We present a carbon-cycle–climate modelling framework using model emulation,
designed for integrated assessment modelling, which introduces a new emulator
of the carbon cycle (GENIEem). We demonstrate that GENIEem successfully
reproduces the CO

Integrated assessment modelling can be used to explore the climatic
consequences of particular climate mitigation policy scenarios. However, most
integrated assessment models (IAMs) do not directly utilize sophisticated
coupled Atmosphere Ocean General Circulation Models, such as those employed
in the Coupled Model Intercomparison Project Phase 5

Instead, many IAMs have used simple mechanistic models to represent the
carbon cycle. One such simplified carbon-cycle/climate model is MAGICC6

It has been suggested that a conceptual advantage of this approach is that
the mechanistic model fit adds some confidence when extrapolating beyond the
training data

To represent regionally varying patterns of climatic change, as opposed to
global mean temperature change, many IAM studies have used pattern scaling

MAGICC/SCENGEN user manual, p. 2:

The Atmosphere–Ocean General Circulation Model (AOGCM) ensembles used in
pattern scaling are usually multi-model ensembles (MMEs). Such ensembles
consist of simulations from different models, and are neither a systematic
nor random sampling of potential future climates

Perturbed physics ensembles (PPEs) offer a more systematic sampling of
potential future climates, but embedding a PPE approach into an IAM framework
requires a computationally fast climate model. In this context, statistical
emulation of complex models is a useful alternative. For example,

In this paper, we demonstrate how model emulation using singular vector
decomposition (SVD) can be used within an IAM framework to generate PPEs, systematically capturing uncertainty in the future climate
state while also providing insight into regional climate change. We introduce
the GENIEem-PLASIM-ENTSem (GPem) climate–carbon-cycle emulator, which
consists of a statistical climate model emulator, PLASIM-ENTSem, to represent
climate dynamics

We demonstrate how these emulators can be applied in an IAM framework to
resolve the regional environmental impacts associated with policy scenarios
by coupling GPem to FTT:Power-E3MG, a non-equilibrium economic model with a
technology diffusion component. Our work builds on that of

The carbon cycle model emulator GENIEem is an emulator of the GENIE-1 Earth
System Model (ESM)

In the integrated assessment framework developed here, the time series of
anthropogenic carbon emissions is provided by E3MG-FTT, while non-CO

Data available via the RCP Database at

The full GENIE-1 ESM comprises the 3-D frictional geostrophic ocean model
GOLDSTEIN

The configuration is the same as that applied in the Earth system model of
intermediate complexity (EMIC) intercomparison project

Schematic describing the construction of GENIEem.

Construction of GENIEem is summarized in (Fig.

The 471 parameter sets are constrained to be plausible in the preindustrial
state by design

In order to identify useful parameter sets, we apply a filter to this
transient historical ensemble. A parameter set is accepted as plausible if
the difference between simulated and observed atmospheric CO

The

These 86 parameter sets from the full GENIE-1 ESM were used to generate an
ensemble of future simulations (2005 to 2105) forced with time-varying
CO

To capture the range of possible future forcing we followed the approach of

Note that Eq. (2) is strictly a linear combination of Chebyshev polynomials such that the first two terms give the linear increase in emissions; we refer to the coefficients henceforth as “Chebyshev coefficients”.

The non-CO

The

For example, the maximum

The 86 parameter sets were replicated three times, and each of these three
86-parameter sets were combined with different future emissions profiles to
produce a 258-member ensemble. To achieve this, the six coefficients were
varied over the above ranges to create a 258-member Maximin Latin Hypercube
design, using the maximinLHS function of the lhs package in R

The emulation approach closely follows the dimension reduction methodology
detailed in

We retain the first four components, which together explain more than 99.9 %
of the ensemble variance. Each individual simulated CO

Emulators of the first four component scores were derived as functions of the
28 model parameters and the six concentration profile coefficients. These
emulators were built in R

While the variance in emulator output is dominated by the Chebyshev forcing
coefficients, uncertainty for a given forcing scenario is generated through
emulator dependencies on GENIE-1 parameters. The most important of these is
the CO

We approximate the prior as a normal distribution with mean 500 ppm and
standard deviation 150 ppm, following the base posterior of

To validate the emulator, we apply leave-one-out cross-validation, which
involves rebuilding the emulator 257 times with a different simulation
omitted and comparing the omitted simulation with its emulation. The
proportion of variance

Carbon cycle emulator output compared with RCP data, for the four RCPs 2.6, 4.5, 6.0 and 8.5. Anomalies are relative to 2005. For RCP8.5, CMIP5 data are presented as a reference.

The cross-validated root mean square error of the emulator is given by

Given that the RCP estimate is 936 ppm, these data appear to show that the
emulator and simulator overstate the RCP8.5 concentration in the median.
However, the reason for this is that this validation did not use the
CO

To further evaluate the emulator's performance, we consider GENIEem's
response to forcing by Representative Concentration Pathways

Data available via the RCP Database at

GENIEem median CO

For RCP2.6, the difference between the RCP value and the emulator median
reaches about 15 ppm. One possible explanation for this is the formulation of
land use change. When land use is changed in GENIE, soil carbon evolves
dynamically to a new equilibrium. Therefore, although the LUC mask is held
fixed after the transient AD 850–2005 spin-up, there are ongoing
land–atmosphere fluxes in the future (2005–2105) due to historical LUC. Since
the RCP emissions data used to force GENIEem already include the contribution
from soil carbon fluxes, the inconsistency of approaches is liable to lead to
a net additional forcing while the historical contribution decays. These
residual emissions would be most significant in RCP2.6 because other
emissions are lowest in this scenario, potentially contributing to the excess
concentrations in the emulation of RCP2.6. This difference could be reduced
by using a more sophisticated treatment of the forcing inputs that separated
fossil fuel and land use carbon emissions, with land use emissions calculated
from spatially explicit scenarios based on above-ground carbon change, as in

