In this study, a multicategory sea ice model with explicit ice classes for ridged and rafted ice was used to examine the evolution of deformed ice during the period 1980–2002. The results show that (1) ridged ice comprises roughly 45–60% of Arctic sea ice volume and 25–45% of the sea ice area, (2) most of the perennial ice consists of ridged ice, and (3) ridged ice exhibits a small seasonal variability. Our results also show an increase in mean ridged ice thickness of 4–6 cm yr−1 during the summer in an area north of the Canadian Archipelago and a corresponding decrease in the East Siberian Sea and Nansen Basin. At the same time, Arctic sea ice age has been observed to decline and ice drift speed to increase during the simulation period. We connect these findings with a modeled regional increase in the production rate of ridged ice. Comparison of the multicategory model and a two category reference model shows a substantially increased ice production rate due to a more frequent occurrence of leads, resulting in an ice thickness increase of up to 0.8 m. Differences in ice physics between the multicategory and reference models also affect the freshwater content. The sum of liquid and solid freshwater content in the entire Arctic Ocean is about 10% lower and net precipitation (P-E) is about 7% lower as compared to the reference model.
 Arctic Ocean pack ice has shrunk and thinned remarkably in recent decades. The most apparent changes are observed in average and annual minimum sea ice extents [Comiso and Nishio, 2008] and in mean sea ice thickness [Rothrock et al., 2008; Kwok et al., 2009; Haas et al., 2008]. Sea ice age and residence time in the Arctic have shortened [Maslanik and Fowler, 2007] and changes in the sea ice motion have been observed. For example, by analyzing drifter data from the International Arctic Buoy Program (IABP) [Rigor et al., 2002], Rampal et al.  showed that the mean pack ice drift speed has increased by 8.5% per decade during summer and by 17% per decade during winter since the late 1970s. They also showed that mean deformation rates of ice, defined as strain rates, have increased by about 50% per decade, indicating that the pattern of the ice motion has changed.
 In contrast to the Antarctic, where most sea ice is seasonal, Arctic ice consists of large amounts of multiyear ice. The age of the pack ice depends on the general circulation pattern and the magnitude of sea ice drift in the Arctic Ocean. Moreover, deformation and redistribution of the sea ice, e.g., lead openings and ridging, are the main processes generating observed sea ice thickness distribution. As deformed ice accumulates over time in areas of perennial ice, the ice dynamics and the sea ice thickness distribution are tightly connected [Haas et al., 2008]. In sea ice models, having a correct description of the motion and mechanical redistribution between ice categories is therefore critical to correctly estimate the volume and area of both ridged and total ice.
 The best tool for describing the variability and change in the pack ice is the ice thickness distribution function (ITD) [Thorndike et al., 1975], which is driven by both thermodynamical and dynamical forcings. Dynamical contributions can be separated into advection and redistribution. Resolving the ITD guarantees that the redistribution by ridging and rafting can be properly represented.
 Modeled redistribution of the ice thickness provides only a very rough approximation when calculated using a sea ice model that can only represent ice of a uniform thickness that has an open water fraction within each grid cell. Therefore, the trend in the modeling community has been to move toward a multicategory approach where ice of different types and thicknesses can coexist within one grid cell [e.g., Hibler, 1980; Flato and Hibler, 1995; Bitz et al., 2001; Haapala et al., 2005; Vancoppenolle et al., 2009]. Observed improvements show higher ice growth rates, larger seasonal variability, increased atmosphere-ocean heat flux, decreased summer albedo and increased ocean salinity [e.g., Massonnet et al., 2011]. These improvements indicate the importance of including a way to represent thin ice within a thicker ice pack. During freezing, the multicategory approach enables higher ice growth rates, while during melting, open water exposed early in the season results in enhanced ice-albedo feedback. Still, despite this noted advantage, only 5 of 15 models used in the Intergovernmental Panel on Climate Change fourth assessment report include an ITD [Intergovernmental Panel on Climate Change, 2007].
 In this paper, we present a coupled ice-ocean model in which the ice thickness distribution is described in terms of ice categories for undeformed, rafted, and ridged ice types. With the inclusion of explicit categories for ridged and rafted ice, we aim to analyze and quantify their contributions to the ice pack. We first investigate seasonal variations in deformed ice volume and area and compare them to the seasonality of the total ice coverage. We also consider the spatial distribution of deformed ice, its role in the transport through Fram Strait, and trends of ridged ice. Finally, we investigate the impact of including an ITD on ice model results through comparisons with a reference two category model.
 The paper is organized as follows. Section 2 describes methods and models. Further detailed information about the multicategory ice model can be found in the Appendix A. In section 3, the model is evaluated for its representation of the annual cycle and long-term variability of ridged ice. The impact of an ITD on the overall freshwater cycle is also briefly addressed. Finally, discussions and conclusions are presented in sections 4 and 5, respectively.
