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  • View in gallery

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

  • View in gallery

    Time series of ice volume in the whole Arctic and in Regions 1 and 2 in (a) Apr and (b) Sep (see text of paper for explanation). (c) The annual mean and Apr and Sep monthly means of the ridge volume in the Arctic Ocean.

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    (a) Annual ridge production (km3 yr−1) and over the Arctic and two chosen regions. (b) Annual (km3 yr−1) and seasonal ridge production (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).

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

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

  • View in gallery

    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.

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

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  • 1 Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan, and Arctic and Antarctic Research Institute, St. Petersburg, Russia
  • | 2 International Arctic Research Center, University of Alaska, Fairbanks, Fairbanks, Alaska, and Arctic and Antarctic Research Institute, St. Petersburg, Russia
  • | 3 Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan, and International Arctic Research Center, University of Alaska, Fairbanks, Fairbanks, Alaska
  • | 4 Seoul National University, Seoul, South Korea
  • | 5 Arctic and Antarctic Research Institute, St. Petersburg, Russia
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Abstract

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

Corresponding author address: Motoyoshi Ikeda, Graduate School of Environmental Earth Science, Hokkaido University Nishi-5 Kita-10 Kita-ku, Sapporo 060-0810, Japan. Email: mikeda@ees.hokudai.ac.jp

Abstract

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

Corresponding author address: Motoyoshi Ikeda, Graduate School of Environmental Earth Science, Hokkaido University Nishi-5 Kita-10 Kita-ku, Sapporo 060-0810, Japan. Email: mikeda@ees.hokudai.ac.jp

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 stimulate attempts to explain this remarkable change in the Arctic climate system. One of the useful ways to understand the reasons for climate changes is to use a numerical model that reproduces observed environmental characteristics and examines the possible mechanisms responsible for such changes. Explanation of these changes, however, depends crucially on the model and the external forcing used for investigation. Many authors (e.g., Maslanik et al. 2000) explain the decrease in sea ice cover in the eastern part of the Arctic Ocean during the last three decades as a consequence of increased open water and thin ice, primarily forced by surface wind. The sensitivity studies (Zhang et al. 2000; Makshtas et al. 2003) support the ice volume increase before 1987, as well as the decrease afterward, which may be attributed to the change in ice drift, principally driven by wind forcing and deformed internally by ice dynamic processes. Prevailing divergent drift leads to a decrease of ice concentration. As a result, the surface albedo decreases, solar radiation absorption at the surface and in the oceanic mixed layer increases and, finally, lateral and bottom melting increases. Hilmer and Lemke (2000), on the other hand, conclude that most of the thinning can be attributed to changes in the surface-level air temperature rather than to those in the atmospheric circulation. In summary, the change in Arctic ice cover was referenced to the Arctic Oscillation/North Atlantic Oscillation (AO/NAO) through ice advection and air temperature (Zhang et al. 1998), and a cyclonic frequency over the central Arctic (Maslanik et al. 1996).

Rothrock et al. (1999) discussed the possible thermodynamic processes that could produce the observed thinning, such as an increase in oceanic heat flux, poleward atmospheric heat transport, and the consequent increase in incoming longwave radiation, or an increase in down-welling shortwave radiation. Serreze et al. (2003) attributed the anomaly in ice extent and area, received from satellite data, to ice advection away from the coast by anomalously warm southern wind, following ice divergence and rapid melting. This was due to cyclones and high summer temperatures over the entire Arctic. Rigor et al. (2002) described the action of this mechanism during the positive phase of the winter AO, as well as Ikeda et al. (2003), based on meteorological data and radiation observations from the North Pole drifting stations.

From observations and model results, some authors found the shift of thick ice cover from regions where most submarine observations were made in response to changes in the AO (Holloway and Sou 2002). Based on the comparison of the two, they have concluded that the decrease of sea ice volume in the Arctic Ocean was smaller than previously estimated and demonstrated that the submarine data from the 1990s lead to an overestimation in ice thickness trend. They have attributed this to undersampling and shown that the changes in the Arctic sea ice thickness distribution had a dominant mode of variability related to the shift of sea ice between the central Arctic bBasin and peripheral regions. This feature could not be captured by the submarine surveys.

Unfortunately, there is no common opinion about the interannual variability of sea ice thickness in the Arctic basin because the authors analyzed different datasets, mainly from submarine cruises sparsely dispersed in season, year, and region. The changes in ice thickness varied regionally (Rothrock et al. 2003; Hilmer and Lemke 2000). The observations indicate that ice draft in the western Arctic and a large part of the central Arctic basin remarkably declined since the late 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 and Johnson 2000; Rothrock et al. 2003) demonstrate ice thickness reduction of 0.5–1 m within a few years as a common feature.

