CPClimate of the PastCPClim. Past1814-9332Copernicus PublicationsGöttingen, Germany10.5194/cp-13-1593-2017Reconstructing Late Holocene North Atlantic atmospheric circulation changes using functional paleoclimate networksFrankeJasper G.jasper.franke@pik-potsdam.deWernerJohannes P.https://orcid.org/0000-0003-4015-7398DonnerReik V.https://orcid.org/0000-0001-7023-6375Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, GermanyDepartment of Physics, Humboldt University, Newtonstraße 15, 12489 Berlin, GermanyBjerknes Centre for Climate Research and Department of Earth Science, University of Bergen, Postboks 7803, 5020 Bergen, NorwayJasper G. Franke (jasper.franke@pik-potsdam.de)17November20171311159316089March201714March201728September20179October2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://cp.copernicus.org/articles/13/1593/2017/cp-13-1593-2017.htmlThe full text article is available as a PDF file from https://cp.copernicus.org/articles/13/1593/2017/cp-13-1593-2017.pdf
Obtaining reliable reconstructions of long-term atmospheric circulation
changes in the North Atlantic region presents a persistent challenge to
contemporary paleoclimate research, which has been addressed by a multitude
of recent studies. In order to contribute a novel methodological aspect to
this active field, we apply here evolving functional network analysis, a
recently developed tool for studying temporal changes of the spatial
co-variability structure of the Earth's climate system, to a set of Late
Holocene paleoclimate proxy records covering the last two millennia. The
emerging patterns obtained by our analysis are related to long-term changes
in the dominant mode of atmospheric circulation in the region, the North
Atlantic Oscillation (NAO). By comparing the time-dependent inter-regional
linkage structures of the obtained functional paleoclimate network
representations to a recent multi-centennial NAO reconstruction, we identify
co-variability between southern Greenland, Svalbard, and Fennoscandia as being
indicative of a positive NAO phase, while connections from Greenland and
Fennoscandia to central Europe are more pronounced during negative NAO
phases. By drawing upon this correspondence, we use some key parameters of
the evolving network structure to obtain a qualitative reconstruction of the
NAO long-term variability over the entire Common Era (last 2000 years) using
a linear regression model trained upon the existing shorter reconstruction.
Introduction
The increasing availability of high-resolution paleoclimate archives and
resulting proxy records allows to study not only local climate variability
before the beginning of the instrumental period but also associated spatial
structures at least at a regional level. Corresponding studies have commonly
been performed using linear multivariate statistical methods like empirical
orthogonal function (EOF) analysis
or, more
recently, Bayesian hierarchical modelling .
However, at the conceptual level, many of the classical statistical
approaches have considerable problems in analysing paleoclimate data. On the
one hand, traditionally used estimators are often inappropriate for coping
with spatially sparse and unevenly sampled time series. On the other hand,
the appealing alternative of data interpolation can lead to a systematic bias
and large uncertainties in the resulting reconstructions of spatial patterns
of past climate variability . Furthermore,
many previously applied methods rely on some kind of linearity and/or
orthogonality assumption, which might result in some unrealistic
representation of the climatic processes or phenomena under study.
Some of the aforementioned challenges can be (at least partially) addressed
by the concept of functional climate networks
, a recently developed nonlinear
approach to studying climate dynamics that can also be employed for
evaluating spatial co-variability among paleoclimate archives
. Here, each time series from a set of climate
observations associated with different geographical locations is represented
as a node of an abstract network embedded in geographical space. Pairs of
such nodes are connected by links if the observed dynamics is sufficiently
similar, which is referred to as functional connectivity to
highlight that similar, mutually dependent physical processes are commonly
reflected by statistical co-variability. Climate networks provide an
intuitive way to quantitatively account for the full complexity of
co-variability and teleconnection patterns. Furthermore, instead of
considering a spatially homogeneous data coverage, they simply ignore regions
without data, which is particularly important in the case of sparse
paleoclimate data.
Beyond the viewpoint of time-independent or average spatial co-variability
patterns, evolving functional networks are constructed from the available
data covering different time windows, which allows us to study the
evolution of such spatial patterns in time. While evolving functional climate
networks have become a widespread tool to analyse modern climate data
, applications to
paleoclimate data sets have been much less common so far
.
Although such network representations rely on the (potentially questionable)
assumption that the underlying spatio-temporally continuous climate system
has been coarse-grained and represented in some meaningful way by the
considered data sets, they take only the existing information into account
and do not make any explicit statements on regions not covered by these
data.
In this study, we highlight the potential of evolving functional paleoclimate
networks for investigating climate variability during the Common Era (last 2 kyr) in the European North Atlantic region. Climate dynamics within this
region is of crucial importance not only at regional scales
, but also as a pacemaker for
the whole Northern Hemisphere . Inter-annual to
multi-decadal climate variability in the North Atlantic sector is strongly
influenced by large-scale variability patterns like the North Atlantic
Oscillation (NAO; ). The NAO is related to the
persistent redistribution of air masses between the Arctic and the central
Atlantic and is commonly defined as a pressure
dipole over the North Atlantic, consisting of a predominant low-pressure
system over Iceland and a high-pressure system close to the Azores. The
strength of the gradient between both varies in time and provides a basis for
the quantitative description of the NAO based on an index where high (low)
values correspond to a strong (weak) gradient. This pressure gradient has
severe consequences for climate variability in Europe, Greenland, and North
America. A positive phase of the NAO is commonly associated with more
moderate temperatures and higher precipitation sums during winter in northern
Europe and the eastern United States, whereas Greenland, Canada, and southern
Europe often exhibit opposite characteristics. While the influence of the NAO
phase is strongest during boreal winter, it also affects summer conditions
.
As the NAO is a key aspect of European climate variability, long-term changes
in the dominant phase of this atmospheric variability mode should also be
reflected in the co-variability structure of existing paleoclimate records.
To this end, there are various types of archives available that could be
utilized for reconstructing such changes. Specifically, most high-resolution
archives in the region are sensitive tracers of inter-annual temperature
variability (commonly seasonal or annual mean values) and, hence, should have
been influenced to a certain degree by the NAO. For example, ice core data
from southern Greenland mostly reflect winter temperatures and, thus,
strongly follow winter NAO conditions
. In turn, tree ring
chronologies mainly trace summer temperatures, but can be additionally
influenced by winter conditions, especially in terms of extreme positive
precipitation anomalies see e.g.and references
therein.
