Due to the chaotic nature of atmospheric dynamics, numerical weather prediction systems are sensitive to errors in the initial conditions. To estimate the forecast uncertainty, forecast centres produce ensemble forecasts based on perturbed initial conditions. How to optimally perturb the initial conditions remains an open question and different methods are in use. One is the singular vector (SV) method, adapted by ECMWF, and another is the breeding vector (BV) method (previously used by NCEP). In this study we compare the two methods with a modified version of breeding vectors in a low-order dynamical system (Lorenz-63). We calculate the Empirical Orthogonal Functions (EOF) of the subspace spanned by the breeding vectors to obtain an orthogonal set of initial perturbations for the model. We will also use Normal Mode perturbations. Evaluating the results, we focus on the fastest growth of a perturbation. The results show a large improvement for the BV-EOF perturbations compared to the non-orthogonalised BV. The BV-EOF technique also shows a larger perturbation growth than the SVs of this system, except for short time-scales. The highest growth rate is found for the second BV-EOF for the long-time scale. The differences between orthogonal and non-orthogonal breeding vectors are also investigated using the ECMWF IFS-model. These results confirm the results from the Loernz-63 model regarding the dependency on orthogonalisation.

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loworder dynamical system orthogonalisation fastest growth of a perturbation normal mode perturbations forecast centres orthogonal and nonorthogonal breeding vectors loernz63 model breeding vector bv method singular vector sv method perturbed initial conditions ensemble forecasts nonorthogonalised chaotic nature of atmospheric dynamics numerical weather prediction systems svs orthogonal set of initial perturbations ecmwf ifsmodel empirical orthogonal functions eof of the subspace

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