Historical ice observations in the Nordic Seas from April through August are used to construct time series of ice edge position anomalies spanning the period 1750–2002. While analysis showed that interannual variability remained almost constant throughout this period, evidence was found of oscillations in ice cover with periods of about 60 to 80 years and 20 to 30 years, superimposed on a continuous negative trend. The lower frequency oscillations are more prominent in the Greenland Sea, while higher frequency oscillations are dominant in the Barents. The analysis suggests that the recent well-documented retreat of ice cover can partly be attributed to a manifestation of the positive phase of the 60–80 year variability, associated with the warming of the subpolar North Atlantic and the Arctic. The continuous retreat of ice edge position observed since the second half of the 19th century may be a recovery after significant cooling in the study area that occurred as early as the second half of the 18th century.
 Sea-ice cover has a major influence on global climate. It serves as an effective insulator between the ocean and the atmosphere, restricting exchanges of heat, mass, momentum and chemical constituents. The higher albedo of sea ice relative to that of the open ocean causes a considerable reduction in the amount of solar radiation absorbed at the Earth's surface. Both the insulation and the albedo effects have important implications for climate change scenarios since they can contribute to climate feedback mechanisms [Aagaard and Carmack, 1994; Barry et al., 1993]. Sea-ice processes affect oceanic circulation through the modification of the density structure of the water column [Aagaard and Carmack, 1989; Hibler and Zhang, 1995], and atmospheric circulation by means of cool air mass formation and generation of polar lows at the ice boundary [Deser et al., 2000; Lemke et al., 1980; Mysak and Power, 1992]. In turn, the climate system influences the transport of heat and moisture to the polar regions, and hence the formation and transport of sea ice, and the amount and timing of snowfall. Changes in global climate will necessarily involve changes in sea-ice cover; therefore the study of its variability may provide a clue to the better understanding of the global climate system.
 The region of the Nordic seas (Iceland, Greenland, Norwegian and the Barents seas) is of particular importance to global climate, being the region where warm, salty water from the Atlantic flows into the Arctic Basin, and where the fresher Arctic Ocean water is exported to the Atlantic Ocean in the East Greenland Current. Processes in this region influence the ventilation of the deep ocean and help to drive the thermohaline circulation, so important to our present day global climate. It is believed, that the time variability of ice extent here may play a role as an indicator of climate change both on regional and global scales [Deser et al., 2000; Dickson et al., 2000; Johannessen et al., 2004].
 Over the past two or three decades a substantial amount of attention has been paid to the study of sea ice using satellite, aircraft and in situ observations. For example, the studies of Gloersen et al. [1996, 1999], Johannessen et al. [1995, 1999], Parkinson et al. , Polyakov et al. [2003b], and Vinje  have revealed a dramatic retreat of ice extent over the past decades in almost all regions where sea ice exists as a seasonal or perennial phenomenon. In particular, the years 2002 and 2003 have demonstrated the absolute minima of ice extent in the Arctic over the entire period with satellite data coverage [Serreze et al., 2003]. But debate continues over whether the recent shrinkage of ice cover gives direct evidence of global warming caused by human activity or is mainly a part of a secular cycle. It is only about 30 years since the era of satellite passive microwave sensing of sea ice began. The time series derived from these sensors has shed light on the spatial and temporal patterns of seasonal and interannual variability in ice extent and concentrations, but is still too short for resolving the multi-year variability in ice cover.
 To gain a better understanding of multi-year variability of ice extent and the factors controlling it, historical observations of ice conditions provide a promising source of data. Despite some shortcomings associated with data quality from older, pre-satellite records, shipborne and early airborne observations of sea ice position can still be helpful in answering many of the climatic questions posed.
 The first records of sea-ice extent in the Nordic Seas are from early voyages of exploration in the middle of the 16th century. In many instances detailed records of these voyages were maintained in ship's logbooks and diaries. Observations remained sporadic until the second half of the 19th century when intensive sealing and whaling began. These observations have recently been collected and assimilated in one ice chart archive [ACSYS, 2003] and thus represent one of the few available directly observed climate records with a duration longer than a century.
Vinje , using the same data, studied the variability of April ice extent in the Nordic seas since 1864 and August ice extent since 1920. This work discusses an extension of his analysis both in time domain and methods applied. We extend the time frames to study the historical variability of ice extent from 1750 to 2002 and use new advanced statistical techniques for data processing. The period 1850–2002 is considered in detail, while the earlier and more sparse data are subject to a comparative analysis only. The time interval covers the 152-year period capturing the Arctic cooling (1880s–1910s, 1960s–1970s) and warming (1920s–1930s, 1980s–1990s) events [Bengtsson et al., 2004; Polyakov et al., 2003b] as well as the recent significant reduction of ice extent. For the purposes of this study we define ice extent in terms of a single line or “ice edge”, separating close pack ice from loose drift ice.