The ice cover variability spreads over a wide range of time scales from a couple of years (Laxon et al. 2003) to decadal–multidecadal (Polyakov et al. 2003; Polyakov and Johnson 2000). The diverse estimations of ice thinning could be attributed to small-scale spatial variability of the ice cover. Once the submarine survey data have been taken for two subsequent years at the same geographical location, a temporal change may reflect spatial variability in a drifting ice cover. This possibility was demonstrated for 1995 and 1996 by the drill hole data for two consecutive years (Haas and Eicken 2001).

In previous papers (Makshtas et al. 2002, 2003), we suggested that the observed decrease of sea ice cover in the early 1990s was the result of the reduction of ridging for dynamic reasons, namely intensification of atmospheric cyclonic circulation above the Arctic basin (Polyakov and Johnson 2000). Furthermore, National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis forcing (Kalnay et al. 1996) extended to 2002 allows us to examine whether sea ice partially recovered at the end of the twentieth century in the Arctic Ocean, at least in the Canadian Arctic. This is supported by the results of Tucker et al. (2001), Winsor (2001) and Rothrock et al. (2003). This recovery may also be attributed to intensification of ridging processes due to changes in atmospheric circulation from cyclonic to anticyclonic periods (Makshtas et al. 2003).

In this paper, we focus on ridges, which are essential for total ice volume estimation. Ridges and hummocks are two of the main features of ice-covered seas, storing an essential part of the ice mass. During summer, when existing leads and thin level ice allow ships to maneuver much easier, the ridges remain as obstacles for navigation. We use a dynamic–thermodynamic model forced by atmospheric data in 1948–2003 for calculations of the spatiotemporal variability of level ice thickness and ridge concentration. Additionally, the present model is assumed to maintain the average ridge shape based on observations in order to describe the ridging and to estimate the long-term variation of the probability of ridge-free navigation in different parts of the Arctic Ocean, including the Northern Sea Route area.

2. Model

Sea ice cover is simulated in the large-scale dynamic–thermodynamic model (Makshtas et al. 2003). The model ice consists of relative areas of level or undeformed ice (thickness hi; area Ni), which undergoes thermodynamic growth and melting; ridged ice (area Nh) with fixed effective thickness hh = 12 m; and leads (area N0). The main equations of the model are the momentum equation, which includes a parameterization of internal ice stress in the framework of a cavitating fluid (Flato and Hibler 1992); the steady heat conduction equation; and the nonstationary mass balance equation. This last equation is
i1520-0442-18-18-3840-e1
where m = hiNi + hhNh and u is the ice drift velocity. Here,
i1520-0442-18-18-3840-e2
is a function describing thermodynamic growth or melting of level ice (first term on the right-hand side of the equation), lateral melting of level ice (second term) and the ridged ice in the leads (third term), and melting at the upper and lower surfaces of the ridges (last term).

The model describes the growth and melting of level ice with a zero-dimensional thermodynamic sea ice model, similar to that of Semtner (1976). We describe the energy fluxes between the atmospheric surface layer and sea ice surface following Jordan et al. (1999). The longwave radiation balance follows the parameterization of Konig-Langlo and Augstein (1994) taken from observations at the polar latitudes, and the shortwave radiation balance contains Shine’s parameterization (Shine 1984). The stratification of the atmospheric surface boundary layer is taken into account during the calculation of turbulent sensible and latent heat fluxes with functional dependence for highly stable stratification from Holtslag and de Bruin (1988). Following Andreas (1996), a windless heat exchange coefficient was included for estimation of the turbulent sensible heat flux. This enables us to more correctly describe the energy exchange between the snow–ice surface and atmosphere during winter conditions when strong stable stratification often occurs. We model the heat processes in the leads following Ebert and Curry (1993). To calculate the redistribution of lateral heat fluxes between ridged and level ice, we use an algorithm proposed by Doronin (1969). We describe the bottom and surface melting of ridges following Thorndike et al. (1975, their Table 1).

Wind and ocean current stresses on sea ice are determined following Brown (1981) and McPhee (1979), respectively. The cavitating fluid model produces the higher ice drift velocities, as they may lead to overestimation of the ridging, suggested by Kreyscher et al. (2000). It is noted also in the same paper that most difficulties 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 viscosity term is added in the momentum equation with a no-slip boundary condition. In the innovative paper by Flato and Hibler (1992), they compared different schemes and mentioned that the cavitating fluid reproduced a realistic circulation under smoothed (monthly averaged) wind forcing. In our case, we use the daily wind field averaged from the 4-times per day SLP field. In spite of these studies, the question of rheology is important but not so evident. Makshtas et al. (2003) used all available data for the validation of the results and showed a good agreement with these data. The comparison was made on lead and ridge concentration, heat fluxes, and ice area and volume fluxes through Fram Strait.

