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Representing model uncertainty in weather and climate

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					        Representing model uncertainty in weather
        and climate: stochastic versa multi-physics
                      representations

                              Judith Berner, NCAR




Judith Berner: Representing Model Error by Stochastic Parameterizations
                                           Key Points
  There is model error in weather and climate models
     from the need to parameterize subgrid-scale fluctuations
  This model error leads to overconfident uncertainty estimates
   and possibly model bias
  We need a model error representation
     Hierarchy of simulations where statistical output from one
      level is used to inform the next (e.g., stochastic kinetic
      energy backscatter)
     Reliability of ensemble systems with stochastic
      parameterizations start to become comparable to that of
      ensembles systems with multi-physics

Judith Berner: Representing Model Error by Stochastic Parameterizations
           “Domino Parameterization strategy”




 Higher-resolution model inform output of lower-resolution model
    Stochastic kinetic energy backscatter scheme provides such a
     framework
    … But there are others, e.g. Cloud-resolving convective
     parameterization or super-parameterization
                                      Multiple scales of motion



1mm       10 m             100 m              1 km             10 km            100 km     1000        10000
                                                                                            km          km

Micro-                                  Cumulus Cumulonimbus Mesoscale Extratropical Planetary
                    Turbulence
physics                                  clouds    clouds    Convective Cyclones      waves
                                                              systems
                   Large Eddy Simulation (LES) Model

                                                Cloud System Resolving Model (CSRM)

                                                                     Numerical Weather Prediction (NWP) Model

                                                                                         Global Climate Model



      Judith Berner: Representing Model Error by Stochastic Parameterizations
The spectral gap …




                     (Stull)
                                                                          Atmospheric
                                                                           Scientists




                                                                     Nastrom and Gage, 1985
Judith Berner: Representing Model Error by Stochastic Parameterizations
TOWARD SEAMLESS PREDICTION
Calibr at ion of Climat e Change Project ions Using Seasonal
For ecasts
                                        BY                      .                                          .
                                             T. N . P LMER, F. J D OBLAS-REY ES, A . W EI SHEIMER, AND M. J RODWELL
                                                     A



          In a seamless prediction system, t he reliabilit y of co upled climat e model forecasts
             made on seasonal time scales can provide useful quantit ative const raint s for
                 improving t he t rust wort hiness of regional climat e change project ions.




                                                                                                                       .... The link between
                                                                                                                       climate forcing and
                                                                                                                       climate impact
                                                                                                                       involves processes
                                                                                                                       acting on different
                                                                                                                       timescales …




                     c g e lust
  FIG .1.A schem a ti fi ur il       ng            n       w
                                 rati th at the li k b et een cl ate f r
                                                                  im                    m    e m       n
                                                                           o cing and cli at i pact i vo l ves pro -
  ces         ng      ff      m
      ses acti on d i erent ti e scal es.T he w h ole ch ai i as stro ng as i w eak est li k.T he use ofa s am l
                                                          n s                ts          n                 e    ess
        c o yst        low         lst c o ecti sofcli ate change t b e const ne d by valdati nso n w e at
  predi ti n s em al s probab ii i pr j         on        m              o         rai          i   o           her
          o
  or seas nalf           m      e .
                orecastti e scal s
           made on seasonal time scales can provide useful quantit ative const raint s for
             improving t he t rust wort hiness of regional climat e change project ions.




                                                            NPW              Climate model
                  Cloud resolving                           model
                    Cloud resolving
                       model
                        model
            Large Eddy
            simulation
  Resolved
 microphysics


                                                       Attempt to capture
                                                      Multi-scale nature of
                                                      atmospheric motion

                  c g e lust i t at the li k b etw een cl ate f r
FIG .1.A schem a ti fi ur il   rat ng h         n             im      o cing and clm at i pact i vo l
                                                                                   i    e m       n         o
                                                                                                      ves pr -
ces         ng     ff       m
    ses acti on d i erent ti e scales.T he w h ol ch ai i as str ng as i w eak est li k.T he use ofa s am l
                                                 e    n s       o       ts           n                e    ess
      c o yst       low         lst c
predi ti n s em al s probab ii i pro j                m
                                         ection sofcli at change t b e const ne d by valdati nso n w e at
                                                          e         o         rai          i   o           her
                   made on seasonal time scales can provide useful quantit ative const raint s for
                     improving t he t rust wort hiness of regional climat e change project ions.
       Hierarchical Parameterization Strategy


                                                                   NPW
                                                                                    Climate model
                                Cloud resolving                    model
                                    model
                  Large Eddy
                  simulation
          Resolved
         microphysics




