PERSPECTIVE • OPEN ACCESS

Origin, importance, and predictive limits of internal
climate variability
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PERSPECTIVE

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Origin, importance, and predictive limits of internal climate
variability

26 December 2022

Flavio Lehner1,2,3,∗ and Clara Deser2

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Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, United States of America
Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, CO, United States of America
3
Polar Bears International, Bozeman, MT, United States of America∗
Author to whom any correspondence should be addressed.
E-mail: flavio.lehner@cornell.edu
Keywords: climate variability, climate change, atmospheric variability, climate modeling, uncertainty quantification, prediction,
projection

Abstract
Adaptation to climate change has now become a necessity for many regions. Yet, adaptation
planning at regional scales over the next few decades is challenging given the contingencies
originating from a combination of different sources of climate projection uncertainty, chief among
them internal variability. Here, we review the causes and consequences of internal climate
variability, how it can be quantified and accounted for in uncertainty assessments, and what
research questions remain most pertinent to better understand its predictive limits andconsequences for science and society. This perspective argues for putting internal variability into
the spotlight of climate adaptation science and intensifying collaborations between the climate
modeling and application communities.

1. Introduction
1.1. What is internal climate variability and where does it come from?
Internal variability refers to fluctuations that arise intrinsically in a non-linear dynamical system, even whenthat system is closed (energy, mass, and momentum are conserved) and not subject to any changes inexternal forcing. In the case of Earth’s climate, internal variability arises primarily from the uneven
distribution of energy across the planet at any given time. Physical processes, such as oceanic or atmosphericheat transport or radiation to space, act to balance this unevenness, but they do so at different temporal andspatial scales. Together with Earth’s rotation, this means that an even energy distribution is never reached,leaving Earth’s climate to shift energy around perpetually. For example, mesoscale processes such as tropicalmoist convection are often used as illustrative ‘starting points’ for internal variability (formally described as
error growth in the context of weather forecasting; e.g. Judt 2018). Such processes individually or inaggregate then affect the larger synoptic scales, leading to baroclinic instabilities in the extratropics, expressed
as mid-latitude weather systems or the meandering jet stream—deviations from the expected climatologicalmean state (Lorenz 2006). Conceptually similar processes exist in slower system components, such as theocean or land, with expression in, e.g. sea surface temperature (SST) or soil moisture.
Fast and slow climate system components interact to create a wide spectrum of variability, which
manifests, for example, as variations in temperature from one day to the next, but also by strengthening andweakening of ocean currents from one decade to the next. Internal variability thus affects virtually every
aspect of the climate system. It is worth noting that for variables such as sea level pressure or terrestrial
temperature and precipitation, a large fraction of the internal variability spectrum can be recovered byintrinsic atmospheric variability alone and does not require oceanic influence (Deser et al 2012b). This canbe shown by comparing a climate model simulation with prescribed climatological SSTs to a fully coupledsimulation with an interactive ocean component (figure 1). Comparing the variances of the two simulations
reveals that the fraction of variance attributable to intrinsic atmospheric variability is between 50% and100% over most land areas for interannual as well as longer time scale variability (warm colors in figure 1).
© 2023 The Author(s). Published by IOP Publishing Ltd

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Figure 1. Fraction of variance explained by intrinsic atmospheric variability, calculated as the variance from a 2600 year CAM5
simulation with prescribed climatological sea surface temperatures (SSTs) divided by the variance from a 1800 year fully coupled
CESM1 preindustrial control simulation. The climatological SSTs for CAM5 were taken from the CESM1 simulation, making it
an apples-to-apples comparison. The variance ratio is shown for (a) interannual variance and (b) variance of 30 year runningmean surface air temperature. (c)–(d) Same as (a)–(b) but for sea level pressure. Hatching indicates where the two variances are
not significantly different (f-test with 95% confidence).

