During the last glacial period, the North Atlantic region experienced a series of Dansgaard–Oeschger cycles in which climate abruptly alternated between warm and cold periods. Corresponding variations in Antarctic surface temperature were out of phase with their Northern Hemisphere counterparts. The temperature relationship between the hemispheres is commonly attributed to an interhemispheric redistribution of heat by the ocean overturning circulation. Changes in ocean heat transport should be accompanied by changes in atmospheric circulation to satisfy global energy budget constraints. Although changes in tropical atmospheric circulation linked to abrupt events in the Northern Hemisphere are well documented, evidence for predicted changes in the Southern Hemisphere’s atmospheric circulation during Dansgaard–Oeschger cycles is lacking. Here we use a high-resolution deuterium-excess record from West Antarctica to show that the latitude of the mean moisture source for Antarctic precipitation changed in phase with abrupt shifts in Northern Hemisphere climate, and significantly before Antarctic temperature change. This provides direct evidence that Southern Hemisphere mid-latitude storm tracks shifted within decades of abrupt changes in the North Atlantic, in parallel with meridional migrations of the intertropical convergence zone. We conclude that both oceanic and atmospheric processes, operating on different timescales, link the hemispheres during abrupt climate change.
Dansgaard–Oeschger (DO) events in the Northern Hemisphere (NH)1,2 and Antarctic isotope maximum (AIM) events in the Southern Hemisphere (SH) are coupled by variations in meridional oceanic heat transport. The large effective heat capacity of the SH oceans integrates the abrupt changes in oceanic heat transport3, leading to the muted, out-of-phase character of Antarctic temperature variations4. The Antarctic temperature response systematically lags abrupt DO transitions by about two centuries, a timescale consistent with oceanic processes5.
To satisfy the top-of-atmosphere energy budget, interhemispheric oceanic heat flux anomalies must be accommodated by opposing changes in atmospheric heat transport6 or changes in local radiative processes. While atmospheric models do not necessarily agree on the relative roles of these mechanisms, some responses are robust, such as migration of the Hadley circulation and intertropical convergence zone (ITCZ) toward the warmer hemisphere6,7. Recent studies suggest that ITCZ migration can influence the position of the SH eddy-driven jet and surface westerlies8,9. The SH mid-latitude westerlies are a key component of the global climate, transporting heat and momentum toward the pole and influencing Southern Ocean wind-driven upwelling10 and ocean–atmospheric CO2 exchange11. Evidence for abrupt changes in tropical circulation and precipitation, synchronous with NH DO events, comes from sediment cores12,13,14 and speleothem records15. In contrast, evidence for corresponding millennial-scale changes in the dynamics or meridional position of the SH westerlies is wanting16.
New constraints from ice core records
Here, we use deuterium-excess data from the West Antarctic ice sheet (WAIS) Divide ice core (WDC) to constrain changes in SH atmospheric circulation during DO events. Deuterium excess (dexcess = δD − 8 × δ18O) of vapour quantifies kinetic fractionation processes and is sensitive to sea surface temperature (SST) and relative humidity at the site of evaporation17. Variability in the SST-normalized humidity, the critical moisture source condition driving kinetic fractionation17, is probably dominated by changes in SST on millennial timescales, although relative humidity may also be important (Supplementary Information). The dexcess is also directly affected by SST through the temperature dependence of fractionation at evaporation17. The dexcess of polar precipitation reflects the weighted-mean evaporative conditions of moisture sources, whose spatial distribution is sensitive to changes in atmospheric circulation.
