Four types of buoys were used in this study (Fig. 1): the Snow and Ice Mass Balance Array (SIMBA) buoy manufactured by the Scottish Association for Marine Science Research Services Ltd, Oban, Scotland; the Snow Buoy (SB) designed by the Alfred Wegener Institute and manufactured by MetOcean Telematics, Halifax, Canada; the ice Surface Velocity Program drifting buoy (iSVP) also manufactured by MetOcean Telematics; and the ice drifter manufactured by the Taiyuan University of Technology (TUT), China. All buoys were equipped with GPS receivers providing a positioning accuracy of better than 5 m and regularly reporting to a land-based receiving system using the Iridium satellite network.

During the CHINARE, 9 SIMBA buoys and 11 TUT buoys were deployed in a narrow zonal section of 156–171∘ W and a wide meridional range of 79.2–84.9∘ N in August 2018 (Figs. 1 and 2). This deployment scheme was designed to facilitate the analysis of changes in ice kinematics from the loose MIZ to the consolidated pack ice zone (PIZ). Of these 20 buoys, 15 were deployed in the northern part of the PAO as a cluster within close distance of each other (black circles in Fig. 2) to allow an estimation of ice deformation rates. In addition, data from five SIMBAs and two SBs deployed by the TICE expedition in the Makarov Basin during September 2018 (Figs. 1 and 2) were also used to estimate ice deformation rates. Because the ice thickness at the deployment sites was comparably large (1.22 to 2.49 m), the buoys were able to survive into winter and beyond. Position data from one iSVP deployed during the previous CHINARE in 2016 (Lei et al., 2020b) and four other IABP buoys were also included in this study. The IABP buoys were deployed by the British Antarctic Survey or Environment Canada in the east of the PAO during August–September 2018. Here we use the position data from these 32 buoys (Fig. 2) to describe spatial variations in ice kinematics between August 2018 and February 2019. We chose this study period because it represents a transition period during which the mechanical properties of sea ice are expected to change considerably (e.g., Herman and Glowacki, 2012; Hutter et al., 2018). Two-thirds of the buoys (22) continued to send data until or beyond the end of the study period. During this study period, the buoy trajectories during the study period roughly covered the region of 76–87∘ N and 155∘ E–110∘ W, which we define as the study region.

All buoys were configured to a sampling interval of either 0.5 or 1 h. Prior to the calculation of ice drift velocity, position data measured by the buoys were interpolated to a regular interval (τ) of 1 h. To quantify meridional (zonal) variabilities of ice kinematic properties, we used data from buoys that were within 1 standard deviation of the average longitude (latitude). This constraint helped to minimize the influence of the zonal (meridional) difference on the meridional (zonal) variabilities. The resulting meridional extent for the assessment of the zonal variabilities of ice kinematics ranged from 350 to 402 km, while the zonal extent for the assessment of the meridional variabilities ranged from 195 to 285 km. Their seasonal changes can be considered moderate (<40 %), although a divergence–convergence of the floes occurred at all times. Using half a standard deviation to constrain the calculation range, there is no essential change in the identified meridional and zonal dependencies of ice kinematics from those obtained using 1 standard deviation. Thus, we consider our evaluation method as robust. Meridional variabilities are related to the transition from the MIZ to the PIZ, while zonal variabilities indicate the change between the region north of the Canadian Arctic Archipelago, where the MYI dominates (Lindell and Long, 2016), and the Makarov Basin, which is mainly covered by seasonal ice (Serreze and Meier, 2018).