 Seven months, March to September, were chosen for consideration. The choice of the period is dictated by the data density, which is highest during the summer “hunting” season and diminishes in winter. This period, however, captures the most significant seasonal features of the ice cover, including maximum and minimum extents. In this study we place the emphasis mainly on April, June and August. In April, ice extent is at, or close to, a maximum [Parkinson et al., 1999]. Ice in the study area usually reaches its minimal extent in September. However, the choice is made in favour of August, since historically the data density is greater in that month.
2. Data Assembling and Handling
2.1. Study Region and Grid
 The geographic domain of our study comprises the Iceland, Greenland, Norwegian and Barents seas, extending from 30°W to 70°E (Figure 1). Three observational data sets have been used to construct a continuous record of ice edge position in the study area: the recently published ACSYS Historical Ice Chart Archive [ACSYS, 2003], Soviet aircraft reconnaissance charts for the Barents Sea [Fetterer and Troisi, 1997; Tanis and Smolyanitsky, 2000], and passive microwave (SMMR/SSM/I) data [Gloerson et al., 1990; Cavalieri et al., 2003]. The earliest chart used in the first data set comes from 1751, while the most recent is from 1979. The satellite-derived passive microwave data of the third data set spans the period of the most recent 24 years (1979–2002).
 In the present work a grid, mapped to a polar stereographic projection which is true at 70°N, is used. The grid is 80 × 140 pixels and is a subset of the SSM/I grid with a cell size of 25 km at this latitude. The grid origin is at 81.398°N 108.778°E which corresponds to node 171,201 of the SSM/I grid. The use of the conformal projection allows disengaging from the geographical coordinates and working on a more convenient Cartesian plane. The integer coordinates of this Cartesian plane correspond to the node indices of the SSM/I grid with a respective shift applied. Ice edge positions are initially defined by an ordered (consecutive) set of geographic coordinates, which specify the observed points along the ice edge. The geographical coordinates are then regridded to a set of Cartesian coordinates. For transitions between the coordinate systems we used a procedure based on locate.for FORTRAN code which is supplied together with SSM/I data.
 The historical records of sea ice extent prior to 1967 are distributed in the form of GIS files where the data is stored as polylines characterizing the ice conditions inward from this line. After selection of the correct lines, an ASCII file with geographical coordinates of the ice edge was produced. If the observation was available as a set of segments (a situation typical for historical ice charts) these were lined up in correct order to form a continuous set of coordinates in the input file.
 Soviet aircraft reconnaissance charts for the Barents Sea and the contemporary data since 1967 are available as gridded data and closed polygons, respectively. To produce contour lines corresponding to a given ice concentration we used the grdcontour program of the Generic Mapping Tools (GMT) [Wessel and Smith, 1998]. The polygonal data were gridded first and then contoured.
2.2. Historical Ice Charts
 Prior to 1966, the ACSYS Historical Ice Chart Archive comprises the records of ice edge position available from ships logbooks, diaries, newspaper reports, letters and maps collected and digitized over a period of more than a decade at the Norwegian Polar Institute and the Norwegian Meteorological Institute. The earliest chart in the data set comes from 1553. Over the following three centuries, observations of ice conditions remained irregular and infrequent, reflecting the remoteness and hostility of the region. Since the beginning of intensive economic activity in the region in the second half of the 19th century the data density becomes sufficient to create an almost continuous time series of ice maps at least for the April–August summer period. However, the spatial data coverage is still irregular, with the highest data density in the northern Iceland and southern Greenland Sea and the western Barents Sea - the areas of the most intensive whale and seal hunting.
 The data for the period 1750–2002 are organized into fortnightly ice charts, providing typically 2 per month. Of these, the chart providing the better data coverage was used. If both charts demonstrated a similar data quality, the map from the second fortnight was used in preference. Given a decreasing ice extent during June–September, this choice for these months could diminish a tendency for the historical data to exaggerate slightly the ice extent [Vinje, 2001; ACSYS, 2003; Ackley et al., 2003]. For the March–May period, the choice is generally insignificant, since the monthly variability of ice edge position is considerably less than the interannual one (see below in section 4); that is, the charts are essentially the same.
 Commonly, sealers and whalers, who provided much of the data prior to 1950, reported ice concentrations from 30% to 60%. It is considered that the wooden ships of the sailing era tried to avoid ice concentrations greater than 30%, so this value is chosen throughout as the definition of the ice edge position. However, when different ice concentrations were reported in the different parts of the study area, they were combined to construct a continuous ice edge. If two neighboring extent lines provided the ice concentrations above and below a conventional 30% line, preference has always been given to the line with higher concentration. As an example, Figure 1 shows processing of the historical ice chart for the second half of May 1906.
