Combined analytical solution of overland flow and sediment transport

With reference to the kinematic wave theory coupled with the hypothesis of constant linear velocity for the rating curve, rising limb analytical solutions have been calculated for overland flow, over an Hortonian-infiltrating surface, and sediment discharge. These analytical solutions are certainly easier to use than the numerical integration of the basic equations and they may be used to obtain an initial evaluation of the parameters of more complex models generally devised for complicated cases.Notation a exponent of the Horton law T^–1] - b exponent of the rill erosion equation - B inter-rill erosion coefficient ML^–m–2T ^m–1] - c sediment concentration ML^–3] - c _o reference sediment concentration ML^–3] - E _I inter-rill erosion ML^–2T^–1] - E _R rill erosion ML^–2T^–1] - f _c final infiltration rate of the soil LT^–1] - f _o initial infiltration rate of the soil LT^–1] - h flow depth L] - h _o reference flow depth L] - i infiltration rate LT^–1] - k rill erosion coefficient ML^–1–b T^–1] - K integration constant - L() Laplace transformation - m exponent of the inter-rill erosion equation - n Manning's coefficient L^–1/3T] - p rainfall intensity LT^–1] - q water discharge per unit width L²T^–1] - q _s sediment discharge per unit width ML^–1T^–1] - t time T] - t _p ponding time T] - x distance along the flow direction L] Greek Letters coefficient of the stage-discharge equation L^2–T^–1] - exponent of the stage-discharge equation - rill erosion coefficient L^–1]