Ensemble Singular Vectors and their use as additive inflation in EnKF

Given an ensemble of forecasts, it is possible to determine the leading ensemble singular vector (ESV), i.e., a linear combination of the forecasts that, given the choice of the perturbation norm and forecast interval, will maximize the growth of the perturbations. Because the ESV indicates the directions of the fastest growing forecast errors, we explore the potential of applying the ESV in Ensemble Kalman Filter (EnKF) for correcting fast growing errors. The ESVs are derived based on a quasi-geostrophic multi-level channel model and data assimilation experiments are carried out under framework of the Local Ensemble Transform Kalman Filter (LETKF). We confirm that even during the early spin-up starting with random initial conditions, the final ESVs with a 12-h forecast window are strongly related to the background errors. The initial ESV is applied in the EnKF framework for constructing the flow-dependent additive perturbations to inflate the analysis ensemble. Compared with random perturbations as the additive inflation, positive impact from using ESVs is particularly found in the areas with large growing errors. When an EnKF is “cold-started” from random perturbations and poor initial condition, results also suggests that the ESV as the additive inflation has the advantage of correcting the fast growing errors so that the EnKF's spin-up can be accelerated.