The Greenland δ18O ice core record is used as a proxy for Greenland surface air temperatures and to interpret Atlantic Multidecadal Oscillation (AMO) variability. An analysis of annual δ18O data from six Arctic ice cores (five from Greenland and one from Canada's Ellesmere Island) suggests a significant AMO spatial and temporal variability within a recent period of 660 years. A dominant AMO periodicity near 20 years is clearly observed in the southern (Dye3 site) and the central (GISP2, Crete and Milcent) regions of Greenland. This 20-year variability is, however, significantly reduced in the northern (Camp Century and Agassiz Ice Cap) region, likely due to a larger distance from the Atlantic Ocean, and a much lower snow accumulation. A longer time scale AMO component of 45–65 years, which has been seen clearly in the 20th century SST data, is detected only in central Greenland ice cores. We find a significant difference between the AMO cycles during the Little Ice Age (LIA) and the Medieval Warm Period (MWP). The LIA was dominated by a ∼20 year AMO cycle with no other decadal or multidecadal scale variability above the noise level. However, during the preceding MWP the 20 year cycle was replaced by a longer scale cycle centered near a period of 43 years with a further 11.5 year periodicity. An analysis of two coupled atmosphere-ocean general circulation models control runs (UK Met Office HadCM3 and NOAA GFDL CM2.1) agree with the shorter and longer time-scales of Atlantic Meridional Overturning Circulation (AMOC) and temperature fluctuations with periodicities close to those observed. However, the geographic variability of these periodicities indicated by ice core data is not captured in model simulations.
 The severity of the consequences of the current global warming depends considerably on how intense the warming is in the Arctic. Climate models (coupled atmosphere-ocean general circulation models) suggest [Intergovernmental Panel on Climate Change, 2007] that due to so called Arctic amplification [Polyakov et al., 2002; Chylek et al., 2009; Kumar et al., 2010], Arctic warming will proceed faster than the global average. It is often assumed that most of the post 1970 Arctic warming is due to increasing concentration of CO2and other greenhouse gases (GHGs), without taking natural Arctic climate variability into consideration. However, the possibility that a non-negligible fraction of the recent Arctic warming has been caused by a multidecadal cycle of the Arctic climate [Parker et al., 2007; Semenov et al., 2010; Chylek et al., 2010; Polyakov et al., 2010, 2011; Mahajan et al., 2011, 2012] linked to the Atlantic Multidecadal Oscillation (AMO), and to changes in the Atlantic Meridional Overturning Circulation (AMOC), is becoming increasingly likely. In this paper, we analyze annual data from six Arctic ice core δ18O records (as a proxy for temperature variability), each about 660 years long, to determine cycles of Arctic natural (forced or unforced) climate change and its spatial and temporal variability.
 Although the annual δ18O is affected by several environmental factors, it has been generally accepted as a reasonable proxy for temperature. A high correlation between the instrumental era AMO index [Parker et al., 2007] and average ice core δ18O data [Chylek et al., 2011], as well as a good agreement between the paleo AMO [Delworth and Mann, 2000] and δ18O data justifies the use of annual δ18O data as a proxy for AMO periodicity. Greenland temperature reconstructed from trapped air [Kobashi et al., 2011] is also in a good agreement with δ18O deduced temperature data.
 The δ18O data for all six ice cores are available at the NOAA Paleoclimate website. Five of the ice cores have 659 years of a common time span from 1302 to 1961, and this time period is used in the analysis below. The Dye 3 δ18O data ends in 1872, and consequently, for the Dye 3 dataset the selected time period of 659 years will be 1213–1872.
 To obtain latitudinal resolution, we group the ice cores into three regions (Figure 1) denoted as South (Dye 3), Central (GISP2, Milcent, and Crete), and North (Camp Century and Agassiz Ice Cap). The Dye 3 site is closest to the North Atlantic Ocean so the oceanic influence is largest there, while a diminished ocean influence is expected at the more northern locations.
 Since we are interested in periodicities rather than trends, we linearly detrended each δ18O time series and normalized it to a unit variance. We averaged Fast Fourier Transforms (FFT) of individual series to obtain the average FFT for each region. Averaging the FFTs of individual time series (rather than the time series themselves) prevents a possible cancellation of coherent δ18O signals due to timing errors in individual ice cores.
 To remove spurious peaks, the raw periodograms were averaged over several frequencies [Shumway and Stoffer, 2006]. Although the number of frequencies to be averaged cannot be unambiguously determined, a general practice is to average over about L = N/100 resolved frequencies where N is the number of data points in the series.
4. Regional Differences
Figure 1a shows the resulting periodogram for the most northern region (Camp Century and Agassiz Ice Cap). No multidecadal periodicity is observed. The central region (GISP2, Milcent, and Crete) is dominated by a 20 year cycle (Figure 1b) that represents the only statistically significant multidecadal periodicity. Additional power is distributed within a broad band of longer time scales (40 to 70 years) that is, however, not statistically significant. This band contains the 60–70 years cycle which is observed in the 20th century North Atlantic region instrumental data [Schlesinger and Ramankutty, 1994; Delworth and Mann, 2000]. In the southern region (Dye 3 site) the dominant multidecadal periodicity is again ∼20 years (Figure 1c).
