Introduction
Ice cores obtained from continental ice sheets and glaciers are a key
climate archive. They store information on past changes in
temperature in the form of stable water
isotopes , in greenhouse gas concentrations
via trapped air and in many other parameters such
as accumulation rates e.g. or
aerosols e.g.. Analysis of the isotope
ratios recorded in single deep ice cores provided milestones in the
palaeo-climate research, including the investigation of
glacial–interglacial climate changes and the
existence of rapid climate variations within glacial periods
.
In contrast to the coherent view established from polar ice cores for
millennial and longer timescales, the reliability of single ice cores
as archives of the Holocene climate evolution is less clear
. The small amplitude of changes and the aim to
reconstruct climate parameters at high temporal resolution poses
a challenge to the interpretation of ice-core signals. This is
especially true for low-accumulation sites, defined here for
accumulation rates below 100mm w.e. yr-1, which holds
for large parts of the East Antarctic Plateau. There, the non-climate
noise – that part of the isotopic record which cannot be
interpreted in terms of temperature variations on regional or larger
scales, hence including any meteorological, pre- and post-depositional
effects that additionally influence the isotopic composition – may
often be too high to accurately extract a climatic temperature signal
. Despite the challenges, quantifying the Holocene
polar climate variability is the key foundation to determine the range
of possible future climate changes e.g.and references
therein as well as to test the ability of climate
models in simulating natural climate variability .
The quantitative estimation of climate variability from proxy data
therefore requires an understanding of the non-climate noise in order
to separate it from the climate signal e.g..
Several mechanisms influence the isotopic composition of snow prior to
and after its deposition onto the ice sheet. On larger spatial scales,
non-climate variability may be introduced by different moisture
pathways and source regions e.g. as well as
spatial and temporal precipitation intermittency
. Irregular
deposition caused by wind and surface roughness along with spatial
redistribution and erosion of snow is a major contribution to
non-climate variance on smaller spatial scales (“stratigraphic noise”,
). Wind scouring can additionally remove entire
seasons from the isotopic record . Vapour exchange
with the atmosphere by sublimation–condensation processes
can influence the isotopic composition of the
surface layers; diffusion of vapour into or out of the firn driven by
forced ventilation may
represent an additional component of post-depositional
change. Finally, diffusion of water vapour through the porous firn
smoothes isotopic variations from seasonal to inter-annual or
longer timescales, depending on the accumulation
rate .
In the last two decades, a number of studies analysed the
representativity of single ice cores in recording sub-millennial
climate changes. One well-studied region is the low-accumulation
(∼40–90mm w.e. yr-1, )
Dronning Maud Land (DML) on the East Antarctic Plateau. Here,
found low signal-to-noise variance ratios (F) in
200-year-long firn-core records for oxygen isotopes (F=0.14)
and accumulation rates (F=0.04), implying that the climate signal
content of a single core is much smaller than the noise level (14
and 4%, respectively). On a similar timescale,
detected no relationship in electrical properties
apart from volcanic imprints between firn cores. Similarly,
high-resolution records of chemical trace species from three shallow
ice cores showed a lack of
inter-site correlation on decadal timescales. These results were
supported by process studies comparing observed and simulated snow-pit
isotope data . Whereas the model–data comparison was
successful for coastal high-accumulation regions of DML
(400mm w.e. yr-1), it largely failed on the dryer East
Antarctic Plateau (70mm w.e. yr-1). This dependency
between accumulation rate and signal-to-noise ratio was further
demonstrated in studies across the Antarctic continent
. From high-accumulation
(140–520mm w.e. yr-1) Greenland ice cores,
estimated signal-to-noise ratios clearly larger
than 1.
Despite this large body of literature, quantitative information about
the signal-to-noise ratios and the noise itself is mainly limited to
correlation statistics of nearby cores. While
a relatively good understanding of stratigraphic noise exists in Arctic
records , this does not apply to low-accumulation
regions of Antarctica where the accumulated snow is considerably
reworked in and between storms .
Here, we provide a direct
visualisation and analysis of the signal and noise in an East Antarctic
low-accumulation region (64mm w.e. yr-1) by an extensive
two-dimensional sampling of the firn column in two 50 m long snow
trenches. Our approach, for the first time, offers a detailed quantitative
analysis of the spatial structure of isotope variability on a centimetre to
100-metre scale. This is a first step towards a signal and noise model to
enable quantitative reconstructions of the climate signal and their
uncertainties from ice cores.
