2.1.1 Coupled atmosphere–ice–ocean regional model

The model used in this study is HIRHAM–NAOSIM 2.0 (Dorn et al., 2019), which consists of the regional atmospheric model HIRHAM5 and the regional ocean–sea ice model NAOSIM (North Atlantic/Arctic Ocean Sea Ice Model). HIRHAM5 is based on the numerical weather forecast model HIRLAM 7.0 (Undén et al., 2002) and applies the physical parameterizations of the atmospheric general circulation model ECHAM 5.4.00 (Roeckner et al., 2003). Köberle and Gerdes (2003) give a basic description of NAOSIM, while Fieg et al. (2010) describe NAOSIM's fine-resolution model version, which is used in HIRHAM–NAOSIM 2.0. NAOSIM's ocean component is based on the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model, MOM-2 (Pacanowski, 1996). The sea ice component is based on the dynamic–thermodynamic sea ice model described by Harder et al. (1998). The internal ice stress is described by a viscous-plastic rheology according to Hibler (1979). Thermodynamic snow-ice processes are handled using the zero-layer approach by Semtner (1976). Detailed information about HIRHAM–NAOSIM 2.0 is given by Dorn et al. (2019). The model is applied over a circum-Arctic domain at a horizontal resolution of 1∕4^∘ (∼27 km) in the atmosphere (HIRHAM5) and 1∕12^∘ (∼9 km) in the ocean (NAOSIM). The ocean–sea ice domain corresponds to the domain shown in Fig. 1.

Figure 1Mean spatial pattern of sea ice drift speed (km d⁻¹) in the model (ensemble mean of HIRHAM–NAOSIM 2.0) for the 2003–2014 (a) winter (DJFM) and (c) summer (JJAS). Panels (b) and (d) are the model differences to the observation (model − KIMURA) for winter and summer respectively. The purple line in each panel indicates the study domain used for the basin-wide analysis.

2.1.2 Long-term simulations of the base configuration

A 10-member ensemble of multidecadal climate simulations for the period 1979 to 2016 was carried out by Dorn et al. (2019) with the base configuration of HIRHAM–NAOSIM 2.0. These ensemble simulations represent the basis for the present study and are referred to as BASE hereafter. The individual ensemble members used the same atmospheric initialization but applied different ice–ocean initial conditions, which were taken from 1 January of the last 10 years of a preceding 22-year-long coupled spin-up run for the period 1979–2000 (see Dorn et al., 2019, for more details). The regional model simulations were driven by ERA-Interim reanalysis data (Dee et al., 2011; referred to as ERA-I hereafter). ERA-I provided 6-hourly lateral atmospheric boundary conditions as well as daily surface boundary conditions where required (outside the coupling domain). The lateral ocean boundary conditions in the northern North Atlantic were taken from the Levitus climatology (Levitus and Boyer, 1994; Levitus et al., 1994).

2.1.3 Sensitivity experiments

To investigate the model's sensitivity to the momentum and heat transfer coefficients which explicitly include sea ice form drag contributions, both a control run (CTRL) and a sensitivity experiment (SENS) for 1 year (year 2007) were performed. CTRL applies the default atmospheric boundary layer parameterization of ECHAM 5.4 (Roeckner et al., 2003) with air–ice momentum and heat transfer coefficients depending only on atmospheric stability. The sea ice form drag effect is not included. SENS includes the improved parameterization of air–ice momentum and heat transfer coefficients adapted based on Lüpkes and Gryanik (2015). There, the transfer coefficients depend on sea ice concentration and include both the sea ice skin drag and form drag effects caused by the edges of ice floes in the marginal sea ice zone and of leads in the inner Arctic. The parameterization could also account for the effect by melt pond edges, but this additional effect would require the knowledge of the pond fraction on top of the ice, which is not available in HIRHAM–NAOSIM 2.0. The model applies a flux averaging method, which means that the total flux over a surface covered with sea ice of concentration A and with open water (1−A) is the concentration-weighted mean of both contributions. We describe here only the fluxes over sea ice, in which form drag is included in SENS, and refer to Roeckner et al. (2003) for the parameterization of fluxes over open water. In CTRL (as in BASE), however, the air–ice momentum transfer coefficient C_d,i and the heat transfer coefficient C_h,i include only the sea ice skin drag effect. They are calculated as

