We examine the basinwide trends in sea ice circulation and drift speed and highlight the changes between 1982 and 2009 in connection to regional winds, multiyear sea ice coverage, ice export, and the thinning of the ice cover. The polarity of the Arctic Oscillation (AO) is used as a backdrop for summarizing the variance and shifts in decadal drift patterns. The 28-year circulation fields show a net strengthening of the Beaufort Gyre and the Transpolar Drift, especially during the last decade. The imprint of the arctic dipole anomaly on the mean summer circulation is evident (2001–2009) and enhances summer ice area export at the Fram Strait. Between 2001 and 2009, the large spatially averaged trends in drift speeds (winter: +23.6%/decade, summer: +17.7%/decade) are not explained by the much smaller trends in wind speeds (winter: 1.46%/decade, summer: −3.42%/decade). Notably, positive trends in drift speed are found in regions with reduced multiyear sea ice coverage. Over 90% of the Arctic Ocean has positive trends in drift speed and negative trends in multiyear sea ice coverage. The increased responsiveness of ice drift to geostrophic wind is consistent with a thinner and weaker seasonal ice cover and suggests large-scale changes in the air-ice-ocean momentum balance. The retrieved mean ocean current field from decadal-scale average ice motion captures a steady drift from Siberia to the Fram Strait, an inflow north of the Bering Strait, and a westward drift along coastal Alaska. This mean current is comparable to geostrophic currents from satellite-derived dynamic topography.
 Our interest in ice motion pertains to its response to wind and ocean currents and to its impact on climate. Large-scale circulation of sea ice determines the advective part of the ice balance, i.e., the regional exchange of sea ice and export to lower-latitude oceans. Regional ice motion imposes a velocity boundary condition on the ocean surface, while the small-scale motion describes the interaction of individual floes, aggregation of floes, and the formation of leads (areas of open water) and ridges. Deformation of sea ice (openings and closings) alters the exchange of heat, gases, and momentum between the atmosphere and polar oceans, and shapes the character of the ice thickness distribution. The redistribution of freshwater via the transport and subsequent melt of relatively fresh sea ice modify ocean buoyancy forcing. Further, expressions of the state of the sea ice cover (e.g., thickness, material strength, and concentration) can be seen in its response to the atmosphere and ocean. Understanding the changes in ice drift over a broad length-time scale is thus of substantial geophysical interest.
 Over the last several decades, the changes in the Arctic sea ice cover have been dramatic. Along with the decline in ice extent [Cavalieri and Parkinson, 2012], recent observational evidence has also shown basinwide thinning of sea ice [Kwok et al., 2009; Kwok and Rothrock, 2009] and the loss of 2 year and older ice inside the Arctic Basin [Maslanik et al., 2007; Kwok et al., 2009; Comiso, 2010]. Recent investigations of ice motion have found increases in drift speed [Rampal et al., 2009; Spreen et al., 2011], ice deformation [Rampal et al., 2009], and advection of old ice to the southern Beaufort [Kwok and Cunningham, 2010]. Trends and variability in ice export are also seen at different passages around the Arctic [Vinje et al., 1998; Kwok, 2009; Spreen et al., 2009; Kwok et al., 2010]. Changes in ice motion are typically attributed to either changes in forcing (by the atmosphere and ocean) or changes in material strength (that is dependent on thickness and concentration). Variability and trends in ice motion, ice extent, and ice export have been linked to decadal shifts in atmospheric circulation patterns [Proshutinsky and Johnson, 1997; Rigor et al., 2002; Vihma et al., 2012]. However, recent changes in drift speed do not seem to be directly related to wind forcing [Rampal et al., 2009; Spreen et al., 2011; Vihma et al., 2012], and thus more likely linked to the changes in the ice thickness rather than the strength of the wind. If so, this implies changes in the response of ice drift to winds or air-ice momentum exchanges on a broad scale.
 In this paper, we examine the large-scale decadal and multidecadal trends in ice drift and, specifically, its connection to recent changes in regional winds, multiyear sea ice coverage, export, and the thinning of the ice cover. The motivation is how a 28 year data set of pan-Arctic sea ice motion informs us about coherent changes and variability in circulation pattern, ice export, and air-ice-ocean interactions especially in relation to a thinning ice cover. In view of the larger variability of short decadal trends, the net effects of these trends at the end of our 28 year period are of particular interest. The scope of this survey is restricted by the resolution and quality of the available data sets: this represents a broad basin-scale study that does not address the smaller scale aspects of ice deformation.
 In terms of time span and data set, our focus is on the decadal and multidecadal changes in the large-scale circulation of Arctic sea ice over a 28 year period (1982–2009). The ice motion data set is derived from the daily time series of satellite passive microwave observations. Even though motion observations derived from these instruments are fairly coarse, the great strengths of the data set are its spatial coverage and the length of the data record, which spans three decades for the combination of the Scanning Multifrequency Microwave Radiometer (SMMR, 1979–1987) and Special Sensor Microwave Imager (SSM/I, 1988–till date). We use these derived fields to examine the spatial and temporal variability of ice drift in the Arctic Basin.
 We divide the data set into three near decadal periods, 1982–1991 (10 years), 1992–2000 (9 years), and 2001–2009 (9 years), to examine decadal-scale shifts in circulation pattern and trends in drift speed. This paper is organized as follows: section 2 describes the ice motion fields and ancillary data sets used in our analysis. To provide a backdrop for examining these trends, we summarize in section 3 the character of the seasonal composites of sea ice and atmospheric circulation associated with the positive, neutral, and negative phases of the AO. In section 4, we describe the computation of the trends and summarize the multidecadal and decadal trends in wind and drift speeds and circulation patterns and their associations with the AO. Shifts in the circulation patterns over the three decades are discussed in section 5. We examine correlation between the spatial patterns of trends in drift speed and multiyear ice (MYI) coverage in section 6. Next, the net impact of circulation changes on ice export is discussed. Section 8 examines these changes in terms of the relationship between ice motion, geostrophic wind, and mean ocean current. Summary remarks and conclusions are provided in the last section.