Interpretation of Antarctic dexcess records has been hampered by the absence of a coherent signal among Antarctic cores18,19 (Fig. 1a). We find that the lack of coherence is largely an artefact of the linear definition of dexcess. Equilibrium fractionation alone leads to a nonlinear relationship between δD and δ18O (ref. 20) that is most evident at the very depleted values in East Antarctic precipitation (Supplementary Information). We instead use a logarithmic definition21 for the parameter, dln = ln(δD + 1) − (8.47 ln(δ18O + 1) − 2.85 × 10−2(ln(δ18O + 1))2), which better represents the underlying distillation physics and is a more faithful proxy for moisture source variability (Supplementary Information). While conventionally defined East Antarctic dexcess records from EPICA Dronning Maud Land (EDML) and EPICA Dome C (EDC)18 show no significant coherence with WDC dexcess at any timescale, the logarithmically defined dln records from all three cores are significantly coherent with each other at all periods greater than 3,000 years (Fig. 1). Degradation of coherence at shorter timescales is expected due to chronological uncertainties. Equilibrium fractionation biases, rather than spatial asymmetries in the climate, clearly dominate the differences among linearly defined dexcess records, while the dln records reveal a coherent signal.
Analysis of millennial-scale variability
We compare high-resolution WDC dln with WDC atmospheric methane (CH4) concentrations and with WDC δ18O, a proxy for site temperature (Fig. 2). Global CH4 variations are in phase with Greenland temperature within a few decades22 and are thought to reflect changes in tropical precipitation and temperature associated with the north–south migration of the ITCZ during DO events15,22, thus serving as an indicator for shifts in tropical circulation5. We compare these records (Fig. 2) to establish the phasing between changes in Antarctic moisture sources and SH, tropical and NH climate during DO events. The WDC records are uniquely suited for this purpose owing to the small and well-constrained gas age–ice age difference (Δage)5. The Δage is calculated continuously through the core and is 351 ± 73 years (2σ) at 40 thousand years ago (ka), a value representative of the last glacial period23.
The dln records from WDC, EDC and EDML on average show gradual millennial-scale variability in phase with the AIM events seen in Antarctic δ18O records (Fig. 1b). However, WDC dln also exhibits variability that tracks CH4 through the DO cycles (Fig. 2). Since the subjective appearance of individual events may be confounded by noise inherent to the proxies and the physical systems they record, we use objective techniques to quantify these relationships across all events.
We first evaluate the WDC data using a multitaper coherency and phase analysis (Methods). The WDC δ18O, dln and CH4 records are all significantly coherent with one another across millennial timescales. The WDC δ18O and CH4 records have a phase relationship of ∼90° at millennial timescales, reflecting integration of the NH DO events by SH climate, and a ∼200 year lag of WDC δ18O behind CH4. The millennial variability in dln is coherent with both δ18O and CH4 at phase angles between 0° (in phase) and 90°, consistent with a signal that contains both DO and AIM modes of variability. Indeed, a simple linear combination of the WDC δ18O and CH4 signals is coherent and in phase with WDC dln at all timescales and is a significantly better predictor of dln than either δ18O or CH4 individually. Together, the CH4 and δ18O signals explain 62% of all variance in dln and more than 85% of the variance at relevant timescales (those longer than 500 years).
Next, to investigate the character of DO-like variability recorded in WDC dln, we construct composites of the dln record during abrupt NH warming and cooling events. We use the stacking procedure described in ref. 5, in which all individual events in all WDC proxies are aligned at the midpoints of the abrupt CH4 transitions and averaged to obtain a composite event; this allows direct comparison with DO events from the North Greenland Ice Core Project (NGRIP) δ18O record from Greenland24 and reduces the noise inherent to any single event. We use objective algorithms25 to determine the timing of significant change in the WDC dln, NGRIP δ18O, WDC CH4 and WDC δ18O composites (Methods).