Data and methods
Near Kohnen Station in the interior of Dronning Maud Land, close to
the EPICA deep ice core drilling site (EDML, -75.0∘ S,
0.1∘ E; altitude 2892m a.s.l.; mean annual
temperature -44.5∘C; mean annual accumulation
rate 64mm w.e. yr-1; ), two
1.2m deep and approximately 45m long trenches in
the firn, named T1 and T2, were excavated during the austral-summer
field season 2012/2013 using a snow blower. Each trench was aligned
perpendicularly to the local snow-dune direction. The horizontal
distance between the starting points of T1 and T2 was
415m.
An absolute height reference was established using bamboo poles by
adjusting their heights above ground with a spirit level. A control
measurement with a laser level yielded in each snow trench a vertical
accuracy better than 2cm. No absolute height reference
between the two trenches could be established, but, based on a stacked
laser level measurement, the vertical difference between the trenches
was estimated to be less than 20cm.
Both trenches were sampled for stable-water-isotope analysis with
a vertical resolution of 3cm. In T1, 38 profiles were taken at
variable horizontal spacings between 0.1 and
∼ 2.5m. In T2, due to time constraints during the field
campaign, only four profiles at positions of
0.3, 10, 30 and 40 m from the trench starting point
were realised. The sampling of each trench was completed within
24 h. All firn samples (N=1507) were stored in plastic
bags and transported to Germany in frozen state. Stable isotope ratios
were analysed using cavity ring-down spectrometers (L2120i and L2130i,
Picarro Inc.) in the isotope laboratories of the
Alfred Wegener Institute (AWI) in Potsdam and Bremerhaven. The isotope
ratios are reported in the usual delta notation in per mil
(‰) as
δ=RsampleRreference-1×103,
where Rsample is the isotopic ratio of the sample
(18O/16O) and Rreference that of
a reference. The isotopic ratios are calibrated with a linear three-point
regression analysis using in-house standards at the beginning of each
measurement sequence, where each standard has been calibrated to the
international V-SMOW/SLAP scale. Additionally, a linear drift-correction
scheme and a memory-correction scheme (adapted from )
is applied, using three repeated measurements per sample. The analytical
precision of the calibrated and corrected δ18O
measurements is assessed by evaluating standards in the middle of each
measurement sequence. This yields a mean combined measurement uncertainty of
0.09‰ (RMSD). The δ18O trench data are
archived under 10.1594/PANGAEA.861675 .
For the analysis of the measurements, we set up two coordinate systems
for each trench (Fig. ). Surface coordinates
refer to a local, curvilinear system with the horizontal axis along
the surface height profile and the vertical axis denoting the firn
depth below the local surface. Absolute coordinates adopt the mean
surface height as a reference for a straight horizontal axis,
completed by an absolute depth scale.
Coordinate systems used for the analysis of the trench
isotope data: (1) a curvilinear coordinate system (ξ,ζ)
(blue dashed lines, surface coordinates) with horizontal axis
along the surface height profile and vertical axis denoting
the depth below the local surface; (2) a Cartesian system (x,z)
(black lines, absolute coordinates) defined by the mean surface
height.
Results
Trench isotope records
The firn samples obtained from trench T1 provide a two-dimensional
image of the δ18O structure of the upper
∼1m of firn on a horizontal scale of ∼ 50m
(Fig. a).
(a) The two-dimensional δ18O data set
of trench T1 displayed on absolute coordinates. The solid black line
shows the surface height profile, the long-dashed black line the
mean surface height. Sampling positions are marked by the black
dots above. White gaps indicate missing data. (b) The
stratigraphy of trench T1 expressed as the seasonal layer profiles
tracking the local δ18O extrema as explained in
the text.
The surface height profile of the trench reflects the typical snow
topography of the sampling region characterised by small-scale dunes
with their main ridges elongated parallel to the mean wind direction
. Trench T1 features one prominent
dune located between 25 and 40 m, accompanied by
a dune valley between 8 and 18 m, and some
smaller-scale height variations. The peak-to-peak amplitude of the
large dune undulation is ∼10cm; the entire height
variations exhibit a standard deviation (SD) of 2.9cm.
Overall, the trench δ18O record shows a diverse
picture. The delta values in T1 (Fig. a)
span a range from -54 to -34‰ with a mean of
-44.4‰ (SD 3.1‰). A similar range of
-50 to -38‰ is observed in T2
(Fig. ) with a mean of -44.0‰
(SD 2.7‰). We can identify 8 to 10
alternating layers of enriched and depleted isotopic composition in
the T1 record. The uppermost layer (first 6cm relative to
the surface) essentially shows enriched (mean of
-42.7‰) but also strongly variable
δ18O values between -54 and
-34‰ (SD 4.4‰), thus already
covering the range of the entire trench record. Stronger
enrichment tends to be found in the valleys; however, the
limited data do not allow one to conclude whether this is a general
feature. In an absolute depth of 5–20cm, a band of
generally more depleted δ18O values is found
exhibiting less horizontal variability compared to the first layer
with a range of -54 to -45‰ (mean
-48.5‰, SD 1.9‰). The layering
appears strongly perturbed in the depth of
∼60–100cm for profile positions
< 30m. Here, a broad and diffuse region of rather constant
δ18O values around -40‰ is
observed, together with a prominent, 20cm thick feature of
high delta values between 18 and 28m.
