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  • View in gallery

    The 52-yr (1948–99) annual mean ice thickness is shown within a subset of the model domain used for subsequent analyses. (Ice field is blanked outside the analysis region.) Locations of data used by RYM, WD, Winsor, and TWEFB are marked. The case shown later in Figs. 1, 2, 3, and 5 is from wind stress calculated from 10-m vector wind and from daily wind speed

  • View in gallery

    Change of ice thickness between latter (Sep 1993, 1996, 1997) and earlier (Sep 1958, 1960, 1962, 1970, 1976) periods are shown with locations 1–29 from RYM as shown in Fig. 1.

  • View in gallery

    Difference of 8-month mean (Jan–Aug) wind stress, averaged over 1993, 1996, 1997 minus the average over 1958, 1960, 1962, 1970, 1976 for the case shown in Fig. 1

  • View in gallery

    Time series of 3-month (Jan–Mar, dashed line) and 8-month (Jan–Aug, solid line) mean AO index, with the years of RYM submarine data indicated

  • View in gallery

    (top) First EOF of ice thickness variation and (bottom) time series of its amplitude coefficient for the case shown in Fig. 1.

  • View in gallery

    Time series of average ice thickness at 29 locations shown in Fig. 2 for three methods of wind stress estimation: reanalysis stress, dashed; geostrophic wind stress from monthly sea level pressure adjusted for daily wind speed, solid; and wind stress from 10-m vector wind, dotted. Samples at RYM times are marked.

  • View in gallery

    Time series of total ice volume from four cases in which wind stress is estimated from (a) reanalysis stress, dashed; (b) geostrophic wind stress from monthly sea level pressure adjusted for daily wind speed, solid; (c) wind stress from 10-m vector wind, dotted, and (d) geostrophic stress from daily sea level pressure without wind speed adjustment, dash–dot. Also included is case (e) using downward longwave radiation after Parkinson and Washington (1979), dash–triple–dot. (top) Annual mean volume; (bottom) annual minimum volume.

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Has Arctic Sea Ice Rapidly Thinned?

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  • 1 Institute of Ocean Sciences, Sidney, British Columbia, Canada
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Abstract

Reports based on submarine sonar data have suggested Arctic sea ice has thinned nearly by half in recent decades. Such rapid thinning is a concern for detection of global change and for Arctic regional impacts. Including atmospheric time series, ocean currents and river runoff into an ocean–ice–snow model show that the inferred rapid thinning was unlikely. The problem stems from undersampling. Varying winds that readily redistribute Arctic ice create a recurring pattern whereby ice shifts between the central Arctic and peripheral regions, especially in the Canadian sector. Timing and tracks of the submarine surveys missed this dominant mode of variability. Although model-derived overall thinning from the 1960s to the 1990s was less than hitherto supposed, there is also indication of accelerated thinning during the early–mid-1990s.

Corresponding author address: Dr. Greg Holloway, Institute of Ocean Sciences, 9860 W. Saanich Rd., P.O. Box 6000, Sidney, BC V8L-4B2, Canada. Email: hollowayg@pac.dfo-mpo.gc.ca

Abstract

Reports based on submarine sonar data have suggested Arctic sea ice has thinned nearly by half in recent decades. Such rapid thinning is a concern for detection of global change and for Arctic regional impacts. Including atmospheric time series, ocean currents and river runoff into an ocean–ice–snow model show that the inferred rapid thinning was unlikely. The problem stems from undersampling. Varying winds that readily redistribute Arctic ice create a recurring pattern whereby ice shifts between the central Arctic and peripheral regions, especially in the Canadian sector. Timing and tracks of the submarine surveys missed this dominant mode of variability. Although model-derived overall thinning from the 1960s to the 1990s was less than hitherto supposed, there is also indication of accelerated thinning during the early–mid-1990s.

Corresponding author address: Dr. Greg Holloway, Institute of Ocean Sciences, 9860 W. Saanich Rd., P.O. Box 6000, Sidney, BC V8L-4B2, Canada. Email: hollowayg@pac.dfo-mpo.gc.ca

1. Introduction

Concern for possible global warming focuses attention on the Arctic where changes may become apparent more quickly than at lower latitudes. Arctic sea ice is both an indicator of change and a mechanism, affecting global climate by insulating the winter atmosphere from a warmer underlying ocean, by ice–albedo feedback, and by influencing the stability of oceanic thermohaline overturning. In this paper we explore how observations, theory, and modeling work together to clarify perceived changes to Arctic sea ice.

