Climate projections are made using a hierarchy of models of different
complexities and computational efficiencies. While the most complex
climate models contain the most detailed representations of many
physical processes within the climate system, both parameter space
exploration and integrated assessment modelling require the increased
computational efficiency of reduced-complexity models. This study
presents a computationally efficient method for generating
probabilistic projections of local warming across the globe, using a
pattern-scaling approach derived from the Climate Model
Intercomparison Project phase 5 (CMIP5) ensemble, that can be coupled
to any efficient model ensemble simulation of global mean surface
warming. While the method can project local warming for arbitrary
future scenarios, using it for scenarios with peak global mean warming
≤2∘C is problematic due to the large
uncertainties involved. First, global mean warming is projected using
a 103-member ensemble of history-matched simulations with an
example reduced complexity Earth system model: the Warming
Acidification and Sea-level Projector (WASP). The ensemble projection
of global mean warming from this WASP ensemble is then converted into
local warming projections using a pattern-scaling analysis from the
CMIP5 archive, considering both the mean and uncertainty of the local
to global ratio of temperature change (LGRTC) spatial patterns from
the CMIP5 ensemble for high-end and mitigated scenarios. The LGRTC
spatial pattern is assessed for scenario dependence in the CMIP5
ensemble using RCP2.6, RCP4.5 and RCP8.5, and spatial domains are
identified where the pattern scaling is useful across a variety of
arbitrary scenarios. The computational efficiency of our WASP–LGRTC
model approach makes it ideal for future incorporation into an
integrated assessment model framework or efficient assessment of
multiple scenarios. We utilise an emergent relationship between
warming and future cumulative carbon emitted in our simulations to
present an approximation tool making local warming projections from
total future carbon emitted.
Introduction
The dominant climate projections, used by the 5th Assessment Report
(AR5) of the Intergovernmental Panel on Climate Change (IPCC, 2013),
are made using the Climate Model Inter-comparison Project phase 5
(CMIP5) ensemble (Taylor et al, 2012). However, due to their high
level of complexity, state-of-the-art CMIP5 Earth system models (ESMs)
are computationally demanding; thus they cannot be used on a regular
basis to inform decision makers about the impacts of arbitrary
carbon-emission scenarios.
While a couple of years separate the different generations of
CMIP-like experiments, many applications rather require climate
simulations to be generated within a much shorter time frame. For
instance, impact assessments may require climate projections for
scenarios not considered by the CMIP5 experiments, for example
scenarios designed to meet Paris Climate Agreement targets and
maintain global mean surface warming below 1.5 or 2 ∘C
(e.g. van Vuuren et al., 2018; Brown et al., 2018; Nicholls et al.,
2018; Goodwin et al., 2018a); physical climate simulations are also
required within integrated assessment models exploring the coupled
economic, societal, ecological and climate systems (e.g. van Vuuren
et al., 2018, 2017; McJeon et al., 2014).
To generate computationally efficient climate simulations, a range of
lower-complexity – but numerically more efficient – climate models
have been developed. They generally use a reduced spatial resolution
and/or a simplified representation of processes included within the
complex models (e.g. Smith, 2012; Meinshausen et al., 2011a; Goodwin
et al., 2018b).
For example, the highly efficient MAGICC6 climate model uses an
upwelling-diffusion representation of the ocean and a hemispherical
averaged spatial resolution (Meinshausen et al., 2011a). MAGICC6 has
been configured to emulate an ensemble of the more complex Climate
Model Intercomparison Project phase 3 (CMIP3) climate models
(Meinshausen et al., 2011a, b) but at a fraction of the
computational expense. To generate spatial projections using MAGICC, a
pattern-scaling approach (e.g. Herger et al., 2015) is applied to
emulate the spatial climate patterns from the CMIP3 models (e.g.
Fordham et al., 2012): the regional climate SCENarioGENerator
(SCENGEN). This MAGICC6 (and combined MAGICC6–SCENGEN) climate model
is computationally efficient enough to usefully couple into integrated
assessment model (IAM) frameworks, including the IMAGE and MESSAGE
frameworks (van Vuuren et al., 2017; McJeon et al., 2014). A key goal
of IAMs is to explore consequences of the coupled human–climate
system, through coupling representations of the physical climate
system with the biosphere and human–society interactions, often
including energy generation and land-use changes.