where C_dn,i (C_hn,i) is the drag (heat transfer) coefficient under neutral atmospheric stratification over ice and f_m,i (f_h,i) is the stability correction function over ice to adjust C_dn,i (C_hn,i) based on atmosphere stability. C_dn,i is calculated as

where k=0.4 represents the von Karman constant, z_L is the height of the lowest atmospheric model level, and z_0,i represents the skin drag roughness length over sea ice. C_hn,i is calculated as

where z_t,i represents the scalar roughness length over ice. Equations (1) to (4) are common descriptions of air–ice momentum and heat transfer coefficients except that “+1” was added to both $z_{\mathrm{L}}/z_{\mathrm{0},\mathrm{i}}$ and $z_{\mathrm{L}}/z_{\mathrm{t},\mathrm{i}}$ in Eqs. (3) and (4). This is done in the model to prevent the argument of the logarithm from going to zero, for which C_d,i (C_h,i) would go to infinity (see also Giorgetta et al., 2013).

In SENS, the new momentum transfer coefficient ${\widehat{C}}_{\mathrm{d},\mathrm{i}}$ and the new heat transfer coefficient ${\widehat{C}}_{\mathrm{h},\mathrm{i}}$ over ice, which both include skin drag and form drag effects, are calculated as

where C_dn,f (C_hn,f) represents the form drag (heat transfer) coefficient related to neutral conditions over ice, f_m,w (f_h,w) is the stability correction function over water to adjust C_dn,f and C_hn,f to atmospheric stability. Equation (5) is obtained by combining the Eqs. (6), (52), and (70) by Lüpkes and Gryanik (2015). Equations (6) is obtained by combining the Eqs. (9), (64), and (74) by Lüpkes and Gryanik (2015). After adding “+1” to both 10∕z₀ and z_L∕z₀ and replacing z₀ with z_0,f in Eq. (65) by Lüpkes and Gryanik (2015), C_dn,f is calculated as

where C_e10 represents the effective resistance coefficient (both the aerodynamic resistance coefficient of individual floes and the shape factor), z_0,f represents the (form) roughness length, and β is a constant exponent describing the dependence of the crosswind dimension of a floe on A. The values of C_e10, z_0,f, and β are $\mathrm{2.8}\times {\mathrm{10}}^{-\mathrm{3}}$, $\mathrm{0.57}\times {\mathrm{10}}^{-\mathrm{3}}$ m, and 1.1 respectively. The value of C_e10 is the average given in Eqs. (48) and (49) by Lüpkes and Gryanik (2015). The value of z_0,f is an average resulting from measured roughness lengths by various campaigns considered by Andreas et al. (2010), Lüpkes et al. (2012a), and Castellani et al. (2014). Note that this value is not critical for the parametrization. The value of β comes from Eq. (59) by Lüpkes et al. (2012a). C_hn,f is calculated as

where

Equation (8) represents a simple algebraic transformation of Eq. (60) by Lüpkes and Gryanik (2015), making use of their Eqs. (59) and (61) with α_f=α. The skin drag roughness length over sea ice is set to

and the scalar roughness length over sea ice is parameterized as mostly done in the literature as

with

The CTRL and SENS simulations each comprise an ensemble of 10 members, which only differ in their ice–ocean initial state. The ice–ocean initial conditions for CTRL and SENS were produced in exactly the same way as for BASE (see Sect. 2.1.2). ERA-I provided the boundary forcing also as in the BASE simulations.