Ice extent has been estimated from satellite observations since 1973 (Carsey 1982). Analyses of total areal extent have showed a statistically confident decrease at about 3% per decade during 1979–98 (Cavalieri et al. 1997; Johannessen et al. 1999; Parkinson et al. 1999; Vinnikov et al. 1999; Serreze et al. 2000).

Ice thickness has been more difficult to observe. Early reports from observations near the North Pole, taken by various means at different times of year (McLaren et al. 1992; Shy and Walsh 1996), did not show significant trends. Broader coverage of the Arctic domain has resulted from submarine-based sonar profiling (Bourke and Garrett 1987; Bourke and McLaren 1992; Rothrock et al. 1999, hereafter RYM; Wadhams and Davis 2000, hereafter WD; Winsor 2001; Tucker et al. 2001, hereafter TWEFB). A startling result from submarine profiling, reported by RYM and supported by WD, was that average thickness decreased more than 40% over a few decades. Specifically, RYM found that, averaging over five cruises in the autumns of 1958, 1960, 1962, 1970, and 1976 and averaging over three cruises in the autumns of 1993, 1996, and 1997, the latter average showed 42% less ice volume than the former average. Comparing single cruises in 1976 and 1996, WD found a strikingly similar reduction in ice volume by 43% over 20 yr, this near a region where Wadhams (1990) previously reported 15% loss of ice volume between 1976 and 1987. However, six submarine cruises from Alaska to 90°N during 1991–97, showed almost no average thinning (Winsor 2001). From nine cruises from 1976 to 1994 on the Alaska to 90°N section, TWEFB found abrupt thinning between 1988 and 1990, prior to the period examined by Winsor. TWEFB remarked that thinning did not occur near 90°N, agreeing with McLaren et al. (1992) or Shy and Walsh (1996) but contrasting with RYM or WD. All these data locations are shown in Fig. 1.

Given the different time periods and locations of data, the different results are not contradictory. An overall perception is that the volume of Arctic sea ice has suffered rapid multidecadal decline, for example, as read in the Houghton et al. (2001) assessment where loss of autumn sea ice by more than 40% was deemed “likely” (66%–90% likelihood). Such rapid loss of sea ice attracted widespread attention among environmental scientists and in popular media. Because of the importance of the issue both for global change studies and for regional Arctic impacts, and because of differences among the reported observations, we seek other sources of information that may provide a more comprehensive view. We incorporate data from the atmosphere, rivers, and ocean along with dynamics expressed in an ocean–ice–snow model.

2. Dynamic constraints on inferred changes of ice volume

Is apparent decline of Arctic ice volume consistent with plausible physical mechanisms? RYM considered three possibilities. First, warming may enhance ice melt and reduce ice growth. Second, changes to snow cover affect net ice growth. Third, varying ice export at Fram Strait alters the ice volume remaining within the Arctic. Interactions among these and other mechanisms can be further quantified in numerical models. From ocean–ice–snow modeling, Zhang et al. (2000, hereafter ZRS) identified spatial variations in wind-forced ice distributions that affect overall growth/melt through feedbacks involving open water fraction and ice–albedo. Using an ice-only model forced by wind and air temperature (no precipitation), Hilmer and Lemke (2000, hereafter HL) also found decreasing ice volume that appeared to respond more to wind than to air temperature. An important further perspective is seen in ocean–ice–snow modeling by Polyakov and Johnson (2000, hereafter PJ) where the volume of ice over the entire Arctic showed no significant trend as decreases in the central Arctic (sampled by submarines) were compensated by increases elsewhere.

There are many uncertainties. Observations of ice thickness depended upon different methods of sonar operation, noncoincident cruise tracks, and differences of seasonal timing among cruises [cf. RYM and Wadhams (1997)]. Model results depend upon uncertain time series of varying winds, changes of radiative forcing, precipitation, and heat transport by ocean currents along with a host of uncertain internal parameterizations.