A recent study (Goodwin et al., 2018b) takes a different approach to
making future projections of global mean surface warming, using the
computationally efficient Warming Acidification and Sea-level
Projector (WASP) climate model (Goodwin, 2016). In Goodwin et al. (2018b) the efficient WASP model is
configured, not by tuning the parameters to emulate existing complex
climate models (e.g. Meinshausen et al., 2011a, b) but instead
by history-matching (Williamson et al., 2015) the efficient model to
real-world data. Goodwin et al. (2018b) first generate 100
million (108) simulations using WASP, by varying the model
properties with a Monte Carlo approach. This includes an input
distribution for climate sensitivity drawn from geological evidence
(PALAEOSENS, 2012). These 108 simulations are then integrated from
year 1765 to 2017, and each of them is checked against a set of
historic observational reconstructions of surface warming (Hansen
et al., 2010; Smith et al., 2008; Vose et al., 2012), ocean heat
uptake (Levitus et al., 2012; Giese et al., 2011; Balmaseda et al.,
2013; Good et al., 2013; Smith et al., 2015; Cheng et al., 2017) and
carbon fluxes (IPCC, 2013; Le Quéré et al., 2016). Only those
WASP simulations that are consistent with the observational
constraints are extracted to form the final history-matched ensemble
of around 3×104 simulations (Goodwin et al., 2018b; see
Table S3 in the Supplement). This final history-matched ensemble is
then used to make future projections (Goodwin et al., 2018b). Note
that the WASP ensemble is not configured to emulate the performance of
more complex models but to be consistent with observations of the
real climate system.
The WASP model (Goodwin, 2016) produces projections for global mean
surface warming only (Goodwin et al., 2018b), so to gain information
to calculate local warming we here apply a pattern-scaling tool. Leduc
et al. (2016) have recently shown that the spatial pattern of warming
across CMIP5 models is relatively robust even though the average
warming varies widely between ensemble members. Using the well-known
pattern-scaling approach (Tebaldi and Arblaster, 2014), Leduc
et al. (2016) calculated the spatial pattern of the local to global
ratio of temperature change (LGRTC) that represented the CMIP5
ensemble, including both the mean and standard deviation in this
spatial pattern.
Globally, the near-linear sensitivity of mean surface warming to
cumulative carbon emissions is expressed via the transient climate
response to cumulative CO2 emissions (TCRE in
∘C(1000PgC)-1), which is estimated to be in the range 0.8 to
2.5 ∘C(1000PgC)-1 (IPCC, 2013; Matthews
et al. 2009). One approach to generating local warming projections
from carbon emission scenarios is to simply multiply the LGRTC
characteristic of the CMIP5 ensemble (Leduc et al. 2016) by the
estimated range for the TCRE and by the cumulative carbon
emissions. However, this approach cannot be used to investigate or
simulate several phenomena of potential interest. Firstly, the
effective TCRE depends on the ratio of CO2 to non-CO2
radiative forcing (Williams et al., 2016, 2017a). Therefore, while the
efficient climate models can be applied to investigate future warming
for arbitrary scenarios, the TCRE cannot be applied unless it is for a
scenario for which the TCRE is already estimated (e.g. Matthews
et al., 2009; Williams et al., 2017a), for example the defined
Representative Concentration Pathway (RCP) scenarios (Meinshausen
et al., 2011c) or an idealised scenario with 1% per year increase
in CO2 concentration (1 % CO2; Taylor
et al. 2012) and no other forcing. Secondly, studies indicate that
there can be a period of continued surface warming following cessation
of annual carbon emissions (Frölicher et al., 2014; Williams
et al., 2017b). This phenomenon cannot be explored using the TCRE
alone but is represented within efficient climate models such as WASP
(Williams et al., 2017b). Thirdly, there is evidence that in some
circumstances there is a path dependence of surface warming from
cumulative emissions (Zickfield et al. 2012), for example where
cooling following negative emissions may not re-trace the previous
warming pathway. Again, this phenomenon is not captured within a
constant TCRE framework but may be explored with climate models. Thus
a TCRE framework is applicable for certain situations, including
idealised scenarios where the TCRE has already been established, but
in the general case a time-dependent Earth system model is required.
In this study, we present a new method for combining the LGRTC
approach with an arbitrary efficient Earth system model to generate
computationally efficient local warming projections for arbitrary
forcing scenarios. Using the WASP model as our example efficient Earth
system model, the combined WASP–LGRTC model makes local warming
projections that are history-matched to constrain the global mean
surface warming (Goodwin et al., 2018b) and pattern scaled to the
CMIP5 ensemble to generate the local information (Leduc et al.,
2016). Our efficient method of ensemble generation is able to produce
warming projections to year 2100 for arbitrary future carbon-emission
scenarios in a matter of seconds on a standard desktop computer (with
the computational efficiency of the particular, WASP, efficient model
used). An approximation tool is also presented making local warming
projections based on future cumulative carbon emitted, for idealised
scenarios where the TCRE has been pre-established.
