3.3. Cycle Periodicity
Spectral analysis of Antarctic paleoclimate records was done previously for the Holocene for the time period from 11,500 ybp to the present [
51]. We extend this analysis here using the more accurate data synchronized on the AICC2012 chronology and including climate records from Vostok, EDC, EDML and TD; [
38,
39]. We evaluate these climate records over broader time spans than previously done, including the Holocene, and over older and longer time periods, to enable detection of a broader complement of cycle periodicities. The resulting spectral power density periodograms show peaks at decadal, centennial, millennial and multi-millennial periodicities (
Figure 2). Spectral peaks occur at similar frequencies in ice-core records from different drill sites (cf.
Figure 2a,b), consistent with the hypothesis that the same temperature cycles manifest at different Antarctic drill sites located on the EAP.
Broadband periodograms covering several hundred millennia exhibit the primary MIS frequency peak at a period of 106–108 Ky, as well as secondary and tertiary peaks of Milankovitch cycles at the orbital obliquity (41 Ky) and precession (21 Ky) cycle periods (
Figure 2a,b), replicating previous results [
36] (cf. our
Figure 2a with Figure 4a in [
36] (p. 432)). Spectral analysis of shorter records shows possible representations of the obliquity orbital cycles in the Talos Dome climate record at 38.3 Ky (
Figure 2c), but corresponding peaks at EDML differ in period by up to 25% and hence their etiology is correspondingly less certain. The spectral periodograms constructed over shorter time periods (
Figure 2c,d) also lack the longer MIS cycle (
Figure 2c,d) as expected, since the time period evaluated is too short to detect it.
Spectral analysis of temperature-proxy records over shorter time periods (narrower frequency bandwidths) were done for the period from ~12,500 to 0 Kyb1950, confirming the results of previous studies [
51]. The Vostok periodogram (
Figure 3) shows six discernible (
p < 0.005) centennial-scale spectral power density peaks ranging from 193 years, near the average period of the ACO across the Holocene, to 1096 years, near the reported millennial period of the Bond cycle in the NH [
17,
18,
19,
20,
21]. Relaxation of confidence limits to 95% (
p < 0.05) adds three discernible spectral peaks at 282, 448 and 580 years which however we do not consider further here owing to the possible exaggeration of precision in the mathematical method used to compute the confidence limits (Methods). These findings confirm previous evidence of multiple centennial peaks over the Holocene [
51] (cf.
Figure 3 here with their Figure 6, p. 356) and they are reminiscent of multiple discernible spectral peaks recorded in climate records from the NH, e.g., [
23].
Periodograms of the remaining three AICC2012 climate records during the Holocene are similar to the periodogram of the Vostok record (
Figure 4). All are bounded near the low end by a peak corresponding approximately to the mean period of the TO
C350V cycles and near the high end by a peak corresponding to the Bond cycle in the NH and ranging from 825 to 1027 years. Between these extremes lie at least four additional centennial-scale peaks in all AICC2012 climate records evaluated.
The periods of these peaks coincide closely with the six discernible (
p < 0.005) spectral peaks identified in the Vostok climate record (adjacent arrows in
Figure 4 demarcated by ovals). The difference between the closest corresponding peaks in other records was computed in both relative terms (positive and negative signs included) and, more conservatively, in absolute terms (signs omitted). The mean (
n = 6) relative and absolute differences, respectively, between the frequency of Vostok and non-Vostok spectral peaks (
Figure 4) are 1.0% and 5.8% (Vostok
versus EDC;
Figure 4a), −1.5% and 3.8% (Vostok
versus TD;
Figure 4b), and −0.7% and 4.7% (Vostok
versus EDML;
Figure 4c). Homologous spectral peaks at different drill sites therefore match each other on average within ±0.2% (relative difference) or ±2.4% (absolute difference).
Most but not all matching spectral peaks at EDC, TD and EDML are as distinct as the corresponding peaks in the Vostok record (
Figure 4). For example, peak 6 at Vostok with a period of 1096 years, which may be analogous with the Bond cycle in the NH (the TO
K1500V cycle), is matched with a comparable peak at 1050 years in the TD record. We did not assess the statistical discernibility of non-Vostok spectral peaks and have no explanation for the occasional apparent differences in relative spectral density energy of peaks that are otherwise matched in period. The findings nonetheless support overall the hypothesis that the same temperature-proxy cycles manifest at geographically-distributed EAP drill sites.