The goal in this paper is to complement sparse observations with results from ocean–ice–snow modeling. To account for model uncertainty with respect both to incomplete physics and to poorly known initial, boundary, and forcing conditions, we execute a range of cases using different choices of internal model parameters and different estimates of atmospheric forcing. Our focus is upon robustness, seeking physically consistent constraints that may refine inferences from sparse observations. As well, model output is used to assess natural variability, identifying dominant modes of Arctic sea ice change.

The numerical model follows Nazarenko et al. (1998), consisting of a 3D ocean with dynamic–thermodynamic sea ice and snow on a spherical finite difference grid. Among changes since Nazarenko et al. (1998), the present model omits flux correction (surface layer restoring). We apply atmospheric forcing from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996) with river inflows from Becker (1995), and initial ocean conditions from the Polar Science Center Hydrographic Climatology (PHC; Steele et al. 2001). The domain has open boundaries across Bering Strait, Baffin Bay, and the Greenland–Norwegian Sea. Specification of open boundary conditions and further model details are listed in the appendix.

Integrations were initialized over 30 yr of climatological annual cycle, followed by 52 yr (1948–99) of monthly atmospheric forcing, adjusted for daily wind variability. Among uncertainties in forcing fields, especially we find results sensitive to estimated evolution of wind stress. Within the set of NCEP atmospheric variables, there are different ways to estimate wind stress. First, there is reanalysis wind stress. Second, NCEP supplies 10-m vector wind which, with estimated wind speed and surface parameters, can be used to calculate stress. Third, NCEP reanalyses of sea level pressure can be used with empirical parameterizations to estimate “geostrophic wind stress.” Stress estimated from sea level pressure have been constructed both from monthly pressure, with stress magnitude rescaled from daily wind speed, and from daily pressure. Details of wind stress and wind speed estimation are discussed by Steiner et al. (2001, manuscript submitted to J. Mar. Syst., hereafter SSH). We have also explored uncertainty to internal model parameters such as ice strength, leads fraction, and downward longwave radiation. Among cases illustrated in this paper, we compare the Parkinson and Washington (1979) with König-Langlo and Augstein (1994) parameterizations of downward longwave. Figure 1 shows a sample 52-yr annual mean ice thickness over a domain for which ice budgets will be evaluated, with ice fields blanked outside the evaluation domain (e.g., excluding Baffin Bay or Greenland Sea). Locations of submarine data are indicated.

Over the range of numerical experiments we found modest reductions in ice area, as also estimated from satellite data. The same experiments exhibited only moderate loss of ice volume by amounts less than reported by RYM or by WD. This raises a question if something is fundamentally wrong in the model dynamics, or in the applied forcing, or if inferences from submarine data have yielded a mistaken impression of changes of overall Arctic ice volume. In part we explored the range of model cases to search for possible sources of model error. Although minor deficiencies were suggested, the search for sources of model errors (subjects of continuing study) produced no clear results. Hence we ask instead how results from submarine data may not have represented the larger Arctic.

3. Cruising in virtual submarines

Using “virtual submarines” to sample the model Arctic at the times and places of the actual submarine cruises, we revisit first RYM. In their study, RYM identified 29 locations at which coincidence of tracks and adjusted seasonal timing were adequate to support comparisons. Those 29 locations are plotted in Fig. 2 on a map of model difference between September ice thickness averaged over 1993, 1996, and 1997 minus September thickness averaged over 1958, 1960, 1962, 1970, and 1976.

In the case shown in Fig. 2, reduction of ice volume as sampled by virtual submarines at RYM times and places was 31% while RYM reported 42%. Other cases show reductions sampled at RYM times and places varying from 25% to 43%. The pattern of change in Fig. 2 can be compared with the pattern in Fig. 4 of RYM. There are differences such as model thinning that is more evident in the Canada basin while RYM showed greater thinning in the Nansen basin. The model pattern is robust across the range of model cases, albeit differing in details. Overall it appears that the location and timing of submarine data used by RYM coincided with locations of thinning while substantial thickening occurred elsewhere, especially nearer Canada where U.S. submarines were excluded. While modeled thinning at RYM locations and dates ranged from 25% to 43%, the analysis domain showed total thinning by lesser amounts ranging from 12% to 15%. Moreover, as will be discussed in section 4c, even this lesser amount is quite specific to the timing of observations.