While these facts have been utilized to reconstruct NAO indices prior to the
instrumental period , caution has to be taken
since the corresponding relationship is non-stationary. Thus, the
principle of uniformitarianism can be violated
. Furthermore,
the actual effect may not be the same at different locations and at
different phases of the NAO. For example, a persistent positive phase of the
NAO can enhance winter precipitation in northern Europe, which in turn has an
indirect influence on tree growth during the subsequent summer. The
corresponding opposite effect of a negative NAO phase is expected to be much
smaller. A similar relationship is expected to be present in central and
southern Europe, but here increased precipitation is commonly associated with
negative NAO phases, while positive NAO phases foster dry conditions and even
droughts.
Following upon these considerations, we anticipate that different types of
terrestrial archives available in different parts of the North Atlantic
region have in common that they all reflect the leading mode of regional
climate variability at inter-annual to multi-decadal timescales in one way
or another. Hence, the main idea of this study is that by exploiting the
temporary presence or absence of similar variability patterns between
different paleoclimate records, especially in southern Greenland versus the
rest of the study region, one can draw conclusions about changing
commonalities between the main atmospheric drivers in different sub-regions
and, thus, the mean state of the atmospheric circulation in the North
Atlantic region.
We emphasize that the aforementioned perspective differs markedly from
previous efforts to reconstruct NAO variability over the past millennia. The
general approach of existing studies, as used by ,
, and others, has been
to find a reasonable set of records and use linear regression techniques, to
infer NAO variability from proxy variability. In contrast to this, the
evolving functional network approach does not assume any stationarity of the
relationship between each individual proxy and the NAO. In fact, we
explicitly utilize the observed non-stationarity and thus offer a
complementary view on the same climatological target variable to common
linear regression models. This fact makes it also challenging to test our
proposed procedure by making use of pseudo-proxies, which present a common
framework for applying statistical methodologies based upon e.g. climate
model outputs, where the “true” target variable (in our case, some NAO
index) is known. However, in the present case, the actual relationship
between the NAO and the considered multiplicity of terrestrial paleoclimate
archives is mediated by multiple climate variables – for example temperature,
extreme winter precipitation and others. The influence of multiple variables
on paleoclimate archives is in many cases not sufficiently well constrained
to infer a particular statistical model. While pseudo-proxies exhibiting the
corresponding level of complexity could probably be constructed, their
application would present a rather novel methodological aspect that deserves
further studies on its own.
The remainder of this paper is structured as follows. In Sect. ,
we describe the ensemble of paleoclimate proxy records used in this study.
Section presents the methods used to construct evolving
functional paleoclimate networks and derive from them a scalar index variable
describing the time-dependent dominant mode of North Atlantic climate
variability over the Common Era. In Sect. , we discuss the
emerging structures and how well they reflect associated changes in the
dominant NAO phase at multi-decadal to multi-centennial timescales. Our
results are compared to findings from other studies in
Sect. , including a discussion on the possibilities and
possible shortcomings of our approach. The paper ends with concluding remarks
in Sect. .
Data
The North Atlantic region comprises a large variety of well-studied
high-resolution paleoclimate archives for the Late Holocene. Existing data
sets include several ice core records from the Greenland ice shelf and
Svalbard, tree ring chronologies from the Scandinavian Mountains, the Alps,
and other mountain ranges, and varved lake sediments, especially in southern
Finland. In addition, there exist also some very long historical temperature
records based upon early instrumental records (see references in the
Supplement Tables S1 and S2). Many of the available proxies are
strongly correlated to seasonal or annual temperature variability and thus
have been used as key input for existing regional and
hemispheric
temperature reconstructions. While there are particularly many archives
covering the last millennium, a considerably lower number spans the full
Common Era at high resolution.
Locations and types of the paleoclimate archives used in this study.
Different markers indicate different paleoclimate archives. Detailed
information on the individual data sets can be found in Tables S1 and S2.
In this study, we concentrate on changes in the inter-annual to multi-decadal
co-variability of temperature-sensitive proxies throughout the Common Era.
Thus, we only include records into our analysis that span at least 300 years
and have close to annual resolution. This leaves us with 37 time series,
which are described in detail in Tables S1 and S2.
They are shown in Fig. . Note that only 12 of these records
cover the full Common Era, all of them being located in either Greenland,
Fennoscandia, or the Alps.
We note that the considered selection criteria exclude some existing
records, which have been related to past NAO variability in previous works,
but are either not temperature sensitive or not of (approximately) annual
resolution (for example, the records used in the recent study of
). Specifically, most of the records studied
in this work have been derived from either tree rings, varved lake sediments,
or ice cores, all of which have been dated rather precisely (for estimates of
the dating uncertainty of some of the selected records, see e.g.
). Thus, age uncertainty is considered to be
negligible in the following. Unfortunately, there is no detailed information
on proxy uncertainty that is consistently available for all records.
Consequently, this uncertainty will not be further addressed explicitly in
the following analysis.
Methods
As mentioned in the Introduction, functional climate network analysis has
recently become an established tool for studies on climate dynamics.
Following upon the success of this approach, a few initial studies have
transferred the corresponding idea to the analysis of spatial co-variability
patterns among paleoclimate archives in a defined region
. Beyond
the original framework, we aim here at studying the statistical
interdependence structure between subsets of archives from different
appropriately defined regions and relate the information inferred from this
analysis to a macroscopic index tracing the dominating mode of inter-annual
North Atlantic climate variability at multi-decadal timescales. Accordingly,
the methodological approach followed in this work comprises the following
four steps:
Identify an ensemble of paleoclimate proxy records that have been influenced by a common climate variable (in our case, temperature).
Construct evolving functional networks based upon this ensemble according to the mutual similarity between individual records.
Temporal changes in the network's connectivity structure represent changes of co-variability between the studied proxies.
Introduce a meaningful grouping of the records to reduce the complexity and increase robustness of the obtained information
in the presence of proxy uncertainty and a varying number of records.