Because the total area occupied by the leads, level ice, and ridges in each cell cannot exceed the cell area, we set the relation
i1520-0442-18-18-3840-e3
Following the large particle method (Belotserkovskii 1984), we integrate Eq. (1) in three steps. In the first (Eulerian) step, values within the cell, as a whole, are estimated under the assumption of solid-body movement. In the second (Lagrange) step, after applying the correction of ice drift velocities from a cavitating fluid, the exchange of properties between cells is calculated under 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 velocity component normal to the cell boundary. We calculate the exchange of area, which shifts from one cell to the other and brings forth the aforementioned properties. After calculating the exchange across all cell boundaries, the new level ice and ridge volume and area in the cell are calculated.
Finally, in the last step, all ice cover parameters are redistributed in the initial grid. The new level ice thickness in the cell is calculated by dividing the new level ice volume by its area. When the total of leads, level ice, and ridge areas in the cell satisfies Condition (3), no correction is applied. If the total ridge and level ice area remains less than that of the cell, we simply increase the lead area. When ice convergence takes place and additional areas of the level ice and ridges come into the cell from the surrounding cells, the new total area of level ice and ridges exceeds the cell area. Then, we suppose that ridging occzurs and apply the simple condition that total 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 ridging process.
i1520-0442-18-18-3840-e4a
i1520-0442-18-18-3840-e4b
In this context, ridging means that level ice area decreases due to the transformation of the excessive level ice area (and volume) to the ridges, whereas the ridge area (and volume) increases. The final new values N fi and Nfh are calculated from the following equations, which are easily obtained from conditions (4a) and (4b):
i1520-0442-18-18-3840-e4d
i1520-0442-18-18-3840-e4c
The model is driven using daily 2-m air temperature and relative humidity, atmospheric surface pressure, total cloudiness amount, monthly mean solid precipitation, and dynamic height of the ocean surface. Horizontal and temporal resolutions are at 50 km by 24 h, respectively. With this model, we can calculate the spatial 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) and shortwave (F) radiation balances at the upper surface for each kind of ice cover, temperature in leads and in the upper ocean, and heat flux from the oceanic mixed layer to the ice bottom.

For future consideration, it needs to be emphasized that the simplest rectangular shape of ridges with a fixed height of 12 m was used in the model. The model reproduces the volume of ridged ice in each cell only. For estimating the number of ridges in a unit area, we must use typical values for the cross-sectional area and length of a single ridge. We calculate the cross-sectional area of a typical ridge profile using data concerning geometrical parameters of cross sections from Burden and Timco (1995), as they analyzed data from more than 250 measurement sites. The generalization of their results gives a mean value of ridge cross-sectional area of about 190 m2, with variations from 100 to 250 m2. Following this estimation, we use the value of 180 m2 in our calculations.

The data concerning ridge extent are much more sparse. Hibler and Ackley (1973) described the difficulties of its estimation due to technical problems, as well as subjective judgment about the definition of height cutoff, which must be applied to obtain ridge length distributions. Based on available aerial photographs and field observations (Hibler and Ackley 1973), it is suggested that the mean ridge length increases slightly with height (sail height) and may be of an order of 2 km for 2.5–3.0-m ridge height and 1 km for 1–1.2-m ridge height. From their Figs. A1 and A2, constructed for the northern part of the Beaufort Sea, we use, in the present model, the value of 1 km for a typical ridge length.

For the estimation of sensitivity of simulation results to the chosen ridge thickness, a case study was made against the control experiment with a ridge thickness of 9 m. The deviations of the averaged ice thickness from the standard case do not exceed−10% during all cyclonic and anticyclonic periods. The open water area changes 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 the Arctic Ocean

In previous papers (Makshtas et al. 2002, 2003), we investigated spatiotemporal variability of sea ice cover in the Arctic basin during 1959–97 and its sensitivity to external forcing. The comparison of modeled sea ice cover with available data showed a reasonable agreement in the ice extent; the spatial distributions of level ice thickness; areas of leads, level ice, and ridges; and the ice flux through Fram Strait (Makshtas et al. 2003). It was found that atmospheric dynamics and related ridging processes determine the main changes in the characteristics of sea ice cover, while an increase in surface air temperature during the investigated period causes only 20% of the ice thickness decrease in the Canada Basin. The smaller changes in ice volume occur after 1993. NCEP reanalysis data from 1948 up to 2003 give a possibility to investigate changes in Arctic sea ice cover for a longer period.

a. Response of modeled sea ice to changes in atmospheric circulation

The model has satisfactorily reproduced the main features of the Arctic ice cover as well as its seasonal and interannual variability, including the thinning of ice during the 1990s and the decreasing trend in the ice extent within the last three decades (Makshtas et al. 2003). Model simulations show the contrast in sea ice variations between the eastern and western parts of the Arctic, found by X. Zhang et al. (2003). The redistribution of sea ice in the Arctic during the positive AO is lower than the normal thickness in the East Siberian Sea and higher in the Beaufort Sea and Canadian Archipelago (Zhang et al. 2000; Holloway and Sou 2002).

