豪雨誘發山崩之研究中，降雨量為相當重要的促崩因子。欲得知空間中任一點的降雨量最直接的方法即為從雨量站觀測求得。惟架設較密的雨量站須耗費大量金錢和人力資源，所以為求得規則網格點雨量值，曾有許多不同的內插方法被用來推估降雨量的空間分佈。本研究使用迴歸克利金（regression kriging，RK），並與其他既有內插方法互相比較，以瞭解新方法之有效性。 本研究以2005年馬莎颱風事件為例，收集水利署及氣象局在馬莎颱風期間之雨量站資料，經檢視與校正後將資料按測站整理成最大時雨量以及總雨量，再進行石門水庫集水區降雨量空間推估。研究中分別以單變量的距離平方反比法與克利金法，以及結合數值高程模型的RK_1D、RK_trend兩種多變量地質統計方法進行降雨空間內插。RK_1D係使用降雨量與高程的一維線性迴歸式做為推估降雨量的趨勢，但台灣地區降雨量與高程之相關係數偏低（0.26），故加入高程值進行推估未能有效改善降雨量分佈推估。為改善此問題，RK_trend使用雨量站座標及高程值擬合出降雨量之超曲面，進行分析後發現其推估結果較其他方法更能表現出細微的空間降雨量分佈，且其估計誤差也較小，表示RK_trend的推估結果較佳。 本研究並針對四種不同內插方法分別進行交叉驗證，結果證實各種地質統計方法的估計誤差值確實具有可信度，尤以最大時雨量的驗證結果為然。雖然以克利金所得的交叉驗證結果整體誤差最小，但詳細探討後發現若兩鄰近雨量站的高程與降雨量相近時，RK_trend的交叉驗證所得真實誤差最小，較無偏估的現象。In storm-induced landslide study, rainfall capacity is an important triggering factor. A direct way to know rainfall value at any point in the study area is interpolation from the rainfall observation gauges. Because the density of gauge stations is commonly inadequate, many different interpolation methods were used for estimate the spatial distribution of rainfall. In this study, we test regression kriging (RK), and compare the effectiveness of this new method with other existing interpolation methods. In this study, we collect rainfall data during the typhoon Matsa from the Water Resources Agency, Taiwan and from the Central Weather Bureau, Taiwan. These data were visually examined and errors were fixed. Good quality data were processed to extract total rainfall and maximum hourly rainfall values. Inverse square distance method and kriging method were used for comparison with two multivariate geostatistical algorithms: RK_1D and RK_trend. RK system uses the rainfall value as primary variable and the elevation as auxiliary variable. Because the rainfall values and the elevations have a correlation coefficient only about 0.26, the auxiliary variable cannot effectively improve the rainfall estimation in RK_1D. To solve this problem, we tested RK_trend. A hypersurface which incorporates locations (x, y) and elevation (z) was used to describe the drift of rainfall values. The results find that the RK_trend method shows better rainfall spatial distribution and smaller estimation errors than that of other methods. The performances of the four interpolators were further examined by cross-validation method. Results confirm that the errors estimated from various geostatistical methods do have reliability, especially for the maximum hourly rainfall case. Although cross-validation result indicates kriging method provides the smallest mean absolute error, however when two rain gauge stations are close, and the rainfall values as well as the elevations are similar, RK_trend method provides the smallest mean absolute error and indicates less bias.