Figure 2 illustrates available data for April and August ice extents from 1850 to 1899 constructed following the technique shown above. As one can see, the data density is generally higher for the Greenland Sea in April and for the Barents Sea in August (see Figure 4). This is caused by migration of the most hunted species of seals (Bearded seal, Hooded seal, Harp seal), which tend to concentrate in the Greenland Sea for breeding in March–May [Kovacs et al., 2004]. During June–August the hunted species of seals and whales are found along the entire marginal ice zone of the Nordic Seas. We suppose that walruses or other land habitants, which populate the Arctic archipelagos around the Barents Sea, might represent a supplementary attraction for hunters, thus explaining somewhat higher number of charts for this region in the summer. There are also two significant gaps in time coverage during the two world wars. If available, we used the data from the adjacent months to fill the gaps in time series of ice edge anomalies. A statistical technique for doing this is given below in section 3 and Appendix A.
 The ACSYS archive also includes modern ice charts compiled by the Norwegian Meteorological Institute (NMI) and subsequently digitised in the Norwegian Polar Institute (NPI). These data are based mainly on satellite imagery and provide high-resolution data for ice edge position and sea ice type. The ice conditions fall into one of six categories: open water (ice concentration below 1/10); very open drift ice (1/10–4/10); open drift ice (4/10–7/10); close drift ice (7/10–9/10); very close drift ice (9/10–10/10); and fast ice. Working with NMI ice charts we used the boundary between open drift ice (4/10–7/10) and very open drift ice (1/10–4/10) as ice edge line. The NMI data taken for this study span the period 1967–1979 with the frequency of observations increasing from 4 to 8 per month towards the end of the period.
2.3. Soviet Aircraft Reconnaissance Charts
 We used Soviet aircraft reconnaissance ice charts for the period 1950–1965 to fill a substantial gap in data coverage for the Barents Sea, existing in the ACSYS archive. The actual data comes from two sources: Fetterer and Troisi , which starts from 1953 and Tanis and Smolyanitsky . The latter provided the data for the first three years of the period. A typical record includes information on total sea ice concentration, multi- and first-year ice concentration, new ice concentration and presence of fast ice mapped to a polar stereographic projection with a grid cell size of 12.5 km [Fetterer and Troisi, 1997] or 25 km [Tanis and Smolyanitsky, 2000]. In the time domain each observation is attributed to one of three 10-days periods of the month, but for the study period only one observation per month is typically available. To represent the ice edge we again used a boundary of ice with total sea ice concentration above 3/10. The data contouring and ice edge construction were performed following the procedure described earlier. The segments of the ice edges obtained for the Barents Sea were subsequently merged with the respective data for the western part of the study area.
2.4. Passive Microwave Data
 Modern satellite data provide grids of sea-ice concentration for the period 1979–2004. Data from two passive microwave sensors, SSMR (1978–1987) and SSM/I (1987–2004), were derived using the NASA team algorithm and are available electronically at the National Snow and Ice Data Center (NSIDC) in Boulder, Colorado DC (www.nsidc.com). Ice concentration maps are available every second day during 1979–1987, and on a daily basis after 1987. Each sea ice concentration grid is mapped to a polar stereographic projection with a grid cell size of approximately 25 km. This grid for the Northern Hemisphere is 304 × 448 pixels and serves as a basis for the work grid. For the SMMR and SSM/I derived ice concentrations the outer boundary of ice having concentration of at least 30% defined the ice edge.
2.5. Data Summary
 The data from the three sources have been merged to create a seamless sequence of monthly charts, using all available data. In some cases between 1950 and 1965, data from more than one source are included in one chart. It should be noted that the historical data (pre-1979) have already been merged successfully with more recent charts, which are based largely on satellite passive microwave data, to create the full ACSYS Historical Ice Chart Archive (1553–2002).
 The historical variability of ice edge position in the Nordic seas has been subsequently analysed by means of defining a monthly mean ice edge position for each month of the year (see section 3 for details). If only one observation a month was available, as is typical for the data prior to 1967, this observation was referred to as a monthly average. For analysis and interpretation of the data, we also defined seven sectors based on oceanographic and geographical considerations (Figure 3). To the north of the southern Iceland Sea (Sector 1) lies the region of the northern Iceland and southern Greenland Sea that is affected by the episodic formation of the Odden ice feature (Sector 2). Like Sectors 1 and 2, the northern Greenland Sea (Sector 3) is dominated by the East Greenland Current. Eastern Fram Strait (Sector 4) is distinctly different, being affected by the inflow of warm Atlantic water to the west of Svalbard, as is the west coast of Svalbard (Sector 5). Sectors 6 and 7 subdivide the Barents Sea into the western and eastern parts, in accordance with the classification given in, for example, Treshnikov . In the summer the ice edge typically retreats to the north of Svalbard and Sector 5 vanishes. Sectors 6 and 7 are then defined as the areas constrained by the 15E°, 50°E and 50°E, 70°E longitudes, respectively.
 The data density is irregular and generally increases over time. The challenge is to choose the most representative areas providing the highest data density both in space and time domains and, respectively, the longest time series of ice edge anomalies which can be further analysed. Examples of such an approach can be found in Vinje  or Ogilvie , who considered the ice extents of the western Barents Sea between 20°E and 45°E, and the Iceland Sea, respectively.