2. Methods and Models
 In this study, a three-dimensional, coupled sea ice ocean model, the Rossby Centre Ocean model (RCO) [Meier et al., 2003; Döscher et al., 2010], is applied to the Arctic Ocean. The RCO is a Bryan-Cox-Semtner primitive equation model with a free surface and open boundary conditions [Webb et al., 1997]. Vertical mixing is calculated utilizing the KPP model by Large et al. .
 The model domain covers the Arctic Ocean and the North Atlantic to roughly 50°N. The Bering Sea is also included in order to present a realistic description of transport variability through Bering Strait. The horizontal resolution is 0.25° or approximately 25 km in a rotated coordinate system centered over the North Pole. There are 59 vertical levels with layer thicknesses between 3 m at the surface and 200 m at the bottom. The model is run using baroclinic and barotropic time steps of 300 s and 4 s, respectively. The topography is interpolated from the ETOPO2v2 data set (Global Gridded 2 min Database, National Geophysical Data Center, U.S. National Oceanic and Atmospheric Administration, http://www.ngdc.noaa.gov/mgg/global/etopo2.html).
 A closed lateral boundary exists at the Aleutian Island chain. In the North Atlantic Ocean, open lateral boundary conditions are implemented according to Stevens . For inflow, temperature and salinity values at the domain boundaries are nudged toward Polar Science Center Hydrographic Climatology (PHC) monthly mean data [Steele et al., 2001]. For outflow, a radiation condition is utilized [Stevens, 1990].
 Six hourly atmospheric surface fields of 2 m air temperature, 2 m specific humidity, 10 m wind speed, sea level pressure (SLP), precipitation and total cloudiness from the ERA-40 reanalysis project [Uppala et al., 2005] are used to force the model for the period from 1 January 1958 to 31 August 2002. River discharge is provided by climatological monthly mean volume fluxes from 19 major rivers discharging into the Arctic Ocean and Nordic Seas [Prange, 2003]. To prevent the model salinity from artificially drifting due to an incomplete description of freshwater fluxes from run off and precipitation minus evaporation, sea surface salinity is restored to the PHC climatology with a timescale of 240 days. RCO is started from PHC and from a 2.5 m thick slab of ice covering the entire Arctic. Ocean currents and ice velocities start from rest. The period 1958–1979 is regarded as spin-up.
 In the reference version of RCO the ocean component is coupled to a Hibler-type [Hibler, 1979], dynamic-thermodynamic sea ice model with an elastic-viscous-plastic (EVP) model for the rheology [Hunke and Dukowicz, 1997] and a three-layer model for the thermodynamics [Semtner, 1976]. Two categories are considered here. One for ice and another for open water. Meier et al.  provide further details of the RCO model.
 In this study, a modified version of RCO is compared with the reference model. The sea ice model is modified by implementing the Helsinki multicategory sea ice model (HELMI) [Haapala et al., 2005]. HELMI is currently used for operational sea ice prognoses in the Baltic by the Finnish Meteorological Institute (FMI) as well as for Arctic modeling research. HELMI parameterizes the ice thickness distribution, that is, the ice concentrations of variable thickness categories, as well as the mechanical redistribution of ice categories. Other parts of the sea ice model (e.g., the rheology and the thermodynamics) are identical for both the modified and the reference versions. In this study, we will also refer to the coupled RCO-HELMI model simply as HELMI.
 The following assumptions about the mechanical redistribution processes have been made: (1) Deformed ice is generated only from undeformed ice categories, that is, rafted ice is not further deformed once it has been created. (2) A crossover thickness determines whether the undeformed ice is rafted or ridged; the latter assumption is based on the Parmerter  law as well as field observations [Rothrock, 1979]. (3) The thinnest 15% of the ice in a grid cell participates in the mechanical redistribution [Thorndike et al., 1975]. (4) Shear deformations are not taken into account. (5) Although observations suggest that ridges are triangular and have a porosity of 0.3, for simplicity they are considered here to be rectangular with zero porosity.
 The present setup of the model uses five undeformed and two deformed ice categories. Ice categories have no thickness constraints, except that the thinnest category is not allowed to exceed 0.1 m. Appendix A provides further details about the multicategory sea ice model.
 Because sea ice has lower salinity than water, the modified ice physics in HELMI might affect the freshwater budget of the Arctic. To examine this potential impact on the freshwater budget we have calculated liquid, solid and total freshwater contents of the Arctic Ocean as well as freshwater transports through Fram Strait both in HELMI and in the reference model. However, the presentation of a closed freshwater budget is outside the scope of the present study and will be presented elsewhere.
 The liquid freshwater content is calculated by integrating (S0 − S)/S0 down to the depth of the S0 = 34.8 g kg−1 isohaline and over the entire Arctic Ocean, which is defined as the area enclosed by Fram Strait, the Barents Sea Opening, the Bering Strait and the Canadian Archipelago. For the solid part, freshwater is calculated by converting the sea ice volume to a water equivalent by multiplying it with the density ratio of sea ice and water. In our model, sea ice has a fixed bulk salinity and hence, constant freshwater concentration per unit volume. The export of liquid (solid) freshwater through Fram Strait is calculated from the currents (ice velocities) normal to the strait's cross section, integrated over the entire cross section. In this study, sea ice is assumed to have a salinity of 4 g kg−1, which is a standard value for Arctic Ocean models [e.g., Johnson et al., 2007]. Model snapshots are saved at midnight in 48 h intervals.