2.2.1 Sea ice drift

For the evaluation of the sea ice drift speed, satellite-based daily sea ice drift observations from Kimura et al. (2013; referred to as KIMURA hereafter) are used. There, the improved maximum cross-correlation method (Kimura and Wakatsuchi, 2000, 2004) was applied to detect ice motions based on AMSR-E (Advanced Microwave Scanning Radiometer for EOS) brightness temperature. The horizontal resolution of the KIMURA dataset is 60 km×60 km. The uncertainty of the KIMURA data over the Arctic in summer is from 1.12 to 1.47 km d⁻¹ and depends on the drift speed (Sumata et al., 2015a). In winter, the uncertainty is at least 50 % smaller than in summer and depends on the drift speed too (Sumata et al., 2015b). Although the accuracy of KIMURA drift speed is lower than that of buoy data, it has a much wider spatial and temporal coverage and is therefore appropriate for regional model evaluation (Sumata et al., 2015a). Another advantage of the KIMURA product is that it provides ice drift data both in winter and summer. More details are given by Kimura et al. (2013) and Sumata et al. (2015a).

In addition, daily sea ice drift speed from the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS; Zhang and Rothrock, 2003) is used. This enables a consistent and simultaneous evaluation of sea ice drift speed, concentration and thickness, and near-surface wind speed. The PIOMAS data are downloaded from ftp://pscftp.apl.washington.edu/zhang/PIOMAS/data/v2.1/ (last access: 1 June 2019). The mean horizontal resolution in the Arctic is approximately 22 km according to the PIOMAS description given in http://psc.apl.uw.edu/research/projects/projections-of-an-ice-diminished-arctic-ocean/model/ (last access: 30 April 2020). Detailed information about the PIOMAS dataset is given by Schweiger et al. (2011).

2.2.2 Sea ice concentration

For sea ice concentration (SIC), the NSIDC bootstrap daily SIC over the Northern Hemisphere, version 3 (https://nsidc.org/data/nsidc-0079, last access: 25 May 2019), is used. This SIC dataset is based on Nimbus-7 SMMR and DMSP SSM/I-SSMIS passive microwave data and has been generated using a bootstrap algorithm with daily varying tie points. It is gridded on the 25 km×25 km polar stereographic grid and provides an overall retrieval accuracy of approximately 5 %–10 %, but the uncertainty could be larger due to factors such as the proximity to land or ice edge, melting during summer, the presence of a large fraction of thin ice or melt ponds within a pixel, and the presence of stormy weather conditions (Comiso, 2017).

2.2.3 Sea ice thickness

Since Arctic basin-wide long-term sea ice thickness (SIT) observations are not available, SIT data from PIOMAS are used in this study as a substitute for observational SIT as done in previous studies (Docquier et al., 2017; Johnson et al., 2012; Shu et al., 2015; Stroeve et al., 2014). However, we have to recall that PIOMAS ice thicknesses represent simulation results of a coupled ice–ocean model, even though this model is constrained through the assimilation of observed sea ice concentrations and sea surface temperatures. Schweiger et al. (2011) showed that the PIOMAS ice thickness agrees with ICESat ice thickness retrievals (in the order of 0.1 m mean difference) and that the spatial thickness patterns agree with each other (pattern correlation coefficients >0.8). However, PIOMAS appears to overestimate thin ice thickness and to underestimate thick ice (Schweiger et al., 2011).

2.2.4 Near-surface wind

For the near-surface wind speed (WS), daily 10 m wind speed from ERA-I is used. The ERA-I data were downloaded from the MARS archive at ECMWF and interpolated to the same $\mathrm{0.25}{}^{\circ }\times \mathrm{0.25}{}^{\circ }$ grid as used in the model's atmosphere component HIRHAM5. More information about this dataset is given by Berrisford et al. (2011). The NCEP/NCAR 10 m wind speed with $\mathrm{1.875}{}^{\circ }\times \mathrm{1.9}{}^{\circ }$ horizontal resolution is used to accompany the PIOMAS sea ice data as this data were used as the wind forcing for PIOMAS. More information about the NCEP/NCAR dataset is given by Kalnay et al. (1996).