We find that the composite dln response at the timing of DO warming and cooling events is step-like and occurs within decades (synchronous within uncertainty) of NH (NGRIP δ18O) and tropical (CH4) step changes. The initial change points in the DO warming event stacks of NGRIP δ18O, WDC CH4, and WDC dln occur at −27 ± 5 years (1σ), 18 ± 14 years, and 45 ± 83 years, respectively, with the timing given relative to the midpoint of the NGRIP δ18O abrupt changes (Fig. 3; see Methods for a full description of uncertainties). For DO cooling events, the initial change points in the NGRIP δ18O, WDC CH4, and WDC dln stacks occur at −36 ± 7 years, −24 ± 14 years, and −27 ± 70 years, respectively. In both cases, the change point in WDC dln occurs significantly before the change point in WDC δ18O; dln leads δ18O by 173 ± 79 years for DO warming, and 235 ± 64 years for DO cooling.
To elucidate the sources of WDC dln variability, we review the processes thought to communicate climate signals between the hemispheres during DO and AIM events. First, variations in northward heat transport by the ocean warm one hemisphere at the expense of the other4. The surface temperature response to heating changes in the North Atlantic is abrupt, driving the DO signal. Second, the Southern Ocean integrates the changes in northward heat transport, resulting in the gradual, out-of-phase variations in Southern Ocean and Antarctic temperature3: the AIM signal. There is a discrete ∼200 year lag between the abrupt DO events and the transition between warming and cooling of the AIM events, probably reflecting an oceanic transport timescale5. Third, the thermal asymmetry between the hemispheres drives a fast (≤decadal) atmospheric response in which the ITCZ migrates toward the warmer hemisphere6. Fourth, a related atmospheric teleconnection links migration of the ITCZ to shifts in the meridional position of the storm tracks in the Southern Hemisphere8. This teleconnection would link the position of the Southern winds to events in the tropics and high NH latitudes on short atmospheric timescales, despite gradual and lagged changes in mean SH temperatures.
A simple framework reconciles the combined AIM-like and DO-like signals in WDC dln in light of the above processes. Variability in dln represents the superposition of two primary mechanisms: changes in moisture source conditions at fixed locations and changes in the spatial distribution of moisture sources for an ice core site. In short, the spatial–temporal pattern of SSTs is weighted by the spatial–temporal pattern of the moisture source distribution (MSD) (Fig. 4). In the zonal mean, and given a linear SST–dln scaling, dln(t) ∝ ∫ MSD(φ, t)SST(φ, t)dφ + ν, where φ and t denote dependence on latitude and time, and ν denotes other sources of variability.
Owing to the first and second processes above, changes in Southern Ocean heat content are thought to drive the gradual Antarctic surface temperature variability of AIM events3 via changes in Southern Ocean SSTs26. Southern Hemisphere SST(t) within the moisture source thus drives AIM-like variations in Antarctic dln (Fig. 4), accounting for the gradual variability observed in the WDC, EDML and EDC records.
A large equator-to-pole gradient dominates the spatial pattern of SST(φ) in the SH (Fig. 4). Meridional shifts in the mean location of the moisture source, toward more equatorward or more poleward surface waters, change the sampled mean SST at evaporation due to the steep underlying gradient. Changes in MSD(φ) can therefore change the dln at an ice core site, independent of any temporal variability in the SSTs themselves. General circulation model simulations (Supplementary Information) show that the latitudinal distribution of moisture sources for WAIS Divide change in parallel with the meridional position of the SH westerly winds and ITCZ, changing the sampled SST and dln of precipitation (Fig. 4).
The atmospheric teleconnections predicted during abrupt climate change, the third and fourth processes described above, are recorded in the WDC dln shifts that occur synchronously with NH DO events (Fig. 3). An abrupt DO event shifts the position of the tropical Hadley cell, causing a parallel shift in the SH surface westerlies and storm tracks in the Pacific sector8,9, changing the moisture origin for West Antarctica. Thus, abrupt changes in moisture source location superimposed on gradual changes in moisture source temperatures lead to the observed combination of DO-like and AIM-like variability in WDC dln (Fig. 4).