 Throughout the paper, the phrase “mean thickness” will denote ice volume per unit area, which has length as unit, while the phrase “average thickness” will denote the area weighted thickness average over the seven ice categories. In the first term the calculation includes the open water fraction, which is not included in the latter term.
 We first evaluate model results, followed by analysis of the mean seasonal cycles of ice area, volume and transport. Finally, we analyze trends and the time evolution of the ice pack.
3.1. Ice Cover and Thickness
 In Figure 1, the results from two model simulations for the September sea ice extent anomaly are compared with the NASA Goddard Space Flight Center (GSFC) satellite record [Cavalieri et al., 1996]. For individual years, the agreement between the simulated and the observed summer ice extent anomaly is within the range of, or close to, the uncertainty of various observational data sets (not shown). The satellite record shows a negative trend of 5 × 104 km2 yr−1 while the multicategory and reference models both show a negative trend of 3 × 104 km2 yr−1. The ridged ice area anomaly from the multicategory model is also shown. While the trend in ridged ice area is similar to the modeled ice extent trend, its year-to-year variations are not significantly correlated with the year-to-year variations of the ice extent.
 For the mean location of the ice edge, defined as the 15% ice concentration contour, the differences between HELMI and the reference model are negligible (Figure 2). The simulations from the two ice model versions are in good agreement with observations, although some problem areas are visible. In September, the ice tongue along the eastern coast of Greenland does not reach as far south as it does in the observations, and the ice edges at the Alaskan and the East Siberian sides do not retreat from the coasts as seen in observations. In December, there is too much ice propagating southward from Baffin Bay. There is also too much ice in the Bering Sea in December, March, and September. On the other hand, in June, the simulated ice edge south of the Franz-Josef Islands does not extend as far south as it does in observations.
 Although the locations of the ice edge in the two models are very close to each other, the ice concentrations differ substantially (Figure 3). The multicategory ice model produces more open water in September than the reference model does, especially on the eastern Siberian Shelf and in the North Pole sector of the Arctic Ocean. Lower ice concentrations during summer are mainly found in regions with low concentrations of deformed ice (Figure 4). In December, ice concentrations are very similar in both models with slightly lower overall concentrations in the multicategory model (not shown). Though the ice edge is similar in both of these models, they differ from ice edge results of other models [e.g., Massonnet et al., 2011]. We elaborate on possible reasons for this in section 4.
 Although deformed ice and multiyear ice are not the same, there is a clear tendency for simulations of the latter to consist mainly of the former. For instance, in our simulation, ridged ice concentration does not vary much between June and December (Figure 4). Furthermore, in regions where observations show a long residence time [Maslanik and Fowler, 2007; Fowler et al., 2004] we find mainly deformed ice (Figure 4).
 According to HELMI, the thickest ice occurs along the northern coasts of Greenland and Canada, where it becomes nearly 5 m thick (Figure 5). The multicategory ice model produces considerably thicker ice than the reference ice model does with an increase typically ranging from a few centimeters on the Siberian Shelf to about 0.8 m north of Greenland and Canada (Figure 5). Thicker ice in HELMI compared to the reference model is expected because leads occur more frequently in the multicategory model than in the reference model, leading to significantly greater ice production.
 Ice draft is the ice thickness below the waterline, and is used as a proxy for ice floe thickness [Rothrock and Wensnahan, 2007; Bourke and Garret, 1987]. For the model, ice draft is computed as d = c(hiceρice + hsnowρsnow)/ρwater, where d is the ice draft, c is the ice concentration, and h is the “floe” thickness of ice and snow. The submarine data are gridded onto the model grid, including measurements of open water. Differences between simulation results and observations are computed using the model output closest to each submarine track in space and time. Tracks where the model has no ice are discarded.
 A histogram of the gridded submarine and model ice drafts shows that the model produces a bimodal distribution in contrast to one peak in the measurements (Figure 6). In the model, the distribution is sharply cut off at about 4 m thickness while the measurements exhibit a bell-shaped distribution. The sharp cut off is partly an effect of using average thicknesses in conjunction with a rather high diffusion to eliminate any local extremes. Even so, the thickness extremes in ridged ice are probably underestimated in the model (not shown). The model underestimates the average sea ice thickness by 0.5 m. The error in ice thickness is largest in the area close to the North Pole and then gradually declines toward the Canada Basin. A difference plot between model and submarine drafts shows an up to 2 m overestimation simulated ice thickness in the Canada Basin (Figure 7). Conversely, in the Nansen Basin, the model underestimates the thickness by up to 4 m in a few extreme cases. For climatological mean values (Figure 7) there is improved agreement between model results and observations [Rothrock et al., 2008, Figure 5], although simulated ice draft is still underestimated by about 0.2 m in the Canada Basin and 0.6 to 0.8 m in the Amundsen and Nansen basins (Figure 7). The model's better agreement with climatological observations is consistent with overly low variability in the sea ice cover and overly high horizontal diffusion in the model.