Spectral power periodograms of non-stationary time series can be ambiguous in the frequency domain inasmuch as the changing frequency of any variable climate cycle can broaden (“smear”) a spectral power peak, rendering it less distinct. Additionally, in the event of discrete frequency shifts in the underlying reference signal, power periodograms can manifest distinct spectral peaks even when they originate from the same, variable (non-stationary) climate cycle. We therefore conservatively sought additional confirmatory evidence for nonrandom periodicity in the time domain of Antarctic climate records in the form of lagged or serial autocorrelation correlelograms. We generated correlelograms over relatively short time frames of the Vostok record dated on the GT4 chronology, including from 75 to 55 Kyb1950, 20 to ten Kyb1950, and ten to 0.149 Kyb1950. The GT4 chronology for Vostok differs only slightly from the AICC2012 chronology over time periods analyzed here, as demonstrated by the near-identity of the respective age models over the time period studied here (
SM Figure S3).
The null hypothesis that TO
C350V cycles comprise random variation in cycle structure was tested by means of cyclic autocorrelation coefficients. We find that autocorrelation coefficients alternate between positive and negative at the same periodicity as the corresponding TO
C350V cycle frequency (
Figure 5). Near peaks and troughs, nearly all of these autocorrelation coefficients are discernibly different from zero at low alpha levels (at least at
p < 0.05). These autocorrelation results supplement and extend spectral periodograms to confirm that TO
C350V cycles comprise nonrandom periodic sequences. Such positive autocorrelation results would not be possible unless the short time series evaluated represent relatively stationary time series over the time periods evaluated.
3.4. Geographic Distribution of ACOs
The demonstration of similar spectral density periodograms at different drill sites on the East Antarctic Plateau suggests that TO
C350V cycles are common to all four ice-core records evaluated here. We tested this hypothesis more directly by examining individual TO
C350V cycles using the identical approach pioneered by previous investigators, namely evaluation of cycle waveform and sequence (Methods). Three of the four AICC2012-synchronized Antarctic climate records over the period 70 to 63 Kyb1950 were sampled originally at a high enough frequency to detect centennial-scale temperature-proxy oscillations in compliance with the Nyquist-Shannon sampling-frequency criterion: Vostok, the nearby (~550 km) and slightly lower-elevation (~248 m) EDC, and the more distant (~2300 km) and still lower-elevation (~596 m) EDML (
Figure 6) (distances between drill sites and elevations are from [
51]).
The time period from 70 to 63 Kyb1950 encompasses two well-studied climate events, Antarctic Isotope Maximum (AIM)
# 19 and AIM
# 18 [
38], which were formerly designated as AIM
# 5 and AIM
# 4 [
40], respectively. These AIMs precede D-O events
# 19 and
# 18, respectively, in Greenland ice cores from the NH, with south-to-north propagation latencies of 1.5 to 3.0 millennia [
38,
40,
49,
52]. Examination of individual TO
C350V cycles shows that AIM
# 19 is composed of multiple TO
C350V cycles, identified as ACO 195a, 195 and 194, while AIM
# 18 is composed of TO
C350V cycles 186–181. These identified TO
C350V cycles are recognizable across the three climate records compared (grey dashed connector lines in
Figure 6), consistent with the hypothesis that TO
C350V cycles are distributed geographically across the EAP to at least these three drill sites.
The identified TO
C350V cycles that compose AIM
# 19 and AIM
# 18 do not occur at the same time in different climate records, i.e., the homologous cycles at one drill site are shifted forward or backward in time relative to other drill sites when displayed on a common chronology (
Figure 6). For example, mean peak-to-peak latencies from Vostok to EDC over ten homologous cycles that encompass AIM
# 19 (cycles 195a-190) was computed as −158.5 years. The negative sign implies that Vostok peaks lag homologous peaks at EDC. Similarly, peaks of the ten TO
C350V cycles associated with AIM
# 18, 186a-178 are asynchronous, occurring at a mean time latency from Vostok to EDC of −211.2 years (Vostok lags). In both of these examples, however, the mean latency is smaller than the reported dating uncertainty for this portion of the respective climate records [
38] and therefore in these examples the observed difference in latencies cannot be distinguished from chronological noise or dating uncertainty.
