The CPC Consolidation Forecast

David UngerDan 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 = a0 + a1fb + 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 ForecastCFS 1-month Lead Forecast

Nino 3.4 SST, May, 1992April 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 TimeCalibrated CFS Vs. Consolidation

CRPS Skill Nino 3.4

0

0.5

1

-2 -1 0 1 2 3 4 5 6

Lead (Months)

CR

PS

S

CFS

CONS

U.S. Temperature and Precipitation Consolidation

• CFS• Canonical Correlation Analysis (CCA)• Screening Multiple Linear

Regression(SMLR)• OCN - Trends.

SON Consolidation Forecast

Performance

.046 .076 .191 -.147 63%

.067 .076 .162 -.334 59%

.063 .100 .215 -.268 73%

.074 .100 .199 -.203 62%

.023 .040 .098 -.858 38%

CCA+SMLR

CFS

CFS+CCA+SMLR, Wts.

All – Equal Wts.

Official

HSSCRPSS RPSS - 3 % CoverBias (C)

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 (29%)

• Constructed Analog

(CA) – 12 members (18%)

• CCA – 1 member (17%)

• MKV – 1 member (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)