Ensemble of Climate Models

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1 Ensemble of Climate Models Claudia Tebaldi Climate Central and Department of Sta7s7cs, UBC Reto Knu>, Reinhard Furrer, Richard Smith, Bruno Sanso

2 Outline Mul7 model ensembles (MMEs) a descrip7on at face value What they are and what they can provide Where to find them How they are used (in par7cular in IPCC AR4) Mul7 model ensembles and future climate change projec7ons What are the main uncertain7es in future projec7ons, even given a specific emission scenario What MMEs can characterize and what they cannot Main issues, challenges and value of mul7 model analysis An example of analysis, summary and way forward

3 hsp://www pcmdi.llnl.gov/ipcc/about_ipcc.php This unprecedented collection of recent model output is officially known as the "WCRP CMIP3 multimodel dataset." It is meant to serve IPCC's Working Group 1, which focuses on the physical climate system -- atmosphere, land surface, ocean and sea ice -- and the choice of variables archived at the PCMDI reflects this focus. A more comprehensive set of output for a given model may be available from the modeling center that produced it. With the consent of participating climate modelling groups, the WGCM has declared the CMIP3 multimodel dataset open and free for non-commercial purposes. After registering and agreeing to the "terms of use," anyone can now obtain model output via the ESG data portal, ftp, or the OPeNDAP server. As of January 2007, over 35 terabytes of data were in the archive and over 337 terabytes of data had been downloaded among the more than 1200 registered users. Over 250 journal articles, based at least in part on the dataset, have been published or have been accepted for peer-reviewed publication.

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5 These are General Circula7on Models They represent fully coupled ocean atmosphere (and land and ice) processes. The most recent ensemble has a median horizontal resolu7on ~250Km. A typical experiment consist of a handful of runs of 250 years worth of simulated climate (output saved as 6 hourly, daily, monthly ). ~2 months worth of (super) computer 7me for a single run. O`en each experiment consists of an ensemble of runs (different ini7al condi7ons).

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7 The way each model discre7zes its domain, the processes that it chooses to represent explicitly, those that it needs to parameterize (and the value for those parameters*) form its structural iden7ty. There is no wrong or right way to do it. No model is the true model. Mul7 model ensembles get at this structural uncertainty. Other uncertain7es are: parameter uncertainty ini7al condi7ons uncertainty boundary uncertainty (SRES scenarios) Perturbed physics ensembles deal with parameter uncertainty within a single model.

8 The most recent mul7 model ensemble is made of about 20 state of theart GCMs When it comes to future projec7ons, each model gives its own projec7on. Some7me only in absolute value, some7me in sign too! Agreement becomes harder to get the finer the spa7al and temporal scale.

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10 S7ppling means 90% of models or more agree in the sign of change

11 S7ppling means 90% or more of models agree in the sign of change

12 What is behind agreement/disagreement: A distribu5on of projected changes Looking at regional averages of temperature change

13 What is behind agreement/disagreement: A distribu5on of projected changes Looking at regional averages of % precipita7on change

14 IPCC AR4 WG1 Chapter 10 and 11, Global and Regional Future Projec7ons: Most of the projected changes are shown as mul7 model means. Inter model standard devia7on/range is o`en used as a measure of the uncertainty What are we looking at? What are the uncertain7es characterized? What are those le` out? Why means? Why standard devia7ons?

15 The problem of synthesizing mul7ple models projec7ons has a Bayesian flavor: We start with a prior distribu7on (of models) which determines their ini7al weight. We observe output and we compare the real quan77es of interest building a likelihood. Combining the two we get at a posterior/final distribu7on. At this point in 7me, for most ques7ons, the likelihood is not robustly constraining the final results, and the prior remains a crucial ingredient. So, what is the prior we are dealing with when we look at mul7ple models, and what kind of sample are these 20 something models we use all the 7me?

16 What kind of sample is the CMIP3 ensemble? A collec7on of best guesses Likely mutually dependent (models share components) Not random, but not systema7c either

17 A simple example and a simple fix

18 The model mean is beeer than a single model But there exist areas where error persists

19 Model errors are not independent Histograms of correla7on coefficients of all possible pairs of model bias (simulated minus observed fields of mean temperature ). Behavior of RMS error with increasing number of models averaged.

