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GLOBAL CIRCULATION MODEL COMPARISON USING A STATISTICAL EMULATOR

Introduction

The University of ChicagoDepartment of Geophysical Sciences

W. Grant Wilder1,2, Stefano Castruccio 2, William B. Leeds1,2, Shanshan Sun1, David J. McInerney3, Michael L. Stein 2, Elisabeth J. Moyer1Departments of Geophysical Science1 and Statistics2, The University of Chicago

School of Civil, Environmental and Mining Engineering3, University of Adelaide

Statistical emulators are computationally inexpensive statistical approximations to computationally expensive computer models. As such, they can be a useful tool for Global Circulation Model (GCM) investigation. There are several advantages:

• computationally inexpensive estimation of temperature under various CO2 trajectories• estimated statistical parameters provide a reduced-dimension summary of the GCM• GCM emulators could be coupled to economic and impact models

A Simple Statistical Model is Sufficient

The Center for Robust Decision Making on Climate and Energy Policy

CMIP5 Enables Multi-Model Comparison• The CMIP5 archive offers a library of output from identically forced GCMs for model inter-comparison.• We examine the Representative Concentration Pathway (RCP) experiments, which are the most relevant for policy analysis and economic models.

• RCP runs are difficult for emulation because they are smooth and similar, with each modeling group providing few independent realizations.

circulation rates, outweighing initial decreases in tropospheric sinks due to lower OHconcentrations (see Section 2.4 and Fig. 5d).

RCP4.5 and RCP6 are both stabilization scenarios, with constant concentrations after2150. By stabilizing CO2 concentrations at 543 ppm, RCP4.5 comes very close to adoubling of pre-industrial CO2 concentration (278 ppm)—and is hence only slightlyhigher than the SRES B1 scenario and its constant extension after 2100 with 540 ppmCO2 (see Bern-CC (reference) case in Appendix II.2.1 in Houghton et al. 2001). TheRCP6 scenario stabilizes 200 ppm higher, at 752 ppm CO2 (see Fig. 5).

5 Discussion

5.1 Ensemble results compared to our default concentration and temperature projections

In the above text we selected a specific (‘best-estimate’) set of MAGICC parameters to usein producing a standard set of RCP concentrations. Starting from the harmonized emissions,we can also produce concentrations (and forcing and temperature projections) using 19individual CMIP3 climate and 9 C4MIP carbon cycle emulations. How does our default setof results compare with the distribution of results from these 171 (=19×9) cases?

We perform this comparison using the highest and the lowest RCP scenarios. The results areshown in Fig. 6. Not surprisingly, because the responses to external forcings in all climatemodels are largely linear, the ‘best-estimate’ results are similar to the median of the individualmodel results, even in the high forcing RCP8.5 case. The ideal test of our projections, although

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Fig. 4 Total radiative forcing (anthropogenic plus natural) for RCPs,—supporting the original names of thefour pathways as there is a close match between peaking, stabilization and 2100 levels for RCP2.6 (called aswell RCP3-PD), RCP4.5 & RCP6, as well as RCP8.5, respectively. Note that the stated radiative forcinglevels refer to the illustrative default median estimates only. There is substantial uncertainty in current andfuture radiative forcing levels. Short-term variations in radiative forcing are due to both volcanic forcings inthe past (1800–2000) and cyclical solar forcing—assuming a constant 11-year solar cycle (following theCMIP5 recommendation), except at times of stabilization

230 Climatic Change (2011) 109:213–241

CMIP5’s smooth, similar trajectories sometimes show little distinction between short and long-term effects. This makes it hard to distinctly estimate β1 and β2, and a clear multicollinearity effect can emerge. Abrupt changes in the CO2 trajectory (i.e., ‘jump’ and ‘drop’ scenarios) can better distinguish short-term and long-term effects to train the statistical model. A reduction in the correlation between predictor variables may improve interpretation of the suite of estimated parameters for more quantitative inter-model comparison.

Interpretation is Affected by Multicollinearity

47 Regions are Emulated Independently

The University of ChicagoDepartment of Statistics

Fig. 1: The emulator is designed to predict surface temperature output (green), given a CO2 emissions scenario (blue). In this study, the CMIP5 RCP26 and RCP85 scenarios (shown) are used to train the statistical emulator’s parameters, and we test the emulator on the RCP45 scenario.

