於2017年6月1日至2日，在八小時內梅雨鋒面為台灣北部帶來超過600毫米的累積雨量。與此同時，系集降雨預報在此區域有極大不確定性。因此，為了瞭解影響此區域降水預報的初始擾動分布，我們採用系集奇異向量（ESV）進行敏感度分析，並將校驗區域與時間選擇於6月2日00 UTC的北部沿海區域。根據初始奇異向量結果，於6月1日12 UTC中國東南沿海的梅雨鋒面附近，沿鋒面的風切會影響在12小時後在台灣北部地區東北風與低層噴流的關係，並進一步導致鋒面位置與走向的差異。 為了進一步驗證，我們將系集以初始奇異向量進擾動並預報，結果顯示12小時預報的差異與最終奇異向量（FESV）吻合，並且當進行正負向擾動時，分別可以有效使雨帶靠近以及遠離台灣北部。然而，當使用較大校驗區域時，由於樣本誤差以及模式非線性的發展，會使FESV與擾動預報的結果有所差異。
因此，我們嘗試建立局地系集奇異向量方法，針對相同的校驗區域逐個計算每個小區域的初始敏感度。整體來說，在這個案中局地與全域奇異向量法結果相近，但可有效減少模糊的訊號，且擾動預報上仍能有效改變降雨的分布。簡而言之，局地奇異向量法可正確地找出初始敏感度的分布，並且兩種方法皆可有效與系集預報結合並且幫助局地分析。

The ensemble forecast for the heavy rainfall event on 2nd June 2017 which precipitated over 600 mm during 8 hours is found to have large uncertainty over northern Taiwan. To investigate the distribution of fast-growing initial perturbations that affect the rainfall distribution, the ensemble singular vector (ESV) sensitivity analysis is conducted, and the verification region is defined along the northern coast of Taiwan at 060200 UTC. The fastest-growing mode represented by the initial ensemble singular vector (IESV) is defined as the wind shift line located near southeastern China offshore, which affects the interaction between the northeasterly and the low-level barrier-jet 12 hours later in northern Taiwan shown by the final ensemble singular vector (FESV). By comparing the unperturbed forecast with the ones perturbed by the IESV, the FESV agrees with the evolution of initial perturbations under the non-linear model dynamic to a great extent and causes variations in the position of the convection line, which allows the rain band being effectively moved close to and away from land with the positive and negative perturbed forecast, respectively. However, the ESV under a global perspective may be less robust when applied to complex mesoscale systems inside a broader final verification region with sampling error problems or strong model nonlinearity.
Therefore, we attempt to construct the local ESV which is computed sequentially redefining the initial domain with a local patch for each grid with the same final verification region. The local FESV can perform a similar sensitivity to global FESV but has IESV with a less ambiguous signal. The perturbed forecast from the local IESV also has a good agreement with the global FESV, which effectively adjusts the rainband as well. The local ESV provides a useful way to properly distribute initial sensitive perturbations. Finally, both global and local ESV has the potential to be incorporated with the ensemble forecast and local analysis framework.

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