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The Interpretation Of Physically Based Climate Models: Statistics .vs. Physics .vs. Philosophy
D A Stainforth1,2
INTEGRATE Meeting Lund University
14th November 2016
1Grantham Research Institute and Centre for the Analysis of Timeseries, London School of Economics, 2Dept. of Physics, Warwick University,
Acknowledgements: L A Smith, M R Allen and a cast of thousands
Layout
• An introduction to global climate models (GCMs). • Perturbed physics ensembles and climateprediction.net • Key elements of the climate prediction challenge. • Challenges in the design and interpretation of multi-model
ensembles (MMEs) and perturbed physics ensembles (PPEs)
19 levels in
atmosphere
20 levels
in ocean
2.5
lat 3.75 long
1.25
1.25
-5km
Complex Climate Models [Global Circulation Models]
Complex Climate Models / Global Circulation Models (GCMs)
DDtρ ρ= − ∇•u
1p
DT Dpc QDt Dtρ
= +
p RTρ=
22D pDt
ηρ ρ
−∇= − − − ∇
uΩ u g u x
Figure source: Emily Black / NERC
Momentum equation
Conservation of mass
Conservation of energy
Ideal gas equation (Eqn of state)
GCMs: Parameterizations
• Clouds • Precipitation • Radiation • Gravity waves • Convection • Land surface • (Carbon cycle) • (Sea ice) • ((Ice sheets))
• Missing: ocean/atmospheric chemistry , ecosystems, stratosphere …
Models Included in the Fifth Coupled Model Intercomparison Project (CMIP5) and used in the IPCC Fifth Assessment report:
Even amongst the most up-to-date models there are a wide variety of different resolutions and different levels of complexity in parameterization schemes.
How Many GCMs are there?
Source: IPCC WG1 AR5 Chapter 9, Table 9.1 For detailed model specifications look at Table 9.A.1
MSc Climate Change: Science, Economics and Policy
Model Simulations from the IPCC Fifth Assessment Report (AR5)
Source: WG1 SPM IPCC 2013
All temperatures are shown relative to the 1986-2005 average Add about 0.6 to get the value relative to pre-industrial
8
Presentation of Global Mean Temperature Change
Source: WG1 SPM IPCC 2013
9
Source: WG1 Ch 12 IPCC 2013
Source: WG1 Ch 9 IPCC 2013
Regional / Local Predictions An Area of Significant Effort
The North American Regional Climate Change Assessment Program (NARCCAP) aims to “investigate uncertainties in regional scale projections of future climate and generate climate change scenarios for use in impacts research.” http://www.narccap.ucar.edu/about/index.html
2080s: 90% probability level: very unlikely to be greater than
2080s : 67% probability level: unlikely to be greater than
Change in Wettest Day in Summer Medium (A1B) scenario
UKCP09: NARCCAP:
“The UK Climate Projections (UKCP09) provide climate information designed to help those needing to plan how they will adapt to a changing climate. The data is focussed on the UK,” “UKCP09 provides future climate projections for land and marine regions.” “They assign probabilities to different future climate outcomes. “ http://ukclimateprojections.defra.gov.uk
ENV.2011.1.1.6-1 “The proposed research activities should […] quantify the impacts of climate change in selected areas of Europe […] arising from a global averaged surface temperature change of 2°C from preindustrial level.” ftp://ftp.cordis.europa.eu/pub/fp7/docs/wp/cooperation/environment/f-wp-201101_en.pdf
€7M European Call:
Tebaldi et al.., JoC, 2005
Stott et al.., GRL, 2006
UK Climate Projections 2009 (2018)
UK Climate Projections 2009: Change in Wettest Day in Summer in A1B scenario
2080s: 90% probability level: very unlikely to be greater than
2080s : 67% probability level: unlikely to be greater than
“The UK Climate Projections (UKCP09) provide climate information designed to help those needing to plan how they will adapt to a changing climate. The data is focussed on the UK,” “UKCP09 provides future climate projections for land and marine regions.” “They assign probabilities to different future climate outcomes. “ http://ukclimateprojections.defra.gov.uk
Critical Assessments:
Frigg, R., L.A. Smith, D. A. Stainforth, The Myopia of Imperfect Climate Models: The Case of UKCP09, Philosophy of Science, 2013.