2. Data Description
2.1. Ice Motion Fields
 The gridded fields of sea ice motion (100 km spacing) used here are constructed by blending ice motion derived from two satellite radiometer channels (37 and 85 GHz) [Kwok et al., 1998; Kwok, 2009] and from buoy drift, viz.,
α, β, and γ are weighting coefficients determined by an optimal interpolation scheme described by Colony and Thorndike . The indices i, j, and k are the available observations from each instrument used to produce a motion estimate at . A spatial correlation length scale of 300 km is used to create the interpolated field. This length scale is selected as an intermediate distance between the density of satellite observations (100 km grid) and the separation between buoy observations (average separations of ∼500 km), but short enough that the expressions of coastal effects are not noticeably degraded.
 A consistent and updated time series of passive microwave brightness temperature and ice concentration fields [Fetterer et al., 2002] were used to produce the satellite ice drifts [Kwok, 2009]. Uncertainties in the 2 day drift estimates from the SMMR (1979–1987) and SSM/I (1988–till date) are about 3–6 km (depending on spatial resolution of the passive microwave channel) for individual displacement vectors. For buoys, uncertainties in displacements are ∼300 m. Ice motion fields from multiple channels on the same instrument (e.g., 37 and 85 GHz on SSM/I) are used when they are available. Together, the length of the data record provided by the combination of the sensors spans more than 30 years. Buoy drifts are from the International Arctic Buoy Programme (IABP). The output motion fields are sampled on a uniform 100-km polar stereographic grid. Based on the number of observation and expected uncertainties in the passive microwave ice motion estimates and buoy drifts, the procedure above provides an analysis of the error of each motion estimate. An expected average uncertainty of 1–2 km/day in the individual interpolated estimates is typical, but the uncertainty varies with the density of measurements available within the neighborhood of each estimate.
2.2. Other Data Sets
 Sea-level pressures (SLP) are from National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) six hourly surface reanalysis on a 2.5° by 2.5° global grid [Kalnay et al., 1996]. Geostrophic winds are computed using the SLP fields. Standardized monthly AO indices are from the Climate Prediction Center (NOAA). Basin-scale estimates of MYI coverage are from the analysis of QuikSCAT data. Estimation and assessment of the spatial distribution of MYI coverage from scatterometer fields are described in the study by Kwok . This data set is primarily used to understand the correspondence between the changes in the coverage of the two dominant ice types in the Arctic Ocean and the changes in drift speed. The mean winter dynamic topography data set (2004–2008) is from ICESat [Kwok and Morison, 2011].
3. Arctic Oscillation and Sea Ice Circulation
 Linkages between large-scale changes in atmospheric and sea ice circulation to the Arctic Oscillation (AO) have been recognized early on, and the reader is referred to Rigor et al.  for a more detailed discussion of these connections. To provide a setting for examining the decadal trends in the next section, we briefly summarize the general features in ice circulation and SLP distribution associated with the positive and negative phases of the AO in our 28 year record. As well, this allows us to assess any large-scale changes in the ice motion and SLP patterns in our longer record (compared to that used by Rigor et al. ). By convention, the positive/negative polarity of the AO is defined, on a hemispheric scale, as lower/higher than normal SLPs over the polar regions and westerly wind anomalies along ∼55°–60° latitude. This zonally symmetric seesaw of SLP between the polar and temperate latitudes was discussed and named by Thompson and Wallace . The seasonal variability and trend of the AO index since 1950 are shown in Figure 1. Below, we describe the key features seen in the Arctic SLP distribution and sea ice circulation for different polarities of the AO index.
 The characteristic winter and summer composite patterns SLP and sea ice circulation associated with the positive (AO+: AO ≥ t), neutral (−t < AO < t), and negative (AO−: AO ≤ −t) phases of the AO are shown in Figure 2. Since the coefficients from the empirical orthogonal function (EOF) analysis capture primarily the characteristics of the cold season AO pattern (i.e., variability of SLP is higher during winter), the threshold t for delineating the phases is higher for winter (t = 1) than that for summer (t = 0.3). Summer indices have lower variability. Based on these thresholds, we use the monthly AO indices to partition the monthly ice motion and SLP fields into their respective winter and summer AO composites. The thresholds were adjusted such that there is nearly symmetric loading of each composite pattern (the number of monthly fields that went into each composite is shown in Figure 2).
 The distinct spatial patterns (locations of the patterns of high and low) of SLP and circulation that are associated with the neutral and opposing AO phases are shown in Figure 2. On average, there is a weaker Beaufort Gyre and no closed isobars in the SLP distribution over the Arctic Ocean in the winter AO+ composites (Figure 2a). Walsh et al.  first noted the weakening of the Arctic anticyclone between 1988 and 1995, which was later shown to be most likely due to the dominance of the Icelandic Low during the prevailing AO+ conditions in the late 1980s and early 1990s. Distinct anticyclonic sea ice circulation patterns with well-defined high-pressure center are seen in the neutral and AO− composites (Figures 2b and 2c). Between the two AO polarities, intermediate SLP distributions and circulation patterns are evident. The difference between the positive (AO+) and negative (AO−) phases (Figure 2d) in winter shows a dominant cyclonic pattern of atmospheric circulation and sea ice motion associated with an intense Icelandic Low—an expression of the more local North Atlantic Oscillation (NAO) (discussed in the study by Kwok ). Near the center of the Icelandic Low, the SLP difference exceeds 12 hPa. This serves to enhance the SLP gradient across the Fram Strait and the strengthened northerly enhances sea ice outflow. During this time span, the squared correlation between sea ice area export and the AO/NAO index is 0.3/0.4 [Kwok, 2009]. It should be noted, however, that the association (squared correlation) between ice outflow and NAO may not be as robust prior to 1978 [Hilmer and Jung, 2000]. From AO+ to AO−, the center of the high-pressure pattern in the Beaufort shifts northward by ∼2–3° in latitude. Further, the characteristic westward/eastward shift of the axis of the transpolar drift stream (TDS) in the AO+/AO− phase serves to change the source regions of the ice export. Because of this shift in the TDS during AO+, thicker ice from interior Arctic is advected toward the Fram Strait.
