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Deriving observational constraints on climate model

predictions

Gabriele Hegerl, GeoSciences, University of Edinburgh

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The Problem

Climate model predictions are uncertain, and quantifying these uncertainties is essential for useful predictions

Only observations can really constrain predictions – so attempts to arrive at probabilistic predictions make use of observations in some form

There are a number of ways to do that, depending on the problem, timescale, information available, climate variable….

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Prediction uncertainty

1. Internal variability uncertainty: weather/climate variability not/not entirely predictable beyond days => uncertainty, can be estimated

2. Forcing uncertainty: Future emissions unknown – scenarios; volcanoes? Sun?

3. Model uncertainty: uncertainty due to unknown physics and unknown parameters in models, structural errors, missing processes…

3 is mainly what we try to estimate, although some recent work also tries to predict 1

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Forcing uncertainty, model uncertainty and internal climate variability also vary with timescale

From Hawkins and Sutton, 2009 BAMS: fraction of uncertainty due to climate variability, model uncertainty, forcing uncertainty and model uncertainty

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How predictons are constrained depends on timescale

Nearterm: initial conditions MAY matter

Intermediate transient warming

Longterm: Equilibrium climate sensitivity

From IPCC AR4, CH10 (Meehl et al.)

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Why? A very simple Energy Balance Model: Held et al., 2010

Total radiative forcing G Surface Temperature change T Change in outgoing radiation T Exchange of heat into deep ocean

H

Equation for surface ocean with heat capacity CF

Equation for deep ocean with heat capacity CD

GHTdt

dTCF

H

cF

cD

Hdt

dTC DD )( DTTH

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There are two distinct timescalesFast response: deep ocean has not yet

significantly taken up heat (TD)=0

Response time:

Dominated by transient climate response

timescale for the deep ocean is much slower. Equilibrium climate sensitivity reached once ocean takes up no more heat

This works well for the GFDL model, with transient near term warming almost completely dominated by the first case

H

cF

cD

)/( FC

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Lets start with the transient climate change

in the 21rst century ‘naïve approach’: models that

do well over the 20th century will do well over the future

But: external forcings driving this are uncertain…

Greenhouse gas forcing is quite well known, but sulfate aerosol forcing, other anthropogenic forcing (BC etc) poorly, solar not well know either

models can agree with data because they are correct, but they could also agree because of cancelling errors

We may also wind up rejecting models that are correct but their forcing was wrong…(CMIP5)

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What we need to do is:- Identify what is the response to

individual forcings that influenced 20th century climate

- Project forward the components that are predictable or projectable (eg greenhouse gas increases)

- Fingerprints can separate the contribution by different external drivers because of different physics of forcing- Eg: solar warms entire atmosphere- Aerosols have different spatial pattern

and temporal evolution than greenhouse gases

- Volcanoes have pronounced shortterm impact

Pinatubo, 1991El Chichón, 1982

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Ingredients for detection and attribution

o Observation y o Climate change signals (“fingerprints”) X=(xi),i=1..n

typically from model simulation: one for each fingerprint, or for a small number of combinations

o Noise: data for internal climate variability, usually from a long model control simulation

o If X contains realizations of climate variability, a total least square fit can be used (Allen and Stott)

uxuXy ii

uvXy )(

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Observed amplitude estimateSignal amplitude

scalar product can reduce noise if using inverse noise covariance yXCyX 1

yXXX TTnii

1

,1 )(

TC

Observational uncertainty:

-Use model data only where observations exist – like with like

-Use samples of observations

Uncertainty in determined by superimposing samples of climate variability onto fingerprint (bit more complicated for tls)

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Attribution results yields range of scaling factors that are consistent with observed change

• Scaling factors that show which range of up-or downscaling of model response is consistent with observations

• Warming due to greenhouse gases

Fig. 9.9c, Hegerl et al., 2007Greenhouse gases; other anthropogenic, natural (solar+volcanic)

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Fig 9.21 after Stott et al.

