A critical question in the global warming debate concerns the causes of the observed trends of the Southern Hemisphere (SH) atmospheric circulation over recent decades. Secular trends have been identified in the frequency of occurrence of circulation regimes, namely the positive phase of the Southern Annular Mode (SAM) and the hemispheric wave-3 pattern which is associated with blocking. Previous studies into the causes of these secular trends have either been purely model based, have not included observational forcing data or have mixed external forcing with indices of internal climate variability impeding a systematic and unbiased attribution of the causes of the secular trends. Most model studies also focused mainly on the austral summer season. However, the changes to the storm tracks have occurred in all seasons and particularly in the austral winter and early spring when midlatitude blocking is most active and stratospheric ozone should not play a role. Here we systematically attribute the secular trends over the recent decades using a non-stationary clustering method applied to both reanalysis and observational forcing data from all seasons. While most previous studies emphasized the importance of stratospheric ozone depletion in causing austral summer SH circulation trends, we show observational evidence that anthropogenic greenhouse gas concentrations have been the major driver of these secular trends in the SAM and blocking when all seasons are considered. Our results suggest that the recovery of the ozone hole might delay the signal of global warming less strongly than previously thought and that effects from all seasons are likely crucial in understanding the causes of the secular trends.

The SH climate and atmospheric circulation has undergone significant changes
over the last few decades. It is important to understand its causes and
anthropogenic contributions because this will not only help to constrain
future climate projections but is also essential to evaluate the ability of
the current generation of climate models to accurately simulate these
changes. Previous attempts at understanding the causes of SH climate change
focused on changes in the mean climate and its variance

Over the recent decades (1980–present) large changes in the SH storm track
modes have occurred in all seasons including the austral winter, when
blocking is at its most active

A recent study

The main method of investigating the role of different forcings of the SH
secular trends has been through coupled climate models

Modeling studies of the effect of various individual and combined radiative
forcings on the SH circulation have largely compared trends in mean zonal
indices, mainly the SAM index, without consideration of related systematic
changes in the spatially coherent zonally asymmetric features of the
circulation

CMIP5 (Coupled Model Intercomparison Project Phase 5) models are known to poorly represent midlatitude blocking and to be
limited in their ability to capture important SH circulation responses such
as the response of the SAM to large volcanic eruptions

Given that the circulation changes are a key signature of the forcing for attribution, the main aim of this paper is to complement model-based results with observationally based studies and to try to separate natural variability from the forced response. For example, the late 1970s climate shift occurred coincident with the shift in phase of the Interdecadal Pacific Oscillation (IPO), so separating the low frequency intrinsic ENSO (El Niño–Southern Oscillation) behavior from a response to the constituent components of the radiative forcing is an important problem.

Here we argue that most studies (see

In Sect. 2 we present the data used in this study and in Sect. 3 we describe the statistical method used for the non-stationary clustering. In Sect. 4 we present the attribution results and also describe in detail our sensitivity tests regarding the number of parameters to be estimated and demonstrate the robustness of our results. We provide our conclusions in Sect. 5.

We use daily NCEP/NCAR (National Centers for
Environmental Prediction/National Center for Atmospheric Research) reanalysis data

As forcing data we use the Cape Grim CO

As internal modes of climate variability, we use an ENSO 3.4 index, the
Madden–Julian Oscillation (MJO) index, the Indian Ocean Dipole (IOD) and the
eastern Indian Ocean Dipole mode indices and the annual cycle here defined as
sin(2

We first give an intuitive description of the clustering method used before we explain it in much more detail in Sect. 3.1. That section can be skipped by readers who are more interested in the clustering results.

Forcing time series: Cape Grim CO

Many studies have provided evidence that the atmospheric circulation can be
efficiently described by a few persistent cluster states

Our approach considers the hemispheric response of not only the zonal annular mode but also systematic changes in wave 3 and blocking. We also use reanalyzed data but consider all possible combinations of the observed radiative forcings and relevant indices of internal variability. Moreover, we make no a priori assumptions on the number of states and employ an approach that considers persistency, changes in the dynamics and that is able to ascertain causation between the time series and the external forcings.

Specifically, we use the non-stationary clustering method FEM-BV-VARX (finite
element method of time series analysis with bounded variation and vector autoregressive factor
of model
parameters;

The FEM-BV-VARX approach is a general variational framework that is reduced to
the well-known methods of linear regression, autoregressive models,

The approach we are following here is that we perform FEM-BV-VARX fits to all
possible combinations of the external forcings. Then we apply a standard
information theoretic criterion: the AIC

The presence of unresolved external covariates (which are not
statistically independent or identically distributed) may result in the
non-stationarity and non-homogeneity of the resulting data-driven statistical
models and may be manifested in the presence of secular trends and/or in
regime-transition behavior. By covariate we not only mean external forcings
but also unresolved physical processes and scales (e.g., due to EOF
truncation). This may then introduce problems when applying the standard
stationary approaches common to machine learning and statistics

Combining the concepts and ideas from pure and applied mathematics (such as
the FEM from numeric of partial differential equations,
regularization in infinitely dimensional spaces from the theory of ill-posed
problems, stochastic calculus and theory of stochastic processes, information
criteria from information theory, and embedding theorems from the theory of
dynamical systems), Horenko and colleagues developed a family of
non-stationary, non-homogeneous and non-parametric time series analysis
methods. This family of time series analysis techniques, which is reviewed
concisely by

Many classical methods of data analysis and machine learning (e.g.,
multilinear statistical regression,

In the FEM-BV methodology, finite element methods are employed in the
numerical representation of indicator functions

