We analyse published oxygen isotope records of annually dated firn cores from two contrasting Antarctic regions (Table ): (1) Dronning Maud Land (DML) on the Antarctic Plateau and (2) the West Antarctic Ice Sheet (WAIS). While the DML core sites are located in a rather flat region relatively isolated from the coast (average elevation 2900 m), the WAIS core sites are lower in elevation (1600 m on average) and therefore potentially more influenced by marine conditions.

For DML, we use a total of 15 records, which were collected during the EPICA (European Project for Ice Coring in Antarctica) pre-site survey and published in . All records cover at least the last ∼ 200 years and form our first data set, DML1. Three of these records (B31–B33) span the last ∼ 1000 years and are therefore included in a second separate data set for this time span (DML2). Core B32 is in close proximity (∼1 km) to the deep EPICA DML (EDML) ice-core site at Kohnen Station . The record chronologies were established from seasonal layer counting of chemical impurity records constrained by tie points from the dating of volcanic ash layers . The resulting uncertainty of the chronologies has been reported to be ∼2 % of the time interval to the nearest tie point , which translates to a maximum time uncertainty of ∼ 1.2 years for the short records and of ∼ 3.5 years for the long records. Since our method (Sect. ) relies on all records having equal lengths, we restrict the time span for the DML1 data set to the period from 1801 to 1994 CE and to the period from 1000 to 1994 CE for the DML2 data set.

The WAIS data set selected for this study consists of five isotope records collected during the US ITASE (International Trans-Antarctic Scientific Expedition) project , including the core WDC2005A from the WAIS Divide ice core (WDC; ), and cover the time interval from 1800 to 2000 CE. The oxygen isotope data of cores ITASE-2000-4 and ITASE-2000-5, previously published at subannual resolution , have been block-averaged in this study to obtain annual resolution data. The core selection was based on the constraint of covering a similarly large area and sufficiently long time period to allow a meaningful comparison with the DML1 records. The relative time uncertainty between the WAIS records, based on dating through annual layer counting of chemical trace species validated by identification of volcanic marker horizons, was reported to be no more than 1 year .

Our approach in general assumes that individual isotope records from a certain region contain two contributions: (i) a signal common to all cores from that region and (ii) independent noise components, which are, for example, related to spatial variability from redistribution of snow (stratigraphic noise) or to precipitation intermittency. By utilising several records we can disentangle both contributions and estimate the underlying common and noise signals. The approach is similar to the analysis of variance e.g. but uses the power spectra of the time series to derive timescale-dependent estimates.

More formally, given a core array of n isotope records, the power spectral density (PSD) of an individual record from site i, Xi(f), where f denotes frequency, is the sum Xi(f)=C(f)+Ni(f), where C(f) and Ni(f) are the original spectra of the common signal and the noise component prior to the smoothing by molecular diffusion of water vapour within the porous firn . To relate this with the actual measured signal, X^i(f), we additionally have to account for the measurement process, which adds additional noise to the diffused record. X^i(f) is thus given by X^i(f)=Gi(f)C(f)+Ni(f)+Σ. Here, Gi(f) is a linear transfer function that acts as a low-pass filter and accounts for the diffusion process (Appendix ), and Σ is the measurement error. At annual resolution, Σ is typically at least 1 order of magnitude smaller than the stratigraphic noise level and is therefore neglected in the following. We now calculate the mean spectrum, M(f), of all individual spectra X^i(f). Assuming that the statistical properties of the individual noise terms are identical for all n records, we obtain M(f)=1n∑i=1nX^i(f)=G‾(f)C(f)+N(f), where G‾(f)=1/n∑i=1nGi(f) is the average diffusion transfer function. In contrast to forming the spectral mean, we can also average the n isotope records in the time domain and then calculate the PSD of this “stacked” record. Here, the noise component will be reduced by a factor of n compared to the mean spectrum in Eq. (), since we assume independent noise between the sites. Additionally, we have to take into account the time uncertainty of the dated records. This does not affect the overall shape of broadband spectra but diminishes the correlation between the records and thus their spectral coherence, which reduces the variance of the common signal in the stacked record. The PSD of the stacked record is thus S(f)≈G‾(f)Φ(f)C(f)+1nN(f), where Φ(f) is a linear transfer function accounting for the effect of time uncertainty. Applying the average diffusion transfer function, G‾(f), also to the spectrum of the stacked record is a valid approximation in the case of similar Gi(f), which we confirmed for our records (Appendix ). From the expressions for the mean spectrum (M, Eq. ) and the spectrum of the stacked record (S, Eq. ) we can now derive expressions for the spectra of the common signal C and the noise N (omitting the explicit frequency dependence in the notation here), C=nn-Φ-1Φ-1G‾-1[S-n-1M],N=nn-Φ-1G‾-1[M-Φ-1S].