Section 2 describes the spatial warming patterns analysed for RCP4.5
(Thomson et al., 2011) and RCP8.5 (Riahi et al., 2011) scenarios in 22
CMIP5 models, following the methodology of Leduc
et al. (2016). Section 3 describes our methods for producing an
ensemble of warming projections for any locality using the combined
WASP–LGRTC Earth system model, while Sect. 4 presents the
approximation approach for cases when the TCRE is
pre-established. Section 5 discusses the wider implications of this
study.
Spatial warming patterns in the CMIP5 ensemble for RCP2.6, RCP4.5 and
RCP8.5
Leduc et al. (2016) demonstrated the utility of considering the
spatial warming over time as a product of the global mean warming,
ΔT‾(t), and the spatial pattern of the local to
global ratio of temperature change, LGRTC(x,y), in the CMIP5
ensemble,
ΔT(x,y,t)=ΔT‾(t)×LGRTC(x,y).
The mean and standard deviation in LGRTC were analysed across 12 CMIP5
models (Leduc et al. 2016), under a 1% per year increase in
atmospheric CO2 concentration (1 % CO2; Taylor
et al. 2012). To first order, for scenarios that do not reach peak
warming before 2100, the mean LGRTC can be treated as being
independent of time and emission scenarios (Leduc et al. 2016, 2015).
Here, the spatial warming patterns in 22 CMIP5 models (see Table S1) are examined for RCP4.5 (Thomson et al., 2011) and
RCP8.5 (Riahi et al., 2011) scenarios that contain also
non-CO2 forcings from for example anthropogenic
non-CO2 greenhouse gas and aerosol emissions. We evaluated the
LGRTC comparing mean global temperature between years 2006–2025 and
2079–2098. RCP2.6 data were not available for models CESM1-BGC,
inmcm4 and IPSL-CM5B-LR. For the other 19 models, we calculated the
RCP2.6 LGRTC for the temperature peak period, defined as a 20-year
time window with the maximum time-average global mean surface air
temperature. Different models had the peak temperature at different
times, so we identified the peak individually for each model
run. For most models, the peak in 20-year running-mean global
temperature was around year 2070. For MIROC-ESM, CSIRO-Mk3-6-0, CCSM4,
MRI-CGCM3 and CSIRO-Mk3-6-0, the period with the highest mean
temperature was the years 2079–2098. The same reference period
(2006–2025) was used as with the calculation of LGRTC using the
end-of-the-century period for RCPs 4.5 and 8.5. Note that for RCP2.6
the LGRTC was calculated using the peak temperature period, rather
than 2079–2098, because the 2078–2098 period had a temperature similar
to or colder than 2006–2025 in some models, making the
calculation of LGRTC impractical since the denominator of the
calculation (the global mean temperature change) was too small or
negative.
The LGRTC in RCP2.6, RCP4.5 and RCP8.5 scenarios analysed from a
multi-model ensemble of CMIP5 simulations. Panels (a–c) show the
multi-model mean LGRTC, μLGRTC, while (d–f) show the
multi-model standard deviation in LGRTC, μLGRTC, for each
scenario.
Figure 1 shows the multi-model mean LGRTC
(μLGRTC) and multi-model standard deviation in LGRTC
(σLGRTC) for the RCP4.5, RCP8.5 and RCP2.6
scenarios. With the exception of oceanic regions where non-linear
processes have important impacts on the climate sensitivity, such as
the sea-ice albedo feedback in the Arctic and the meridional
overturning circulation in the North Atlantic (Leduc et al., 2016),
LGRTC is very similar in the RCP4.5 and RCP8.5 scenarios (Fig. 1b and
c). The uncertainty of the warming patterns within each scenario,
defined as standard deviation of LGRTC within the model ensemble
(σLGRTC), was largest in the Arctic Ocean and in the
Southern Ocean for RCP4.5 and RCP8.5 (Fig. 1e and f). The spatial
average of the multi-model standard deviation was larger in the RCP4.5
than in RCP8.5 over most areas of the globe. Over continents, it was
around 0.15–0.45 in RCP4.5 and mostly below 0.3 in RCP8.5. The RCP2.6
scenario shows greater multi-model mean LGRTC at low latitudes
(Fig. 1a–c) and has more inter-model variation in the LGRTC at high
latitudes (Fig. 1d–f), compared to the RCP4.5 and RCP8.5 scenarios.
