Bred vectors of the Lorenz63 system

The breeding method has been widely used in studies of data assimilation, predictability and instabilities. The bred vectors(BVs), which are the nonlinear difference between the control and perturbed runs, represent the time-evolving rapidly growing errors in dynamic systems. The Lorenz(1963) model(hereafter Lorenz63 model) has chaotic dynamics similar to weather and climate. This study investigates the features of BVs of the Lorenz63 model and its impact on regime prediction of the Lorenz63 model. The results show that the Lorenz63 model has two different BVs for each breeding cycle, and the two BVs approach being identical when growth rate is high. The duration of the current and next regime is associated with the relative directions between the BV with high growth rate and the model trajectory.