Depending on the time scale and region, the ocean can amplify variability beyond what the atmospheregenerates intrinsically—for example through the El Niño-Southern Oscillation (ENSO).
Importantly, internal variability occurs around a mean state, which is dictated by the long-term balanceof the system at hand. Internal variability thus almost always occurs within a certain range (for example a
range of temperature values) and does not drive the system unidirectionally. In Lorenz’ seminal papers on
chaos, a set of differential equations describe a non-linear system with one or more attractors around which
the system varies (Lorenz 1963). In a simplified analogy, Earth’s long-term average climate is such an attractor
and variations around it represent internal variability. However, it is still debated what constitutes a climate
attractor and thus how many attractors the climate system has (Nicolis and Nicolis 1984, Grassberger 1986,
Lorenz 1991). The Lorenz model, for example, describes convection arising from heating below and coolingatop a fluid layer, much like atmospheric convection. The domain size, boundary conditions, and heating
gradient set behavioral bounds to the system and establish the attractors—in other words, while individual
convective cells can behave chaotically, their long-term statistics converge to a well-defined distribution. For
an example on completely different timescales, one could think of Earth’s thermostat as an attractor
mechanism, in which warming increases rock weathering, which accelerates burying of carbon, which thencools temperatures (e.g. Brantley et al 2023). Transitions between warming and cooling could be chaotic but
would vary around an attractor that reliably prevents run-away warming or cooling during Earth’s history.
The Lorenz model offers insight into a key feature of internal variability: its inherent unpredictability.
Even in a deterministic system such as the Lorenz model, miniscule differences in the initial conditions used
to solve the equations can lead to very different trajectories after a while. This phenomenon exists in reality as
well, where fluid mediums, such as the atmosphere and ocean, are intrinsically unstable to tiny
perturbations. Because the initial conditions of a system under prediction (for example, weather) are neverknown perfectly, this inevitably leads to a gradual divergence between the prediction (for example, a weather
forecast) and the actual outcome.
1.2. Why care about internal variability?
The example of weather forecasting and initial condition predictability suggests that internal variability arises
from small spatial and temporal scales and grows to encompass global and decadal scales. This leads toimportant issues for climate science. The historical climate record reflects not only a response to various
external forcings affecting its energy balance (such as changes in orbital parameters, solar irradiance,
greenhouse gas concentrations, or aerosols), but it has also imbedded fluctuations that are the expression of a2

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unique realization of internal variability. ‘Unique’ here means that it is just one of many possible and equallyplausible realizations that could have occurred. Taking this insight to the extreme has led to the analogy thatthe flap of a butterfly could cause a hurricane. While proving such causality is beyond our reach, this conceptof ‘contingency’ (Gould 1989) is useful when thinking about the possible consequences of even the smallest
perturbations to the atmosphere and, once they grow, to the larger climate system—or, conversely, how thesystem would have evolved had that butterfly not flapped its wing.
This superposition of external and internal influences complicates the interpretation of the historicalclimate record (e.g. Sippel et al 2020), as our understanding of climate variability and change relies on arobust separation of these influences (Thompson et al 2009). Like the past, future climate will also reflect the
combined influence of external forcing (for example, an increase in greenhouse gas concentrations) andinternal variability. Precise prediction of future climate for lead times longer than a few years is thus notpossible, but the importance of internal variability can be illustrated and quantified with climate models,
which encapsulate enough relevant physical processes to also produce internal variability when integrated intime (e.g. Deser et al 2012a). Internal variability can also lead to extreme events beyond anything experienced
so far (Fischer et al 2021). Because people’s lived experience of extreme events influences their risk awarenessand consequently adaptation actions (Moore et al 2019), this can leave them underprepared for surprising
events (e.g. Bradshaw et al 2022). Internal variability thus poses a communication challenge and calls forprobabilistic predictions—again very similar to weather forecasts, where a chance of rain rather than a binary
forecast of rain or no rain is given.
This perspective reviews the role of internal variability in climate projections using the example of air
temperature, provides an overview of methods used to separate and quantify external and internal drivers ofclimate variability, and assesses their predictability. An additional aim of this perspective is to discuss
outstanding scientific challenges in the field of climate projections, as well as how physical understanding ofinternal variability and its manifestation in large ensemble model simulations, a primary tool in climate
science, can be used to better inform climate change adaptation. For the case studies featured herein, we rely
on internal variability as simulated by climate models and will also briefly discuss associated model biases.

