The CPC Consolidation Forecast
David Unger
Dan Collins, Ed O’ Lenic, Huug van den Dool NOAA/NWS/NCEP/Climate Prediction Center
Overview
• A regression procedure designed for ensembles. Derive a relationship between the BEST member of an N-member ensemble and the observation: Y = a 0 + a 1fb + ε
Ensemble Regression
• Weights represent the probability of a given member being the best. • If weights are known, coefficients can be calculated from the ensemble set. (No need to explicitly identify the best member)
Ensemble Regression
Example Forecast
CFS 1-month Lead Forecast Nino 3.4 SST, May, 1992
April Data June-August Mean SST’s A series of forecasts • Start with the ensemble mean • Gradually increase the ensemble spread K = The fraction of the original model spread
Multi Model Consolidation
• At least 25 years of “hindcast” data • Standardize each model (means and standard deviations) • Remove trend from models and observations • Weight the various models • Perform regression • Add trends onto the results
Nino 3.4 Consolidation
• CFS, CCA, CA, MKV (Statistical and Dynamic models mixed) • Lead -2 and Lead -1 are a mix of observations and the one and two-month forecast from the CFS
Skill May Initial Time Calibrated CFS Vs. Consolidation
CRPS Skill Nino 3.4
1
CRPSS
0.5 0 -2 -1 0 1 2 3 4 Lead (Months) 5 6
CFS CONS
U.S. Temperature and Precipitation Consolidation
• CFS • Canonical Correlation Analysis (CCA) • Screening Multiple Linear Regression(SMLR) • OCN - Trends.
SON Consolidation Forecast
Performance
CRPSS RPSS - 3 HSS Bias (C) % Cover
CCA+SMLR
CFS CFS+CCA+ SMLR, Wts. All – Equal Wts. Official
.046
.067 .063 .074 .023
.076
.076 .100 .100 .040
.191
.162 .215 .199 .098
-.147
-.334 -.268 -.203 -.858
63%
59% 73% 62% 38%
Future Work
• • • • Add more tools and models Improve weighting method Trends are too strong Improve method of mixing statistical and dynamical tools
END
Recursive Regression
• Y = a0 + a1fi a+ = (1-α) a + α Stats(F,Y) Stats(F,Y) represents error statistic based on the most recent case α = .05 a+ = .95 a + .05 Stats(F,Y)
SST Consolidation
• CFS – 42 members • Constructed Analog (CA) – 12 members • CCA – 1 member • MKV – 1 member (29%) (18%) (17%) (36%)
Advantages
• Ideally suited for dynamic models. • Uses information from the individual members (Variable confidence, Clusters in solutions, etc.)
Disadvantages
• Statistical forecasts are not true Solutions • Trends are double counted when they accelerate • Weighting is not optimum (Bayesian seems appropriate)