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1 Joint Frequency Distributions for Future European Climate Change Glen Harris, Ben Booth, Kate Brown, Mat Collins, James Murphy, David Sexton, Mark Webb Quantifying Uncertainty in Model Predictions (QUMP) Research Theme, Hadley Centre for Climate Prediction and Research, Met Office, Exeter, UK. Jonty Rougier, Durham University. Ensembles Work Package 6.2 Meeting, Helsinki, April 2007

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2 Gulf of Finland joint frequency distribution Joint frequency distributions for annual temperature and annual precipitation anomalies, with respect to baseline climate. A1B forcing, mean anomaly. 129 time-scaled versions of HadSM3 equilibrium response (blue points). Sample distribution of scaling error, including internal variability (black points). Medians: T=5.1K, P=12%

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3 HadCM3 European Land Grid-points FinnmarkWestern_TverHungary North_CapeMoscow_NorthNorth_West_Romania VarangerfjordDenmarkNorth_East_Romania WestfjordWest_LithuaniaMoldova Swedish_LaplandEast_LithuaniaLower_Dniepr North_BothniaVitebskDonetsk Finnish_LaplandSmolenskSouth_West_France Russian_LaplandMoscow_SouthSouth_East_France MurmanskHollandFrench_Italian_Alps Kola_PeninsulaNorth_GermanyPo_Dolomites Central_NorrlandBerlinSlovenia_Croatia West_BothniaNorth_PolandBosnia East_BothniaWarsawSouth_West_Romania North_West_KareliaPripetSouth_East_Romania North_East_KareliaSouth_East_BelarusPyrenees White_SeaBrianskTuscany SognefjordKurskAlbania_Montenegro TrondheimIrelandCentral_Balkans South_Norrland ChannelEastern_Bulgaria Western_FinlandBelgium_NE_FranceGalicia Eastern_FinlandRhineNorthern_Spain North_LadogaSouth_East_GermanyEastern_Spain OnegaCzech_RepublicGreece South_West_Archangel Slovakia_South_PolandWest_Marmara TelemarkSouth_East_PolandBosphorus OsloWestern_UkraineAnkara SvealandKievBlack_Sea_Turkey Gulf_of_FinlandSumiNorthern_Portugal Saint_PetersburgKharkovCentral_Spain East_LadogaWestern_FranceSouth_West_Turkey West_VologdaBurgundyTaurus_Mountains GotalandSwitzerlandTurkish_Euphrates LatviaAustrian_AlpsSouthern_Portugal PskovEastern_AustriaAndalucia Exclude 4 UK points (avoid potential conflicts with UKCIP08 project). Eastward to Moscow only. Rather coarse resolution ( deg). 102 points in this set.

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4 Where are the uncertainties? Natural unforced variabilityUnknown future forcing Modelling of Earth system processes QUMP: focus on modelling uncertainties

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5 QUMP approach Predictions are uncertain so… 1.Run an ensemble of simulations with a climate model in which perturbations are made to the uncertain inputs and processes. 2.Compare each model simulation with observations and assign a relative score to each. 3.Produce a weighted distribution of the forecast variable of interest. i.e.: Posterior = Prior Likelihood QUMP project pragmatically uses a Bayesian framework.

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6 Parameter Perturbations – 31 quantities perturbed Large Scale Cloud Ice fall speed. Critical relative humidity for formation. Cloud droplet to rain: conversion rate and threshold. Cloud fraction calculation. Convection Entrainment rate. Intensity of mass flux. Shape of cloud (anvils). Cloud water seen by radiation. Radiation Ice particle size/shape. Cloud overlap assumptions. Water vapour continuum absorption. Sea Ice Albedo dependence on temperature. Ocean-ice heat transfer. Boundary layer Turbulent mixing coefficients: stability- dependence, neutral mixing length. Roughness length over sea: Charnock constant, free convective value. Dynamics Diffusion: order and e-folding time. Gravity wave drag: surface and trapped lee wave constants. Gravity wave drag start level. Land Surface Processes Root depths. Forest roughness lengths. Surface-canopy coupling. CO 2 dependence of stomatal conductance.

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7 Some issues for ensemble climate prediction Limited computational resources. use HadSM3/HadCM3 models, not expensive flagship HadGEM model mainly use mixed-layer (slab) ocean models. predict pdfs for equilibrium climate response. Large number of uncertain climate model parameters. to obtain robust predictions independent of sampling, emulators are required to predict response for parts of parameter space unsampled by GCM simulation. Sample prior distributions of uncertain model parameters. use expert ranges, prior distribution shape (triangular, uniform,…) test sensitivity to sampling assumptions. Likelihood weighting. want to choose as many observational constraints as possible to down-weight unrealistic model variants. Scale equilibrium response, to create pseudo-transient ensemble validate scaling with GCM ensemble Physics perturbations upset radiative balance, potential for climate drift. flux-correct transient GCM simulations.

