Ice-core-based records of isotopic composition are a proxy for past
temperatures and can thus provide information on polar climate variability
over a large range of timescales. However, individual isotope records are
affected by a multitude of processes that may mask the true temperature
variability. The relative magnitude of climate and non-climate contributions
is expected to vary as a function of timescale, and thus it is crucial to
determine those temporal scales on which the actual signal dominates the
noise. At present, there are no reliable estimates of this timescale
dependence of the signal-to-noise ratio (SNR). Here, we present a simple
method that applies spectral analyses to stable-isotope data from multiple
cores to estimate the SNR, and the signal and noise variability, as a
function of timescale. The method builds on separating the contributions from
a common signal and from local variations and includes a correction for the
effects of diffusion and time uncertainty. We apply our approach to firn-core
arrays from Dronning Maud Land (DML) in East Antarctica and from the West
Antarctic Ice Sheet (WAIS). For DML and decadal to multi-centennial
timescales, we find an increase in the SNR by nearly 1 order of magnitude
(
Ice cores represent key archives for studying polar climate variability on
timescales beyond instrumental observations. The isotopic composition of water
stored in the ice serves as a proxy for reconstructing past temperature
variations (
However, the interpretation of isotope records in terms of local atmospheric
temperatures is complicated by a multitude of processes that distort the
original relationship present in precipitation
Previous studies provided first insights into the relationship between climate
signal and noise for short spatial and temporal scales
We analyse published oxygen isotope records of annually dated firn cores from
two contrasting Antarctic regions (Table
For DML, we use a total of
The WAIS data set selected for this study consists of five isotope records
Overview of the firn cores (sorted into three data sets) used in this
study. Listed are the covered time spans of each core array (in yr CE), the
number of records in each array (
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
More formally, given a core array of
For estimating the transfer functions for diffusion and time uncertainty, the
inverses of which are used to correct the signal and noise spectra
(Eq.
The frequency-dependent SNR,
Missing years in the published records (
In order to illustrate our method (Sect.
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.
Detailed results of estimated PSD for the DML1 data set. Thin grey lines show
the individual power spectra for each record with the mean spectrum indicated
by the thick black line. The dashed black line shows the null hypothesis
according to which all isotope variations are noise; the brown line depicts
the spectrum from averaging all records in the time domain (the stacked
record). The extent of the blue (red) shading is proportional to the
uncorrected PSD of the signal (noise) (Eq.
The mean spectrum divided by the number of records (
Estimated signal
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.
Estimated timescale dependence of ice-core isotope signal-to-noise ratios. Results are shown for the DML (black) and WAIS (blue) isotope records. The results for DML are based on combining the spectra from DML1 and DML2 (see text).
A difference between the regions can also be seen in the noise spectra
(Fig.
The corrected signal and noise spectra directly provide an estimate of the
timescale dependence of the SNR (Eq.
Estimated correlation of stacked isotope records from
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.
We presented a method and the results of separating the variability recorded by
Antarctic isotope records into two contributions: local variations (noise,
Eq.
Classically, the isotopic composition of firn and ice cores is interpreted as
being related to variations in local air temperature
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
Major additional contributions to the overall variability of isotope data arise
from precipitation intermittency, i.e. interannual variations in the seasonality
of precipitation events
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
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
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.
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
Comparison of DML noise spectra as a function of intersite distance. The red
curve (array scale,
This supports the interpretation of the estimated DML signal spectra
(Fig.
The resulting SNR (Fig.
For WAIS, the higher SNR at interannual timescales compared to DML (average
SNR between 5 and 10-year periods of
The shape of the signal and noise spectra at subdecadal timescales is sensitive
to the diffusion and time uncertainty corrections
(Fig.
