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Explore an ensemble regression method for climate predictions using weighted probabilities to derive relationships between ensemble members and observations. This method combines various models and forecasts to enhance performance and accuracy.
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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 = 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)
Example ForecastCFS 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
U.S. Temperature and Precipitation Consolidation • CFS • Canonical Correlation Analysis (CCA) • Screening Multiple Linear Regression(SMLR) • OCN - Trends.
Performance CRPSS RPSS - 3 HSS Bias (C) % Cover CCA+SMLR CFS CFS+CCA+SMLR, Wts. All – Equal Wts. Official
Future Work • Add more tools and models • Improve weighting method • Trends are too strong • Improve method of mixing statistical and dynamical tools
Recursive Regression • Y = a0 + a1fi a+= (1-α) a+ αStats(F,Y) Stats(F,Y) represents error statistic based on the most recent case α = .05 a+= .95a + .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)