The algebraic structure of the above problem allows us to deploy efficient
numerical algorithms based on the iterative application of linear and/or
quadratic programming problems (optimizing for fixed

The number of different spatiotemporal

We have chosen to examine a time series of 500 hPa geopotential height
anomalies (seasonal cycle subtracted) projected on the 20 leading EOFs and with

In order to choose the optimal model

Additionally, the log-normal distribution was fitted to the model errors, the
respective log-likelihoods computed and used to calculate the AIC for the
non-stationary models. The most informative non-stationary model that emerged
using the AIC criteria (with posterior probability almost equal to one in
each case) was the model with Cape Grim CO

In our study we have included only a selected number of several external
forcings. One might argue now that we have neglected some additional forcing
(e.g., sea ice extent or the strength of the Antarctic Circumpolar Current)
which might be responsible for the observed secular trend. However, if we
include something like sea ice extent into the set of forcings and
get a result showing that sea ice extent is more statistically
significant, then this would not contradict this study simply because the
variable

A previous study with the FEM-BV-VARX method

Composites of 500 hPa geopotential height anomalies
(in m) over 1979–2010:

Our FEM-BV-VARX analysis finds strong evidence that anthropogenic greenhouse
gas concentrations have caused the secular trends in the SAM and hemispheric
wave-3 pattern. The clustering analysis with CO

The Akaike weight value

Percentage of time in either the hemispheric wave-3 state (black dashed) or the zonal state (blue dashed) for the NCEP reanalysis 500 hPa geopotential height field for all seasons and annually. The dashed lines are a LOESS fit to the time-averaged data where the solid lines indicate the values and averaging periods of the data.

We tested the sensitivity of our results using different information criteria
like the BIC

Figure

Our results are in contrast to earlier studies which found that ozone
depletion is up to 9 times more important than anthropogenic CO

Surface air temperature trend (K decade

To increase the confidence in our results, we systematically examined the sensitivity of our results to the treatment of the ozone data. Considering a 365-day-averaged and time-lagged seasonally varying OMD leads to more robust results because we account for the strong annual cycle of stratospheric ozone and its delayed impact on the tropospheric circulation. Ozone has a strong seasonal component with OMD known to impact the tropospheric circulation (from the observational record) in December–January. Thus, we repeated our analysis using lagged (by 0, 1, 2 and 3 months), seasonally varying and 365-running-mean OMD data. While we did find some sensitivity to lag interval, our results were qualitatively unchanged.

In order to try and address this problem, and given that we have ascertained
that a minimum of 20 PCs should be retained, we have considered additional
sensitivity experiments in which we diagonalize the matrix

We further note that even such a diagonally restricted VARX model is
much more general than when applying multilinear regression:

One might further seek to reduce the number of parameters such that the
problem is not ill posed. While reducing the number of EOFs is a possible
approach even a reduction from 20 to 9 EOFs (the absolute minimum number of
modes required to capture the Southern Hemisphere wave-3 blocking state) will
not sufficiently reduce the number of parameters such that the FEM-BV-VARX
with full

One strategy that was comprehensively tested was the sensitivity to
persistency over a large range of values as

Clearly time-series analysis where persistency of the respective metastable
states is weak represents a serious challenge. One approach we explored
assumes that – for fixed time-series

The sensitivity experiments we describe effectively bound the problem of overfitting inherent in analyzing atmospheric observational data. Importantly, we achieve the same results for diagonalization (well-posed, with no cross terms) and for the full FEM-BV-VARX (ill conditioned, with all cross terms).

Next we examined whether intrinsic climate variability statistically significantly affected the regime behavior. We find that the combination of ENSO and the first component of the multivariate MJO index (MJO1) provide the major intrinsic driver of the observed atmospheric regime behavior. The next best combinations are MJO1, MJO1 together with the eastern Indian Ocean Dipole index and the annual cycle together with MJO1.

The low frequency variability of ENSO is highly correlated to the IPO and, as
pointed out earlier, the IPO shifted phase in the late 1970s coinciding with
the transition to reduced blocking. Thus, it is natural to expect ENSO to be a
major component of internal variability driving changes in the wave 3. The
first component of the MJO index corresponds to enhanced convection over the
maritime continent (Indonesia, Philippines and Papua New Guinea) close to the
tropical warm pool

Smoothed (365-day backward running mean) Viterbi path of blocking (black line), SAM (red line) state, and stratospheric aerosol optical thickness (blue line).

We also find evidence that the Mt. Pinatubo volcanic eruption in 1991, as
measured by stratospheric aerosol optical thickness, could have triggered a
dramatic sudden increase in the regime frequency of occurrence in its
immediate aftermath. Figure

Our examination of reanalysis data together with observed forcing data
reveals that greenhouse gas emissions are an important driver of SH
circulation changes over the last few decades. Recent studies have suggested
that stratospheric ozone depletion is many times more dominant than CO

Our observationally based results are also confirmed by numerical modeling
studies

Our finding that anthropogenic CO

We thank one anonymous reviewer and S. Vannitsem for constructive reviews. C. L. E. Franzke is supported by the German Research Foundation (DFG) through the cluster of excellence CliSAP (EXC177). T. J. O'Kane is supported by the Australian Research Council Future Fellow program. T. J. O'Kane, J. S. Risbey and D. P. Monselesan are supported by the Australian Climate Change Science Program. I. Horenko is partly supported by the DFG (Mercator Fellowship in the CRC 1114 Scaling cascades in complex systems) and the Swiss National Science Foundation (SNF, grant 156398). Edietd by: S. Vannitsem