以不同網格數值地形解析度和計算方法析取坡度之比較

A Comparison of Slope Gradients Derived by Different Methods and in various Resolutions

黃誌川(Jr-Chuan, Huang) ； 徐美玲(Mei Ling, Hsu)

《中華水土保持學報》 32卷3期 (2001/09) Pp. 199-205

https://doi.org/10.29417/JCSWC.200109_32(3).0004

摘要

要坡度的計算一直是水利工程、水土保持及地形學者所關心的重要課題，坡度乃地表面上坡降的程度，也間接代表位能轉換成動能的速率，常應用在水利演算、土壤沖蝕及崩塌地預測等領域。近年來隨著數值地形模型的發展及地理資訊系統功能的加強，許多坡度的計算方法相繼提出，因此瞭解不同演算法所計算的坡度與數值地形模型解析度之間的關係，以及傳統利用地形圖進行地勢分析所析取的坡度值與數值地形所擷取的坡度值兩者之間的差異，將有助於相關領域的應用。本研究採用平均變異，三次加權，框架有限差異和二次有限差異四種坡度計算方法，比較各種方法在不同解析度（5×5m、10×10m、20×20m、40×40m）下的穩定性，以林口的橫窠溪集水區為研究區，並與地勢分析後的結果作比較。結果顯示，坡度隨著解析度的降低而遞減一般而言，二次有限差異的坡度計算方法所得的結果穩定性較差;在緩坡處四種方法皆有高估的趨勢，地勢分析的結果似乎與三次加權法（解析度20×20m）所得的結果較為接近。

關鍵字

數值地形模型 ； 坡度 ； 地理資訊系統 ； 解析度 ； 地勢分析

並列摘要

Slope parameter is an important measure in hydraulic engineering, soil conservation and topographical evaluation. It is the gradient of surface and the ratio of momentum from potential. This parameter is wildly applied in several fields, such as flow routing, soil erosion and landslide analysis. With the progress of GIS(geographic information system) and DEM(digital elevation model), many methods calculating slope in DEM have been developed. Understanding the relationship between different methods and different resolutions, and also between the slope from map analysis and the slope extracting from DEM, will provide much benefit in related fields. The research compares four methods (average variance, 3rd order weighted, frame finite difference, 2^(nd)-order finite difference) in different resolutions (5×5m、10×10m、20×20m、40×40m) and evaluates their stability. The result shows that slope gradient is decreased with resolution and all methods might overestimate slope extracting from DEM in general slopes. Generally speaking, the stability of 2^(nd)-order finite difference is poorer than the others because of the weighting factors. The slope from terrain analysis is approximately equal to the result from DEM in 20×20m using 3^(rd)-order weighted method.

並列關鍵字

digital elevation model ； slope parameter ； GIS ； resolution ； terrain analysis