For estimating the transfer functions for diffusion and time uncertainty, the inverses of which are used to correct the signal and noise spectra (Eq. ), we use numerical simulations, since no closed form expressions are available. For this, we create surrogate records mimicking the individual core arrays and simulate the effects of diffusion and time uncertainty on the surrogate spectra of the stacked records. We model the firn diffusion as the convolution of the original time series with a Gaussian kernel . The width of the kernel is set by the diffusion length σ, which is site-specific and a function of depth. For modelling the time uncertainty we use the approach of . Model parameters are the rates of missing and double-counted annual layers, which we set to match the reported time uncertainties of the isotope records. Appendix  gives a detailed description of the simulations including the estimated transfer functions (Fig. ). Because the diffusion correction (G‾-1 in Eq. ) strongly amplifies both the raw spectra as well as their uncertainties on the fast frequencies, we restrict our analyses to the frequency region where the estimated transfer function, G‾, assumes values ≥0.5, equivalent to a correction factor ≤2 in Eq. (). This avoids large uncertainties and translates to a maximum frequency that is used for the analyses (hereafter the cut-off frequency) of 1/5 yr-1 for DML1, 1/8.5 yr-1 for DML2 and 1/2.8 yr-1 for WAIS (Fig. ).

The frequency-dependent SNR, F(f), is defined as the ratio of the signal and noise spectra, F(f)=C(f)N(f). As we explicitly neglect measurement noise, this quantity is unaffected by the effect of diffusion or its correction (Eq. ) but directly influenced by time uncertainty, which biases the uncorrected SNR towards zero. Typically, firn or ice-core isotope records are averaged onto a fixed temporal resolution Δt (the “averaging period”) during preprocessing. The signal-to-noise variance ratio after this averaging step is given by F‾(fNyq)=∫f0fNyqC(f)df∫f0fNyqN(f)df, where f0 is the lowest frequency of the spectral estimates and fNyq is the Nyquist frequency for the chosen averaging period, i.e. 1/(2Δt). Since our records have different lengths, we choose a common minimum value for f0 of 1/100 yr-1 for the integrations in Eq. (). The value of F‾ can then be used to obtain the correlation between the time series of the common signal c and a stacked record x‾ built from the spatial average of n individual records : r(c,x‾)(fNyq)=11+nF‾(fNyq)-1.

Missing years in the published records (∼1.6 % of all data points) are linearly interpolated. Power spectra are then estimated using Thomson's multitaper method with three windows with linear detrending before analysis. This approach is known to introduce a small bias at the lowest frequencies, and we omit the lowest frequency from all plots and calculations. In general, spectral smoothing is necessary to improve the quality of the estimates from short time series. Here, we use a Gaussian smoothing kernel with varying width that is proportional to the applied frequency and thus constant in logarithmic frequency space . The smoothing width in logarithmic units is chosen to be 0.1 for the WAIS data and 0.15 for the DML data. To avoid biased estimates at the low- and high-frequency boundaries, the kernel is truncated on both sides to maintain its symmetry. Logarithmic smoothing preserves power-law scaling of spectra and is thus useful for climate spectra.

In order to illustrate our method (Sect. ), we first use the DML1 data set to demonstrate the individual steps involved in the analysis.

