Advanced uncertainty evaluation of climate models and their future climate

projections

H Järvinen, P Räisänen, M Laine, J Tamminen, P OllinahoFinnish Meteorological Institute

A Ilin, E OjaAalto University School of Science and Technology , Finland

A Solonen, H HaarioLappeenranta University of Technology, Finland

Closure parameters• Appear in physical parameterization schemes where

some unresolved variables are expressed by predefined parameters rather than being explicitly modelled

• Span a low-dimensional non-linear estimation problem

• Currently: best expert knowledge is used to specify the optimal closure parameter values, based on observations, process studies, model simulations, etc.

• Important when:

(1) Fine-tuning climate models to the present climate

(2) Replacing parameterization schemes with new ones

2/19

3/19

Markov chain Monte Carlo (MCMC) • Consecutive model simulations while updating the

model parameters by Monte Carlo sampling

• Proposal step (parameter values drawn from a proposal distribution)

• Acceptance step (evaluate the objective function and accept/reject the proposal)

• “A random walk” in the parameter space (a Markov chain) and exploration of the Bayesian posterior distribution

• Not optimization ... Instead, a full multi-dimensional parameter probability distribution is recovered

4/19

MH (non-adaptive)

AM

DRAM (adaptive)

ECHAM5 closure parameters

CAULOC = influencing the autoconversion of cloud droplets (rain formation, stratiform clouds)

CMFCTOP = relative cloud mass flux at level above non-buoyancy (in cumulus mass flux

scheme)

CPRCON = a coefficient for determining conversion from cloud water to rain (in convective

clouds)

ENTRSCV = entrainment rate for shallow convection5/19

ECHAM5 simulations

• Markov chain in the 4-parameter space

• One year simulation with the T21L19 ECHAM5 model repeated many times with perturbed parameters

• Several objective function were tested

• All formulations: Top-of-Atmosphere (ToA) net radiative flux

6/19

7/19

cost 2

2

modelGLOBAL

obs

obsFF

Global-annual mean net flux in ECHAM5

Global-annual mean net flux in CERES data (0.9 W m-2)

Interannual standard deviationIn ERA40 reanalysis (0.53 Wm-2)

2

2obs,model,

12

1t121

costZONAL

yt

ytyt

yy

FFw

Monthly zonal-mean values

Interannual std. dev. of monthly zonal means

8/19

cost 2

2

modelGLOBAL

obs

obsFF

Global-annual mean net flux in ECHAM5

Global-annual mean net flux in CERES data (0.9 W m-2)

Interannual standard deviationIn ERA40 reanalysis (0.53 Wm-2)

2

2obs,model,

12

1t121

costZONAL

yt

ytyt

yy

FFw

Monthly zonal-mean values

Interannual std. dev. of monthly zonal means

Small cost function implies model to be close to CERES data

- global annual-mean net radiation

- annual cycle of zonal mean net radiation

9/19

Longwave Shortwave

CERES observations

Global annual mean ToA radiative flux

Net

• cost =costGLOBAL + costZONAL

10/19

Longwave Shortwave

Default model

Net

• cost =costGLOBAL + costZONAL

11/19

Longwave Shortwave

The cost function only included net ToA radiation…

both the LW and SW biases decreased

Net

= default value

T42L31 :: Cloud ice particles, SW scattering

14/19

CAULOC CMFCTOP CPRCON ENTRSCV

CPRCON ENTRSCVCMFCTOP ZASICCAULOC ZINPAR ZINHOMI

Uncertainty of future climate projections (principle)

• Climate sensitivity :: Change in Tsurf due to 2 × CO2

• Sample from the closure parameter posterior PDF’s

• Perform a climate sensitivity run with each model

• Result: a proper PDF of climate sensitivity

- conditional on the selected closure parameters and cost function

15/19

Practical problem: at T21L19, ECHAM5 is hypersensitive!

16/19

Warming 8.9 Kwhen model crashes!

Warming 9.6 Kwhen model crashes!!

Glo

bal-m

ean

tem

pera

ture

(K

)

Conclusions (so far)

17/19

Can we use MCMC for parameter estimation in climate models?

Yes, we can! But …

2) It is computationally expensive - chain lengths of > 1000 model runs are needed

1) Choice of the cost function is critical

Means to fight the computational expense• Adaptive MCMC

• parallel MCMC chains ( reduced wallclock time)

• re-use of chains (off-line tests of new cost functions through ”importance sampling”)

• Early rejection scheme …

18/19Month

Rejection limit

Many thanks

19/19

heikki.jarvinen@fmi.fi

petri.raisanen@fmi.fi