Ensembles and Probabilistic Forecasting

Probabilistic Prediction

• Because of forecast uncertainties, predictions must be provided in a probabilistic framework, not the deterministic single answer approach that has dominated weather prediction during the last century.

• Interestingly…the first public forecasts were probabilistic

“Ol Probs”

Professor Cleveland Abbe, who issued the first public“Weather Synopsis and Probabilities” on February 19, 1871

Cleveland Abbe (“Ol’ Probabilities”), who led the establishment of a weather forecasting division within the U.S. Army Signal Corps.

Produced the first known communication of a weather probability to users and the public in 1869.

The Trend to Deterministic Forecasts During the Later 19th

and First Half of the 20th Centuries.

Foundation for probabilistic prediction

• The work of Lorenz (1963, 1965, 1968) demonstrated that the atmosphere is a chaotic system, in which small differences in the initialization…well within observational error… can have large impacts on the forecasts, particularly for longer forecasts.

• Not unlike a pinball game….

• Similarly, uncertainty in our model physics also produces uncertainty in the forecasts.

• Lorenz is a series of experiments demonstrated how small errors in initial conditions can grow so that all deterministic forecast skill is lost at about two weeks.

• Talked about the butterfly effect…

The Lorenz Diagram…chaosIs not necessarily random

Probabilistic NWP• To deal with forecast uncertainty, Epstein (1969) suggested

stochastic-dynamic forecasting, in which forecast errors are explicitly considered during model integration, but this method was not computationally practical.

• Another approach, ensemble prediction, was proposed by Leith (1974), who suggested that prediction centers run a collection (ensemble) of forecasts, each starting from a different initial state. The variations in the resulting forecasts could be used to estimate the uncertainty of the prediction. But even the ensemble approach was not tractable at this time due to limited computer resources.

Ensemble Prediction•Can use ensembles to provide a new generation of products that give the probabilities that some weather feature will occur.

•Can also predict forecast skill!

•It appears that when forecasts are similar, forecast skill is higher.

•When forecasts differ greatly, forecast skill is less.

•To create a collection of ensembles one can used slightly different initializations or different physics.

Ensemble Prediction

• By the early 1990s, faster computers allowed the initiation of global ensemble prediction at NCEP and ECMWF (European Centre for Medium Range Weather Forecasts).

• During the past decade the size and sophistication of the NCEP and ECMWF ensemble systems have grown considerably, with the medium-range, global ensemble system becoming an integral tool for many forecasters. Also during this period, NCEP has constructed a higher resolution, short-range ensemble system (SREF) that uses breeding to create initial condition variations.

NCEP Global Ensemble System• Begun in 1993 with the MRF (now GFS)• First tried “lagged” ensembles as basis…using runs of various

initializations verifying at the same time.• For the last ten years have used the “breeding” method to find

perturbations to the initial conditions of each ensemble members.• Breeding adds random perturbations (+ and -) to an initial state, let

them grow, then reduce amplitude down to a small level, lets them grow again, etc.

• Give an idea of what type of perturbations are growing rapidly in the period BEFORE the forecast.

• Does not include physics uncertainty.• Coarse spatial resolution..only for synoptic features.

NCEP Global EnsembleAt 00Z:• T254L64 high resolution control out to 7 days, after which this run gets

“truncated--just larger scales” and is run out to 16 days at a T170L42 resolution

• T62 control that is started with a truncated T170 analysis • 10 perturbed forecasts each run at T62 horizontal resolution. The

perturbations are from five independent breeding cycles.

At 12Z:• T254L64 control out to 3 days that gets truncated and run at T170L42

resolution out to 16 days• Two pairs of perturbed forecasts based on two independent breeding

cycles (four perturbed integrations out to 16 days).