The results are compared with Johannessen et al. (1999). The comparison is not straightforward because we divide sea ice into ridged ice and level ice, in contrast to the division into multiyear (MY) and first-year (FY) ice in their study. The modeled sea ice shows a negative trend of total ice volume in September from 1978 to 2003 at 31% (12.6% decade−1) and a total ice area decrease of 5.26% (2.1% decade−1), as comparable to Parkinson et al. (1999). At the end of winter (in April), the ice also has negative trends of total volume at 18% (7.1% decade−1) and ice area at 2.1% (0.85% decade−1). The annual mean ice thickness averaged over the whole region decreases during this period as well at 13% decade−1, along with 17% decade−1 in September and 9% decade−1 in April. We assume that sea ice, which has survived (outlived) the previous summer melting will become MY during the next winter. We then estimate the area of MY ice and also FY from the difference between total ice area and MY area. The MY area decreases since 1978 by 4.66% (1.86% decade−1), and FY decreases by 7.5% (3% decade−1). These values are half of those estimated by Johannessen et al. (1999), and it can be noted that our estimate of the MY area (4.7 × 106 km2) is comparable with their value.

Figure 1 presents spatial distributions of level ice thickness and the number of ridges per unit area. The latter values were recalculated from the model results with the use of the available data concerning the geometry of ridges, described in section 2. The first two averaging periods (1984–88 and 1989–93) were chosen as periods with dominant anticyclonic and cyclonic circulations of polar atmosphere (Proshutinsky and Johnson 1997). The last averaging period (1999–2001) was chosen as the nearest one to the present. Here, and also later, we refer to cycles from Proshutinsky and Johnson (1997), who described the two circulation regimes of wind.

Figure 1 also shows a partial recovery of level ice thickness in the Canadian region in 1999–2001, especially noticeable in May, with a seasonal maximum in the ice thickness. It corresponds to the change in atmospheric circulation from cyclonic to anticyclonic after 1996 (Polyakov and Johnson 2000). In the Eurasian region, a small decrease in level ice thickness can be recognized. The most remarkable feature is the temporal variability of ridged ice. In 1989–93 the ridge number decreased in comparison to that in 1984–88 by more than 50%, especially in the central part of the Canadian region. In 1999–2001, the number of ridges was almost the same as that during 1984–88 and was even larger in the northeastern part of the Beaufort Sea, which was also pointed out by Kwok (2002). The present results support the conclusion of Rothrock et al. (2003) in relation to the absence of evidence that the decline of sea ice thickness through 1996 should be extrapolated as a prediction of its future behavior.

The yearly averaged ice volume systematically grows in the Arctic Ocean (Figs. 1 and 2), especially in the Canadian region, during the periods with anticyclonic circulation (Makshtas et al. 2003), but the prevailing cyclonic regime leads to a shrink of ice cover, as noted by Walsh et al. (1996). Cyclonic circulation results in reducing MY concentration along with increasing the fractional coverage of FY in the central Arctic during winter. The model also shows that periods with the anticyclonic circulation in the atmosphere lead to a decrease in ridging intensity in the Canada Basin, adjacent parts of the central Arctic, and marginal seas. This decrease causes, on average, the thinning of sea ice in the early 1990s, when cyclonic circulation in the polar atmosphere was well developed.

The supporting evidence of the increasing ridge number in the last few years of the twentieth century can also be found in the data, reproduced in Laxon et al. (2003, their Fig. 3a). They showed, along with continued thinning of the Arctic ice cover beyond 1998, an increase in the mean winter ice thickness in 1997 and 1998 and the subsequent decrease in 1999 and 2000. The reversal of Arctic circulation in 1997 might lead to a thickening of Arctic ice pack during the late 1990s (Zhang et al. 2000; Rothrock et al. 2003). Transition from a negative anomaly in the Arctic in 1995 to a large positive one in 1996 was reproduced by model simulations (Fichefet et al. 2003).

b. Contrast in sea ice variability

Since sea ice variability has various patterns for different parts of the Arctic Ocean, it may be useful to divide it into two regions for characterizing the large-scale features of the change in ice cover. The east–west Arctic anomaly pattern (EWAAP) as a response of Arctic sea ice to the North Atlantic Oscillation was described by Zhang et al. (2000; X. Zhang et al. 2003). Their model shows a reduction of thick ice in the eastern Arctic and an increase in the western Arctic, and total ice volume over the whole Arctic decreased during 1989–96. A different regional contrast in sea ice variability is connected with AO, which shows a decrease of sea ice area and volume over the eastern Arctic, whereas ice volume increases without any essential change of ice area in the western Arctic.

In contrast to the division to the western and eastern Arctic along meridian 0°–180° (Zhang et al. 2000), we divide the Arctic area into two regions by meridians 140°E and 40°W across the North Pole (Fig. 4). The first region (Region 1) extends from the Lincoln Sea to the New Siberian Islands and from Greenland to Norway’s coast. It covers the Greenland, Barents, Kara, and Laptev Seas and has an open boundary to the Atlantic Ocean. This region is exposed to the AO and/or NAO along with an inflow of Atlantic water and, as a result, has weaker ice cover characterized by strong seasonal and interannual variability. Region 2 is situated from the Canadian coast to the East Siberian and Chukchi Seas. This region is characterized by thicker ice. The strongest ice remains in the Beaufort Gyre, while it shifts and changes its size in response to AO. In contrast, the division into western and eastern Arctic leads to the inclusion of areas adjacent to the Atlantic Ocean in both regions, and hence, both regions undergo the common influence of the AO and/or NAO.

