Judith Berner: Representing Model Error by Stochastic Parameterizations
Representing model uncertainty in weather Representing model uncertainty in weather and climate: stochastic versa multi-physics and climate: stochastic versa multi-physics
representationsrepresentations
Judith BernerJudith Berner, NCAR, NCAR
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
“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
10 m 100 m 1 km 10 km 100 km 1000 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
The spectral gap …
(Stull)
Judith Berner: Representing Model Error by Stochastic Parameterizations
Atmospheric
Scientists
Nastrom and Gage, 1985
459APRIL 2008AMERICAN METEOROLOGICAL SOCIETY |
TOWARD SEAMLESS PREDICTIONCalibration of ClimateChangeProjectionsUsingSeasonalForecasts
BY T.N. PALMER, F. J. DOBLAS-REY ES,A .W EISHEIMER, AND M. J.RODWELL
In aseamless prediction system,the reliabilityof coupled climatemodel forecastsmade onseasonal time scales canprovideusefulquantitativeconstraints for
improvingthetrustworthiness of regional climatechange projections.
Inweatherandclimatepredictioncircles, thephrase_seamlesspredic-tion_ isverymuchinvogue„ indeedthenotionofseamlesspredictionliesattheheart of the WorldClimateResearchProgramme_srecent
strategicframework(availableonlineathttp://wcrp.wmo.int/pdf/WC RP_strategImple_LowRes.pdf). However, what doesthisphrasemean, andwhatisitsrelevancefor thepracticeofweatherandclimateforecasting?
FIG .1.A schem a tic fig ure illustrating th at the lin k b etw een clim ate fo rcing and clim ate im pact in vo lves pro -cesses acting on d ifferent tim e scales.T he w h ole ch ain is as stro ng as its w eak est lin k.T he use ofa se am lesspredictio n system allow s probab ilistic pro jection sofclim ate change to b e constraine d by validatio nso n w e atheror seaso nalforecasttim e scale s.
.... The link between
climate forcing and
climate impact involves
processes acting on
different timescales …
459APRIL 2008AMERICAN METEOROLOGICAL SOCIETY |
TOWARD SEAMLESS PREDICTIONCalibration of ClimateChangeProjectionsUsingSeasonalForecasts
BY T.N. PALMER, F. J. DOBLAS-REY ES,A .W EISHEIMER, AND M. J.RODWELL
In aseamless prediction system,the reliabilityof coupled climatemodel forecastsmade onseasonal time scales canprovideusefulquantitativeconstraints for
improvingthetrustworthiness of regional climatechange projections.
Inweatherandclimatepredictioncircles, thephrase_seamlesspredic-tion_ isverymuchinvogue„ indeedthenotionofseamlesspredictionliesattheheart of the WorldClimateResearchProgramme_srecent
strategicframework(availableonlineathttp://wcrp.wmo.int/pdf/WC RP_strategImple_LowRes.pdf). However, what doesthisphrasemean, andwhatisitsrelevancefor thepracticeofweatherandclimateforecasting?
FIG .1.A schem a tic fig ure illustrating th at the lin k b etw een clim ate fo rcing and clim ate im pact in vo lves pro -cesses acting on d ifferent tim e scales.T he w h ole ch ain is as stro ng as its w eak est lin k.T he use ofa se am lesspredictio n system allow s probab ilistic pro jection sofclim ate change to b e constraine d by validatio nso n w e atheror seaso nalforecasttim e scale s.
NPW NPW
modelmodel
Climate modelClimate modelCloud resolving Cloud resolving
modelmodel
Resolved Resolved
microphysicsmicrophysics
Large Eddy Large Eddy
simulationsimulation
Cloud resolving Cloud resolving
modelmodel
Attempt to capture Multi-scale nature of atmospheric motion
Attempt to capture Multi-scale nature of atmospheric motion
Judith Berner: Representing Model Error by Stochastic Parameterizations
459APRIL 2008AMERICAN METEOROLOGICAL SOCIETY |
TOWARD SEAMLESS PREDICTIONCalibration of ClimateChangeProjectionsUsingSeasonalForecasts
BY T.N. PALMER, F. J. DOBLAS-REY ES,A .W EISHEIMER, AND M. J.RODWELL
In aseamless prediction system,the reliabilityof coupled climatemodel forecastsmade onseasonal time scales canprovideusefulquantitativeconstraints for
improvingthetrustworthiness of regional climatechange projections.