2. The role of internal variability in climate projections
2.1. An example: temperature projections
To illustrate the influence of internal variability on climate projections, we show projections of wintertime airtemperature over North America from many different simulations with the same climate model under thesame radiative forcing scenario, specifically the Community Earth System Model 1 Large Ensemble, or
CESM1-LE (Kay et al 2015; figure 2). As with the Lorenz model, any individual simulation is started fromslightly different initial conditions (here, round-off errors in atmospheric temperatures at year 1920 of eachsimulation—the butterfly wing flap), while the rest of the model setup is kept identical between the different
simulations (Kay et al 2015). Specifically, each simulation is subject to the same historical external forcing,such as volcanic eruptions or changes in greenhouse gas concentrations, as well as an emissions scenario
going out to year 2100. Such a setup is sometimes referred to as a single-model initial-condition large
ensemble (SMILE; Lehner et al 2020, Maher et al 2020, Deser et al 2020a). The initial perturbations to eachsimulation are so small that the weather on the model planet over the first few days looks almost identicalbetween simulations. Then, gradually, the different simulations diverge and eventually become decorrelatedwith regard to their interannual variability. At that point, the climate system has ‘forgotten’ about the initialconditions and the resulting range of temperature represents the many possible trajectories of climate
around its climatological attractor.
Here, the different trajectories are illustrated by linear trends over the next 30 years (2021–2050) fromeach of the first 30 SMILE ensemble members (figure 2). All ensemble members show wide-spread increases
in winter temperature, consistent with the expectation of warming with future greenhouse gas emissions.
The spatial pattern of this warming, however, shows substantial variations—there are even ensemble
members with regional cooling trends over 2021–2050. Due to the identical experimental setup in all
ensemble members, any member-to-member differences are attributable solely to internal variability.
The average of the 30 trend maps is shown in the bottom left panel of figure 2. This ‘ensemble mean’
trend pattern represents the response of the climate model to the external forcing imposed to eachsimulation, as the differences between the individual ensemble members are largely averaged out. In otherwords, the forced response or ‘signal’ common to all simulations is distilled from the ‘noise’ of internalvariability through the averaging process. This ‘signal’ shows a poleward-amplified pattern of warming
throughout North America. The ‘noise’ pattern, quantified by computing the standard deviation across the
30 individual maps, also shows a poleward-amplified pattern (bottom middle panel of figure 2). As a result,the signal-to-noise map shows a more amorphous pattern than either the signal or the noise (bottom right3

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Figure 2. Linear trend in winter (December–February) mean temperature over the period 2021–2050 from 30 individual CESM1
large ensemble simulations (panels labeled 1–30), all under the identical forcing protocol of RCP8.5 (Kay et al 2015). The bottom
panels (from left to right) show the ensemble mean (EM) trend, the standard deviation (STD) across the 30 trend maps, and thesignal/noise (EM/STD).

panel of figure 2). Importantly, the signal-to-noise values are larger than 1 over almost all of North
America—this indicates the emergence of the forced response from the background climate noise.
Assuming that the internal variability of this particular climate model is realistic (a point discussed later),any projection of temperature for the real world is subject to irreducible uncertainty of the magnitude shownin figure 2. In other words, the real world could end up looking like any one of the maps in figure 2, and wewould not be able to predict ahead of time which one it might resemble.
2.2. Contribution of internal variability to total projection uncertainty
Besides internal variability, other sources of uncertainty are important for climate change projections: model
response uncertainty and scenario or socio-economic uncertainty. How does internal variability compare tothese other sources of uncertainty? A common framework to quantify this is to calculate a ‘total projection
uncertainty’ from a collection of simulations from different modeling groups run under a common set ofemissions scenarios (Hawkins and Sutton 2009).
Taking all available models from the sixth Coupled Model Intercomparison Project (CMIP6) that provide
simulations for multiple emissions scenarios results in a subset of 29 models and 4 different emissions
scenarios (Lehner et al 2020). For each model and scenario, the forced response can be estimated either by
averaging all of the available simulations, or—as is more common due to the lack of multiple simulations
from some models—it can be estimated as a statistical fit to each model’s simulation (for example, a4th-order polynomial is fit to a temperature time series as done in Hawkins and Sutton 2009). The residualfrom this fit provides an estimate of internal variability (quantified by computing the variance of the residual
time series). The variance across the estimated forced responses in each model for a given emissions scenario
constitutes an estimate of response uncertainty. Finally, averaging the forced responses across all the models
for each scenario separately and then calculating the variance across the scenarios constitutes an estimate of
the scenario uncertainty. These uncertainties are approximately additive (Yip et al 2011), such that the total
uncertainty can be estimated as the sum of the individual sources of uncertainty.
Each source of uncertainty can now be expressed as a time-varying fraction of total uncertainty. For
example, for projections of decadal global mean temperature (figure 3(a)), internal variability initiallydominates total uncertainty (figures 3(b) and (c)). Moving further into the future, internal variability
contributes increasingly less to total uncertainty, while response uncertainty and eventually scenario
uncertainty become the dominant sources of uncertainty (figures 3(b) and (c)). At regional or local scales,
4Environ. Res.: Climate 2 (2023) 023001

F Lehner and C Deser

Figure 3. Projections, sources of uncertainty and relative contribution of sources of uncertainty for temperature from 29 CMIP6
models for (a)–(c) annual global mean and winter (December–February) mean for (d)–(f) North America and (g)–(i) a grid cell
near Anchorage, AK. The decomposition follows Hawkins and Sutton (2009), using a 4th order polynomial fit to estimate theforced response of a given model. See text for details.

