Is unequal weighting significantly better than equal weighting for multi‐model forecasting?

This article proposes a statistical test for whether a multi‐model combination with unequal weights has significantly smaller errors than a combination with equal weights. A combination with equal weights includes the case of a no‐skill model, in which all weights equal zero, and the multi‐model mean, in which all weights equal 1/M, where M is the number of models. The test is applied to seasonal hindcasts of 2 m temperature and precipitation generated by five state‐of‐the‐art coupled atmosphere–ocean models. The hypothesis of equal weights could not be rejected over 75% the globe for temperature and 90% of the land for precipitation, implying that strategies for unequal weighting of forecasts may be of value only over a relatively small fraction of the globe. The fact that the test does not require pre‐specifying a specific strategy for weighting forecasts suggests that it should be useful for exploring a wide range of multi‐model strategies. Copyright © 2012 Royal Meteorological Society

[1]  N. L. Johnson,et al.  Multivariate Analysis , 1958, Nature.

[2]  F. Graybill.  An introduction to linear statistical models , 1961 .

[3]  Michael H. Kutner.  Applied Linear Statistical Models , 1974 .

[4]  V. Barnett,et al.  Applied Linear Statistical Models , 1975 .

[5]  George A. F. Seber,et al.  Linear regression analysis , 1977 .

[6]  R. Clemen.  Combining forecasts: A review and annotated bibliography , 1989 .

[7]  W. Collins,et al.  The NCEP–NCAR 50-Year Reanalysis: Monthly Means CD-ROM and Documentation , 2001 .

[8]  F. Zwiers,et al.  Climate Predictions with Multimodel Ensembles , 2002 .

[9]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[10]  Huug van den Dool,et al.  An analysis of multimodel ensemble predictions for seasonal climate anomalies , 2002 .

[11]  J. Janowiak,et al.  Global Land Precipitation: A 50-yr Monthly Analysis Based on Gauge Observations , 2002 .

[12]  Alan J. Lee,et al.  Linear Regression Analysis: Seber/Linear , 2003 .

[13]  Renate Hagedorn,et al.  The rationale behind the success of multi-model ensembles in seasonal forecasting — I. Basic concept , 2005 .

[14]  Renate Hagedorn,et al.  The rationale behind the success of multi-model ensembles in seasonal forecasting-II , 2005 .

[15]  Timothy DelSole,et al.  A Bayesian Framework for Multimodel Regression , 2007 .

[16]  T. Palmer,et al.  ENSEMBLES: A new multi‐model ensemble for seasonal‐to‐annual predictions—Skill and progress beyond DEMETER in forecasting tropical Pacific SSTs , 2009 .

[17]  Bodo Ahrens,et al.  On the Weighting of Multimodel Ensembles in Seasonal and Short-Range Weather Forecasting , 2009 .

[18]  Reto Knutti,et al.  Risks of Model Weighting in Multimodel Climate Projections , 2010 .

[19]  T. DelSole,et al.  Field Significance of Regression Patterns , 2011 .

[20]  Michael B. Miller.  Linear Regression Analysis , 2013 .