20 They are not designed to sample a wide range of uncertainty IPCC AR4 wg1 Ch10 Climate sensi7vity of CMIP3 models is green curve

21 Ensemble means and ensemble ranges are easy to interpret, but they are not jus7fied by the nature of the sample The models have systema7c and common errors Likely, the uncertainty is larger than what is represented by the ensemble of best guesses

22 Different models have different strengths and weaknesses Metrics of performance for different models (columns), across different diagnos7cs (rows). Blue is good, Red is bad. First two columns are ensemble mean and median. Gleckler et al., (2008) JGR Atmos

23 Not all models are created equal Should we use model performance in replica5ng observed climate to weigh a model more or less?

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25 Why sta5s5cal modeling of climate model output? Simple means and standard devia7ons are not supported by the nature of the data. Through sta7s7cal modeling of GCM data and observa7ons we can combine informa7on in ways that bring valida7on and performance to bear on the final op7mal es7mates of what we are a`er: Usually, es7mates of temperature or precipita7on change for specific regions/seasons/7me periods. Usually average quan77es, since by defini7on combining models produces a smoothed version of the quan7ty we are a`er.

26 An example of how we combine GCM output/observa5ons to produce probabilis5c projec5ons of Temperature and Precipita5on change The analysis is performed over regional and decadal averages, for a given season (e.g., DJF) and a specified emission scenario.

27 Data Observed decadal means of temperature and precipita7on O t = O t T O t P t =1950,1960, Modeled decadal means of temperature and precipita7on X jt = X T jt P X jt t =1950,1960,...,2000,2010,...,2100 j =1,..., M

28 Assump5ons behind the sta5s5cal model, in words the true climate signal 7me series (both temperature and precipita7on) is a piecewise linear trend with an elbow at 2000, to account for the possibility that future trends will be different from current trends; superimposed to the piecewise linear trends is a bivariate gaussian noise with a full covariance matrix, which introduces correla7on between temperature and precipita7on; observed decadal averages provide a good es7mate of the current series and their correla7on, and of their uncertainty; GCMs may have systema7c addi7ve bias, assumed constant along the length of the simula7on; a`er the bias in each GCM simula7on is iden7fied there remains variability around the true climate signal that is model specific.

29 Likelihood Model O t T ~ N µ t T ;η T [ ] [ ] [ ] T µ T t d T j ) + d P P [ j ;φ j ] O t P ~ N µ t P + β xo (O t T µ t T );η P X T jt X jt ~ N µ t T + d j T ;φ j T P ~ N µ t P + β xj (X jt µ t T µ t P = α T + β T t + γ T (t T 0 )χ t α P + β P t + γ P (t T 0 )χ t All unknown quan77es α T,α P,β T,β P,γ T,γ P,d j T,d j P,φ j T,φ j P β xo, β xj have uninforma7ve prior distribu7ons, and their joint posterior is es7mated through MCMC.

30 Temperature change GLOB, JJA mm/day degrees C decades % Precip change!"#$%&'('!))%*+,%")('!)) PDF % Precip change PDF mm/day degrees C degrees C decades % of baseline average Temp. change, degrees C

31 This analysis Can quan7fy systema7c biases, models reliability. Can provide a probabilis7c best guess for the climate signal as a weighted mean between observa7ons and models central tendency. Can provide a predic7ve distribu7on for a new model, It is an informed synthesis of the data You can accept it as such if you agree with its assump7ons (likelihood of the data, priors on the unknown parameters) What does it tell us about the real world?

32 Conclusions Combining mul7 model ensembles can help quan7fy uncertain7es in future climate projec7ons, exploring and comparing models structural characteris7cs. The non systema7c nature of the sampling, the in breeding among the popula7on of models the complexi7es of choosing and drawing inference from diagnos7cs, the impossibility of verifica7on present unique challenges in the formula7on of a rigorous sta7s7cal approach at quan7fying these uncertain7es.

33 Conclusions Things are bound to become even more interes7ng, with the introduc7on of more complex GCMs and the increasing heterogeneity of these ensembles; ever increasing demands on compu7ng resources and the consequent trade offs of resolu7on vs scenarios vs ensemble size. The way forward: coordinated experiments, mul7 model plus single model ensembles, processbased evalua7on translated into metrics, representa7on of model dependencies, quan7fica7on of common biases. All along, transparency and two way communica7on between scien7sts and users, stake holders, policy makers.