Quantifying uncertainty in simulations of past, present and future climate Alan M. Haywood School 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 Global mean projections from different models using the same GHG concentrations are different Global mean carbon cycle feedbacks from different models using the same GHG emissions are different Source: IPCC Fourth Assessment Report

Uncertainties Source: IPCC Fourth Assessment Report Regional patterns of change from different models are different

Uncertainties 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.

The data are wrong We did the wrong experiment The models are wrong The data are wrong or its interpretation is flawed We did the wrong experiment 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 = {y h,y f } 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

Probabilistic Approach xyhyh yfyf input space historical/observable climate future climate o f(x 1 ) f(x 2 ) x1x1 x2x2

© Crown copyright Met Office Bayesian Probabilities The probability expresses the uncertainty in the prediction (e.g. p(ΔT 2100 > 6ºC)=0.05) not the frequency of occurrence of a particular event (ΔT 2100 > 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 ? 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 cooling but 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