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Time–Area method is one of the most widely applied techniques of watershed routing, and can be potentially used as a distributed model. In this paper, a fundamental flaw in the arrangement of subareas in the original time-area histogram is identified for one-dimensional flow. This is conducted on the basis of comparing time-area hydrograph with that of the kinematic wave theorem. Accordingly, a revised time-area algorithm is developed as a substitute for the original time-area. It is proved that in the revised approach, subareas must be reversely arranged. It is also shown that the revised time-area hydrograph is in perfect agreement with the hydrograph derived by the kinematics wave theory.

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In almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are

simulated as a rectangular plane. However, the converging plane is the closest shape to an actual upstream subbasin. The

intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an

analytical or semi analytical solution to define the rising limb of the resulted hydrograph. In the present research, a new

geomorphologic semi analytical method was developed that tries to establish a relationship between the parallel and converging

flows to reduce the complexity of the equations. The proposed method uses the principals of the Time Area method modified to

apply the kinematic wave theory and then by applying a correction factor finds the actual discharge. The correction factor, which

is based on the proportion of the effective drained area to the analytically calculated one, introduces the convergence effect of

the flow in reducing the potentially available discharge in a parallel flow. The proposed method was applied to a case study and

the result was compared with that of Woolhiser's numerical method that showed the reliability of the new method.