We have further decomposed domain volume loss (12%–15%) over the RYM period into two parts, one due to thermodynamic changes (net growth and melt) and one due to changing export. Across the range of cases studied, loss during this period was dominated by wind-induced greater export (principally via Fram Strait).

Similarly to the analysis concerning RYM, we have sampled along the approximate line reported by WD and in the sector reported by Winsor and by TWEFB. In the case of WD, two cruises between Fram Strait and 90°N in September–October of 1976 and 1996 were found to show decrease of ice volume by 43%, remarkably similar to the 42% loss reported by RYM from eight cruises through the larger Arctic. Our range of model results show the Nansen basin region to be highly sensitive, as we obtain volume losses along the WD line from 28% to 73%. Differencing between fall 1996 and 1976, total ice volume over the analysis domain decreased between 27% and 36%, values not so different from the 43% that is specific to the line reported by WD. A caution is that this represents only differences between two points in time.

From six cruises between Alaska and 90°N from 1991 to 1997, Winsor found no discernable trend in ice volume. These data are more difficult to evaluate however because three cruises in 1991, 1992, and 1994 occurred during spring near the time of maximum ice, while three cruises in 1993, 1996, and 1997 occured in late autumn near the time of minimum ice. Winsor was obliged to attempt to adjust autumn cruises to late spring by adding 0.9 m after a model-derived thickness cycle (RYM). Along the Winsor track, model cases show a volume loss, such that differences between May 1997 and 1991 fall in the range 7% to 24% (for which difference Winsor shows a 9% loss). For this time period we obtain more rapid total loss (10% to 21%) over the analysis domain.

Examining nine cruises between Alaska and 90°N, all in late spring from 1976 to 1994, TWEFB find a large (32%) decrease of volume occurring quite rapidly between 1987 and 1991 all along the section except close to 90°N where there was no significant change. TWEFB note the coincidence of rapid decrease with extreme positive values of Arctic Oscillation (AO; Thompson and Wallace 1998) and North Atlantic Oscillation (NAO; Hurrell 1995) indices, and with decreased central Arctic sea level pressure (Walsh et al. 1996). The correspondingly weaker anticyclonic winds, leading to weakened Beaufort gyre (cf. Kwok 2000), may have allowed ice to be more freely advected across the central Arctic to Fram Strait (TWEFB). While the range of model results support broadly the description given by Kwok or by TWEFB, we encounter a vexing discrepancy as model runs sampled at the times and locations of TWEFB yield erratic results from 8% loss to 4% gain where TWEFB find a 32% loss. Over the analysis domain at the TWEFB times, losses from 1987 to 1991 range from 3% to 9%, while this period stands at the beginning of a longer period (through about 1997) during which overall losses range from 16% to 25%. We do not understand the discrepancy from TWEFB, and return in section 5 to discuss this in the larger context of volume change during the 1990s. Here we summarize in Table 1 several comparisons.

4. Why?

a. The wind did it

Whenever model results are reported, a concern must be how much depends upon uncertain detail of any model, and how much we can understand in a robust, physically motivated way. Studies, leading to the pattern such as in Fig. 2, reveal that this is largely due to changing wind patterns interacting with a mobile ice cover. Do changes of winds explain the changed ice? Examining the history of wind prior to times of ice sampling, a question is over how much prior time? Since we are not sure, we have varied the time window, ranging from a few winter months to the eight calendar months prior to September observations (for RYM's evaluation). Results obtained for these different time windows are broadly similar and Fig. 3 shows a representative difference between wind stress prior to the latter (1993, 1996, 1997) and earlier (1958, 1960, 1962, 1970, 1976) periods from RYM.

In fact the wind stress differences in Fig. 3 are themselves model dependent insofar as the NCEP reanalysis products are model based. We only suppose that plausible changes of wind stress over the indicated periods resembled the pattern seen in the figure. Although ice response is complicated by nonlinear dynamics, qualitatively we can interpret ice distribution in Fig. 2 in a quasi-linear way, expecting difference ice to be forced by difference wind stress while drifting somewhat to the right. The mean stress (not shown) acting on the difference ice contributes also. Figure 3 shows that, when submarines returned in 1993, 1996, and 1997, changes of wind had plausibly expelled ice from the central Arctic mainly into the Canadian sector. If this is true then previously inferred rapid loss of ice volume (e.g., Houghton et al. 2001), was mistaken due to undersampling, an unlucky combination of ever varying winds and readily shifting ice.