Establish a statistical relationship between the characteristics of the paleoclimate network and some climate variable or
index (in our case, an existing long-term NAO reconstruction).
This general workflow of functional paleoclimate network analysis is illustrated in Fig. .
We have already discussed the first step of this workflow in the
previous section. We highlight in the following the methodological
realization of the three remaining steps.
Schematic overview on the methodological approach of this study.
Based upon a network of paleoclimate proxy records, we construct evolving
functional networks encoding the co-variability among the different time
series. Using cluster analysis, we simplify the emerging network structures
and obtain quantitative measures of the inter-cluster linkages as key
characteristics of the obtained networks. These variables are then related to
an established long-term reconstruction of the NAO index via linear
regression.
Functional network construction
In general, an evolving functional network represents the time-dependent statistical co-variability structure
among a set of time series. In the case of a perfect climate recording, this information can be used to infer
teleconnections between distant regions. For paleoclimate archives, however, one has to recall the existence of additional
influencing factors represented in the recorded proxies. Thus, co-variability might not just indicate direct physical
linkages but possibly also secondary (external) effects that manifest in a similar way in different archives. For
example, extremal winter precipitation can affect both tree ring records and lake sediments, even though the archives
considered in this work primarily record temperature variations.
More specifically, a functional network is a graph-theoretical representation of the mutual similarity structure
among a set of time series {xti}(i=1,…,Nr), in our case a set of Nr=37 paleoclimate proxy records,
which are considered as nodes of the network. Here, the effective number of available records Ntr varies in time,
with maxtNtr≤Nr, and each node is identified with the respective geographical location of the underlying
paleoclimate archive. Links between different nodes are established if the corresponding time series are significantly
similar according to some corresponding measure of pair-wise statistical dependence. The details of this similarity
assessment are discussed in Sect. .
Evolving functional networks describe a time-ordered sequence of such
functional networks, each being constructed from data within a given time
window of length W, which span different periods of time. Here, a
time coordinate is assigned to each window according to its respective end
point. Thus, any statistical measure calculated from a subset of a time
series {xi}tW corresponding to the time window of length
W ending at time t is associated with the set of time indices
tW:={t′|0≤t-t′≤W}. The window size
W determines the temporal resolution of the analysis. Thus, we
obtain a sequence of networks associated with different time intervals.
Within this sequence, changes in the network structure allow tracing changes
in the spatio-temporal co-variability among the studied proxies through
time.
Each individual network is described by the Nr×Nr adjacency
matrix A, defining the connections between nodes,
AtWi,j=1if{xi}tWand{xj}tWare similar0else.
Similarity assessment
In general, functional networks can be constructed based upon different types
of similarity measures, including classical linear approaches like the
Pearson correlation, but also other measures suitable for detecting
nonlinear or event-based relationships, like mutual information or event
synchronization see e.g.for a comparison of possible
measures.
Specifically, to determine the strength of co-variability between two
paleoclimate records, a suitable similarity measure has to be able to cope
with unevenly sampled and/or discontinuous time series. Here, we use a
Gaussian kernel-based variant of the Pearson correlation coefficient (gXRF)
. Given two (normalized) time series
{xi}i=1Nx and {yj}j=1Ny (exhibiting zero mean and
unit variance) with observation times {tix}i=1Nx and
{tjy}j=1Ny, this correlation is defined as
ρx,y=∑i=1Nx∑j=1NyxiyjK(tjy-tix)∑i=1Nx∑j=1NyK(tjy-tix).
Here, the kernel function K(⋅) is given by
K(tjy-tix):=12πhe-(tjy-tix)2/2h
with h=maxΔtx,Δty/4, where Δtx,y
denote the mean sampling intervals of the corresponding time series.
Specifically, as the same atmospheric driving variable can have qualitatively
different effect on different proxies or at different locations, we take the
absolute value of this correlation to quantify the strength of similarity.
Since our analysis makes use of different types of paleoclimate proxies, it
is advisable to define similarity in a way that takes the different
characteristics of the proxies into account. Time series originating from the
same type of archive record climate variability in a similar fashion and thus
might intrinsically exhibit stronger mutual correlations than such from
different types of archives. Specifically, long-range auto-correlations and
associated low-frequency variability can lead to spurious correlations, which
have to be corrected for . To account for this
problem, we apply a surrogate-based significance test to calculate p values
corresponding to the probability that two records are similar just by chance,
given their inherent auto-correlation structures. For this purpose, we use
1000 amplitude-adjusted Fourier transform (AAFT) surrogates
, which leave the auto-correlation structure
of each time series intact (generated using the pyunicorn package; Donges et al., 2015). Note that among the considered set of archives,
all but four proxy records are complete and actually evenly distributed at
annual timescale (one having lower sampling resolution and the three others
containing gaps). In this regard, using the Gaussian kernel correlation
(developed for unevenly sampled data) instead of classical Pearson
correlation coefficient accounts for these four records with different
properties, while AAFT surrogates can still be generated with standard
procedures (using linear interpolation for the very few missing data) for
all records. The estimated p values resulting from the surrogate ensembles
provide a generally applicable measure of similarity, and two proxies are
considered to be similar if their p value (rather than the estimated
correlation value itself) is below a defined threshold value αpr.
Network analysis
In the case of paleoclimate time series, there are some particular
complications to be addressed in the context of functional network analysis.
First, many records do not cover the full time span under study. Thus, the
effective number of nodes Ntr varies with time (see Supplement Fig. S1). Second, while different archives might be significantly
affected by the same climate variable, they still exhibit both local and
proxy-specific effects, so that the outcomes of pair-wise similarity
assessments can be highly case specific, even though the shared climatic
influence might be the same. Furthermore, paleoclimate networks often already
exhibit too many nodes to allow for an intuitive climatic interpretation (in
particular, of individual links between pairs of proxies) but are at the
same time too small to apply more sophisticated methods from complex network
theory like community detection or structural characterization by means of
more complex measures like network transitivity or betweenness centrality,
which have been recently applied in the context of functional networks
constructed from recent climate data .
