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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, 26-27 April 2007

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Gulf of Finland joint frequency distribution

Joint frequency distributions for annual temperature and annual precipitation anomalies, with respect to 1961-90 baseline climate.

A1B forcing, 2080-2100 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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HadCM3 European Land Grid-points

Finnmark Western_Tver Hungary

North_Cape Moscow_NorthNorth_West_Romania

Varangerfjord DenmarkNorth_East_Romania

Westfjord West_Lithuania Moldova

Swedish_Lapland East_Lithuania Lower_Dniepr

North_Bothnia Vitebsk Donetsk

Finnish_Lapland SmolenskSouth_West_France

Russian_Lapland Moscow_SouthSouth_East_France

Murmansk HollandFrench_Italian_Alps

Kola_Peninsula North_Germany Po_Dolomites

Central_Norrland BerlinSlovenia_Croatia

West_Bothnia North_Poland Bosnia East_Bothnia Warsaw

South_West_RomaniaNorth_West_Karelia Pripet

South_East_Romania North_East_Karelia South_East_Belarus Pyrenees

White_Sea Briansk Tuscany

Sognefjord Kursk

Albania_Montenegro Trondheim Ireland

Central_Balkans South_Norrland Channel

Eastern_Bulgaria Western_Finland Belgium_NE_France Galicia Eastern_Finland Rhine

Northern_Spain North_Ladoga South_East_Germany

Eastern_Spain Onega Czech_Republic Greece

South_West_Archangel Slovakia_South_Poland

West_Marmara Telemark South_East_Poland Bosphorus

Oslo Western_Ukraine Ankara

Svealand Kiev

Black_Sea_Turkey Gulf_of_Finland Sumi

Northern_Portugal Saint_Petersburg Kharkov Central_Spain

East_Ladoga Western_France

South_West_Turkey West_Vologda Burgundy

Taurus_Mountains Gotaland Switzerland

Turkish_Euphrates Latvia Austrian_Alps

Southern_Portugal Pskov Eastern_Austria Andalucia

Exclude 4 UK points (avoid potential conflicts with UKCIP08 project).

Eastward to Moscow only.

Rather coarse resolution (3.752.5 deg).

102 points in this set.

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Where are the uncertainties?

Natural unforced variability Unknown future forcing

Modelling of Earth system processes

QUMP: focus on modelling uncertainties

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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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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. • CO2 dependence of stomatal conductance.

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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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“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, 2004. Stainforth et al, 2005. Webb et al, 2006.

Typical slab member

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Simple example for climate sensitivity

Murphy et al., 2004, Nature, 430, 768-772

histogram of “perturbed physics” ensemble

“emulated” prior predictive distribution

likelihood weighting via comparison with real world

posterior predictive distribution

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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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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 CO2 doubling.

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Compare models with observations (likelihood weighting)

Each “ensemble member” gets a weight w, something like:

n

i iii

ii

Oed

OMw

1

2

))var()var()(var(2

)(exp

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)

11log ( ) log | | ( ) ( )

2 2T

o

nL c m V m-o V m -o

More precisely, model skill is likelihood of model data given some observations:

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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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Compare model prior pdf with observationally-constrained pdf

Equilibrium warming for England-Wales for a doubling of CO2.

Observational-constraints: narrow the spread in pdf, and can also move it (e.g., less than 2C 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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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 + A1Bforcing

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Compare perturbed physics ensemble with multi-model ensemble

Increase CO2 by 1% per annum.

Spread in transient response comparable in the two ensembles.

Collins et al., Clim. Dyn.

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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 AOGCM’s had been developed.

F in principle any climate surface variable, e.g. mean temperature, seasonal precipitation, soil moisture, percentiles of daily Tmax

( , ) ( , ) ( ),pred scm slabj j jF x t T t s x 2 2 1 2

2 2 1 2

( ) ( )( )

( ) ( )

slab slabslab CO CO

slab slabCO CO

F x F xs x

T x T x

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Time-Scaling to Produce Pseudo-Transient Ensembles

129 SCM projections for global surface temperature anomaly, using diagnosed equilibrium feedbacks (1% p.a. CO2 inc).

Typical response patternfor annual surface temperature to a doubling in CO2 concentration.

Frequency distributions for Northern Europe annual temperature (including scaling error).

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Scaling Assumptions

1. 20 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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Scaling – validation with 17 member GCM ensemble

GCM anomalySCM scaled prediction SCM-GCM error

Global(ghg only)

Mediterranean Basin(all forcing)

.

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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.

129

1

( , ) ( )( , ) ;16

( )

predj

j

F F x t bias tD F t t

t

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 60-80 during 1% per annum CO2

increase).

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Time-scaling equilibrium patterns of change

Example: djf precipitation, 1% CO2 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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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).

( ) ( ) ( ) ( ) ( ) ( ) ( , )ghg slab aero aero tot gcmF T t s x T t s x T t c x error x t

Improvement of scaling to reduce errorUsing the A1B and A1B-GHG GCM ensembles, we can calculate

- additional patterns for the normalised aerosol response saero

- correction patterns to represent differences between the slab anddynamic ocean response cgcm

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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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Gulf of Finland future annual temperature/precipitation

2080-2100 anomalies with respect to 1961-90 baseline.

80%, 90% and 95% confidence ranges.

17 GCM anomalies

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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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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 (1950-2100).

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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Additional perturbed physics ensembles (PPE)

Atmosphere PPE (equilibrium response)

Timescalingtransient changes

Structural modelling errors

Terrestrial ecosystem PPE

Sulphate aerosol PPE

Ocean PPE

Downscaling transient changes

Earth System PPE

Regional climate model PPE

Probabilistic climate predictions from perturbed physics ensembles

Atmosphere PPE (transient response)

Probabilistic predictions

Observational constraints

A

C

D

E

F

G

H

J

M

N

Emulation of equilibrium climate in parameter space

B

K L

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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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.