多流向與單流向法集流面積估算結果之空間分佈特性

Spatial Characteristics of Contributing Area Calculated by Multiple Flow Direction and Single Flow Direction Methods

黃誌川(Jr-Chuan, Huang) ； 徐美玲(Mei-Ling, Hsu) ； 楊奕岑(Yi-Chen, Yang)

《中華水土保持學報》 33卷1期 (2002/03) Pp. 57-68

https://doi.org/10.29417/JCSWC.200203_33(1).0007

摘要

一般而言，利用DEMs析取集流面積的水流演算法主要分成兩類：一是單流向（single flow direction）作法，其乃以3×3的網格視窗中，外緣八格中的最低網格點爲中心網格點水流的去向；另一是多流向（multiple flow direction）作法，該方法視高度低於中心網格之所有鄰近網格皆會接收水流，而依地勢坡度分配水量；由於演算法的不同，兩種方法所析取的集水面積（contributing area）和集水區邊界也不盡相同。以往的研究多著重在水系空間型態的剖析（Band，1986；Galland，1996），甚少觸及集流面積與集流邊界的探討，本研究擬針對正、反半圓形理想曲面的網格地形模型，在不同的網格解析度下，分析和比對單流向和多流向演算法的所得結果，並與利用數學所得結果進行比較，以評估其正確性。結果顯示，單流向所析取的集流面積值在凸球面受方向性控制，而多流向則較爲穩定；在凹球面部分，單流向法在求算北北東和東北東方向的集流面積值有明顯的低估現象，肇因於單流向法的演算無法散留所造成。此外，在集水區邊界部分，多流向法會因爲球面無明顯的稜線導致邊界計算時有較爲嚴重的錯估現象，至於在自然地表時所可能造成的影響則仍須進一步評估。

關鍵字

集水面積 ； 數值地形模型 ； 單流向法 ； 多流向法

並列摘要

There are two categories of flow routing algorithms used in digital elevation models. One is the single flow direction method. Where water from the center of a 3 x 3 grid cell window is allocated to the lowest neighboring grid. The other is the multiple flow direction method where all the neighboring grids which are lower than the center grid will receive water from the center grid, and the amount of water is dependent on the relative slope gradients among them. The contributing area and watershed boundary derived from different routing algorithms were found to differ. However, most of the previous studies emphasized on comparing the drainage patterns resulted from different algorithms, and neglected the problems of watershed delineation. This study aims to simulate the flow on ideal dome-shaped and bowl-shaped digital elevation models of various resolutions, in order to examine the effects of the two routing algorithms on contributing area calculation and watershed delineation. The results show that the contributing area derived from the multiple flow direction is more stable than that from the single flow direction. The orientation conducts the major errant estimation in the single flow direction resulting in the artificially parallel drainage pattern. In the bowl-shaped situation, the values of the contributing area from the single flow direction overestimate in north-north-east and east-north-east direction. On the other hand, in the dome-shaped situation, the multiple flow direction method cannot delineate the boundary of watershed because an ideal dome has no marked divides. This phenomenon should be evaluated and tested on the earth surface.

並列關鍵字

contributing area ； digital elevation model ； single flow direction ； multiple flow direction