 A conceptual ocean model [Frankcombe et al., 2010], as well as AOGCM studies [Zhang, 2008; Dong and Sutton, 2005, Mahajan et al., 2011, 2012] connects a 20-year cycle to changes in the Atlantic Meridional Overturning Circulation (AMOC). Since the 20 year quasi-periodic signal originates in the Atlantic Ocean, it is expected that the signal strength will decrease with the distance from the ocean. A diminishing strength in the northern region is also affected by low snow accumulation rates and smoothing by diffusion processes [Johnsen et al., 2000]. The origin of the 45–65 year cycle is less certain. While conceptual models [Frankcombe et al., 2010; Frankcombe and Dijkstra, 2010, 2011] suggest that this longer scale of the AMO may originate in the Arctic, others have proposed a wider area of the Atlantic as a source region of this longer time scale variability [e.g., Knight et al., 2005].
 We have used control runs of the two AOGCMs (HadCM3 and GFDL CM2.1) to compare the basic features of our ice core analysis with model simulations. In the HadCM3 control run (Figure 2a) we see a shorter periodicity between 20 and 30 years and a longer cycle close to 90 years in both the AMOC (defined as by Knight et al.  and Mahajan et al. ) and the North Atlantic temperature (between 10–70° W and 10–60° N). The GFDL control run suggests periodicities of 19 and 24 years and a longer scale periodicity between 40 and 50 years (Figure 2b). Model surface air temperatures averaged over three regions (Figures 2c and 2d) show a longer scale periodicity appearing at all three regions, in disagreement with the ice core data.
6. Long-Term Changes in Multidecadal Variability
 The longest ice core δ18O record available at an annual resolution is the Dye 3 record which spans the period 1899 BC to 1872 AD. To capture the time variability in our FFT analysis we divide the Dye 3 record into four equal length segments of 983 years and perform the FFT on each segment. The raw periodograms are averaged over L = 9 spectral frequencies.
 The most recent segment (930–1872 AD) confirms the dominance of a 20 year cycle, with slightly elevated power within the longer multidecadal band (Figure 3a). The first millennium AD segment (7 to 930 AD) does not show any multidecadal highly statistically significant periodicity (Figure 3b). During the first millennium BC (956 BC to 7 AD) the only multidecadal periodicity elevated above the noise level is centered close to 32 years, although its significance remains below 80% level (Figure 3c). The earliest segment (1899 BC to 956 BC) is similar to the most recent one (930–1872 AD). Here the 20-year oscillation is significant at the 95% confidence level and the longer timescale oscillation approaches the 80% confidence level (Figure 3d). At all times we see also sub-decadal frequencies possibly related to NAO and ENSO.
 We note a significant difference between the Little Ice Age (LIA) dominated by a 20 year cycle, and Medieval Warm Period with multidecadal cycle between 40 and 50 years (Figures 3e and 3f). We note that the observed shorter time scale during the cold LIA period agrees with recent work [Kobashi et al., 2010] using an independent temperature proxy.
 A wavelet analysis (Figure 3g) confirms the shifts of periodicities over millennia. If the AMO is a damped oscillatory internal ocean mode excited by atmospheric noise [Frankcombe et al., 2010], then large differences in dominant variability time scales are not unexpected.
7. Discussion and Summary
 The regionally and temporally resolved spectral analysis of six Arctic annual ice core δ18O time series points towards a considerable natural spatial and temporal variability of the Greenland climate and one of its driving forces the Atlantic Multidecadal Oscillation (AMO). The most dominant observed quasi-periodicity is that of ∼20 years followed by a longer multidecadal band between 45 and 65 years. The observed intermittency of these modes over the last 4000 years supports the view that these are internal ocean-atmosphere modes, with little or no external forcing. The Little Ice Age was dominated by a ∼20 year AMO cycle with no other decadal or multidecadal variability above the noise level. During the preceding Medieval Warm Period the 20 year cycle was replaced by a longer scale cycle centered near a period of 43 years and an additional ∼11.5 year periodicity.
 The observed large temporal variability of the AMO as captured by the ice core records points to the difficult task of capturing and forecasting these pronounced multidecadal quasi-oscillations in global and regional Arctic climate models for assessing future Arctic climate.
 The reported research (LA-UR-11-11228) was supported in part by the DOE OBER, Climate and Environmental Sciences Division, by the LANL branch of the IGPP, and by the Joint UK DECC/Defra Met Office Hadley Centre Climate Programme (GA01101). We thank Jeff Knight and Salil Mahajan for providing HadCM3 and the GFDL CM2.1 data, respectively, and Louise Sime for helpful comments on early version of this paper.
 The Editor thanks the two anonymous reviewers for assisting in the evaluation of this paper.