          Related: Grabowski 1999, Shutts
          and Palmer, 2007


                          c g e Error by t at t   he Parameterizations
Judith Berner: Representing Model lustratingStochasticli k b etw een cl ate f rcing and cli ate i pact i vo l pro -
        FIG .1.A schem a ti fi ur il          h        n              im    o             m     m      n    ves
       ces        ng    ff        m
          ses acti on d i erent ti e scales.T he w h ol ch ai i as str ng as i w eak est li k.T he use ofa se am les
                                                       e    n s       o      ts           n                         s
                   Validity of spectral gap …




Judith Berner: Representing Model Error by Stochastic Parameterizations
   The spectral gap …




Mathematicians   Atmospheric
                  Scientists
    The spectral gap …




M pathematicians   Atmospheric
                    Scientists
    Spectral gap not necessary for stochastic
               parameterizations




Judith Berner: Representing Model Error by Stochastic Parameterizations
              Kinetic energy spectra in 500hPa

                    Rotational part                                       Rotational part




            Kinetic energy spectrum is closer to that of T799 analysis !


Judith Berner: Representing Model Error by Stochastic Parameterizations
             Limited vs unlimited predictability




                                                                          Rotunno and Snyder, 2008
                  Lorenz 1969;

Judith Berner: Representing Model Error by Stochastic Parameterizations
  Stochastic parameterizations have the potential
              to reduce model error


Potential

                                                                            Stochastic parameterizations
                                                                            can change the mean and
                                                                            variance of a PDF
            Weak noise                       Strong noise
                                                                            Impacts variability of model
                                                                            (e.g. internal variability of the
 PDF                                                                        atmosphere)
                                                                            Impacts systematic error (e.g.
                                                                            blocking, precipitation error)


          Unimodal                         Multi-modal

  Judith Berner: Representing Model Error by Stochastic Parameterizations
                                             Outline
 Parameterizations in numerical weather prediction models and
  climate models
 A stochastic kinetic energy backscatter scheme
    Impact on synoptic probabilistic weather forecasting
      (short/medium-range)
    Impact on systematic model error
     (seasonal to climatic time-scales)

                            Acknowledgements
 Aime Fournier, So-young Ha, Josh Hacker, Thomas Jung, Tim
    Palmer, Paco Doblas-Reyes, Glenn Shutts, Chris Snyder,
                      Antje Weisheimer
Judith Berner: Representing Model Error by Stochastic Parameterizations
                Sensitivity to initial perturbations




Judith Berner: Representing Model Error by Stochastic Parameterizations
     Representing initial state uncertainty by an
                ensemble of states
                             RMS error
                        spread


                                                   ensemble mean
        t0                                         analysis

                          t1
                                             t2
 Represent initial uncertainty by ensemble of states
 Flow-dependence:
    Predictable states should have small ensemble spread
    Unpredictable states should have large ensemble spread
 Ensemble spread should grow like RMS error
 True atmospheric state should be indistinguishable from ensemble
  system
Systems
      Underdispersion of the ensemble system


       ------- spread around ensemble mean                                 The RMS error grows faster than
                RMS error of ensemble mean                                 the spread
                                                                           Ensemble is underdispersive
                                                                           Ensemble forecast is
                                                                           overconfident

                                                                           Underdispersion is a form of
                                                                           model error
                                                                           Forecast error = initial error +
                                                                           model error + boundary error


      Buizza et al., 2004

 Judith Berner: Representing Model Error by Stochastic Parameterizations
              Manifestations of model error
 In medium-range:
  Underdispersion of ensemble system (Overconfidence)
     Can “extreme” weather events be captured?
 On seasonal to climatic scales:
  Systematic Biases
  Not enough internal variability
     To which degree do e.g. climate sensitivity depend on a
      correct estimate of internal variability?
  Shortcomings in representation of physical processes:
     Underestimation of the frequency of blocking
     Tropical variability, e.g. MJO, wave propagation

Judith Berner: Representing Model Error by Stochastic Parameterizations
        Representing model error in ensemble
                      systems
         The multi-parameterization approach: each ensemble
          member uses a different set of parameterizations (e.g.
          for cumulus convection, planetary boundary layer,
          microphysics, short-wave/long-wave radiation, land
          use, land surface)
         The multi-parameter approach: each ensemble member
          uses the control pysics, but the parameters are varied
          from one ensemble member to the next
         Stochastic parameterizations: each ensemble member is
          perturbed by a stochastic forcing term that represents
          the statistical fluctuations in the subgrid-scale fluxes
          (stochastic diabatic tendencies) as well as altogether
          unrepresented interactions between the resolved an
          unresolved scale (stochastic kinetic energy backscatter)
Judith Berner: Representing Model Error by Stochastic Parameterizations
Recent attempts at remedying model error in
                    NWP
 Using conventional                                         Outside conventional
  parameterizations                                           parameterizations
 Stochastic parameterizations                               Cloud-resolving convective
  (Buizza et al, 1999, Lin and                                parameterization (CRCP) or super-
                                                              parameterization (Grabowski and
  Neelin, 2000)                                               Smolarkiewicz 1999, Khairoutdinov
 Multi-parameterization                                      and Randall 2001)
  approaches (Houtekamer, 1996,                              Nonlocal parameterizations, e.g.,
  Berner et al. 2010)                                         cellular automata pattern generator
 Multi-parameter approaches                                  (Palmer, 1997, 2001)
  (e.g. Murphy et al,, 2004;                                 Stochastic kinetic energy
  Stainforth et al, 2004)                                     backscatter in NWP (Shutts 2005,
                                                              Berner et al. 2008,2009,…)
 Multi-models (e.g. DEMETER,
  ENSEMBLES, TIGGE,
  Krishnamurti et. al 1999)