The four δ18O profiles obtained from trench T2
(Fig. ) show similar features as trench
T1. We can identify roughly five cycles in each profile. However, the
profiles diverge considerably at depths of 50–90cm,
which coincides with the region of strong perturbations identified in
T1.
To further analyse the isotopic layering, we determine the pronounced
local maxima and minima of each T1 δ18O profile
and visually assign summer and winter to the depths of these
extrema. This results in consecutive horizontal curves tracing the
vertical positions of seasonal extrema along the trench (seasonal
layer profiles, Fig. b). Assuming that
respective isotopic extrema occur at the same point in time
(summer/winter), the seasonal layer profiles reflect the surface height
profile for a given season. However, considering the highly variable
isotopic composition observed at the current trench surface
(Fig. a), this is a rough approximation
and the seasonal layer profiles will likely overestimate the past
surface height profiles. Nevertheless, the vertical undulations of the
layer profiles show peak-to-peak amplitudes of 6–24cm
(average SD 3.7cm), comparable to the present surface
undulations, and the layers are vertically separated by approximately
20cm, in accord with the local mean annual accumulation
rate of snow (64mm w.e. yr-1) and the mean firn density
measured in trench T1 (ρfirn=340kg m-3). To
study the similarity between the seasonal layer profiles and the
present surface height profile, we calculate the standard deviation of
their height differences (SDsurface, hence, the SD of
each layer profile on surface coordinates). This is compared to the
standard deviation of the layer profiles on absolute coordinates
(SDhoriz). We find that the first layer profile
closely follows the present surface
(SDhoriz-SDsurface=1.8cm).
For the second layer profile, the link with the surface is weaker
(SDhoriz-SDsurface=1.5cm),
and the layer profiles below 20cm are on average
horizontally aligned
(SDhoriz-SDsurface=-0.6cm).
This can be explained by an annual reorganisation of the stratigraphy
so that aligning the isotopic variations on absolute coordinates is on
average more appropriate than the alignment according to
a specific surface height profile. The positive autocorrelation with
a decorrelation length of ∼ 6cm that is found from the
vertical T1 δ18O variations after subtraction of
the mean trench profile is consistent with this hypothesis.
Due to the on average horizontal stratigraphy of the isotopic
composition in the larger part of the trench record all further plots
and calculations will be evaluated on absolute coordinates.
The four δ18O profiles obtained from trench
T2 displayed on absolute coordinates.
Histogram of all possible pairwise correlations (N=152)
between single profiles of trench T1 and single profiles of trench
T2. Displayed are the maximum correlations allowing vertical shifts
of the T2 profiles of up to ±12cm. Shown in red is
the correlation between the mean profiles of T1 and T2
(Fig. ).
Single-profile representativity
The isotope record of trench T1 (Fig. a)
allows the quantification of the horizontal isotopic variability of the snow and
firn column in our study region. We observe considerable horizontal
variability with a mean variance of
σh,T12≃5.9(‰)2, directly
affecting the representativity of single trench profiles. To mimic the
potential result obtained from correlating two snow pits taken at
a distance of 500m, similarly done in many firn-core
studies e.g., we calculate the pairwise
Pearson correlation coefficient between single profiles of T1 and
single profiles of T2. We account for potential surface undulations
between the trenches by allowing bin-wise vertical shifts of
±12 cm between the T1 and T2 profiles to maximise their
correlation. The estimated correlations (Fig. )
are substantially scattered around a mean correlation of ∼ 0.50
(SD=0.13). The relative majority (∼43%) of all
possible profile pairs (N=152) shows a maximum correlation at a
shift of +3cm, which is well below the estimated upper
vertical height difference of the trenches.
Mean trench profiles
Spatial averaging is expected to improve the correlation between the
trenches compared to the single profiles. We therefore correlate the
mean trench profiles of T1 and T2, allowing again for bin-wise
vertical shifts of the T2 profile to maximise the correlation.
The mean trench profiles (Fig. ) are
highly correlated (rT1,T2=0.81 for an optimal shift of
+3cm; p=0.01, accounting for the full autocorrelation
structure and allowing for vertical shifting), indicating a common
isotopic signal reproducible over a spatial scale of at least
500m. It is interesting to note that this value is above
most of the single inter-trench correlations
(Fig. ).