The difference between one scenario LGRTC and another, expressed as
the spatially averaged number of multi-model standard deviations in LGRTC.
The multi-model mean LGRTC is from the second scenario relative to the
first: ∫|μj-μiσi|dA/∫dA, where A is surface area, μj
and μi are the mean LGRTC of scenarios i and j, and
σi is the standard deviation in LGRTC for
scenario i.
The difference in LGRTC between two scenarios, relative to the
multi-model variation within a scenario, is expressed via a spatially
averaged ratio of |μLGRTC,i(x,y)-μLGRTC,j(x,y)|/σLGRTC,i(x,y), where i signifies the
reference scenario and j the scenario for comparison. Table 1
expresses how many multi-model standard deviations each of the three
scenarios multi-model mean LGRTC lies relative to the other
scenarios. Considering the mid-range scenario (RCP4.5) as the
reference, the LGRTC for RCP8.5 lies a spatial average of just 0.17
standard deviations away from RCP4.5 (Table 1), indicating that the
variation in LGRTC between models within the RCP4.5 scenario is more
significant than the variation between RCP4.5 and RCP8.5 scenarios. In
contrast, the LGRTC for the RCP2.6 scenario lies 2.8 standard
deviations away from RCP4.5 (Table 1). The multi-model-mean LGRTC for
RCP4.5 and RCP8.5 scenarios lie a spatial average of 0.78 and 0.75
standard deviations away from the RCP2.6 scenario respectively
(Table 1). Note that the asymmetry in Table 1, with lower difference
when RCP2.6 is used as the reference scenario, reflects the larger
values of σLGRTC in the RCP2.6 scenario (Fig. 1d–f).
Local warming projections in the pattern-scaled WASP–LGRTC ensemble
The aim here is to generate computationally efficient future
projections of local warming across the globe, including a measure of
the uncertainty in those local warming projections. This is distinct
from generating a spatial warming projection that is internally
physically consistent, maintaining physically plausible
teleconnections between warming at different locations. Each CMIP5
model simulation creates a unique, internally physically consistent
spatial warming pattern for the prescribed forcing. When projecting
local warming, including a measure of uncertainty, one method is to
use information on the average and variation in the LGRTC information
from multiple CMIP5 models (Figs. 1 and 2). However, as soon as the
information from multiple CMIP5 models is combined, the averaged
result may not be internally physically consistent in terms of the
spatial pattern of warming.
The LGRTC in the arbitrary, generic≤2∘C and generic≥2∘C
scenarios. Panels (a–c) show the scenario mean
LGRTC. Panels (d–f) show the
scenario standard deviation in LGRTC. Panels (g–i) show the ratio
of the maximum absolute discrepancy in the mean LGRTC from the underlying
RCP scenarios, Δμ, to the standard deviation in the LGRTC,
σ, in the combined scenario: Δμ/σ.
Section 3.1 describes how an observation-constrained projection of
global mean surface warming is generated, including
uncertainty. Section 3.2 then combines this global mean projection
with the LGRTC information from the CMIP5 models (Sect. 2, above) to
generate local warming projections.
Generating global mean warming projections
The WASP Earth system model comprises an eight-box representation of
carbon and heat fluxes between the atmosphere, ocean and terrestrial
systems (Goodwin, 2016), with surface warming solved via a functional
equation linking warming to cumulative carbon emitted (Goodwin
et al. 2015). For the terrestrial system, carbon uptake by
photosynthesis is dependent on temperature and CO2, while
carbon release via respiration is temperature dependent. Heat and
carbon initially enter the ocean at the surface ocean mixed
layer. Once in the surface ocean mixed layer, heat and carbon are
exchanged with the subsurface ocean regions over e-folding timescales
that vary between each simulation in the ensemble.
Here, the WASP model configuration of Goodwin et al. (2018b) is
used. First, WASP is used to generate 3×106 initial
simulations in a Monte Carlo approach, each one integrated from years
1765 to 2017. A history-matching approach (Williamson et al., 2015) is
then adopted to assess these initial 3×106 simulations for
observational consistency against historic warming, ocean heat uptake
and carbon fluxes (Table S2 in the Supplement; and see Goodwin et al.,
2018b for how the history-matching approach is applied to the WASP
model). A total of 1×103 simulations are found to be
observationally consistent such that their simulated values of
surface warming, ocean heat uptake and carbon fluxes are consistent
within observational uncertainty (Table S2; Goodwin
et al., 2018b).
