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Judith Berner: Representing Model Error by Stochastic Parameterizations Representing model uncertainty in weather and climate: stochastic versa multi-physics representations Judith Berner, NCAR

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Judith Berner: Representing Model Error by Stochastic Parameterizations 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 Key Points

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“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

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Judith Berner: Representing Model Error by Stochastic Parameterizations 4 10 m100 m1 km10 km100 km1000 km 10000 km Turbulence Cumulus clouds Cumulonimbus clouds Mesoscale Convective systems Extratropical Cyclones Planetary waves Large Eddy Simulation (LES) Model Cloud System Resolving Model (CSRM) Numerical Weather Prediction (NWP) Model Global Climate Model Multiple scales of motion 1mm Micro- physics

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The spectral gap … (Stull)

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Judith Berner: Representing Model Error by Stochastic Parameterizations Atmospheric Scientists Nastrom and Gage, 1985

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

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NPW model Climate model Cloud resolving model Resolved microphysics Large Eddy simulation Cloud resolving model Attempt to capture Multi-scale nature of atmospheric motion

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Judith Berner: Representing Model Error by Stochastic Parameterizations NPW model Climate model Cloud resolving model Resolved microphysics Large Eddy simulation Related: Grabowski 1999, Shutts and Palmer, 2007 Hierarchical Parameterization Strategy

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

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The spectral gap … Atmospheric Scientists Mathematicians

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The spectral gap … Atmospheric Scientists M pathematicians

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Judith Berner: Representing Model Error by Stochastic Parameterizations Spectral gap not necessary for stochastic parameterizations

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Judith Berner: Representing Model Error by Stochastic Parameterizations Kinetic energy spectra in 500hPa Kinetic energy spectrum is closer to that of T799 analysis ! Rotational part

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Judith Berner: Representing Model Error by Stochastic Parameterizations Limited vs unlimited predictability Rotunno and Snyder, 2008

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Judith Berner: Representing Model Error by Stochastic Parameterizations Stochastic parameterizations have the potential to reduce model error Weak noise Multi-modal Strong noise Unimodal Stochastic parameterizations can change the mean and variance of a PDF Impacts variability of model (e.g. internal variability of the atmosphere) Impacts systematic error (e.g. blocking, precipitation error) Potential PDF

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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) Aime Fournier, So-young Ha, Josh Hacker, Thomas Jung, Tim Palmer, Paco Doblas-Reyes, Glenn Shutts, Chris Snyder, Antje Weisheimer Acknowledgements

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Judith Berner: Representing Model Error by Stochastic Parameterizations Sensitivity to initial perturbations

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Representing initial state uncertainty by an ensemble of states analysis spread RMS error ensemble mean 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

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Judith Berner: Representing Model Error by Stochastic Parameterizations Buizza et al., 2004 Systems Underdispersion of the ensemble system ------- spread around ensemble mean RMS error of ensemble mean RMS error of ensemble mean The RMS error grows faster than the spread Ensemble is underdispersive Ensemble forecast is overconfident The RMS error grows faster than the spread Ensemble is underdispersive Ensemble forecast is overconfident Underdispersion is a form of model error Forecast error = initial error + model error + boundary error Underdispersion is a form of model error Forecast error = initial error + model error + boundary error

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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

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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)

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Judith Berner: Representing Model Error by Stochastic Parameterizations Recent attempts at remedying model error in NWP Using conventional parameterizations Stochastic parameterizations (Buizza et al, 1999, Lin and Neelin, 2000) Multi-parameterization approaches (Houtekamer, 1996, Berner et al. 2010) Multi-parameter approaches (e.g. Murphy et al,, 2004; Stainforth et al, 2004) Multi-models (e.g. DEMETER, ENSEMBLES, TIGGE, Krishnamurti et. al 1999) Outside conventional parameterizations Cloud-resolving convective parameterization (CRCP) or super- parameterization (Grabowski and Smolarkiewicz 1999, Khairoutdinov and Randall 2001) Nonlocal parameterizations, e.g., cellular automata pattern generator (Palmer, 1997, 2001) Stochastic kinetic energy backscatter in NWP (Shutts 2005, Berner et al. 2008,2009,…)

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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

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Judith Berner: Representing Model Error by Stochastic Parameterizations Forcing streamfunction spectra by coarse- graining CRMs from Glenn Shutts

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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

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Judith Berner: Representing Model Error by Stochastic Parameterizations

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Forecast error growth For perfect ensemble system: the true atmospheric state should be indistinguishable from a perturbed ensemble member forecast error and model uncertainty (=spread) should be the same Since IPs are reduced, forecast error is reduced for small forecast times More kinetic energy in small scales

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Judith Berner: Representing Model Error by Stochastic Parameterizations 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

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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”)

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No StochasticBackscatter Stochastic Backscatter Reduction of systematic error of z500 over North Pacific and North Atlantic

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Judith Berner: Representing Model Error by Stochastic Parameterizations Increase in occurrence of Atlantic and Pacific blocking ERA40 + confidence interval No StochasticBackscatter Stochastic Backscatter

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Wavenumber-Frequency Spectrum Symmetric part, background removed (after Wheeler and Kiladis, 1999) No Stochastic Backscatter Observations (NOAA)

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Improvement in Wavenumber-Frequency Spectrum Stochastic Backscatter Observations (NOAA) Backscatter scheme reduces erroneous westward propagating modes

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Judith Berner: Representing Model Error by Stochastic Parameterizations 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

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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)

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Judith Berner: Representing Model Error by Stochastic Parameterizations Multiple Physics packages

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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

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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

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Judith Berner: Representing Model Error by Stochastic Parameterizations Spread-Error Relationship Backscatter Control Multi-Physics

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Judith Berner: Representing Model Error by Stochastic Parameterizations Brier Score, U Backscatter Control Multi-Physics

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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

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Judith Berner: Representing Model Error by Stochastic Parameterizations Multiple Physics packages

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Judith Berner: Representing Model Error by Stochastic Parameterizations Brier Score Backscatter Control Multi-Physics

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Judith Berner: Representing Model Error by Stochastic Parameterizations Spread-Error Relationship Backscatter Control Multi-Physics

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Judith Berner: Representing Model Error by Stochastic Parameterizations Seasonal Predication Multi-model Stochastic Ensemble Curtosy: TimPalmer UncalibratedCalibrated

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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

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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

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Judith Berner: Representing Model Error by Stochastic Parameterizations Challenges How can we incorporate the “structural uncertainty” estimated by multi-models into stochastic parameterizations?

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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

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