因真實大氣系統的自由度遠大於業務預報上所使用的系集成員數，抽樣誤差與過小的系集離散度限制了系集預報與資料同化系統的表現。而增加系集數需要耗費大量的計算資源，在有限的計算資源中較不易達成。故如何在有限的系集數中，維持合理且足夠的系集離散度，在系集同化與預報的研究中是極具挑戰性的問題。 本篇研究的目的希望在資料同化前，加入新擾動方向至原有的系集當中，藉此讓系集能夠掌握到更多預報誤差的方向，改善分析場以及後續預報。本研究使用Centered Spherical Simplex ensemble法以保持系集平均以及系集離散度不變，並避免背景誤差協方差反矩陣ill-condition的問題，還可以節省計算資源。而實驗中使用三種方法產生新向量，第一種是利用奇異值分解(Singular eigenvalue decomposition, SVD)所產生的null space的奇異向量作為正交向量，第二種則為利用初始系集奇異向量(Initial ensemble singular vector, IESV)與系集空間垂直的部分作為正交向量。最後一種向量則是以系集平均作為新向量，加入到原有系集當中。透過Offline測試與Online同化測試，觀察加入正交向量與系集平均後，新的系集在分析場與後續預報的表現。 實驗結果顯示，加入兩種正交向量與系集平均方向後，分析誤差在不穩定地區以及系集擾動成長最快的地區有所改善，特別是在原本系集無法掌握預報誤差方向的資料同化循環時間，分析誤差的改善更為顯著，而對於整個模式範圍的預報場也有顯著的改善。研究結果顯示，當系集空間受限於樣本誤差，導致無法提供正確預報誤差的資訊時，這三種方法都可以強化系集結構並改善預報表現。;Finite ensemble size cause ensembles underestimate the uncertainty in numerical weather prediction, resulting in under-dispersive ensemble spread and degrading the performance of ensemble forecast/data assimilation. However, increasing ensemble sizes requires large computational costs, which is difficult to achieve in limited computational resources. Therefore, how to maintain reasonable and sufficient ensemble spread in a limited ensemble size is a challenging question in the research of ensemble based forecast/data assimilation. The purpose of this study is adding new perturbation vectors to the original ensemble, so that the ensemble can capture more directions of the forecast error to improve the analysis state and forecasting. The method of adding the new perturbation vector is to use Centered Spherical Simplex ensemble, which can keep the ensemble mean and ensemble spread same as the original ensemble. Therefore, this study uses three methods to create new perturbation vectors. The first method is to use Singular eigenvalue decomposition (SVD) to find the orthogonal vector. The second method is to use the Initial ensemble singular vector (IESV) to find the vertical direction of the ensemble space and the third method new direction is ensemble mean. By using the Offline test and the Online test observe the performance of the new ensemble in the analysis state and forecasting after adding the orthogonal vector and the direction of ensemble mean. The experimental results show that after adding the orthogonal vectors and ensemble mean the analysis error has improved in the unstable areas and areas where the ensemble perturbation have been growing fastest. Especially in the data assimilation cycle where the original ensemble space was unable to capture the direction of forecast error and also improvement the performance of analysis state and forecasting for whole model’s domain. The results show that when the ensemble space is constrained by the sample error, which cannot provide accurate forecast error information, these three methods can strengthen the ensemble space structure and improve the performance of the forecast.