In both mean profiles, we observe five seasonal cycles spanning a range of
∼6–7‰ at the surface, but being attenuated
further down and exhibiting no clear sinusoidal shape in the depth range of
65–90cm. Interestingly, this obscured part without
clearly depleted δ18O “winter” values is found in both
trenches, indicating that this feature persists over at least
500m and is thus likely of climatic origin, e.g. a winter with
unusually low precipitation. Despite the statistically significant
correlation, pronounced differences between the mean profiles are present,
such as a significantly more
depleted, and partially more enriched, isotopic composition of the T2 mean
between 50 and 80 cm.
Comparison of the mean δ18O profiles (lines:
seasonal, points: annual mean) from T1 (black) and T2 (red). To
maximise the seasonal correlation (rT1,T2=0.81), trench
T2 was shifted by +3cm. For the first three depth bins,
the number of existing observations varies on absolute coordinates
between the trench profiles. To obtain non-biased seasonal mean
profiles only the depth range covered by all profiles is
used. Shading represents the range of the approximate annual-mean
profiles due to different binning definitions. Note that their first
and last value are biased since the trench data are incomplete
here. Vertical dashed grey lines mark the six local maxima of the
average of both seasonal mean profiles.
Observed and modelled inter-profile correlation as a function of
profile spacing for T1. Observations for a given spacing are the
mean across all possible profile pairs. Shading denotes the standard
error of the mean assuming maximum degrees of freedom (DOF) of
N=12 (estimated from the effective DOF of the horizontal trench
data accounting for autocorrelation).
To analyse annual-mean δ18O time series we use
different binning methods to average the seasonal trench data
with bins defined by (1) the six local maxima determined from the
average of the two mean trench profiles, (2) the five local minima,
(3) the midpoints of the ascending slopes flanking the maxima and
(4) the midpoints of the descending slopes. To display the data on
an absolute time axis we assign the year 2012 to the first annual
bin. The annual-mean time series derived from the four possible
binning sets are averaged to obtain a single time series for each
trench (Fig. ). The correlation of the
average annual-mean δ18O time series of
rT1‾,T2‾=0.87-0.20+0.07
(range represents the four binning methods) is comparable to that of
the mean seasonal profiles (0.81). However, five observations of
annual means are too short to reliably estimate the correlation and
its significance.
Spatial correlation structure
We have shown that spatial averaging significantly increases the
correlation between the trenches. To learn more about the spatial
correlation structure of the trench isotope record, we investigate
(1) the inter-profile correlation as a function of profile spacing for
T1 and (2) the inter-trench correlation between different sets of mean
profiles from T1 and the mean T2 profile.
The inter-profile correlation is estimated as the mean of the
correlations obtained from all possible T1 profile pairs separated by
a given spacing, allowing a tolerance in the horizontal position of
5%. For the inter-trench correlation, we define a T1
profile stack as the spatial average across a certain number of T1
profiles separated by a given distance, and determine all possible
equivalent stacks. The inter-trench correlation with the mean T2
profile is then recorded as the mean across the correlations between
the mean T2 profile and all possible T1 stacks.
The inter-profile correlation approaches 1 for nearest neighbours
and rapidly drops with increasing inter-profile spacing before it
stabilises around a value of ∼ 0.5 for spacings
≳10m (Fig. ). For the
inter-trench correlation, we find a steady increase in the correlation
with the T2 reference with increasing number of profiles used in the
T1 stacks (Fig. ). Additionally, the
correlation increases with a wider spacing between the individual
profiles of a stack.
The observed decrease of the inter-profile correlation with distance
suggests a horizontal autocorrelation of the isotopic composition.
Indeed, a positive autocorrelation of the horizontal
δ18O variations of T1 with a decorrelation length
of λ≃1.5m is found by applying a Gaussian
kernel correlation which accounts for the
irregular horizontal sampling. As we do not expect any climate-related
part of the isotopic record to vary on such small spatial scales, we
attribute the observed autocorrelation to noise features.
Observed and modelled correlations between T1 profile stacks and the
mean of all T2 profiles depending on the number of profiles in the
T1 stack for three selected inter-profile spacings. Observed
results for given spacing and number of profiles are the mean
across the correlations obtained for all possible unique stacks and
only calculated when at least 15 stacks are available.
Statistical noise model
The inter-profile correlation rXY provides an estimate of the
signal-to-noise variance ratio F of single profiles
,
F=rXY/(1-rXY).
Neglecting the small-scale correlation, we estimate F from the data
using the mean inter-profile correlation for the profile spacings
between 10 and 35 m and find F=0.9±0.1.
Based on our findings, we develop a simple statistical model: we
assume that each trench profile consists of the sum of a common
climate signal S and a noise component w independent of the
signal. The noise component is modelled as a first-order
autoregressive process (AR(1)) in the horizontal direction. Then, the
inter-profile correlation coefficient between profiles X and Y
becomes a function of their spacing d (see Appendix ),
rXY=11+F-11+F-1exp-dλ.
