以多變量地質統計方法進行雨量空間內插

Spatial Interpolating of Rainfall Using Multivariate Geostatistical approaches

張永欣(Yun-hsin Chang)

指導教授 ： 李錫堤

國立中央大學/地球科學學院/應用地質研究所/碩士(2007年)

摘要

豪雨誘發山崩的研究中，雨量為重要的促崩因子。由於雨量站的空間密度不足，導致雨量的內插結果無法反映真實情況。因此，推求準確的雨量空間分布是相當重要的課題。本研究以2004年艾利颱風事件為例進行石門水庫集水區雨量空間分布特性之分析，分別以單變量的距離平方反比法與克利金法，以及結合雷達回波使用聯合克利金法、Kriging with varying local means及Kriging with varying local means（trend）等多變量地質統計方法進行雨量空間內插，以改善雨量站密度不足的問題。
　　針對篩選過的艾利颱風雨量資料及雷達回波資料進行半變異圖分析，顯示雨量的影響範圍約43公里，雷達回波資料的影響範圍約35公里；對石門水庫集水區及其鄰近地區地表雨量站總雨量值與該點上方2000公尺高度的總雷達回波值進行迴歸分析，顯示兩者相關性甚高，R2可達0.7以上。
　　本研究並針對五種內插方法以研究區域內10個雨量站作總雨量的驗證，發現對全區而言Kriging with varying local means（trend）方法所得的整體誤差最小，距離平方反比法的誤差最大；聯合克利金法與Kriging with varying local means內插方法推估的雨量結果，能表現較細微的雨量空間分布。除了研究區南區缺乏雷達資料的區域外，對其餘地區而言使用聯合克利金法估計誤差明顯小於克利金法的估計誤差，顯示使用雷達回波資料做為輔助變數確實能改善空間內插之結果。

關鍵字

聯合克利金法 ； 克利金法 ； 雷達回波 ； 多變量地質統計學 ； 雨量內插 ； 距離平方反比法

並列摘要

How to estimate the spatial distribution of precipitation is a critical subject in the study of storm-induced landslides. Because the density of rain stations is not adequate, the estimated result can not reflect the real feature. This study presents characteristic of the rainfall spatial distribution of Typhoon Aere in the Shihmen Reservoir watershed by using two univariate techniques (inverse square distance method and kriging) and three multivariate geostatistical algorithms (cokriging, kriging with varying local means and kriging with varying local means(trend)). The multivariate geostatistics incorporate rainfall data and radar reflectivity data in the interpolation.
　　The spatial variability of rainfall and radar data, were processed by semivariogram analysis. It shows that the effective range of rainfall is 43 km and the effective range of radar reflectivity is 35 km. Rainfall and radar reflectivity data at the elevation 2000 m shows high correlation in the study area (R2>0.7).
　　The performances of the five interpolators were validated by comparing with data of each of the ten rain station in the Shihmen Reservoir watershed, when the target station is not included in the interpolation. For the entire watershed, Kriging with varying local means(trend) method provides the smallest mean absolute error, whereas the inverse square distance method provides the largest one. The estimated precipitation map by using cokriging and krigng with varying local means show more detailed spatial variation of precipitation. For the area, besides the southern area where lack of radar reflectivity data, the estimated error is smaller by using cokriging method than by kriging apparently. It appears that radar reflectivity data could offer more detailed rainfall variability, and should be a good auxiliary variable for rainfall interpolation.

並列關鍵字

rainfall ； Kriging with varying local means ； inverse square distance method ； interpolation ； radar reflectivity ； cokriging ； kriging ； multivariate geostatistics

參考文獻

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