In order to address these peculiarities and to simplify the interpretation of
the resulting network structures, it appears reasonable to combine spatially
close records into clusters (as will be further detailed below) to
yield smaller networks with fewer, but weighted connections. In the present
context, a cluster is a subset of records CtWM⊂x•ii∈M with M⊂1,2,…,Nr and CtWM≥2 (here, |•|
denotes the cardinality, the number of members of a set). Note that we will
consider the assignment of any archive to a specific cluster as being fixed
over the entire analysis period (see below). Hence, the existence and size of
a given cluster vary only due to the (non-) availability of the given
archives during different periods of time.
Having obtained a climatologically meaningful grouping of our archives into
spatially connected clusters, we define the cross-link density (CLD) between
any two clusters CtWK and CtWL as
CLDtWK,L:=#links betweenCtWKandCtWL#possible links betweenCtWKandCtWL=∑i∈K∑j∈LAtWi,jCtWK⋅CtWL.
Note that as we are generally considering evolving (i.e. time-dependent)
network structures, the CLD for each pair of clusters will commonly vary in
time. However, the CLD values are expected to be more robust tracers of the
essential network structure than other commonly used network characteristics,
since they combine information from various links and are properly normalized
by the (time-dependent) number of records. If the paleoclimate archives were
perfect recorders of the same climate variable, these simplified networks
would then provide a coarse representation of the teleconnectivity structure
between larger regions. In the case of real-world paleoclimate records, the
attribution of any specific physical process to a link between clusters is
less clear. However, we can still interpret the existence of such links
(rather than the actual directionality of the represented correlations) as
being indicative of joint dynamical patterns and/or influences of different
regions.
By making use of the approach detailed above, for SC denoting the number
of clusters CM|CM≥2 we can
define an S=SC2 dimensional vector of cross-link densities
XtW=CLDtWK,L|K,L∈1,…,SC,K≠L. In this way, we effectively
obtain coarse-grained networks with fewer nodes (associated with each
cluster) and weighted links (CLD values). In turn, we disregard any
information on the intra-cluster statistical linkages between individual
archives, since we expect the latter to mainly reflect the intrinsic spatial
correlation length of the influencing climate variable. Combining information
on intra- and inter-cluster linkages would result in a paleoclimate “network
of networks” approach; a framework that has already been employed in a few
studies on recent climate variability
, but might
suffer from the low number of nodes in a paleoclimate setting.
Spatial clustering of proxies
As discussed above, it is advisable to simplify the functional paleoclimate
network by grouping several archives into spatially connected and
climatologically meaningful clusters and study exclusively the temporal
changes in the mutual similarity of proxies at the resulting cluster level.
Specifically, the obtained clustering should meet the conditions that
clusters (i) comprise spatially close archives and (ii) are large enough to
reduce the impact of individual records and thus lead to a robust
representation of the large-scale spatial co-variability structure.
Given the distinct individual characteristics of the different proxy time
series and local as well as archive-specific effects, it is difficult to
perform a cluster analysis directly at the set of time series originating
from the archives, since such a procedure would likely result in a highly
fragmented cluster structure. Instead, given that all proxies in our ensemble
are temperature sensitive, we define clusters as regions which have shown
similar inter-annual temperature variability over the modern (instrumental)
period. For this purpose, we make use of the gridded ERA-20C reanalysis
summer temperature data spanning the whole 20th century
. Based upon this data set, we generate a
functional climate network reflecting only the strongest absolute linear
(Pearson) correlations (as determined by a threshold value αC) among
the time series of seasonal mean (annually averaged boreal summer, JJA)
temperatures for each grid point over land in the study region. From this
network representation, we identify subsets of grid points with high
intrinsic and low extrinsic connectivity (referred to as network communities)
by applying the so-called Louvain algorithm (for details, see
; calculated using the community Python package).
We emphasize that the described spatial clustering procedure introduces an
additional parameter αC into the analysis. In general, we observe
that small values of αC yield more but smaller clusters, while larger
values lead to a lower number of larger clusters (not shown). One of the main
differences between the obtained clusters using different values of
αC (from a reasonable range of values) is the division of Greenland
and the border between central and eastern Europe. This is also the main
difference in using different variables (e.g. ERA-20C winter mean
temperature) for the clustering (Fig. S2).
Statistical modelling by regression
Beyond simple visual analysis of the evolving network structures, we aim to
statistically link the obtained time-dependent CLD values with a
climate-related variable (in our case, an existing NAO reconstruction by
, in the following referred to as
NAOOrtega) that reflects a common influence on
the co-variability between different regions. The simplest model to establish
such a relationship between XtW and some variable
Y would be a linear model
YtW=DtWXtW+ϵtW
with a coefficient vector D and a noise process
ϵtW. Such a model implies that the connectivity
between different regions is linearly related to the strength and the sign of
the NAO as given by Y. Note that while in general the CLD values should rather be
described as a superposition of different climatic influences, we take here
the opposite approach, which is potentially useful for obtaining a
reconstruction of the (unknown) climate driver based upon our evolving
functional paleoclimate network properties. For a detailed discussion on
different (regular vs. inverse) versions of this regression problem and
their implications in the context of paleoclimate reconstructions, we refer
to and and references therein.
We emphasize that the analysis procedure described above has two free
parameters, the threshold values αpr (for generating the
paleoclimate network) and αC (for obtaining the spatial clustering).
Given that our general aim is to maximize the inferred information about the
mean state of the leading mode of North Atlantic climate variability at
inter-annual to multi-decadal scales (which we assume here to largely
reflect the respective NAO phase) from the simplified networks, we vary the
values of αpr and αC to obtain an ensemble of sequences of
evolving networks as well as geographical clusterings, each ensemble member
corresponding to a different combination of both parameters. For each member,
we individually perform a multiple linear ordinary least-squares (OLS)
regression of all associated CLD values to the 50-year averaged
NAOOrtega reconstruction
– in the following denoted as
NAO‾Ortega,50 yr – using the model
in Eq. (). Application of larger smoothing windows
essentially yielded results very similar to those presented in the following,
while for shorter windows, the statistical uncertainty of the regression
substantially increased (not shown). In this regard, our choice of averaging
over 50-year periods represents a reasonable trade-off. The parameter
combination (αpr,αC) for which the resulting regression model
describes the largest fraction of variability in
NAO‾Ortega,50 yr (see Fig. S3) is then selected for further analysis. In general the
results obtained are robust for different window sizes (not shown).