Figure 4 summarizes the available data accumulated from the different sources for the months of April and August. The numbered columns on the diagram refer to the seven regions shown in Figure 3. Over the past 150 years, the northern Iceland and southern Greenland Sea (Sector 2) and the western Barents Sea (Sector 6) have the highest data coverage because of the almost continuous spring/summer economic activity there since the second half of the 19th century. Prior to 1850 most data come from Sectors 3, 4 and 5. Sector 3 data was found to vary in similar fashion to Sector 2, but Sector 4 showed different patterns of behaviour. Sector 5 shows limited variability since the ice edge position there is controlled by the warm West Spitzbergen current and typically hugs the western coast of Svalbard during the winter and spring. In this study, therefore, we mainly considered Sectors 2 and 3 and Sector 6, concentrating on the time interval between 1850 and 2002, and the summer months from April through to August.
3. Mean Ice Edge and the Function of Ice Edge Anomaly
Shapiro et al.  gives a statistical technique for defining mean ice edge position and the function of ice edge anomaly. The core idea of the method consists of the treatment of every observed ice edge and correspondently a mean ice edge as a random line. The mean ice edge position is a parametric function [x(s); y(s)] on the rectangular coordinate plane, where parameter s is the distance measured along the ice edge. Conventionally we count out the points along the observed ice edge and measure distances along the mean ice edge from their westernmost endpoints. The ice edge anomaly at any given point of the observed ice edge is defined as the perpendicular distance from the mean ice edge to this point [see Shapiro et al., 2003, Figures 5 and 6]. We associate positive anomalies with increases in ice extent and negative with decreases, respectively.
 Moving along the mean ice edge we determine a function ϕ(s) of ice edge anomaly for any given observed ice edge relative to this mean. The advantage of this formalism is a subsequent operation with a scalar function of ice edge anomaly which is a function of a single spatial variable s.
 Following Shapiro et al. , we define the mean anomaly and mean standard deviation of the ice edge position relative to an arbitrary [a, b] sector of the mean ice edge as:
where Lab is the arc length along the mean ice edge between the points a and b.
 If the ice edge anomaly for a particular observation is not a continuous function on [a, b] (a frequent case for historical observations), the average is taken over the available data (i.e., all infinite anomaly values are ignored, whether due to missing data, lack of ice or the geometry of the mean ice edge). The perpendicular from the mean may also intersect the observed ice edge more than once, and under these circumstances the lowest anomaly (first point of intersection) is used. There is also the possibility that any particular observation may correspond to more than one point on the mean ice edge, and that some observed points may not correspond to any point on the mean edge. However, the iterative and smoothing processes involved in determining the mean ice edge reduce the occurrence of such situations, and the few instances where they do occur do not significantly affect the calculated mean anomaly for a particular sector.
 The main advantage of this technique, which uses ice edge position, lies in its capability of working with the historical data. These data are often segmented, but can still be processed without the need to guess the ice conditions in parts of the study area, where data are unavailable (as is required when using ice extent or area). To test the validity of this approach, we modeled the segmented historical observations from the modern data with a 100% spatial data coverage using the random selection of samples of different lengths for each month and sector. The averages derived from the artificially segmented data were subsequently compared against the true sector averages. A Student's t-test for paired samples showed that nearly 70% spatial data coverage is sufficient for the mean drawn from segmented data to match the true mean with 95% confidence level. All historical observations after 1850 for studied sectors satisfy this 70% coverage criterion on average, supporting the validity of this approach.
4. Results and Discussion
4.1. Variability of Mean Ice Edge Position
 The mean annual cycle of the ice edge variability, based on modern data from 1967 to the present, is shown in Figure 3. To make the figure readable, the ice edge positions only for April through August are displayed.
 We subsequently used the derived monthly means to calculate mean ice edges in April–August for four study subperiods: 1870–1920, 1921–1961, 1962–1988 and 1989–2002. The subperiods were chosen to match the periods of warming and cooling in the Arctic, according to Polyakov et al. [2003b], who found a low frequency oscillation (LFO) in sea level pressure, air temperature, ice extent of the Siberian Arctic seas and temperature of the Atlantic water layer in the Arctic [Polyakov et al., 2003a, 2003b, 2004]. Analysis of Svalbard proxy air temperatures has shown that this multidecadal variability has persisted in this area for at least 800 years [Isaksson et al., 2005].
 Three other subperiods (not shown) 1850–1899, 1900–1949 and 1950–2001 were used for comparing our results (not shown) with the work of Shapiro et al.  on April ice extent in the Barents Sea. The analysis demonstrated a reasonable consistency (within 25–50 km) for the mean ice edge positions and the standard deviations of the ice edge anomaly.
 The mean for each month from the last 36 years served as a reference for producing the time series of functions of ice edge anomalies. As a rule we count off the anomalies from the mean for the corresponding month, except in cases when we used the data from the adjoining months for filling gaps in the time series.
