A New Measure of Ensemble Central Tendency
Ensemble prediction is a widely used tool in weather forecasting. In particular, the arithmetic mean (AM) of ensemble members is used to filter out unpredictable features from a forecast. AM is a pointwise statistical concept, providing the best sample-based estimate of the expected value of any single variable. The atmosphere, however, is a multivariate system with spatially coherent features characterized with strong correlations. Disregarding such correlations, the AM of an ensemble of forecasts removes not only unpredictable noise but also flattens features whose presence is still predictable, albeit with somewhat uncertain location. As a consequence, AM destroys the structure, and reduces the amplitude and variability associated with partially predictable features. Here we explore the use of an alternative concept of central tendency for the estimation of the expected feature (instead of single values) in atmospheric systems. Features that are coherent across ensemble members are first collocated to their mean position, before the AM of the aligned members is taken. Unlike earlier definitions based on complex variational minimization (field coalescence of Ravela and generalized ensemble mean of Purser), the proposed feature-oriented mean (FM) uses simple and computationally efficient vector operations. Though FM is still not a dynamically realizable state, a preliminary evaluation of ensemble geopotential height forecasts indicates that it retains more variance than AM, without a noticeable drop in skill. Beyond ensemble forecasting, possible future applications include a wide array of climate studies where the collocation of larger-scale features of interest may yield enhanced compositing results.