Hillslope process-response models based on the continuity equation M. J. Kirkby

目錄 介紹 模式架構 ◇連續方程式與運輸條件 ◇特徵形式 結論

介紹 本篇的研究目的是檢視一系列的邊坡過程發 展反應模式是否能合理應用，並具體說明實 地測量的經驗公式運用於斜坡過程模式。 連續性方程式是任何邊坡反應模式的基礎， 土石運輸速率是連續性方程的重要形式，該 研究的關鍵點是在地勢起伏的變化。

解連續性方程式除了關鍵的坡度和與流域 距離的變化量外，還需要其他條件： (1) 邊坡剖面的初始形態 (2) 邊界條件

(A) The continuity equation: M is the rate of mechanical lowering, D is the rate of chemical lowering, y is the elevation, t is time elapsed. 模式架構 ◇連續方程式與運輸條件

(B) The relationship between mechanical lowering and mechanical transport: indicates the vector divergence, S is the vector sediment transport.

(C) The relationship between rate of lowering and soil thickness: z is the soil depth W is the rate of lowering of the soil-bedrock interface

slope development

物理和化學的降低速率與岩石土壤界線的關 係式可表示如下： 土壤發育程度遠小於物理降低速率，因此本 文只考慮物理搬運能力與邊坡發展關係 μ 表示岩石不風化的比例

(D) The relationship between the rate of weathering, S, and the transporting capacity of the process, C. (i) Transport limited removal: C = S 堆積 (ii) Weathering limited removal: C>>S 沖刷 (iii) Erosion-limited removal:

(E) The boundary conditions. (i) At x=0, S=0 and y is a maximum (ii) At x=x 1, y is a function of time alone (x 1 fixed in horizontal position at distance) (F) The initial form will usually be taken to be a straight slope.

(G) The transport law or process law is specified by the transport capacity, C. a is the area drained per unit contour length f(a) is a positive function of a n is a constant exponent describing the influence of increasing gradient.

in the case where the exponent of slope n = I, and for a fixed base level, that there exists a solution to the continuity equation of the form U, V are functions of x alone T is a function of time alone. 模式推導 ◇特徵形式

(a) The continuity equation is taken in the form ── 近似解

boundary conditions Applying the inequality

m ≧ 1 ，凹坡 m ≦ 0 ，凸坡

同一研究區域的邊坡剖面假設都遵循一樣的 過程定律，則可由坡度和與流域的距離推導 出運輸能力的關係式。

結論 本文試圖探討模式與邊坡演化過程之間 的關係，如連續性方程式與經驗條件之 關係。 連續方程式可描述地形的變遷，可求得 地形的剖面。

謝謝玲聽