Each power spectrum derived from an individual record of the DML1 firn-core array provides a timescale-dependent representation of the isotope variations in the study region (Fig. , thin grey lines). The differences between the individual spectra are not only due to differences in the isotope variability between the records, but also caused by the spectral uncertainty from the finite length of each record. The mean spectrum, M, of all individual spectra reduces this spectral uncertainty and thus provides a more robust estimate of the single records' spectrum (Fig. , black line). It shows a two-part structure with a near-constant PSD above decadal timescales (i.e. is “white”) and a strong decrease in spectral power towards shorter timescales, which is expected from vapour diffusion in the firn (Eq.  and Appendix ).

The mean spectrum divided by the number of records (M/n; here, n=15; Fig. , dashed line) is the expected spectrum if all isotope variations present in the firn-core records were independent noise. In comparison, averaging in the time domain across records that contain noise and additionally a common (i.e. spatially coherent) signal will result in a spectrum S, where the noise component is also reduced by 1/n but with the common signal left unaltered (Eq. , neglecting time uncertainty), and which is thus located between the mean spectrum and the mean spectrum divided by n. This spectrum S for the DML1 stack (Fig. , brown line) is for short timescales (periods from ∼ 3 to 5 years) nearly identical to the mean spectrum divided by n, which suggests that here the variability of the individual records is consistent with the null hypothesis of independent noise. The divergence from the white-noise level close to the 2-year Nyquist period is likely an artefact from the jitter of the annual averages as a result of the uncertainty in defining annual depth increments upon dating. In contrast to the short periods below 10 years, the individual records clearly contain a common isotope signal on longer timescales that “survives” the averaging process when building the stacked record and which increases in power with increasing timescale (Fig. , brown line). Hence, the differences between S and M/n and between S and M inform us about the average signal and noise content of the individual isotope records, but they need to be corrected for the residual amount of noise contained in S and for the loss of variance from diffusion and time uncertainty (Eq. ).

After this detailed description for DML1, we now turn to the results of the estimated signal and noise spectra for all three data sets. In general, the shape of the signal spectra is, as a result of the corrections, clearly distinct from the mean spectrum of the individual isotope variations. This is seen, for example, in the corrected DML1 signal spectrum which indicates a much more steady increase in PSD from short to long timescales (Fig. a, solid blue line) compared to the mean spectrum (Fig. , black line). This is confirmed by the three 1000-year-long DML2 records, which have a common signal that exhibits a roughly similar power spectrum in the range of timescales that overlap (∼ 10- to 100-year period). We partly expect this, since the longer cores are also part of the DML1 data set, but the increase in signal power in this frequency band seems to be a general feature over the last 1000 years. In addition, the DML2 signal spectrum shows a further and similar increase for timescales beyond the 100-year period. This change in spectral shape from the mean to the signal spectrum results from two contributions in the correction process: firstly, the average isotope variability is corrected for the noise contribution (“uncorrected signal”, dotted lines in Fig. a). This correction is mostly apparent on the longer timescales, leading to a higher slope in PSD of the signal spectrum compared to the mean spectrum (for DML1, the signal increases from the 10- to 100-year period by a factor of ∼2.6, the mean spectrum by a factor of ∼1.4). Secondly, the corrections for the loss in spectral power by the effects of diffusion and time uncertainty (here important for time periods from ∼ 20- to 5-years) lead to a smaller increase in PSD of the signal spectra with increasing timescale compared to the raw estimates (compare dotted, dashed and solid lines in Fig. a). In sharp contrast to DML, the corrections for the WAIS records yield a signal spectrum (Fig. c, solid line) that exhibits a rather flat appearance throughout and indicates decreasing PSD towards centennial timescales. Much of the flat character is caused by the diffusion and time uncertainty corrections, which strongly amplify the raw signal power on the subdecadal timescales; the decrease in PSD on the long timescales is a result of the correction for the noise contribution. We note, however, that the spectral uncertainty at the lowest frequency is high, since fewer data points contribute to the estimated PSD for lower frequencies when using logarithmic smoothing.