such as North America or a grid cell near Anchorage, AK, respectively, internal variability remains importantor even dominant for a longer time, as climate tends to be more variable at smaller spatial scales(figures 3(d)–(i); see also Hawkins and Sutton 2009, Kumar and Ganguly 2018). In fact, the orange area inthe right-most column of figure 3 nicely illustrates the gradually increasing fraction of uncertainty explainedby internal variability.
It is worth noting that a robust separation into different sources of uncertainty becomes more difficult
the smaller the spatial scales considered. This is due to the generally higher signal-to-noise ratio at smallerscales, which leads to internal variability aliasing into the estimate of the forced response (Lehner et al 2020).
Ideally, the ensemble mean of a SMILE is used to estimate the forced response of a model, rather than a 4thorder polynomial fit, as the latter has a higher potential to conflate internal variability and forced response.

3. Drivers of internal variability
3.1. Drivers of temperature variability
Generally, temperature changes as shown in figure 2 can be thermodynamically- and/or
dynamically-induced (Wallace et al 2015). ‘Thermodynamically-induced’ refers to changes caused bytime-varying radiative fluxes or changes in sensible and latent heat fluxes at the Earth’s surface. Formally, this5

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F Lehner and C Deser

excludes any concomitant changes in the atmospheric circulation. ‘Dynamically-induced’ refers totemperature changes attributable to changes in the atmospheric circulation, irrespective of their cause.
Together with the presence of external forcing, the cause for a given temperature trend can be partitioned
into four categories: forced-thermodynamic, forced-dynamic, unforced-thermodynamic, andunforced-dynamic (Deser et al 2016). ‘Forced’ refers to the externally forced radiative imbalance of Earth(e.g. due to greenhouse gases) and ‘forced-thermodynamic’ then indicates that the external forcing impacts
temperature via a thermodynamic process (e.g. changes to radiative fluxes caused by increasing greenhousegases). Conversely, ‘unforced-thermodynamic’ also refers to a thermodynamic process influencing
temperature, except this process is not caused by external forcing but just arises from unforced internalvariability (e.g. changes in surface fluxes due to intermittent states of snow cover or soil moisture). Finally,‘forced-dynamic’ and ‘unforced-dynamic’ refers to changes in temperature via forced or unforced changes inatmospheric circulation variability (e.g. changes in sea level pressure). Such a decomposition has previously
been applied to the past 50 years (Deser et al 2016), but is here applied to future projections.

3.2. Decomposition of drivers
The categories laid out above enable a decomposition of the relative contributions of internal variability andforced response to a given temperature trend—for example the 2021–2050 winter trend pattern over North
America in one of the simulations shown in figure 2—and also a means of diagnosing the processes throughwhich internal variability and forcing exert influence (figure 4). In practice, several steps are needed to
conduct the partitioning quantitatively. As illustrated in figures 2 and 3, the forced contribution can be
estimated either by using the ensemble mean of a SMILE, the multi-model mean of a set of CMIP models, orby making statistical assumptions about the forced response, with the residual representing the internal(or ‘unforced’) contribution. For certain variables such as atmospheric circulation or precipitation, it can bedifficult to diagnose the forced trend from observations alone because of their typically small signal-to-noise
ratio. Even a statistically significant trend within an observational dataset could be unforced, as the
population distribution from which the confidence interval is derived might undersample the true
distribution (Wittenberg 2009, Horton et al 2015). While time series models exist to estimate the magnitudeof internal variability from observations alone, even for noisy variables (Thompson et al 2015), they cannot
reliably estimate the forced response (Lehner et al 2020). Using SMILEs avoids this issue, at the cost of relying
on models to provide a more complete distribution and robust estimate of the forced response. With theadvent of multiple SMILEs, across-SMILE comparison can strengthen confidence in model-derived estimatesof the forced response (Deser et al 2020a, Maher et al 2021).
To further partition the forced and unforced components into thermodynamic and dynamic
contributions, the method of dynamical adjustment is used (Smoliak et al 2015, Deser et al 2016). Thismethod aims to estimate the contribution of the atmospheric circulation to a given temperature pattern.
Briefly, using the example of monthly mean data, the atmospheric circulation (e.g. sea level pressure) pattern
in a given target month (say, January 1980) is reconstructed from the circulation patterns in all the other
Januaries in the data set, for example using regression or analogs. Each circulation reconstruction isassociated with a temperature reconstruction, which thus gives an estimate of the typical temperature patternthat occurs with this type of circulation pattern. Once repeated for all the months in the dataset, one obtains
an estimate of the role of atmospheric circulation in bringing about the temperature changes seen in theoriginal data—the dynamic contribution. The residual between the original data and the dynamic
contribution is an estimate of the thermodynamic contribution. Further decomposition into forced-dynamic
and forced-thermodynamic is achieved by conducting the above analysis for each member of a SMILE andthen averaging the respective estimates. There exists now a range of other methods to achieve this separation,
including tools of statistical learning and pattern recognition (Sippel et al 2019, Wills et al 2020,
Heinze-Deml et al 2021).
The pattern seen in figure 4(a) can now be decomposed completely. This particular ensemble member
was chosen for its interesting pattern of cooling over Western North America (which occurs despite theprojected increase in greenhouse gases over the next 30 years), along with pronounced warming over Eastern
North America. The decomposition reveals that internal variability contributes substantially to this cooling(figure 4(b)), in particular when compared to the total forced response which shows ubiquitous warming(figure 4(c)). Most of the cooling occurs due to atmospheric circulation, i.e. the dynamic contribution,
specifically a strong trend towards atmospheric ridging off the west coast (figure 4(d)). This
dynamically-induced cooling is entirely internal (figure 4(e)) as there is essentially no forced trend inatmospheric circulation (figure 4(f)). On the other hand, the warming over Eastern North America is almost
entirely due to thermodynamic processes (figure 4(g)), of which the forced component dominates(figure 4(i)); indeed, the internal-thermodynamic component drives a weak cooling trend (figure 4(h)).
6