Frigg, R., L.A. Smith, D. A. Stainforth, “An assessment of the foundational assumptions in high-resolution climate projections: the case of UKCP09”, Synthese, 2015.
Model Differences: Individual Model
Results: Temperature
[CMIP3]
Source: IPCC AR4 WG1 Supplementary Information
Model differences: Individual Model Errors
in Annual Mean Temperature
[CMIP3]
Source: IPCC AR4 WG1 Supplementary Information S8.1b
Model differences at the global scale CMIP5 timeseries of Global Mean Temperature
through the 20th Century
Climateprediction.net History
• Climateprediction.net is a project which engages the public to use spare capacity on their PCs to do climate simulations.
• Conceived in 1998 by Myles Allen • Development began in earnest in 2000 when I joined Myles to
do model and software development and experimental design.
• Launched in 2003 • First results published in 2005. • Includes a wide variety of experiments.
I’m presenting results from the first experiment which has by far the largest exploration of model uncertainty of any climateprediction.net or other climate model experiment.
Climateprediction.net: The first (slab) Experiment
Unified Model with thermodynamic ocean. (HadSM3)
15 yr spin-up 15 yr, base case CO2
15 yr, 2 x CO2
Derived fluxes
Diagnostics from final 8 yrs.
Calibration
Control
Double CO2
Stan
dard
mod
el
set-u
p
Perturbed Physics
Ensemble
Initial Condition Ensemble
Grand Ensem
ble
10000s 10s P1 Low High Stnd
Stnd
Low
High P2
Parameter Space, Sampling Strategy and the need for large ensembles
P1 Low High Stnd
Stnd
Low
High P2 • There are hundreds of uncertain parameters in
a GCM. • To study them one at a time is easy. • But they interact non-linearly so we need to
explore multiple perturbations simultaneously.
No. of parameters
One at a time
All combinations
1 3 3 2 5 9 3 7 27 6 13 729 21 42 1010
Required number of simulations:
Public Resource Distributed Computing Projects (PRDC – aka Volunteer Computing)
Climateprediction.net
GIMPS SETI@home Folding@home
LHC@home Einstein@home Lifemapper
Find-a-drug FightAIDS@home Evolution@home
Eon Compute Against Cancer
Drug Design Online
Muon1 Seventeen of Bust
Climateprediction.net (a bit out of date) Statistics • > 300,000 participants over last 10 years • > 130M years simulated. • >> 600,000 completed simulations.
(Each 45 years of model time or more) • >30000 active hosts
Frequency Distribution of Simulations (>2000 simulations)
15 yr spin-up 15 yr, base case CO2
15 yr, 2 x CO2
Derived fluxes Diagnostics from
final 8 yrs. Calibration
Control
Double CO2
From Stainforth et al. 2005
Frequency Distribution of Simulations and Model Versions
To find potentially realistic model versions we remove those which are unstable in the control. The remaining negatively drifting 2xCO2 model versions are an unrealistic consequence of using a slab ocean.
From Stainforth et al. 2005
From Stainforth et al. 2005
Frequency Distribution of Climate Sensitivity
Climate sensitivity is the equilibrium global mean surface temperature change in response to a doubling of atmospheric CO2 concentrations.
Sample model outcomes
Temperature Change Precipitation Change
Unperturbed model:
Model version with low climate sensitivity:
Model version with high climate sensitivity:
Regional Distributions (Later analysis: More simulations but similar to analysis in Phil Trans paper)
• 20,000 simulations • 6203 model versions with points
representing average over initial condition ensembles.
From Stainforth et al. 2005
Frequency Distribution of Climate Sensitivity No statement that this reflects probability of real world
behaviour
Lack of independence: The model versions are not independent samples of versions of this model let alone of the space of all possible models (whatever that might mean).
Climate sensitivity is the equilibrium global mean surface temperature change in response to a doubling of atmospheric CO2 concentrations.
From Stainforth et al. 2005
Parameter dependency of frequency distribution of climate sensitivity
Blue: No perturbations to entrainment coefficient
Red: No perturbations to cloud to rain conversion threshold
Climate sensitivity is the equilibrium global mean surface temperature change in response to a doubling of atmospheric CO2 concentrations.