A difference between the regions can also be seen in the noise spectra (Fig. b and d). Prior to any correction, the DML1 and DML2 noise spectra are different on shorter timescales (≲ 20-year period), but become consistent with each other after the correction, showing essentially white PSD (Fig. b). In comparison, the corrected WAIS noise spectrum shows an increase in spatially incoherent isotope variations towards longer timescales (Fig. 2d), which correlates with the decrease in signal power on centennial timescales (Fig. c).

The corrected signal and noise spectra directly provide an estimate of the timescale dependence of the SNR (Eq. ). To derive a single estimate for DML, we combine the DML2 spectra for timescales above the decadal period with the respective DML1 spectra from the subdecadal frequency band. Again, the results are very different between DML and WAIS (Fig. ). For DML, the SNR shows a continuous increase with timescale, with values ranging from ∼ 0.1 at the 5-year period to ≲ 0.2 at the decadal timescale and increasing further to ∼1 at multi-centennial timescales. The estimate for WAIS exhibits the opposite timescale dependence, with SNR values of ∼0.5–0.7 for interannual timescales that continuously decrease to ∼0.1 at centennial timescales.

A complementary picture is obtained from the expected correlation between the time series of a stacked record and the underlying common signal as a function of both the number of averaged records and the temporal averaging period (Eq. , Fig. ). For DML, the correlation for an individual record at interannual resolution is rather low, with roughly 0.4–0.5 (Fig. a); for WAIS, this correlation is slightly higher (∼0.5–0.6, Fig. b). For longer averaging periods, the correlation for DML shows a steady increase with the averaging period, in line with the increase in SNR, reaching values around 0.6 for single records and multi-decadal averaging periods (Fig. a). Naturally, the correlation further increases with the number of averaged cores. For WAIS, the correlation with the underlying signal decreases with the averaging period and only increases when more records are averaged (Fig. b).

We presented a method and the results of separating the variability recorded by Antarctic isotope records into two contributions: local variations (noise, Eq. b) and spatially coherent variations (signal, Eq. a). We now assess the physical meaning of these terms by discussing the relevant spatial scales of the major processes that influence the isotopic composition of the records: (i) temperature variations, (ii) atmospheric circulation, (iii) precipitation intermittency and (iv) stratigraphic noise.

Classically, the isotopic composition of firn and ice cores is interpreted as being related to variations in local air temperature . The extent to which spatially distributed isotope records are influenced by a common temperature signal then depends on the decorrelation scale of the temperature anomalies, which is, for annual mean temperatures, typically of the order of hundreds to thousands of kilometres and increases with timescale . For our study regions, annual mean temperature variations from the ERA-Interim reanalysis exhibit decorrelation scales of ∼1200 km (Appendix ), which are much larger than the individual intercore distances (<400 km, Table ). This implies that, if the temperature variations were fully recorded by the array of firn-core records, they would to a large extent contribute to the estimated signal spectrum. In fact, for the temperature reanalysis fields in the study regions, the average of all correlations between sites separated by less than the maximum intercore distances (Fig. ) suggests that the estimated signal spectra for DML (WAIS) would contain 87% (94%) of the total temperature variability, while the remaining fraction would be interpreted as noise.

However, changes in large-scale atmospheric circulation can lead to variations in the source and the pathways of the moisture, which can affect the isotopic composition of the precipitation that is formed, independently of local temperature changes e.g.. In general, the spatial scales of such variations are unclear. For the studied DML core array, which is located on the rather flat and remote Antarctic Plateau, one could expect that the effect is small and possibly spatially coherent, thus contributing to the estimated signal term. For WAIS, isotope data have been interpreted to also reflect changes in atmospheric circulation and sea-ice cover of the adjacent oceans . These processes might exhibit, through the ice-sheet topography, a regional expression at the individual firn-core sites, which are generally lower in elevation and located near the ice divide, as suggested by the significant spatial differences in observed intercore correlations . Such effects would affect the estimated noise component.

