Ensemble Singular Vector in the Ensemble Kalman Filter and Its Application to Typhoon Assimilation and Prediction

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 andforecast interval, will maximize the growth of the perturbations. Because the ESV indicates thedirections of the fastest growing forecast errors, we explore the potential of applying the ESV inEnsemble Kalman Filter (EnKF) for correcting fast growing errors.In the first stage of this project (MOST-104-2111-M-008 -011), ESV has been implemented under theframework of WRF-LETKF. By choosing a perturbation norm related to typhoon development, thetyphoon-associated ESVs are constructed. In MOST-104-2111-M-008 -011, we first confirm that thesetyphoon-associated ESVs are strongly flow-dependent and have positive impact when they wereapplied to the ensemble forecasting for track prediction. In the next stage, we propose to examine thecharacteristic of the typhoon-associated ESV and investigate the relationship between ESVs andforecast errors. In addition, ESVs will be applied as the additive covariance inflation for augmenting theflow-dependent background error covariance in the WRF-LETKF system. We will also investigate thesensitivity of ESVs to the perturbation norms and optimization periods.