Here, F-1=var(w)/var(S) is the inverse of the
signal-to-noise variance ratio. Using our estimate for F and the
value for λ obtained in the previous section, the model
reproduces the observed inter-profile correlations
(Fig. ). Applying the same parameter
values, the theoretical inter-trench correlation
(Eq. ) is also in good agreement with the
empirical results (Fig. ). This validates the
model and the parameter values (F,λ) from the intra-trench
(∼10m) to the inter-trench spatial scale
(∼500m).
Discussion
Our trench data confirm earlier results that individual
δ18O firn-core records from low-accumulation
regions are strongly influenced by local noise
. Going beyond this
finding, our two-dimensional δ18O data set also
allows one to determine the spatial structure and to learn about the
causes of the noise. In this section, we discuss our findings in the
context of the possible noise sources and derive implications for
seasonal to inter-annual climate reconstructions based on firn cores.
Local stratigraphic noise and regional climate signal
A horizontally stratified trench without horizontal isotopic variations
would yield perfectly correlated single profiles. Opposed to that, our
records (Table ) show a significant variability in
horizontal direction with mean variances
σh,T12≃5.9(‰)2,
σh,T22≃5.3(‰)2
that are smaller but of the same order of magnitude as the mean
down-core variances
σv,T12≃9.5(‰)2,
σv,T22≃7.3(‰)2.
In consequence, coherent isotopic features between single profiles
separated by the trench distance are only found by chance
(Fig. : the median correlation is 0.49, only
for two pairs (∼1.3%) the correlation is > 0.8). Thus,
single firn profiles from our study region are no representative
recorders of climatic isotope signals on the vertical scales analysed
here.
On the horizontal scale of the trenches
(∼10–500m), we expect that stratigraphic noise
dominates the isotopic variations . The observed
length scale of the horizontal decorrelation of the noise
(λ∼1.5m) is similar in magnitude as that on
which the local small-scale surface height variations occur,
indicating that stratigraphic noise is in fact the prominent noise
component in our data.
Despite the low single-profile representativity, the trench record
contains a climate signal becoming apparent
through the inter-profile correlation of ∼ 0.5 remaining on
scales on which the stratigraphic noise is decorrelated
(≳ 10m). It appears to be regionally
(≲ 1km) coherent as suggested firstly by the
comparable values of the inter-profile correlation for spacings
≳ 10m and the mean correlation between single T1–T2
records (Fig. ), and secondly by the common
seasonal signal observed in the mean trench profiles
(Fig. ).
Noise is always reduced by averaging profiles; here, the
autocorrelation causes nearby profiles to share more common noise
variance than profiles at a larger spacing. Therefore, albeit the same
number of profiles is averaged, stacks using a larger profile
spacing will exhibit less common noise variance and hence
a larger proportion of the underlying signal
(Fig. ). Our results show a minimum profile
spacing of ∼10m to be optimal.
Representativity of a δ18O firn profile
stack expressed as the correlation with a hypothetical
climate signal depending on the number of profiles averaged and
their inter-profile spacing. For annual resolution, the two limiting
cases discussed in the text are displayed (a best-case
scenario, b worst-case scenario), each for 2m
(black) as well as 10m (blue) inter-profile spacing. As
a reference, in each case the seasonal representativity is shown in
red for 10m inter-profile spacing.
Representativity of isotope signals on seasonal to
inter-annual timescales
For quantitative climate reconstructions from proxy data, a robust
estimate of the climate signal is necessary. Based on our
statistical noise model, we can estimate the isotopic climate signal
content of a profile stack for our study region depending
on the number of averaged profiles and their spacing.
To this end, we define the climate representativity of a trench
profile stack as the correlation between the stack and a common
climate signal (Eq. ). This signal
is identified with the coherent isotope signal of the trench
records. A physical interpretation of the climate
representativity is then the upper bound of the correlation with a
local temperature record, for example from a weather station. However,
bearing in mind other influences such as meteorology (variable storm
tracks, changing moisture source regions, precipitation-weighting),
the true correlation will be lower. In the limit of independent
noise our definition of climate representativity is equivalent to the
expression derived by .
In general, climate signals are timescale-dependent. For example,
the seasonal amplitude of the isotopic signal is much larger than any
variations between the years. On the other hand, one expects larger
changes of the climate signal on longer timescales, such as
glacial–interglacial cycles. Moreover, not only the climate signal but
also the noise can be a function of the timescale. One extreme
example for this is the non-climate oscillations of the
isotopic composition on up to centennial timescales which have been
indicated by snow-pit studies around Vostok station and linked to the
movement of accumulation waves on various scales .