We calculate the scaling of dln variations to source-region SSTs in a simple distillation model and an isotope-enabled general circulation model (Supplementary Information). SH SST changes on the order of 1–2 K, in phase with the AIM events, and meridional MSD shifts of 1°–2° latitude, in phase with DO events, together account for the bulk of observed variability in WDC dln (Fig. 4). Southern Ocean SST changes of this magnitude are in line with independent estimates from sediment cores26. The required MSD shifts are comparable to those associated with westerly wind displacement at the 1–1.5σ level of interannual variability, amounting to 15–20% anomalies in surface winds (Supplementary Information). Storm track shifts of this magnitude during DO events are in good agreement with estimates of ITCZ displacement from proxy data27 and the modelled relationship between the ITCZ and the SH circulation8. Our results are supported by previous modelling showing anti-correlation between Antarctic deuterium excess and the Southern Annular Mode index28.
Did the atmospheric circulation shift zonally across the entire SH during DO events8, or were changes limited to the Pacific sector (ref. 9)? East Antarctic records may inform this question. EDC dln shows variability during DO 8 and 12 out of phase with local δ18O (ref. 19) and similar to WDC (Supplementary Information). However, unambiguous characterization of the variability in East Antarctic dln records is currently hampered by uncertainties in East Antarctica Δage, and the lack of synchronization between the WD201423 and AICC201229 age scales.
Our new data from WDC demonstrate the importance of both oceanic and atmospheric teleconnections linking the climate of the Northern and Southern hemispheres on millennial timescales. SH SSTs followed the temporal signature of the AIM events, driven by oceanic heat transport changes. SH winds shifted in phase with the NH DO events, reflecting coupled changes in global atmospheric circulation. These atmospheric teleconnections were rapid, shifting the position of the moisture source locations for WDC (recorded in dln) within decades of NH DO events and about two centuries before significant Antarctic temperature change (recorded in δ18O). Our findings complement evidence for atmospheric-circulation-imposed variability in Greenland deuterium excess30. Atmospheric dynamics link the tropical Hadley circulation to the mid-latitude storm tracks in both hemispheres. A global ‘atmospheric seesaw’ is superimposed on the classic oceanic bipolar seesaw, and may be important to the dynamics of millennial climate change.
Water 18O/16O and 2H/1H composition (expressed as δ18O and δD, respectively) were measured at IsoLab, University of Washington, Seattle, Washington, USA. Measurement techniques are described in refs 31,32. Measurements were made at 0.5 m depth averaged resolution, using laser spectroscopy (Picarro L2120-i analyzer). Data are reported relative to the VSMOW (Vienna Standard Mean Ocean Water) standard, and normalized to SLAP (Standard Light Antarctic Precipitation, δ18O = −55.5 ‰, δD = −428 ‰ relative to VSMOW). Measurement resolution is generally better than 40 years per sample for the 67 kyr record, with a mean temporal resolution of 17.2 years per sample between 10–67 ka. Measurement uncertainties are better than 0.08‰ for δ18O and 0.8‰ for δD.
Atmospheric methane concentrations were measured on discrete samples at Pennsylvania State University (0–67 ka, 0.5–2 m resolution). Air was extracted from ∼50 g ice samples using a melt–refreeze technique, and analysed on a gas chromatograph with a flame-ionization detector. Corrections for gas solubility, blank and gravitational enrichment are described in ref. 32.
Dansgaard–Oeschger event compositing.
The stacking procedure used in this study is identical to that used in ref. 5. The reader is referred to that study for a complete description of the method and its uncertainties. We summarize and describe additions here. The midpoint of each abrupt DO transition in NGRIP δ18O and WDC CH4 is identified following ref. 23 and used as a tie point for each DO/AIM event. A time vector, t, is defined from −1,200 years to 1,200 years with 1-year spacing. For each DO/AIM event, the NGRIP δ18O and WDC CH4, δ18O and dln data are linearly interpolated onto time vector t. The midpoints of each DO transition in NGRIP δ18O are fixed to time t = 0 years, and WDC CH4 midpoint at time t = 56 years, which is the average lag of atmospheric CH4 behind Greenland δ18O as identified by ref. 22. The relative timing of the WDC isotope records to WDC CH4 are linked by the small and relatively well-constrained gas age–ice age difference (Δage) of the WAIS Divide core23. All DO/AIM events are then stacked and averaged creating a composite DO/AIM event for each proxy. Our results are robust to the set of events composited, for example, the dropping of random events from the composite and the exclusion of large or small events.
