系集卡爾曼濾波器(EnKF)進行同化分析時，其同化的表現取決於準確的系集平均與合理的系集擾動結構這兩個因素。但因所使用的樣本數有限，而有低估或忽略擾動次成長特徵(sub-growing mode)的狀況，使系集預報無發揮應有優勢。本研究藉由在WRF-LETKF(Weather Research and Forecast-Local Ensemble Transform Kalman Filter)資料同化系統下進行觀測系統模擬實驗(OSSE)，探討由系集卡爾曼濾波器(EnKF)同化系統建立的系集奇異向量(ensemble singular vector)對於動力敏感度的代表性，及應用於系集預報系統的可行性。並藉由使用系集奇異向量擾動WRF-LETKF分析系集並進行系集預報，並從預報表現了解系集奇異向量對於改善系集結構的效益。
此研究主要分為兩個部分，針對颱風路徑進行系集預報實驗與敏感度測試。在OSSE實驗中，CTRL組為利用虛擬觀測建立之六小時同化分析場所進行之三天系集預報，其結果顯示分析時間離颱風轉向 (recurvateure) 期越遠的分析場，其預報路徑因初始場對副熱帶高壓附近的掌握度較差，呈現過度東偏的路徑誤差。本研究利用WRF-LETKF分析與6小時預報系集計算以颱風為目標之系集奇異向量，發現在副熱帶高壓前緣明顯的高值區域。再利用初始系集奇異向量擾動分析系集，再進行預報三天預報，其各組路徑預報誤差都有明顯的降低，且在副高位置的改善最明顯。
敏感度測試主要藉由改變改善系集奇異向量的計算設定，探討不同加入不同大小、不同正負值與不同範圍對於預報結果的影響。由系集預報的結果可知以系集奇異向量擾動系集時，加入分析系集標準差10%大小的擾動可以有效的改善颱風路徑預報，並確認不同正負號的系集奇異向量分別可造成副高位置的西伸與東退，因而進一步確認所得系集奇異向量在副高的動力敏感區具有代表性。最後，加入颱風周圍環境場為標靶區域會比只納入颱風所得的ESV結構對路徑誤差的改善較多。綜合各組結果可知系集奇異向量能有效調整分析系集的結構，並改善後續系集預報。

In ensemble Kalman filter (EnKF), a finite ensemble size may underestimate or ignore sub-growing mode in the original ensemble. The growing errors cannot be well captured and the performance of ensemble forecasting can be limited. Given that the ensemble singular vectors (ESVs) indicate a set of perturbation directions that will maximize the growth of the errors, we explore the potential of ESVs for improving the structures of ensemble perturbations and focus on the application to typhoon ensemble prediction. This study is carried out by conducting observing system simulation experiments (OSSEs) using the Weather Research and Forecasting model (WRF) and WRF-Local Ensemble Transform Kalman Filter (WRF-LETKF) data assimilation system.
In the OSSEs, the natural run is a WRF simulation that mimics the behavior of Typhoon Sinlaku (2008) and a 6-hr assimilation cycle is performed to generate the WRF-LETKF analysis ensemble. ESVs are derived by taking the analysis and background ensemble as the initial and final ensemble, respectively and targeting on the typhoon movement. Results show that the dominant ESV has large amplititude in the circulation of the typhoon and near the ridge of the subtropical high, indicating the dynamic sensitivities in this area. The dominant ESV is added to and subtracted from the analysis ensemble to generate a set of new initial ensemble. In comparison with the 3-day ensemble forecasts without using ESV, results show that the mean track error can be greatly reduced due to a better representation of the subtropical high and the improvement is particularly significant before typhoon recurves.
A series of sensitivity experiments are performed to investigate to optimize the strategy for calculating and using ESVs.It is found that a rescaling amplitude of an order of 10% of the analysis ensemble spread would be adequate for perturbating the initial ensemble. Also, the development of the subtropical high as a response of applying ESV with different signs suggests that the dynamical sensitivity area for this case is near subtropical high. At last, the targeting area for calculating the ESVs is important and the dynamical sensitivity in the typhoon environment is more critical than the circulation of typhoon. As a conclusion, without assimilating extra observations, the dominant Typhoon-targeted ESV is effective in adjusting the structure of ensemble perturbations for improiving typhoon track prediction.

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