U.S. Navy Also Has A Global Ensemble System Using NOGAPS

NCEP Short-Range Ensembles (SREF)

• Resolution of 32 km• Out to 87 h twice a day (09 and 21 UTC

initialization)• Uses both initial condition uncertainty (breeding)

and physics uncertainty.• Uses the Eta and Regional Spectral Models and

recently the WRF model (21 total members)

SREF Current System

Model Res (km) Levels Members Cloud Physics ConvectionRSM-SAS 45 28 Ctl,n,p GFS physics Simple Arak-SchubertRSM-RAS 45 28 n,p GFS physics Relaxed Arak-Schubert

Eta-BMJ 32 60 Ctl,n,p Op Ferrier Betts-Miller-JanjicEta-SAT 32 60 n,p Op Ferrier BMJ-moist prof

Eta-KF 32 60 Ctl,n,p Op Ferrier Kain-FritschEta-KFD 32 60 n,p Op Ferrier Kain-Fritsch

with enhanced detrainment

PLUS

* NMM-WRF control and 1 pert. Pair* ARW-WRF control and 1 pert. pair

UW Short Range Ensemble System

UW Mesoscale Ensemble System• Single limited-area mesoscale modeling system

(MM5)• 2-day (48-hr) forecasts at 0000 UTC and 12 UTC

in real-time since January 2000. 36 and 12-km domains.

Configurations of the MM5 short-range ensemble grid domains. (a) Outer 151127 domain with 36-km horizontal grid spacing. (b) Inner 103100 domain with 12-km horizontal grid spacing.

a) b)

36-km 12-km

UW Ensemble System• UW system is based on the use of analyses and forecasts of

major operational modeling centers.• The idea is that differences in initial conditions of various

operational centers is a measure of IC uncertainty.• These IC differences reflect different data inventories,

assimilation schemes, and model physics/numerics and can be quite large, often much greater than observation errors.

• In this approach each ensemble member uses different boundary conditions--thus finessing the problem of the BC restraining ensemble spread.

• Also include physics diversity

Resolution (~ @ 45 N ) ObjectiveAbbreviation/Model/Source Type Computational Distributed Analysis

avn, Global Forecast System (GFS), Spectral T254 / L64 1.0 / L14 SSINational Centers for Environmental Prediction ~55 km ~80 km 3D Var cmcg, Global Environmental Multi-scale (GEM), Finite 0.90.9/L28 1.25 / L11 3D VarCanadian Meteorological Centre Diff ~70 km ~100 km eta, limited-area mesoscale model, Finite 32 km / L45 90 km / L37 SSINational Centers for Environmental Prediction Diff. 3D Var gasp, Global AnalysiS and Prediction model, Spectral T239 / L29 1.0 / L11 3D VarAustralian Bureau of Meteorology ~60 km ~80 km

jma, Global Spectral Model (GSM), Spectral T106 / L21 1.25 / L13 OIJapan Meteorological Agency ~135 km ~100 km ngps, Navy Operational Global Atmos. Pred. System, Spectral T239 / L30 1.0 / L14 OIFleet Numerical Meteorological & Oceanographic Cntr. ~60 km ~80 km

tcwb, Global Forecast System, Spectral T79 / L18 1.0 / L11 OITaiwan Central Weather Bureau ~180 km ~80 km ukmo, Unified Model, Finite 5/65/9/L30 same / L12 3D VarUnited Kingdom Meteorological Office Diff. ~60 km

“Native” Models/Analyses Available

Relating Forecast Skill and Model Spread

Mean Absolute Error of Wind Direction is Far Less WhenSpread is EXTREME (Low or High)

Ensemble-Based Probabilistic Products

The Thanksgiving Forecast 200142h forecast (valid Thu 10AM)

13: avn*

11: ngps*

12: cmcg*

10: tcwb*

9: ukmo*

8: eta*

Verification

1: cent

7: avn

5: ngps

6: cmcg

4: tcwb

3: ukmo

2: eta

- Reveals high uncertainty in storm track and intensity- Indicates low probability of Puget Sound wind event

SLP and winds

Ensemble-Based Probabilistic Products

Ensemble Prediction in the U.S.