Since the climate representativity (Eq. ) depends
on the ratio F of signal and noise variance, it is in consequence
also a function of the timescale.
Here, we assess the climate representativity of firn isotope profiles
from our study region for two specific timescales: (1) the original
resolution of the trench data and (2) an annual resolution based on
binning the trench data.
Analysing the original data, which is dominated by variations on
seasonal timescales, the climate representativity can be readily
calculated with the model parameters obtained in
Sect. . For the analysis at annual resolution,
estimates of both annual signal and noise variance are necessary
to assess the variance ratio F. However, the shortness of our trench
data only allows heuristic estimates (see Appendix for
details). Specifically, for the annual noise variance we discuss two
limiting cases: for case I we assume that the vertical noise is white
(best-case scenario), for case II that the vertical noise shows
complete inter-dependence on the sub-annual timescale (worst
case). The inverse of the annual signal-to-noise variance ratio,
Fannual-1=var(w)annual/var(S)annual,
used in the model is then ∼ 1.2 for case I and ∼ 8.7 for case
II. A summary of the noise levels is given in
Table .
Variance levels of the two trenches: the horizontal variance is the
mean variance of all depth layers on absolute coordinates; the
down-core variance is the mean vertical variance of all respective
trench profiles. The seasonal as well as the annual variance levels
denote the variances of the respective mean seasonal and annual
δ18O time series of the two trenches
(Fig. ). All numbers are in units of
(‰)2.
Trench
Horizontal σh2
Down-core σv2
Seasonal σ‾v2
Annual σ‾a2
T1
5.9
9.5
5.1
1.15
T2
5.3
7.3
3.3
0.21
For single profiles, the climate representativity estimated at
seasonal resolution is 0.69 (Fig. ). At
annual resolution, single profiles show a representativity
of 0.67 in the best-case scenario (Fig. a)
and of 0.32 in the worst-case scenario
(Fig. b).
Noise variance and standard deviation (SD) of the trench data
together with the ratio of measurement uncertainty
(σCRDS=0.09‰) and respective noise SD,
given for different resolutions and for the two limiting cases of
the annual noise variance. The decadal noise level estimates are
calculated from the annual noise variances accounting for full
forward diffusion.
Resolution
Variance in (‰)2
SD in ‰
σCRDS/SD
seasonal
5.9
2.43
4 %
annual: case I
0.84
0.92
10 %
annual: case II
5.9
2.43
4 %
decadal: case I
0.08
0.28
32 %
decadal: case II
0.56
0.75
12 %
Similar to the correlation between the trenches
(Fig. ), the representativity increases with
the number of profiles averaged with a stronger increase for larger
inter-profile spacings. However, spacings above 10m do
not yield a further increase as the stratigraphic noise is largely
decorrelated. To obtain a climate representativity of 0.8 at
annual resolution with profiles separated by 10m,
a minimum of 3–16 cores are needed (from best to worst
case). Demanding a representativity of 0.9, the number of cores
required increases to 6–37.
Probability of detecting a linear temperature trend of
0.5∘C (50 yr)-1 (p=0.05) (solid lines)
and of determining the strength of the trend with an accuracy of
25% (dashed lines) as a function of the number of firn
cores averaged and for the two scenarios of the annual noise
variance discussed in the text (black: best case, blue: worst
case).
The modelled single-profile climate representativity at
annual resolution appears consistent with previous findings from
Dronning Maud Land. estimated a low signal-to-noise
variance ratio of F=0.14 obtained from the cross-correlations of
16 annually resolved δ18O records from an area
of 500km× 200km. Due to the large inter-core
spacings, the stratigraphic noise in the records is decorrelated
and the variance ratio F can be translated into a single-profile
representativity of rSX=1/1+F-1≃ 0.35, consistent
with our findings for the worst-case scenario. However, the records
analysed in are also subject to dating uncertainties,
additional variability caused by spatially varying
precipitation-weighting and other effects. Therefore, the similar
representativities are not necessarily caused by the high
stratigraphic noise level assumed in the worst-case scenario. In
addition, our trench data indicate vertical autocorrelation of the
noise (Fig. b and
Sect. ). Thus, the true climate representativity
for our study region will likely be in between our limiting
estimates.
Stratigraphic noise affects not only isotopes but also other
parameters measured in ice cores, such as aerosol-derived chemical
constituents. investigated the seasonal to
inter-annual representativity of ion records from five Greenland firn
cores taken at varying distances from 7 to 10 m in
the vicinity of the NEEM drilling site. Using the definition of
representativity based on , they found inter-annual
representativities of ∼0.55–0.95, depending on the number
of averaged cores and the ion species considered. These numbers are
slightly higher than our best-case-scenario results for
δ18O, which is expected since the accumulation
rate at the NEEM site is about 3 times higher than at Kohnen
Station .