Fig. 3: The emulator is independently trained and applied to an RCP scenario in 47 regions.

Emulator Can Quickly Build a Multi-Model Suite of Climate Trajectories

Quantifying Goodness of Fit

Fig. 2: The RCP scenarios are smooth and difficult to emulate well. For economic impacts modeling, these are the type of pathways that must be accurately emulated.

Fig. 4: The emulator captures the trend in the CCSM4 temperature output without capturing annual-scale variability. The variability over land is greater than over the ocean. Regions shown are chosen arbitrarily.

To quantify the error in emulation, we use the Root Mean Squared Error, normalized by the variance from the CMIP5 pre-industrial control experiments. Each model is treated independently. For one region from one model,

I = (

�(TEmulated − TGCM )2/n1�

(T̄GCM control − TGCM control)2/n2)1/2

1

where n1 is the number of years emulated and n2 is the number of years in the pre-industrial control experiment. A value of I close to 1 indicates that the emulator captures the trend of the RCP experiment. This avoids the problem of GCMs’ different amount of preindustrial annual-scale variability so we can quantify emulation error purely due to trend and changing variability.

Fig. 8: In some GCMs, the coefficient parameters become strongly correlated.

Our model uses the approximate relationship between log[CO2] and temperature. The model includes terms that reflect fast growth and slow growth that result from an increase of log[CO2]. Specifically:

where current temperature is regressed on current log[CO2] and a weighted average of log[CO2] in previous years. To account for remaining temporal variation in the error structure, we use an AR(1) model for the error process.

The parameters are estimated using the profile likelihood method (see Gelfand et al. 2008, Ch. 4).

I = (

�(TEmulated − TGCM )2/n1�

(T̄GCM control − TGCM control)2/n2

)1/2

T (t) = βo + β11

2(log[CO2](t) + log[CO2](t− 1)) + β2

+∞�

i=2

ωi−2log[CO2](t− i) + ηt

1

I = (

�(TEmulated − TGCM )2/n1�

(T̄GCM control − TGCM control)2/n2

)1/2

T (t) = βo + β11

2(log[CO2](t) + log[CO2](t− 1)) + β2

+∞�

i=2

ωi−2log[CO2](t− i) + ηt

ωi =ρi�∞j=0 ρ

j

1

Tibetan Plateau Caribbean Sea

Fig. 5: This method can successfully recreate an ensemble of models forced by the same scenario for easy visual intercomparison.

Fig. 7: In FGOALS, the overall fit is worse, and is especially bad in the North Atlantic.

Fig. 6: The emulation fit index in CCSM4 is generally close to 1, and globally fairly consistent

Better Interpretation and Intercomparison Requires Diverse Training Experiments

We separate the globe into 47 regions to capture the physical response to CO2 forcing. For stable estimates of the parameters, we compute ρ and φ for ocean and land separately. We then estimate a set of β parameters for each region independently. This technique can significantly outperform pattern scaling because it can capture more complex temporal variety in transient climate.

The physics of climate model intercomparison projects may be better targeted by more types of experiments rather than different levels of the same experiments. Training the emulator with ‘jumps’ and ‘drops’ (e.g. CMIP5’s ‘Sudden 4x CO2’) will allow a more meaningful interpretation and comparison of both transient climate and climate sensitivity. We can, however, use this emulator to create a suite of future global and regional mean temperatures to recreate a multi-model response to the steady global change in CO2 concentration on the century timescale.

Emulator Fits Some Models Better than OthersIn CCSM4, the fit index is fairly consistent over the globe; most of the fits are close to 1, identified by the white portions of these maps. Some sections of the ocean have a fit index greater than one, but I, the fit index, is not robust to increasing annual-scale variability.

In FGOALS, however, the fit indices vary more. For example, emulation does not successfully capture the negative trend in the North Atlantic (NNA):

An important model assumption is a positive relationship between the log[CO2] history and temperature, which does not apply here and confounds parameter estimation.

Fig. 9: GCM output and Emulation for 9 identically forced experiments’ GMT at the RCP45 level.

RCP85 CO2 and GCM output

RCP30 CO2 and GCM output

CO2 growth pathways are extremely similar

Annual-Scale Variability