As a final step, we further investigate the linear model
(Eq. ) for
NAO‾Ortega,50 yr using a Bayesian
approach, Markov chain Monte Carlo (MCMC) regression
. Unlike OLS regression, this method does not result in
individual estimates of the different regression coefficients but in joint
distributions for all model parameters. Thereby, we implicitly account for
the uncertainty in the description of the target variable. Since some of the
considered clusters of paleoclimate archives do not cover the full Common
Era, we can furthermore use the parameter distributions of the full set of
clusters as priors to find the new distributions of the reduced set of CLD
values, thus utilizing the knowledge of the full data for cases of lower data
availability. For performing the MCMC regression, we use the pyMC3 package (Salvatier et al., 2016) with a NUTS
with 104 samples with one-quarter of these
as burn-in.
Results
We have followed the procedure described in Sect. to study
the evolving paleoclimate networks derived from the set of 37 paleoclimate
records described in Sect. . The window size W of
our analysis has been selected as 50 years, consistent with the averaging
window in NAO‾Ortega,50 yr. We have
considered sliding windows with a mutual offset of 1 year, implying an
overlap of 49 years between subsequent windows. The threshold values
αpr and αC have been determined by maximizing the explained
variance of the 50-year averaged NAOOrtega
reconstruction (see Fig. S3), yielding αpr=0.46 and αC=0.0104. The resulting spatial clusters of archives
used in the analysis are displayed in Fig. .
Division of the study area as obtained by cluster analysis of the
ERA-20C summer mean temperatures, together with the paleoclimate archives
used in this study (αC≈0.01). Non-adjacent regions of the
same colour represent different clusters, as are indicated by different
symbols (squares vs. circles) showing the spatial locations of the
considered archives.
Simplified functional paleoclimate networks for different exemplary time windows illustrating the great
variety of spatial connectivity patterns during the time interval covered by this study. The red circles indicate the
centre of each group of records (only shown if any record of a cluster has values at the specific time window). The
thickness of each link is proportional to the CLD of that connection. The time intervals have been chosen such that
they demonstrate the general patterns of zonal and meridional connectivity. For a more objective analysis we employ a linear model.
Figure shows the simplified networks and dominating
cross-cluster links for some exemplary time windows, using a lower threshold
value of αpr=0.1 to better highlight the strongest correlations
(for illustrative purposes only). The most informative clusters are those
with the highest regression coefficients. These are located in southern
Greenland (SG), Fennoscandia (FS), and central Europe (CEU) and cover all of
the Common Era.
During the first millennium CE (of the Common Era), we can distinguish two
common, qualitatively different states of the network, one being dominated by
connections between FS and the other two clusters (Fig. a, c) and
another exhibiting strong correlations between archives from SG and CEU
(Fig. b, d). During the second millennium CE (with considerably
more archives available), we more clearly identify periods during which
mainly west–east connections between Greenland (G), Svalbard (S), and FS are
present (Fig. f, i). During other times, north–south connections
involving CEU are more strongly expressed (Fig. e, g, h). The
latter is commonly the case during time intervals for which
NAO‾Ortega,50 yr indicates a
negative mean reconstructed NAO index, while cross-cluster links are more
concentrated within the northern North Atlantic sector during positive NAO
phases.
The time intervals presented in Fig. and the aforementioned
general patterns are still subjective and thus call for a more objective
approach. For this reason, we employ the linear model (Eq. )
for NAO‾Ortega,50 yr. The resulting
mean regression coefficients of this model support the general patterns
discussed before. The respective strengths and signs of the most relevant
regression coefficients are illustrated in Fig. and
summarized in Table S3. In that figure, thick red
lines indicate that positive (negative) NAO phases coincide with relatively
many (few) cross-cluster links, while the relation is just the opposite in
case of linkages represented by blue lines. The time evolution of the six
CLDs associated with the largest coefficients is shown in Fig. S4. The explicit values of all CLDs are given in . The corresponding results further demonstrate that the
presence of strong west–east connections is indicative of a positive NAO
phase, while north–south connections, especially between CEU and the rest of
the network, point toward negative NAO phases. The largest regression
coefficients correspond to CLDs between SG and FS and CEU.
Regression coefficients between the 15 cross-link densities (CLD)
among the spatial clusters of records and
NAO‾Ortega,50 yr. Note that these
linkages represent statistical relations and do not necessarily relate
to (temperature) teleconnections between different regions, but may also
reflect common factors influencing the respective regional climate dynamics
as recorded by the proxies in a similar way. Black circles mark the centres
of each group of records. Each line indicates the correlation between the CLD
for two groups of records and the NAO reconstruction by
. Red (blue) colours indicate a positive
(negative) sign of the coefficient, whereas the width of the drawn links is
proportional to the mean coefficient value as given in
Table S3.
As an additional test for the validity of our estimated linear model
describing multi-decadal NAO variability, we split the
NAO‾Ortega,50 yr reconstruction into
two parts of equal size, using one part as training period and the other for
validation. We apply OLS regression of the cross-link densities to
NAO‾Ortega,50 yr during the training
period and then compare the values predicted by the obtained model for the
validation period with the actual values of
NAO‾Ortega,50 yr. Using both parts as
respective training and validation periods, the resulting r2 values are
very low (0.15 and 0.28, respectively). Hence, the linear model can
scarcely explain the amplitude of the supposed long-term average NAO
variability as expressed by
NAO‾Ortega,50 yr. Nevertheless, the
obtained sign of the NAO phase is identified correctly in 68% and 71%
of the considered time windows covered by
NAO‾Ortega,50 yr, respectively. In
the following, we will refer to this quantity as the true sign ratio (TSR).
Notably, taking the second (more recent) half of
NAO‾Ortega,50 yr as regression
period (which corresponds to a period with more records than the first one)
results in higher values of both r2 and TSR. This finding suggests that
using additional records which do not have data outside of the regression
period can still lead to a better performance of our model due to a better
interpretation of the existing links. Future work along the lines of the
present paper might explicitly utilize this observation in a Bayesian
analysis framework.
