本文推导出了以物理概念为基础,用以模拟斜坡梯田上水流的数学模型,在推导过程中认为斜坡梯田是由一个已受侵蚀的、渗水的地块和一个梯田排水沟组成.为了推求地表径流和排水沟水流中水和泥沙的流量,采用了非线性的运动波方程组.利用闭合形式的方程建立了地表径流侵蚀和运移泥沙能力、侵蚀率和泥沙浓度之间的关系,排水沟输移泥沙的能力是根据单位水流能量的概念确定的.利用有限差分法求解数学模型中的偏微分方程,并且利用实测资料对模型进行了验证. In this paper, a mathematical model based on physical concepts to simulate water flow on terraced terraces is deduced. In the process of derivation, the terraced terraces are considered to consist of an infiltrated and permeable block and a terraced drainage channel. And the flow of water and sediment in drainage flow, a nonlinear motion wave equation is adopted.The relationship between surface runoff erosion and sediment transport, erosion rate and sediment concentration is established by the closed form equation, The ability of drainage ditch to transport sediment is determined according to the concept of unit water flow energy.The finite difference method is used to solve the partial differential equation in the mathematical model and the model is verified by the measured data.