以碎形為基礎的臺灣地形分區

Geomorphological Provinces of Taiwan Based on Fractal Model

陳彥傑(Yen-Chieh Chen) ； 宋國城(Quo-Cheng Sung)

《環境與世界》 3期 (1999/11) Pp. 1-15

https://doi.org/10.6304/EAW.1999.3.1

摘要

近年來以地形碎形維度描述地表幾何特性的研究發展迅速，已有研究指出許多地形的碎形參數，例如：碎形維度值(D(下標 surf))、變異曲線的截距值(r)與碎形玫瑰圖上各方向碎形維度值的異向性(Anisotropy)等可以反應出“岩性”與“構造”等地質特徵。(D(下標 aurf))值與地表粗糙度有關，反應岩層的抗蝕能力，r值與地形起伏度指標成正相關，而Anisotropy值則主要反應地形面受構造線影響的程度。本研究即是以變異曲線法(Variogram Method)分析全台灣數值地形模型(DTM)，並嘗試利用分析所得之上述三個碎形參數為分區依據，配合統計學群集分析中的K均值法(K-means Clustering)，初步將台灣分成九個地形區。如此分出的地形區雖不能有較完整的封閉區塊，但卻有精確的大地座標與嚴謹的數據依據，在未來許多相關的地形、地理研究中，這些數據便可直接提供給地理資訊系統(GIS)使用。
分析這九個地形區的空間分布與統計數據可獲得下列幾項結論：
1.A、B、C區相當於等高線500m以上的山地地區；D區大致為丘陵地區；E、F區屬於丘陵與平原區的交界；G、H、I區屬於地勢較低的盆地、沖積平原及離岸沙洲地區。
2.r值在山地區部分較大，漸往平原區而漸小；(D(下標 surf))值在山地區部分較小，漸往平原區而增大。而麓山帶則可能由於局部地區分布著許多重要的新期構造線（如活動斷層等），造成部分空間單位呈現強烈的異向性。由A至I區，地表的形貌由坡度大但較平滑漸變至坡度小但較崎嶇。

關鍵字

地形分區 ； 碎形模式 ； 變異曲線法 ； K均值群集分析 ； 連續亂數加點模擬

並列摘要

The use of fractal geometry to describe the nature of landscapes is now a growing field of research. The fractal parameters, including the surfaces fractal dimension (D(subscript surf)), the gamma (r), and the anisotropy of the angular fractal dimension, can reflect the lithologic variations and major structural trend of the landscape. The surfaces fractal dimension is correlated with surface roughness that reflects differential resistance of different types of rock to erosion. The gamma value has positive relation to the relief, and the anisotropy indicates the structural trend of a landscape. The directional variogram method is applied to analyze the digital elevation model of Taiwan to acquire the fractal parameters in a grid size of 1.28km×1.28km. Nine geomorphological provinces of the entire island are classified based on the above-mentioned fractal parameters using K-means clustering method. Although each classified province may not have a closed region as shown in the conventional geornorphological maps, the grid-based geomorphological province renders itself to be integrated in Geographical Information System.
The geoniorphological provinces of Taiwan based on the fractal model have the following characteristics:
1. A, B and C are the mountainous provinces with elevation higher than 500m; D is the hilly province; E and F are the transitional provinces between the hilly and the plain; G, H and I provinces consist of basins, alluvial plains and coastal zones.
2. The mountainous provinces have smaller D(subscript surf) and larger r than the alluvial plains. The hilly and transitional provinces have strongly structural trend probably due to neo-tectonic activities.
As a whole, the landscape changes from a smooth but sloping surface to a rough but gentle surface as one goes from the province A through province I.

並列關鍵字

geomorphological provinces ； fractal model ； variogram method ； K-means clustering ； and successive random addition simulation