3.2. Ice Transport
 In addition to ice concentration and ice thickness, ice velocity is an important parameter for evaluating ice dynamics and physics. Figure 8 compares observed ice velocities from the IABP [Rigor et al., 2002] with model results. For each buoy observation, the closest model result in space and time is selected. Buoy data locations where the model does not show ice are discarded. On average, modeled velocities are close to the buoy velocities. When observations are available, the velocity difference is usually zero (Figure 8, bottom). However, the spread is relatively large, indicating that although the climatological mean velocities are realistically simulated, the deviations in time might be quite large. In addition, the histogram of the model-buoy differences is not symmetric. Simulated velocities are systematically larger than observations, especially at low speeds (Figure 8, top). Both HELMI and the reference model (not shown) underestimate the frequency of slow moving ice. Even when we performed a sensitivity experiment with increased compressive ice strength (Cf = 50, see Appendix A), low ice velocities occurred less frequently than observed.
 One way to evaluate both ice thickness and ice velocity is to look at ice transports in, for example, Fram Strait. In Figure 9, we compare model transports and observations by Kwok et al. [2004, Figure 7 and Table 3]. The simulated annual, winter (October–May), and summer (June–September) mean transports are biased by −424, −429, and +28 km3 yr−1, respectively. The interannual variability is larger than in observations with standard deviations of 618, 505, and 193 km3 yr−1 from our model results compared to 497, 472, and 82 km3 yr−1 from Kwok et al.  for the annual, winter, and summer periods, respectively.
3.3. Seasonal Cycle
 In this section, we focus on simulated mean seasonal cycles of ridged ice area, ridged ice volume and transport of ridged ice through Fram Strait. We compare ridged ice behavior with total ice behavior.
Figure 10 shows ice area and volume for total, ridged, and rafted ice, as well as area and volume transports through Fram Strait. We used data collected over 22 years (1980–2002) to calculate the mean seasonal cycle, and the model results have been smoothed with a 120 day Gaussian running mean filter. As a measure of year-to-year variation, the standard deviation from the mean (shaded area) is also shown. Occurrences of the maxima and minima and their values for total, ridged, and rafted ice are presented in Table 1.
Table 1. Maxima and Minima in the Seasonal Cycle of Total, Ridged, and Rafted Ice and Time of Occurrencea
Seasonal cycles are calculated from the years 1980–2002 and the error estimate is taken as the standard deviation of the mean.
14.2 ± 0.3 × 106 km2 (Feb)
7.1 ± 0.5 × 106 km2 (Aug)
3.8 ± 0.4 × 106 km2 (May)
3.1 ± 0.4 × 106 km2 (Oct)
0.46 ± 0.05 × 106 km2 (Feb)
0.02 ± 0.02 × 106 km2 (Aug)
3.6 ± 0.2 × 103 km3 (Apr)
1.6 ± 0.3 ⋅ 103 km3 (Sep)
1.7 × ± 0.2 × 103 km3 (May)
1.0 ± 0.2 × 103 km3 (Sep)
0.32 ± 0.09 × 103 km3 (Mar)
0.01 ± 0.01 × 103 km3 (Sep)
 One noteworthy observation is that the seasonal cycle of ridged ice area is of the same magnitude as the year-to-year variations, in contrast to the total ice area and volume where the seasonal variations are much larger than the year-to-year variations. The behavior of the ridged volume falls somewhere in between where the seasonal cycle dominates, but the year-to-year variations are still relatively large. Rafted ice volume is two orders of magnitude smaller than the total volume. The maximum and minimum of both the area and volume of the deformed ice lag the corresponding extrema of the total ice by about 0.5–3 months.
 Undeformed ice of the thinnest ice categories exhibits characteristics similar to those of rafted ice. During the melt period the area and volume of these classes are almost zero (not shown).
 Area transports through Fram Strait show a distinct minimum in late July and a maximum during the period of late November to early March (Figures 10e and 10f, black line). The year-to-year variations are very large as shown by the gray shaded area representing ±1 standard deviation. For ridged ice (white line), year-to-year variations are even larger compared to variations of the mean seasonal cycle.
Figure 10f shows the corresponding volume transport. The similarity in behavior to that of the area transport indicates that ice thickness variations play a less important role in the variability than do area flux variations. Note that the interannual variability on the monthly scale is relatively large compared to the seasonal cycle.