Inweatherandclimatepredictioncircles, thephrase_seamlesspredic-tion_ isverymuchinvogue„ indeedthenotionofseamlesspredictionliesattheheart of the WorldClimateResearchProgramme_srecent
strategicframework(availableonlineathttp://wcrp.wmo.int/pdf/WC RP_strategImple_LowRes.pdf). However, what doesthisphrasemean, andwhatisitsrelevancefor thepracticeofweatherandclimateforecasting?
FIG .1.A schem a tic fig ure illustrating th at the lin k b etw een clim ate fo rcing and clim ate im pact in vo lves pro -cesses acting on d ifferent tim e scales.T he w h ole ch ain is as stro ng as its w eak est lin k.T he use ofa se am lesspredictio n system allow s probab ilistic pro jection sofclim ate change to b e constraine d by validatio nso n w e atheror seaso nalforecasttim e scale s.
NPW NPW
modelmodel
Climate modelClimate modelCloud resolving Cloud resolving
modelmodel
Resolved Resolved
microphysicsmicrophysics
Large Eddy Large Eddy
simulationsimulation
Related: Grabowski 1999, Shutts and
Palmer, 2007
Hierarchical Parameterization Strategy
Judith Berner: Representing Model Error by Stochastic Parameterizations
Validity of spectral gap …
The spectral gap …
Atmospheric
Scientists
Mathematicians
The spectral gap …
Atmospheric
Scientists
M pathematicians
Judith Berner: Representing Model Error by Stochastic Parameterizations
Spectral gap not necessary for stochastic Spectral gap not necessary for stochastic parameterizationsparameterizations
Judith Berner: Representing Model Error by Stochastic Parameterizations
Kinetic energy spectra in 500hPaKinetic energy spectra in 500hPa
Kinetic energy spectrum is closer to that of T799 analysis !
Rotational part Rotational part
Judith Berner: Representing Model Error by Stochastic Parameterizations
Limited vs unlimited predictabilityLimited vs unlimited predictability
Rotunno and Snyder, 2008
Judith Berner: Representing Model Error by Stochastic Parameterizations
Stochastic parameterizations have the potential Stochastic parameterizations have the potential to reduce model errorto 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
Judith Berner: Representing Model Error by Stochastic Parameterizations
OutlineOutline 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
AcknowledgementsAcknowledgements
Judith Berner: Representing Model Error by Stochastic Parameterizations
Sensitivity to initial perturbationsSensitivity to initial perturbations
Representing initial state uncertainty by an Representing initial state uncertainty by an ensemble of statesensemble of states
2t
0t
1t
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
Judith Berner: Representing Model Error by Stochastic Parameterizations
Buizza et al., 2004
Systems
Underdispersion of the ensemble systemUnderdispersion of the ensemble system
-------------- spread around ensemble meanspread around ensemble mean
RMS error of ensemble meanRMS 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
Judith Berner: Representing Model Error by Stochastic Parameterizations
Manifestations of model errorManifestations 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 blockingTropical variability, e.g. MJO, wave propagation
Judith Berner: Representing Model Error by Stochastic Parameterizations
Representing model error in ensemble Representing model error in ensemble systemssystems
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 Recent attempts at remedying model error in NWPNWP
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,…)
Judith Berner: Representing Model Error by Stochastic Parameterizations
Stochastic kinetic energy backscatter Stochastic kinetic energy backscatter schemes 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, SteinheimerMOGREPS, MetOffice Bowler et al 2008, 2009; Tennant et al 2010Canadian Ensemble System Li et al 2008, Charron et al. 2010AFWA mesoscale ensemble system, NCAR Berner et al. 2010
Judith Berner: Representing Model Error by Stochastic Parameterizations