Before stacking, we filter the WDC dln record to reduce noise. WDC dln has power at millennial frequencies comparable to that in WDC CH4 and δ18O as well as high-frequency noise unrelated to the millennial variability of interest here. We wish to reduce high-frequency noise due to measurement, which is normally distributed in the depth domain. We apply a 1-2-1 filter to the raw dln data on the measured depth scale, which is a tapered weighting function similar to a 3-point moving average but twice the weight is given to the central point. Its response function has a relatively sharp frequency cutoff and is never negative (unlike moving averages); thus, no phase shifting of the data occurs. Below, we assess the influence of this light filtering on change point detection.
Breakpoint determination and uncertainties.
The stacking procedure demonstrates the average response of dln to abrupt DO transitions and quantifies lags. To objectively identify change points in the composites we use the RAMPFIT25 and BREAKFIT33 algorithms. The use of a modified BREAKFIT change point detection on the WDC δ18O is discussed extensively in ref. 5. RAMPFIT is better suited to this study than BREAKFIT, due to the ramp-like shape of the dln, CH4 and NGRIP δ18O composites, although results from both algorithms are comparable (discussed below) and do not affect the conclusions of this study. RAMPFIT has been used previously to detect abrupt change in deuterium-excess records34. The RAMPFIT algorithm fits a ramp function, consisting of three linear sections and two break points (t1 and t2), to the data in a least-squares sense. We let the algorithm search for the initial breakpoint, t1, within the bounds −200 to 200 years, and the second break point, t2, within the bounds −100 to 350 years on the WDC dln composite (recall that the midpoint of the DO transition in NGRIP δ18O is defined at t = 0 years, and the WDC CH4 midpoint at time t = 56 years). The algorithm finds the best-fit ramp function defined by the mean of the ‘before’ and ‘after’ line segments, the duration of the ramp, and the timing of t1 and t2. The algorithm uses a Monte Carlo moving block bootstrap (MBB) technique33 to address uncertainty in the identification of the breakpoints. We report the mean and standard deviation of the initial breakpoint, t1, as the timing of initial dln change.
We investigate the influence of the choice of smoothing filter applied to the raw dln record prior to the stacking procedure. We evaluate three different types of smoothing: a 1-2-1 filter; a 1-1-1 filter, that is, a 3-point symmetrically applied moving average; no filtering. The results are summarized in Supplementary Table 1 and shown in Supplementary Fig. 1. The choice of filter slightly influences the mean timing of the change points as detected by RAMPFIT, but in all cases the initial change points, t1, are in agreement within uncertainty. Further, in all cases t1 is synchronous with the initiation of abrupt change in WDC CH4 within uncertainty.
In the stacking procedure, the individual events in all proxies from WDC are aligned at the midpoint of the WDC CH4 transitions. However, the exact alignment of events is subject to uncertainty. We perform a Monte Carlo sensitivity analysis (1,000 realizations) in which random perturbations in timing are applied to the individual dln events that make up the dln stacks, following ref. 5. These timing uncertainties are discussed in detail in ref. 5. We use the non-systematic errors from that study, which include uncertainty in determining the midpoint of the abrupt shifts in both NGRIP δ18O and WDC CH4; variability in the stated 56 yr lag of WDC CH4 behind shifts in NGRIP δ18O; and non-systematic errors related to the age-scale construction5,23. Random timing errors within the stated uncertainties of ref. 5 are applied to the unfiltered, individual dln events. The events are stacked as above and 1,000 realizations are averaged. The resulting composite has a very high signal-to-noise ratio, as uncorrelated variations are heavily reduced. The RAMPFIT routine was performed on the resulting composite dln response, yielding an initial dln breakpoint at t1 = 51 ± 33 yr and t1 = −35 ± 36 yr for the DO warming and cooling phases, respectively. Our results are thus robust to timescale uncertainties.