To examine the tolerance of this choice, we use our simulation results for April and September to represent the end of winter and summer seasons, respectively. We calculate the correlation coefficients (Table 1) between total ice volume (V) and area (S) over the entire Arctic Ocean for each month (left column) and the main characteristics of ice cover within the chosen regions and the whole Arctic (R1, R2, and A in column titles). These characteristics for the regions include the total ice area and volume (S and V), level ice area and volume (Si and Vi), and only the area of ridges (Sr) because the correlation for ridge area and volume are the same owing to fixed ridge thickness in the model. Bold values show important correlations.

Table 1 testifies to a highly positive correlation in April between total ice cover area in the Arctic and both total ice area (0.98) and level ice area (0.91) in Region 1. An area of ice cover during wintertime is strongly dependent on the position of the ice edge in the Barents and Greenland Seas, while the coastal boundaries along the Canadian and Siberian coasts form the upper limit on spreading ice cover. Hence, only low correlations of total ice area in the Arctic with areas of all ice gradations in Region 2 exist along with the low correlation with ridge area in Region 1 due to weak ridging. At the same time, a high correlation exists in April between total ice volume and ridge area (0.90) as well as total ice volumes (0.92), but a negative correlation (−0.89) exists with the level ice area in Region 2, in compensation to ridging processes by the ice growth in newly formed leads.

During summertime, there is no lower limit, and total ice area is positively correlated with total area of both regions and depends on level ice area (row three), as a result of low ridging production compensated by fast melting. Again, there is a high positive correlation for September between the total ice volume in the Arctic and total ice (0.92) and ridge volume (0.92) in Region 2, as well as between the total ice area in the Arctic and level ice area in Region 1. The last three columns testify that total ice volume in the whole Arctic Ocean is well correlated to the ridge areas for both seasons (0.96), although the total ice area is correlated (0.84) to the level ice area for summer months only.

In summary, total ice volume in the Arctic is connected to total volume in Region 2, which is characterized by the heaviest ice cover, and stays in close connection to the ridge volume in this region. This is evidence of the role of ridges as a storage of ice mass. This remark is supported by the suggestion that the most important change of ridging processes occurs in Region 2 as a result of intensification, spread or weakening, and shift of the Beaufort Gyre in response to changes in the AO index. These variations in spatial distribution of ridging zones and changes in ridging intensity should be responsible for long-term variability of the Arctic ice cover along with the advective displacement of the thick ice area from one region to the other, driven by changes in atmospheric circulation (Zhang et al. 2000).

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

Annual mean ice thickness has an average of 2.3 m for the period of simulation with a range of variation of 0.8 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 and Lemke 2000; Holloway and Sou 2002) demonstrate greater ice thickness but similar ranges of variation.

Mean ice thickness in April in the Arctic Ocean has an average of 3.05 m (4.06 and 2.12 for Regions 1 and 2, respectively) over the simulation period. April mean ice thickness and volume reach their maxima during 1964–66 (3.51 m and 29143 km3, respectively) and minima in 1990 (2.59 m and 21029 km3) as well as annual mean ice volume, in agreement with results of Fichefet et al. (2003) and in contrast to local maxima only, at times of the others models (Dumas et al. 2003, Polyakov and Johnson 2000).

Annual mean ice volume has an average of 20 270 km3 and scale of interannual variability of 40% of this value, whereas variations of total ice volume in April do not exceed 30% of the mean. The decrease of annual mean ice volume in the model between 1984–88 (21 166 km3) and 1989–93 (17 311 km3) is 17%, but since 1996 the volume begins to rise and increases by 7% before 1999–2001. These values of total ice volume over the Arctic are close to those of the model estimation by Zhang et al. (2000; X. Zhang et al. 2003), but the range of its change is twice as large in their simulation. Rothrock et al. (2003) noted that the ice thickness during the mid-1990s was thinner by 1.4 m than the 3.5-m maximum in 1966 (a decrease of 40%), and there was a local maximum value of 3.0 m in 1987, whereas the mean ice thickness over 50 years is 2.9 m.

The wind field, which is responsible for sea ice motion, was stronger in 1979–88 than in 1989–96. As another possible cause, the 1979–88 anomaly of the geostrophic wind field (differences between the means of 1979–88 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 and Sou (2002) estimated a decrease in total ice volume in their model simulation from 1987 to 1997 varying between 16% and 25% in response to wind forcing data.

