崩塌密度表示一地區的崩塌面積相對總面積的比例，是在研究崩塌的發生特性及其影響因子或分析山崩潛感時的重要指標。然而崩塌密度會因為選取的範圍大小而有差異，甚至沒有代表性。因此本研究嘗試分析有效代表研究區崩塌密度特性的取樣範圍。
2009年極端降雨事件-莫拉克颱風，在台灣南部高屏溪流域造成大範圍崩塌，因此有足夠的大尺寸的取樣樣本，適合用來分析尺度。本研究採用事件前後的福衛二號衛星影像所判釋的崩塌分佈資料，與QPESUMS雷達估計雨量，來分析不同尺度下的降雨與崩塌密度的Pearson積差相關。若尺度過大或過小，都會使相關性降低，這意謂著最高相關性可用來指示最適尺度。
研究結果顯示，降雨觸發崩塌的最適尺度，在旗山溪集水區是直徑6公里，在荖濃溪集水區是直徑10公里，在板岩區則為直徑12公里；若尺度選取範圍分別小於最適尺度，其選取範圍內的崩塌密度等特徵代表性不足，若大於最適尺度，則其選取範圍內的雨量及崩塌密度等特徵會被均化，因而降低其相關性。另外以莫拉克颱風為例，雨量因子以連續12小時累積雨量的最大值為觸發崩塌的最適時間長度；但在板岩區則為連續48小時累積雨量的最大值，這可能是因為岩性差異所致。

Landslide density is used to describe the ratio of the landslide area to total area in studying the characteristics of landslide occurrences, the causes of landslide occurrences, and the landslide susceptibility analysis. However, the landslide density may vary much because of the different dimensions selected. In this study, we try to analyze the optimal dimensions which landslide density can be representative effectively.

The Typhoon Morakot brought extreme rainfall and caused thousands of landslides across quite large areas in southern Taiwan. Therefore, it’s a good opportunity to study the scales for landslides. We use the images from FORMOSA-2 and estimation rainfall data from QPESUMS (quantitative precipitation estimation and segregation using multiple sensors) system during Morakot typhoon. As for the method, the Pearson’s correlation coefficient is used to analyze the association between rainfall and landslide density at different scales. The correlation coefficient is found to diminish when the scales is too large or too small, indicating that an optimal scale is necessary for studying the landslides.

The results indicated that the optimal scale to analyze the rainfall-triggered landslides is 6 kilometer diameter scale at Chi-Shan River watershed, 10 kilometer diameter scale at Laonong River watershed, and 12 kilometer diameter scale at slate region. When the selected dimensions smaller than the optimal dimension, the characteristics of landslides can’t be representative. While the selected dimensions larger than the optimal ones, the variability of characteristics of landslides are obscured by average. The analysis of Morokot typhoon event showed that the maximum 12-hour rolling rainfall is the optimal time length to study the rainfall-triggered landslides. However, for slate region, the optimal time length is the maximum 48-hour rolling rainfall. The difference in result could be resulted from the difference in lithology.

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