page 1© crown copyright 2004 development of probabilistic climate predictions for ukcip08 david...

© Crown copyright 2004

Development of probabilistic climate predictions for UKCIP08

David Sexton, James Murphy, Mat Collins, Geoff Jenkins , Glen Harris, Kate Brown , Robin Clark, Penny Boorman, Simon Brown, Richard Jones,

Jason Lowe, Ben Booth, B. Bhaskaran, David Hassell, Ruth McDonald, Tom Howard, Lizzie Kennett

UEA, October 19, 2007


Content

UKCIP08 Probabilistic climate prediction system

Modelling uncertainty and perturbed physics ensembles

Weighting with observations Time Scaling Other components of Earth System Downscaling

Assumptions


UKCIP ‘02

Based on the state-of-the-art at the time - HadCM3, HadAM3H time-slice, 50km HadRM3 experiments

Used by many private and public-sector organisations to make decisions and spend money

“Scenario” based with no quantification of uncertainties (although plenty of caveats pointing this out)


Emission scenariosEffects of internal variability

Modelling of Earth system processes

Uncertainties in model projections

… which includes how informative are models about reality


Modelling uncertainty

Set of international climate models are all ‘tuned’ to observations

But there is no guarantee these are the actual optimal models

Other choices of values for model input parameters could have provided equally plausible simulations of observations whilst providing a wide range of responses in the future

So tuning could affect the decisions planners make based on climate predictions


UKCIP08 – Probabilistic predictions

To provide joint probability distribution functions (pdfs) of predicted changes in a selection of key UK climate variables at 25km resolution for 2010-2039, 2020-2049,…,2070-2099

Results will be presented for each variable by month

We aim to deliver the final report and the pdfs October 2008


UKCIP08 Products

Report Three types of output:

Probabilistic PDFWeather Generator (change factors from PDFs)Raw daily data from 17 regional climate models

Web-based data delivery package (UI)Will produce nice graphicsProvide some analysisProvide some guidance

Documentation on guidancePreparatory workshops


Probabilistic climate predictions are …

It is not a probability distribution from which the real world samples what it does

So not an ensemble weather forecast for the future. It is just a representation of the degree to which each

possible future climate is plausible given the evidence (climate models and observations). As the evidence changes so will the prediction.

Underlying value is to reduce the risk of a user making a bad decision

So instead of giving a policy maker all our modelled and observed data we give them a summary statement of the extent to which various possible future climates are consistent with the evidence.


Production of UKCIP08 predictions

EBMTime-scaling Down-

scalingPerturbed physics ensemble

Ocean PPE

Aerosol PPE

Carbon cycle PPE

No computer in world is big enough to run many variants of a 25km Earth system model so we have developed a framework to combine lots of pieces (Murphy et al, Phil. Trans. Royal Society, 2007).


Perturbed physics ensembles


..use “perturbed physics ensembles” to sample systematically a space of possible model configurations

• Relatively large ensembles designed to sample modelling uncertainties systematically within a single model framework

• Executed by perturbing model input parameters controlling key model processes, within expert-specified ranges

• Key strength: Allows greater control over experimental design cf multi-model “ensembles of opportunity”

• Key limitation: does not sample “structural modelling uncertainties”, e.g. changes in resolution, or in the fundamental assumptions used in the model’s parameterisation schemes – need to include results from other models to account for these.


First steps

• Take one climate model (in this case version 3 of the Hadley Centre model)

• Specify distributions for multiple uncertain model parameters controlling atmospheric physical processes

• Run an ensemble of simulations (@300km horizontal resolution) of the equilibrium response to doubled CO2


..gives a large (~300 member) sample of possible changes (e.g. summer UK rainfall)


Making probabilistic climate predictions

for 2xCO2 response


Bayesian prediction – Goldstein and Rougier

Aim is to construct joint probability distribution p(X, mh , mf ,y,o,d) of all uncertain objects in problem.

Input parameters (X)Historical Model output (mh)Model prediction (mf)True climate (yh,yf)Observations (o)Model imperfections (d)

It measures how all objects are related in a probabilistic sense


Best-input assumption

Physical and dynamical processes in a climate model are controlled by numbers called model input parameters.

We assume that one choice of these values, x*, is better than all others

( *)y f x

True climate DiscrepancyModel output of best choice of parameter values x*



We only know the probability that any combination of parameter values is the best-input model. But that means we need millions of model variants.