Likewise we find variable wind forcing primarily responsible for ice loss along the WD, Winsor, and TWEFB sections. Both the rapid loss reported by WD and the mild nonloss reported by Winsor fall consistently within the range of model results. However, a very large loss reported by TWEFB between 1987 and 1991 is greater than we can account for over the ranges of wind forcing and model parameters we have studied. We return later to discuss issues of rapid ice loss during the early–mid-1990s in section 5.

Concerning robustness, we have made further tests. To isolate the role of varying wind forcing from changing thermodynamic forcing, we have preformed two experiments. First wind stress was assigned from its 52-yr mean seasonal cycle while other atmospheric variables (temperature, humidity, precipitation, wind speed, etc.) evolved from their full time series. Second, atmospheric variables except wind stress were assigned from their 52-yr seasonal cycles while wind stress evolved from its full time series. Strictly, dynamic and thermodynamic forcing are not separated in this way since forcing that modifies ice cover alters thermodynamic forcing, as described also by ZRS. However, time series of total ice volume, as well as specific patterns of thickness, were found to be more responsive to time series including wind stress variability than to time series including other atmospheric variability.

We ask if the changes of wind stress patterns as seen in Fig. 3 are unusual or are part of larger patterns that may be related to AO or NAO indices. Time series of winter (January–March) and 8-month (January–August) AO are shown in Fig. 4 with the years of RYM analyses indicated. Averaged over the latter (1993, 1996, 1997) and earlier (1958, 1960, 1962, 1970, 1976) periods, the winter index was 1.9 points higher and the 8-month index 0.6 points higher during the latter period. More cyclonic wind stress seen in Fig. 3 is characterized by more positive AO values seen in Fig. 4.

b. A natural model of Arctic ice variability

As we asked if the pattern of wind change seen in Fig. 3 is unusual, we ask if the pattern of changed thickness in Fig. 2 is unusual or typical of Arctic change. This question can be addressed within the context of model results by decomposing thickness variations (relative to mean annual cycle) over 52 yr (1948–99) into principal components or EOFs. A first EOF, accounting for 27% of thickness variance, is shown in Fig. 5 along with the time series of its amplitude coefficient. Across the range of cases, patterns vary and the fractions of variance in the first EOF range from 23% to 31%.

Notably, the pattern of the EOF is like the pattern of change seen in Fig. 2, which is also like Fig. 10 of ZRS, enabling us to say that these patterns are not mere accidents of sampling but are representative of typical variability. An important point is contributed by PJ who average ice thickness over periods of positive AO, obtaining a pattern (Fig. 4 of PJ) like our Figs. 2 and 5. Hilmer (2001) also performed EOF analysis on model ice thickness, showing that the ice shift from the East Siberian coast to north of the Canadian Archipelago is primarily related to the AO.

Timing of the RYM sampling, marked in Fig. 5, shows the coefficient having shifted to more negative values during the latter period (1993, 1996, 1997), corresponding to thinning in the central Arctic with thickening in the Canadian sector. While there is negative trend over the 50-yr time series of the amplitude coefficient, the trend is not fit by a linear slope but rather is dominated a jump to negative values occurring in 1989–90 coincident with the strongly positive peak in AO. Although the section examined by TWEFB slices somewhat obliquely through the EOF pattern, the time series in Fig. 5 and corresponding AO peak in Fig. 4 support the view suggested by TWEFB.

c. Timing is important

While Arctic change is sometimes characterized on decadal timescales (e.g., on the averaging intervals used by ZRS), it is clear from the time series in Fig. 5 that temporal variability on much shorter timescales is relevant to inferences occasional submarine data. This is illustrated in Fig. 6 where we imagine the 29 locations reported by RYM to have been occupied continuously over 50 years. The figure shows the average of thickness over those 29 locations with the timing of RYM analyses marked. It is interesting that, if one supposed a climatic trend toward reduced ice volume, then one might better realize the signal by extending the analysis interval. Yet if we only reset the five earlier cruises to just 1 yr earlier (September 1957, 1959, 1961, 1969, 1975) and the three latter cruises to 1 yr later (September 1994, 1997, 1998), the modeled results would have showed 11%–15% thinning rather than 25%–43% over model cases or 42% per RYM. The caution here is about undersampling in time as well as biasing spatial patterns seen in previous figures.