Two parameters were used to characterize sea ice kinematics. First, the IWSR was used to investigate the response of the sea ice motion to wind forcing. Impacts of data resampling intervals (1–48 h), meridional and zonal spatial variabilities, intensity of wind forcing, near-surface air temperature, and ice concentration on the IWSR were assessed. These parameters are related to either spatiotemporal changes in atmospheric and sea ice conditions or the frequency distributions of ice and wind speeds. The data used to characterize the atmospheric forcing, including sea level air pressure (SLP), near-surface air temperature at 2 m (T2m), and wind velocity at 10 m (W10m), were obtained from the ECMWF ERA-Interim reanalysis dataset (Dee et al., 2011). Sea ice concentration was obtained from the Advanced Microwave Scanning Radiometer 2 (AMSR2) (Spreen et al., 2008). To identify the state of the atmospheric forcing and the sea ice conditions relative to the climatology, we also calculated anomalies of SLP, T2m, W10m, ice concentration, and ice drift speed relative to the 1979–2018 averages. To estimate ice concentration anomalies, we used ice concentration data from the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) and its successors (SSM/I and SSMIS) (Fetterer et al., 2017) because they cover a longer period compared to the AMSR2 data. We used the daily product of sea ice motion (Tschudi et al., 2019, 2020) provided by the National Snow and Ice Data Center (NSIDC) to estimate anomalies of ice speed. However, this could only be estimated for August–December 2018 because of the delayed release of NSIDC data.

Second, the inertial motion index (IMI) was used to quantify the inertial component of the ice motion. To obtain the IMI, we applied a fast Fourier transformation to normalized hourly ice velocities. Normalized ice velocities were calculated by scaling the velocity values to monthly averages, allowing seasonal change to be assessed independently of the magnitudes of ice velocities. The frequency of the inertial oscillation varies with latitude according to 1f0=2Ωsin⁡θ, where f0 is the inertial frequency, Ω is the Earth rotation rate, and θ is the latitude. f0 ranges from 2.01 to 1.94 cycles d-1 between 90 and 75∘ N. Rotary spectra calculated from sea ice velocity using complex Fourier analysis were used to identify signals of inertial or tidal origin, both of which have a frequency of ∼2 cycles d-1 in the Arctic Ocean (Gimbert et al., 2012). According to Gimbert et al. (2012), the complex Fourier transformation U⌢(ω)is defined as 2U⌢(ω)=1N∑t=t0tend-Δte-iωtux+iuy, where N and Δt are the number and temporal interval of velocity samples, t0 and tend are the start and end times of the temporal window, ux and uy are the zonal and meridional ice speeds at t+0.5Δt on an orthogonal geographical grid, and ω is the angular frequency. The IMI is defined as the amplitude at the negative-phase inertial frequency, i.e., -f0, after the complex Fourier transformation. The energies that contributed to the amplitude at -f0 comprise the potential contributions from quasi-semidiurnal inertial and tidal oscillations, as well as the high-frequency components of wind and oceanic forcing. Those in the positive phase, f0, exclude contributions from the inertial oscillation and only comprise other components compared to that at -f0. This is because the spectral peaks associated with the tidal oscillation are roughly symmetric at positive and negative phases as a first-order approximation (Gimbert et al., 2012). On the contrary, the spectral peak associated with the inertial oscillation is asymmetric and only occurs in the negative phase in the Arctic Ocean. Thus, we will identify the seasonal changes in the contributions of the inertial oscillation by comparing the amplitude at the negative-phase quasi-semidiurnal frequency, i.e., IMI, to the positive-phase amplitude (PHA). Such a method to separate the inertial oscillation from the tidal oscillation has been used by Lammert et al. (2009), who attempted to identify cyclone-induced inertial ice oscillation in Fram Strait. The background noise originating from high-frequency components of wind and oceanic forcing can slightly shift the local maxima from the targeted frequencies of the IMI and PHA (Geiger and Perovich, 2008). Thus, we identify the local maximum amplitude in the range of -f0±0.03 for the IMI and in the range of 2±0.03 for the PHA. If no local maximum can be identified within the predefined ranges, we use the amplitudes at -f0 and 2 as the IMI and PHA, respectively. Such a situation is encountered in 15 % of the IMI cases and in 95 % of the PHA cases. This implies that the inertial oscillation is much more prevalent, while the tidal oscillation can be ignored regardless of seasons and buoys under consideration. This result might be related to the fact that, throughout the study period, all the buoys drifted over the deep basins far beyond the continental shelf.