 The left panels of Figure 5 show the positions of mean ice edges for the four study subperiods in April, June, and August. Panels on the right show the respective standard deviations of the ice edge departures along the mean ice edge.
 As can be seen, the mean ice edge positions exhibit a retreat during the whole study period (1850–2002) in each of April, June and August. A similar pattern was found in shorter time series for the autumn and winter months. The retreat is most pronounced in the Greenland and the Barents seas in winter-spring and in the Barents Sea in late summer. The Greenland Sea shows a greater reduction of ice extent in spring than the Barents Sea. The Barents Sea shows a greater reduction in summer than in spring, indicating stronger annual melt-back in the most recent decades. Vinje  found similar results for shorter time series for April and August. There also seems to be a tendency over the last two decades for the ice with concentrations above 30% to retreat in August to the north of 72°N along the eastern coast of Greenland - a phenomenon which was not frequently observed in the past. Note a decreased standard deviation of the ice edge anomaly during 1989–2002 in August, sector 1, as seen in the bottom right panel in Figure 5. This indicates that the ice edge in this area mainly hugs the shore-line, i.e., sea ice predominantly exists in the form of patches of loose drift ice along the coast. The years 1985 and 2001–2003 are the extreme examples of such a behaviour of the ice pack: the ice to the south of 75°N had already disappeared by July of these years. A similar phenomenon is observed in the eastern Barents Sea (sector 7). In the most recent 15 years the ice edge here tends to retreat to the Novaya Zemlya coast in June, while for the earlier periods it did not retreat so far until July.
 The magnitude of the ice edge retreat, comparing 1989–2002 to 1870–1920, is about 250–375 km in the Greenland Sea in spring and about 250–350 km in the Barents Sea in late summer (see Figure 5). These values are twice as much as the standard deviation of the mean ice edge position due to its interannual variability. Note also that the standard deviations (right panels in Figure 5) for different periods covered by different data types have similar magnitudes. This points out consistency between the data sets and supports the validity of the merging process. It also indicates that past natural variability of ice extent has been similar to present day variability at least in the region of study, a fact that has not always been apparent in previous Arctic ice climatologies [e.g., Chapman and Walsh, 1993]. This natural variability of ice extent is superimposed on the decreasing trend, and further analysis of the time series of ice edge anomalies supports this statement.
 The ice edge position shows its maximum interannual variability in the northern Iceland and southern Greenland Sea and the central and northern Barents Sea (see Figure 5). The first maximum is better pronounced in April due to the recurring formation of the Odden ice feature [Shuchman et al., 1998]. The second maximum corresponds to the area of warm Atlantic water inflow to the Barents Sea from the Norwegian Sea [Jones, 2001]. Note a decreased standard deviation in sector 2 for the most recent 13 years of data, the result of a less frequent formation of Odden during this period, when it was only prominent (in terms of the 30% ice concentration) in April of 1991, 1996 and 1997.
4.2. Construction and Analysis of Trends in Time Series of Spatially Averaged Ice Edge Anomalies
 We calculated the annual ice edge anomalies for each month during March–September relative to the mean ice edge during 1967–2002 with 25 km spacing. The spatially averaged ice edge anomalies were produced for each of the 7 sectors in March–September and for the whole study area. In the latter case, the observations covering less than 50% of the ice edge in a particular sea, were omitted.
 Data from sector 2 show very high variability of ice extent likely due to the episodic formation of the Odden ice feature. This feature, which only occurs during the November–May period [Shuchman et al., 1998], was expected to complicate the analysis for sector 2. However, a detailed comparison of the April time series for sectors 2 and 3 has shown that the ice edge experiences the same type of interannual and interdecadal variability in both areas. These two time series were therefore combined to yield a Greenland Sea ice-edge anomaly time series for subsequent analysis and display in this manuscript.
 We compared our results with April and August time series of ice extent from Vinje . From each time series we subtracted the mean and normalized by the respective standard deviation to subsequently operate with dimensionless sequences. The correlation coefficients between our results and Vinje's are 0.8 and 0.85 for the Greenland and the Barents seas in April, respectively, for the whole data time range available in Vinje's work (1864–1998). The correlation for August is somewhat lower and amounts to 0.65 for the Barents Sea. The correspondence is reasonably high, given the difference in methods and in data interpretation. In particular, Vinje  applied ice edge extrapolation to obtain complete coverage in the study area for any segmented ice chart. This is necessary to estimate ice extent. In contrast, our use of ice edge positions means that we utilize the data as they are, without making assumptions about the ice edge conditions in the areas where data is lacking. To fill in the gaps in our time series we did, however, use the data from the adjacent months, whenever possible, with the respective correction applied (see Appendix A for further details about the technique).
Figures 6, 7, and 8 show the time series of the spatially averaged ice edge anomalies for sectors 2–3 (Greenland Sea), 6 (western Barents Sea) and for the whole study area in April, June, and August.
