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The Weighted-Average Lagged Ensemble
T DelSole1,2, L Trenary1,2, M K Tippett3,4
1Department of Atmospheric, Ocean, and Earth Sciences George Mason University Fairfax VA USA.
Journal of Advances in Modeling Earth Systems
|February 6, 2018
Summary
Optimal weighting of lagged ensemble forecasts can improve skill. This study reveals conditions where weights become negative or non-monotonic, particularly with rapid error growth and high error correlation.
Area of Science:
- Meteorology and Climate Science
- Data Assimilation and Ensemble Forecasting
Background:
- Lagged ensembles combine forecasts from the same model initialized at different times.
- Weighted-average lagged ensembles optimize forecast skill by assigning weights.
- Optimal weights typically decay monotonically with lead time for uncorrelated errors.
Purpose of the Study:
- To investigate conditions leading to non-standard optimal weights in weighted-average lagged ensembles.
- To analyze scenarios where optimal weights become negative or depend non-monotonically on lead time.
Main Methods:
- Development of analytic examples to study optimal weight behavior.
- Examination of the relationship between error characteristics and weight behavior.
- Analysis of mean square error constancy across forecast lead times.
Main Results:
- Negative weights are probable when forecast errors grow rapidly and exhibit high cross-lead-time correlation.
- Non-monotonic weights are likely when mean square error remains constant across the ensemble's lead time range.
- An extreme case demonstrates optimal weights concentrating only at the shortest and longest lead times.
Conclusions:
- The behavior of optimal weights in lagged ensembles is sensitive to error dynamics.
- Understanding these conditions is crucial for accurate ensemble forecast interpretation and application.
- Non-standard weight behavior can arise even in bias-corrected, unbiased weighted ensembles.
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