Buoy position data were also used to estimate differential kinematic properties (DKPs) of the sea ice deformation field. The DKPs include divergence (div), shear (shr), and total deformation (D) rates of sea ice estimated within the area enclosed by any three buoys, as shown by Itkin et al. (2017). Following Hutchings and Hibler (2008), DKPs were calculated as follows: 3div=∂u∂x+∂v∂y,4shr=∂u∂x-∂v∂y2+∂u∂y+∂v∂x2, and 5D=div2+shr2, where ∂u∂x, ∂u∂y, ∂v∂x, and ∂v∂y are the strain components on an orthogonal geographical grid. Sea ice strain rate was only estimated for those buoy triangles with internal angles in excess of 15∘ and for ice speeds larger than 0.02 m s-1 to ensure a high accuracy (Hutchings et al., 2012). Total deformation D was used to characterize the spatial and temporal scaling laws as follows: 6D∝L-β, and 7D∝τ-α, where L is the length scale, τ is the sampling interval, and β and α are spatial and temporal scaling exponents which indicate the decay rates of ice deformation in the spatial or temporal domains. These scaling laws can only indicate the fractal properties of the first moment of ice deformation because of the multi-fractal properties of ice deformation (e.g., Marsan et al., 2004; Hutchings et al., 2011, 2018). To estimate the spatial exponent β for the CHINARE buoy cluster, the length scale was divided into three bins of 5–10, 10–20, and 20–40 km because only a few samples were outside these bins. To estimate the temporal exponent α, the position data were resampled to intervals of 1, 2, 4, 8, 12, 24, and 48 h. Because the TICE buoy cluster was mostly (>70 %) assigned to the 40–80 km bin, data from this cluster were not suitable for the estimation of the scale effect. A space–time coupling index, c, denoting temporal (spatial) dependence of the spatial (temporal) scaling exponent, can be expressed as 8β(τ)=β0-cln⁡(τ), where β0 is a constant. The areal localization index, δ15%, was used to quantify the localization of the strongest sea ice deformation, defined as the fractional area accommodating the largest 15 % of the ice deformation in the research domain (Stern and Lindsay, 2009). The δ15% was calculated for the 10–20 km length bin for the CHINARE buoy cluster, since this bin contained more samples to ensure a statistical rationality. To identify the influence of the temporal scale on the localization of ice deformation, all data were resampled to intervals of 1, 2, 4, 8, 12, 24, and 48 h.

We calculated the seasonal Central Arctic Index (CAI) and DA index to relate these large-scale atmospheric circulation patterns to the potential of sea ice advection from the study region to the AAO. Further, we calculated the seasonal AO and BH indices to relate them to the strength of the BG (Lei et al., 2019). Monthly SLP data north of 70∘ N obtained from the NCEP/NCAR reanalysis I dataset were used to calculate the empirical orthogonal functions (EOFs), with the AO and DA as the first and second modes of the EOF (Wang et al., 2009). The CAI was defined as the difference in SLP between 90∘ W and 90∘ E at 84∘ N (Vihma et al., 2012). The BH index was calculated as the SLP anomaly over the domain of 75–85∘ N, 170∘ E–150∘ W (Moore et al., 2018) relative to 1979–2018 climatology.

The BH index for autumn (September, October, and November) 2018 was moderate, ranking the 10th highest in 1979–2018 (Fig. 3a). However, the BH index for the following winter (December, January, and February) was much lower (-5.6 hPa), ranking the fourth lowest in 1979–2018 (Fig. 3b). Both CAI and DA were positive in autumn 2018, but still within 1 standard deviation of the 1979–2018 climatology (Fig. 3c and e). However, both indices were strongly positive in winter 2018/19, ranking the third and second highest in 1979–2018, respectively (Fig. 3d and f). The sea ice in the PAO is expected to be considerably impacted by these seasonal changes in atmospheric circulation patterns as a result of the enhanced northward advection of sea ice to the AAO (e.g., Bi et al., 2019). As an example, a pronounced sea ice reduction has been observed in the Bering Sea in March 2019, where sea ice extent was 70 %–80 % lower than normal (Perovich et al., 2019).