 For each sector we performed a linear regression on the time series to identify the statistical significance of the revealed retreat of the ice edge. Trends were calculated for the historical data from 1850–1966, for the modern data (1967–2002), and for the entire study period 1850–2002. Note that we have included observations prior to 1850 in the figures, but have not performed the linear regression analysis due to the low data density for this early period.
 We assessed the statistical significance of the slopes using an F-test with 1 and n-2 degrees of freedom [Draper and Smith, 1998]. The trend magnitudes for sectors 2–3, 6 and for the whole study area are shown in Table 1.
Table 1. Magnitudes of Linear Trends in the Time Series of Ice Extent for April, June, and August in Sectors 2–3, 6, and the Whole Study Areaa
Units are in km/year. The trends are computed for the H, historical data (1850–1966); M, modern data (1967–2002); and W, whole study period. Standard deviations of the slopes are shown in parentheses. Asterisks mark the trends that are statistically significant at the 95% confidence level according to the F-test.
 The results shown in Table 1 confirm the conclusions drawn from Figure 5. The strongest reduction of ice extent is observed in the Greenland Sea in spring. For both study areas and all months shown, the ice edge anomalies exhibit negative trends during the whole period considered. Other months and sectors demonstrate similar results. As an exception, the ice edge anomaly in the western Barents Sea in the recent three decades shows a weak, though statistically insignificant, positive trend. The retreat of the ice, however, is not uniform, with periods of advances (1860s, 1880s, 1910s, 1940s, 1960s and 1980s) among the general retreat. The well-documented [Gloersen et al., 1999] (see also the results presented in Table 1) recent reduction of ice extent follows the last maximum of the 1960s associated with the so-called “Great salinity anomaly” [Dickson et al., 1988], a period of enhanced wind-driven transport from the Arctic through Fram Strait. The inspection of the ice edge time series reveals that such a reduction is not something extraordinary over the period considered. An even more abrupt retreat of ice edge was observed in the first half of the 20th century, between about 1910 and 1940 in April–August in the Greenland Sea and August in the Barents Sea. The Barents Sea ice edge position in April and June for this period does not demonstrate any prominent retreat, in agreement with the results of Vinje . However, the greatest retreat registered during the 1930s still has more ice than the modern position, which is in fact the minimum observed since 1850. Examination of the sparse data prior to 1850 gives some evidence that minima of ice cover similar to the present one may have occurred in the past. In particular, mean August Barents Sea ice edge position in the second half of the 18th century exhibits values close to the recent ones. The Greenland Sea data for this period are unfortunately lacking, making it impossible to determine exactly whether similar retreat occurred over the whole study area. The positive correlation of about 0.4 between the Greenland and the Barents seas ice edge anomalies suggests, however, that this could be the case for this period.
 The ice edge anomalies averaged over the whole study area show generally weaker decline with a mean value for the ice edge retreat of about 100–150 km during the last 100 years. Note also that the contrast between the slopes of trends calculated for the entire period and the period covered by modern data is less significant compared to those found for the particular study areas. This is due to a contribution to the mean of areas where the interannual ice edge variability is lower. One should note, however, that the latter results are less reliable compared with the conclusions drawn from the time series for particular sectors, since the data coverage for the whole study area is generally lower. In particular, the time series are shorter and more data more data are missing, especially during the 1930s–1950s.
 Available observations for the 19th century show evidence that ice edge position at that time was generally greater than in the 20th century. There is agreement between the increased ice extent in the first half of the 19th century and colder climate for this period. The general retreat of ice edge position observed during the last 150 years is therefore in agreement with the ongoing warming trend, that started well before the industrial age [Moberg et al., 2005].
4.3. Functions of Spatial Correlation of Ice Edge Anomaly
 The extent to which ice edge variations at any one point correlate with variations at another can be determined by calculating the spatial correlation, defined as:
where ϕ(si) and ϕ(sj) denote the time series of ice edge anomaly at points si and sj on the mean ice edge for a given month. Figure 9 shows spatial correlation functions for April, June and August, based on 35 years of contemporary data. Data for January–March are not shown, but the general picture is essentially the same as for April. The Greenland Sea (sectors 2 and 3) demonstrates a higher spatial persistence of the ice edge anomaly than the Barents Sea, perhaps due to a dependence of the Greenland Sea ice extent on ice export from the Arctic. For both the western and the eastern parts of the study area the link between remote locations tends to decrease in August, likely due to the summer decrease in the intensity of atmospheric circulation, which partly controls the ice edge position. Figure 9 (April and June) shows that the time series of ice edge anomalies in sector 6 and sectors 1–3 are correlated. The link is relatively weak (r ≈ 0.6) but essentially positive, indicating the agreement in sign of ice edge anomaly in the southern and central Greenland and the western Barents Seas. It agrees well with a co-phase behavior found in the leading EOF of winter ice concentrations of the Greenland-Barents Seas [see Deser et al., 2000, Figure 3]. Vinje , based on April ice extent data, reported a similar correlation between April ice extents in these areas. Note that the link tends to weaken from winter to summer, which may indicate that this is an imprint of the North-Atlantic Oscillation (NAO) -induced circulation which is most active in the winter months.