While the observed TSR provided by our model is markedly larger than that of
a random guess (TSR ≈50%), it is still rather low in comparison
with common requirements if using such models for predictive purposes. To
better understand the ∼30% of time intervals during which the sign of
NAO‾Ortega,50 yr is not correctly
represented by our model, we perform an additional type of
cross-validation, this time independently leaving out consecutive 50-year
windows as validation periods and taking the rest of the data for model
estimation. The results of this analysis are shown in
Fig. S5. We find that whenever the TSR in a given validation period is
clearly lower than the mean value of 0.69,
NAO‾Ortega,50 yr is either
consistently close to zero or exhibits a transition between positive and
negative NAO phases. Nevertheless, there are some periods during which our
model differs markedly from
NAO‾Ortega,50 yr, e.g. in the
17th century. Hence, we conclude that if our model is used
for the purpose of hindcasting the (themselves statistically reconstructed)
NAO values according to , this might result
in incorrect identifications of the mean NAO phase at values where
NAO‾Ortega,50 yr is close to zero,
since under these conditions, our ensemble of equally likely NAO
“trajectories” obtained from MCMC regression includes both positive and
negative estimates for the corresponding time window. In turn, the model
performs well in correctly identifying strong and persistent positive and
negative NAO phases. However, we observe that the actual timing of
transitions between distinct NAO phases can differ between
NAO‾Ortega,50 yr and our model
(Fig. S5). Thus, the relatively low predictive skill
of our reconstruction method might in part be due to a possibly lagged
representation of NAO shifts in the connectivity between regional clusters of
proxies. Further possible reasons and suggestions for improvements are
briefly mentioned in Sect. .
Degree of belief (probability) that the NAO is in a specific
(positive vs. negative) phase during each 50-year time window. The figure
has been smoothed by a 10-year moving-average filter to enhance its
readability. The brighter areas indicate time intervals for which less than
66 % of all considered MCMC ensemble members agree upon the sign of the
reconstructed NAO variable. Gray bars correspond to known major drought
episodes in the western Mediterranean as discussed in
Sect. . For better comparison, the NAO reconstruction by
is shown as a black line, indicating a
general agreement with our probabilistic reconstruction over the common
period as expected.
Despite the fact that only four geographical clusters of paleoclimate
archives cover the full Common Era, our model allows us to qualitatively expand
the existing “smoothed” NAO reconstruction by
over the last two millennia and thus obtain
relevant information about the dominant NAO phase at multi-decadal timescales. To do so, we draw 10 000 realizations of the regression coefficient
distributions of our model and calculate the corresponding NAO index for
each point in time based on the available CLDs. The probability that during
a specific time interval, the NAO was in a positive (negative) phase is then
estimated by the percentage of values above (below) zero in the ensemble of
realizations. This value is subject to several proxy and model uncertainties
and is thus called the degree of belief that a certain NAO phase was
present. The results of this probabilistic description are shown in
Fig. and detailed in . We find that during the Common Era, there have been
several phases during which the multi-decadal NAO variability was
preferentially characterized by a positive phase (e.g. during the migration period and the
late medieval times), which alternated with strong negative phases (e.g.
during the Little Ice Age, LIA) or intervals with generally more variability
(e.g. the late Roman period or the centuries around 1000 CE), indicating more
unstable conditions of the large-scale atmospheric circulation over the North
Atlantic region.
Finally, we have additionally tested the robustness of the estimated
regression model by varying αC over a reasonable range (similar
variations of αpr were found not to alter the obtained results
markedly, which is not explicitly shown here). Figure S6
shows the corresponding results in terms of OLS-based regression models
obtained with different parameter values. While most parameter sets close to
the selected optimal one yield very similar results, there are few exceptions
demonstrating the importance of this sensitivity analysis. A particularly
remarkable example is found in the second half of the 5th
century, where a transition from a predominantly negative NAO phase to a
positive one is observed, the exact timing of which, however, differs
significantly among the different regression models. This observation
underlines, that our model has some uncertainty – in terms of not only
reconstructed values but also the timing of changes – which cannot be
accounted for outside an ensemble-based approach.
DiscussionClimatological interpretation
In our analysis, we have related evolving functional paleoclimate networks to
the dominant mode of multi-decadal variability of the atmospheric circulation
in the North Atlantic region as reported by ,
which has been associated with long-term changes of the NAO. As seen from
Figs. and , the number of statistically
relevant connections between Greenland, Svalbard, and Fennoscandia is enhanced
during positive phases of the NAO (according to the reconstruction by
), whereas links involving central Europe are
more pronounced during negative NAO phases. Thus, we interpret strong
west–east correlations in the study region as indicators of a positive NAO
phase, while north–south connections point to negative NAO phases. This
observation can be qualitatively addressed by visualizing the obtained
networks as in Figs. and .
More detailed statements can be made based upon a systematic inter-comparison
between the time-dependent CLDs associated with distinct cluster pairs, as
well as the evaluation of the regression to the existing reconstruction
NAO‾Ortega,50 yr in terms of the
linear model (Eq. ). The latter analysis helps to relate
different NAO phases to certain cross-cluster links in a more objective
fashion.
The interpretation of a preferred presence or absence of certain CLDs during
specific NAO phases agrees well with the known NAO impact on European climate
variability during the instrumental period. A positive NAO phase is commonly
related to a northward shift of the westerlies, which causes milder
temperatures and stronger precipitation in northern Europe during boreal
winter. Thus, from the observation that tree ring chronologies are strongly
influenced by intense winter precipitation, it is reasonable that the
considered archives from Fennoscandia (central Europe) are particularly
affected by positive (negative) NAO phases. The non-stationary influence of
winter conditions is further illustrated in Fig. S7.
While many of the ice core records from Greenland which were instrumental in
obtaining the NAOOrtega reconstruction
exhibit strong negative correlations with that reconstruction throughout the
last millennium, there is much more variability in the correlations with
NAOOrtega for all the other records. More
important than variability in magnitude is the fact that a linear
relationship is absent for most records at most times. In turn, they are
co-varying with the NAO at certain times, but are unaffected at others.
Suppose that we are given a reference time series which exhibits a stationary
relationship with the “true” NAO (in our case, the aforementioned Greenland
ice cores). If the variability of any particular record shows a strong
similarity with this reference series during a specific time, we expect that
this record carries significant information about the NAO phase. As the
actual imprint of the NAO is different for different regions, this
information is present in different proxy groups at different times. In our
case, the Greenland ice cores act as a filter to indicate which regions are
strongly influenced by the NAO and thus which NAO phase is more probable.