Associated with the seasonal change in the BH index, there was a distinct contrast in the pattern of the BG from anticyclonic in autumn to cyclonic in winter. Wind vectors and ice drift trajectories during autumn 2018 were generally clockwise, while those during the following winter were counterclockwise. The latter resulted in all buoys drifting northeastward and integrating into the TDS from December 2018 onward (Fig. 4). In autumn 2018, strong northerly winds only appeared in the northwestern part of study region (Fig. 4a) and were associated with a moderately positive CAI and DA. However, in winter 2018/2019, enhanced northerly winds prevailed almost across the entire study region (Fig. 4b) and were associated with an extremely positive CAI and DA. The T2m anomalies averaged over the study region were 3.9 ∘C in autumn and 0.7 ∘C in winter (Fig. 4c and d), ranking the second and 11th highest in 1979–2018, respectively.

The CHINARE buoys were deployed within a narrow meridional section at about 170∘ W. On 20 August 2018, sea ice concentration in this section, and especially in the southern part, was considerably lower than that in the eastern part of the study region at about 120∘ W, where other buoys had been deployed (Fig. 5a). Subsequently, ice concentration increased considerably, with almost all buoys being located in the PIZ by 20 September 2018 (Fig. 5b). However, the CHINARE buoys in the south and all TICE buoys remained within 70 km from the ice edge, which retreated further during August–September 2018. By 20 October 2018, ice concentration surrounding all buoys had increased to over 95 % (Fig. 5c).

In September and early October 2018, ice concentrations were considerably lower than the 1979–2018 average. Ice concentrations increased after early October and became comparable with climatological values (Figs. 6b and 7b). In October 2018, ice concentration was much lower in the southern and western parts of the study region compared to the north and east. Subsequently, the spatial gradient of sea ice concentration gradually decreased. Compared to the 1979–2018 climatology, wind speed was lower throughout most of the study period except for episodic increases as a result of intrusions of low-pressure systems (Figs. 6c and 7c). In September 2018, ice speed in the south was higher compared to the north (Fig. 6d), suggesting that the sea ice response to wind forcing was stronger in the south because of the lower ice concentration. From October 2018 onwards, this north–south difference gradually disappeared. The study region was dominated by a low SLP during December 2018 and February 2019, which was related to an anomalously low BH index and subsequent increases in both wind and ice drift speeds (Figs. 6c, d, 7c, d).

Temporal resampling has little effect on wind speed. However, applying longer resampling intervals to buoy position data may filter out ice motions that occur at higher frequencies (Haller et al., 2014), resulting in reduced ice speed and IWSR (Fig. 8). For example, ice drift speed and IWSR in September 2018 were 0.13 m s-1 and 0.027 at a resampling interval of 1 h, and they decreased to 0.01 m s-1 and 0.021 at a resampling interval of 48 h. Both ice speed and IWSR decreased considerably from September to November 2018; afterwards, both variables remained low until the end of the study period. At a resampling interval of 6 h, the IWSR was 0.026 in September 2018 (Fig. 8), which is much higher than that (0.013) obtained in the region close to the North Pole in the same month of 2007 (Haller et al., 2014) because most parts of our study region included the MIZ at that time. This value decreased to 0.008–0.015 from November to February (Fig. 8), which is comparable to those obtained from the regions north of Siberia or Greenland and the region close to the North Pole during the freezing season, but much smaller than that obtained in Fram Strait (Haller et al., 2014). This implies that, during the freezing season, the response of the sea ice to wind forcing is relatively uniform for the entire Arctic Ocean except for the regions close to Fram Strait where ice speeds markedly increase. In January 2019, a more consolidated ice pack and a relatively weak wind forcing led to both ice drift speed and IWSR reaching minima for the entire study period (Figs. 6c and 7c). The influence of resampling on the IWSR was reduced considerably during the freezing season, implying significant reductions of meandering and sub-daily oscillations in ice motion compared to the melt season. The ratio between IWSRs at 1 and 48 h intervals in October was 70 % of that in September and remained almost unchanged between November and February.