Projections of global mean surface warming from the history-matched WASP ensemble for different future carbon emission sizes. (a)
Frequency distributions of projected warming in the WASP ensemble for
different future carbon emission sizes after the start of 2018. (b)
Ensemble-mean global warming as future cumulative carbon emitted increases.
(c) Ensemble standard deviation in global warming as future carbon emitted
increases. Panels (b) and (c) show the RCP8.5 (blue), RCP6.0 (red), RCP4.5 (orange)
and RCP2.6 (purple) scenarios. A quadratic approximation, Eq. (3) for (b) and
Eq. (4) for (c), is a good fit to the RCP8.5 scenario (thin black line). All
panels show warming calculated relative to the 1850–1900 average.
The 1×103 observation-consistent simulations are extracted
to form the final history-matched ensemble. This ensemble is then
integrated into the future to generate the distribution of global mean
surface warming over time (Fig. 3). The distributions of global mean
surface warming, ΔT‾i(t), projected by this
configuration and history-matching approach using the WASP ensemble
are similar to the CMIP5 projections from highly complex ESMs for the
four RCP scenarios (Goodwin et al., 2018b; see Fig. 2
therein). However, possibly because the WASP projections are more
tightly constrained to observations, they show reduced ensemble spread
in future warming compared to the CMIP5 ensemble.
Generating local warming projections
We now utilise projected distributions from the same configuration of
the WASP model to calculate distributions of local warming across the
globe using the LGRTC pattern-scaling approach of Leduc
et al. (2016). The aim is to generate an ensemble of projections of
local warming at time t for some scenario, ΔTi(x,y,t),
by using the history-matched WASP projections of ΔT‾i(t), and the mean and standard deviation of the LGRTC for the CMIP5
models, μLGRTC(x,y) and σLGRTC(x,y)
respectively (Figs. 2 and 3).
Constructing the LGRTC suitable for a range of non-RCP scenarios
The aim here is to apply a LGRTC calculation that will likely apply
for multiple potential future scenarios, not just the three RCP
scenarios evaluated (Fig. 1). To achieve this, we now combine the LGRTC
fields for the different RCP scenarios to find aggregated LGRTC
fields, considering the spatial domain over which this is likely to be
feasible. The mean and standard deviations for the LGRTC at location
x,y, in the new combined scenarios are calculated from the
underlying RCP scenarios, using
μLGRTC(x,y)=∑i=1nμi(x,y)/n
and
σLGRTC(x,y)=∑i=1n(σi(x,y))2,
where n is the number of underlying RCP scenarios used.
The domain of the LGRTC in the new combined scenarios is assumed valid
where the variation in LGRTC between underlying RCP scenarios is less
than the variation ascribed within the new scenario,
σLGRTC(x,y). This is calculated such that
μLGRTC(x,y) exists where the variation between the
mean of the LGRTC from the different scenarios is less than the
combined standard deviation in the LGRTC |μj-μk|/σLGRTC<1.0, for all combinations of two underlying RCP
scenarios j and k.
This method (Eqs. 2 and 3) is used to generate LGRTC fields for three
potential generic scenarios (Fig. 2). First, a scenario for any
arbitrary future warming scenario (arbitrary scenario) is
constructed by combining all three RCP scenarios (RCP2.6, RCP4.5 and
RCP8.5) (Fig. 2a, d and g). Second, a LGRTC scenario for warming
consistent with Paris Climate Agreement targets of 1.5 and
2 ∘C (generic≤2∘C
scenario) is constructed by combining RCP2.6 and RCP4.5 (Fig. 2b, e
and h), the two RCP scenarios containing (at least some) model
simulations that do comply with the Paris Agreement. Lastly, a LGRTC
scenario for future warming that is likely to exceed the Paris Climate
Agreement targets (generic≥2∘C
scenario) is constructed using RCP4.5 and RCP8.5 (Fig. 2c, f and i),
the scenarios where most (RCP4.5) or all (RCP8.5) simulations exceed
2 ∘C.
The arbitrary and generic≤2∘C
LGRTC scenarios are problematic to use in practice. Firstly, the large
values of σLGRTC(x,y) across many regions,
especially over land (Fig. 2d and e), make any local warming
projection highly uncertain. The high σLGRTC(x,y)
values arise from the high inter-model variation in the LGRTC in the
RCP2.6 scenario (Fig. 1b, Eqs. 2 and 3). Secondly, both
arbitrary and ≤2∘C generic scenarios
have regions that fail the validity criteria, |μj-μk|/σLGRTC<1.0, and so are outside of the prescribed
LGRTC domains (Fig. 2a and b, white regions). The largest of these
regions lie in the low-latitude oceans, with most areas outside the
valid domain being marine. Most densely populated areas on land are
within the valid domain, and so the LGRTC approach can be applied to
project future local warming. Areas outside the applicable domain
(Fig. 2a and b) are generally where inter-model variation,
σLGRTC(x,y), is small (Figs. 2d, e and 1d–f), rather
than where inter-RCP scenario variation, μj-μk, is large
(Fig. 1a–c).
