Logarithmic bred vectors. A new ensemble method with adjustable spread and calibration time

摘要

The breeding method is a conceptually simple and computationally cheap ensemble generation technique. Bred vectors (BV) are dynamically obtained from the nonlinear model and correspond to the spatial structures with fast-growing fluctuations at each time. These vectors have a characteristic localized spatial structure, with only a small number of significant values corresponding to the leading fluctuation areas. The temporal and spatial growth of the BV interacts making the spatial structure a key factor of the dynamics. In this paper we introduce a new breeding technique, Logarithmic Bred Vectors (LBV), which allows growing vectors with tuneable spatial structure, more (or less) localized. This yields ensembles with different spatiotemporal dynamics (different spread, etc.). This is done by introducing a new parameter (the geometrical mean) which controls the spatial correlation of the bred vectors, from uncorrelated vectors similar to random perturbations, to fully correlated and localized vectors similar to standard bred vectors. The new method increases the diversity of the ensemble and allows the spread to grow faster preserving the model performance in terms of the root mean square error. Consequently, the ensembles can be calibrated for a desired lead time (for instance a shorter forecast range). The concepts are illustrated using a chain of diffusively coupled Lorenz systems. Preliminary evidence of the possible application in operative weather prediction models is also presented.