地形複雜度是一個抽象的概念，用以描述地形變化的整體趨勢，可以使用不同的量度指標來描述地形起伏的崎嶇特性。張石角（1987）提出的「簡確工程地質災害調查與評估法」在評估動態因子蝕溝時，係依照等高線的彎曲度分成無蝕溝、小蝕溝、中蝕溝與大蝕溝四個級序。簡確法中的蝕溝等級之判定方式，係依照等高線彎曲的角度，這種判定方式也是一種等高線地形圖概括化的過程，要連結真實地表的複雜現象以及概括化的等級判定方式，可用碎形的概念表示地表的起伏崎嶇程度。等高線的彎曲角度是一種幾何型態量度，本研究使用統計型態量度的方式，以蝕溝規模所呈現的地形複雜度為量度的對象，探討等高線彎曲度所對應的地形參數。
本研究以4公尺解析度的規則網格之數值高度模型（Digital Elevation Model, DEM）為量度的資料，並找出地形崎嶇度以及起伏度的組合，量度蝕溝等級所對應的地形複雜度。引用碎形分析方式中的空間自相關統計概念，探討DEM之高程變化的空間分布特性與傳統等高線地形圖中所呈現地形起伏資訊之異同。
本研究發現，利用變異元法求得的碎形參數可以確定碎形截距與地形起伏度有關、碎形維度與地形崎嶇度有關、最大碎形維度值的方向與單元區的最大坡度方向相似，可以偵測出最大地形侵蝕方向，據此得到最大碎形維度方向的碎形截距值與最大碎形維度之比值作為量度蝕溝等級的指標。在影響地形複雜度量度的因子中，碎形參數值與單元區的蝕溝頻率以及坡度成正比。此外，由同一個資料解析度、同一個量度視窗（單元區）大小與同一個計算方法所產生的碎形參數值可以納入判釋地形複雜度的函式庫，比較其地形侵蝕程度的高低，並可以應用在自動產生坡單元的研究上。

Information extracted from grid-based digital elevation model (DEM) can be used in terrain classification and applied in geomorphological studies (Evans, 1972; Wood, 1996). The terrain characteristics can be interpreted in three models, the statistical model, the geometrical model, and the verbal model. Recently, the statistical model is frequently to design the terrain complexity indicator which can be represented by the gully scale, and traditionally is measured manually by the curvature of the contours. In the heavier slopeland, the higher terrain complexity indicator is, the higher potential soil erosion can also be. Therefore, the terrain complexity indicator can be used as one of the major parameters to evaluate the potential geological hazards for the landuse management purposes. In order to measure the terrain complexity automatically and objectively, a geostatistical method needed to be proposed for analyzing gully scale based on DEM.
In the research, the fractal dimension and association parameters were selected as the measure of terrain complexity, obtained from variogram analysis. The general method used in the variogram analysis was to calculate the fractal dimension (D) and the log-log plot ordinate intercept (γ), which is in the length of the regression line with a correlation greater than 0.99. Then, the ratio of D and γ was designed to measure the classification of the gully scale. The ratio is proposed as the measure for classifying the terrain complexity. The Keelung City in Taiwan is selected as the study site in the research. There are two types of data acquired from the Keelung City Government. One is the 1:5,000-scale contour map, and the other type of data is the 4-meter resolution DEM. The DEM in 32×32 window size unit is analyzed with the variogram to measure the terrain complexity. The coefficients of the models were used to fit the four types of variogram plots, which represent the terrain characteristics of the gully scale.
The new measure for complexity fitting the gully scale classification was quite well. Moreover, the D can successfully represents the terrain roughness, and the vertical variability of the regression line (γ) was proof to represents the terrain relief. The fractal parameters provide adequate results to characterize the gully scale. Therefore, this new measure of terrain complexity should be further used in a terrain evaluation with success.

第壹章 緒論 ……………………………..…………………………… 1
第一節 前言 …………………………….……….…………...…… 1
第二節 研究動機與目的 ……………….……..……………….… 3
第三節 研究定位與範疇 ……………………………….……...… 4
第貳章 文獻回顧 ……………………….……………………………. 7
第一節 地形複雜度 …………………….……………….……….. 8
一、 地形崎嶇度 ……………………………………………. 8
二、 地形起伏度 …………………………………………... 10
第二節 簡確法之蝕溝等級定義 ……….…..……………..….. 10
一、 蝕溝之定義 …………………………………………... 10
二、 簡確法之土地單元 ………………………………….. 11
三、 蝕溝的量度方式 ……………………………………. 13
第三節 地形表面參數 ……………….……………………….… 14
一、 數值地形的簡介 ……………………………………... 14
二、 型態式參數 ………………………………………….. 17
三、 尺度的重要性 ……………………………………….. 27
四、 地形參數的空間關聯性 ……………………………. 29
第四節 碎形參數 ………………………………………………... 35
一、 碎形特性 ……………………..……………………..… 35
二、 DEM之碎形維度計算方法的比較 ……………..… 35
三、 碎形參數與傳統地形參數之間的關係 …………... 40
第參章 研究方法 ……………………………………………………. 45
第一節 研究架構 ……………………………………………….. 45
第二節 研究內容及流程 ………………...………………..…… 46
第三節 地形複雜度實驗設計流程 …………………………... 49
一、 資料之使用－研究區與使用的資料 …………....… 51
二、 方法之採用－資料分析的工具 …………………... 52
三、 樣本之設定 …………………………………………. 53
第肆章 DEM地形複雜度量度分析 …………….……………… 59
第一節 數學模擬表面分析 ………………….…..………….. 60
第二節 真實地表蝕溝等級分析 ……………………..……… 68
第三節 分析結果討論 ………………………………………..… 72
一、 變異元法的計算特性 …………………………..…... 73
二、 碎形參數的特性 ……………………...……….…… 73
第伍章 結論與建議 ……………..……………………………….…. 75
第一節 結論 ……………………………………………………... 75
第二節 未來研究方向 ………………………………………….. 77
參考文獻 ……………………………………………………...………. 79
附錄 ………………………..………………………………….………. 87
附錄一：空間統計－變異元法 ……………………..…………. 87
附錄二：數值高度模型擷取河系集流域值之比較 ………… 90
附錄三：坡度<30%的各蝕溝等級之碎形玫瑰圖 ………… 103
附錄四：坡度>30%的各蝕溝等級之碎形參數值 ………… 108
附錄五：坡度>30%的各蝕溝等級之碎形玫瑰圖 ………..... 109

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黃金聰 1999 應用碎形維數為地理特徵物指標之研究，國立交通大學土木工程學研究所博士論文。
黃誌川、徐美玲 2001 以不同網格數值地形解析度和計算方法析取坡度之比較，中華水土保持學報，32（3）：199-205。
馮臻傑 1996 遙測影像分類誤差度量之研究，國立台灣大學地理學研究所碩士論文。
張石角 1987 簡確工程環境地質調查及評估法，行政院農委會。
張石角 1992 台灣各地質分區邊坡崩坍類型及其預測方法（一）：技術轉移講習班講義，行政院農委會：49-80。
趙培文 1995 台灣地形之碎形幾何特性與地形模擬，國立成功大學地球科學研究所碩士論文。
蔡宗勳 1994 數值高度模型之地形量度研究，國立台灣大學地理學研究所碩士論文。
賴進貴 1994 數值地形模型之比較研究，台灣大學地理學報，17：87-100。
賴進貴 1996 自動化地形計測之研究，行政院國科會專題研究計畫。
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