 Likewise, the summer composites show distinct but different patterns than that of the winter. During AO+, a low-SLP pattern with associated cyclonic ice circulation is seen covering most of the Arctic Ocean; only the edge of a high-pressure cell is evident in the southern Beaufort Sea. With a distinct anticyclonic pattern of circulation, the AO− ice motion composite during summer resembles the winter AO− pattern with its center shifted further to the southeast. Also seen is a well-developed TDS that is nearly aligned with the prime meridian. In the neutral phase, the SLP field is rather flat with a high and a low-pressure pattern centered in the southern Beaufort and eastern Arctic, respectively. Differences between the positive (AO+) and negative (AO−) phases show a cyclonic pattern of atmospheric/ice circulation as in the winter, but with the center located near the North Pole. At the center of the low, the SLP difference exceeds 8 hPa.
 Over the 28 year record of sea ice motion, the AO index time series has a positive trend in both the winter and summer (Figures 1a and 1b). The winter AO index started at a fairly neutral value near the beginning of the first decade (1982–1991) that culminated at a record high (AO >> 1) near the end of the decade—the largest positive excursion since 1950. The summer AO (Figure 1b) indices show lower variability (as discussed above) and a less-significant positive trend compared with that of the winter. In general, the large features in the SLP and circulation patterns associated with the high and low index of the AO are similar to that reported by Rigor et al. .
4. Amplitude and Vector Trends in Wind and Ice Motion
 In this section, we discuss decadal circulation trends associated with these shifts in the AO. At each grid point, we compute the linear trends in wind and drift speeds, and the vector trends in ice motion using the time series of 2 day motion vectors. The scalar amplitude of the vectors (wind or ice) is used in the calculation of the speed trends. To compute the circulation trends, the components of the motion vectors ( ) are thought of as the real and imaginary parts of a complex number, and the regression analysis produces a complex coefficient that is our vector trend. Prior to regression analysis, the 28 year seasonal cycle of 2 day averages is first removed. The amplitude and vector trends inform us of different things about the response of the ice cover to external forcing. Although the amplitude trends describe the changes in variance (or energy) of the motion field, the vector trends are indicative of the directional changes in the circulation pattern regardless of its variance. The amplitudes of these two trends are not necessarily correlated or coupled to each other. Henceforth, we use motion or circulation to refer to the vector quantities and speed to refer to the amplitudes.
 The overall and decadal trends in wind speed, drift speed, and ice motion for winter and summer are summarized in Figures 3 and 4. For reference, we also show the mean motion for each period. In particular, the background colors in Figures 3d and 4d represent the normalized dot product between the mean motion ( ) and the vector trend ( ) (viz., ) at each grid point. This quantity informs us of the tendencies of the vector trend relative to the mean motion. In Figures 3d and 4d, when the background is between white and red, the vector trend is aligned with the mean motion, whereas blue indicates that the vector is against the mean motion. Henceforth, slowdown/speedup is when the trend vector is against/aligned with the mean motion vector.
 Winter (October-May) and summer (June-September) trends are examined separately. The transitional months of May/June and September/October are used as rough delineations of the growth (winter) and melt seasons (summer). Below, we discuss the overall trends and decadal shifts in drift speed and circulation, in view of the positive trend in the AO index over the nearly three decades.
4.1. Winter Trends
 Broadly, the overall 28 year trends in winter drift speed and motion (see Figure 3, top row) are only statistically significant regionally (dashed contours within the figures show significance) and rather weak when contrasted to the stronger decadal trends. Geographically, the 28 year circulation trend is significant only in that region north of the Alaskan coast and the tongue that stretches from the southwestern Beaufort Sea to the North Pole. Consistent with the results reported by Spreen et al. , the widespread positive trends in drift speed over the Arctic basin are dominated by the large overall increases in drift speed since 2001 (23.5%/decade), and not explained by changes in wind speed (1.46%/decade). This pattern is also seen in the motion trends between 2001 and 2009. (For a specified period of interest, the spatially averaged trends (in percentage) are calculated by dividing the mean trend by the mean value over the spatial field of wind or drift speed.) We shall return to this in section 6 to discuss the likely attribution of increases in drift speed to the thinning ice cover.
 This period is marked by a transition from a near neutral phase of the AO in the early 1980s to the positive AO extreme in the early 1990s (see characteristic composites in Figure 2). A cyclonic pattern in motion trend, centered in the Eastern Arctic, captures the expected spatial differences between the AO+ and AO− in Figure 3c (second row). First, a slowdown of the southern arm of the Beaufort Gyre is evident: the motion trends are against the mean motion (blue background colors in Figure 3d). A second feature is the eastward tilt and speedup of the TDS in the central Arctic: the motion trend advects the ice farther east before turning toward the Fram Strait. The trend vectors in the TDS are nearly aligned with the mean vector fields (red) during that period along the drift stream. It should be noted that these trends do not extend all the way to the Fram Strait (the red background in second row of Figure 3d) and thus there was no observed increase in ice area export during this period (see Figure 7).
 The spatial trends wind and drift speeds are similar regionally and in the central Arctic (Figures 3a and 3b, second row): spatially averaged trends in wind and drift speeds are 3.89%/decade and −0.11%/decade, respectively. The trends in drift speeds in the East Siberian Sea (positive offshore) are visually correlated with the trend in offshore motion (see Figure 3c second row). This would cause increased coastal divergence/thinning in the East Siberian Sea. This suggests the importance of this cyclonic trend on coastal divergence/convergence and local thinning of the ice cover. Ice strength and dynamics are thus considerations in the interpretation of these trends of motion and speed. Rigor et al.  also discussed the potential impact of offshore wind and thinning during the positive phase of the AO on Siberian coast divergence.