The generic≥2∘C LGRTC pattern, a
combination of RCP4.5 and RCP8.5 (Eqs. 2 and 3), is usable in practice
for more generic future warming scenarios. The generic≥2∘C LGRTC pattern retains a small
σLGRTC(x,y) (Fig. 2: compare f to d and e) and, due to
the similarities between LGRTC fields for RCP4.5 and RCP8.5 scenarios
(Fig. 1, Table 1), the LGRTC pattern for the generic ≥2∘C scenario remains within the validity criteria
for the entire globe (Fig. 2c, f, and i). The generic≥2∘C LGRTC pattern (Fig. 2) assumes idealised future
pathways within the range of the RCP4.5 and RCP8.5 scenarios (Fig. 3b
and c), including a similar ratio of CO2 to non-CO2
radiative forcing and spatial emissions of anthropogenic
aerosols. This generic≥2∘C LGRTC field
should not be used for extreme scenarios that differ widely from the
underlying societal assumptions of the RCP scenarios, for example in
their spatial aerosol forcing (e.g. see Liu et al., 2018).
Combining the LGRTC patterns with a probabilistic ensemble for global
mean warming
Here, we combine LGRTC patterns (Figs. 1 and 2) with global mean warming
projections from an efficient Earth system model. While we use the
WASP model here, other efficient models could be used. For the ith
ensemble member of this history-matched WASP ensemble, the WASP–LGRTC
projection of local warming at location x,y,ΔTi(x,y,t)
is constructed using both the mean and standard deviation in the LGRTC
from the CMIP5 models,
ΔTi(x,y,t)=ΔT‾i(t)×μLGRTC(x,y)+ziσLGRTC(x,y),
where zi is randomly chosen from a standard normal
distribution. This distribution of local warming at time t (Eq. 4)
includes both the uncertainty in global mean warming in the WASP
ensemble (Fig. 3; Goodwin et al., 2018b) and uncertainty in the
spatial pattern of warming, σLGRTC, which is
statistically derived from the CMIP5 ensemble (Fig. 2; Leduc
et al. 2016). Note that Eq. () does not assume that the
distribution of global mean temperature projections, ΔT‾i(t), from the efficient Earth system model is Gaussian.
The distribution of ΔT‾i(t) may not be Gaussian if,
for example, the assumed climate sensitivity distribution has a long
tail of high values (e.g. see Knutti et al., 2017). Thus, this method
for generating the local warming distribution, Eq. (), can be
applied to any arbitrary distribution of global mean surface warming
from any arbitrary efficient climate model. If, however, the
distribution of global mean surface temperature, ΔT‾i(t), were known in advance to be Gaussian, then it may be preferable
to generate the local warming distribution, ΔTi(x,y,t),
by multiplying the Gaussian distributions for global warming and LGRTC
directly, rather than applying Eq. (), which multiplies the
individual values within each distribution.
Projected warming for the period 2081–2100 relative to the
1850–1900 average from 1×103 history-matched simulations of
the ultra-fast WASP–LGRTC ensemble. Panels (a–c) is for the RCP4.5
scenario and (d–e) is for the RCP8.5 scenario. Panels (a, d),
(b, e) and (c, f) represent the mean, 83rd percentile and 17th
percentile of the model ensemble.
The full WASP–LGRTC-ensemble local warming projections for RCP 4.5 and
RCP 8.5 are given in Fig. 4, which shows the mean, 17th percentile and 83rd
percentile of the warming across the globe from the 1×103
WASP–LGRTC ensemble members. To generate the local projections (Eq. 4)
for RCP4.5 and RCP8.5, we apply the pattern scaling analysed from the
CMIP5 models for the appropriate scenario (Fig. 2). In both scenarios,
there is more uncertainty (i.e. a higher range of responses between
the 17th and 83th percentiles) in local warming at high northern
latitudes (Fig. 4), consistent with this area showing a larger
ensemble spread between CMIP5 models (Fig. 1).