3.2.1 Climatological view

As shown in previous studies (Docquier et al., 2017; Kushner et al., 2018; Olason and Notz, 2014; Tandon et al., 2018), the observed distinct mean seasonal cycle of SID (maximum in autumn, minimum in spring) is obviously not solely controlled by the wind speed, which is strongest in winter and weakest in summer (Fig. 2). The phase lag between the seasonal cycle of SID and WS is about 3–4 months in observations/reanalysis (KIMURA ice drift/ERA-I wind). The modeled seasonal cycle and magnitude of the WS agrees well with ERA-I. According to the delayed SID minimum (Sect. 3.1), the phase lag between the simulated seasonal cycle of SID and WS is reduced to about 1 month, like in many CMIP3 and CMIP5 models (Rampal et al., 2011; Tandon et al., 2018), leading to a higher correlation between SID and WS. This indicates that the modeled SID is much more strongly controlled by the wind speed than the observed SID.

Another metric to quantify the mean relationship between SID and WS is the wind factor, which is the ratio of SID to WS. Averaged over the study domain, the simulated wind factor is 1.77 % in winter and 1.87 % in summer, which agrees with the observations/reanalysis (KIMURA ice drift/ERA-I wind) in the sense that the averaged wind factor is smaller in winter (1.42 %) than in summer (1.96 %). However, compared to the observations, the simulated wind factor is too large in winter. As mentioned in Sect.3.1, too-high sensitivity of the SID to the wind in winter may be related to the underestimated SIT and model parameters governing the sea ice dynamics.

Figure 3 shows the spatial patterns of the multiyear mean wind factor over the Arctic. In winter, the simulated wind factor has its maximum associated with strong wind and low ice thickness over the Baffin Bay and Greenland Sea. Within the study domain, the maximum occurs along the Transpolar Drift Stream (∼2 %) and the minimum over the north of Greenland and the Canadian Arctic Archipelago where sea ice is thickest (<0.5 %). The simulated pattern roughly agrees with the corresponding pattern of KIMURA ice drift/ERA-I wind (Figs. 3 and S4) and previous results using SSM/I ice drift/NCEP wind (Spreen et al., 2011). In winter, however, the simulated wind factor is overestimated compared to the KIMURA/ERA-I data almost everywhere over the study domain, with the maximum bias reaching 1 % over the thick ice north of the Canadian Arctic Archipelago (Fig. 3). In summer, the modeled wind factor peaks (∼3 %) along the marginal ice zone, such as in the coastal Beaufort Sea. This could be the result of a dynamical coupling between sea ice and the coastal ocean as suggested by Nakayama et al. (2012): in a coastal ocean covered with sea ice, wind-forced sea ice drift excites coastal trapped waves and generates fluctuating ocean currents. These ocean currents can enhance the sea ice drift when the current direction is the same as the wind-driven drift direction. In contrast to winter, the modeled wind factor in summer is underestimated over the study domain. These seasonally different bias patterns in the wind factor are associated with those of the SID (Fig. 1b and d).

Figure 3Mean spatial pattern of wind factor (%) in the model (ensemble mean of HIRHAM–NAOSIM 2.0) for the 2003–2014 (a) winter (DJFM) and (c) summer (JJAS). Panels (b) and (d) are the model differences to the observation/reanalysis (model − KIMURA/ERA-I) for winter and summer respectively. The purple line indicates the study domain used for the basin-wide analysis.

3.2.2 Daily and grid-scale view

Previous studies reported on the ice drift's nearly linear increase with increasing wind for high and moderate WS (Thorndike and Colony, 1982) but no clear relationship for low WS (Leppäranta, 2011; Rossby and Montgomery, 1935). To investigate this in detail, Figs. 4 and 5 present the analysis of the dependency of SID on WS based on daily data and on the grid scale. For the observation/reanalysis reference we use KIMURA ice drift and ERA-I wind.