3.4. Interannual Variability
 Despite our short time series, HELMI model results for ice area and volume transports through Fram Strait indicate variability on a decadal timescale (Figure 11). For total area transport, undeformed ice is, during most years, more important than ridged ice (Figure 11, middle). However, ridged ice is the most important component of the total volume transport (Figure 11, bottom). The area transports in the reference model are slightly higher than in the multicategory model, while the situation is reversed for the volume transports. For the period 1988–1996, we find above average volume transports through Fram Strait, with the exception of the years 1990 and 1991 (Figure 11, top). The summer area of ridged ice in the Arctic reaches its maximum during the 1980s and its minimum during the 1990s (Figure 1). Furthermore, during the same period, 1988–1996, the total ice volume and liquid freshwater content decreased (Figure 12). Most of the variability of volume transport through Fram Strait results from variability in the ridged ice. Thus, the long-term variability of ridged ice is closely linked to the variability of the freshwater content, ice volume and ice transport through Fram Strait. Atmospheric circulation may be the driver for correlation or anticorrelation between the variables. Noting similar behavior, Zhang et al.  linked ice variability to the NAO index and the corresponding atmospheric circulation. Maslanik et al.  noted increased cyclone activity over the Arctic Ocean associated with the increased NAO index of the early 1990s. However, the NAO index can only partly explain the transport variations (Figure 11, top). For the period 1979–1995 investigated by Zhang et al. , the NAO index and the simulated transport are weakly correlated, whereas they are anticorrelated during the years 1990–2000.
 Calculating the trend for September in each grid cell, we found an increase in the mean ridged ice thickness of about 4 to 6 cm yr−1 in an area north of the Canadian Archipelago (Figure 13). On the opposite side of the basin, in the East Siberian Sea as well as in the Nansen Basin, a clear reduction is seen with values again ranging from −4 to −6 cm yr−1, with the highest values in the Chukchi Sea. These trends are statistically significant at the 90% level or higher, as given by the two-sided p value from a least squares regression with a null hypothesis of no trend. For the undeformed ice, no such trend could be found except close to the ice edge, corresponding to the reduction in ice cover.
3.6. Impact on the Freshwater Cycle of the Arctic Ocean
Figure 12 shows the liquid, solid and total freshwater contents together with the differences in the freshwater transports through Fram Strait between HELMI and the reference model. In HELMI, more solid freshwater is transported out of the Arctic through Fram Strait (see also Figure 11). On the other hand, liquid freshwater transports are decreased compared to the reference model. In HELMI, more freshwater is stored in the Arctic as ice. However, the total freshwater content is about 10%lower in HELMI compared to the reference run. We found that net precipitation into the oceans is decreased by about 7% compared to the reference model because of increased evaporation in connection to more frequent leads. This is a significant change in the freshwater budget as net precipitation is the third largest sink of liquid freshwater (2000 km3 yr−1) in the Arctic Ocean [Serreze et al., 2006]). According to Serreze et al. , the freshwater exports through Fram Strait and the Canadian Archipelago amount to 2400 km3 yr−1 and 3200 km3 yr−1, respectively.
 The implementation of a multicategory sea ice model in RCO applied to the Arctic Ocean shows the importance of resolving the ice thickness distribution for the ice mass balance. Our results agree with the findings of Bitz et al.  who did an extensive analysis of the impact of adding an ice thickness distribution to a sea ice model. Massonnet et al.  also showed similar results. Thus, the agreement between various models underlines the robustness of the multicategory approach. In our study, the use of explicit ridged and rafted ice categories allowed us to quantify the importance of ridged sea ice for the Arctic sea ice mass balance.
4.1. Ice Cover and Thickness
 Thin and thick ice may coexist in each HELMI grid cell. Thus, significant ice production is possible even in grid cells where the mean ice thickness is close to the thermodynamic equilibrium thickness, and no open water is present. Furthermore, since HELMI uses only the 15% of the area containing the thinnest ice in each grid cell for calculating ice strength, the model permits simulation of weaker resistance to compression compared to the reference model, even when the mean ice thickness increases. The increased mobility causes more leads and openings in the ice resulting in greater ice production.
 Due to more frequent leads in HELMI, increased ice production causes up to a 0.8 m increase in ice thickness and a ∼7% decrease in net precipitation into the ocean. Still, the model does not produce enough thick ice which is evident when comparing it to observed ice drafts (Figure 7). Furthermore, the locations of the thickest ice in the model and in measurements by Rothrock et al.  differ slightly. Compared to observations, the maximum in the model is shifted west toward the Beaufort Sea. Thus, in HELMI, Beufort Sea ice thickness is overestimated, but the thickness is underestimated close to the North Pole. This is a common pattern in sea ice models [e.g., Miller et al., 2005; Vancoppenolle et al., 2009; Massonnet et al., 2011]. Miller et al.  demonstrated that in the CICE model [e.g., Lipscomb and Hunke, 2004; Hunke and Dukowicz, 1997], the location of the maximum could be improved by adjusting the yield curve of the rheology so that shear strength is increased. However, a shear strength which is higher than the compressive strength, is difficult to explain with current knowledge in ice physics. Wilchinsky et al.  suggest modifying the ice physics in CICE by, among other things, adding sliding friction, which improves the results. Moreover, Kwok et al.  shows that four models with different variations of the viscous-plastic rheology: (1) produced smaller ice drift along the coast of Alaska, (2) exhibited poor skill in reproducing time series of regional divergence, and (3) produced deformation-related volume production that was consistently lower compared to RADARSAT Geophysical Processor System (RGPS) data. Girard et al.  show that an Elasto-Brittle approach to sea ice rheology produces much improved statistical and scaling properties of the ice compared to a reference viscous-plastic rheology case. Girard et al.  found that the viscous-plastic rheology framework “does not consider long-range elastic interactions which are the root of strain localization, intermittency and scaling”. In essence, the standard viscous-plastic framework seems to be in need of revision in order to meet the increased demands we put on model results.