Major additional contributions to the overall variability of isotope data arise from precipitation intermittency, i.e. interannual variations in the seasonality of precipitation events , and from stratigraphic noise created during deposition of the snow. Both processes exhibit significantly different decorrelation scales. The decorrelation scale of precipitation intermittency is related to the decorrelation scale of the precipitation itself, which is expected to be coherent on a local scale (i.e. ∼100 m) and to decorrelate on scales generally smaller than the temperature decorrelation scales. In both regions, the similar analyses of ERA-Interim data as for the temperature variations suggest decorrelation scales of the precipitation of 300–500 km (Appendix ). This is supported by an analysis of measurements from autonomic weather stations that indicate that accumulation in DML arises from many small (1–2 cm) and a few larger events (≳5 cm) of snowfall, where the major events occur only a few times per year without any clear seasonality but often over large areas. In contrast, stratigraphic noise is a short-scale phenomenon. Its generation is related to the uneven deposition and the constant erosion and redeposition of the surface snow by wind . Both processes are connected to the local surface undulations, as these directly interact with the snow deposition but also strongly shape the near-surface wind field. This is suggested by the observed decorrelation scale of the stratigraphic noise at EDML (<5 m, ), which is similar to the typical scale of the surface undulations.

These differences in decorrelation scales also become apparent when analysing the relative contributions of both processes to the total isotope variability. At EDML, stratigraphic noise provides ∼50% of the total variance on the seasonal timescale, as suggested from the average correlation of individual shallow isotope profiles separated above (>5 m) the decorrelation scale of the stratigraphic noise but below 1 km . A much higher noise level of at least 80% of the total variance (i.e. higher by a factor of ≥1.6) has been independently inferred from comparing the observed seasonal isotope variability to the expectation from a profile that is a mixture of a deterministic seasonal cycle and diffused noise . The apparent mismatch with the noise level from stratigraphic noise can be reconciled by asserting that a significant part of the common isotope signal at EDML on the local scale is coherent noise from precipitation intermittency, leading to an underestimation of the total noise level when analysing only the interprofile correlations. On the larger spatial scales of the firn-core arrays (array scale) analysed here, the effect of precipitation intermittency should then appear, at least partly, as a noise term, since the spatial precipitation patterns are expected to decorrelate on these scales. Therefore, in general, the variability contribution by stratigraphic noise will fully appear in the noise spectra, while precipitation intermittency is expected to partly contribute to the noise spectra but also partly appear in the signal spectra.

In summary, given the large decorrelation scales of atmospheric temperature variations and the generally smaller scales of the other terms, one could interpret the estimated isotope signal spectra to a first approximation as temperature signals. However, this clearly will be an upper bound of the true temperature signal, since other processes can also lead to spatially coherent isotope signals. Furthermore, we have neglected the transfer function from isotopic ratios to temperatures, and other less constrained effects that affect the isotope signal from the atmosphere to the snow e.g..

The raw noise spectra, i.e. prior to correction, derived from the two DML data sets, exhibit a clear imprint from the diffusional smoothing in the firn. This is suggested by their common decrease in PSD towards shorter time periods (Fig. b), since the effect of diffusion is stronger at higher frequencies. It is corroborated by comparing the loss in PSD between the two data sets, which for DML2 is stronger towards the high-frequency end and also extends further towards longer time periods. This is due to the stronger diffusional smoothing in the older sections of the cores that are only contained in the DML2 records, since the diffusion process had more time to act there since the deposition of the snow. The applied correction reconciles both noise estimates, as it takes these differences into account, and reveals a close-to-constant noise level (white noise) across the range from subdecadal to multi-centennial timescales.