Figure 4Box–whisker plots of the relationship between sea ice drift speed and sea ice concentration for different near-surface wind speed classes (different colors) for the 2003–2014 (a) winter (DJFM) and (c) summer (JJAS) in the model (HIRHAM–NAOSIM 2.0). Panels (b) and (d) are the same as (a) and (c), respectively, but based on the observation/reanalysis data. For the model, all 10 ensemble members are included. The plot is based on daily data and on all grid points within the study domain indicated in Fig. 1. The horizontal bar represents the median, the notch represents the 95 % confidence interval of the median, the dot represents the mean, the top and bottom of the box represent the 75th and 25th percentiles, and the upper/lower whiskers represent the maximum/minimum value within 1.5 times the interquartile range (IQR) to 75th/25th percentiles. The numbers above the boxplots represent the slopes of near-surface wind and sea ice drift speed fit lines (unit: km d⁻¹ per 1 m s⁻¹ wind speed change; font colors as for the wind speed classes). The numbers right of the boxplots represent the slopes of sea ice concentration and sea ice drift speed fit lines (unit: km d⁻¹ per 10 % sea ice concentration change). A bold and asterisked number indicates that the slope of the fit line is significant at the 95 % level. In the labels of different sea ice concentration and 10 m wind speed classes, “(” means exclusive and “]” means inclusive.

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Figure 5Relationship between sea ice drift speed and sea ice concentration for different near-surface wind speed classes (different colors) for the 2003–2014 (a) winter (DJFM) and (d) summer (JJAS) in the model (HIRHAM–NAOSIM 2.0). Panels (b) and (e) are the same as (a) and (d), respectively, but based on the observation/reanalysis data. Panels (c) and (f) are the same as (a) and (d), respectively, but based on PIOMAS data. The points in the plot are the median value of all the daily data and on all grid points for a certain wind speed and sea ice concentration, within the study domain indicated in Fig. 1. In the labels of different sea ice concentration and 10 m wind speed classes, “(” means exclusive and “]” means inclusive.

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During winter, the simulated SID significantly increases with increasing WS. According to the median values of SID and the associated best fit line slope of SID vs. WS, the increase in SID varies from 1.29 to 1.49 km d⁻¹ per 1 m s⁻¹ WS increase under different SIC classes (Figs. 4a and 5a). The strongest SID increase per WS increase occurs for SIC of 50 %–70 % (Fig. 4a). In the observations/reanalysis, the SID only consistently increases with increasing WS when SIC is higher than 90 % (Figs. 4b and 5b). The corresponding slope indicates 0.93 km d⁻¹ per 1 m s⁻¹ WS increase, which is an approximately 40 % smaller increase than the modeled value. Both the model (for all SIC classes) and the observation/reanalysis (for SIC >90 %) show a linear increase in SID with increasing WS for strong winds (WS >4 m s⁻¹) but a weak dependency of SID on WS for lower winds.

During summer, both the model and the observation/reanalysis show a consistent general increase in SID with increasing WS for all SIC classes when WS >4 m s⁻¹ (Figs. 4c, 4d, 5d and 5e). The simulated magnitude of SID increase per 1 m s⁻¹ WS increase is similar to that in winter. Again, the simulated SID increases faster with increasing WS than the observed SID, by a factor of about 2–2.5. Another striking difference between the simulations and the observation/reanalysis is that the simulated SID–WS relation is rather linear (only slightly attenuated when WS ≤2 m s⁻¹). In contrast, this relation is highly nonlinear in the observation/reanalysis (Figs. 4d, 5e). The observed increase in SID with increasing WS is much stronger when WS passes a threshold (of ca. 4 m s⁻¹), compared to lower WS. For weak winds (WS lower than 4 m s⁻¹), SID is not much affected by WS changes.

Generally, the observed SID (for a certain WS and SIC class) shows an about 2 times higher spatiotemporal variability (indicated by the larger IQR; Fig. 4) than the modeled one. This discrepancy might be linked to a data source difference or inconsistency between the used KIMURA SID observations and ERA-I reanalysis WS data, but it might also hint to a model weakness.

The PIOMAS-based SID–WS relation (PIOMAS ice drift, NCEP/NCAR wind) is very similar to that in the HIRHAM–NAOSIM 2.0 simulations: SID increases with increasing WS for all SIC classes, both in winter and summer (Fig. 5c and f). However, the SID–WS relation in PIOMAS is stronger than in HIRHAM–NAOSIM 2.0 during winter and summer (Fig. 5). This may reflect a higher air–ice drag in PIOMAS than in HIRHAM–NAOSIM 2.0.