An important source of uncertainty in the timing of the breakpoint relative to the abrupt DO transitions is the gas age–ice age difference (Δage). An extensive analysis of this uncertainty is presented in ref. 5. As the δ18O and dln are measured on the same ice, the 2σ uncertainty bound of 69 years due to Δage, found by ref. 5, is applicable to the dln composite as well. However, the relative timings of breakpoints in the WDC δ18O and dln stacks are not subject to any uncertainty associated with Δage, since they are measured on the same ice samples. Thus, our claim that the breakpoint in the dln stack occurs significantly before the δ18O breakpoint relies solely on the identification of the breakpoint, and not Δage uncertainties. We find that the dln change point occurs significantly before that in δ18O by an amount of 173 ± 79 yr for the DO warming, and by 235 ± 64 yr for DO cooling.
As a further test of the robustness of our change point detection, we apply the BREAKFIT algorithm to the dln composite of DO warming events (instead of the RAMPFIT routine used above). The dln breakpoint as found by the BREAKFIT method (t = 23 ± 38 yr for raw data, and t = 38.4 ± 25.4 yr for filtered data) is in good agreement with results from the RAMPFIT method.
Summary of change point uncertainties.
Here we briefly synthesize the above sensitivity studies and uncertainties in the timing of the dln breakpoints. For the phasing of WDC dln breakpoints to NGRIP δ18O we consider: the RAMPFIT MBB uncertainty, ±74 yr (1σ) for DO warming and ±59 yr for DO cooling; the Δage uncertainty5, ±69 yr (2σ); the systematic uncertainty in the NGRIP δ18O-WDC CH4 phasing from ref. 5, ±27 yr (2σ). Adding all uncertainties in quadrature yields ±83 yr (1σ) for DO warming events, and ±70 yr (1σ) for DO cooling events, as reported in the main text.
We can similarly quantify the uncertainty in the WDC CH4, and NGRIP δ18O initial break points, as found by the RAMPFIT analysis. In the case of WDC CH4, we consider the RAMPFIT MBB uncertainty, ±4 yr (1σ) for DO warming and ±2 yr for DO cooling; and the systematic uncertainty in the NGRIP δ18O-WDC CH4 phasing, ±27 yr (2σ). Adding all uncertainties in quadrature yields ±14 yr (1σ) for both DO warming and cooling events (rounding uncertainties to the nearest year). For the NGRIP δ18O change points, we consider only the RAMPFIT MBB uncertainty of ±5 yr (1σ) and ±7 yr, for warming and cooling events, respectively. Note that owing to the much higher signal-to-noise ratio of the NGRIP δ18O and WDC CH4 stacks, the MBB uncertainties are much lower than those of WDC dln.
For the phasing of WDC dln to WDC δ18O breakpoints we consider only the RAMPFIT MBB uncertainty for the dln breakpoint, ±74 yr (1σ) for DO warming and ±59 yr for DO cooling, and the BREAKFIT uncertainty for the δ18O breakpoint5, ±50.8 yr (2σ). Adding in quadrature yields phasing uncertainties of ±79 yr (1σ) for DO warming events and ±64 yr (1σ) for DO cooling events.
Frequency domain methods.
We use the Thompson multitaper method for coherence and phase estimates, correcting for coherence bias and using a Monte Carlo approach to estimate the 95% confidence limits on the phase estimation (for example, ref. 35). We also use the Thompson multitaper method to estimate spectral power density, employing the MATLAB pmtm.m routine with an improved confidence limit estimation that correctly accounts for the degrees of freedom as implemented by P. Huybers (http://www.people.fas.harvard.edu/∼phuybers/Mfiles). We linearly interpolate the data to even time intervals (Δt = 10 yr spacing) before analysis. We perform the analysis on the records over the interval 10–67 ka, 20–67 ka (excluding the deglaciation), 6–67 ka (including the early Holocene), and for different interpolated time spacing (Δt = 10, 20, 40 years). These analytical choices do not meaningfully impact the conclusions of this study.
