Stochastically perturbed bred vectors
The breeding method is a computationally cheap procedure to generate initial conditions for ensemble forecasting which project onto relevant synoptic growing modes. Ensembles of bred vectors, however, often lack diversity and align with the leading Lyapunov vector, which severely impacts their statistical reliability. In previous work we developed stochastically perturbed bred vectors (SPBVs) and random draw bred vectors (RDBVs) in the context of multi-scale systems. Here we explore when this method can be extended to systems without scale separation, and examine the performance of the stochastically modified bred vectors in the single scale Lorenz 96 model. In particular, we show that the performance of SPBVs crucially depends on the degree of localisation of the bred vectors. It is found that, contrary to the case of multi-scale systems, localisation is detrimental for applications of SPBVs in systems without scale-separation when initialised from assimilated data. In the case of weakly localised bred vectors, however, ensembles of SPBVs constitute a reliable ensemble with improved ensemble forecasting skills compared to classical bred vectors, while still preserving the low computational cost of the breeding method. RDBVs are shown to have superior forecast skill and form a reliable ensemble in weakly localised situations, but in situations when they are strongly localised they do not constitute a reliable ensemble and are over-dispersive.