That is too expensive - can only afford hundreds of runs but they have to sampled in a way that is consistent with your beliefs about where the best model is.

Need a cheap alternative..


Emulators e.g. climate sensitivity

Ensemble member

Sqrt(clim

ate sensitivity)

Dots – actual runs

Lines – 95% credible interval from emulator

Emulators are statistical models, trained on ensemble runs, designed to predict model output at untried parameter combinations


Sampling different model variants with emulator


Climate sensitivity – before weighting with observations

FOCUS ON BLACK CURVE

The Prior


Parameter Constraints due to weighting


Weighting different model variants


Climate sensitivity

“Truncation level” = amount of independent information from observations

FOCUS ON RED CURVE

The Posterior


Climate sensitivity


FOCUS ON RED CURVE


Weighting models with observations and discrepancy


Physics/dynamics matter…

Compare models against several observational variables – with just one variable you can simulate climate well for the wrong reasons

Will compare with present-day mean climate - Indirect assessment of key processes for our climate prediction but adds confidence to our prediction of one-off event

We are not going to assume models are perfect so using better models has an impact



Physical and dynamical processes in a climate model are controlled by numbers called model input parameters.

We assume that one choice of these values, x*, is better than all others

( *)y f x

True climate DiscrepancyModel output of best choice of parameter values x*


Comparing models with observations

Use likelihood function i.e. skill of model is likelihood of model data given some observations

11log ( ) log | | ( ) ( )

2 2T

o

nL c m V m - o V m - o

V = obs uncertainty + emulator error + discrepancy

Discrepancy is ‘distance’ between real system and ‘best’ choice of input parameters

Truncation level = dimensionality of m, o


Discrepancy – a schematic of what it does

• Avoids observations over-constraining the pdfs.

• Avoids contradictions from subsequent analyses when some observations have been allowed to constrain the problem too strongly.


Specifying discrepancy

Use multimodel ensemble from AR4 and CFMIP

For each multimodel ensemble member, find emulated model variant that is closest to that member

There is a distance between climates of this multimodel ensemble member and this “best” emulated model variant i.e. effect of processes not explored by slab model variants.

Pool these distances over all multimodel ensemble members


Four types of data…


Errors in predicting multimodel ensemble

•Each dot is a member of multimodel ensemble

•Grey shading represents 95% confidence interval from internal climate variability

A choice: select 10 as this is as large as possible whilst still providing a robust estimate

Number of observable quantities in cost function used to find ‘best input’


Climate sensitivity


FOCUS ON RED CURVE


Joint probabilities


Time scaling


Production of UKCIPnext predictions


scalingEquilibrium PPE

Ocean PPE

Aerosol PPE

Carbon cycle PPE

For A1B, B1, A1FI scenarios…


Coupled Atmosphere-Ocean Ensembles

Smaller ensembles of HadCM3 because of spin-up issues

Perturbations to atmosphere-model parameters with equivalent HadSM3 versions

Flux adjustments used to keep models stable and reduce SST biases

Observations

Historical + A1Bforcing

Collins et al. 2006


Pattern Scaling to Produce Pseudo-Transient Ensembles - Methodology


Some plumes…Wales August temperature

No carbon cycle feedback yet


Other components of Earth System





Ocean PPE

Aerosol PPE

Carbon cycle PPE

For A1B, B1, A1FI scenarios…


Uncertainties in the transient response of global mean surface temperature

Ocean parameters perturbed

Sulphur Cycle parameters perturbed

Atmosphere parameters perturbed

Ocean parameter perturbation experiments (17 member ensemble) run to quantify effects of uncertainties in ocean transport processes

Sulphur cycle parameter perturbation experiments (another 17 member ensemble) also run


Impact of terrestrial uncertainties on CO2

Standard HadCM3, 16 variants of terrestrial carbon cycle

Black crosses - observations

Total atmospheric CO2 concentration


Downscaling





Ocean PPE

Aerosol PPE

Carbon cycle PPE


Downscaling

• Have also run a 17-member 25km resolution ensemble of perturbed physics regional model versions.

• Driven by boundary forcing from the HadCM3 A1B transient simulations (1950-2100).

• We will construct regression relationships between the 17 GCM and 17 RCM simulations of future climate.