The median values of the regression model correlate well with
NAO‾Ortega,50 yr (squared Pearson
correlation of r2=0.58). However, this value could simply result from
overfitting, as indicated by our cross-validation. While the obtained
quantitative values of the reconstructed NAO index of
are thus not reliably described by our
model, the latter performs well in resolving the dominant NAO phase. Drawing
upon the knowledge about relationships between certain cross-cluster links
and the NAO phase as discussed above, it is generally possible to extend the
existing (smoothed) NAO index reconstruction
NAO‾Ortega,50 yr to the entire first
millennium. However, since our linear model is not capable of describing the
amplitude variability of NAO‾Ortega,50 yr adequately, this should only be considered as qualitative information
about the likely NAO phase.
While there is an influence of the NAO on regional temperatures at
multi-decadal timescales, strong low-frequency temperature variations could
be associated with both multiple modes of internal variability as well as
external factors like solar activity changes and explosive volcanism
, to different degrees that are the subject of ongoing
studies (see e.g. ). Thus,
the observation of elevated temperatures reported for most of the Roman Warm
Period (RWP) and Medieval Climate Anomaly (MCA) as opposed to lower
temperatures during Late Antiquity
does not contradict our qualitative reconstruction of the predominant NAO
phase. Instead, there might be common causes for such apparently
contradictory observations. For example, explosive volcanism has been
discussed as a major driver of the Late Antiquity Little Ice Age climate
, but is also known to frequently trigger
positive NAO-like atmospheric dynamics during the years following strong
eruptions . Even though this is mostly a
short-term effect, a high frequency of strong eruptions, as present during
Late Antiquity , might have had a more persistent
influence.
We emphasize that there are certain limitations to the usage of CLDs and our
linear model to draw conclusions about the predominant NAO phase. First, most
of the CLDs exhibit downward trends and progressively decreasing variance
throughout the Common Era (Fig. S4), which is probably
related to the lower number of records as one goes back in time. This might
add a considerable bias to any application of our methodological framework
extending further back in time than the last millennium. In our case, this
effect might favour positive NAO phases, since the regression coefficient for
the connection between southeast Greenland and Fennoscandia is by far the
largest among all coefficients. Furthermore, our regression is based on a
proxy-based reconstruction, which contains large uncertainties itself and
therefore has limited value as a “ground truth”.
reported that their reconstruction explains
only about 40% of the variance of the observed NAO. In turn, the
explanatory value of the time series
(NAO‾Ortega,50 yr) upon which our
regression analysis is based is a key assumption beyond our procedure.
Moreover, our cross-validation showed that the linear model can disagree with
NAO‾Ortega,50 yr especially in cases
in which that reconstruction has values close to zero, as well as in the
timings of some transitions between positive and negative NAO phases. This
intrinsic uncertainty of our qualitative reconstruction has been addressed by
using MCMC regression to take a probabilistic view on the NAO phase. At time
periods where the reconstructed
NAO‾Ortega,50 yr is close to zero,
no particular phase is preferred in general (Fig. ).
Following upon the considerable uncertainties in using our linear model to
obtain qualitative estimates of the NAO phase during the entire Common Era,
we will next compare our corresponding results to other long-term NAO-related
climate reconstructions. Moreover, we will utilize further independent
information in terms of documented drought periods for an independent
validation of our reconstruction. Finally, we will discuss how long-term NAO
variability might have affected European societies during the first
millennium CE.
Comparison with other NAO reconstructions
Our model is able to reproduce most features of the
NAO‾Ortega,50 yr reconstruction,
including a dominant positive NAO phase during the late MCA, generally
stronger variability during the LIA, with a tendency towards a more negative
NAO phase, and another strongly positive phase during the
20th century, which is also in accordance with instrumental
records .
In contrast to other previous findings by , we
do not observe strong west–east correlations during the early MCA, which
suggests that this time interval has not been characterized by a strongly
positive NAO.
Another recent NAO reconstruction by used a
more than 5000-year-long lake record from southern Greenland to trace the
predominant NAO phase during the entire Late Holocene. Our mean model
correlates only extremely weakly with their reconstruction during the common
period (r2=0.04). One probable reason for this disagreement could be time
uncertainty in their very long-term reconstruction, which
report as being of multi-decadal order during
the first millennium CE. Furthermore, their record has been adjusted to the
reconstruction by , which disagrees with
NAOOrtega at many times.
Finally, it is worth considering a recent study by
, who used 11 European speleothem records and
analysed their mutually coherent dynamics, which can be connected with
changes in the North Atlantic circulation regimes reflecting long-term NAO
variability. Their results indicate a strong, persistent positive NAO phase
during the entire MCA and a tendency towards a negative NAO phase during the
LIA, the first being in partial disagreement and the second in accordance
with the NAOOrtega reconstruction. In
addition, report a dominant negative NAO
phase between about 250 and 500 CE and a neutral-to-positive NAO phase
thereafter. This observation agrees with our qualitative extension of
NAO‾Ortega,50 yr.
Comparison with historical droughts
Winter NAO and the corresponding precipitation anomalies exhibit known
linkages to droughts in many parts of Europe, most significantly in the
western Mediterranean region
. Due to their
severe impacts on agricultural productivity, droughts are some of the best
documented weather extremes across historical times. Thus, existing reports
of historical drought periods can be used as an independent source of
information to test the consistency of our qualitative NAO reconstruction.
For this purpose, we use three accounts of droughts during the Common Era.
collected climatic evidence from the period of
the Roman Empire (up to 800 CE) and reported eight large droughts in the western
Empire accessible through.
summarized historical evidence from
Muslim sources for southern Spain, a region exceptionally vulnerable to
NAO-related droughts , from 711 to 1010 CE.
They identified three major drought periods during this time. In addition,
discussed droughts during the last millennium
in the Mediterranean region based upon the Old World Drought Atlas (OWDA; ). They reported that the drought index constructed for
the western Mediterranean correlates well with
NAOOrtega. Therefore, we consider here only the
five strongest drought events as discussed in Fig. 5 of their paper.