Our estimates for the climate representativity of firn cores hold as
long as the signal-to-noise variance ratio F does not
change. Variance-affecting processes such as diffusion and
densification have equal influence on signal and noise and thus do
not alter the ratio F. On the other hand, only one component might
change over time; for example, the noise variance might vary due to changing
environmental conditions, or the variability of the climate could
have been different in the past for certain time
periods. Nevertheless, given the stability of the Holocene climate, we
do not expect first-order changes of the signal and noise properties
over time. However, we do expect a timescale dependency of the
climate signal with more variance associated with longer timescales
e.g.. The signal-to-noise variance ratio and
the climate representativity of firn cores will improve considerably
on these scales.
Implications
Our noise level and implied climate representativity estimates
underline the challenge of firn-core-based climate reconstructions at
seasonal to annual resolution in low-accumulation regions. For our
study site, we now discuss implications of our noise model concerning
(1) the required measurement precision of water isotopes in the case
of classical isotope thermometry, (2) the potential noise fraction in
isotope signals of the EDML ice core and (3) the detectability of a
temperature trend.
Our estimates of the stratigraphic noise level are based on the upper 1 m of
firn. Due to the shortness of the data our results are limited by
insufficient knowledge of the vertical noise covariance structure for
inter-annual and longer timescales for which we now assume white-noise
behaviour. The noise of isotopic data obtained from deeper parts of the firn
column is affected by diffusion and densification. Densification is only of
importance when studying the isotopic time series in the depth domain since in that case constantly sampled data will
contain noise levels on varying timescales. We estimate the effect of
diffusion and find that at decadal resolution below the firn–ice transition
the noise level at Kohnen Station is only 5% smaller as compared to the
undiffused case (Appendix and Table ).
The noise of an isotopic signal includes the stratigraphic noise
as well as noise caused by the measurement process. Since the
stratigraphic noise is a function of the number of analysed cores, and
measurement precision is often related to measurement time, obtaining
the best signal is a trade-off between measurement precision and the
amount of analysed samples.
At seasonal as well as annual resolution, the measurement uncertainty
of the trench data of σCRDS=0.09‰ is much
lower (∼4–10%) than the standard deviation of
the stratigraphic noise (Table ).
This ratio is independent of the temporal resolution if a lower
resolution is obtained by averaging annually resolved
data as both contributions decrease by the same amount in the
averaging process, assuming independence between the samples. In such
a case, priority should be given to measuring and averaging across
multiple cores in order to reduce the (stratigraphic) noise levels
instead of performing high-precision measurements on single cores. As
an example, with the cavity ring-down spectrometers used for this work
faster measurements are possible by reducing the number of repeated
measurements per sample and applying a memory correction
. We explicitly note that this possibility
is limited to classical single-isotope (δ18O)
reconstructions as it can affect the data usability for
diffusion- or deuterium-excess-based
inferences.
If a lower temporal resolution is obtained by a coarser sampling of
the cores, the measurement error to stratigraphic noise ratio
will depend on the analysed resolution (Table ).
For a resolution corresponding to 10 years, our measurement
uncertainty might amount to up to 32% of the stratigraphic
noise level, accounting for full diffusion. The noise level of single
cores would become comparable to the measurement uncertainty for
averages over ∼ 104 or ∼ 735 years (best- or
worst-case scenario of annual noise level).
The deep EPICA DML ice core obtained in the vicinity of Kohnen Station
reflects the climate evolution in Antarctica over the last
150 000 years .
studied a core section covering the last 6000 years
at decadal resolution. We find a δ18O
variance for this section of ∼ 0.57(‰)2.
Using our diffusion-corrected stratigraphic noise variance estimates
would imply that ∼ 15–100% (from best to worst
case) of the observed decadal variance in the core might be noise
(Table ), masking the underlying climate
variability. We note that this is only a rough estimate as the
shortness of the trench data does not allow one to fully assess the
decadal noise covariance. In any case, averaging across multiple cores
seems necessary in low-accumulation regions to reconstruct the
climate variability of the last millennium. Alternatively, if only the
magnitude of variability is of interest, the proxy variability has to
be corrected for the noise contribution e.g..
As a final example of applying our noise model, we test the influence of
stratigraphic noise on the detectability of a linear trend at Kohnen Station.