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F Lehner and C Deser

Figure 4. Decomposition of the winter (December–February) mean temperature (color shading) and sea level pressure (contours:
increment of 2 hPa/30 yr, starting at ±1 hPa/30 yr) trend over the period 2021–2050 in one particular CESM1 ensemble member(#15). (a) The total trend and its contributions from (b) internal variability and (c) the forced response. (d) The trend
attributable to dynamics and its contributions from (e) internal variability and (f) the forced response. (g)–(i) Same as(d)–(f) but for the trend attributable to thermodynamic processes. See text and Deser et al (2016) for details.

More generally, figure 4 shows that, for western North America, changes in atmospheric circulation are ofalmost negligible importance compared to thermodynamic processes for understanding regionaltemperature trends due to anthropogenic forcing. However, large internal variability of the atmosphericcirculation can at times overwhelm the anthropogenic response in a given realization.

4. Prospects for uncertainty reduction
Uncertainty from internal variability has here been portrayed as being irreducible—and for good reason(Hawkins et al 2016): initial conditions that would provide predictability are typically quickly forgotten by
the climate system, unless they are tied to components with substantial memory such as the ocean. Efforts in
decadal prediction via initialized climate model simulations are advancing rapidly, but currently show
regionally limited skill for lead times of 2–9 years (Meehl et al 2014, Yeager et al 2018, Smith et al 2019,
Moulds et al 2023). Additional progress might be possible as climate models improve their representation of
atmosphere-ocean coupling (e.g. Simpson et al 2019) or overcome the signal-to-noise paradox (Smith et al
2019; see also section 5).
The expected uncertainty reduction from initialized prediction can be illustrated using the CESM1
Decadal Prediction Large Ensemble (CESM1-DPLE; Yeager et al 2018), which provides 40-member ensemble
predictions for lead times of up to 10 years with the same model as used in figure 3. The CESM1-DPLE is
initialized using observations every November from 1954 to 2017, so its last prediction runs from November
2017 to December 2027. For illustration, we compare the CESM1-DPLE prediction for the period 2013–2022
with the uninitialized CESM1-LE over the same time period (figure 5(a)). Interestingly, the CESM1-DPLE
predicted the accelerated pace of global warming from 2013–2016, followed by a slowed warming rate, bothfeatures seen in observations but not in the uninitialized CESM1-LE; thus, these changes in the rate of global
warming are potentially attributable to information contained in the 2012 initial conditions. For wintertemperatures over North America and Alaska (figures 5(c) and (g)), on the other hand, no skill is visible (norexpected given the highly variable winter weather, even at continental scale). This is consistent with the morecomprehensive CESM1-DPLE skill assessment conducted in Yeager et al (2018).
Besides prediction skill, important here is the spread across CESM1-DPLE ensemble members as anindicator of the potential uncertainty reduction from initialization (figures 5(b), (e) and (h)). For global
7