Total ice volume in April demonstrates the same behavior (Fig. 2a), but the extreme values are less significant than the annual mean due to averaging for the entire month, while the ice reaches maximum thickness at the end of April. The mean thickness of level ice for the Arctic in April is 1.97 m, with a maximum value of 2.24 m in 1964 and a minimum of 1.80 m in 2000. The mean level ice thickness in Region 1 is 1.56 m and 2.47 m in Region 2. This is explained by the fact that in the Beaufort Gyre sea ice stays long enough to remain close to the thermodynamical equilibrium, but in Region 1, the sea ice has a much shorter residence time.

Total ice volume for September in the present simulation is more fickle, and the amplitude of variation exceeds 50% of its mean value of 14 346 km3. The highest volume of 17 962 km3 was reached in 1966, and the lowest of 9530 km3 in 1990 (Fig. 2b). The mean ice thickness over the period of simulation is 3.04 m, being slightly above Rothrock’s value (Rothrock et al. 2003). The maximum value of 3.77 m was in 1980 and the minimum of 2.16 m was in 1992. The higher values of mean thickness in summer are explained by melting of the thin ice fraction.

The present model shows the current gradual decrease since 2000 in total ice volume in April and September in Region 2 and a small increase in Region 1. As a result, it also shows the stepwise reduction of ice volume over the whole Arctic in September, when it is accompanied by open water expansion and ice extent decrease. This fact was also noted by Serreze et al. (2003) from analyses of satellite observations in September 2002 when the Arctic sea ice extent and area were at their lowest since 1978. However, these processes in Regions 1 and 2 are partially compensated by each other, without any essential change over the Arctic in April (Figs. 2a and 2b), as ice volume increases in Region 1 along with a decrease in Region 2.

The annual mean ridge volume varied from 13 680 km3 in 1980 to 6974 km3 in 1992 and had an average value of about 10 682 km3 over 56 years (Fig. 2c). There are local maxima in 1988 (13 486 km3) and 1966 (13 498 km3). Thus, the amplitude of variation in the modeled ridge volume is larger than 50% of the average ridge volume. The areal percentage of ridges in total ice volume in April is 46%, on average, within the range from 53% in 1981 to 37% in 1992. Hence, it contributes to the mean ice thickness by 1.45 m. These estimations are close to those by the model of J. Zhang et al. (2003) with assimilations of ice motion observations for the 1990s. Ridges occupy about 67% of total ice volume in September because ice extent decreases and, hence, level ice volume and area decrease more substantially during the summer months than ridge volume. The range of ridge volume variation is also larger in September. The present results show that the role of ice deformation is very important for the mass balance of the Arctic ice cover.

d. Ridge production

The model in this paper allowed us to estimate the ridge production rate. An annual ridge production over the Arctic has an average of about 5950 km3 yr−1 and varies from year to year by 20% of the mean amount. Maximum annual production occurs in 1987 (7229 km3), whereas the minimum of 4840 km3 occurs in 2003 (Fig. 3a). The annual and seasonal ridging production over the Arctic falls stepwise after 1999 and reaches the minimum over the whole period in 2003 (Fig. 3b). Total winter production from November to April (mean value of 4629 km3 over 56 years) is 3.5 times more than the summer production from May to October (mean value of 1324 km3) and occupies about 77% of the annual amount. Minimal winter ridge production occurred in 2003 (3905 km3 season−1), while the maximal value was reached in 1980 (5390 km3 season−1).

Figure 3c demonstrates the mean annual cycle of total ice volume and ridge volume over the Arctic Ocean along with the mean monthly ridge production. Total ice volume reaches the maximum value of 25 170 km3 in April and has a minimum of 14 345 km3 in September, whereas ridge volume has a maximum of 12 150 km3 in June and minimum of 9490 km3 in October. This annual cycle is explained by the fact that before June, ice stays adequately compact in the Arctic basin and ridging continues, but before October the amount of leads exists sufficiently, which reduces ridging.

The monthly volume of the ridging divided by the monthly mean level ice thickness gives us the value of level ice area involved in ridging and, hence, allows estimations on the convergence of the level ice. As the next step, we will estimate the convergence over the entire region.

Only a small percentage of the level ice volume is involved in the ridging processes during each month. This amount varies between 0.2% and 7.4% and has an average of 2.2% for August when monthly ridge production is minimal (156 km3 month−1), whereas the highest value of about 6%–10% is typical for January (708 km3 month−1) and December (Fig. 3c). Meanwhile, the monthly ridge production reaches only the value of 6%–7% of ridge volume for the same month in the winter season, but only 1.5%–3% in summer. As a result, the summer seasonal production (May to October) reaches, on average, about 30% of the winter production (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 Arctic Ocean or, in other words, about 50% of the initial level ice area from October to November (9.5 × 106 km2). Meanwhile in winter, about 36% (3.5 × 106 km2) of this area 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 per unit area (m2, km2, or area of cell) over a chosen time interval. The average annual ridge production over the Arctic is about 0.81 m, while Region 2 gives more than 63% of this amount. The ridge production reaches 0.61 m in winter and 0.21 m in summer.