Judith Berner: Representing Model Error by Stochastic Parameterizations
         Stochastic kinetic energy backscatter
                       schemes
 Stochastic kinetic energy backscatter LES
  Mason and Thompon, 1992, Weinbrecht and Mason, 2008
 Stochastic kinetic energy backscatter in simplified models
  Frederiksen and Keupert 2004
 Stochastic kinetic energy backscatter in NWP
    IFS ensemble system, ECMWF:
     Shutts and Palmer 2003, Shutts 2005, Berner et al. 2009a,b,
     Steinheimer
    MOGREPS, MetOffice
     Bowler et al 2008, 2009; Tennant et al 2010
    Canadian Ensemble System
     Li et al 2008, Charron et al. 2010
    AFWA mesoscale ensemble system, NCAR
     Berner et al. 2010
Judith Berner: Representing Model Error by Stochastic Parameterizations
  Forcing streamfunction spectra by coarse-
               graining CRMs

                                                              from Glenn Shutts




Judith Berner: Representing Model Error by Stochastic Parameterizations
                 “Domino Parameterization strategy”




 Higher-resolution model inform output of lower-resolution model
    Stochastic kinetic energy backscatter scheme provides such a
     framework
    … But there are others, e.g. Cloud-resolving convective
     parameterization or super-parameterization
 Judith Berner: Representing Model Error by Stochastic Parameterizations
 Model error in weather forecasting and climate models
 A stochastic kinetic energy backscatter scheme (SPBS)
 Impact of SPBS on probabilistic weather forecasting
  (medium-range) ->
 Impact of SPBS on systematic model error
 Impact in a mesoscale model and comparison to a multi-physics
  scheme




Judith Berner: Representing Model Error by Stochastic Parameterizations
                     Forecast error growth




For perfect ensemble system:             Since IPs are reduced, forecast
the true atmospheric state should be    error is reduced for small forecast
indistinguishable from a perturbed       times
ensemble member
                                         More kinetic energy in small
 forecast error and model uncertainty
                                         scales
(=spread) should be the same
 Model error in weather forecasting and climate models
 A stochastic kinetic energy backscatter scheme: SPectral
  Backscatter Scheme
 Impact of SPBS on probabilistic weather forecasting (medium-
  range)
 Impact of SPBS on systematic model error
 Impact in a mesoscale model and comparison to a multi-
  physics scheme




Judith Berner: Representing Model Error by Stochastic Parameterizations
  Experimental Setup for Seasonal Runs
“Seasonal runs: Atmosphere only”
 Atmosphere only, observed SSTs
 40 start dates between 1962 – 2001 (Nov 1)
 5-month integrations
 One set of integrations with stochastic
   backscatter, one without
 Model runs are compared to ERA40 reanalysis
   (“truth”)


Judith Berner: Representing Model Error by Stochastic Parameterizations
Reduction of systematic error of z500 over
    North Pacific and North Atlantic

 No StochasticBackscatter   Stochastic Backscatter
            Increase in occurrence of Atlantic and
                       Pacific blocking



                                                                          ERA40 + confidence
                                                                          interval

                                                                            Stochastic Backscatter

                                                                          No StochasticBackscatter




Judith Berner: Representing Model Error by Stochastic Parameterizations
Wavenumber-Frequency Spectrum
     Symmetric part, background removed
       (after Wheeler and Kiladis, 1999)

Observations (NOAA)          No Stochastic Backscatter
Improvement in Wavenumber-Frequency
              Spectrum


  Observations (NOAA)                     Stochastic Backscatter




  Backscatter scheme reduces erroneous westward propagating modes
 Model error in weather forecasting and climate models
 A stochastic kinetic energy backscatter scheme: SPectral
  Backscatter Scheme
 Impact of SPBS on probabilistic weather forecasting (medium-
  range)
 Impact of SPBS on systematic model error
 Impact in a mesoscale model and comparison to a multi-
  physics scheme




