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Designing Multimodel Applications with Surrogate Forecast Systems

Smith, Leonard A.; Du, Hailiang; Higgins, Sarah

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Leonard A. Smith

Sarah Higgins


Probabilistic forecasting is common in a wide variety of fields including geoscience, social science, and finance. It is sometimes the case that one has multiple probability forecasts for the same target. How is the information in these multiple nonlinear forecast systems best “combined”? Assuming stationarity, in the limit of a very large forecast–outcome archive, each model-based probability density function can be weighted to form a “multimodel forecast” that will, in expectation, provide at least as much information as the most informative single model forecast system. If one of the forecast systems yields a probability distribution that reflects the distribution from which the outcome will be drawn, Bayesian model averaging will identify this forecast system as the preferred system in the limit as the number of forecast–outcome pairs goes to infinity. In many applications, like those of seasonal weather forecasting, data are precious; the archive is often limited to fewer than 26 entries. In addition, no perfect model is in hand. It is shown that in this case forming a single “multimodel probabilistic forecast” can be expected to prove misleading. These issues are investigated in the surrogate model (here a forecast system) regime, where using probabilistic forecasts of a simple mathematical system allows many limiting behaviors of forecast systems to be quantified and compared with those under more realistic conditions.


Smith, L. A., Du, H., & Higgins, S. (2020). Designing Multimodel Applications with Surrogate Forecast Systems. Monthly Weather Review, 148(6), 2233-2249.

Journal Article Type Article
Acceptance Date Oct 31, 2019
Online Publication Date May 5, 2020
Publication Date Jun 30, 2020
Deposit Date Jun 3, 2020
Publicly Available Date May 5, 2021
Journal Monthly Weather Review
Print ISSN 0027-0644
Electronic ISSN 1520-0493
Publisher American Meteorological Society
Peer Reviewed Peer Reviewed
Volume 148
Issue 6
Pages 2233-2249


Published Journal Article (2.5 Mb)

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