應用多元方格網模式比較坡度計算法差異之研究

Applying a Multifactor Gridded Network Model to Compare the Difference of Gradient Calculating Techniques

邱景升(Ching-Sheng Chiu)

《地理學報》 51期 (2008/03) Pp. 47-63

https://doi.org/10.6161/jgs.2008.51.03

摘要

不管是利用等高線或數值地型模型資料，坡度計算方法大多以方格作爲計算單元。爲探討不同方格劃分方式對坡度計算結果的影響，本研究提出多元方格網模式，藉由變動方格大小(grid size)、原點位移(origin shift)及座標軸旋轉(axis rotation)來產生多種方格網，以探討不同變動因素對等高線方格交點法(8L)、三次非加權法(3X)及三次加權法(3W)在坡度計算穩定度與限制開發比例(ratio of restricted development, RRD)的影響。經於比例尺1:1,000實測地形圖測試結果顯示，方格大小、原點位移及座標軸旋轉等三項因素，均會影響前述三種坡度計算方法的計算結果。不管是8L、3X、或是3W法，當方格大小由50m遞減至5m時，較高坡度值的方格數逐漸變多，限制開發比例也隨之增加。就穩定度與限制開發比例而言，以8L法的穩定度最佳，限制開發比例也最高。由於變動座標軸旋轉因素所計算出的坡度值離散度過大，因此無明顯規則可推論各方法在計算限制開發比例上差異。坡度乃是評估坡地適不適合開發眾多因素中極重要的一項，然若僅依據坡度等級此項因素來判斷坡地適不適合開發，且審查的原則係希望盡量降低坡地可開發比例，則建議法規中僅納入8L法作爲坡度計算的方法，而3X法及3W法則不建議納入。其次，在方格網的劃分原則方面，建議於法規中僅允許變動原點位移，並且維持現行法規中方格大小必須小於25m此一規定來產生方格網，或是規定更小的方格，以提高限制開發比例。

關鍵字

方格網模式 ； 數值高程模型 ； 坡度

並列摘要

The grid is the basic unit for gradient estimation for both contour-line-base and DEM-base gradient calculating methods. To understand the impact of different gridded networks on computed gradient, the calculating stability and ratio of restricted development (RRD) of different gradient calculating techniques have been tested by the proposed multifactor gridded network model, which generates enormous types of gridded networks by altering grid size, origin shift, and axis rotation. Based on the test which utilizes a 1:1000 scale topographic map, it is found that the gradient estimated by contour-line-intersection (8L), third-order infinite difference (3X) and weighting third-order infinite difference (3W) is affected by grid size, origin shift, and axis rotation. The percentage of higher gradient and RRD increase as the grid size decreased from 50m to 5m. The test results show that the 8L method has the best calculating stability and highest RRD. Owing to the high variance of gradient determined by altering the axis rotation, there are no obvious clues to conclude the difference among gradient calculating techniques on the RRD. Since the gradient is one of the most important evaluation criteria for hillside land development, it is strongly recommended that only the 8L is suggested to be listed as the candidate techniques for calculating gradient in compliance with the regulation of hillside land development, if the gradient is the only evaluation criterion and if the policy for hillside land development tends to deflate. It is also worth to note that the way for generating grid networks only allows by altering the origin shift and the grid size lower than 25m, if the development goal is set to increase the RRD.

並列關鍵字

gridded network model ； DEM ； gradient/slope

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