This near constancy of the noise level suggests that the noise-creating processes are independent of the timescale. This seems plausible for stratigraphic noise as it is also indicated by the observed small memory in the interannual variations of the surface topography at EDML . Furthermore, we would not expect strong changes in surface wind regimes or depositional characteristics for the rather stable climatic conditions over the studied time periods. To test whether the effect of precipitation intermittency additionally contributes to the noise spectrum, as suggested from the decorrelation scales of the ERA-Interim precipitation fields, we apply our spectral analysis to the available isotope profiles on the local scale (∼100 m) at EDML and compare the estimated noise spectra between the local scale and the array scale (Fig. ). Although the spectral estimates do not overlap, the results indicate an offset between the noise levels at both spatial scales. For the 5-year period, the PSD of the noise on the array scale is about 1.7 times higher than at the local scale. Some increase in the noise level is expected from the small contribution of uncorrelated temperature variability, but the ∼1.7-fold increase suggests that most of the additional noise arises from spatially incoherent precipitation intermittency.

This supports the interpretation of the estimated DML signal spectra (Fig. a) as temperature variability, assuming that the influence of atmospheric circulation changes is small. Fitting a power law of the form f-β, where f denotes frequency, yields a slope of the DML2 signal spectrum of roughly β∼0.6 for variations above the 20-year period. This is higher than the slopes of the mean spectra of the single records (β∼0.2 for DML2, β∼0 for DML1), which underlines again that the high noise level in individual records strongly masks the true spectral shape of the signal. Such a power-law increase in temperature variability is not unexpected since it was also observed in spectra from marine-proxy-inferred sea surface temperature variations and from other proxy and instrumental temperature records e.g..

The resulting SNR (Fig. ) of the DML data illustrates on which timescales the signal dominates the isotope variability recorded in individual records, and how this translates into the representativity of isotope variations when averaging records in space and time (Fig. ). We can test the validity of our spectral approach by comparing the estimated SNR to published estimates. analysed the same data set as the present study and found an SNR at annual resolution of F‾=0.14 based on the average intercore correlations (r=0.35). Similar values have been obtained using a larger set of cores from the same region that cover a shorter time period . From integrating the estimated signal and noise spectra up to the minimum averaging period constrained by the diffusion correction (∼ 2.5 years), we find an SNR of F‾∼0.2 (correlation r∼0.4, Fig. a), which is, as expected, slightly higher than the published estimates, since we corrected for the effect of time uncertainty, as well as due to the effect of the slightly different underlying averaging periods. Our results further explain the strong agreement between individual ice cores on glacial–interglacial timescales. Averaging to multi-decadal resolution results in a correlation between a single core and the signal of around 0.6 (Fig. a), which rises to ∼0.7 for the available centennial averaging periods. Moreover, the steady increase in SNR on the analysed timescales (Fig. ) might indicate a further increase in SNR towards even longer timescales. However, clearly our results also underline again that for assessing Holocene temperature variability on timescales shorter than multi-decadal, the averaging of records is essential to increasing their representativity (Fig. a).

For WAIS, the higher SNR at interannual timescales compared to DML (average SNR between 5 and 10-year periods of 0.43 for WAIS compared to 0.13 for DML; Fig. ) is consistent with the general notion that higher accumulation rates (on average, ∼3 times as high as at DML; Table ) result in higher SNR . However, one would expect, to a first approximation, a similar increase in SNR with timescale in both regions. In contrast to this expectation, the WAIS results show strongly different timescale dependencies with the tendency of a decrease in signal power and an increase in noise level on longer timescales (Fig. ), resulting in an overall decrease in SNR (Fig. ). This explains the only slightly higher correlations at interannual timescales of a stacked isotope record with the common signal at WAIS compared to DML (Fig. ), since the correlation is based on the integrated value of the SNR (Eqs.  and ). If they are correct, these findings suggest that there is, in general, no simple scaling of the SNR with accumulation rate but that additional effects need to be involved.