Characterization of millennial frequencies.
We characterize the WDC dln, CH4 and δ18O spectra, providing context for interpreting the phase relationship of WDC dln to the AIM and DO patterns of climate variability. Normalized (z-score over the 10–67 ka period) CH4 and δ18O have red power spectra, with increasing power toward lower frequencies through the millennial band; AIM and DO cycles are not periodic but span a range of timescales from ∼500 to 5,000 years. Millennial-scale power in normalized dln is comparable to that of CH4 and δ18O. It is important to note that while the δ18O and CH4 signals are both expressions of millennial variability in the coupled climate system, they do not have the same power distribution across frequency. Specifically, millennial-band power in WDC δ18O is weaker than that in CH4 (or Greenland δ18O). The distribution of millennial power in WDC dln has similarities to that of both CH4 and WDC δ18O.
The unique nature of the millennial band is shown clearly in the coherence and phase between WDC CH4 and δ18O (Supplementary Fig. 2). The phase relationship transitions from in phase at orbital frequencies, to ∼90° out of phase at millennial frequencies (∼5 to 1 kyr periods of the DO/AIM cycles). This relationship reflects the integrand–integrator relationship between NH and SH climate: temperature change in the North Atlantic (highly correlated with WDC CH4) is inversely related to the time rate of change of temperature in the Southern Hemisphere36. Any signal is 90° out of phase with its derivative across frequency, and has reduced power compared with the derivative. The smoothly decreasing phase angle between WDC CH4 and δ18O at periods below ∼2,000 yr is equivalent to the discrete ∼200 yr time lag between the Northern and Southern hemispheres during these events5. A discrete time lag between two signals, −Δτ, is equivalent to a smoothly changing phase angle = −Δτ × ω × 360° with frequency ω (ref. 37).
The dln record is significantly coherent with both CH4 and δ18O (Supplementary Fig. 2), but shows a distinct phase relationship: at periods <2.5 kyr, dln and CH4 are essentially in phase; at timescales between ∼2.5 kyr and 5 kyr, dln is out of phase with both δ18O and CH4, with a phase angle between 0° (in phase) and 90° (quadrature). One should expect dln to show phase angles between 0° and 90° with δ18O and CH4, if its variability were composed of a superposition of two modes of variability, one in phase with δ18O and the other in phase with CH4 (which are 90° to each other). Below we show that the relationship of phase angle to frequency observed among the records is expected if dln represents a combination of the CH4 and δ18O modes of variability, given the distribution of power in the CH4 and δ18O records.
Sensitivity of phase relationships to chronological uncertainties.
We investigate the sensitivity of the coherence analysis to chronological uncertainties in the age model and Δage history arising from the dynamical firn densification model on which they are based23. We perform a Monte Carlo sensitivity study in which the coherence and phase between WDC CH4, δ18O and dln are calculated for an ensemble of 103 different possible Δage histories that are generated by varying input parameters to the firn densification model23 within stated uncertainties, as well as four different depth interpolation schemes38 for a total of 4 × 103 possible WDC chronologies. The mean coherence and phase of the Monte Carlo sensitivity study are shown in Supplementary Fig. 2a, b with ±1σ of the spread of results (shading). The results demonstrate that the coherence and phase analysis is insensitive to the small chronological uncertainties of the WDC timescale. The 95% confidence intervals on the estimation of the phase relationship between WDC CH4, δ18O and dln calculated by the cmtm.m routine using an iterative method35 are shown in Supplementary Fig. 2c.