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8 Perturbed-Physics Atmosphere-Slab Equilibrium Ensemble Simulations Additional simulations underway to explore interesting regions of parameter space (currently ~300 members). Distribution differences due to different sampling strategies and parameter choices. Murphy et al, Stainforth et al, Webb et al, Typical slab member

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9 Simple example for climate sensitivity Murphy et al., 2004, Nature, 430, histogram of perturbed physics ensemble emulated prior predictive distribution likelihood weighting via comparison with real world posterior predictive distribution

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10 Probabilistic Predictions - Framework 1.Perform a limited ensemble of GCM experiments with perturbed input parameters. 2.Build an emulator which can estimate the GCM output at untried parameter values. 3.Sample emulator to produce model prior predictive distributions of climate variables. 4.Use observations to produce a likelihood function and posterior (observationally-constrained) predictive distributions. 5.Sample weighted posterior distribution and time-scale with Simple Climate Model (SCM) to predict pdfs for transient regional future climate change, at GCM resolution. 6.Run ensemble of 25km Regional Climate Model (HadRM3) variants driven by equivalent GCM transient runs, and downscale responses to predict regional pdfs.

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11 Emulation for any perturbed-parameter value. Rougier, Sexton et al, J.Clim (submitted) Multiple linear regression; entertain many possible functional relationships for explanatory variables. Emulator error used to select interesting parameter combinations to create additional members, and improve emulator. Emulator uncertainty is propagated through to the final PDFs. Emulator: statistical model designed to predict the outputs of a climate model which one could in principle run. Emulators predict not only the mean response, but also the error in the predicted response. Built from a sample of runs. Joint prior equilibrium pdf for Eng-Wales summer temperature and precipitation response, for CO 2 doubling.

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12 Compare models with observations (likelihood weighting) Each ensemble member gets a weight w, something like: observed variablesimulated variable variance of discrepancy variance of emulator error variance of observations (including natural variability, obs. error etc.) Sum over all observables Sexton et al, J.Clim (in prep) More precisely, model skill is likelihood of model data given some observations:

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13 Discrepancy Following Murphy et al (Nature, 2004), began collaboration with statisticians (Rougier and Goldstein, Durham Univ.) to improve robustness of predictions. Introduce discrepancy: Measure of uncertainty associated with model imperfection: distance between unknown true future climate and best possible choice of the uncertain model input parameters. Unknown, but we assume this distance similar to that between other climate models and our best perturbed-physics emulation of the future predictions from these same models. Discrepancy therefore also a quantification of structural modelling error.

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14 Compare model prior pdf with observationally-constrained pdf Equilibrium warming for England- Wales for a doubling of CO 2. Observational-constraints: narrow the spread in pdf, and can also move it (e.g., less than 2 C warming unlikely). Discrepancy: flattens likelihood, and broadens spread in observationally- constrained posterior. Need discrepancy to avoid over- confidence, spiky posterior distributions. model prior pdf observationally- constrained posterior pdf (no discrepancy) posterior pdf, with discrepancy D.Sexton, J.Rougier

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15 Transient Ensembles Need coupled model experiments to capture time- dependent climate change. Run 17 of the perturbed atmosphere HadSM3 versions coupled instead to dynamic ocean, i.e. HadCM3 setup. Transient ensembles smaller because of spin-up, additional ocean model, and longer runtime required. Flux adjustments used to prevent model drift, and reduce SST biases. HadCRUT observed series. Observations Historical + A1B forcing

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16 Compare perturbed physics ensemble with multi-model ensemble Increase CO 2 by 1% per annum. Spread in transient response comparable in the two ensembles. Collins et al., Clim. Dyn.

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17 Scaling the equilibrium response Problem: Can only afford relatively few simulations in transient GCM ensemble (17 here). Aim: Want to predict the transient response for the 129 slab-ocean experiments (or indeed any emulated equilibrium response), if they were coupled instead to a dynamic ocean (HadCM3). Solution: Scale anomaly patterns for each slab member by global mean surface temperature anomaly ΔT(t) predicted by a Simple Climate Model (SCM) Proposed in 1990 by Santer, Wigley, Schlesinger & Mitchell as way of predicting transient regional response from slab equilibria, before fully-coupled AOGCMs had been developed. F in principle any climate surface variable, e.g. mean temperature, seasonal precipitation, soil moisture, percentiles of daily T max

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18 Time-Scaling to Produce Pseudo-Transient Ensembles 129 SCM projections for global surface temperature anomaly, using diagnosed equilibrium feedbacks (1% p.a. CO 2 inc). Typical response pattern for annual surface temperature to a doubling in CO 2 concentration. Frequency distributions for Northern Europe annual temperature (including scaling error).