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F Lehner and C Deser

Figure 5. Influence of initialized prediction on uncertainty from internal variability. (a) Global annual mean temperature fromobservations, the uninitialized CESM1 (LE) and initialized CESM1 (DPLE), the latter at the example of the 2012 initialization.
For CESM1 35 ensemble members and the ensemble mean are shown. Simulations were de-drifted with a lead time-dependentclimatology (see Yeager et al (2018) for details). (b) Inter-member spread (1 standard deviation or σ) as a function of lead timefrom CESM1-LE and CESM1-DPLE. Mean, 1σ, and min/max across all initialization dates from 1954–2017 are shown, andcorresponding values from CESM1 over the same time period. (c) CMIP6 multi model mean projection and associatedsymmetric 90% uncertainty range and uncertainty sources. Orange shading shows the uncertainty from internal variability anddotted lines how that uncertainty is constrained by initialized prediction. (d)–(f) Same as (a)–(c) but for winter temperature over
North America and (g)–(i) a grid cell near Anchorage, AK.

annual temperature, the CESM1-DPLE spread at lead time 1 year is about 50% of the CESM1-LE spread(measured by standard deviation), thus initialization can reduce uncertainty from internal variability by
about half. However, the memory from initial conditions quickly fades and the spread approaches 100% after
lead year 5 (figure 5(b)). This pronounced but short-lived constraint on internal variability uncertainty isvisualized alongside the other sources of uncertainty for CMIP6 global temperature projections until 2030
(figure 5(c)). For winter temperatures over North America and in Anchorage, AK, on the other hand, theensemble spreads from the CESM1-DPLE and CESM1-LE are indistinguishable already at lead time 1, whichnota bene is the December–February mean right after initialization in November (figures 5(e) and (h)). Thus,
there appears to be no general benefit from initialization for this region on seasonal time scales and beyond(figures 5(f) and (i)). As these examples show, the potential for uncertainty reduction from initialization
depends on the location, season, and lead time (and also physical quantity) and thus needs to be assessed andcommunicated carefully. Recent discovery of a signal-to-noise paradox (Scaife and Smith 2018) brought
forth new methods to better isolate the predictable signal in large ensemble simulations, leading to improved
prediction skill in regions affected by the North Atlantic Oscillation (Smith et al 2019, 2020, Moulds et al2023). Application of these methods to other regions and climate indices might lead to improved skill overwhat is reported here.
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Environ. Res.: Climate 2 (2023) 023001

F Lehner and C DeserAs for constraining the other sources of uncertainty—response and scenario uncertainty—recent years
have seen some progress that is worth exploring but is not covered in detail here. First, new climate-social
system models suggest that some emissions scenarios are less likely to actually occur in the future (Moore
et al 2022). These models simulate feedbacks between socio-economic dynamics and climate based on
empirical relationships and argue that there exist dampening feedbacks in the system, e.g. society
implementing more stringent climate mitigation in response to mounting extreme event damages. These
feedbacks allow us to rule out the highest emissions scenarios, thus substantially reducing the scenario
uncertainty that often dominates total projection uncertainty later this century (figure 3(c)). Second, newphysically-based constraints on global and regional climate projection uncertainty (Lorenz et al 2018, Lehneret al 2019, Brunner et al 2020, Sherwood et al 2020, Qasmi and Ribes 2022) promise to reduce response
uncertainty, whose importance tends to peak mid-century when initial conditions are forgotten but
scenarios have not yet diverged substantially (figure 3(c); see also Lehner et al 2020). Future work will seek tocombine these two pathways to constrain projection uncertainty at regional scales.

