颱風時期降雨所產生的大量地表逕流，往往造成下游人口稠密地區受到的洪水威脅，對於高降雨強度且集流時間短促的台灣，集水區降雨逕流的模擬，為往後水利工程建設、水理演算及洪水預報的基本要求。降雨的空間分佈為降雨逕流模擬必要的輸入條件，不同的降雨分佈會造成逕流結果有所不同，因此本研究欲透過逕流歷線結果，探討空間內插法之適用性。
研究區域為西部高屏溪及東部和平溪流域，以2010年凡那比、2012年泰利及2012年天秤颱風事件，作為高屏溪流域之研究案例；以2013年天兔及2010年凡那比颱風事件，作為和平溪流域之研究案例。本研究利用距離權重反比法、一般克利金法、最小曲率法、徐昇網法以及趨勢面分析法等五種空間內插法建置降雨分佈及歷程，結合地文性淹排水模式模擬演算水位站水位歷線，並與水位站水位觀測值做比較。
本研究使用四個統計誤差包括均方根誤差、平均絕對誤差、相關係數及峰值誤差，以量化水位模擬結果與觀測水位資料，五場颱風事件於各水位站誤差統計分析結果，方均根誤差及平均誤差均低於1公尺，而相關係數均在0.8以上，模擬與觀測水位結果大致相符。
降雨空間分佈取決於其不同之內插特性，對於大尺度的高屏流域，以趨勢面分析法產置的降雨分佈歷程，透過降雨逕流演算，模擬結果較佳；相較於局部地區的和平溪流域而言，則以一般克利金法較為適合。

The heavy rainfall of Typhoons usually causes nationwide floods, in turn, yielding huge loss of human lives and economics. Taiwan is located in the zone where active tropical cyclone frequently forms in the western Pacific Ocean, so rainfall intensity is typically high yet with very short the concentration time of flow. An accurate estimation of areal precipitation by interpolating point observations is essential to hydrological modeling for water resources planning. Various interpolation algorithms have been suggested for calculating areal precipitation from point measurements; however, the influence of interpolation algorithms on the prediction of river stage still remains unclear and thus has to be investigated in a more scientific way to compare with recorded stage measurements. Therefore, in the current study, five widely-applied interpolation methods, the Thiessen polygon method, the ordinary Kriging method, the spline surface method, the inverse distance weighted method, and the trend surface analysis method, were selected as illustrative examples to quantitatively investigate this impact. The rainfall-runoff simulation was implemented using the physiographic drainage-inundation (PHD) model. Two different-size watersheds which are respectively located in southwestern Taiwan (Gaoping creek watershed) and eastern (Hoping creek watershed) were selected. Three Typhoon events (Typhoon Fanapi, 2010; Typhoon Talim, 2012; Typhoon Tembin, 2012) were used for hydrological modeling in the former watershed; two Typhoon events (Typhoon Fanapi, 2010; Typhoon Usagi, 2013) were used for hydrological modeling in the latter watershed.
Four objective functions, root mean square error (RMSE), mean absolute error (MAE), correlation coefficient, and error rate of peak water level, were applied to evaluate the error in determining river stages. Our results reveal that all values of RMSE and MAE are below 1 meter and the value of R is above 0.8, indicating good agreement between simulated and observed stages. It is shown that the accuracy of hydrological modeling using different interpolation methods for estimating areal precipitation is significantly sensitive to watershed geological attributes. Among all interpolation, the trend surface analysis method provides the best interpolation in the greater watershed (Gaoping creek watershed) whereas the best one in the smaller watershed (Hoping creek watershed) is the ordinary Kriging method. Thus, an appropriate areal-precipitation interpolation technique is very crucial to obtain better rainfall-runoff simulation result.

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