In contrast to these examples, the mean latency between the peaks of homologous TO
C350V cycles from Vostok to EDML for cycles 195a-190 is −335.1 years (Vostok lags EDML), while the mean latency between homologous cycles 186a-178 is −557.7 years (
Figure 6a). These means are discernibly greater than the corresponding mean latencies between Vostok and EDC (
t-test,
p < 0.0006,
n = 10). The Vostok-to-EDML mean latency also exceeds the sum of the decadal variance that arises from averaging and the estimated dating uncertainty for this glacial period, which is 500 years [
38] (p. 1737). These latency differences from Vostok to EDML cannot, therefore, be attributed to dating uncertainty. Instead, the differences in latency between homologous cycles at different drill sites are genuine (non-artifactual) climate signals.
The corresponding mean peak-to-peak latency from EDC to EDML between homologous cycles 195a-190 is −176.6 years (EDC lags), discernibly smaller than the mean latency from Vostok to EDML of −335.1 years (
t-test,
p < 0.0009,
n = 9). For cycles 186a-178, the comparable mean homologous peak-to-peak latencies are −322.6 years (EDC to EML) and −557.6 years (Vostok to EDML), discernibly different from each other (
t-test,
p < 0.0006,
n = 10). Chronological uncertainty reported for this period of the AICC2012 chronology is from 20 to 100 years [
38] (p. 1737). The measured differences in mean latencies are therefore not only discernible with high probability but again exceed the dating uncertainty of the AICC2012 chronology, in these examples by a factor up to >30. Comparing Vostok-to-EDC latency with EDC-to-EDML latency yields non-discernible differences for cycles 195a-190 (
p > 0.66) and cycles 186a-178 (
p > 0.13). In both cases the corresponding mean latencies nonetheless exceed reported chronological uncertainty.
The century-scale and discernible differences in peak time latencies across different climate records therefore signify that within the limits of chronological uncertainty, homologous TO
C350V climate cycles arrive at different times at the four drill sites analyzed. Homologous cycles appear first at the lowest drill site nearest the ocean (EDML) and centuries later on the high EAP at Vostok and EDC. The latency between sites exceeds the duration of individual cycles and yet the characteristics and sequences of TO
C350V cycles are retained across climate records as they propagate from drill stations close to the ocean to more distant sites high on the EAP. Although the expansion and contraction of the probably-homologous Antarctic Oscillation (AAO; see below) comprises a standing wave, its cyclic variation imparts apparent movement that is reflected here as changes in latencies between homologous ACO cycles at different drill sites. Retention of the internal architecture of ACO cycles and their sequences as the cycles propagate over time and space reflects a “memory” in the Antarctic climate system at least a few centuries in duration. The differences in latencies of TO
C350V cycles identified here parallel and corroborate the timing differences reported between major climate events in Antarctica identified from methane-synchronized Antarctic climate records [
53,
54].
To enable a more direct visual comparison of relative waveforms, amplitudes and timing of homologous ACOs, the corresponding temperature-proxy records were shifted in time by the mean latency between peaks so that they appear in artificial temporal register (
Figure 6b–d). Waveforms and relative amplitudes of homologous TO
C350V cycles appear qualitatively most similar between Vostok and nearby EDC, although comparisons across drill sites separated by greater distances and elevations also often show similar waveforms and relative amplitudes. Smaller-amplitude cycles in one climate record invariably manifest as larger-amplitude cycles in one or more other records, e.g., cycles 193a and 184 at Vostok and cycles 189a and 183 at EDC (
Figure 6c,d, respectively). This finding, repeated across all time frames evaluated in this study (not shown), establishes the requirement to include the smallest temperature oscillations under cycle definition 3 (Methods). Waveform matching is 1:1 not only for homologous signpost cycles (
Figure 6a,c) but also for homologous non-signpost cycles (
Figure 6b).
Spectral analysis of the time period from 70 to 63 Kyb1950 across a narrower (centennial) bandwidth reveals the same spectral density structure seen above in similar records over comparable time periods of the Holocene. That is, the periodogram is bounded near the high-frequency (short-period) end of the spectrum by a centennial-scale peak of approximately the same period as mean TO
C350V cycles and on the low-frequency (long-period) end by a long-period cycle of 1471 years (
Figure 7). Both of these periods are larger than the corresponding values in more recent time periods, however (cf.