It has to be noted that although droughts are strongly related to
precipitation deficits potentially associated with the dominant NAO phase,
they are complex phenomena with multiple causing factors. Thus, we do not
expect the timing of all droughts in the considered region to be fully
explained by any particular NAO reconstruction.
In Fig. , the major drought periods discussed in the
aforementioned publications are marked as grey bars. Among the 20 drought
events, there is a clear tendency towards a positive NAO (P(NAO+) > 0.5) (17
cases, with 12 of these showing P(NAO+) > 0.66). Thus, most droughts indeed
coincide with positive NAO phases. However, a larger number of reported
droughts during a specific time period does not necessary imply a higher
frequency of droughts. In the case of historical documents, an increase in
reported events could also indicate that a society was more vulnerable to the
impacts of droughts and, thus, found them more worth reporting.
Conclusions
In this study, we have demonstrated that functional networks based on
paleoclimate proxy records from multiple, spatially distributed archives
offer great potentials for identifying spatial patterns of atmospheric
circulation in the European North Atlantic sector together with information
on their associated long-term variability.
Specifically, we have obtained a new 2000-year-long qualitative
reconstruction of the leading mode of regional inter-annual temperature
variability probably associated with multi-decadal NAO variability. By
combining visual inspection of changing patterns in the (coarse-grained)
network representations with a simple linear regression model, we have
presented a climatologically consistent interpretation of the time-dependent
strength of correlations between groups of proxies from different parts of
Europe and the northern North Atlantic as indicators of different NAO phases.
In general, we relate strong east–west connections with a positive NAO phase
and north–south connections with a negative phase. While the linear model
does not trace the exact variability of the reconstructed NAO index by
very well, it still provides a good
qualitative explanation of the succession of different phases at
multi-decadal timescales.
The relatively low skill of our probabilistic reconstruction (true sign rate
of ∼70% when taking the reconstruction by
, as a reference) indicates that the method
proposed in this work provides only a first step towards establishing a novel
tool, rather than being a conclusive framework to reconstruct the NAO from
functional networks. A more restrictive proxy selection, inclusion of
additional proxies, consideration of more general methods of similarity
assessment (e.g. replacing linear correlations by nonlinear mutual
information), and applying different clustering schemes are possible future
steps to further improve the performance of the general scheme introduced in
this work.
Uncertainties of the obtained NAO reconstruction arise mainly from an
insufficient description of the observations by the linear model, a possible
bias induced by a decreasing number of records when going further back in
time, and existing uncertainties in the
NAO‾Ortega,50 yr time series, upon
which the regression is based. Thus, future consideration of additional
high-resolution paleoclimate records from the North Atlantic region,
especially from regions like Svalbard, Greenland, and eastern Europe, might
further improve the model fit substantially. Notably, using standard
similarity measures like the Pearson correlation coefficient, it is not
feasible to use shorter time windows than the 50-year windows used in the
present analysis. Thus, our approach cannot yet be directly applied to the
instrumental record as regression target. Since the longest instrumental
record of the NAO goes back to 1821 only ,
there are not enough independent data points available for proper calibration
and validation when using multi-decadal time windows.
Our qualitative expansion of the
NAO‾Ortega,50 yr reconstruction
demonstrates that the Common Era has been characterized by time periods with
different behaviour of the NAO. In general, multi-decadal changes of the
predominant NAO phase occurred relatively frequent during Roman and early
medieval times, while there have been other periods characterized by a
persistent positive or negative NAO phase. The first is the case for most of
the migration period, the late medieval times and the 20th
century, while the latter is found during the late Roman times and the Little
Ice Age. These long-term changes in the NAO phase might have had a
considerable impact on European societies, as the NAO phase is associated
with the likelihood of regional droughts as well as precipitation and
temperature extremes, which may have directly affected agricultural
productivity. In this spirit, specific phases might have supported some
European societies while negatively affecting others.
In general, the procedure introduced in this study could also be applied to
other large-scale climate variability patterns like the Atlantic Meridional
Oscillation . Besides the NAO reconstruction, we
have therefore performed the same analysis based upon the same set of proxies
and a reconstruction of the Atlantic Multidecadal Variability
as a reference time series. Unlike for the NAO, this
endeavour did not yield a reconstruction performing substantially different
from a random one. This indicates that the proxy selection is a crucial part
of the proposed type of analysis, and that the set of records used in this
study do not exhibit the necessary regional non-stationary relationship with
the target variable that have been successfully utilized in reconstructing
the NAO.
All calculations in this work have been based upon open source software. AAFT
surrogates have been generated using the Python package pyunicorn. Cluster analysis of reanalysis data has been
conducted using the community package. MCMC regression has been
performed with the pyMC3 package
. The corresponding references and data citations are provided in
Table S2. The obtained qualitative NAO reconstruction
is provided as part of the Supplement accompanying this paper
and is additionally available via the data repository PANGAEA
.
The Supplement related to this article is available online at https://doi.org/10.5194/cp-13-1593-2017-supplement.
JGF designed and conducted the analysis and prepared the paper. RVD designed and
supervised the analysis. JPW advised the data selection. RVD and JPW critically revised the paper and
the interpretation of the obtained results.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Climate of the past 2000 years: regional and trans-regional syntheses”.
It is not associated with a conference.
Acknowledgements
This work has been financially supported by the German Federal Ministry for
Education and Research (BMBF) via the BMBF Young Investigators Group
“CoSy-CC2 – Complex Systems Approaches to Understanding Causes and
Consequences of Past, Present and Future Climate Change” (grant no.
01LN1306A), and by the joint German–Norwegian project “Nonlinear variability
and regime shifts in Late Holocene climate: regional patterns and
inter-regional linkages in multi-proxy networks and climate simulations”
jointly funded by the German Academic Exchange Service (DAAD project no.
57245873) and the Research Council of Norway. Reik V. Donner acknowledges additional
support by a Bjerknes Visiting Fellow grant. The authors thank Dmitry Divine
for fruitful discussions stimulating the developments described in this work.
The data used in this study have been kindly provided by the Arctic2k group
of the PAGES2k initiative and Saija Saarni.
Edited by: Hugues Goosse
Reviewed by: three anonymous referees
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