5. Discussion

Everywhere environments change, and ability to sample those changes is limited. Inferences from sparse observations can be unrepresentative. Additional information concerning atmospheric forcing together with the demand that inferences be physically consistent within the capability of modern ocean–ice–snow modeling helps constrain inferences.

Previous reports that Arctic sea ice volume decreased nearly by half in recent decades have been widely cited in popular media and scientific considerations (e.g., Houghton et al. 2001). However, attempts to estimate a comprehensive history of Arctic sea ice volume are troubled with uncertainty. To help address uncertainty about forcing and about model representations of ocean–ice–snow physics, we have executed a range of experiments. Finding that patterns of ice thickness and of total volume are especially sensitive to assumed wind stress, we have employed different estimates of wind stress. Experiments have included stress from NCEP reanalysis, from estimated vector winds and wind speeds, and from monthly and daily sea level pressure utilizing empirical “geostrophic stress” formulas (SSH). Model sensitivity was tested by different parameterizations in the ice and snow components and in air–sea exchanges and radiative transfers.

Over this range of tests we find, consistently with submarine data, with estimated forcing, and with physics of ocean–ice–snow interaction, that Arctic sea ice volume has decreased more slowly that was hitherto reported. Previous inferences of rapid loss are attributed to undersampling, as varying wind stress forced a natural component of sea ice variability. In particular a dominant mode of variability, moving ice between the central Arctic and the Canadian sector, was missed by the timing and tracks of submarine surveys.

Modeled 50-yr histories of Arctic ice volume are shown in Fig. 7, including four methods of estimating wind stress and a case using an alternative calculation of downward longwave radiation. While shapes of the curves are similar, differences of mean ice volume are obvious. Clearly no linear trend over 50 yr is appropriate and it is interesting to observe that the volume estimated in 2000 is close to the volume estimated in 1950. Importantly, none of the cases show losses of total ice volume exceeding 40%. A robust characterization over the half-century time series consists of increasing volume to the mid-1960s, decadal variability without significant trend from the mid-1960s to the mid-1980s, then a loss of volume from the mid-1980s to the mid-1990s. Time series of annual volume minima (bottom) are similar to the time series of annual means (top) but with more interannual variability.

Model results from the late 1980s to the mid-1990s, showing steep decline with possible leveling off or recovery during the late 1990s, pose a new research challenge. These results (Fig. 7) correspond with independent model results including ZRS (their Fig. 11), HL (their Fig. 1) and PJ (their Fig. 5). Whereas observations reported by RYM, WD, and Winsor fall within the range of plausible model results, we are confronted by the abrupt loss (32% between 1987 and 1991) reported by TWEFB and not evidenced in our model. At this point, we can only say that over the range of model cases total volume loss from 1987 to 1997 varies from 16% to 25%. Most ice loss in the late 1980s and early 1990s was due to wind-forced enhanced export via Fram Strait and southeast of Spitzbergen. Weaker net thermodynamic growth during 1987–97 accounts for only 2%–4% volume loss. However, in the later 1990s the model cases show below-average exports compensated by below-average net thermodynamic growth, which results in moderate overall change. Detailed analyses of heat and freshwater budgets (ongoing research) through the 1990s, along with yet unpublished data from submarine, from altimetric satellites (S. Laxon 2001, personal communication), and from moored sonar (H. Melling 2001, personal communication) should refine future assessments.

Acknowledgments

We are grateful for assistance from Daniel Roberge and Nadja Steiner and for discussions with many colleagues. John Walsh, Peter Winsor, and the anonymous reviewers provided valuable critical advice. Terry Tucker and Yanling Yu kindly provided station data from submarine surveys. This research has been supported in parts by the Climate Change Action Fund, Natural Resources Canada, by the Ocean Climate Program, Fisheries and Oceans Canada, and by the U.S. Office of Naval Research.

