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Advanced uncertainty evaluation of climate models and their future climate projections

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

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Advanced uncertainty evaluation of climate models and their future climate projections

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  1. 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

  2. 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

  3. 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. MH (non-adaptive) AM DRAM (adaptive)

  5. 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

  6. 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

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

  8. Small cost function implies model to be close to CERES data • global annual-mean net radiation • annual cycle of zonal mean net radiation Global-annual mean net flux in ECHAM5 Global-annual mean net flux in CERES data (0.9 W m-2) Monthly zonal-mean values Interannual standard deviation In ERA40 reanalysis (0.53 Wm-2) Interannual std. dev. of monthly zonal means

  9. CERES observations Costfunction Net Longwave Shortwave Global annual mean ToA radiative flux • cost =costGLOBAL + costZONAL

  10. Costfunction Net Longwave Shortwave Default model • cost =costGLOBAL + costZONAL

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

  12. ECMWF seminar 2010

  13. = default value ECMWF seminar 2010

  14. T42L31 :: Cloud ice particles, SW scattering CAULOC CMFCTOP CPRCON ENTRSCV CAULOC CMFCTOP CPRCON ENTRSCV ZINPAR ZINHOMI ZASIC

  15. 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

  16. Warming 9.6 K whenmodelcrashes!! Warming 8.9 K whenmodelcrashes! Practical problem: at T21L19, ECHAM5 is hypersensitive! Global-mean temperature (K)

  17. Conclusions (so far) Can we use MCMC for parameter estimation in climate models? Yes, we can! But … 1) Choice of the cost function is critical 2) It is computationally expensive - chain lengths of > 1000 model runs are needed

  18. 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 … Cumulativecostfunction Rejection limit Month

  19. Many thanks heikki.jarvinen@fmi.fi petri.raisanen@fmi.fi

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