• Use these to create regional response pdfs at 25km scale. Will add further uncertainty to the regional responses.


Downscaling uncertainty

16 realisations of the difference in response of the regional model relative to its driving global model, for January precipitation (% change for 2071-00 relative to 1950-79).


Downscaling relationships…

RCM GCM error


Assumptions


What are the main assumptions we cannot test

Local feedbacks between atmosphere and other components of Earth System (carbon cycle, aerosol chemistry and ocean) are of second order importance to effects linked to global temperature change.

Structural model uncertainty is a good proxy for difference between HadCM3 family of models and real system

Pattern scaling, downscaling relationships applicable across parameter space

Multimodel members have equal contribution to discrepancy


THE END

ANY QUESTIONS?


UKCIPnext (Hadley Centre contribution) – Aims and Objectives

To provide joint probability distribution functions (pdfs) of predicted changes in a selection of key UK climate variables at 25km resolution for each decade during the 21st century

Results will be presented for each variable by month indicating mainly mean outcomes but also extremes for e.g. max/min temperature, precipitation

We aim to deliver the pdfs and final report summer 2008


Sensitivity to prior – climate sensitivity

Before observational After observational constraint constraint


Sensitivity to prior - %ΔUK summer rainfall

Before observational After observational constraint constraint


Monte Carlo Sampling

Monte Carlo iteration Sampled Value 1 -0.4 2 0.3 3 -0.1 4 0.9 5 -0.2

Emulated Samples

Em

ula

ted

D

istribu

tions


Reducing uncertainty

Improve observational uncertaintiesImprove model i.e. reduce discrepancyRun larger ensemblesUse more observational constraints independent of the ones used already

Remove pattern scaling and downscaling steps

Remove assumptions about linking sub-modules


Weather Generators

We will make probabilistic predictions for the variables that are inputted into the weather generator

Weather Generators will be used to generate time series consistent with probabilistic predictions

If need spatially coherent time series at high temporal and spatial resolution, can use output from 17 regional climate model runs


Ideal for future UKCIPs

Run 1860-2120 with fully coupled Earth System Models perturbing parameters in all components simultaneously and then downscale

That is, no equilibrium runs, no ensembles on individual components

Would need other climate centres to run this experiment for their standard model and ideally they would have these downscaled.


Response surface predicted by emulator

Climate Sensitivity as a function of two parameters according to mean prediction of the emulator – note emulator also predicts uncertainty of response surface


Summer UK % precipitation change

Another choice: what truncation level to choose…

FOCUS ON RED CURVE


Probabilistic climate prediction

Probabilistic prediction is a function of ModelObservationsChoicesAssumptions

Choices guided by principle that we think it is important to model the Earth System correctly.


Bayesian framework by Goldstein and Rougier:some terms

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

histogram of “perturbed physics” ensemble

“emulated” prior distribution

posterior distribution


Ensemble Simulations

“Bedrock” provided by a relatively large ~300 member ensemble of HadSM3 (atmosphere-slab ocean) run at 1x and 2xCO2

Results sensitive to how you select parameter combinations Murphy et al., 2004

Webb et al., submittedStainforth et al., 2005


Weights

As truncation level increases, have to be luckier to land on a quality point in parameter space


Precision of percentile estimates

Number of Monte Carlo samples 1-0.5 million

Precision of 95th percentile estimate

CHOOSE THIS ONE!


Emulators are statistical models, trained on ensemble runs, designed to predict model output at untried parameter combinations

Emulators


Monte Carlo sampling of parameters combined with an emulator overcomes dependency on sampling strategy to produce prior prediction (blue line) consistent with beliefs about where the best input lies.

Prior distribution – prediction before any observations used

Emulators and priors


Discrepancy on future variable

Model not perfect so there are processes in real system but not in our model that could alter model response by an uncertain amount.

Places extra uncertainty on prediction variable in form of a variance


Where is the ‘best’ input?Observations reduce uncertainty about which points are best in parameter space

Most effective if a strong relationship exists

Constraining predictions


Standard carbon cycle, 3 versions of atmosphere GCM

Dashed – no carbon cycle

Solid – with carbon cycle


Estimating discrepancy

Four ways I can think of…

ElicitationObservationsSuper-parameterised models Ensemble of international climate models

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