10
9
10
10
10
24
10
24
10
FORECAST SST
TROP. PACIFIC (multi-models, dynamical and statistical)
TROP. ATL, INDIAN (statistical)
EXTRATROPICAL (damped persistence)
GLOBAL ATMOSPHERIC
MODELS
ECPC(Scripps)
ECHAM4.5(MPI)
CCM3.x(NCAR)
NCEP(MRF9)
NSIPP(NASA)
COLA2.x
ForecastSST
Ensembles3/6 Mo. lead
PersistedSST
Ensembles3 Mo. lead
IRI DYNAMICAL CLIMATE FORECAST SYSTEM
POSTPROCESSING
MULTIMODELENSEMBLING
PERSISTED
GLOBAL
SST
ANOMALY
2-tiered OCEAN ATMOSPHERE
Empirical toolsalso used
Mason & Goddard, 2001, Bull.Amer.Meteor.Soc.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190
200
| || ||| ||||.| || | | || | | | . | | | | | | | | | |
Rainfall Amount (mm)
Below| Near | Below| Near | Above Below| Near |
The tercile category system:Below, near, and above normal
(30 years of historical data for a particular location & season)
Forecasts of the climate
Data:
33% 33% 33%Probability:
OCT | Nov-Dec-Jan* Dec-Jan-Feb
Jan-Feb-Mar Feb-Mar-Apr
Monthly issued probability forecasts of seasonal global precipitation and temperature
*probabilities of extreme (low and high) 15% issued also
Four lead times - example:
Atmospheric General Circulation Models Used in the IRI's Seasonal Forecasts, for Superensembles
Name Where Model Was Developed Where Model Is Run
NCEP MRF-9 NCEP, Washington, DC QDNR, Queensland, Australia
ECHAM 4.5 MPI, Hamburg, Germany IRI, Palisades, New York
NSIPP NASA/GSFC, Greenbelt, MD NASA/GSFC, Greenbelt, MD
COLA COLA, Calverton, MD COLA, Calverton, MD
ECPC SIO, La Jolla, CA SIO, La Jolla, CA
CCM3.x NCAR, Boulder, CO NCAR, Boulder, CO
(forthcoming) GFDL, Princeton, NJ GFDL or IRI
Sources of the Global Sea Surface Temperature Forecasts
Tropical Pacific Tropical Atlantic Indian Ocean Extratropical Oceans
NCEP Coupled CPTEC Statistical IRI Statistical Damped PersistenceLDEO Coupled Constr Analogue
Ranked Probability Skill Score (RPSS)
3
RPSfcst = (Fcsticat – Obsicat)2
icat=1
icat ranges from 1 (below normal) to 3 (above normal)
RPSS = 1 - (RPSfcst / RPSclim)
Skill of Model Hindcasts Using Observed SST
Skill of Model Hindcasts Using Observed SST
RPSS Skill of Individual Model Simulations: JAS 1950-97Precipitation
Real-timeForecast
Skill
Real-timeForecast
Skill
1998-2001 Reliability Diagram
Reliability Diagramlonger “AMIP”
period
from Goddardet al. 2003
(EGS-AGU-EUG)
Next:Bayesian weighting methodfor multi-model ensembling
IRI uses two multi-model ensembling methods:
Bayesian method
Canonical variate method
Both methods analyze historical model performance in responding to observed
SST.
JAS 2003: Six GCM Precip.Forecasts
Likelihood
L(w) E(Qk*t
)t1
N
k
* represents the category that was observed at time t
"a multi-year product of the probabilities that were hindcast for the category that was observed..."
• Dirichlet distribution is appropriate for a multinomial process (i.e. terciles)– Combination of a and b is also Dirichlet with parameter
a+b
Rajagopalan et al., 2002:. Mon. Wea. Rev.
Ways to compute weights
Effective sample sizesEffective sample sizes
E[Qkt ] wcn
13 wmm mk
m
wcn wmm
Individual GCM + Climatology:1
f (Q t | Pt(y)) D(wcnPt(x) wmmPt(y))
Multiple GCMs + Climatology:
2
E[Qkt ] w j m j Pktj (y)
j1
Jw j m jj1
J
Combine the individual weights from several models using a Two-Stage scheme:
3
E[Qkt ] wcn
13 wmm mk
m
wcn wmm(a) For each model in turn:
E[Qkt ] wcn
13 wpmp
1
wjj
wj
mjkt
mj
j1
J
wcn wpmp
mp m jj1
J
(b) For the pooled ensemble thus created:
w j mj
mpwpFinal weights:
Model Weights – “Two-Stage”JAS
Model Weights – Two-Stage, Cross-Validated (XV)JAS
Climatological Weights JAS
Combination Forecasts of Jul-Sep PrecipitationOne-Stage Two-Stage
Two-Stage, xv, Spatial Smoothing
Two-Stage Cross-Validated
JAS 2003
Canonical variate method:
A kind of discriminant analysis.
Input: ensemble mean, ensemble spread,ensemble skewness
Algorithm finds linear combinations ofpredictors leading to each catergorical
(tercile) result. Differences amongthe sets of predictor weights are
maximized.
Multi-model ensemblingof dynamical predictions appearsto be slightly superior to currently
used statistical tools at NOAA/NCEP/CPC
temperature
precipitation
Most important current needsin IRI forecast system:
Improvement of SST prediction in 2-tiered system1) Tropical Pacific: better model consolidation, with
development of multiple evolving scenarios2) Outside tropical Pacific:“Smarter” persistence scenario,
or multivariate statistical model (e.g. CCA)
Use of 1-tiered climate model for some regionsSlab ocean model in locations where 2-tiered system fails
(Indian Ocean, far west Pacific and tropical Atlantic oceans)