考量降雨及地文特性之集水區稽延時間公式推估

Abstract

在台灣以往稽延時間大多採用民國六十至七十年代所推導之公式推求之，然而隨著地形改變及像莫拉克颱風此類的極端降雨事件之發生，造成集水區降雨及地文特性具有明顯的改變，進而影響了現行稽延時間公式之適用性及準確性。因此如何考量降雨及地文特性之不確定性藉以修正稽延時間公式，為目前水文分析中之重要的課題。 本研究主要推導稽延時間與不確定性因子之相關式，其中將影響稽延時因之不確定因子區分為降雨、水理及地文因子三類型。降雨因子主要包括降雨特性(降雨延時、降雨量及雨型)，水理因子為河道曼寧n值及地文因子為集水區面積、河道流長、河道坡度。稽延時間公式推導步驟主要為首先蒐集研究區域內降雨事件特性且分析其統計特性，再配合降雨特性模擬機制衍生多場降雨事件，並輸入SOBEK水理模式推得各水位站水位歷線，且根據定義(最大降雨強度到達水位最高之時間間距)找出稽延時間。最後採用多變量迴歸分析推得稽延時間與不確定因子相關式。 本研究選用八掌溪流域為應用案例，蒐集流域內各雨量站2004-2013年5場降雨事件及各水位站上游子集水區內地文特性以建置其稽延時間相關式。由本研究可推知八掌溪流域各水位站（觸口站、軍輝站、八掌溪橋站、汫水港橋站、常盤橋站及頭前溪橋站）之稽延時間平均值分別為1.05、1.68、3.07、5.02、1.74、及1.71hr，也就是平均來說稽延時間隨水位站位置由上游至下游遞增。此外，本研究亦採用其他五場颱洪事件降雨及水位資料進行公式驗證，並與治理規劃報告中之傳統公式做比較。由驗證可發現本研究所得稽延時間相關式與傳統公式推估結果與觀測值之誤差平均值分為0.5hr及2.5hr，顯示本研究所推得稽延時間公式不僅可適用於不同降雨事件於八掌溪流域各水位站所造成洪峰稽延時間之推估，且其更優於傳統公式推估結果。綜合上述可知，本研究所提供的稽延時間相關式不僅能夠使相關水文分析結果更為準確，並且未來可搭配警戒水位以或警戒雨量以提供更可靠之防洪預警資訊。

In Taiwan, the formulas for estimating the lag time have been derived in 1970s and 1980s. However, due to the change in the topography and extreme storm events, such as Typhoon Markot, the rainfall and geographical characteristics in the watershed are significantly changed, so as to influence the applicability and validity of the early developed lag-time equations. Therefore, it is an important issue to revisit the lag-time formulas under the consideration of the aforementioned rainfall and geographical characteristics This study aims at developing a relationship of the lag time with the uncertainty factors, including the rainfall, hydraulic and geographical factors. The rainfall factors include the duration, depth and storm pattern of the rainstorm event. The roughness coefficient (i.e. the Manning coefficient) in the river serves as the hydraulic factor, and the area of watershed, the length and slope of the river are defined as the geographic factors. The framework of developing the lag-time estimation equation in the study involves into four steps: (1) the generation of rainstorm events; (2) the estimation of the water level by means of the hydraulic routing model (i.e. SOBEK 1D-2D model); (3) the determination of the lag time based on the associated definition; and (4) the derivation of the lag-time equation by using the multivariate regression analysis. The Bachang river watershed is chosen as the study area, and corresponding rainfall data of five storm events recorded in 2004-2013 are used in the development of lag-time equation. The results from the model development indicate the average lag times at the water-levels gauges from upstream to downstream (i.e., Chukou station, Jiunhuei station, Bachang river bridge station, Jingshueigang station, Changpan bridge station, Touchain river bridge station) are 1.05 hr, 1.68 hr, 3.07 hr, 5.02 hr, 1.74 hr and 1.71hr, respectively. This reveals that, on average, the lag time clearly increases with the distance of the gauge from the upstream. To verify the proposed lag-time equation, additional five storm events are used to estimate the lag-time values. These estimated lag-time values could be compared with those calculated using the conventional formulas on the basis of the observed values extracted in accordance with two definitions. It is found that the difference of the lag time estimated by the proposed formula from the observed values is about 0.5 hr which is superior to the result from the conventional formula (about 2.5 hr). That is, the proposed formula can be applied to the estimation of the lag-time attributed to storm events of interest at various stream flow gauges in Bachang river watershed. In summary, the proposed lag-time formula not only facilitates the accuracy of the relevant hydrologic analysis, but also provides more reliable information for the flood warning and prevention by incorporating with the warning stages and rainfalls.