The radiative forcing from aerosols can be highly localised, and so
the ensemble mean and variation of local warming,
μLGRTC(x,y) and σLGRTC(x,y) in
Eq. (), depend on how the CO2 and
non-CO2 agents evolve in the scenario. For that reason, we
include local warming patterns for the 1 % CO2 scenario as
well as the RCP4.5, RCP8.5 and generic≥2∘C scenarios in the pattern scaling for the
WASP–LGRTC model code (10.5281/zenodo.4001523). This allows
future users to choose the spatial pattern scaling that is most
suitable for their scenario. The next section utilises the
generic≥2∘C LGRTC pattern (Fig. 2c) to
project spatial warming patterns for scenarios where the cumulative
carbon emission is specified.
Approximation for arbitrary cumulative carbon emission scenarios
This section explores further increasing the computational efficiency
for making spatial warming projections for idealised future scenarios,
by approximating to the history-matched WASP ensemble projections of
global mean surface warming as a function of cumulative carbon emitted
after 2018, Iem in PgC.
The distribution of global mean surface warming in the WASP–LGRTC
ensemble is approximately normally distributed for the RCP scenarios
(Fig. 3a). The history-matched ensemble mean and standard deviation,
μΔT‾ and σΔT‾ respectively,
are both well approximated by second-order polynomials in cumulative
carbon emitted (Fig. 3b and c). The ensemble mean warming projections
is given by
μΔT‾(Iem)=a1Iem2+b1Iem+c1,
and the ensemble standard deviation by
σΔT‾(Iem)=a2Iem2+b2Iem+c2,
where a1=3.50257×10-7, b1=2.50924×10-3,
c1=1.02159, a2=2.14129×10-8, b2=2.28077×10-4 and c2=8.79361×10-2 for RCP8.5. Both the RCP4.5
and RCP2.6 scenarios see very similar warming per unit future carbon
emitted to RCP8.5, while the RCP6.0 scenario sees only slightly less
warming per unit future carbon emitted (Fig. 3b and c).
Therefore, for emission scenarios over the 21st century in which the
ratio of radiative forcing from sources other than CO2 to
cumulative carbon emitted during the 21st century lies within the
range of the RCP scenarios, the distribution of global mean surface
warming from the history-matched WASP ensemble can be approximated by
quadratics in future carbon emitted (Eqs. 5 and 6; Fig. 3)
Warming projections when future emissions reach 500 PgC from the
start of 2018. (a) The spatial distribution of the central warming
projection. (b) The probability distributions of local warming for seven
locations (solid colour lines) and the global surface average (black dashed
line). All warming projections given relative to the average temperature
from 1850 to 1900. Global mean warming projected from the quadratic
approximation to the history-matched WASP ensemble (Eqs. 3 to 6) using the
generic ≥2∘C spatial pattern.
The mean warming at location x,y is calculated by simply multiplying
the mean of the 1×103 WASP ensemble members of the global
average warming by the CMIP5 mean of the LGRTC,
μΔT(x,y,Iem)=μΔT‾(Iem)×μLGRTC(x,y).
The standard deviation in local warming at location x,y after
cumulative emissions Iem, σΔT(x,y,Iem) is then calculated from the standard deviation
in the global average warming in the i ensemble members,
σΔT‾(Iem), and the standard
deviation in the LGRTC, σLGRTC(x,y), using
σΔT(x,y,Iem)=μΔT(x,y,Iem)8×σΔT‾(Iem)μΔT‾(Iem)2+σLGRTC(x,y)μLGRTC(x,y)2.
Note that in this approximation tool the uncertainty in local warming
is calculated directly by multiplying the assumed Gaussian
distributions of LGRTC and global mean warming, Eq. (). This
is unlike the uncertainty calculation for the generic method,
Eq. (), which does not assume a Gaussian distribution for
global mean warming. Applying Eqs. () and ()
provides a method to approximate local warming projections as a
function of the future carbon emitted after the start of 2018
(Fig. 5a; code available at 10.5281/zenodo.4001523), including
uncertainty in the warming at any location (Fig. 5b). This method
assumes idealised future pathways within the ranges of the RCP4.5 and
RCP8.5 scenarios (Fig. 3b and c), including a similar ratio of
CO2 to non-CO2 radiative forcing. The
generic≥2∘C scenario LGRTC field
(Fig. 2) is applied (Fig. 4), and as such the approximation tool
should be utilised for cumulative carbon emission values that give a
best estimate for global mean warming of 2 ∘C or
more. While this approximation tool (Fig. 5; Eqs. 5–8) is not as
general as the full WASP–LGRTC Earth system model in its potential
applications, we anticipate it will still be a useful tool for
back-of-the-envelope approximations and pedagogical applications.