4.4. Analysis of the Time Series of Ice Edge Anomalies Using Wavelets
 To investigate further the variability of ice cover in the study area we apply wavelet analysis to the time series of ice edge anomalies. For a brief description of the technique, see Appendix B and Torrence and Compo  for further details. Figure 6 shows the wavelet power spectra for the Greenland Sea (combined sectors 2 and 3) in April, June and August. The wavelet analysis of the western Barents Sea time series (sector 6) for the same months is presented in Figure 7. The spectra for May (not shown) demonstrates the same type of the variability and closely resembles those for April and June.
 It can be seen that the time-scale behaviour of ice edge variability in the Greenland and the Barents seas is somewhat different. The analysis reveals a low-frequency mode of ice edge variability in the Greenland Sea with a period of about 70 years. Note that the last two maxima of the wavelet power in this mode lie inside the cone of influence, so it is unclear whether these maxima are true or just an artifact caused by edge effects. However, the analysis carried out using the much narrower “Mexican Hat” wavelet, which provides a better localization in time (and respectively a narrower cone of influence), but somewhat poorer frequency discrimination, revealed virtually the same positions for these maxima. In the Barents Sea the 70-year periodicity is weakened and appears as insignificant.
 The maxima and minima of the multidecadal variability (1880s–1890s, 1960s and 1920s–1930s, 1980s–1990s, respectively) correspond reasonably well to well-known periods of cooling and warming in the Arctic, identified in Polyakov et al. [2003a, 2003b, 2004] as the LFO signature. The warming of the surface and Atlantic waters in the northern North Atlantic and the Arctic in the past two decades [Belkin et al., 1998; Grotenfendt et al., 1998; Polyakov et al., 2004] thereby can be interpreted as a manifestation of the positive phase of this multidecadal oscillation.
 Both the Greenland and the Barents Sea also demonstrate well-pronounced two- to three-decadal variability. In the Greenland Sea, a 24 to 30-year mode of ice edge variability is observed during April–August throughout the whole period where the data density is sufficient. In the Barents Sea this mode is manifested on a broad range of scales from 16 to 40 years and is most apparent in June.
 Similar multidecadal oscillations identified in the ice edge variability are found in different instrumental [Schlesinger and Ramankutty, 1994; Mann et al., 1995] and proxy records [Delworth and Mann, 2000; Isaksson et al., 2005; Gray et al., 2004] as well as being predicted by some models. The modeling studies suggest that these phenomena might be an imprint of a multidecadal oscillation in the thermohaline circulation of the North Atlantic. The level of atmosphere-ocean coupling in these models and the role of sea ice are different, which appears to have a significant influence on the variability. The suggested cycles therefore vary significantly from model to model: 50–80 year variability in Delworth et al.  and Delworth and Mann , 40–60 year in Griffies and Bryan , 35-year cycle suggested in Timmermann et al.  or 20-year cycles in Holland et al.  and Wohlleben and Weaver . This topic therefore still needs further research. Note, that a superposition of oscillations with different periods may promote especially strong positive and negative anomalies. The extreme ice conditions of 1890s, 1930s and current anomalies occurred when positive (negative) LFO events were co-phased with positive (negative) phases of the two to three decadal mode of variability (Figure 6).
 The weak manifestation of the long-term oscillations in the Barents Sea may arise from the higher ice edge variability there, compared to the Greenland Sea (see Figure 5), so that the LFO is hidden behind the interannual variations, which are superimposed on the centennial negative trend. The modeling results of Delworth et al.  and Delworth and Mann  also suggest that it is the Greenland Sea that primarily takes part in the multidecadal cycle, while in the Barents Sea these oscillations are not so well pronounced. The generally poorer data quality for the Barents Sea must also be taken into account. In particular the gap associated with the Second World War is longer, and more years in the time series are missing than in the Greenland Sea.
 We do not apply the wavelet analysis to the ice edge anomalies averaged over the whole study area because of the substantial data gaps in these time series. One can, however, notice the traces of the multidecadal variability in these data as well: in particular the decreased ice edge anomalies in the early part of the record before 1880 and in the 1920s–1930s, and increased in the 1900s–1910s and 1950s–1960s.