Factors regulating the IWSR are summarized in Table 1. The impact of the geographical location was significant in autumn, with relatively high IWSRs in the southern or western parts of the study region. However, meridional changes in the IWSR became very small in January–February because the north–south gradient in ice conditions was negligible by that time. The west–east gradient was more pronounced, with a significant relationship between longitude and IWSR throughout the study period. This is consistent with the results given by Lukovich et al. (2011), who identified that the west–east gradient of sea ice kinematics is larger than that in the north–south direction for the southern PAO during the freezing season. In summer and early autumn, the consolidation of the ice field is low, and interactions between individual ice floes approximate rigid particle collisions (Lewis and Richter-Menge, 1998). Thus, in August–October 2018, a lower IWSR is related to stronger wind forcing that enhanced the interactions between floes, leading to a significant negative statistical correlation between the IWSR and wind speed. Similarly, based on the data obtained from the buoys deployed in the TDS region, Haller et al. (2014) also identified that some spikes of the IWSR tend to be associated with a low wind speed. Consolidation of the ice field between November and February 2018 led to reduced ice motion and weaker sea ice response to wind forcing. Thereby, impact of wind forcing on IWSR was insignificant from November onwards. Variations in T2m across the study region between 20 August and 30 September 2018 were relatively small (-1.7 to -3.5 ∘C) because of the thermodynamic balance between the sea ice and the atmosphere during the melt season (e.g., Screen and Simmonds, 2010). The statistical relationship between T2m and the IWSR was insignificant during this period. On the contrary, the relationship became significant during October–December 2018, with a higher T2m being associated with a larger IWSR because warmer conditions may have weakened ice pack (e.g., Oikkonen et al., 2017). As the continuing thickening of the ice cover further reduced the influence of air temperature on ice kinematics, the statistical relationship between T2m and the IWSR was insignificant in January and February 2019.

The initial strength of the inertial oscillation mainly depends on the wind stress. However, the sustainability of the inertial oscillation is restricted by the internal friction within the Ekman layer in regions with low ice concentration and much open water, or by the ice internal stress in the PIZ (Gimbert et al., 2012). Thus, the inertial component of ice motion is closely associated with the seasonal and spatial changes in ice conditions. Figure 9 shows monthly IMI and PHA obtained from each buoy displayed at the midpoint of the buoy's trajectory for various months. The combined average monthly IMI of all buoys was 0.099±0.088 for the entire study period, with the average for September 2018 (0.227) being considerably higher. The monthly average IMIs from all buoys decreased from 0.136 in October 2018 to 0.037 in February 2019. Spatial variability of the IMI had almost disappeared by February 2019; the IMI standard deviation in February 2019 was 13 %–22 % of that in September–October 2018. Both the magnitude and the spatiotemporal variations in the PHA were much smaller than those of the IMI. The monthly average PHA of all available buoys during the entire study period was only 18 % of the IMI. The monthly ratio between the PHA and IMI ranged from 0.06 in September 2018 to 0.46 in February 2019. The seasonal damping of this ratio is mainly due to the decrease in the IMI because no statistically significant trend can be identified for the PHA. The standard deviation of the IMI revealed a significant decreasing trend (P<0.01) from 0.069–0.117 in September–October 2018 to 0.015 in February 2019, which suggests that the spatial variation in the IMI gradually decreased as the winter approached. Similar to the ratio between the absolute magnitudes, the ratio between the standard deviations of the PHA and IMI increased from 0.08 in September to 0.50–0.70 in January–February. The seasonal increase in this ratio was also mainly due to the decrease in the standard deviation of the IMI. From comparisons between the seasonalities of the IMI and PHA, we infer that the seasonal changes and spatial variations in the IMI could be mainly related to the changes in the inertial oscillation, and the contributions of the tidal oscillation can be ignored throughout the study period.

To eliminate the influence of large-scale spatial variability, we inspected subsets of data obtained from the buoys that were deployed in clusters. The IMI obtained from the CHINARE buoy cluster (black circles in Fig. 2) decreased markedly from 0.223 to 0.081 during September–October 2018. However, a similar change was observed 1 month later in October–November 2018 for the TICE buoy cluster. During the freezing season from November to February, the IMI gradually decreased to 0.038 for the CHINARE cluster and to 0.035 for the TICE cluster. Sea ice growth rates of the thin ice in the MIZ in the western and southern PAO are expected to be higher than that in the PIZ in the northern and the eastern PAO (e.g., Kwok and Cunningham, 2008). Accordingly, the spatial variability of the ice inertial oscillation observed in early autumn gradually disappeared.