This is motivated by the finding of that in the last
50 years the surface temperature over East Antarctica has warmed by
about half a degree. While both the climate signal as well as the
relationship between local temperature and isotopic signal are complex, we
assess the detectability with a simplified model experiment. For this, we
assume the climate signal to be a purely linear trend
(0.5∘C (50 yr)-1) and a
linear isotope-to-temperature relationship (1‰ K-1),
further influenced only by post-depositional noise. In a Monte Carlo approach
repeated 105 times, we create stacks from 50yr long
δ18O profiles with post-depositional noise variances
based on our two limiting cases (Table ), accounting
for an average effect of diffusion on the annual noise level over the
50 years (Appendix ) and assuming independent noise between the
profiles (inter-profile spacings ≳ 10m), and vary the
number of averaged profiles. A trend in the stacked profile is successfully
detected for an estimated trend that is significantly larger than zero
(p=0.05); the estimated slope is defined to be correct when it lies in
a range of 25% around the true slope. The probability of trend
detection/slope determination is then the ratio of successful reconstructions
to total number of realisations.
Drilling a single core, the probability of detecting the trend or
reconstructing its slope is around 25% in the best-case
and below 10% in the worst-case scenario
(Fig. ). To reliably (>80% of the
cases) detect the warming over the East Antarctic Plateau, our results
suggest that averaging across at least ∼5–35 firn cores
taken at spacings of 10m (Fig. ) is
needed, depending on the scenario for the annual noise
variance. Inferring the right slope would need 3 times that number
of cores. We note that more realistic assumptions about the isotopic
signal (natural climate and atmospheric variability, varying
isotope–temperature relationship, etc.) further complicate the trend
detectability.
Conclusions
We presented extensive oxygen stable water isotope data derived from two snow
trenches excavated at Kohnen Station in the interior of Dronning Maud Land,
Antarctica. The two-dimensional approach allowed a thorough investigation of
the representativity of single firn-core isotope profiles, as well as of the
spatial structure of the signal and noise over spatial scales of up to
500m and a time span of approximately 5 years.
The trench data confirm previous studies that single low-accumulation
(≤100mm w.e. yr-1) isotope profiles only show a weak
coherent signal at least on sub-decadal timescales. We also
demonstrate that the spatial average of a sufficient number of
profiles provides representative isotopic signals, consistent with our
finding that the local noise has a small horizontal decorrelation
length (∼1.5m). This also suggests stratigraphic noise
to be the major contribution to the horizontal isotopic
variability. A statistical noise model based on a first-order
autoregressive process successfully explains the observed covariance
structure and allows one to reproduce the correlation statistics between
the trenches.
Based on these results we infer appropriate sampling strategies. At our
low-accumulation (64mm w.e. yr-1) site an optimal spacing of
about 10m is necessary for a sufficient decorrelation of the
stratigraphic noise. We estimate the climate representativity of isotope
profiles depending on the number of averaged firn cores and the inter-core
spacing. Our estimates show that at seasonal resolution five cores at
the optimal spacing are necessary to
obtain representative (r>0.9) isotope signals; at annual resolution up to
∼8 times as many cores are needed. As climate variations are typically
stronger on longer timescales than analysed here, the climate
representativity of firn- and ice-core reconstructions for slower climate
changes will likely be higher.
We present two examples of how the stratigraphic noise might hamper
the quantitative interpretation of isotope in terms of climate
variations at our study site. Our data suggest that at least
15% of the decadal variations seen in the EPICA DML ice core
over the last 6000 years might be post-depositional noise, but
the climate signal might also be masked by a much higher decadal noise
level. A simplified model experiment shows that the faithful reconstruction
of the recent positive temperature trend observed over the East
Antarctic Plateau likely requires averaging across at least 5–35
firn cores. For single-proxy (δ18O)
reconstructions this task could be rendered more easily by the fact that
the annual noise level is substantially larger than typical
measurement uncertainties. Thus, monitoring the measurement error
depending on sample throughput could allow fast measurements for the
benefit of analysing many cores. Alternatively, using indirect methods
based on diffusion or gas isotope
ratios might circumvent the problem of
stratigraphic noise.
Since the stratigraphic noise is related to irregular re-deposition
and erosion of snow and the formation of surface dunes, it primarily
depends on the local accumulation rate, besides further factors
such as wind strength, temperature, seasonal timing of the
precipitation and snow properties. Therefore, we expect that our
representativity results improve (worsen) for regions with higher
(lower) accumulation rates. In effect, our results are likely
applicable for large parts of the East Antarctic Plateau, but similar
studies in West Antarctica and Greenland – regions with considerably
higher accumulation rates – are needed. In addition, studies with
deeper trenches that cover a longer time period, complemented by
spectral analyses of nearby firn cores, are necessary to enhance our
knowledge of the vertical noise covariance structure. This is crucial
to determine the climate representativity on longer timescales. Deeper trenches would also allow one to link our representativity
results to actual correlations with temperature time series derived
from weather stations. The latter is part of ongoing work at Kohnen
Station.