3.3.1 Climatological view

Figure 6a shows the relationship between SID and SIC in terms of the mean seasonal cycle. An inverse correlation between SID and SIC is expected because a reduction in SIC reduces the internal friction, brings the SID closer to free drift conditions, and increases SID. We find such an inverse correlation between SID and SIC both in the model and in the observations (KIMURA ice drift, NSIDC bootstrap ice concentration), as well as in PIOMAS from June to September when SIC is low. The corresponding fit line slope in the model is 4.04 km d⁻¹ SID increase per 10 % SIC decrease, which agrees with the slopes in the observations and in PIOMAS. During the winter months (January to May) when SIC >95 %, such a relationship is not found both in the observations and in the models. The SID of the 12 months can be categorized into two groups based on SIC values: group one for SIC smaller than 95 % and group two for SIC larger than 95 %. The observed mean SID value in group one (9.23 km d⁻¹) is obviously larger than in group two (7.28 km d⁻¹). This is also found in PIOMAS. The model reproduces the SID in group one but largely overestimates the SID in group two. Therefore, the simulated mean SID values in group one (9.24 km d⁻¹) and two (8.95 km d⁻¹) are quite close to each other. This model deficit may result from the too-strong coupling between the SID and the WS in the model (Fig. 2; Sect. 3.2.1). Following Docquier et al. (2017), we also calculate the slope of the SID–SIC best fit line based on data from 12 months, even though there is no clear SID–SIC linear relation over the full year data. The slope in the model (0.66 km d⁻¹ SID increase per 10 % SIC decrease) is much weaker than in the observations (6.93 km d⁻¹ SID increase per 10 % SIC decrease) and in PIOMAS (3.16 km d⁻¹ SID increase per 10 % SIC decrease). The simulated relationship is also much weaker than in the ocean model NEMO–LIM3.6 as reported by Docquier et al. (2017). The underestimated relationship in the model can be explained by the overestimated SID in winter (Fig. 2).

Figure 6Scatter plots of monthly mean sea ice drift speed against (a) sea ice concentration and (b) sea ice thickness, averaged over the period of 2003–2014 and the study domain (indicated in Fig. 1). Numbers denote the months. Results are shown for the model (HIRHAM–NAOSIM 2.0) ensemble simulations (red), KIMURA for ice drift speed plus NSIDC bootstrap for ice concentration (black), and for PIOMAS data (blue).

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3.3.2 Daily and grid-scale view

On daily grid scale, the model shows an inverse correlation of SID with SIC during winter (Figs. 4a, 5a), differently to the climatological view (Sect. 3.3.1). SID increases with decreasing SIC when SIC is larger than ca. 30 %. The slopes of the simulated SID–SIC relation across all SIC and WS classes vary from 3.41 to 5.64 km d⁻¹ SID increase per 10 % SIC decrease. In the observation, there is no clear SID–SIC relation because the median SID uncertainty is very high when SIC is lower than 90 % (Figs. 4b, 5b). The small sample size is one of the reasons for the high uncertainty (Table 1). However, considering the uncertainty of the median value (represented by the notch), the statistically lower SID for high SIC (>90 %), compared to the SID for lower SIC, stands out both in the observations and in the simulations. The observations indicate an abrupt drop of SID at 90 % SIC. This is in accordance with observations by Shirokov (1977), who showed that SID starts to decrease linearly with increasing SIC but drops abruptly at a SIC of 90 % when internal friction forcing starts its significant influence on SID. This is not reproduced by the simulations and indicates too-low internal friction in the model.

Table 1The sample sizes of sea ice drift speed data under different 10 m wind speed and sea ice concentration classes in Fig. 4. In the labels of different sea ice concentration and 10 m wind speed classes, “(” means exclusive and “]” means inclusive.

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The model also shows an inverse correlation of SID with SIC for WS >2 m s⁻¹ during summer (Figs. 4c and 5d). Under different WS classes, the modeled SID–SIC relation varies from 2.12 to 3.16 km d⁻¹ SID increase per 10 % SIC decrease. The higher WS is, the stronger the SID–SIC relation is. However, these findings from the simulations are not confirmed by the observations. The observations (KIMURA drift/NSIDC bootstrap ice concentration) do not show an inverse correlation between SID and SIC for all SIC and WS classes in summer (Figs. 4d and 5e).