5. Discussion
5.1. Summary
This paper provides a review of the role of internal variability in climate projections using the example oftemperature trends over the coming decades. The significant influence of internal variability, especially atregional scales, is illustrated by the range of possible future temperature trends simulated by the individual
members of a SMILE (figure 2). The influence of internal variability is also shown to be important whencompared to other sources of uncertainty such as response uncertainty originating from structuraldifferences across models or the choice of future emissions scenario (figure 3). Its relative importancedecreases with lead time but increases with progressively smaller spatial scales and can account for 50% of
local projection uncertainty even by year 2100 (figure 3). The chaotic nature of the atmospheric circulation isa key driver of internal variability in regional temperature trends (figure 4). The prospect for reducing
uncertainty from internal variability is limited, as shown by the prediction skill and ensemble spread
reduction achieved with a state-of-the-art decadal prediction system (figure 5), though it might carry value
for certain applications. Despite the focus on seasonal to annual temperature here, the lessons-learned apply
equally to other variables and research questions, for example precipitation (Deser et al 2012b, 2017, Lehneret al 2018, Guo et al 2019), extreme event attribution (van Oldenborgh et al 2020, Philip et al 2022),
compound event research (Bevacqua et al 2022, Zscheischler and Lehner 2022), temperature response tovolcanic eruptions (Lehner et al 2016, McGraw et al 2016), or ocean biogeochemical tracers (Rodgers et al2015, Lovenduski et al 2016). Generally, the smaller the scales and the noisier the variables of interest, themore likely is the research to benefit from including climate model large ensembles (Milinski et al 2020,
Bevacqua et al 2023). The implications of internal climate variability are therefore far-reaching, for bothscience and society.
5.2. Implications for climate science
Internal variability continues to complicate our interpretation of the historical record, which relies on cleanly
separating observed climate trends into contributions from external forcing and internal variability.
Interestingly, this challenge has neither gotten easier nor less important over the last 20 years. If anything,
one could argue that several recent developments in climate science urge a renewed focus on better
understanding internal variability.
First, CMIP6 showed a relatively larger response uncertainty than CMIP5 for temperature and many
temperature-related quantities, puzzling the community (Zelinka et al 2020). As a result, a flurry of emergent
constraints were developed that use the agreement (or lack thereof) between observations and models toassess the models’ credibility, arguing for example that models which warm too much over the historicalperiod are also likely to warm too much in the future (Tokarska et al 2020). Such constraints can be powerful
but rely critically on a robust understanding of the historical record. Is the historical record our best-guess
central estimate of how the climate responds to external forcing or did a combination of forced response andinternal variability render it more of an end-member of a plausible but elusive distribution of historical
records that could have been? The answer to this question directly determines which climate models are
considered to be in agreement or disagreement with observations. While much progress has been made in
developing emergent constraints with the necessary care (Hall et al 2019, Sherwood et al 2020), theuncertainty from past aerosol forcing in particular still looms large as a confounding influence on ourinterpretation of the historical record and the inference we draw from it (Persad and Caldeira 2018, Deseret al 2020b, Lehner and Coats 2021).
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Second, and relatedly, while one can generally expect our understanding of the magnitude of internalvariability to solidify with a longer observational record, it can also harbor surprises. One prominent current
example is the long-term evolution of tropical Pacific SST, which has been trending La Niña-like for decades,
while the forced response from climate models consistently predicts a more El Niño-like response (e.g. Seager
et al 2019). The tropical Pacific ocean drives a myriad of impactful teleconnections; thus, its future state is ofgreat interest for many regions around the world. Until a few years ago, this discrepancy between
observations and models could readily be chalked up to internal variability, as one could find individual
simulations in SMILEs that replicated the observed trend (Watanabe et al 2021), suggesting that reality is justan end-member of its own distribution of plausible trends and that observations will eventually reverse andfall in line with the models’ forced response. With every passing year that this discrepancy persists, however,it has become more difficult to defend that interpretation, such that it is now suggested that models either
underestimate the magnitude of internal variability in this region or, worse, are misrepresenting the forced
response of tropical Pacific SSTs (Wills et al 2022). Similarly, recent unprecedented extreme events, such as
the Pacific Northwest heatwave (Philip et al 2022) have brought into focus that our observational records are
sometimes still too short to robustly constrain all aspects of internal variability and that we need to continue
to observe and study it. Finally, there is evidence from subseasonal to decadal prediction experiments thatclimate models might be less predictable than the real world: in other words, their signal-to-noise ratio is too
small, especially for mid-latitude atmospheric circulation (Scaife and Smith 2018, Smith et al 2020, Klavans
et al 2021). It is possible that this so-called ‘signal-to-noise paradox’ also applies to the response toanthropogenic forcing, which would have implications for our confidence in uncertainty partitioning aspresented here (figures 3 and 5) and elsewhere. Resolving the signal-to-noise paradox thus remains animportant goal for the climate modeling community.
While the search for the true magnitudes of internal variability and forced response will thus continue
into the foreseeable future, it is indeed on the topic of model validation where progress can be made today.
The advent of multiple SMILEs (Deser et al 2020a) and the development of observational large ensembles(McKinnon and Deser 2018, 2021) enable a probabilistic comparison of models and observations (e.g. Deserand Phillips 2023, Wieder et al 2022) with the goal not necessarily of identifying which model is right orwrong, but which ones are more or less plausible. Such nuances are surprisingly important as we rethinkmodel evaluation in light of internal variability. Model behavior that was previously viewed as inconsistent
with observations is suddenly compatible, as the latter is revealed to under-sample variability (Deser et al2018). On the other hand, if a model has too much variability (like CESM1 for winter temperature over highlatitudes; Simpson et al 2022) this can create a wider range of future temperatures than might actually occur
in reality (Thompson et al 2015). Thus, if needed, certain models can now be rejected or down-weighted
more confidently thanks to the larger sample sizes (van Oldenborgh et al 2020, Zscheischler and Lehner2022).
Further, internal variability itself can change with external forcing (Rodgers et al 2021). For example,
precipitation variability is expected to increase with warming (Pendergrass et al 2017, Stevenson et al 2022)
and mid-latitude winter temperature variability is expected to decrease (Screen 2014), while the future of the
ENSO remains uncertain (Maher et al 2018). With the increasing number of SMILEs and their publicavailability, quantitative assessments of changes in variability become possible, also for typicallyunder-sampled phenomena such as extreme events or modes of internal variability (Haszpra et al 2020,
O’Brien and Deser 2023). It does, however, require confidence in the models’ ability to correctly simulateinternal variability itself.
5.3. Implications for society
Despite the remaining scientific challenges, the implications of internal variability for society are clear.
Internal variability and the uncertainty it injects into projections for the coming decades will continue toaccompany any climate change impact assessment and decision making. This suggests that a perspective
focused on risk and robust decision making (Sutton 2019, Mankin et al 2020, Reed et al 2022) is more
pertinent to users of climate model information than the focus on a ‘best-estimate’. This is increasingly being
recognized by application communities dependent on climate science, such as climate-related health impacts(Garcia-Menendez et al 2017, Fiore et al 2022) or water resource management (Harding et al 2012,
Chegwidden et al 2019, Smith et al 2022). A current example is the scoping of new guidelines for the
management of the Colorado River in the Western U.S. The co-occurrence of declining precipitation sincethe 1980s (largely attributed to internal variability, e.g. Lehner et al 2018) with anthropogenic warming andincreased water demand from socio-economic growth has led to rapid reservoir depletion (Lukas and Payton
2020). This puts pressure on new guidelines to be more robust to the full range of possible hydrologic

