Quantifying uncertainty in simulations of past, present and

future climate

Alan M. HaywoodSchool of Earth & Environment, University of Leeds

What inspires me...

Combining geological data and models

Rationale• Evidence from observations (palaeo), climate models

and basic understanding indicates that climate can change and anthropogenic climate change is real

• Society needs scientific evidence in order to act

• Consider types of actions– Mitigation - reduce emissions of greenhouse gases– Adaptation – learn to live with climate change that

we are already committed to– If it gets too bad what about Geoengineerg?

Mitigation• United Nations Framework Convention on Climate Change

(UNFCC) remit to limit greenhouse gas concentrations to avoid “dangerous” climate change

• Need to know what a “safe” level of greenhouse gas concentrations is:– Sensitivity of the global climate system to different levels

of GHGs (climate sensitivity)– Relationship between GHG emissions and concentrations

(carbon cycle feedback)– Risk of dangerous/abrupt/rapid/irreversible events e.g.

shutdown of Atlantic Meridional Circulation, melting of Greenland, death of Amazon rainforest...

Adaptation• Society needs to adapt to some level of climate change that is

inevitable• Adaptation decisions are in the hands of many different

bodies e.g. governments, water companies, energy companies, large and small commercial businesses, farmers, individuals.

• Requires:– Information about climate change at regional and local

scales– Multivariate information; temperature, precipitation,

winds, fluxes, etc.– Information about extreme events; storms, droughts,

heatwaves etc.

Uncertainties

Figure 10.5

Global mean projections from different models using the same GHG concentrations are different

Figure 10.20

Global mean carbon cycle feedbacks from different models using the same GHG emissions are different

Source: IPCC Fourth Assessment Report

Figure 10.9

Uncertainties

Source: IPCC Fourth Assessment Report

Regional patterns of change from different models are different

Uncertainties

Figure 10.15

Source: IPCC Fourth Assessment Report

Models differ in their projection of dangerous events

Why do uncertainties exist?• Models have “errors” i.e. when simulating present-day

climate and climate change, there is a mismatch between the model and the observations

• Differences in model formulation can lead to differences in climate change feedbacks

How to deal with uncertainties?Continue to improve models until global and regional projections converge

Climate change already happened by the time models converge

Is convergence a useful indicator of reliability?

Use techniques other than comprehensive climate modelling

Cannot extrapolate from noisy (possibly non-existent) time series

Simple models cannot provide all the information

Climate change may not be linear

Combine information from climate models, observations (+ palaeo) and understanding to quantify the uncertainty in projections

Risk-based approached used in other disciplines where scientific uncertainties exist

Climate Change Projection/Retrodiction

• In the presence of uncertainties in climate model projections adopt a probabilistic approach

• Sources of uncertainty:– Initial conditions, natural variability– Boundary conditions, emissions/concentrations of

greenhouse gases and other forcing agents– Model errors and uncertainty, different models

giving different projections

• Probabilistic climate projections (for e.g. 2100) cannot be easily verified in the way that probabilistic weather forecasts are. Challenges in the world of palaeo data/model comparisons too.

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DMC Triangle

Climate Change Projection/Retrodiction• …however, we can still use ensemble and probabilistic

techniques in climate change projection/retrodiction

• Need a different strategy for generating the ensemble as initial conditions are not the leading source of uncertainty

– The “multi-model” ensemble, MME– The “perturbed-physics” ensemble, PPE

• Need something in place of the verification cycle – assume that models which are good at reproducing observed/palaeo climate change are also good at simulating future climate change

Types of ensembles in palaeoclimate• Boundary condition ensembles: understanding palaeoclimate

– Too many to mention (Valdes et al. etc)• Multi-model ensembles (MMEs): understanding models

– PMIP, PlioMIP• Perturbed parameter ensembles: quantifying model uncertainties

– Calibration of models for future climate prediction• updating model parameters

– Physically-based reconstruction of palaeoclimate• updating model state

– EBM: Hegerl et al. (2006)– EMIC: Schneider von Deimling et al. (2006)– GCMs slab: Annan et al. (2005); Hargreaves et al. (2006); CPDN H. Muri

PhD– GCMs low res: CPDN Millennium; Gregoire et al. (2010)– GCMs: Brown et al. 2007, Pope et al. (2011); Stone et al. (submitted);

Edwards et al. (in prep.); Valdes/Sagoo et al....