Figure 7 with
Figure 3 and
Figure 4), suggesting that the period of the millennial cycles identified here declines over time, as confirmed more directly below from individual ACO cycles in the time domain. The spectral peak at 1471 y shows nearly the same periodicity as the reported 1470-year period of Bond events in the NH ([
17,
18,
19,
20,
21], but see [
22,
23]). This cycle is designated here as the TO
K1500V cycle using the climate-cycle nomenclature modified here from Wunsch [
42].
Decomposition of the millennial-scale cycle from the original temperature-proxy time series data (
Figure 6a) reveals a characteristic temporal pattern in the sequence of TO
C350V cycles that underlies a stereotypic architecture of the TO
K1500V cycle. This pattern consists of a largely-monotonic increase over several centuries in the amplitude and frequency of successive TO
C350V cycles culminating at the end of each such sequence in a single extreme warming peak followed by a single extreme cooling trough. This stereotypical pattern of TO
C350V cycle trains is evident in the internal temperature-proxy structure of AIM
# 19 and AIM
# 18 (
Figure 6a) and throughout the 226.4 Ky period studied here (not shown) including the Holocene (see below). These observations suggest that AIMs are formed by the periodic (millennial-scale) algebraic summation of sequences of high-frequency TO
C350V cycles of which they are composed.
The hypothesis that TO
C350V and TO
K1500V cycles at Vostok comprise more widely-dispersed Antarctic climate signals was evaluated more directly by tracking single, identifiable signpost centennial cycles across the four AICC2012-synchronized climate records over the last 21 millennia (
Figure 8). During the LGM and the start of the LGT (
Figure 8a), TO
C350V signpost cycles include those that occur at the beginning of termination from 18,677 yb1950 (TD) to 18,364 yb1950 (EDC), namely, cycles 74–69. These signpost cycles appear near the time of the onset of the LGT at 18,934 yb1950, as estimated independently from observed sea level minima (19,000 ybp ± 250) [
55], and are matched one-to-one across all four AICC2012-synchronized climate records (gray dashed connector lines in
Figure 8a). Additional TO
C350V signpost cycles associated with the ACR from 14,872 (TD) to 14,456 (Vostok) yb1950, including cycles # 64–62 at the onset of the ACR (
Figure 8a), are among the most recognizable TO
C350V signpost cycles identified in this study.
Peak-to-peak latencies between homologous cycles at different drill sites from 21 to 14 Kyb1950 (
Figure 8a) follow a different pattern from those described above for the older time period of 70 to 63 Kyb1950 (
Figure 6a and
Figure 8a). Prior to the LGT (
Figure 8a), latencies from TO
C350V cycle peaks at Vostok to homologous peaks at EDC are near zero or weakly positive. Latencies from Vostok ACOs to homologs at EDML and especially TD are strongly negative, i.e., Vostok lags. After the LGT begins, however, latencies from Vostok to EDC remain near zero or weakly negative while latencies from Vostok to EDML and especially from Vostok to TD shift toward positive (
Figure 8a), i.e., Vostok tends to lead. These latency shifts manifest within a few centuries following the onset of glacial termination. The latency shifts are not ascribable to dating uncertainties across these records, which they exceed by up to more than an order of magnitude as noted above. TO
C350V cycle latencies between different drill sites are therefore variable and reversible on relatively short geologic time scales. These results suggest that glacial termination and the associated increase in temperature transiently synchronized TO
C350V peaks across the four AICC2012-synchronized climate records. Cycle coherency, i.e., the percent of identified centennial cycles that are matched 1:1 with homologs in this time frame across all cycles, exceeds 99%. Systematic changes in the latencies between homologous cycles at different drill sites are significant in part because they may bear upon the method of teleconnection between the different drill sites (see below).