Judith Berner: Representing Model Error by Stochastic Parameterizations
                 Experiment setup
 Ensemble A/B: 10 member ensemble with and without SPBS
 Ensemble C: 10 member multi-physics suite
 Weather Research and Forecast Model
 30 cases between Nov 2008 and Feb 2009
 40km horizontal resolution and 40 vertical levels
 Limited area model: Continuous United States (CONUS)
 Started from GFS initial condition (downscaled from NCEPs
  Global Forecast System)
                      Multiple Physics packages




Judith Berner: Representing Model Error by Stochastic Parameterizations
WRF short-range ensemble: 60h-forecast for
  Oct 13, 2006: SLP and surface wind
                                 Control
                                  Physics
                                 Ensemble




Judith Berner: Representing Model Error by Stochastic Parameterizations
WRF short-range ensemble: 60h-forecast for
  Oct 13, 2006: SLP and surface wind
                                  Stochastic
                                  Backscatter
                                   Ensemble




Judith Berner: Representing Model Error by Stochastic Parameterizations
                       Spread-Error Relationship




                                                                            Control

                                                                          Backscatter

                                                                          Multi-Physics




Judith Berner: Representing Model Error by Stochastic Parameterizations
                                      Brier Score, U




                                                                            Control

                                                                          Backscatter

                                                                          Multi-Physics




Judith Berner: Representing Model Error by Stochastic Parameterizations
Scatterplots of
 verification
   scores
Both, Stochastic backscatter                    and Multi-
physics are better than control
Stochastic backscatter is better than
Multi-physics is better
Their combination is even better
Judith Berner: Representing Model Error by Stochastic Parameterizations
                      Multiple Physics packages




Judith Berner: Representing Model Error by Stochastic Parameterizations
                                         Brier Score


                                                                             Control




                                                                          Multi-Physics




                                                                            Backscatter

Judith Berner: Representing Model Error by Stochastic Parameterizations
                       Spread-Error Relationship




                                                                            Control

                                                                          Backscatter

                                                                          Multi-Physics




Judith Berner: Representing Model Error by Stochastic Parameterizations
                             Seasonal Predication
                                       Uncalibrated                       Calibrated




 Stochastic
 Ensemble



                                                            Multi-model
    Curtosy: TimPalmer


Judith Berner: Representing Model Error by Stochastic Parameterizations
       Summary and conclusion
 Stochastic parameterization have the potential to reduce
  model error by changing the mean state and internal
  variability.
 It was shown that the new stochastic kinetic energy
  backscatter scheme (SPBS) produced a more skilful
  ensemble and reduced certain aspects of systematic model
  error
    Increases predictability across the scales (from
      mesoscale over synoptic scale to climatic scales)
    Stochastic Backscatter outperforms Multi-physics Ens.
 Stochastic backscatter scheme provides a framework for
  hierarchical parameterization strategy, where stochastic
  parameterization for the lower resolution model is informed
  by higher resolution model
              Future Work
Understand the nature of model error better
Inform more parameters from coarse-
 grained high-resolution output
Impact on climate sensitivity
Consequences for error growth and
 predictability
                                         Challenges

  How can we incorporate the “structural
   uncertainty” estimated by multi-models into
   stochastic parameterizations?




Judith Berner: Representing Model Error by Stochastic Parameterizations
                                       Bibliography
 Berner, J., 2005: Linking Nonlinearity and non-Gaussianity by the
  Fokker-Planck equation and the associated nonlinear stochastic model,
  J. Atmos. Sci., 62, pp. 2098-2117
 Shutts, G. J., 2005: A kinetic energy backscatter algorithm for use in
  ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 612, 3079-
  3102
 Berner, J., F. J. Doblas-Reyes, T. N. Palmer, G. Shutts, and A.
  Weisheimer, 2008: Impact of a quasi-stochastic cellular automaton
  backscatter scheme on the systematic error and seasonal predicition
  skill of a global climate model, Phil. Trans. R. Soc A, 366, pp. 2561-
  2579, DOI: 10.1098/rsta.2008.0031.
 Berner J., G. Shutts, M. Leutbecher, and T.N. Palmer, 2009: A Spectral
  Stochastic Kinetic Energy Backscatter Scheme and its Impact on Flow-
  dependent Pre- dictability in the ECMWF Ensemble Prediction System,
  J. Atmos. Sci.,66,pp.603-626
 T.N. Palmer, F.J. Doblas-Reyes, A. Weisheimer, G.J. Shutts, J.
  Berner, J.M. Murphy, 2008: Towards the Probabilistic Earth-System
  Model, J.Clim., in preparation

Judith Berner: Representing Model Error by Stochastic Parameterizations

				
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