 Comparison of HELMI results and submarine ice draft measurements shows that the error in ice draft thickness is comparable to corresponding errors in well-established models [e.g., Vancoppenolle et al., 2009]. The discrepancies in HELMI are most likely caused by erroneous location of ridged ice. In the Canada Basin and Chukchi Sea regions, where HELMI produces high concentrations of ridged ice, overestimations of ice draft are most frequent, while in the Nansen Basin, where the model produces low amounts of ridged ice, the ice draft thickness is often underestimated (Figure 7).
 We found a larger seasonal variability in the sea ice cover in the multicategory model than we did in the reference model. The thin ice disappears rapidly during the melting period, reducing the ice concentration, which in turn leads to a darker surface and increased absorption of short-wave radiation. In our model, the reduced concentration causes only minor differences in the ice edge. The largest ice edge differences are found in areas where ice velocities are high. This suggests that ice extent is mostly thermodynamically controlled by the given atmospheric forcing. Without a coupled atmosphere, the impact of ice albedo feedback is limited.
 Reduced ice concentrations during melting were also found by Vancoppenolle et al. , among others when incorporating an ITD. Holland et al.  argued that the albedo feedback is important for the future of Arctic sea ice. Their simulations with a coupled atmosphere-ice-ocean model showed a rapid sea ice cover decline related to decreased albedo, increased basal melting, and a delay in the onset of ice growth due to heat stored in the ocean as a result of increased solar absorption.
 In our simulations with HELMI, the onset of ice growth is delayed by only 2 days when compared to the reference model. On the other hand, even though the melt period is virtually the same length in the two model versions of this study, roughly 2500 km3 more ice is melted in the multicategory model compared to the reference model.
 One shortcoming of both sea ice models investigated in this study may be the forcing. Both models simulate overly thin ice, and ice that does not retreat far enough from the Siberian coast during summer. This result could be an artifact of applying the 2 m air temperature and humidity, 10 m wind, and total cloud cover from ERA-40 for the calculating surface fluxes of heat and momentum. For instance, Graversen et al.  showed that downward long-wave radiation from aloft, which would not necessarily be captured in the 2 m temperature, can play a significant role in sea ice melting. For the forcing, Vancoppenolle et al.  used a setup similar to ours and noted similar problems with the ice retreat in the Siberian Seas, although the shortcomings are less severe in their study. In fact, problems with too much ice close to Siberia have been reported in several other modeling studies [e.g., Döscher et al., 2010; Gerdes and Köberle, 2007].
 Another reason that the ice extents in the two versions of our study are almost identical might be that we do not use an explicit parameterization for lateral melting. The only differences between our two models are as follows: (1) the inclusion of an ITD, (2) a scheme for calculating deformed ice, and (3) a more sophisticated ice strength formulation that utilizes the information provided by the ITD. Otherwise, the two versions are identical. Because earlier simulations with our reference model have suggested that the results are slightly better without lateral melting, we have not included this parametrization here.
4.2. Ice Transport
 We have found that simulated mean ice velocities are close to observed buoy data. However, the distribution of ice velocities differs from observations. The model seems to overestimate the probability of low ice velocities, regardless of whether HELMI or the reference model is used. This bias mainly affects the areas north of the Canadian Archipelago and north of Greenland, where the ice is usually very thick. One partial explanation for the bias might be found in the older EVP formulation by Hunke and Dukowicz  used in RCO. The modifications by Hunke  result in narrower and more realistic boundary layers, better simulation of the marginal ice zones, and improved damping of elastic waves. These improvements were achieved by maintaining the stresses within the elliptical yield curve through a new subcycling scheme and a new linearization of the internal ice stress equation. The underestimation of the transport through Fram Strait is a consequence of underestimating the ice volume in the Eurasian region. According to our results, ridged ice plays a key role in volume transport. This is illustrated, for instance, in data for 1988 where the total area and volume transport anomalies have opposite signs (Figure 11, top). Due to the dominance of ridged ice in volume transport, the source region affects the transport as well because ridged ice is not evenly distributed over the Arctic.
 Earlier studies [e.g., Zhang et al., 2000], suggest that the NAO index is a good indicator for Arctic circulation patterns. However, we found that the correlation between Fram Strait ice export and NAO does not exist in data for the 1990s. Overland et al.  showed that for the period 2000–2007 the spatial SLP patterns differ from the patterns found during most of the twentieth century, highlighting the degree of variability within the Arctic. Similar findings were made by Wang et al. . Hence, other modes than AO/NAO have to be considered as well. It is clear however, that the local SLP gradient is a strong driver for sea ice export through Fram Strait [e.g., Jung and Hilmer, 2001; Koenigk et al., 2006].
