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Abstract: Considering the short length of building roofs, a theoretical analysis of the first flush of roof runoff was conducted based on the kinematic wave and pollutant erosion equations. This mathematical derivation with analytical solutions predicts pollutant mass first flush (MFF), mean concentration of initial runoff (MCIF), mean concentration of roof runoff (MCRR) with diversion of initial portion and residual mass available on the bed surface (RS) after the entire runoff under the condition of constant excess rainfall. And the effects of the associated influencing factors (roof length, roof gradient, roof surface roughness, rainfall intensity, rainfall duration, and erosion coefficients) on them were discussed while the values of parameters referred to the previous studies. The results showed that for roofs whose length is shorter than 20 m, both the increase in roof length and roof gradient and the decrease in roof surface roughness result in larger MFF and MCIF and smaller MCRR and RS, which is beneficial to water reuse and pollution reduction. The theoretical relationship between the first flush and the influencing factors may aid the planning and design of roof in terms of rainwater utilization or diffuse pollution control.

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