 From the positive extreme in the early 1990s, the AO index quickly relaxed to a more neutral value (i.e., AO ∼ 0) toward the middle of this decade. The ice motion trend map shows an anticyclonic pattern (again centered in the Eastern Arctic) that looks to be an opposite of the cyclonic pattern in the past decade (Figure 3c, second and third rows). In fact, the underlying color pattern shows the dot product of the mean motion and trend vectors (in Figure 3d, second row) to be a close mirror of opposite sense (sign) to that pattern in Figure 3d (third row). The results show a speedup of the southern arm of the Beaufort Gyre and a slowdown of the TDS. Compared with 1982–1991, this nearly reverses the large-scale motion trends of the first period, except that the center of the anticyclonic trend pattern is displaced southwest toward the Laptev Sea.
 The spatially averaged trends in wind speed (−6.46 m/s/decade) and drift speed (−7.36%/decade) are similar (Figure 3, third row). The tongue of negative trends in drift speed (Figure 3b, third row) extending from the East Siberian Shelf again seems to be associated with trends of onshore ice motion (in opposite direction to that in the previous section) associated with the anticyclone trend pattern. This perhaps led to less offshore advection, allowing the local ice cover to thicken and strengthen, thus reducing the drift speed.
 The annual ice export peaked in 1994 (see Figure 7). Weighted by this peak in the early part of this period, the overall trend in ice area export is negative for this decade as the AO index returns to neutral. This is consistent with what is expected: the slowing of the motion vectors (blue background in Figure 3d, third row) near the Fram Strait can be clearly seen.
 The AO index was fairly neutral throughout this decade except for the large plunge in December of 2009—the last month of this period (Figure 1a). Since this decade is not dominated by large transitions of the AO index, the spatial pattern of ice motion trends (in Figure 3c, bottom row) does not manifest in the composite fields shown in Figure 2a. The ice motion trend exhibits the following features: a tight anticyclonic trend (in terms of radius) centered near 140°W and just north of Banks Island, and a distinct crosspolar drift trend that emanates from the western arm of the anticyclonic pattern. There is also a slowdown of the westward drift north of the East Siberian Shelf and the Chukchi Sea. These motion trends are suggestive of the shifts to a pattern characteristic of the positive phase of the arctic dipole anomaly (DA) during the latter part of this decade (discussed elsewhere by Wu et al. , Wang et al. ). Briefly, the DA features a high-pressure pattern centered over the northern Beaufort Sea and low-pressure pattern centered over the Kara Sea, along the Eurasian coast. Briefly, the DA corresponds to the second leading mode of EOF of monthly mean SLP north of 70°N during the winter season. In its positive phase (i.e., negative SLP anomalies appear between the Kara Sea and the Laptev Sea with concurrent positive SLP over from the Canadian Archipelago extending southeastward to Greenland), there is a shrinkage of the Beaufort High and a strengthening of the TDS.
 These ice motion trends are reflected in the mean field as a strengthening of the Beaufort Gyre (Figure 3c, bottom row) and a significant eastward swing of the TDS toward the Canada Basin. There is also the associated circulation trend toward farther eastward flow of riverine shelf water from the Laptev Sea along the Siberian Coast. These are larger than expected shift seen in the AO+ composites (Figure 1). As a result, the Beaufort Sea became a significant source of sea ice advected toward the Fram Strait. For this period, there is indeed a statistically significant increase in annual ice export at the Fram Strait, reversing the negative trend in the previous decade (Figure 7).
 Even though the ice motion trends suggest enhancement of Fram Strait area outflow, the trends in wind speed are not significant. In fact, the spatially averaged wind speed trends for the entire 28 year period are small, possibly due to the reduction of sea ice cover in eastern Fram Strait [van Angelen et al., 2011]. However, as discussed by Spreen et al. , the positive trend in the drift speed over most of the Eastern Arctic and parts of the Western Arctic cover almost half the Arctic Ocean (Figure 3b, bottom row). The spatially averaged trends in drift speed of 23.5%/decade are quite remarkable compared to the negligible trends in wind speed of 1.46%/decade. The spatial pattern drift speed overlaps the region with negative trends in multiyear sea ice coverage (discussed in more detail in section 7). Thinner and weaker seasonal ice types are more responsive to wind forcing and thus the positive trends in drift speed.
4.2. Summer Trends
 The overall 28 year trends in summer drift speed and motion (see Figure 4, first row), even though statistically significant, are rather weak compared to the stronger and more variable decadal trends. In summer, the widespread positive trends in drift speed (3.60%/decade), covering a large part of the Arctic basin, are not explained by the smaller trends in wind speed of only −1.13%/decade. The 28 year drift speed trend is dominated by the large regional increases since 2001. The overall spatial trends in circulation suggest a persistent linear drift from Siberia to the Fram Strait. These fields show tendencies for increased advection of sea ice along the TDS and increased advection of sea ice westward from the Canadian Arctic Archipelago into the southern Beaufort Sea. In the following subsections, as above, we discuss the observed trends and features within the three periods considered here and their association with the AO. As mentioned earlier, the variability of the AO index is low during the summer, thus the associations are weaker. Except for the obvious decline of the index toward the end of the last period, the average AO index had remained fairly neutral (Figure 1b).
 Even though there are some relatively large seasonal excursions of the AO (Figure 1b), the average index during this period remained fairly neutral. Spatially averaged trends in wind (3.89%/decade) and drift speeds (−0.11%/decade) are small. Regionally, there are significant negative trends in drift speeds along the Alaska coast and positive trends in the central Arctic and north of Fram Strait that are similar to patterns in the trends in wind speed. The patterns resemble those during the winter (see Figure 3, second row). The motion trends are weaker and different from that during the winter for this period. Further, there are no statistically significant or coherent patterns in motion trends that standout during this period.
 As in the previous decade, the average summer AO index remained fairly neutral, but the AO time series seems to be dominated by large excursions. Clearly, the significant negative trends in wind speed (−16.1%/decade, i.e., generally weaker winds)—also seen in the winter patterns during this period—that cover a large fraction of the Arctic Ocean dominate the spatial pattern (see Figure 4, third row). These negative trends are also seen in the trends in drift speed (−7.16%/decade) as well as weakening of the circulation (see Figure 4d, third row). The anticyclonic pattern in the motion trend, centered in the eastern Arctic Ocean north of the East Siberian Islands, is against the mean motion of the period (this can be seen in the blue-colored background of the mean motion field).