To study the temporal changes in the IMI and PHA in more detail, we used a complex Fourier transformation to obtain time series of the IMI and PHA based on a 5 d temporal window. Here, we only show selected results from three representative buoys for comparison (Fig. 10). Those buoys were initially located in the southernmost and northernmost domain of the CHINARE cluster and in the southernmost domain of the TICE cluster (Fig. 2). The timing of the distinct seasonal attenuation of the IMI was different between the buoys, occurring in mid-October, late September, and late October 2018 for the CHINARE southernmost and northernmost buoys and the TICE southernmost buoy, respectively (Fig. 10). During the freezing season, the IMI remained at a low level but was still always larger than the PHA. The magnitude of the IMI was mainly regulated by wind forcing during the freezing season. The wind speed can significantly explain the magnitude of the IMI in November–February by 22 % (P<0.05), 45 % (P<0.001), and 21 % (P<0.05) for the CHINARE southernmost and northernmost buoys and the TICE southernmost buoy, respectively. The relatively large wind speed is related to a relatively low IMI because the enhanced wind forcing might increase the ice internal stress and reduce the response of ice motion to inertia forcing. This mechanism is most obvious in the northern PIZ because of the relatively large ice internal stress.

For all buoy triangles that were used to estimate ice deformation, the ice concentration within the CHINARE buoy cluster increased most rapidly during late August and early September 2018, and it remained close to 100 % from then onwards (Fig. 11a). A comparable seasonal increase in ice concentration was observed within the TICE buoy cluster 1 month later. To facilitate a direct comparison of the data obtained by the two different buoy clusters, we estimated the ice deformation rate of the TICE buoy cluster at the 10–20 km scale using the value at the 40–80 km scale and a constant spatial scaling exponent of 0.55. The scaling exponent of 0.55 is a seasonal average obtained from the CHINARE buoy cluster. A change of the scaling exponent by 10 % would lead to an uncertainty of about 0.03 for the ice deformation rate. Thus, a constant scaling exponent can be considered acceptable for a study of seasonal variation. In early and mid-September 2018, the ice deformation rate was low for the CHINARE cluster (Fig. 11b) because of low and relatively stable wind forcing (Fig. 2). For the TICE cluster, both ice deformation rate and ratio between ice deformation rate and wind speed decreased rapidly between 20 September and 10 November 2018, associated with a consolidation of the ice field as ice concentration and thickness increased and ice temperature decreased. However, over the same period, the ice deformation rate obtained by the CHINARE buoy cluster decreased only slightly, which is likely linked to its relatively low initial deformation rate in late September 2018 and to the higher ice concentration (by 15 %–20 %) compared to the TICE region.

For the CHINARE buoy cluster, the daily wind speed can explain 35 % (P<0.001) of the daily ice deformation rate estimated from hourly position data throughout the study period. However, for the TICE cluster, changes in ice deformation were mainly regulated by the seasonal evolution of ice concentration between September and early November 2018. The relationship between ice deformation rate and wind speed was insignificant at the statistical confidence level of 0.05 during this period. The ice field had sufficiently consolidated by mid-November 2018, and the relationship between daily ice deformation rate and daily wind speed changed to significant (R2=0.12, P<0.01) from then onwards.