Multi-Model Ensemble

• A collection of the world’s climate models• Sometimes called an “ensemble of opportunity”• Currently coordinated by projects like CMIP-

Coupled Model Intercomparison Project and housed at PCMDI, California, PMIP (LSCE, France)

• A relatively large “gene-pool” of possible models, although it is common to share some components

• Models are “tuned” to reproduce observed data – although formal tuning is not performed

Perturbed Physics Ensemble• Take one model structure and perturb uncertain

parameters and possible switch in/out different subroutines

• Can control experimental design, systematically explore and isolate uncertainties from different components

• Potential for many more ensemble members• Unable to fully explore “structural” uncertainties• HadCM3 widely used (MOHC and

climateprediction.net) but other modelling groups are dipping their toes in the water

For PPE’s and MME’s think cars!

Comparison of MMEs and PPEs

Global mean temperature change in MMEs and PPEs under different scenarios

PPEs capable of sampling global response uncertainties

Some Notation

y = {yh,yf} historical and future climate variables (many)

f = model (complex)x = uncertain model input parameters (many)o = observations (many, incomplete)

• Our task is to explore f(x) in order to find y which will be closest to what will be observed in the past and the future (conditional on some assumptions)

• Provide probabilities which measure how strongly different outcomes for climate change are supported by current evidence; models, observations and understanding

f(x)y

Probabilistic Approach

x yh

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historical/observable climate

future climate

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© Crown copyright Met Office

Bayesian Probabilities

• The probability expresses the uncertainty in the prediction (e.g. p(ΔT2100 > 6ºC)=0.05) not the frequency of occurrence of a particular event (ΔT2100 > 6ºC, 5% of the time)

• Fundamentally different to a weather or seasonal forecast prediction (which can be verified)

• Probabilities are conditional on assumptions; emissions pathways for example

PPEs and the Green Sahara

Climateprediction.net ~60 HadSM3 (H. Muri PhD)

PalaeoQUMP 17 HadCM3

MMEs and PPEs and the Last Glacial Maximum

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MARGO

Updated from Edwards et al. (2007), Prog Phys Geog

State-dependence of uncertain parameters

Feedback parameter (–Q/ΔT)

most show greater sensitivity to warming than cooling

can constrain sea ice parameter with LGM coolingbut less relevant for warming scenario

MIROC3.2 slab PPE (Annan, pers. comm.)PMIP2 MME (Crucifix, pers. comm.)

PalaeoQUMP 17 HadCM3 PPE

FAMOUS PPE (Gregoire et al., 2010, Clim Dyn)

best models

Types of approach using PPEs

• Picking the best– maximum likelihood, confidence sets (by any

other name...)• Downweighting the worst

– reweighting with skill scores• Probabilistic calibration or predictions

– reweighting within statistical framework

Picking the best model(s)10 of 100 FAMOUS Gregoire et al. (2010) Clim Dyn

Pifalls, questions, looking forward• Scientific

– Need reliable uncertainties of proxy-based reconstructions– Good experimental design to avoid (much, much) pain later– Important to learn from others about important parameters– Different parameter sensitivity and variability in palaeoclimates– Advantages / disadvantages of flux correction– Maximum likelihood vs reweighting vs probability distributions– How to estimate model uncertainty (parametric and structural)

• Technical– Mistakes are amplified, propagated by N– Problem of spin-up is multiplied by N– Sufficient person power to analyse data– Share tools to strip data and automate analysis– Give simulations citable DOI (BADC) to crowd-source analysis