 The large decline of the AO index toward the end of the period is evident (see Figure 4, bottom row). There are regional negative trends in the wind speed in the Canada Basin, with an overall wind speed trend of −3.42%/decade. As in the winter of this period, the pattern of drift speed trend (spatially averaged trend: 17.71%/decade) seems well correlated with the negative trend in multiyear sea ice coverage (discussed in section 7).
 The motion trend (Figure 4c, bottom row), showing the strongest decadal trend, is anticyclonic over the entire Arctic Ocean with the center of action in the Canada Basin north west of Banks Island—an even more pronounced strengthening of the Beaufort Gyre compared to that observed in the winter over this period. The mean motion field is an expression of the AO− pattern as shown in Figure 2g. It is also interesting to note the similarity between the winter and summer circulation trends during this period. The motion trends are generally in the same direction as that of the mean motion field as evidenced by the red background. In this case, the motion trend in the TDS extends to the Fram Strait. For this period, this can be seen in the increased Fram Strait ice export during the summer (see Figure 7). Also evident is the trend of southward motion that increased the advection of old ice just west of the coast of the Canadian Arctic Archipelago to the southern Beaufort [Kwok and Cunningham, 2010].
5. Decadal Shifts in Circulation Patterns
 While the previous section discussed the decadal trends over our 28 year period, this section examines the decadal shifts in mean drift pattern and speed within the Arctic Ocean associated with the trends in the previous section. As reference, the mean summer and winter sea ice circulation patterns and SLP distribution for the three periods are shown in Figure 5. The three periods correspond to P1 (1982–1991), P2 (1992–2000), and P3 (2001–2009). To visualize the changes, we show the winter and summer differences between the three periods (P2 − P1, P3 − P2, and P3 − P1) to highlights the decadal shifts. A similar analysis of the response of sea ice to the AO, for the years between 1979 and 1998, can be found in the study by Rigor et al. ; we add an additional 11 years to the analysis.
 In winter, an observable feature is the anticyclone drift pattern when P3 is differenced with P2 (Figure 5e) and P1 (Figure 5f). The largest change can be seen in the strengthening of the Beaufort Gyre over the 28 year period; this shift in the circulation can be clearly seen in Figure 3c. Overall, however, the interperiod differences are small compared with the mean drift—a consequence of the small multidecadal trends.
 In summer, the mean ice motion and SLP fields in P1 (Figure 5g) show a relatively weak cyclonic pattern throughout the Arctic Ocean. The TDS in P1 follows a cyclonic path from the Laptev Sea toward the Fram Strait as defined by the low-pressure pattern. The mean fields in P2 show a strengthened Beaufort Gyre and TDS (Figure 5h) with an even stronger gyre and wider TDS in P3 (Figure 5i). In P3, the TDS is more parallel to the prime meridian delivering ice from the Beaufort Gyre instead of the Siberian Arctic. This shift in the mean atmospheric pattern that has tilted the axis of TDS eastward can be seen in the difference fields. The summer interperiod difference shows a much lower pressure (1–2 hPa) over much of the Arctic during P1. However, the P3−P2 (Figure 5k) and P3−P1 (Figure 5l) fields show the result of the significant changes due the decadal and multidecadal motion trends in Figure 4c. These patterns are characteristic of the shifts to a pattern characteristic of the Arctic DA—discussed earlier—that features a high-pressure pattern centered over the northern Beaufort Sea and low-pressure pattern centered over the Kara Sea, along the Eurasian coast. The imprint of this pattern on the strength of the summer Beaufort Gyre and the TDS is quite remarkable.
 To summarize, the net changes over the 28 years can be seen in the strengthening of the Beaufort Gyre as well as the TDS in both seasons, but the net summer changes are more significant.
6. Drift Speed and MYI Coverage
 Using buoy drift, Rampal et al.  found an increase in sea ice drift speed over the Arctic Ocean. With the sparse sampling of the buoys, however, they were not able to resolve the regional pattern of these changes. Recently, Spreen et al.  provided an analysis of trends in winter drift speed using a 19 year satellite record (1992–2009). Regionally, they report significant positive trends in drift speed (of 10.6%/decade) that are not explained by the small increases in wind speed of 1–2%/decade.
 Here, we examine our more extensive 28 year record that includes the summer and winter and with changes in multiyear sea ice coverage. Compared to the larger positive trends in drift speed (winter: 6.15%/decade, summer: 3.60%/decade—Figures 3 and 4, see also discussion in section 4), the wind speed trends are negligible over the 28 year record (winter: 0.47%/decade, summer: −1.13%/decade). The drift speed trends between 1982 and 2009 are dominated by the changes between 2001 and 2009 (winter: 23.5%/decade, summer: 17.71%/decade). The comparison suggests that these trends are associated with changes in the ice cover as these trends in drift are not evident during the first two decades (1982–2000, we spatially averaged trends in Figures 3 and 4). The likelihood that this is the case is borne out by the regional correspondence between the locations of the positive drift speed trends and areas with large reductions in multiyear sea ice coverage (shown in Figure 6). Between 1982 and 2010, positive trends in drift speed and negative trends in MY sea ice coverage are seen over 90% of the area of the Arctic Ocean (covered by grid cells). The large decline in MYI coverage within the Arctic basin during the last decade of our record is quite remarkable. Between 2005 and 2008, there was an ∼42% decrease in MYI coverage and associated thinning of 0.6 m in MYI thickness over the same time span [Kwok et al., 2009]. Weaker and thinner first-year sea ice now occupies a larger expanse of the Arctic Ocean. This thinner and weaker ice type is more responsive to wind forcing, with consequences of higher drift speed and increased deformation. Where the ice remained thick (e.g., north of the coast of Greenland and Ellesmere Island—Figure 6b), the trends are less significant. This evidence suggests that the trend in drift speed over a large portion of the Arctic is associated with thinning. In regions that were previously covered by MYI—more momentum is transferred from the atmosphere into the ice and the ocean. A recent analysis of model results supports our conclusion: Zhang et al.  reported increases in drift speed due to decreases in mechanical strength of the ice cover associated with thinning.
