Fractional Kinetic Model for First Flush of Stormwater Pollutants

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Abstract
By generalizing the urban ground as a fractal surface and revising the classical Fick’s formula as a law of dispersion with a fractional-order derivative, a fractional kinetic model is developed for simulation of the first flush phenomenon of urban stormwater pollutants. The model is comprised of (1) a fractional dispersion-advection equation (FADE); (2) the kinematic-wave overland flow equation; and (3) methods for numerical solution of the equations. A split-operator method is proposed for numerical solution of the FADE by means of a newly presented F.3 finite-difference scheme for fractional partial differential equations. The kinematic-wave overland flow equation is solved using the Lax–Wendroff explicit scheme. Under a constant rainstorm the hydrograph displays an initial rising limb followed by a constant flow discharge. The pollutograph exhibits a steep receding limb (the first flush), followed by a long stretched tail (heavy tail process). The agreement between simulated and measured dispersion ch...

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