WDC dln variability is related to the variability in both WDC CH4 and δ18O. We illustrate this explicitly by multiple linear regression of the combined CH4 and δ18O signals to WDC dln, 〈dln〉 = a〈δ18O〉 + b〈CH4〉, where 〈x〉 indicates that time series x has been normalized by its z-score over the interval 10–67 ka. The combined regression model (a = 0.4589 and b = 0.3951) accounts for 62% of variance of the dln record at all timescales (Supplementary Fig. 3). The F statistic of the combined model, 4666.3, has a p value within rounding error of zero, indicating that the combined regression model is a significantly better predictor of the dln record than the δ18O or CH4 component alone. Much of the remaining variance in WDC dln not described by the combined model can be attributed to high-frequency noise in WDC dln; the linear model explains over 87% of the variance in WDC dln if high-frequency noise (<1 cycle per 500 yr) is excluded.
We use a Monte Carlo method to test whether the additional variance explained by the combined linear model is significant over that explained by its components alone, accounting for autocorrelation in the time series. We compare the linear regression model, a〈δ18O〉 + b〈CH4〉, against two dummy regression models, M1 = a1〈δ18O〉 + b1noise1, and M2 = a2noise2 + b2〈CH4〉, where noise1,2 are randomly generated AR-1 time series whose mean, standard deviation, and lag-1 autocorrelation match those of the normalized CH4 and δ18O time series, respectively. We compare the r2 of the real linear model with the distribution of r2 values resulting from 103 random iterations of each dummy model. The distributions of r2 values for M1 and M2 have a greatest-likelihood value equal to that of δ18O-only and CH4-only models, respectively (r2 = 0.54 and r2 = 0.51), with a decreasing but non-zero probability of a higher r2 value due to noise fitting of the additional random, but autocorrelated, time series. The real linear model’s r2 (0.62) exceeds that of 99.95% and 100% of iterations for M1 and M2, respectively. These results demonstrate conclusively that the additional variance in dln explained by the combined δ18O and CH4 variability is significant and not due to noise fitting.
The linear model analysis is consistent with the observed spectral coherency. An arbitrary linear combination of two normalized signals approximately 90° out of phase with each other can result in a signal with any phase relationship to the components. In this case, approximately equal weighting of the components (a = 0.4589 and b = 0.3951) yields a resulting phase relationship of ∼45° between WDC dln and the components of the model (CH4 and δ18O). WDC dln is not precisely 45° to CH4 and δ18O at all millennial frequencies. For example, dln and CH4 have a phase angle slightly greater than 45° at lower millennial frequencies and closer to 0° at higher millennial frequencies. This reflects differences in the power distribution across millennial frequencies of each proxy and how they combine. The linear model captures the combination of power distribution and phase relationships of dln to the other proxies: the phase relationship of CH4 to the linear model is equivalent to the phase relationship of CH4 to dln, and likewise for δ18O to dln (Supplementary Fig. 4).
The data that support the findings of this study are available at http://dx.doi.org/10.17911/S9MW2F.
We thank A. J. Schauer and P. D. Neff for assistance with the measurements, E. J. Brook, V. Gkinis and H. C. Steen-Larsen for insightful discussions, and B. Stenni for sharing data. We acknowledge grants from the US National Science Foundation Division of Polar Programs (0537930, 1043092 to E.J.S.; 0537593, 1043167 to J.W.C.W.; 0538538, 1043500 to T.S.; 0944197 to T.J.F.; 1043518 to E. J. Brook; and 1341497 to C.M.B.). We acknowledge grants from NOAA Climate and Global Change postdoctoral fellowship program, administered by the University Corporation for Atmospheric Research (to C.B.); support from the Joint Institute for the Study of the Atmosphere and Ocean (JISAO Contribution no. 2462) and from a Marie Curie International Incoming Fellowship (to J.B.P.); NASA National Earth and Space Sciences Fellowship (to T.J.F.); and ARCS Foundation scholarship (to B.R.M.).