 In examining the linear relationship between wind and ice motion (section 8), we also found spatially coherent increases in the scaling factor between the two parameters (wind and motion), and the changes in drift speed are consistent with our attribution to thinning.
7. Fram Strait Ice Export
 The location of the flux gate is shown in Figure 5. Figure 7 shows the overall and summer (June-September) trends in ice area export at Fram Strait between 1982 and 2009 (from Kwok ). The 4 months of summer account for only ∼13% of the annual average. There is a small negative trend in area export over this time span. Seasonally, the summer trend is positive but small. Over the record, the mean annual area outflow at the Fram Strait is highest in 1994/1995 (1002 × 103 km2) when the NAO index (correlated with the AO) was near its 28 year peak. The NAO [Hurrell, 1995] represents that a major source of interannunal variability in the atmospheric circulation pattern in the North Atlantic is most pronounced during winter and thus a more relevant index for examining Fram Strait outflow. During high NAO years, a more intense Icelandic Low increases the gradient in the SLP across the Fram Strait, thus increasing the atmospheric forcing on ice transport.
 Decadal trends are higher and more variable (Figure 7) but because of the large variability in annual export, trends in export are extremely sensitive to the length of period and choice of endpoints. We did not find significant overall or decadal trends in wind speed (Figures 3 and 4) at the Fram Strait that would enhance the wind-driven part of ice export. Compared to winds over relatively flat sea ice, the wind speed over the Fram Strait is dependent on the Greenland ice sheet as well as the mix of sea ice and open water to the east. With decreasing ice coverage, there is additional modulation of the wind speeds due to changes in thermal gradients across the strait [van Angelen et al., 2011].
 As seen in the circulation patterns (discussed in section 5; Figure 4c, first row), there has been an average strengthening of the TDS during summer over the three decades. This can be seen in the ice motion trends (i.e., changes in circulation patterns) rather than the trends in wind or drift speeds. Examination of the sea ice exchanges between the Pacific and Atlantic sectors shows a long-term motion trend [Kwok, 2009] that also favors the summer advection of sea ice toward the Atlantic (not seen during the winter) associated with shifts in the mean summer circulation to a dipole pattern discussed earlier (Figures 3 and 4). In terms of delivering ice to the Fram Strait, our results suggest that between 2001 and 2009, the changes in the circulation and drift speed are contributing factors to the positive trend in ice area export during both the summer and winter (Figure 7).
8. Motion, Wind, and Ocean Current
 Here, we examine the response of sea ice to geostrophic wind. This provides another perspective on the changes in ice drift due to thinning (discussed in section 6). Following the work by Thorndike and Colony [1982, hereinafter referred to as TC82], we use a linear model to relate the observed ice motion (u) with geostrophic wind (G) and mean ocean current ( ), viz.:
where A is a complex constant and the vectors u, G, , and are thought of as complex numbers. represents that part of the ice velocity that is neither a constant nor a linear function of the geostrophic wind. TC82 examined the relationship using available buoy drift in the 1990s. We explore how the changes in the relationship with our more spatially and temporally extensive 28 year data set, and compare the results with their findings.
 Complex regression is used to compute the complex coefficient (A) and intercept ( ). Of particular interest from the regression analysis is the time-space variability of the following variables: , θ, and ρ2. Changes in the scaling factor in time and space tell us about changes in the coupling between the wind and ice, and changes in the internal ice stresses that tend to oppose ice motion. θ is the angle between the geostrophic wind and ice motion vectors (negative is to the right of the wind), and the squared correlation coefficient (ρ2) is that fraction of the ice motion explained by the geostrophic wind. With the daily motion and geostrophic wind data sets, we explore how these parameters vary spatially and seasonally, and how they have changed over the 28 years between 1982 and 2009.
8.1. , θ, and ρ2
 The fields of and ρ2 are shown in Figure 8. Prior to discussing their decadal variability, we first summarize their spatial and seasonal variability over the 28 year period (1982–2009—Figures 8a and 8e). Overall, is generally higher in the summer than in the winter. Geographically, the scaling factor is lower away from the Alaskan and Siberian coasts in both the winter and summer; the lowest can be found in the region north of the coasts of Greenland and Ellesmere Island. TC82 estimate of A = 0.0077 exp(−i5°) for the winter and spring, and 0.011 exp(−i18°) for the summer, can be compared to our estimates of 0.009 ± 0.0015 exp(i1.9 ± 2.6°) in October-May and 0.01 ± 0.0010 exp(−i7.1 ± 3.6°) in June-September.
 TC82 attributes the variability in and θ to two factors: (1) the relationship between geostrophic wind and the wind at 10 m (wl0) above the surface and (2) the changes in internal ice stress. With field data, TC82 showed that the ratio wl0/G increased from 0.55 in winter to 0.60 in summer and the clockwise angle from wl0 to G decreased from 30° to 24°. For the same geostrophic wind, in effect, the stress on the ice is expected to be 10%–20% larger (since it varies as wl0) in summer than in winter and 6° further to the right (or more negative by our convention). In the mean, our results with ∼ 10% higher during the summer and ∼9° further to the right are consistent with what was observed with buoy drift.
 To achieve the same ice velocity during winter, higher wind stresses are required to oppose ice stress where ice is thick or more compact (i.e., higher ice strength). While TC82 found no evidence of geographic variations in , we find significant spatial variability (in addition to the seasonal variability) in this parameter that is most likely associated with changes in internal ice stress, which is dependent on ice strength and consequently its thickness. As noted earlier, the lowest is found in the regions of thickest ice in the Arctic Ocean north of the coasts of Greenland and Ellesmere Island. The in these areas can be contrasted to higher 's in the seasonal ice zone and during the summer. Perhaps, TC82 did not find any geographic contrast because of the preferential deployment of buoys on multiyear sea ice, and during a time (1979–1980) when the Arctic sea ice was much thicker [Kwok and Rothrock, 2009].