 Decadal-scale oscillations are found in all spectra analyzed, but often appear as insignificant. The significant peaks in the power on this scale are found during 1860s–1890s, 1910s–1930s and 1960s–1980s. The high-frequency variability in the annual ice edge position shows the leading role of the North Atlantic Oscillation (NAO) [Hurrell, 1995], in agreement with other studies on this subject [Deser et al., 2000; Vinje, 2001]. The maxima of the power are typically found in the periods with alternation in sign or during the periods with lasting positive winter NAO. The ice edge anomaly time series and winter NAO index (DJFM) demonstrate a nearly anti-phase behavior (see Figure 5, right panels), which is consistent with a mechanism of atmospheric forcing on sea ice. The positive NAO indices are indicative of enhanced northerly meridional circulation promoting a retreat of ice cover. This explains the appearance of the peaks of significant power on the multiyear scale in these particular periods with the positive NAO. The characteristic atmospheric pattern presumes that the study area is under control of more intensive cyclonic circulation contributing to a higher variability of ice cover. The correlation coefficients reach maximum values of about −0.5 to −0.6 in the southern and central Greenland Sea and the western Barents Sea. This is in good agreement with the studies of Deser et al.  and Dickson et al. , which identify these areas as the most susceptible to the influence of the NAO-related forcing mechanisms.
 The results presented in this study support the conclusions of Vinje , who found evidence of persistent ice retreat since the second half of the 19th century. Wavelet analysis of the time series presented in this work gives evidence that this decreasing trend is being superimposed on multidecadal oscillations in ice edge position in the Nordic Seas. The analysis suggests the presence of a 60–80 year variability and also of two- to three-decadal oscillations in ice extent. We associate the multidecadal mode with the so-called low-frequency oscillation (LFO) found in Arctic climate and possibly associated with the North Atlantic thermohaline circulation variability.
 Given the last cold period observed in the Arctic at the end of the 1960s, our results suggest that the Arctic ice pack is now at the periodical apogee of the low-frequency variability. This could explain the strong negative trend in ice extent during the last decades as a possible superposition of natural low frequency variability and greenhouse gas induced warming of the last decades. However, a similar shrinkage of ice cover was observed in the 1920s–1930s, during the previous warm phase of the LFO, when any anthropogenic influence is believed to have still been negligible. We suppose therefore that during decades to come, as the negative phase of the thermohaline circulation evolves, the retreat of ice cover may change to an expansion. However, the verification of this hypothesis requires a variety of modeling studies involving global coupled ocean-atmosphere models and further observational analysis.
Appendix A:: Reconstruction of the Time Series of Spatially Averaged Ice Edge Anomalies
 To fill in the gaps in the time series of the spatially averaged ice edge anomalies the data from the adjacent months were used with the respective correction applied. The correction coefficients (not shown) for each month and sector were estimated from the 35-year long time series of the modern data by regressing the time series for one particular month upon the time series for the adjacent month. The ice edge anomalies for the reconstructed and the reference time series were measured using the same mean ice edge, corresponding to the time series month that was being reconstructed. High correlations (all above 0.7, typically about 0.85) between the time series of ice edge anomalies for the neighboring months indicate the persistence of the monthly averaged ice edge anomalies. The correlation coefficients did not change significantly when the whole data series were used in calculation rather than only the modern data, supporting the validity of the correction procedure.
Appendix B:: Wavelet Analysis
 Decomposing a time series using wavelets allows highlighting of the variability of features on different time-scales. We performed a continuous wavelet analysis using a real Morlet wavelet with the main goal of identifying low-frequency patterns in variability of sea ice cover in the study area. Although lacking in detail on finer time-scales, the real wavelet decomposition, in contrast to a complex one, allows highlighting of the peaks in oscillations with different frequencies. A visual inspection of the time series of ice edge anomalies shows the presence of the non-linear trend in the data which can be nearly approximated by the 4th order polynomial for April and 2nd order for August time series. Before applying the wavelet transform we subtracted them from each time series. To keep the 1 year time increment we filled in the gaps in the time series by zeros. The wavelet transform routine applied in the present work is based on the cwt function of the Wavelet Toolbox extension package for Matlab. The wavelet power spectra were derived from the wavelet coefficients and subsequently normalized using the respective standard deviations for each time series. The normalization gives a measure of the wavelet power relative to a white noise background, thus simplifying the comparison of different spectra. Significance of the maxima in the decomposition was tested at the 95% confidence levels against a red noise background. The respective lag-1 autocorrelations for each time series were estimated from the last 36 years covered by modern data. Note that the results obtained from the scattered data between 1750 and 1850 should be interpreted with caution. However, we retain these data in the time series for the Greenland Sea for analysis to reduce the coverage of the cone of influence over the high quality data after 1850. This cone of influence results from the assumption that the data is cyclic, which produces edge effects in the resulting spectrum. The Barents Sea data before 1850 is too sparse for reliable interpolation, so we applied the wavelet transform to the data for the periods from 1865–2002 (April) and 1850–2002 (June, August) only.
 This study is supported by the Norwegian Research Council, project 148812/S30. The helpful comments of two anonymous referees are also gratefully acknowledged. We would like to acknowledge T. Vinje, H. Goodwin, T. Lyning, V. Pavlov, and O. Pavlova for their helpful discussions and contributions to this work.