Discussion
A highly computationally efficient Earth system model has been
presented for projecting local warming projections, based on a history-matched global mean warming projection using an efficient ESM
(Goodwin, 2016; Goodwin et al., 2018b) and pattern scaling of the
CMIP5 ensemble (Leduc et al., 2016): the WASP–LGRTC model. Along with
the full WASP–LGRTC model is an easy-to-use normal error propagation
approximation variant producing projected ranges of both global mean
warming and the spatial distribution of warming for future cumulative
carbon-emission values.
The WASP–LGRTC model presented here is an alternative to existing
efficient climate models. For example, the MAGICC6–SCENGEN efficient
model is often configured as an “emulator” of the CMIP3 ensemble
(Meinshausen et al. 2001): the
MAGICC6–SCENGEN model parameters are tuned such that the ensemble
members emulate the properties of the more complex CMIP3 models in
both global mean warming and spatial warming patterns. However, even
the most complex of climate model ensembles show discrepancy to
observations (Goodwin et al. 2018b), and this discrepancy will be
reproduced by an emulating ensemble. In contrast, the WASP–LGRTC model
is not tuned to emulate more complex models. Instead the WASP model
parameters are empirically constrained using the observed histories of
warming, heat uptake and carbon fluxes to generate global mean surface
warming projections (Goodwin et al. 2018b). Meanwhile, the LGRTC
spatial pattern applies the mean and standard deviation in the spatial
warming from across the CMIP5 ensemble (Leduc et al. 2016) but does
not seek to emulate any specific CMIP5 model within any specific
WASP–LGRTC ensemble member.
At present, the WASP model requires prescribed radiative forcing from
greenhouse gases and agents other than CO2, for example
methane or aerosols (Goodwin, 2016; Goodwin et al. 2018b). Future work
will seek to implement an emission-based representation of other
significant greenhouse gases and aerosols, allowing the WASP–LGRTC
model to explore a wider range of future scenarios.
Both the WASP–LGRTC model and the quadratic approximation to
WASP–LGRTC model are easy to use. The full WASP–LGRTC model can
quickly generate output for arbitrary future scenarios, while the
approximated model makes projections for different future cumulative
emissions assuming that the relative CO2 and non-CO2
radiative forcing is in the range of the RCP8.5, RCP4.5 or RCP2.6
scenarios (Fig. 3b and c: compare black dashed line to red, orange and
purple).
We anticipate that our full and approximated models will be beneficial
both for scientific and pedagogical applications, where available
computational resources or climate-model expertise exclude the use of
highly complex models
Code availability
Versions of the WASP model is available from the public
GitHub repository at
https://github.com/WASP-ESM/WASP_Earth_System_Model, last access: 26 August 2020. The specific code for both the WASP–LGRTC
combined model approach used in this study and the local warming projection
approximation tool are archived on Zenodo (10.5281/zenodo.4001523).
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-13-5389-2020-supplement.
Author contributions
PG conducted the numerical modelling and coded the
WASP–LGRTC model and approximation tool, with input from AR. AIP, MD and HDM
analysed the spatial patterns in the CMIP5 models and supplied the spatial
arrays used by the WASP–LGRTC model and approximation tool. All authors
contributed to writing the manuscript.
Competing interests
Authors declare no competing interests.
Acknowledgements
Philip Goodwin acknowledges funding from UK NERC grant NE/N009789/1
and combined UK Government Department of BEIS and UK NERC grant
NE/P01495X/1. Martin Leduc thanks Ouranos and Concordia
University. Antti-Ilari Partanen was supported
by Emil Aaltonen Foundation, The Fonds de recherche du Quebec – Nature et
technologies (grant no. 200414), Concordia Institute for Water, Energy
and Sustainable Systems (CIWESS), and Academy of Finland (grant no.
308365). We acknowledge the World Climate Research Programme's Working Group
on Coupled Modelling, which is responsible for CMIP, and we thank the
climate modelling groups (listed in Table S1 in the Supplement) for producing
and making available their model output. For CMIP the US Department of
Energy's Program for Climate Model Diagnosis and Intercomparison provides
coordinating support and led development of software infrastructure in
partnership with the Global Organization for Earth System Science Portals.
Financial support
This research has been supported by the Natural Environment Research Council (grant nos. NE/N009789/1 and NE/P01495X/1), the Emil Aaltonen Foundation (grant no. 200414) and the Academy of Finland (grant no. 308365).
Review statement
This paper was edited by James Annan and reviewed by Christopher Smith and one anonymous referee.
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