4.3. Mean Seasonal Cycle and Interannual Variability
 The seasonal cycle ice volume maximum lags the area maximum by about two months, although the minimum ice volume and area are fairly well synchronized. As the total volume increases faster than the ridged ice volume (Figure 10), we conclude that in addition to ridging, basal freezing continues to be a contributor to ice volume increase well after the ice edge has started to retreat. The seasonal cycles for both ridged ice area and volume lag even further behind the seasonal cycle of the total ice area. Two factors might explain this behavior: (1) ridged ice production can occur as long as undeformed ice is available and the ice concentration is high and (2) most of the ridged ice is located in northern regions where melting occurs late in the year. The first factor may perhaps explain the late minima, as it takes some time for undeformed ice to build up and for ice concentration to increase. Furthermore, the production rate must exceed the loss rate through southward transports. The first factor might also explain why rafted ice plays only a minor role. Before ice concentration approaches 100%, the ice has already grown thick enough to make rafting a rare event. We found that the ice volume is correlated by a factor 0.9 to the ridged ice area, which exhibits a pronounced minimum during the 1990s (Figure 1). The same minimum is found in both the solid and the total freshwater contents (Figure 12). Additionally, there are similarities between the ice age maps of Maslanik and Fowler  and the position of ridged ice in our simulation, and the simulated seasonal cycles of ridged ice in our study and modeled ice age in the study by Hunke and Bitz  are similar. The matches are not perfect, however, as ridged and perennial ice represent different quantities of the ice pack. Nevertheless, the similarities raise questions. Is the amount of ridged ice mainly a the residence time factor in the Arctic? If the residence time for the ice is reduced in a warmer climate, the consequence will very likely be thinner undeformed ice. How does this affect the ratio of ridged and rafted ice and the overall mass budget?
 In our simulations, ridged ice volume has a positive trend in an area where perennial ice is common (Figure 13). Everywhere else, the trend is either negative or zero. We know from recent findings that the age of the ice in the Arctic is declining [Maslanik and Fowler, 2007]. Hence, in agreement with findings by Rampal et al. , who observed increased ice strain rates, our study suggests that the long-term trends of ice age and ridged ice will differ. We therefore expect higher production rates for ridged ice in the perennial ice cover in the future.
 Arctic sea ice consists of large portions of heavily deformed multiyear ice [e.g., Rothrock et al., 2008]. The temporal evolution of this ice plays a key role in the Arctic sea ice cover [i.e., Maslanik and Fowler, 2007], which is an important component of the Arctic climate system. To properly model the Arctic sea ice, it is therefore important to be able to describe the multiyear ice and its dynamics realistically. For this purpose, we have analyzed results of a multicategory sea ice model applied to long-term simulations of the Arctic Ocean. The main conclusions of this study are as follows:
 1. Ice concentration, ice thickness and ice velocities are well simulated by the multicategory sea ice model. Comparing it to the reference model, we find two major improvements relative to observations: the average ice thickness is significantly thicker with up to 0.8 m, and during summer, mean ice concentrations along the eastern Siberian Shelf and in the North Pole sector of the Arctic Ocean are lower. However, there are only minor changes in ice extent.
 2. Analysis of the seasonal variability in the multicategory model shows that in the Arctic, (1) rafted ice plays a minor role in terms of ice area and volume; (2) the amount of ridged ice continues to grow until May, about three months longer than does the total ice area, and 1 month longer than the total volume; (3) ridged ice is more important for the ice volume than for the ice area; (4) the seasonal variability is less pronounced for ridged ice than for the total ice cover while the year-to-year variations are about the same; and (5) the volume transport of ice through the Fram Strait is dominated by the transport of ridged ice with interannual variations that dominate seasonal variations.
 3. Despite a modeled negative overall trend of ridged ice area during the period 1980–2000, on the regional scale, we find a statistically significant increase of 4–6 cm yr−1 in the mean thickness of ridged ice during summer in an area north of the Canadian Archipelago, and a corresponding decrease in the East Siberian Sea and the Nansen Basin. This relocation indicates a general change in the ice flow pattern.
 4. Choices in parameterizations of the ice physics impact the freshwater cycle of the Arctic Ocean. Total and liquid freshwater contents in the multicategory ice model simulation are 10% lower compared to the reference model, and net precipitation into the ocean is 7% lower. Furthermore, ice volume export through the Fram Straight is closer to observations in the multicategory than in the reference model.
Appendix A:: Model Implementation
 The thickness space is discretized into five categories of undeformed ice. Deformed ice is divided into two categories, ridged and rafted ice, bringing the total number of categories to seven. These categories are not fixed in thickness space but can grow or shrink freely, with the exception of a special thin ice category that is not allowed to exceed 10 cm.