At a regional scale, the level ice area, which undergoes 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 large as 2.15–1.41 (× 106) km2 but smaller for summer [0.52–0.43 (× 106) km2]. Larger values of level ice area, which transform into the ridges in Region 1 in comparison to Region 2, can be explained by Region 1 consisting of more thin ice and can more easily make this transition than thicker ice. Hence, more resistant ice is formed in Region 2. Figure 3d presents the average seasonal cycle of total ice and level ice area along with the cycle of monthly values of level ice area transforming into the ridges. This figure shows that this level ice area increases from September to December. This change is connected with new ice growth over open water and increases in young ice area and ice extent during fall.

An annual ridge production rate (m3 m−2) for the different phases of the AO is represented in Fig. 4. The distribution of ridge production is rather nonuniform over the Arctic Ocean. It should be noted that the high ridge production around the islands, comparable to the ridge production in the Beaufort Gyre, is the reflection of ridge accumulation under onshore winds. This natural effect is an essential feature of the coastal area, where the ridged ice zones and rubble fields actually exist. Meanwhile, this ridging around the islands is not reflected in the average ice thickness here because the model does not reproduce grounded ice, fast ice, and ice freezing to the beach. Therefore, winds with changeable direction lead to ridged ice floating away from shore and spreading over the Arctic.

Figure 4 demonstrates that Region 1 is characterized by low ridge production, which is usually less than 0.1 m3 m−2 yr−1, whereas Region 2 has the highest value, reaching 0.5–0.7 m3 m−2 in the Beaufort Gyre, particularly along the Canadian coastal line. For the central part of region 2, a remarkable decrease of annual ridge production occurred after 1988 from 0.5–0.7 to 0.2–0.5 m3 m−2, while Region 1 had no significant change. Over the period from 1994 to 1998, the model shows a slight increase in ridging, to 0.4–0.5 m3 m−2, for most of Region 2, and then another increase, to 0.5–0.9 m3 m−2. It may be thought that this increase leads to the recovery of previous thinning and future thickening of ice cover.

4. Application of the model results to navigation in the Arctic

It is well known that a main obstacle for navigation in the Arctic Ocean, the best trade route from Asia to Europe, is the presence of drifting and fast ice. Even navigation along the Northern Sea Route, as being the most investigated and convenient way, is rather complicated and relatively unpredictable from a point of view of voyage duration and cost, despite the existence of powerful nuclear icebreakers and the long period of exploration. Some suggestions are also made about a possibility to use not only the Northern Sea Route, but also a route from Bering Strait to the entrance of the Northwest Passage through the Canadian Archipalago for commercial navigation in the near future. These suggestions are based on some model estimations or extrapolation of the sea ice cover decrease in the early 1990s, described in section 3, though the results of the present model calculations for 1999–2003 (Figs. 1 and 5) do not confirm such optimistic expectations.

Together with data of level ice thickness and ice concentration, the information about ridges is very important. Usually, it is presented by the number of ridges per unit length or by relative area occupied by ridges from observations (Boradachev et al. 1994). We introduce a new parameter: a ridge-free navigation index (RFNI). This is defined as being the probability for which no ridge is met per unit length, under the condition of isotropic and random distribution of ridges with a fixed length:
i1520-0442-18-18-3840-e5
where l is a characteristic length of a ridge, a is the unit length of linear displacement, and N is ridge concentration.

Equation (5) is obtained through a generalization of the classical Buffoon problem. Despite some restrictions related to the peculiarities of ridge space distribution (Davis and Wadhams 1995), it is a useful objective index for the forecasting of navigation conditions with prognostic numerical models, which usually produce relative areas of different sea ice types. RFNI allows conversion of data of an areal ice distribution to the linear measures (along a ship track), useful for planning of navigation.

Figure 5 demonstrates the spatial distribution of RFNI during three periods. The most favorable ice conditions for navigation are evident during 1989–93 when RFNI exceeded 0.1 for one-half of the Arctic Ocean. However, RFNI remained very small in the Canadian Arctic, supporting the suggestion of a problematic use of the Northwest Passage in the future. The present model result also shows the severe conditions, particularly at the beginning of the twenty-first century.

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

As seen in Fig. 6, the modeled characteristics of sea ice cover do not demonstrate any significant trend from 1950 to 2000. There is a strong interannual variability, especially in ridge concentration and RFNI, in the Laptev, East Siberian, and Chukchi Seas. The open northern boundaries of these seas are located along the southern periphery of the Beaufort Gyre and undergo a strong influence on ice drift in the Canadian region of the Arctic Basin. In turn, ice drift in this region depends on the modalities of atmospheric circulation (cyclonic or anticyclonic). As a result, we have a dominant increase of ridge concentration and a decrease of RFNI from the 1950s to 1980s, followed by a strong decrease and increase of the first and second parameters, respectively, in the early 1990s, and the return to previous values during the late 1990s. In the Kara Sea modest negative trends of level ice thickness and ice concentration could be noticed, as well as an increase of RFNI in the 1990s. The weak negative correlation between characteristics of sea ice cover in this region and the other seas could be marked and is known as “ice opposition.”