 The fraction of the variance of the ice motion, which is explained by the geostrophic wind, is given by the squared correlation coefficient, ρ2. Time and space variations in ρ2 can be seen in Figures 8e–8h. TC82 reports that, at distance of 400 km away from the coast, ρ2 is about 0.75 ± 0.05 in winter and 0.8 ± 0.06 in summer and fall, while the values of ρ2 are generally smaller within 400 km of the coast. Coastal geometry, or mechanical constraints on ice drift, tends to reduce the correlation between wind and motion. Our distribution of ρ2 during the winter of 0.73 ± 0.07 (Figure 8e) is comparable with that observed by TC82. In winter, the parts of the Arctic with ρ2 > 0.75 are at least 400 km from the coasts of Greenland, Canadian Arctic Archipelago, Alaska, and Siberia. During the summer, the same general pattern, with ρ2 higher away from the coast, can be seen. However, in recent years, ρ2 near the ice edge tends to be higher when the ice cover is not longer mechanically constrained, i.e., after it looses contact with the coast during summer retreat. Thus, the linear model explains all but about 25% of the variance of the ice motion.
 The decadal fields of and ρ2 show noticeable and expected shrinkage of the area enclosed by the = 0.01 isopleths, and the expansion of the area enclosed by the ρ2 = 0.75 isopleths (Figures 8b–8d and 8f–8h). This is broadly consistent with physical attribution of the changes in and drift speed (discussed earlier) to the thinning of the ice cover. As the ice cover weakens over the past several decades, with thinner ice and the replacement of MYI with seasonal ice, the basin-averaged scale factor and the squared correlation ρ2 have both increased. In effect, lower winds are required to achieve the same drift speed. Conversely, ice drifts faster at the same wind speed. The opposing ice stresses are lower where ice is thinner and less compact. Changes in these spatial patterns highlight ice conditions that are very different from those three decades ago and show a progression toward a thinner ice cover.
8.2. Mean Ocean Current ( )?
 The mean ocean current ( ), in the linear model, represents only that portion of the ice motion that is a constant over a given interval of time that is not linearly related to the local geostrophic wind. The component of current that is linearly related to the wind is subsumed by the first term (AG) in the linear equation. As admonished by TC82, the interpretation of these vectors as ocean currents requires faith that the linear model is a good approximation to the theory, and thus our question mark in the title of this subsection. In this section, we examine the patterns in the current field and compare it with the geostrophic current derived from dynamic topography.
 Figures 10 and 9 show the three time-averaged terms in linear relation u = AG + over the same periods as previously defined. Isobars show the averaged SLP distributions. While Figures 10b and 9b show the mean ice circulation that is explained by geostrophic wind, Figures 10a and 9a show the relative misalignment of the centers of the AG and that of the mean sea ice circulation. For the winters of the first two periods (1982–1991 and 1992–2000), the centers of the atmospheric (AG) circulation—Beaufort High—are located to the southwest of the mean ice circulation. Of note is that the centers of the atmospheric (AG) circulation and Beaufort Gyre are closely aligned (or in phase) during the last period (2001–2009). Similarly, during the summers, the centers of the AG and u patterns are noticeably displaced relative to each other except for the last period.
 All the current fields (u – AG in Figures 10c and 9c) suggest a persistent linear drift from Siberia to the Fram Strait during both the winter and summer. In the winter, the poleward flow just north of the Bering Strait and the westward flow along coastal Alaska stand out. The Bering inflows are not sampled during ice-free summers. Over most of the Arctic Ocean, the currents are less than 1–2 cm/s and increases to 3–4 cm/s near the Fram Strait. As direct measurements of surface ocean currents in the Arctic Ocean are limited, we compare our results with the currents from TC82, as well as the drift from the Fram and the Sedov (following TC82). To estimate currents, Nansen  and Petrichenko  searched their wind records for time intervals where the integrated wind was zero, thus eliminating the need to remove the wind contribution. They estimated currents of about 2 cm/s flowing from the Siberian coast toward the Fram Strait. Using buoy drift and geostrophic winds, TC82 found currents with similar magnitude and direction. These are similar to our results. TC82 also commented that their vectors seem to agree fairly well with the general circulation deduced from the observed density field [Coachman and Aagaard, 1974] during a period. However, a detailed assessment remains difficult due to the lack of these types of measurements.
 In nearly all of our current fields, the northern arm of the clockwise circulation of the Beaufort Gyre is not distinct. This suggests that this is primarily a wind-driven component that has been subsumed by the first term (AG) of the linear equation, as only that portion of the ice motion that is a constant over the intervals of interest appear as the surface current. Potentially, the coarse sampling of the field may not represent the fine structure of the Gyre properly.
 How does this constant term compare with of the magnitude of the geostrophic current field? Here, we compare the vector field from the linear model (from the winter of 2001–2009) with the geostrophic current derived from the winter dynamic topography from ICESat described by Kwok and Morison  (see Figure 11). While the overall circulation patterns are similar, the magnitudes of vector fields are quite different suggesting that the geostrophic current contains four times the energy of that in the constant term. Since represents only that part of the ice motion over a given interval of time not linearly related to the geostrophic wind and since the Beaufort Gyre is related to the wind field at some time scale, it is likely that this anticyclonic feature has been subsumed by the term AG. Certainly, the Beaufort Gyre is not correlated to the wind field at monthly time scales [Kwok and Morison, 2011]. But, the time scales and dynamics related to the maintenance and variability of the Beaufort Gyre remain a subject of research.
 From a dynamic topography perspective, the linear drift from Siberia to the Fram Strait during both the winter and summer resembles a tilt of the Arctic Ocean between the Pacific and Atlantic Ocean. Also, the inflow north of the Bering Strait may be due to the pressure head between the Bering Sea and the Arctic Ocean [Woodgate et al., 2006].