Similar analysis of the time period from 15 to 9 Kyb1950 (
Figure 8b) shows that signpost TO
C350V cycles are matched 1:1 across all four climate records. The most recognizable signpost TO
C350V cycles in this time period occur at the beginning and end of the ACR, namely TO
C350V cycles # 63-61a and cycles # 56–51, respectively. TO
C350V cycle # 55 demarcates the end of the LGT and the start of the Holocene across all four climate records evaluated and is the single most recognizable TO
C350V signpost cycle identified in this study. All remaining non-signpost TO
C350V cycles in the Vostok record can also be matched with putative homologs in the other records. Cycle coherency across all cycles in all records is 98.3%, i.e., most centennial-scale cycles in the Vostok record, including both signpost and non-signpost cycles, are matched 1:1 with homologous cycles in the three AICC2012 records, and conversely.
The relative timing of TO
C350V cycle peaks over this time period (
Figure 8b) shows that Vostok typically lags the other three drill sites and that peak-to-peak latencies generally exceed dating uncertainty. For example, TO
C350V signpost cycle # 62 at Vostok lags its homolog at EDC by 139 years, EDML by 230 years, and TD by 427 years. All three latencies exceed the ten-to-200-year dating uncertainty reported for this time frame [
38] (p. 1737) and are larger by up to two orders of magnitude than the decadal variance associated with averaging. Therefore TO
C350V cycles # 62 and # 55 occur earlier at TD and EDML than the homologous TO
C350V cycles at Vostok and this time difference is genuine rather than artifactual.
The time lag between homologous TO
C350V cycle peaks from TD to Vostok is equivalent to at least two TO
C350V cycles, implying retention in the climate system of information about the relative amplitude, waveform and sequence of TO
C350V cycle # 62 as this climate signal propagates from TD to Vostok over hundreds of years and thousands of kilometers. These latency differences between the four AICC2012 sites, particularly TD and Vostok, persist throughout this six-Ky period and increase to 750 years, equivalent to from three to four complete TO
C350V cycles at the cycle frequency that prevails over this time period. This latency exceeds the corresponding 200-year dating uncertainty and exceeds the uncertainty estimated for comparisons between TD and Vostok of 20–100 years [
38] (p. 1737) by a factor of up to 37.5. These findings therefore further exemplify the aforementioned “climate memory”, which is expressed as the conservation of TO
C350V sequences and cycle parameters across multiple TO
C350V cycles and across distances of thousands of kilometers.
The time period from ten to five Kyb1950 (
Figure 8c) encompassing the early Holocene shows a different pattern from the earlier time periods analyzed. During the early Holocene, the latencies between homologous TO
C350V peaks approach zero across the four AICC2012 climate records. The peak-to-peak latency from TD to Vostok reverses for several cycles starting at approximately eight Kybp, when TO
C350V peaks at TD follow corresponding peaks at Vostok. This reversal entails changes in peak-to-peak latencies of up to a few hundred years, which exceed by more than an order of magnitude the summed variance of dating uncertainty (ten to 100 years) and averaging noise (decadal). During this period, the Holocene Climate Optimum, temperature is greater than at any other time analyzed in this study and peak latencies across sites shifts from negative to positive (Vostok leads). These results illustrate that the latencies at different drill sites shift from synchrony to reversal during the warmest climate studied here, the early Holocene. Cycle coherency over the time frame from ten to five Kyb1950 including both signpost and non-signpost cycles is 98.0% (
Figure 8c).
The most recent Holocene (
Figure 8d) is characterized by four millennial-scale (TO
K1500V) cycles culminating in temperature maxima followed immediately by temperature minima (e.g., TO
C350V cycles # 24, 18, 13 and 4). These cycles are evident to variable degrees across all four of the AICC2012-synchronized climate records (
Figure 8d). In contrast to the pre-Holocene and early Holocene, however, the TO
C350V cycle peaks occur nearly simultaneously at different drill sites, i.e., the mean peak-to-peak latencies between identified TO
C350V cycles at different drill sites approach zero. The reversal of latencies seen in the early Holocene (i.e., the shift from Vostok-lags to Vostok-leads) is absent, particularly for the most recent two millennia of the Holocene. Corresponding peak-to-peak latencies are less than the summed variance of averaging and chronological uncertainty. The warmest portion of the paleoclimate record analyzed here is, therefore, also characterized by the closest synchrony of homologous TO
C350V cycles, which may provide clues about the mechanism of regional propagation of the ACO as discussed below. Cycle coherency over the recent Holocene is 100% across all cycles, signpost and non-signpost (
Figure 8d).