To the extent that any simulations are a plausible future, they all are:
“Domain of possibility” “Non-discountable envelope” “Lower bound on the maximum range of uncertainty”
Can the independence issues be solved by greater sampling of parameter space? A: No
• The shape of a model’s parameter space is arbitrary. It can depend on choices made by programmers to optimise the speed of the simulation.
• There is no objective or relevant subjective prior.
P1 Low High Stnd
Stnd
Low
High P2
Choice of parameter definition
The “in-sample” problem A Conflict of Physics and Statistics
In-Sample Analysis: • Out-of-sample data can not be obtained in the
future. • Once published, further analysis becomes
biased. • Physicists tend to look at the extreme
behaviour but that process can’t be used to restrict the statistical inference.
Stainforth et al., 2005
Low Entrainment Coefficent: Rodwell & Palmer, 2007. Joshi et al., 2011
Setting aside the in-sample issue can we cull or down-weight some model versions?
When is a model too bad to be considered informative?
CMIP-2 coupled models
Single perturbations
Original model
All models are fundamentally different to reality what’s the basis for saying some are better than others as predictive tools?
Setting aside the in-sample issue can we cull or down-weight some model versions?
When is a model too bad to be considered informative?
CMIP-2 coupled models
Single perturbations
Original model
All models are fundamentally different to reality what’s the basis for saying some are better than others as predictive tools?
Murphy et al., 2004
None of this undermines the physical basis for expecting increasing greenhouse gases to lead to increasing
temperatures and severe climate disruption
Indeed one might argue it provides additional supporting evidence.
• It only undermines the quantitative interpretation of the details of complicated global climate model output.
What are we left with?
Due to: • Lack of independence. • Fundamental difference
between the model and reality.
• Misleading consequences of in-sample analysis.
“Domain of possibility” “Non-discountable envelope” “Lower bound on the maximum range of uncertainty”
Going forward
We should design ensembles to try to push out the bounds of the envelope. (Increase uncertainty?) Finding that we can not “push” models to produce certain responses can perhaps suggest (provide evidence for) constraints on how the real world system can respond. Note: This is counter to most funding calls which often seek for efforts to reduce uncertainty.
Challenges in Climate Prediction
• Extrapolation The task involves predicting the behaviour of a system in a state never before observed.
• Nonlinearity The system is a complex nonlinear system so we might expect sensitivity to the finest details of initial conditions (the butterfly effect) and to model formulation (the hawkmoth effect).
• Non-physical models While significant elements of the models attempt to solve well understood physical behaviour, many other elements do not. The relevance of such elements to the future is questionable.
• Model imperfections The models we use omit significant factors which one might expect to have a first order impact and fail to reproduce many others.
The Logistic Map and the Hawkmoth Effect
Model: Nt+1 = 4 Nt(1- Nt) System: Nt+1 =
−−+−− )1(
54)1()1(4 2
tttt NNNN εε
Laplace’s Demon and Climate Change, Frigg et al., 2013
Nt
Nt+
1
A Good Looking Model, Not A Good Forecasting System
Laplace’s Demon and Climate Change, Frigg et al., 2013
Timestep: 8
Timestep: 1 Timestep: 2
Timestep: 4
Questions, Debate, Arguments References
• Stainforth, D. A., Allen, M. R., Tredger, E. R. & Smith, L. A. Confidence, uncertainty and
decision-support relevance in climate predictions. Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci. 365, 2145-2161
• Stainforth et al. Issues in the interpretation of climate model ensembles to inform decisions. Phil Trans Roy Soc. 365 (1857), 2163 (2007).
• Stainforth DA, Aina T, Christensen C, Collins M, Faull N, Frame DJ, et al. Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature. 2005;433(7024):403-6.
• Frigg, R., L.A. Smith, D. A. Stainforth, The Myopia of Imperfect Climate Models: The Case of UKCP09, Philosophy of Science, 2013.
• Frigg, R., L.A. Smith, D. A. Stainforth, “An assessment of the foundational assumptions in high-resolution climate projections: the case of UKCP09”, Synthese, 2015.
Papers available from: [email protected]