entire period investigated.Figures 6b–e present 5-yr moving averages of the levelice thickness and total ice, level ice, and ridge concen-trations, along with RFNI.

As seen in Fig. 6, the modeled characteristics of seaice cover do not demonstrate any significant trend from1950 to 2000. There is a strong interannual variability,especially in ridge concentration and RFNI, in the

Laptev, East Siberian, and Chukchi Seas. The opennorthern boundaries of these seas are located along thesouthern periphery of the Beaufort Gyre and undergo astrong influence on ice drift in the Canadian region ofthe Arctic Basin. In turn, ice drift in this region dependson the modalities of atmospheric circulation (cyclonicor anticyclonic). As a result, we have a dominant in-crease of ridge concentration and a decrease of RFNIfrom the 1950s to 1980s, followed by a strong decreaseand increase of the first and second parameters, respec-tively, in the early 1990s, and the return to previousvalues during the late 1990s. In the Kara Sea modestnegative trends of level ice thickness and ice concen-tration could be noticed, as well as an increase of RFNIin the 1990s. The weak negative correlation betweencharacteristics of sea ice cover in this region and theother seas could be marked and is known as “ice op-position.”

5. Discussion and conclusions

From the present model results, we can conclude thatthe ice volume in the entire Arctic Ocean and its inter-

FIG. 5. Spatial distributions of RFNI (values shown � 10�5) in (top) May and (bottom) Sep averaged for (firstcolumn) 1984–88, (second column) 1989–93, and (third column) 1999–2001.


FIG. 6. Ice conditions along the Northern Sea Route. (a) Route map and points chosen for investigation. (b) Ice thickness,(c) ice concentration, (d) ridge concentration in number km�2, and (e) RFNI are plotted at the chosen points.


annual variability are mostly contributed by ridges inRegion 2, from Greenland through the Beaufort andChukchi Seas to the East Siberian and Laptev Seas.The most drastic change in ice volume was the rapidreduction occurring at around 1990, while there wereseesaw oscillations between Regions 1 and 2. This re-duction is consistent with the observed thinning (Roth-rock et al. 1999) and is in qualitative agreement with theanalysis of sea ice cover in the 1990s done by Tucker etal. (2001) and Winsor (2001), and the seesaw patternhas also been reported by Zhang et al. (1998). Themodel has shown the contrast in ice cover variabilitybetween two chosen regions in connection to the peri-ods of atmospheric circulation.

Although most models have produced results consis-tent with the observed ice cover trend and variability,the ice thickness may have lower amplitudes than thosereported by submarine observations. Interannual vari-ability is also indicated by thermodynamical processes;that is, as shown by surface ice temperature maps, theice cover retreated during 1997–99 in the Beaufort Sea,while northern Russia experienced a cooler period.

The model reproduced the partial recovery of icecover in the Canadian region near the end of the twen-tieth century and the following decrease in ice volumeover Region 2 along with a decrease in ice area and anincrease in open water since 2000. These results stay inagreement with the same recovery as the steep declineof ice area after 1990. A possible recovery during thelate 1990s is also shown by other models and observa-tions (Rothrock et al. 2003; Comiso 2002; Holloway andSou 2002).

The negative trend in simulated ice cover shows lowvalues in comparison to the data collected by satellites,but reliability depends on the accuracy of the modeland estimations based on satellite data. The winter icearea and ice extent show a smaller trend than that ofthe summer because an annual cycle of ice extentcomes from younger ice. On the other hand, thicknessand volume can decrease even if the extent does notdecrease. Comiso (2002) has revealed the periodicity tobe about 5 yr and also found the trend of the ice extentin 1981–99 to be less than that reported by Parkinson etal. (1999).

The newly presented ridge production has providedan insight on a process important for ice volume vari-ability. Ice volume and number of ridges are correlatedwell with ridge production rates (Figs. 2 and 3) and withice drifting patterns. The high AO yields an increase inconvergence over the Beaufort Gyre leading to a ridgevolume increase but simultaneously tends to reduceridge production. Therefore, the ice volume and ridge

numbers are not directly related with a large-scale at-mospheric circulation pattern, but rather a conse-quence of ridge production and drifting pattern. The icevolume indicates the history of ice storage caused by aatmospheric circulation variability at interannual timescales. Long-term variability of ridge production in theArctic has periods from about 5 to 7 yr.

The employment of the average ridge shape hasgiven us an opportunity to simulate ice thinning as aresult of ridging reduction. We have introduced a newindex, a ridge free navigation index (RFNI), and pro-vided information on the spatial distribution of theridges and planning of ship routes. This index is moreclosely related to the length of ridge-free routes, crucialto shipping along the Northern Sea Route, rather thansimple information on ice thickness.

The diminishing of Arctic ice cover is one of the mostconcerning issues of this century. However, recentlycollected data are too sparse to obtain reliable infor-mation on the trend and are often masked by interan-nual to decadal variability. Therefore, archives of his-torical submarine data for the 1960s and 1970s, alongwith other sources, are strongly desired for a more com-prehensive estimation of future ice cover.

Acknowledgments. We are grateful to the Interna-tional Arctic Research Center, University of Alaska,Fairbanks; the Graduate School of EnvironmentalEarth Science of Hokkaido University, (Sapporo, Ja-pan); the Arctic and Antarctic Research Institute (St.Petersburg, Russia); and Seoul National University(South Korea) for the support in preparation of thispaper. The work was supported financially through cat-egory 7 of the Ministry of Education, Culture, Sports,Science and Technology (MEXT) Research Revolution2002 (RR2002) Project for Sustainable Coexistence ofHuman, Nature and the Earth; Frontier Research Sys-tem for Global Change; and NTP of the Russian Min-istry of Industry and Science. Proofreading by T. Ikedawas appreciated.

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Dynamic–Thermodynamic Sea Ice Model: Ridging and Its ...123userdocs.s3-website-eu-west-1.amazonaws.com/d/0c/31/... · Arctic. Rigor et al. (2002) described the action of this mechanism