The anthropogenic radiative forcing (IPCC 2013). The respon­­­se can

The
Earth’s climate is changing rapidly in response to anthropogenic radiative
forcing (IPCC 2013). The respon­­­se can
manifest as changes in not only the mean state of the climate but also in the
variability about the mean state. While the potential con­­sequences of mean
state changes have long been recognized (Houghton et al. 1990), variability changes are
also important (e.g: Katz and Brown 1992, Addo-Bediako et al. 2000, Wheeler et al. 2000, Schar et al. 2004, Porter and Semenov 2005). Changes in interannual (and
longer time-scale) variability are of particular interest because of the protracted
nature of the associated climate anomalies (Rajagopalan and Lall 1998; Meehl 2004). The occurrence of an
extreme anomaly that is of an extended duration (a month, a season or longer)
can translate into catastrophic outcomes. For example, the 2003 extreme
European summer, which was attributed to an increased temperature variability
regime in combination with mean climate warming (Schar et al. 2004), claimed more than 52000
lives (Larsen 2006). The low rainfall and
unprecedented heat further resulted in crop failures, reduced plant respiration
and growth, and consequently a large positive flux of CO2 into the
atmosphere (Ciais et al. 2005).

Recognizing
such severe societal and ecological effects of extended climate anomalies, a
natural question to ask is: how will interannual variability change in a warmer
climate? Using climate models, previous work has addressed this question for various
climate variables at global (e.g.: Räisänen 2001, Stouffer and Wetherald 2007; Boer 2009; Wetherald 2009) and regional (e.g.: Schar et al. 2004; Scherrer et al. 2008; Fischer et al. 2012) scales under different
anthropogenic forcing scenarios. While these studies have uncovered robust
variability changes that can be expected with a high degree of confidence in a
warmer climate (see Holmes et al. 2016 for a review) and have
improved our understanding of the climate system, they leave two key areas
unexplored that are of specific interest to this paper.

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            First, existing model studies on
interannual variability have largely focused on the influence of external
climate forcing on the variance. On interannual (and longer) timescales,
climate variables can exhibit covariations across distant locations through
numerous well-known circulation patterns (e.g.: Bjerknezs 1969; Wallace and Gutzler 1981; Simmons et al. 1983; Trenberth and Shea 1987; Thompson and Wallace 1998) as well as potentially
undiscovered patterns in the coupled climate system. These covariations often
are associated with enormous impacts on a global scale (IPCC 2013). Therefore, the problem of
interannual variability is in general a problem of not only the variances but
also the covariances associated with
interacting regions. While the joint variability associated with a system of
interacting regions can alternatively be investigated in terms of empirical
orthogonal functions or variants thereof (Jolliffe 2002), these techniques are often
hard to interpret physically. The variances and covariances on the other hand
are directly physically interpretable. Despite its obvious physical relevance
and importance, only a few studies have considered the covariance response
(e.g: Leeds et al. 2015; LaJoie and DelSole 2016; Poppick et al. 2016) to anthropogenic forcing.

A
further area of interest that has received little attention is the time of
emergence of forced interannual variability from an unforced climate. Changes
in interannual variability that are of considerable magnitude relative to the
variability that might naturally occur in an unforced climate can translate
into major impacts (e.g.: Kunkel et al. 1999; Fischer et al. 2007; Robine et al. 2008). As such, assessing the time
of emergence of forced variability is important for adaptation and mitigation
planning. It is also an important step in attributing variability changes to a
specific cause, for example, anthropogenic forcing (Bindoff et al. 2013). While the emergence of
forced mean state signals has received a lot of attention (e.g.: Madden and Ramanathan 1980; Weatherhead et al. 1998; Giorgi and Bi 2009; Deser et al. 2012; Hawkins and Sutton 2012; Thompson et al. 2015), the emergence of
interannual variability signals under projected forcings has been explored in
only a few studies (e.g: Stouffer and Wetherald 2007; LaJoie and DelSole 2016).

Estimating
forced variability statistics using a single model simulation is challenging.
Variability statistics under rapidly changing forcing can evolve in time
periods shorter than those that are required for their accurate estimation with
a single model realization. That is, the conventional idea of computing
variability statistics from a long model simulation (Leith 1978) is of limited use in a
transient climate change setting and one necessarily has to resort to using
ensembles of model simulations. Initial condition climate model ensembles are
particularly useful here (Rowell 1998; Collins and Allen 2002; Kay et al. 2015). The members of such an
ensemble are simulated under the same external forcing with small perturbations
introduced at the start of their integrations. After the memory of the initial
conditions is lost, each member evolves independently (Deser et al. 2012). As such, the members of
such an ensemble serve as independent samples for the computation of forced
statistics.

In
this paper, we develop a framework for analyzing an initial condition ensemble
under transient forcing that facilitates a unified assessment of the regional
variances and covariances and their contributions to global variance. We
accomplish three specific goals with the framework. First, we decompose global
variance into subjectively chosen regional variance and covariance components.
Such a decomposition is useful in understanding the contributions of the
regional variances and covariances to global variance. Second, we offer a
simple method for calculating the evolving regional variances and covariances
along with their sampling uncertainties in climates undergoing transient
forcing using initial condition climate model ensembles. Third, we address the time
of emergence of forced variability statistics. Specifically, we derive the
estimates of the regional variances and covariances along with their sampling
uncertainties in long unforced control simulations. By comparing the forced
variability statistics with their unforced estimates in the presence of
sampling uncertainties, the time of emergence can be quantified.

After developing the
framework, we demonstrate its application in a state-of-the-art initial
condition ensemble: the Community Earth System Model Large Ensemble (CESM-LE, Kay et al. 2015). The CESM-LE consists of multiple realizations of a single
model (CESM-CAM5, Hurrell et al. 2013) under historical and RCP 8.5 (Meinshausen et al. 2011) forcing scenarios while a companion multicentury
preindustrial control run provides a stationary climate for the
derivation of baseline statistics. Leveraging the CESM-LE and the preindustrial
run, we explore the
forced evolution and emergence of the surface temperature variability statistics associated
with two distinct regional decompositions. The first decomposition consists of
two regions: the land and the ocean. The second decomposition consists of three
regions: the Arctic (700 N – 900
N), the
Northern Hemisphere midlatitudes (300 N – 700
N, midlatitudes hereafter) and the rest-of-the-globe.

We
organize the paper as follows: In Sect. 2, we detail our methods and describe
the model. In Sect. 3, we utilize the framework to explore the variability
statistics in the two decompositions of simulated global interannual variance.
As we will show, our results highlight the importance of regional covariances
to global interannual variance. Finally, in Sect. 4, we offer a summary and
concluding remarks.