To demonstrate the utility of emulation within an integrated assessment
framework, we describe how GENIEem, along with PLASIM-ENTSem, has been used to
explore the climate change implications of four policy scenarios for
the electricity sector, as presented in

PLASIM-ENTSem is an emulator of the GCM PLASIM-ENTS; both simulator and
emulator are described by

As an emulator of PLASIM-ENTS, PLASIM-ENTSem emulates mean fields of change
for surface air temperature and precipitation well, while emulations of
precipitation underestimate simulated ensemble variability, explaining

The response of PLASIM-ENTSem to RCP forcing was analysed in

FTT:Power is a simulation model of the global power sector

Here we consider four scenarios, a subset of the 10 scenarios explored in

Scenario ii introduces carbon pricing, which rises to 200–400 2008 USD

Total CO

As FTT:Power-E3MG runs until 2050, emissions for 2050–2105 are estimated
using a linear best-fit trend, except in the case of successful mitigation
scenarios, where such an approach could lead to implausible emissions
reductions by 2105. In these scenarios, the emissions in Pg C yr

Chebyshev coefficients are calculated to provide least-squares fits to each emissions profile produced by FTT:Power-E3MG. If we conservatively assume that any error in emissions due to differences between the FTT:Power-E3MG emissions profile and the corresponding Chebyshev curve has an infinite lifetime in the atmosphere, the accumulated error does not exceed 4.5 ppm in any scenario over the period 2005–2105, well within the 5th–95th percentiles of GENIEem.

As FTT:Power-E3MG does not simulate non-CO

This approach maintains comparability across the different scenarios,
although we expect some small reductions in CH

Climate–carbon feedbacks are emulated entirely within GENIEem. No climate
information is passed from PLASIM-ENTSem to GENIEem. PLASIM-ENTSem takes inputs of
both actual CO

Thus, PLASIM-ENTSem is forced with three sets of six coefficients (three
actual CO

We calculate the median warming of the PLASIM-ENTSem ensemble based on the 5th and 95th percentiles of the GENIEem ensemble. These bounds, therefore, illustrate parametric uncertainty of the carbon cycle model alone.

We also calculate the median and 5th–95th percentiles of warming of the PLASIM-ENTSem ensemble from the median GENIEem ensemble output. These bounds reflect parametric uncertainty in the climate model alone.

Finally, we calculate the 5th percentile of warming from the PLASIM-ENTSem
ensemble based on the 5th percentile of CO

Top panels: median CO

We applied GPem to determine the atmospheric CO

2095–2105 temperature anomalies relative to 1995–2005 for DJF and
JJA under the baseline scenario i (right panels) and the mitigation
scenario iv (left panels). The 5th, 50th and 95th percentile of the
PLASIM-ENTSem ensemble are calculated independently at each grid point. The
PLASIM-ENTSem ensembles are forced with GENIEem median CO

2095–2105 precipitation anomalies (ensemble means) relative to 1995–2005 under the baseline scenario i, and the mitigation scenario iv (top panels) and proportion of ensemble members simulating increased precipitation (bottom panels).

Figure

Figure

Precipitation patterns are similar for the two scenarios presented (

We have described and validated a new carbon cycle model emulator, GENIEem,
and applied it along with PLASIM-ENTSem to demonstrate the utility of
statistical model emulation in an IAM setting. The climate–carbon-cycle
emulator GPem was used to examine atmospheric CO

Even the most successful mitigation strategy considered here results in
warming of above 3.5

The latest IPCC AR5 notes that in 2010, the energy supply sector accounted
for 35 % of total GHG emissions

Furthermore, the inadequacy of the electricity sector to solve the emissions
problem is in spite of the fact that the inclusion of non-linear feedbacks on
technology uptake is expected to promote decarbonization in our model,
compared to the equilibrium models in the IPCC AR5 database, which may not
capture the complexities of real-world human behaviour in mitigation
decision making

The 2

While uncertainties associated with carbon cycle and climate modelling in this framework are accounted for through the use of ensembles, it is still possible that the actual future climate state may fall outside the simulated range. Uncertainties associated with emissions profiles are more difficult to quantify as these depend, ultimately, on human decision making. Therefore many policy contexts should be modelled in order to find out which ones effectively lead to desired outcomes.

We acknowledge the support of D. Crawford-Brown. We thank F. Babonneau for providing code to generate Chebyshev coefficients, P. Friedlingstein for provision of CMIP5 data and M. Syddall for his advice regarding data visualization. This work was supported by the Three Guineas Trust (A. M. Foley), the EU Seventh Framework Programme grant agreement no. 265170 “ERMITAGE” (N. Edwards and P. Holden), the UK Engineering and Physical Sciences Research Council, fellowship number EP/K007254/1 (J.-F. Mercure), Conicyt (Comisión Nacional de Investigación Científica y Tecnológica, Gobierno de Chile) and the Ministerio de Energía, Gobierno de Chile (P. Salas), and Cambridge Econometrics (H. Pollitt and U. Chewpreecha). Edited by: J. Dyke