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
We presented a simple spectral method to separate the variations recorded by
isotope records into a local (noise) and a common (i.e. spatially coherent)
signal component. We applied this method to firn cores from the East
Antarctic Dronning Maud Land (DML) and the West Antarctic Ice Sheet (WAIS) to
estimate, for the first time, the isotopic signal-to-noise ratio (SNR) as a
function of timescale. This is of fundamental interest for interpreting isotope
records obtained from individual ice cores, since it provides an upper limit on
the SNR of the temperature signal recorded by the cores. For DML, the SNR at the
interannual timescale is very low, but it steadily increases with timescale
reaching values above
Our method further allows the estimation of the power spectra of the coherent
isotope signal. For DML, the spectra of single cores largely resemble white
noise. In contrast, the derived signal spectrum shows increasing variability
towards longer timescales. Such an increase is also observed in instrumental
temperature records and other climate proxies. The marked difference between the
raw interpretation of single cores – as it is usually done – and the signal
spectra derived from the core array demonstrates the relevance of the signal and
noise separation. The interpretation of the WAIS isotope signal is more
challenging, since the signal shows a close-to-constant spectral power even after
applying our method. We speculate that this might be due to atmospheric
circulation variations that create a local imprint at the different firn-core
sites. This might prevent a coherent recording of the large-scale atmospheric
temperature field. To test this hypothesis, we suggest to analyse firn-core
arrays as a function of the average separation distance between the individual
core sites within each array. This could allow us to investigate whether the
stable-isotope data record a stronger coherent signal on a regional scale (e.g.
We conclude that the pronounced differences seen between East and West
Antarctica could thus be related to the differences in the topographic settings
and the different marine influences
Finally, our approach of separating signal and noise from a set of spatially distributed records is also applicable beyond Antarctic ice cores. The challenge of low and timescale-dependent SNR is common to many high-resolution climate archives, and the number of nearby core sites is continuously increasing. Therefore, we envision our approach to better constrain the reliability of proxy records as a function of timescale in general and to allow a significant improvement of our knowledge of past climate variability.
Software for the spectral analyses, the implementation
of the method and the plotting of the results is available as the R package
The original DML firn-core and trench oxygen isotope data are archived at the
PANGAEA database under
We derive the effect of site-specific diffusion on the estimates of the mean
spectrum and the spectrum of the stack given a core array consisting of
The spectrum of a time series We note that there is no closed form expression for
The average in the time domain of
By contrast, the spectrum of the average of
To estimate the transfer functions for diffusion (
For the diffusion simulations, each surrogate record is smoothed by convolution
with a Gaussian kernel of width
To simulate the effect of time uncertainty, we apply the modelling approach by
The resulting transfer functions used for the main results are shown in
Fig.
Estimates of the spectral transfer functions for the effects of site-specific
diffusion
To estimate the present-day spatial decorrelation scales of the atmospheric
temperature and the precipitation fields in our study regions, we resort to
ERA-Interim reanalysis data
To obtain decorrelation scales, we calculate the correlations between reanalysis
time series from the grid box closest to the location of the EDML site
(
Present-day temperature decorrelation across DML and WAIS. Shown are the
correlations (grey dots) of ERA-Interim annual-mean temperatures
For annual mean temperatures, the analysis yields decorrelation scales of
around
TM and TL designed the research, developed the methodology and interpreted the results. TM reviewed the relevant literature, established the database and performed all analyses. TM wrote a first version of the manuscript, which was revised by both authors.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Paleoclimate data synthesis and analysis of associated uncertainty (BG/CP/ESSD inter-journal SI)”. It is not associated with a conference.
We thank all scientists, technicians and the logistic personnel who contributed to the sampling of the firn cores and the measurement of the used stable-isotope data, and we are grateful for making the data publicly available. We are thankful for valuable discussions with and comments by Torben Kunz, Jürgen Kurths, Johannes Freitag and Maria Hörhold. All plots and numerical analyses were carried out using the open-source software R: A Language and Environment for Statistical Computing. This project was supported by Helmholtz funding through the Polar Regions and Coasts in the Changing Earth System (PACES) programme of the Alfred Wegener Institute, by the Initiative and Networking Fund of the Helmholtz Association Grant VG-NH900 and by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 716092). It further contributes to the German BMBF project PalMod. We thank Lukas Jonkers for his kind handling of the manuscript as well as Dmitry Divine and one anonymous referee for their detailed review and helpful comments. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Lukas Jonkers Reviewed by: Dmitry Divine and one anonymous referee