This translates directly to transient climate response:

• Estimated warming at the time of CO2 doubling in response to a 1% per year increase in CO2

• Constrained by observed 20th century warming via the estimated greenhouse gas signal

Observational constraints suggest …

• very likelyvery likely >1°C• very unlikelyvery unlikely >3.5°C

• supports the overall assessment that TCR very unlikelyvery unlikely >3°C

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Probabilistic prediction of global mean change: one of the pdfs is based on TCR, others on other obs. constraints

Scalability: the pattern does not change much with signal strength

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Other approaches: select models based on observational feedbacks

Hall et al., 2006: spring albedo against temperature change vs seasonal cycle

Using information from climate model ‘quality’ ie ability to simulate mean climate and short term variations used particularly for regional scales – needs to be demonstrated that it is relevant for predictions

Use of observations: compare like with like; sample as observations do, not models do; bring models to observations

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Can we get closer with initial conditions for the near term:

Can climate change be predicted based on initial condition just like weather? => initial value problem

Initialization is not easy Large ensemble of such runs

done right now for nearterm Problem: evidence for useful

predictability beyond a year or few is weak, particularly for things that matter (regional climate)

Smith et al., 2006, scienceTop: 1yr, middle 9 yr, bottom ave 1-9 yrs, 5-

95% ranges

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EQUIP: End to End Quantification of Impacts Prediction

Heatwaves: Summer

maximum daily temperature – predictions capture not only trend, but some of the structure (is this just plain lucky?)

Hanlon and Hegerl, in prep.

EQUIP lead by Andy Challinor, Leeds

Other work: Crop predictions, Water deficit, fisheries

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How to

First: Bias correct the model

Needs to be done differently for hot extremes than mean

Is there any added value from initial conditions? – not clear based on correlation

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• Use skill score based on Murphy 1988

• Forecast system Y vs W (eg climatology, noninitialized)

• MSSS can be composed into correlation, conditional bias and mean bias

• Updated to compare against NoAssim (no ICs) rather than persistence (Goddard et al., in prep)

WY AAXWYMSSS /1),,(

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Decadal predictions raise many questions

Is there skill that is statistically significant

How can the prediction be quantified – arrive at uncertainty ranges

How long does skill last So far: predictability largely for fish…

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Approach for long term: Estimating climate system properties

Equilibrium climate sensitivity First: example single line of evidence

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1. What can we learn about climate sensitivity from the last millennium?

Decadal NH 30-90N land temperature; Hegerl et al., J Climate, 2007

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CH-blend reconstruction

Weighted average of decadal records, many treering data (RSS)

Calibration: Total least square scales communality between instrumental and proxy data to same size

Method tested with climate model data to assess if uncertainties estimated properly

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Climate forcing over the last millennium

Northern Hemispheric 30-90N mean radiative forcing (decadally smoothed) from Crowley

Uncertainties:

~ 40% in amplitude of volcanic forcing

Large in amplitude and shape of solar forcing

And in aerosol forcing

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Simulate observed climate change not with a single best fit, but a large ensemble of model simulations with different sensitivities

Determine probability of models in agreement with data, given: internal variability, uncertainty in data, uncertainty in model

ECS [K]

p

Miss uncertainties: too narrow

Use information incompletely: too wide

1. Estimating equilibrium climate sensitivity

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Estimating ECS

Run EBM with > 1000 model simulations, varying ECS, effective ocean diffusivity, and aerosol forcing

Residuals between reconstruction and range of EBM simulations with different climate sensitivity

Var(Res-resmin ) ~ F(k,l)(after Forest et al., 2001) Uncertainties included:

• Calibration uncertainty of reconstruction

• Noise and internal variability• Uncertainty in magnitude of past

solar and volcanic forcing

Uncertainties:Simple representation of efficacySystematic biases in reconstructions

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Estimated PDF for climate sensitivity

Result for different reconstructions,

13th century to 1850

Larger amplitude

Smaller forcing

Nonlinear relationship sensitivity – volcanic cooling

Response small ~ climate variability

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Results vary between reconstructions

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2. Multiple lines of evidence

Hegerl et al. 06, nature

Bayesian update, using a prior pdf based on late 20th century (Frame et al)

Multiple lines of evidence reduce probability of high sensitivity, and of very small sensitivity

Independence? Proper error estimate?

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Estimates from many different sources

Difficult question: can these estimates strengthen each other? How?

Knutti and Hegerl, 2008

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Towards improving use of observations for constraints on predictions

Make sure that the model is brought as closely to the observational product as possible: synthetic satellite data; synthetic palaeo data

Use uncertainty estimates; models can be used to test processing uncertainty

Be wary of spatial and temporal autococrrelation

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If using observations to provide constraints on predictions

Relevance of observed evidence for prediction needs to be established

Uncertainty in observations needs to be included in estimate

Approach will vary with timescaleMany questions remain: Decadal predictions with reasonable

uncertainty How to predict regional changes? How to combine information from different

sources into an overall estimate of uncertainty of ECS

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Future change uncertainty ranges reflect uncertainty in transient response

• Are based, among other things, on observational constraints

• This is a significant advance

SPM Fig. 5 Likely (>66%) range