Download Glen Harris

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
 Exclude 4 UK points (avoid potential
conflicts with UKCIP08 project).
 Eastward to Moscow only.
 Rather coarse resolution (3.752.5 deg).
 102 points in this set.
Finnmark
North_Cape
Varangerfjord
Westfjord
Swedish_Lapland
North_Bothnia
Finnish_Lapland
Russian_Lapland
Murmansk
Kola_Peninsula
Central_Norrland
West_Bothnia
East_Bothnia
North_West_Karelia
North_East_Karelia
White_Sea
Sognefjord
Trondheim
South_Norrland
Western_Finland
Eastern_Finland
North_Ladoga
Onega
South_West_Archangel
Telemark
Oslo
Svealand
Gulf_of_Finland
Saint_Petersburg
East_Ladoga
West_Vologda
Gotaland
Latvia
Pskov
Western_Tver
Moscow_North
Denmark
West_Lithuania
East_Lithuania
Vitebsk
Smolensk
Moscow_South
Holland
North_Germany
Berlin
North_Poland
Warsaw
Pripet
South_East_Belarus
Briansk
Kursk
Ireland
Channel
Belgium_NE_France
Rhine
South_East_Germany
Czech_Republic
Slovakia_South_Poland
South_East_Poland
Western_Ukraine
Kiev
Sumi
Kharkov
Western_France
Burgundy
Switzerland
Austrian_Alps
Eastern_Austria
Hungary
North_West_Romania
North_East_Romania
Moldova
Lower_Dniepr
Donetsk
South_West_France
South_East_France
French_Italian_Alps
Po_Dolomites
Slovenia_Croatia
Bosnia
South_West_Romania
South_East_Romania
Pyrenees
Tuscany
Albania_Montenegro
Central_Balkans
Eastern_Bulgaria
Galicia
Northern_Spain
Eastern_Spain
Greece
West_Marmara
Bosphorus
Ankara
Black_Sea_Turkey
Northern_Portugal
Central_Spain
South_West_Turkey
Taurus_Mountains
Turkish_Euphrates
Southern_Portugal
Andalucia
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Where are the uncertainties?
Natural unforced variability
Modelling of
Earth
system
processes
Unknown future forcing
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.
Dynamics
• Diffusion: order and e-folding time.
• Gravity wave drag: surface and
trapped lee wave constants.
• Gravity wave drag start level.
Convection
• Entrainment rate.
• Intensity of mass flux .
• Shape of cloud (anvils).
• Cloud water seen by radiation.
Boundary layer
• Turbulent mixing coefficients: stabilitydependence, neutral mixing length.
• Roughness length over sea: Charnock
constant, free convective value.
Radiation
• Ice particle size/shape.
• Cloud overlap assumptions.
• Water vapour continuum absorption.
Sea Ice
• Albedo dependence on temperature.
• Ocean-ice heat transfer.
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
Typical slab member

 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.
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Simple example for climate sensitivity
“emulated”
prior
predictive
distribution
posterior
predictive
distribution
likelihood
weighting via
comparison
with real world
histogram of
“perturbed physics”
ensemble
Murphy et al., 2004, Nature, 430, 768-772
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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.
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.
 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.
Joint prior equilibrium pdf for Eng-Wales summer temperature
and precipitation response, for CO2 doubling.
Rougier, Sexton et al, J.Clim (submitted)
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Compare models with observations (likelihood weighting)
Each “ensemble member” gets a weight w, something like:
Sum over all
observables
simulated variable
observed variable
 n

( M i  Oi ) 2

w  exp   
 i 1 2(var( di )  var( ei )  var( Oi )) 
variance of
“discrepancy”
variance of
emulator error
variance of observations
(including natural variability,
obs. error etc.)
More precisely, model skill is likelihood of model data given some observations:
n
1
log Lo (m)  c  log | V |  (m - o)T V 1 (m - o)
2
2
Sexton et al, J.Clim (in prep)
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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
observationallyconstrained posterior
pdf (no discrepancy)
 Equilibrium warming for EnglandWales for a doubling of CO2.
 Observational-constraints: narrow the
spread in pdf, and can also move it
(e.g., less than 2C warming unlikely).
model
prior pdf
posterior pdf,
with discrepancy
 Discrepancy: flattens likelihood, and
broadens spread in observationallyconstrained posterior.
 Need discrepancy to avoid overconfidence, spiky posterior distributions.
D.Sexton, J.Rougier
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Transient Ensembles
 Need coupled model
experiments to capture timedependent climate change.
Historical + A1B
forcing
Observations
 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.
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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.
Fj
pred
( x, t )  T
scm
( j , t )  s
slab
j
( x),
s
slab
slab
F2slab
CO 2 ( x)  F1CO 2 ( x)
( x)  slab
T2CO 2 ( x)  T1slab
CO 2 ( x)
 F in principle any climate surface variable, e.g. mean temperature, seasonal
precipitation, soil moisture, percentiles of daily Tmax
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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 pattern
for 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
SCM scaled prediction
GCM anomaly
SCM-GCM error
Global
(ghg only)
.
Mediterranean
Basin
(all forcing)
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Frequency distribution for Transient Climate Response (TCR)
 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).


 F  Fjpred ( x, t )  bias(t )


D(F , t )   t
;16 

 (t )
j 1 


129
 Parameter uncertainty more important
than scaling uncertainty.
(TCR: surface temperature response for
years 60-80 during 1% per annum CO2
increase).
 Distribution shape here mainly reflects
sample design, not model prior
distribution.
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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).
Improvement of scaling to reduce error
Using 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 and
dynamic ocean response cgcm
F  Tghg (t ) sslab ( x)  Taero (t ) saero ( x)  Ttot (t )cgcm ( x)  error ( x, t )
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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
80%, 90% and
95% confidence
ranges.
17 GCM
anomalies
2080-2100
anomalies with
respect to 196190 baseline.
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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. Also done two
other forcing scenarios: A1B-GHG,
and B1. Will also do A1FI.
RCM ensemble
Probabilistic climate predictions from perturbed physics ensembles
4 additional
transient
ensembles
Ocean PPE
E
Atmosphere PPE
(transient response)
Regional climate
model PPE
C
M
Sulphate F
aerosol PPE
Timescaling
transient changes
D
Downscaling
transient changes
N
G
Terrestrial
ecosystem PPE
Earth
System PPE
H
Atmosphere PPE
A
(equilibrium response)
B
Emulation of
equilibrium climate in
parameter space
Probabilistic
predictions
K
Structural
modelling errors
Observational
constraints
J
L
Murphy et al (to appear in Phil. Trans. special issue, 2007)
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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.
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