The average ratio of ice deformation rate to wind speed in autumn was 1.15×10-6 m-1 for the CHINARE cluster and 0.62×10-6 m-1 for the TICE cluster; the ratio in winter decreased to 0.86×10-6 and 0.17×10-6 m-1, respectively. This seasonal pattern is consistent with the results given by Spreen et al. (2017), who used the RADARSAT geophysical processor system (RGPS) data to reveal that the annual maximum ice deformation rate occurred in August and decreased gradually to the annual minimum in March. Except for late September 2018, when the ice concentration in the TICE cluster was less than 85 %, the ice deformation rate from the CHINARE cluster was generally larger than that of the TICE cluster, with average values of 0.45 and 0.13 d-1, respectively, for October 2018 to February 2019. Sea ice in the region of the TICE cluster was generally thinner compared to the region of the CHINARE cluster. Thus, the difference in ice deformation rate cannot be absolutely explained by a difference in ice conditions between the two regions and is most likely also related to the spatial heterogeneity of wind and/or oceanic forcing. Changes in the direction of wind vectors were more frequent around the CHINARE cluster than around the TICE cluster. Frequent changes in ice drift direction lead to larger ice deformation events, such as those on 11 October and 11 and 26 November 2018 for the CHINARE cluster as shown in Fig. 11b. The drifting trajectories of the TICE cluster were much straighter than those of the CHINARE cluster. Since the CHINARE cluster was located in the core region of the BG, the vorticity of the surface current must be greater than that in the TICE cluster, located at the western boundary of the BG (Armitage et al., 2017). As a result, ice deformation rate and its ratio to wind speed were lower for the TICE cluster.

Ice deformation rates obtained from the CHINARE buoy cluster at three representative lengths of 7.5, 15, and 30 km were estimated using Eq. (6). Figure 12 shows that the monthly average ice deformation decreased as the length scale and resampling interval increased, implying an ice deformation localization and intermittency. The ice deformation decreased rapidly at all spatial and temporal scales during the seasonal transition period of September–October and remained low from then onwards. Ice deformation rate obtained using hourly position data from the CHINARE buoy cluster in September 2018 was 0.38 d-1 at the length scale of 30 km, which is comparable to that in September 2016 (0.31 d-1) and much larger than that in September 2014 (0.18 d-1) also observed in northern PAO (Lei et al., 2020a). These observed differences can be related to the strong storms in late September 2018 (Fig. 11b) and early September 2016 (Lei et al., 2020a), in contrast to the relatively stable synoptic conditions and relatively compact ice conditions in September 2014 (Lei et al., 2020a).

Accordingly, the spatial scaling exponent β estimated from hourly position data was 0.61 in September 2018, which is comparable to β from September 2016 (0.60), but slightly larger than in September 2014 (0.46) observed in northern PAO (Lei et al., 2020a). β decreased markedly from September to October 2018 and varied little from then onwards (Fig. 13). With increases in ice thickness and concentration as well as a cooling of the ice cover from October onwards, the consolidation of the ice field is enhanced, and sea ice deformation can spread over longer distances. By February 2019, β obtained from hourly position data decreased to 0.48, which is comparable to February 2015 (0.43) in the northern PAO (Lei et al., 2020b). This suggests that the interannual changes in the spatial scaling of ice deformation during winter are not as large as that in early autumn, which is in line with the evolution of ice thickness (e.g., Kwok and Cunningham, 2008). β decreased exponentially with an increase in resampling frequency for all months, which indicates that the spatial scaling would generally be underestimated when using data of coarser resolution. Interpolated to 3 h, β was 0.42 and 0.44 in January and February 2019, respectively, which is comparable with the result (0.40) obtained from the southern PAO during March–May (Itkin et al., 2017). The ice growth season generally lasts until May–June in the PAO (Perovich et al., 2003), which implies that the sea ice consolidation in March–May is comparable to, or even stronger than, that in January–February. Thus, our β is essentially consistent with that given by Itkin et al. (2017). Extrapolated to 48 h (120 h), our estimated β decreased to 0.29 (0.25) in January and 0.33 (0.28) in February 2019, respectively, which is comparable to that (0.20) obtained from the estimations using RADARSAT images with temporal resolution of 48–120 h during the freezing season for the pan-Arctic Ocean (Stern and Lindsay, 2009). We further use the seasonal bin to test the sensitivity of the estimation of β to the number of samples. Consequentially, the seasonal β was estimated at 0.54 and 0.48 for autumn and winter, respectively, which is close to those (0.53 and 0.49) averaged directly from the monthly values. Therefore, we believe that the monthly segmentation for estimations of β is statistically appropriate and can better reveal seasonal changes.

