Advanced uncertainty evaluation of climate models and their future climate projections H Järvinen, P Räisänen, M Laine, J Tamminen, P Ollinaho Finnish.

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Advanced uncertainty evaluation of climate models and their future climate projections H Järvinen, P Räisänen, M Laine, J Tamminen, P Ollinaho Finnish Meteorological Institute A Ilin, E Oja Aalto University School of Science and Technology, Finland A Solonen, H Haario Lappeenranta 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 convection 5/19

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 Global-annual mean net flux in ECHAM5 Global-annual mean net flux in CERES data (0.9 W m -2 ) Interannual standard deviation In ERA40 reanalysis (0.53 Wm -2 ) Monthly zonal-mean values Interannual std. dev. of monthly zonal means

8/19 Global-annual mean net flux in ECHAM5 Global-annual mean net flux in CERES data (0.9 W m -2 ) Interannual standard deviation In ERA40 reanalysis (0.53 Wm -2 ) 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 Cost function CERES observations Global annual mean ToA radiative flux Net cost =cost GLOBAL + cost ZONAL

10/19 Longwave Shortwave Cost function Default model Net cost =cost GLOBAL + cost ZONAL

11/19 Longwave Shortwave The cost function only included net ToA radiation … both the LW and SW biases decreased Cost function Net

ECMWF seminar /46

ECMWF seminar /46 = default value

T42L31 :: Cloud ice particles, SW scattering 14/19 CAULOCCMFCTOPCPRCONENTRSCV CPRCONENTRSCVCMFCTOP ZASIC CAULOCZINPARZINHOMI

Uncertainty of future climate projections (principle) Climate sensitivity :: Change in T surf 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 K when model crashes! Warming  9.6 K when model crashes!! Global-mean temperature (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 … 18/19 Cumulative cost function Month Rejection limit

Many thanks 19/19