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19 Scaling Assumptions year mean for equilibrium response sufficient to give good signal (compared to internal variability). 2. Slab equilibrium response patterns represent transient patterns. 3. Climate anomalies linear in global temperature anomaly ΔT(t). 4. ΔT(t) can be predicted by a Simple Climate Model (SCM), driven by emulated equilibrium climate feedbacks λ. 5. Assume equilibrium climate feedbacks represent transient feedbacks. Justification and Validation Compare pattern-scaling with the 17 fully-coupled simulations to give scaling error, and include this in predicted transient distributions. Any partial failure in assumptions quantified by validation: errors in scaling bigger uncertainty.

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20 Scaling – validation with 17 member GCM ensemble GCM anomaly SCM scaled prediction SCM-GCM error Global (ghg only) Mediterranean Basin (all forcing).

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21 Frequency distribution for Transient Climate Response (TCR) Parameter uncertainty more important than scaling uncertainty. Distribution shape here mainly reflects sample design, not model prior distribution. Assume distribution of error in scaled response to be Gaussian (no evidence to contrary). Estimate variance and bias from validation with 17 member GCM ensemble. For each region and time, sum 129 t distributions (red curve) to obtain frequency distribution (blue curve). (TCR: surface temperature response for years during 1% per annum CO 2 increase).

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22 Time-scaling equilibrium patterns of change Example: djf precipitation, 1% CO 2 pa increase Transient regional frequency distributions, using 129 perturbed atmosphere models. Plumes of evolving uncertainty (median, 80, 90, 95% confidence ranges) Harris et al., 2006, Clim.Dyn. 27, p357.

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23 Pattern scaling A1B scenario SCM uses forcing diagnosed from GCM runs. compare here internal variability for one GCM run (green), with parameter and scaling uncertainty (red). Improvement of scaling to reduce error Using the A1B and A1B-GHG GCM ensembles, we can calculate - additional patterns for the normalised aerosol response s aero - correction patterns to represent differences between the slab and dynamic ocean response c gcm

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24 Production of interim data - summary 1. Scale 129 equilibrium responses, to predict transient joint temperature-precipitation response if we were to run with dynamic ocean and A1B forcing. 2. For each equilibrium member, sample (40 times for this test) the scaling error distribution (red curve), with variance and bias obtained from validation. Still a lot more to do…

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25 Gulf of Finland future annual temperature/precipitation anomalies with respect to baseline. 80%, 90% and 95% confidence ranges. 17 GCM anomalies

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26 European pdfs – still to do Will do - Instead of annual data, process seasonal means and produce frequency distributions, based once again on 129 member ensemble. - Data now all back so can be done. Possible (time/resource constraints) - Build emulators for selected European GCM grid-points, and at same time obtain weights to observationally-constrain model variants. - Then resample weighted equilibrium distributions and time-scale to produce observationally constrained pdfs for future European climate change (HadCM3 resolution). Unlikely at moment - Redo UKCIP08 but for other parts of European domain, down-scaling to 25km resolution.

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27 Down-scaling to the UK (and Europe?): UKCIP08 Also running a 17-member 25km resolution HadRM3 (regional model) ensemble. Driven by boundary forcing from the HadCM3 A1B ensemble ( ). Runs will finish in July. We will construct regression relationships between the 17 GCM and 17 RCM simulations of future climate. Then sample predicted GCM transient pdfs and use these regression models to deliver regional response pdfs at 25km scales (this will introduce further uncertainty). R.Clark, D.Sexton, K.Brown, G.Harris, many others…

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28 Additional perturbed physics ensembles (PPE) Murphy et al (to appear in Phil. Trans. special issue, 2007) 4 additional transient ensembles RCM ensemble Atmosphere PPE. Also done two other forcing scenarios: A1B-GHG, and B1. Will also do A1FI.

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29 Acknowledgments QUMP Team: David Sexton, Mat Collins, Ben Booth, James Murphy, Mark Webb, Kate Brown Also: Robin Clark, Penny Boorman, Gareth Jones, B. Bhaskaran, Jonty Rougier And: Hadley Centre, Met Office, DEFRA (Department for the Environment, Food and Rural Affairs) UK Govt, ENSEMBLES, ClimatePrediction.net. Thank You.

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