5. Discussion and conclusions

From the present model results, we can conclude that the ice volume in the entire Arctic Ocean and its interannual variability are mostly contributed by ridges in Region 2, from Greenland through the Beaufort and Chukchi Seas to the East Siberian and Laptev Seas. The most drastic change in ice volume was the rapid reduction occurring at around 1990, while there were seesaw oscillations between Regions 1 and 2. This reduction is consistent with the observed thinning (Rothrock et al. 1999) and is in qualitative agreement with the analysis of sea ice cover in the 1990s done by Tucker et al. (2001) and Winsor (2001), and the seesaw pattern has also been reported by Zhang et al. (1998). The model has shown the contrast in ice cover variability between two chosen regions in connection to the periods of atmospheric circulation.

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

The model reproduced the partial recovery of ice cover in the Canadian region near the end of the twentieth century and the following decrease in ice volume over Region 2 along with a decrease in ice area and an increase in open water since 2000. These results stay in agreement with the same recovery as the steep decline of ice area after 1990. A possible recovery during the late 1990s is also shown by other models and observations (Rothrock et al. 2003; Comiso 2002; Holloway and Sou 2002).

The negative trend in simulated ice cover shows low values in comparison to the data collected by satellites, but reliability depends on the accuracy of the model and estimations based on satellite data. The winter ice area and ice extent show a smaller trend than that of the summer because an annual cycle of ice extent comes from younger ice. On the other hand, thickness and volume can decrease even if the extent does not decrease. Comiso (2002) has revealed the periodicity to be about 5 yr and also found the trend of the ice extent in 1981–99 to be less than that reported by Parkinson et al. (1999).

The newly presented ridge production has provided an insight on a process important for ice volume variability. Ice volume and number of ridges are correlated well with ridge production rates (Figs. 2 and 3) and with ice drifting patterns. The high AO yields an increase in convergence over the Beaufort Gyre leading to a ridge volume increase but simultaneously tends to reduce ridge production. Therefore, the ice volume and ridge numbers are not directly related with a large-scale atmospheric circulation pattern, but rather a consequence of ridge production and drifting pattern. The ice volume indicates the history of ice storage caused by a atmospheric circulation variability at interannual time scales. Long-term variability of ridge production in the Arctic has periods from about 5 to 7 yr.

The employment of the average ridge shape has given us an opportunity to simulate ice thinning as a result of ridging reduction. We have introduced a new index, a ridge free navigation index (RFNI), and provided information on the spatial distribution of the ridges and planning of ship routes. This index is more closely related to the length of ridge-free routes, crucial to shipping along the Northern Sea Route, rather than simple information on ice thickness.

The diminishing of Arctic ice cover is one of the most concerning issues of this century. However, recently collected data are too sparse to obtain reliable information on the trend and are often masked by interannual to decadal variability. Therefore, archives of historical submarine data for the 1960s and 1970s, along with other sources, are strongly desired for a more comprehensive estimation of future ice cover.

Acknowledgments

We are grateful to the International Arctic Research Center, University of Alaska, Fairbanks; the Graduate School of Environmental Earth Science of Hokkaido University, (Sapporo, Japan); the Arctic and Antarctic Research Institute (St. Petersburg, Russia); and Seoul National University (South Korea) for the support in preparation of this paper. The work was supported financially through category 7 of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) Research Revolution 2002 (RR2002) Project for Sustainable Coexistence of Human, Nature and the Earth; Frontier Research System for Global Change; and NTP of the Russian Ministry of Industry and Science. Proofreading by T. Ikeda was appreciated.

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Fig. 1.
Fig. 1.

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

Citation: Journal of Climate 18, 18; 10.1175/JCLI3484.1

Fig. 2.
Fig. 2.

Time series of ice volume in the whole Arctic and in Regions 1 and 2 in (a) Apr and (b) Sep (see text of paper for explanation). (c) The annual mean and Apr and Sep monthly means of the ridge volume in the Arctic Ocean.

Citation: Journal of Climate 18, 18; 10.1175/JCLI3484.1

Fig. 3.
Fig. 3.

(a) Annual ridge production (km3 yr−1) and over the Arctic and two chosen regions. (b) Annual (km3 yr−1) and seasonal ridge production (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).

Citation: Journal of Climate 18, 18; 10.1175/JCLI3484.1

Fig. 4.
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.

Citation: Journal of Climate 18, 18; 10.1175/JCLI3484.1

Fig. 5.
Fig. 5.

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

Citation: Journal of Climate 18, 18; 10.1175/JCLI3484.1

Fig. 6.
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.

Citation: Journal of Climate 18, 18; 10.1175/JCLI3484.1

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). The characteristics for these regions include (in column headers): total ice area and volume (S and V), level ice area and volume (Si and Vi), and only the area of ridges (Sr), because the correlation for ridge area and volume are the same due to ridge thickness being fixed in the model. Bold values show the highest and most important correlations, also discussed in main the text.

Table 1.
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