The temporal scaling exponent α also exhibited a strong dependence on the spatial scale, which means a relatively large intermittency of ice deformation can be obtained by fine-scale observations (Fig. 14). Seasonally, the value of α decreased between September and October 2018 because of enhanced consolidation of the ice cover. The value of the space–time coupling coefficient c increased monotonously from 0.034 in autumn to 0.062 in winter, suggesting a gradual enhancement of the brittle rheology of the ice cover. This is consistent with the results derived from RADARSAT images (Stern and Moritz, 2002), which revealed that sea ice deformation is more linear in winter and more clustered and spatially random in summer. The value of c in September 2018 is comparable to that in September 2016 (0.03). However, it is only about half that in September 2014 (0.06) (Lei et al., 2020a) because of the different ice conditions. The value of c in January–February 2019 (0.059–0.062) is comparable with the values obtained in January–February 2015 (0.051–0.077) from the northern PAO (Lei et al., 2020b) and the value obtained from the region north of Svalbard in winter and spring (Oikkonen et al., 2017).

The areal localization index denotes the area with the highest (15 %) deformation. It increased linearly (P<0.001) as the logarithm of the temporal scale increased (Fig. 15), which implies that the localization of ice deformation would be underestimated when using coarser temporal resolution. Seasonally, the areal localization index decreased significantly from September to November 2018, indicating that ice deformation was increasingly localized during the transition from melting to freezing. In the freezing season, ice deformation mainly occurs along linear cracks, leads, and/or ridges, which corresponds to a high localization. During melt season, the ice-deforming zones are in clumps rather than along lines. The spatial distribution of ice deformation rate is more even and amorphous (Stern and Moritz, 2002), which corresponds to a low localization. From November to February, the degree of ice deformation strongly regulated the localization of ice deformation, with the monthly ice deformation rate explaining 96 % of the monthly areal localization index (P<0.01). This means that an extremely high ice deformation can spread over longer distances. The areal localization index for January–February 2019 corresponding to a temporal resolution of 1 h and a length scale of 10–20 km was 1.9 %–2.3 %. This is close to values estimated using RADARSAT images at scales of 13–20 km (1.6 %) (Marsan et al., 2004) and of 10 km (1.5 %) (Stern and Lindsay, 2009), as well as that estimated at a scale of 18 km using a high-resolution numerical model (2.4 %–2.7 %) (Spreen et al., 2017). We also analyzed other fractional areas accommodating the largest 10 % or 20 % of the ice deformation. Although the adjusted indices would have different magnitudes, their overall seasonal patterns and dependence on the temporal scale are consistent with those using the threshold of 15 %. We therefore conclude that the understanding of the ice deformation localization derived from this study is not very sensitive to the selected threshold.

Sea ice conditions in the melt season have profound effects on sea ice dynamic and thermodynamic processes in the following winters. For example, enhanced divergence of summer sea ice leads to increased absorption of solar radiation by the upper ocean and delays onset of ice growth (e.g., Lei et al., 2020a). As shown in Fig. 16, the long-term decrease in sea ice concentration in the first half of September, when Arctic sea ice extent typically reaches its annual minimum (Comiso et al., 2017), is stronger in the southern and western PAO than in the northern and eastern PAO. The southern and western PAO have become ice free in September during recent years. On the contrary, there is no significant trend in ice concentration in the first half of September along the trajectory of the easternmost buoy (Fig. 16e). This suggests that the melting period is getting longer in the southern and western PAO compared to the northern and eastern PAO. Consequently, the spatial gradient of ice thickness in the PAO, especially during autumn and early winter, will be further enhanced by the delay in sea ice freezing onset in the south and west. A deformation of the ice field in the seasonal ice zone creates unfrozen ice ridges (Salganik et al., 2020). These new ridges, together with the newly formed thin ice in leads, are mechanically vulnerable components of the ice field during the freezing season and predispose the ice field to further deformation under external forces. At the end of the freezing season, the enhanced ice deformation will promote the sea ice breaking up and expand the MIZ northward, which is conducive to the advance of the melt season. Thus, the north–south and east–west differences in sea ice kinematics are likely to be more pronounced in the future.