第五章 結論與建議
5.2 建議
(1) 本論文在計算坡度上假設 DEM 誤差之空間變異性具有指數型態之共變異函 數，而依據現地狀況之不同應考慮假設之合適性，後續可進一步探討共變異 函數為其他型態時之影響。
(2) 於不確定性分析時，輸入參數之機率密度函數假設為常態、均勻或對數常態，
現實中參數機率密度函數型態可能與假設不同，當應用到其他區域時模擬結 果也會有所差異，故往後可致力於參數之收集調查，以期能獲得更加確切之 參數機率密度函數，使模擬結果更加準確。
(3) 本論文點估計法係假設模式輸出 FS 值具有常態分佈，進而以模式輸出前二 階動差求得崩塌機率，未來可以 FS 前三、四階動差求取 FS 實際機率密度函 數並計算崩塌機率。
(4) 本論文於不確定性分析時，不考慮降雨量(或降雨強度)之不確定性，而採用
實際颱洪事件進行分析，未來可以設計不同的雨型進行分析，亦可由分析結 果求取臨界雨量，作為相關單位之決策參考。
(5) 未來可以不同之不確定性分析方法計算安全係數之統計特性，例如改良一階 二次矩法(Advanced first-order second-moment method)，並比較其應用於降雨 引發坡地淺崩塌模式之適用性。
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附錄A ArcGIS軟體內建坡度計算方法
坡度是指一段距離內的高差起伏程度。坡度可用角度或百分比來表示，如下 圖所示，圖中 run 表示水平距離，rise 表示垂直距離。
坡度計算公式以角度表示如下：
29578 . 57 ) ) / ( ) / (
( 2
2
ATAN dz dx dz dy
slope
(A-1)ArcGIS 所分析的坡度為網格式高程資料，單一網格坡度計算頇考慮鄰近網格的高 程變化，下圖為一個 3×3 的網格資料：
中心網格 e 在 xy 方向的高程變化率可表示如下：
(c 2f i)-(a 2d g)
/ (8 x_cellsiz e)=
(dz/dx)
(A-2)
(g 2h i)-(a 2b c)
/ (8 y_cellsiz e)=
(dz/dy)
(A-3) 式 A-2 與式 A-3 代入式 A-1 即可求得坡度值。References：Burrough, PA and McDonell, RA, 1998. Principles of Geographical Information Systems (Oxford University Press, New York), p. 190。
附錄B 正交轉換
利用轉換矩陣 T(transformation matrix)，將具相關性之標準變數 X’轉為無相
相關係數對稱且正定(positive definite)，利用 cholesky decomposition method 及特徵拆解法(eigenvector decomposition)將 Rx進行拆解：
t
2 /
1
V
T (B-11)
藉由式(B-3)可整理得：
Y V TY
X 1/2 (B-12) 因此轉換矩陣可寫成：
Y V
X
x
x 1/2 (B-13) 式(B-13)為具相關性統計變數與無相關性統計變數之轉換式。附錄C 坡度與土壤厚度迴歸式
陳本康(2005)依據現場量測資料提出之坡度與崩塌深度迴歸公式如下：
6563 . 5 0716
.
0
dLZ (C-1) 式中 dLZ為崩塌深度，即土壤厚度；α 為坡度。
由圖 C.1 可發現實際量測資料與線性迴歸式間具有迴歸誤差。如圖 C.2 迴歸 誤差經測詴後發現其呈常態分佈，平均值與標準差分別為 0 與 0.3076。由圖 C.3 可以發現誤差項與坡度或土壤厚度互為獨立，綜合上述討論，迴歸式可改寫如下：
d
dLZ 0.07165.6563 ；
d ~N(0,0.30762) (C-2) 式中 dLZ為崩塌深度，即土壤厚度；α 為坡度；εd為常態分佈之隨機誤差項。圖 C.1 坡度與崩塌深度現場量測資料
y = -0.0716x + 5.6563 R² = 0.9371
0 1 2 3 4 5
10 20 30 40 50 60 70 80
崩塌深度(m)
坡度 (°)
圖 C.2 誤差項常態測詴圖
圖 C.3 散佈圖