Abstract
In order to clarify physical meanings of conceptual runoff models and runoff parameters, models such as the rational method, tank model and storage function model were theoretically derived in this paper. The conceptual rainfall-runoff models are derived by the kinematic wave theory for the subsurface or surface flow with three types of the flow resistance law (Darcy's law, Manning's law and saturated-unsaturaged flow) in a hill slope. From this analysis, it was found that the storage function model was derived by assuming a steady state solution for direct runoff every moment and the tank model was derived if mean surface flow velocity in a hill slope was proportional to the slope length. Furthermore, on the assumption that the flow resistance law took the saturated Darcy's law or under steady state condition, the rational method was derived. Runoff parameters of the tank model and storage function model that have been calibrated using historical rainfall and discharge records can be uniquely determined by the quantities of a surface soil layer such as a saturated hydraulic conductivity, an exponent in hydraulic conductivity function, surface soil layer thickness and an effective porosity from theoretical derivation of the models in this paper.