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F Lehner and C Deser

outcomes in the face of internal variability and forced climate change. Yet, hydrologic projections based on
climate model simulations show a paralyzingly wide range of outcomes (Lukas et al 2020). The water
management community thus uses methods of Robust Decision Making to develop guidelines that perform
optimally across this wide range of futures rather than assuming a best estimate (Smith et al 2022). However,these approaches do not currently distinguish sources of climate projection uncertainty, continue toundersample internal variability (Mankin et al 2020), and do not incorporate new observational constraints
on regional climate projections (e.g. Brunner et al 2020, Grise 2022), thus motivating closer collaborations
between the climate modeling community and practitioners.
Also, the integration of internal variability and large ensemble simulations into decision making isperhaps not happening fast enough, as the superposition of internal variability and the forced response cancreate a rapid increase in unprecedented events (Fischer et al 2021), causing unanticipated socio-economic
damages. This, in turn, prompts decision-makers and even scientists to conclude that climate change is‘happening faster than we thought’, when, really, often internal variability has not been considered to thedegree it should have. Various new approaches with large ensembles, such as developing storylines of‘unseen’ but plausible extreme events through resampling and ‘boosting’ of large ensembles (e.g. Gessner
et al 2021, Kelder et al 2022) are poised to advance not just our scientific understanding of internalvariability, but also societal communication around what to expect in a changing climate. Thus, thedecade-old seminal call to improve communication around internal climate variability (Deser et al 2012a),
especially when engaging with decisionmakers, remains as relevant as ever. Beyond communication, lessons
learned from the seasonal prediction community on co-designing information (e.g. Sánchez-García et al2022) might also be applicable for decision-making on longer time scales: deriving impact-relevant metrics
from climate model output, stress-testing real-world systems with unseen events from large ensembles, anddiscussing where projection uncertainty is potentially reducible—and where it is not.

Data availability statement
CESM1 data is available from www.earthsystemgrid.org/. CMIP6 data is available from https://esgf-node.llnl.
gov/search/cmip6/. Observational temperature data is available from https://berkeleyearth.org/data/. Code to
reproduce the figures is available on https://github.com/flehner/lehner23erc/.

Acknowledgments
We thank the two anonymous reviewers for their constructive comments and suggestions. F L acknowledges
support from the U.S. Department of Energy, Office of Science, Office of Biological & Environmental
Research (BER), Regional and Global Model Analysis (RGMA) component of the Earth and Environmental
System Modeling Program under Award Number DE-SC0022070 and National Science Foundation (NSF) IA
1947282. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

ORCID iD
Flavio Lehner  https://orcid.org/0000-0003-4632-9701

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