 Transformation of ice between the different categories is done by mechanical redistribution and a “house cleaning” mechanism. The house cleaning is not a physical process but was added to increase the performance of the scheme. The intent is to optimize variance in thickness between the categories. A more common approach is to place bounds on each ice category's thickness to ensure that ice of all relevant thicknesses can be represented. Our technique instead allows for higher thickness resolution where desired. The trade-off is that acquiring optimal variance is nontrivial. In addition, while the use of two explicit categories for deformed ice allows us to track the deformed ice, it also places some restrictions on the thickness resolution at the thicker end. The undeformed ice classes are numbered 1 to N where the Nth ice category denotes the special thin ice category. Ice is then transferred slowly from category n to n − 1 via a simple advection scheme
where A denotes ice concentration and k = 0.001, which is a tunable parameter. The same is also done for ice and snow volume.
 The time evolution equations for the undeformed ice are
where Au is the area of a particular undeformed category, and Hu is mean thickness of the ice category defined as H = Ah where h is the ice floe thickness, is the ice velocity, Ψu and Ωu represent losses due to mechanical redistribution, and ΘAu and ΘHu are changes due to thermodynamics.
 Time evolution equations for the deformed ice where the d subscript denotes deformed ice are
The deformed ice is considered incompressible hence the slight difference.
 We do not consider redistribution due to shear. For undeformed ice we can therefore write
where ωu describes how the converging ice is deformed and f is a function that describes the relative area of the resulting deformed ice. The term ωu can be broken down to
where α(h) is the participating function. We assume that only the thinnest ice that makes up 15% of the total grid cell area is deforming. Categories are weighted by their concentration that falls within this 15%. The term γ(A) describes whether the ice is packing or deforming, and the terms rra(h) and rri(h) divide the redistribution into ridging and rafting. Whether the ice is packing is a function of the ice free fraction
where C = 20 is a constant and Atot is the total ice concentration in the grid box.
 Thin ice has a tendency to raft while thick, level ice creates ridges. The crossover thickness, hcri, between these modes is set to 17 cm according to Parmerter . A logistics curve is used to discriminate between rafting and ridging. Both modes are equally important at the crossover thickness, but one singe mode dominates smaller or larger thicknesses
The sum of the two is always one so that
 The presence of newly deformed ice means that an “extra” patch of ice needs to be consumed as well, increasing the volume flux to the deformed ice. The function f describing this area can be split into rafting and ridging events, f = fra + fri. For rafted ice, the ice that deforms takes up the same area as the convergent motion, thus for pure rafting fra = 1. For ridged ice fri is a function of hu as defined in equation (A17).
 The volume flux for undeformed ice is described by
 Since these simple formulae have a clear upper limit where they are no longer valid, the more general formula hd = 2.86(1.1hu + 3.4hu0.5) was adopted. The form of this function was chosen to resemble the original formulation for ice thicknesses that is likely to occur in the Arctic.
 Knowing the resulting thickness we can compute the area by volume conservation
and we can write
Compressive ice strength is a measure of the potential energy change due to mechanical redistribution. This is computed by integrating over the thickness space
Cp = 0.5g(ρi/ρw)(ρw − ρi) where ρw and ρi are densities of water and ice, respectively. Cf = 22.1 is total energy loss (irreversible process). Cf = 17 was used by Haapala et al. , following Flato and Hibler . We have a slightly different formula for Ψri that yields a difference of about 30% that we compensate for here with Cf = 22.1 to obtain roughly the same ice strength. More details about this parameter are provided by Rothrock .
 If the amount of deformed ice exceeds 85%, ice strength is calculated as a weighted sum of equation (A19) and the equation below, following Hibler , to provide a smooth transition between the formulations as deformed ice approaches 100%
where P∗ = 1.25 × 104 N m−2 and γ is defined in (A9). All other variables of state are advected and redistributed between the ice classes analogously as to the ice.
 This study was performed within the project “Modeling climate variability of the Arctic Ocean in past and future climates with special focus on changing sea ice” (reference 621-2006-5030), funded by the Swedish Research Council (Vetenskapsrådet) and within the strategic research area “Advanced Simulation of Arctic climate change and impact on Northern regions” (ADSIMNOR, reference 214-2009-389), funded by the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (FORMAS). HELMI simulations were performed on the climate computing resources “Ekman” and “Vagn” that are operated by the National Supercomputer Centre (NSC) at Linköping University and the Centre for High Performance Computing (PDC) at the Royal Institute of Technology in Stockholm, both funded by a grant from the Knut and Alice Wallenberg foundation. We are very thankful for all grants and computational support. We thank Andrey Proshutinsky for inviting us to workshops organized by the Arctic Ocean Model Intercomparison Project (AOMIP) and Mike Steele for travel support to attend some of these meetings. Further thanks go to I. Rigor from the Polar Science Center in Seattle for the compilation and distribution of the IABP data set. We also acknowledge two anonymous reviewers and Martin Vancoppenolle for very valuable comments that helped to improve our manuscript considerably.