The SID–SIC relation in PIOMAS is just the opposite compared to HIRHAM–NAOSIM 2.0, both in winter and in summer: SID increases with increasing SIC when SIC is lower than 90 % (Fig. 5c and f). PIOMAS shows a SID–SIC relation inconsistent with the observed relation. Thus, the PIOMAS relation might violate physical consistency due to the optimal interpolation method used to obtain a realistic sea ice field (concentration). This assimilation method contains addition/subtraction of sea ice into the system at every assimilation time step, when the modeled sea ice concentration differs from the observed one. Due to the addition/subtraction of sea ice (called increment or innovation in the terminology of data assimilation), PIOMAS does not necessarily preserve the physical relations described in the underlying sea ice–ocean model. Such an inconsistency is one of the drawbacks of the optimal interpolation method. Therefore, relations to assimilated physical variables should be examined with caution.

Generally, the obvious difference between the SID–SIC relation on the multiyear Arctic mean scale and on the daily grid scale emphasizes its strong dependency on the temporal and spatial scale.

3.4.1 Climatological view

All datasets (HIRHAM–NAOSIM 2.0 simulations, KIMURA drift/PIOMAS thickness, and PIOMAS drift/PIOMAS thickness) show that SID decreases with increasing SIT (Fig. 6b). The SID–SIT fit line slope calculated based on HIRHAM–NAOSIM 2.0 is 1.10 km d⁻¹ SID decrease per 1 m SIT increase. The observed SID–SIT relation is stronger. Data of KIMURA drift/PIOMAS thickness and PIOMAS drift/PIOMAS thickness indicate 2.17 and 1.83 km d⁻¹ SID decrease per 1 m SIT increase, respectively. The simulated weaker dependency of SID on SIT is mainly due to the overestimated SID during winter and spring (December to May), when the ice is thick. As pointed out by Olason and Notz (2014), the inverse correlation between drift speed and thickness in winter, when the ice concentration is high, is physically plausible, but the inverse correlation in summer, when the ice concentration is lower, is probably only of statistical nature.

3.4.2 Daily and grid-scale view

As in the climatological view, the simulations show generally that SID decreases with increasing SIT (Figs. 7a and c and S5a, c), both in winter and in summer. In winter, this relation occurs only for SIT smaller than approximately 4 m. The simulated SID–SIT relation that calculated based on all thickness categories varies from 0.38 to 0.95 km d⁻¹ SID decrease per 1 m SIT increase across different wind categories (Supplement Fig. S5a). PIOMAS simulates a stronger SID–SIT relation (Supplement Fig. S5b); the slope of the SID–SIT fit line varies from 0.65 to 2.64 km d⁻¹ SID decrease per 1 m SIT increase, which is larger by a factor of up to 3.5 compared to the simulations. In summer, the simulated inverse SID–SIT correlation is stronger than in winter, particularly for high WS (Figs. 7a and c and S5a, c). The SID–SIT slope varies from 0.71 to 1.69 km d⁻¹ per 1m SIT increase across different wind categories. In PIOMAS, the SID–SIT slopes are not significant when WS >4 m s⁻¹. This is mainly influenced by the increase in SID when SIC increased from (0.1,0.3] to (0.3, 0.5]. Furthermore, Fig. 7 confirms the nonlinearity of the SID–WS relation, with a strong impact of WS changes on SID for high and moderate wind speeds, but with a lower impact for low wind speeds (WS ≤4 m s⁻¹).

Figure 7Relationship between sea ice drift speed and sea ice thickness for different near-surface wind speed classes (different colors) for the 2003–2014 (a) winter (DJFM) and (c) summer (JJAS) in the model (HIRHAM–NAOSIM 2.0). Panels (b) and (d) are the same as (a) and (c), respectively, but based on PIOMAS data. The points in the plot are the median value of all the daily data and on all grid points within the study domain based on Fig. 1. In the labels of different sea ice thickness and 10 m wind speed classes, “(” means exclusive and “]” means inclusive.

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