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APPENDIX

Model Specification

Because results in this paper are model dependent, specifics of the model are listed below with a focus upon some of the terms affecting energy balance in sea ice. The model follows Nazarenko et al. (1998), here incorporating parameterizations of all surface fluxes with no restoring terms. The ocean is based on the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model (Bryan 1969; Pacanowski 1995) with 0.5 arc-degree grid spacing under grid rotation after Eby and Holloway (1994). Vertical resolution is at 29 levels varying from 10 to 4350 m. A flux-corrected transport scheme after Gerdes et al. (1991) is used for tracer advection and eddy–topography interactions are represented by the Neptune parameterization (Holloway 1992).

The domain has open boundaries with assigned (nonvarying) 0.8 × 106 m3 s−1 inflow at the Bering Strait, 1.0 × 106 m3 s−1 outflow through Baffin Bay, and 0.2 × 106 m3 s−1 net inflow through the Greenland–Norwegian Sea. On inflow, water properties are assigned from a climalogical seasonal cycle from PHC (Steele et al. 2001). Thus we do not, in the present study, consider possible changes of inflowing temperature and volumes in the Greenland–Norwegian Sea. However, flows from the Greenland–Norwegian Sea into the Arctic via Fram Strait and the Barents Sea change in dynamic response to varying wind.

Surface fluxes are evaluated from bulk formulas.
i1520-0442-15-13-1691-eq101
where
i1520-0442-15-13-1691-eq102
Longwave radiation [after König-Langlo and Augstein (1994)]:
σT4ac3
Shortwave radiation:
i1520-0442-15-13-1691-eq3
 where e = pqa[qa(1 − ε) + ε]−1.
i1520-0442-15-13-1691-eq4

Ice dynamics follow Hibler (1979) with prognostic equations for thickness and concentration. Momentum dynamics are nonlinear viscous-plastic. Both snow and ice thermodynamics are determined from heat budget calculations after Parkinson and Washington (1979) using their approximations for sensible and latent heat fluxes, outgoing longwave radiation, shortwave radiation, and conduction though ice and snow. Incoming longwave radiation is calculated after König-Langlo and Augstein (1994). Snow converts to ice when snow has sufficient weight to displace the ice surface below sea surface. Values of parameters cited above and of other key parameters are listed below in Table A1.

Table A1. Parameter definitions.
i1520-0442-15-13-1691-eq5

Fig. 1.
Fig. 1.

The 52-yr (1948–99) annual mean ice thickness is shown within a subset of the model domain used for subsequent analyses. (Ice field is blanked outside the analysis region.) Locations of data used by RYM, WD, Winsor, and TWEFB are marked. The case shown later in Figs. 1, 2, 3, and 5 is from wind stress calculated from 10-m vector wind and from daily wind speed

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Fig. 2.
Fig. 2.

Change of ice thickness between latter (Sep 1993, 1996, 1997) and earlier (Sep 1958, 1960, 1962, 1970, 1976) periods are shown with locations 1–29 from RYM as shown in Fig. 1.

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Fig. 3.
Fig. 3.

Difference of 8-month mean (Jan–Aug) wind stress, averaged over 1993, 1996, 1997 minus the average over 1958, 1960, 1962, 1970, 1976 for the case shown in Fig. 1

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Fig. 4.
Fig. 4.

Time series of 3-month (Jan–Mar, dashed line) and 8-month (Jan–Aug, solid line) mean AO index, with the years of RYM submarine data indicated

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Fig. 5.
Fig. 5.

(top) First EOF of ice thickness variation and (bottom) time series of its amplitude coefficient for the case shown in Fig. 1.

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Fig. 6.
Fig. 6.

Time series of average ice thickness at 29 locations shown in Fig. 2 for three methods of wind stress estimation: reanalysis stress, dashed; geostrophic wind stress from monthly sea level pressure adjusted for daily wind speed, solid; and wind stress from 10-m vector wind, dotted. Samples at RYM times are marked.

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Fig. 7.
Fig. 7.

Time series of total ice volume from four cases in which wind stress is estimated from (a) reanalysis stress, dashed; (b) geostrophic wind stress from monthly sea level pressure adjusted for daily wind speed, solid; (c) wind stress from 10-m vector wind, dotted, and (d) geostrophic stress from daily sea level pressure without wind speed adjustment, dash–dot. Also included is case (e) using downward longwave radiation after Parkinson and Washington (1979), dash–triple–dot. (top) Annual mean volume; (bottom) annual minimum volume.

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1691:HASIRT>2.0.CO;2

Table 1. 

Comparison summary

Table 1. 
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