Forcing streamfunction spectra by coarse-Forcing streamfunction spectra by coarse-graining CRMsgraining 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
Forecast error growthForecast 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
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
Judith Berner: Representing Model Error by Stochastic Parameterizations
Experimental Setup for Seasonal RunsExperimental 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”)
No StochasticBackscatterNo StochasticBackscatter Stochastic BackscatterStochastic Backscatter
Reduction of systematic error of z500 over Reduction of systematic error of z500 over North Pacific and North AtlanticNorth Pacific and North Atlantic
Judith Berner: Representing Model Error by Stochastic Parameterizations
Increase in occurrence of Atlantic and Increase in occurrence of Atlantic and Pacific blockingPacific blocking
ERA40 + confidence ERA40 + confidence intervalinterval
No StochasticBackscatterNo StochasticBackscatter
Stochastic BackscatterStochastic Backscatter
Wavenumber-Frequency SpectrumWavenumber-Frequency Spectrum Symmetric part, background removed Symmetric part, background removed
(after Wheeler and Kiladis, 1999)(after Wheeler and Kiladis, 1999)
No Stochastic BackscatterNo Stochastic BackscatterObservations (NOAA)Observations (NOAA)
Improvement in Wavenumber-Frequency Improvement in Wavenumber-Frequency SpectrumSpectrum
Stochastic BackscatterStochastic BackscatterObservations (NOAA)Observations (NOAA)
Backscatter scheme reduces erroneous westward propagating modes
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
Experiment setupExperiment 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)
Judith Berner: Representing Model Error by Stochastic Parameterizations
Multiple Physics packagesMultiple Physics packages
Judith Berner: Representing Model Error by Stochastic Parameterizations
WRF short-range ensemble: 60h-forecast for WRF short-range ensemble: 60h-forecast for Oct 13, 2006: SLP and surface windOct 13, 2006: SLP and surface wind
Control Physics
Ensemble
Judith Berner: Representing Model Error by Stochastic Parameterizations
WRF short-range ensemble: 60h-forecast for WRF short-range ensemble: 60h-forecast for Oct 13, 2006: SLP and surface windOct 13, 2006: SLP and surface wind
Stochastic Backscatter Ensemble
Judith Berner: Representing Model Error by Stochastic Parameterizations
Spread-Error Relationship Spread-Error Relationship
BackscatterBackscatter
ControlControl
Multi-PhysicsMulti-Physics
Judith Berner: Representing Model Error by Stochastic Parameterizations
Brier Score, U Brier Score, U
BackscatterBackscatter
ControlControl
Multi-PhysicsMulti-Physics
Judith Berner: Representing Model Error by Stochastic Parameterizations
Scatterplots of Scatterplots of verification verification
scoresscores
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 packagesMultiple Physics packages
Judith Berner: Representing Model Error by Stochastic Parameterizations
Brier ScoreBrier Score
BackscatterBackscatter
ControlControl
Multi-PhysicsMulti-Physics
Judith Berner: Representing Model Error by Stochastic Parameterizations
Spread-Error Relationship Spread-Error Relationship
BackscatterBackscatter
ControlControl
Multi-PhysicsMulti-Physics
Judith Berner: Representing Model Error by Stochastic Parameterizations
Seasonal PredicationSeasonal Predication
Multi-model
Stochastic Ensemble
Curtosy: TimPalmer
Uncalibrated Calibrated
Summary and conclusionSummary 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 WorkFuture 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
Judith Berner: Representing Model Error by Stochastic Parameterizations
ChallengesChallenges
How can we incorporate the “structural uncertainty” estimated by multi-models into stochastic parameterizations?
Judith Berner: Representing Model Error by Stochastic Parameterizations
BibliographyBibliography
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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