 In this paper, we examined the decadal and multidecadal trends and variability in Arctic Ocean sea ice circulation and drift speed using satellite-derived ice drift. The 28 year record, between 1982 and 2009, provides a coherent spatial and temporal look at pan-Arctic changes for all seasons. Observed trends in drift and circulation are related to large-scale changes in atmospheric circulation, ice export, and air-ice-ocean interactions, especially in connection to a thinning ice cover. In this section, we summarize the salient points on ice circulation, drift speed, ice motion and geostrophic wind, and ocean current that are of geophysical interest. For contrasting decadal and multidecadal variability, the satellite ice motion data set is divided into three periods: 1982–1991, 1992–2000, and 2001–2009. In winter, the 28 year trends in motion and drift speed are weak compared to the stronger decadal trends (Figure 3). Overall motion trends (vector trends) are insignificant over most of the Arctic except for the strengthening of the southern arm of the Beaufort Gyre. Decadal trends in motion are broadly explained by the changes in circulation patterns associated with large positive or negative transitions of the AO indices during the first two periods. With nearly equal but large opposing transitions in the AO indices found in 1982–1991 and 1992–2000, the net changes in the mean circulation over the two periods were small (Figure 5). As opposing regional trends during the first two decades canceled each other, the changes during 2001–2009 dominated the overall 28 year circulation trend (Figure 3c).
 Similarly, the 28 year trends in summer ice motion and drift speed are weaker than the decadal trends (Figure 4), but the patterns are distinct from that of the winter. Linkage of these patterns with the AO is also weaker because the variability of SLP during the cold season dominates the AO index. The strong anticyclonic trend in summer (Figure 4d) during 2001–2009 dominates. As there were no opposing trend patterns over the 28 year period, the net changes in drift and circulation for the 28 years were larger (Figures 5k and 5l). The multidecadal circulation trend features a linear drift pattern from the Pacific Sector toward the Fram Strait (Figure 4c) as well as the statistically significant southward motion trend (as in the winter) just west of the Canadian Arctic Archipelago. This increased delivery of old ice just west of the Canadian Arctic Archipelago to the southern Beaufort was significant volume loss due to summer melt during the latter half of the last decade [Kwok and Cunningham, 2010]. The imprint of the positive phase of the Arctic DA on mean summer circulation between 2001 and 2009 is evident (Figure 5l) and ice area export at the Fram Strait is enhanced. However, the overall ice export trend is almost negligible.
 The weaker circulation trends can be contrasted to the widespread and large positive trends in drift speed, which are not explained by concurrent changes in the magnitude of wind speed, over the Arctic Basin in all seasons. This 28 year spatial pattern in drift speed is dominated by the large trends between 2001 and 2009 (winter: 23.5%/decade, summer: 17.71%/decade), compared with the small trends in wind speed (winter: 1.46%/decade, summer: −3.42%/decade). There is a remarkable regional correspondence between the locations of the positive drift speed trends in the eastern Arctic Ocean and areas with large reductions in multiyear sea ice coverage. Between 1982 and 2010, positive trends in drift speed and negative trends in MY sea ice coverage are seen over 90% of the area of the Arctic Ocean (covered by grid cells). North of the Greenland coast and Ellesmere Island, where the ice is still relatively thick, the trends in speed are less significant. This suggests that the increases in drift speed are likely associated with the large observed thinning and the reduction in MY sea ice coverage over this decade [Kwok et al., 2009], and there is robust evidence of the thinning of the sea ice in these same areas since 1980 [Kwok and Rothrock, 2009].
 Over the 28 years, the net impact of the decadal trends in circulation and drift speed can be seen in the overall strengthening of the Beaufort Gyre as well as the TDS in both winter and summer, but with the changes more prominent during the summer. This is consistent with the strengthening of the wind-driven Beaufort Gyre circulation reported by Proshutinsky et al.  and Giles et al. . Also, the pathways of freshwater runoff from the Siberian rivers feeding the Beaufort Gyre (as suggested by Morison et al. ) is also manifest, although not as pronounced, in the sea ice circulation trends. These changes are largely modulated by the shifts in large-scale atmospheric circulation and changes in the ice cover rather than changes in wind speed. Also of interest are the relative location of the centers of mean atmospheric circulation and the mean ice circulation. Although the centers of mean atmospheric circulation are located to the southwest of the mean ice circulation in the Beaufort Sea between 1982 and 2000, they were closely aligned (or in phase) during the last period (2001–2009) that seemed to enhance the strength of the Beaufort Gyre (Figure 10).
 We found distinct seasonal, decadal, and geographic variability in the response of ice motion to geostrophic wind. Over the regions where we find increases in drift speed, the multiplier that relates ice motion to wind has increased during both the winter and summer (Figure 8). This is consistent with our expectation of reduced ice resistance over regions with a thinner, weaker ice cover (discussed in section 6). That fraction of the variance of the ice motion, which is explained by the geostrophic wind, has increased. On average, the ice cover is now more responsive to geostrophic wind and implies changes in air-ice momentum exchanges on a broad scale.
 The mean ocean current ( ) derived from a linear model exhibits a persistent drift from Siberia to the Fram Strait, an inflow north of the Bering Strait, and the westward flow along coastal Alaska. We found this pattern in all decadal intervals, and during summer and winter. As the mean current includes only that portion of the ice motion that is constant and not linearly related to the geostrophic wind, it contains only a fraction of the energy in the geostrophic current from satellite-derived dynamic topography. The linear drift pattern during both the winter and summer is suggestive of the tilt of the Arctic Ocean between the Pacific and Atlantic Ocean.
 While a large fraction of the variance in sea ice motion is explained by the wind on the short term (days), the winds are less successful in explaining the longer-term (months to years) average ice motion. The longer time-scale ice motion and drift trends presented here have provided a coherent geophysical picture and insight into the multidecadal changes in the circulation the ice cover (e.g., strengthening of the Beaufort Gyre and Transpolar Drift), the character of ice drift of a mechanically weaker ice cover as a result of the widespread thinning in the past decade, and estimates of the mean ocean current.
 We thank M. Steele and J. Morison (University of Washington) for helpful discussions regarding the interpretation of the ocean currents. The SMMR and SSM/I data sets were provided by the National Snow and Ice Data Center, University of Colorado, Boulder, Colorado. The QuikSCAT data were provided by the Physical Oceanography DAAC at the Jet Propulsion Laboratory, Pasadena, California. R.K., G.S., and S.P. carried out this work at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.