The shape of the signal and noise spectra at subdecadal timescales is sensitive to the diffusion and time uncertainty corrections (Fig. ), which could thus contribute to the discrepant SNR estimates. While the diffusion correction for DML led to a consistent white-noise level of both noise estimates (Fig. b) at these timescales, lending support to our approach, the WAIS noise spectrum keeps decreasing towards higher frequencies, even after applying the diffusion correction (Fig. d). This result could be caused either by a too weak diffusion correction or by an overestimation of the time uncertainty leading to an excessive reduction in high-frequency noise levels that cannot be compensated by the low diffusion correction. To test both hypotheses, we varied the strengths of the diffusion and time uncertainty corrections. This has different impacts on the estimated spectra: while the diffusion correction equally applies to both raw signal and noise spectra, the time uncertainty correction has a proportional influence on the signal spectrum but only an indirect influence on the noise spectrum (Eq. ). Indeed, halving the time uncertainty would increase the noise spectrum close to the cut-off frequency only by a maximum factor of ∼1.4, and this therefore cannot reconcile the remaining decrease in the corrected noise spectrum. By contrast, an overall doubling of the diffusion length for all WAIS records would amplify the noise spectrum much more strongly with a maximum factor of ∼4 at the cut-off frequency, leading to interannual noise levels similar to those observed for centennial periods. However, a much stronger diffusional smoothing at WAIS compared to the expectation seems implausible given that the same physical mechanisms of the diffusion process should be valid for East Antarctica as well as West Antarctica, and no anomalously high diffusional smoothing has been observed for the upper part of the WAIS Divide ice core . Additionally, a much stronger diffusion correction would also imply a much steeper decrease in the signal spectrum towards longer timescales (Fig. c), contrary to the expectation. We conclude that there is no obvious reason for the applied correction approach to strongly over- or underestimate the WAIS signal and noise spectra on the interannual timescales. Moreover, by also taking into account the shape of the spectra for the signal and noise on the longer timescales (periods from ∼30 to 100 years), our results might therefore indicate a true increase in local variability at the WAIS sites across the timescales studied and a close-to-constant, or even decreasing, coherent signal variability.

These results suggest firstly that an additional noise process, apart from stratigraphic noise and precipitation intermittency, must contribute to the noise spectrum towards longer timescales. Secondly, the shape of the signal spectrum either implies a nearly white-noise temperature signal or some process that destroys the coherence of the large-scale temperature field on longer timescales upon recording by the firn-core isotope records. Since there is no obvious reason for a fundamentally different Holocene climate variability in West compared to East Antarctica, the second possibility seems more likely.

WAIS isotope data have been reported to covary with local temperatures, but also with the large-scale atmospheric circulation and the sea-ice cover of the adjacent oceans . A pronounced regional imprint on the recorded isotope variability is also suggested from the spatial differences in intercore correlations for an extended set of the available WAIS firn cores . In particular, cores east of the WAIS Divide display strong differences in the recorded isotope variability despite their rather small spatial separation , which is suggested to be related to slow variations in the dominant circulation patterns. While such differences have not explicitly been reported for the core sites west of the divide studied here, we hypothesise that signatures of sea-ice variations or meridional inflow could affect the isotopic composition at the individual firn-core sites to different extents. This is motivated by model-based results linking an increase in sea-ice cover to an earlier ascent of long-range transported air masses to the continent, reducing the influence of local air from the surface, while less sea ice inhibits this early ascent and allows more mixing of surface air. Variations in sea ice could thus influence the isotopic composition of air masses by controlling the influence of local moisture, which might only be recorded by certain WAIS cores depending on the elevation of the air mass transport and characteristics of the core positions, such as their surrounding topography, elevation, or distance to the coast. Decadal trends or slower changes in these variations could then destroy the recording of the large-scale coherent temperature field by the firn cores and thus cause a loss in spectral signal power in the isotope record towards longer timescales and an increase in the noise level (Fig. c, d). In contrast, the East Antarctic Plateau including the DML firn-core sites is higher in elevation and might be more shielded from marine influences by the steep topographic slopes leading to a more coherent signal. This might also explain, besides differences in core quality, the rather low agreement among deep West Antarctic cores on millennial timescales compared to East Antarctic cores . However, since our inferences are speculative, further studies are needed to help disentangle the role of variations in West Antarctic temperature, atmospheric circulation and sea ice on the recorded isotope variability.