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Overview of Ensemble Forecasting
Steven L. Mullen
Univ. of Arizona
COMET Faculty 99 CoursePresented by Steve MullenWednesday, 9 June 1999
Benefactors• Dave Baumhefner, NCAR
• Joe Tribbia, NCAR
• Ron Errico, NCAR
• Tom Hamill, NCAR
• Harold Brooks, NSSL
• Chuck Doswell, NSSL
• Dave Stensrud, NSSL
• Eugenia Kalnay, NCEP-UO-UM-?
• Steve Tracton, NCEP
• Zoltan Toth, NCEP
• Ron Gelaro, NRL
• Rolf Langland, NRL
• Jeff Anderson, GFDL
• Mike Harrison, UKMO
• Tim Palmer, ECMWF
• Roberto Buizza, ECMWF
• Peter Houtekamer, AES
Presentation Overview
• Philosophy and Benefits of Ensembles
• Estimate of Initial Uncertainty
• Design of Initial Perturbations for EPS
• Inclusion of Model Uncertainty in EPS
• Ensemble Size
• Integration of EPS and Data Assim System
• Model Validation
• Evaluation and Utility of EPS
• Classroom Activities
Philosophy and Benefitsof Ensemble Forecasting
• Initial Condition Uncertainty (ICU)
• Probability Density Function (PDF) of initial conditions about “Truth”
• GOAL: predict evolution of PDF
• Gives information on 1st & 2nd moments Forecast uncertainty from dispersion
• Thought to be most applicable to MRF (6-10 day) and seasonal (30-90 day) forecasts
• Beneficial to SRF (06 h-2 day) for QPF
• KEY: IC error versus model error More skillful model, more beneficial PIC
• Now includes dispersion from uncertainty in initial state and model formulations
Univ Utah Ensemble12 km inner grid
Univ Utah Ensemble12 km inner grid
Precipitation Dispersion32 km NSSL Mixed Ensemble
Oct 97-Dec 97
1
2
3
4
5
6
7
8
0 3 6 9 12 15 18 21 24 27 30 33 36
forecast time (h)
rms
(mm
)
12 h
6 h
3 h
1 h
Perturbation Design
• What is the goal?
1) Robust estimate of PDF? 2) Sample extremes of PDF?3) Make up for deficiency in EPS?
• Requirements1) Properly constrained by estimates
of analysis error2) Equally-likely probability
for each perturbation field• What are some of the attributions of
current perturbation schemes for global ensemble models?
Dave Baumhefner, in progress
Ranked Probability Scoreby Model and Perturbation
0.2
0.4
0.6
0.8
24h 48hFcst Time
Grand EnsETA DiffETA BredRSM Bred
Ranked ProbabilitySkill Score
Relative to Climatology
0.0
0.1
0.2
0.3
0.4
0.5
24h 48hFcst Time
RP
SS
Grand EnsETA DiffETA BredRSM BredETA OpnlMeso ETA
Perturbation DesignConclusions
• Perturbation methods control dispersion characteristics out to 5-7 days
• SV: linear growth 1-3 days
• Random: classic error growth curve
• Random: project onto SVs 1-5 days
• BV: unique, different than analysis error, but has improved with recent changes
• Perturb strategy is unimportant after 5-7 days, once growth is strongly nonlinear
Model Uncertainties
• Specification of Subgrid Scale Processes
• GOAL: improve transient variability and increase ensemble
dispersion
• Methodologies / Philosophies1) Fixed during model integration:
different parameterization schemeschange tunable parameters 2) Stochastic element during integration:
to a scheme’s tunable parameters to model tendencies directly
• What are some of the attributes?
Rank Histogram24 h Rain Totals
24h Rank ECMWF
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Fixed
Stoch
Stochastic Cb Parameterization
Model Uncertainties Conclusions
• Increases dispersion
• Changes predictability estimates
• Model validation issues?
Model Validation
• Major Challenge for Mesoscale LAMs• Inclusion of stochastic dynamics/physics into
model requires consideration ofamplitude spatial scaletemporal scale
• Statistics for model and observations are currently lacking, so need for
long-term model integrationsbetter utilization of obs networkin absence of obs statistics, validate by comparison with explicit models
• GOAL: model PDFs match obs PDFs
Ensemble Size (N)
• Increased N or finer model resolution
• Partitioning N among perturbed IC’s and different physics parameterizations
• Depend on model, forecast objective etc.
• Choice is not always clearResolution of complex terrain
• Larger N always decreases sampling uncertaintyDiminishing returns N exceeds 10-20
• N sets limits on resolution of PDF1% event requires N of 200 or larger
• Large N warranted for accurate EPSModel with good climateAbility to simulate phenomenonSound perturbation strategy
EPS and Data Assimilation System
• Current status of Data Assimilation 3DVAR and OI techniques
homogeneousisotropic
flow independent• Kalman filter and 4DVAR can account
for these shortcomingsKalman filter expensive
4DVAR lacks cycling
• Ensemble of perturbed 6h SRFs may provide an alternative to 4DVAR
inexpensivecontains cycling
• Houtekamer and Mitchell (1998) study
Utility of EPS
• Challenge: convey info in ensemblesReduce flow dimensionality
clusters, EOFs, indices, envelopes User friendly and flexible
wide spectrum of needs and abilities
“problem of day” changes
• Enhance utility by stat. post-processingMLR MOS-techniques
Kalman filteringAI-neural
networks
• Rigorous assessment of stat. significance
• Cost-benefit analysis
Neural Net Post-ProcessingReliability Diagram 0.25”
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Forecast Probability
Obs
erve
d Fr
eque
ncy NET
RAW
MOS
NET(MOS)
Cost-Benefit AnalysisPrecipitation
Fav SitesReal-Time Ensemble Products
• NCEP MRF Ensembles
CDC Boulderwww.cdc.noaa.gov/~map/maproom/ENS/ens.html
NCEP Ensemble Homepagesgi62.wwb.noaa.gov:8080/ens/enshome.html
Univ of Utahwww.met.utah.edu/jhorel/html/models/model_ens.html
• MOS for MRF Ensembles
Penn Statewww.essc.psu.edu/~rhart/ensemble/ensmos.html
• Short-Range Mixed Ensembles
NSSL/NOAAvicksburg.nssl.noaa.gov/mm5/ensemble/index_all.html
• SAMEX? NCEP ETA/RSM?
Ask Kelvin D. and Steve T., respectively!
Univ. Utah
Univ. Utah
MRF Ensemble MOSfrom Penn State
NSSL Experiment Ensemble Model Physics/Uncertainty
FNMOC/UA Products
Classroom ActivitiesAppropriate for Undergrads
• Probabilistic ForecastingQPF
Use MOS thresholds
MAX-MIN
Credible Interval Forecasts
(e.g. Prob. within 2oF)
Be willing to stumble and be humbled!
• Hands-On NWPBarotropic Model Experiments