In this paper we study the runoff volume V(t) per unit area generated by the overland flow in the time interval [0,t], under a stationary rainfall r and initially dry conditions. For all positive values of the rating exponent m we express V(t) in closed form in terms of the solution q(t) of the overland flow equation. We define a simpler, approximated value of V(t) and show that, for m≥1, the error is smaller than a quantity of the form c e^{-pt}. Finally, for 1≤m≤3, we find an explicit upper bound for the time to equilibrium t_e, by showing that q(t) differs from the equilibrium outflow r by a quantity of the form c e^{-pt}.

Pavone, M. (2011). The overland flow equation for constant rainfall excess: an evaluation of runoff volume and time to equilibrium. BOLLETTINO DI MATEMATICA PURA E APPLICATA, IV, 11-23.

### The overland flow equation for constant rainfall excess: an evaluation of runoff volume and time to equilibrium

#### Abstract

In this paper we study the runoff volume V(t) per unit area generated by the overland flow in the time interval [0,t], under a stationary rainfall r and initially dry conditions. For all positive values of the rating exponent m we express V(t) in closed form in terms of the solution q(t) of the overland flow equation. We define a simpler, approximated value of V(t) and show that, for m≥1, the error is smaller than a quantity of the form c e^{-pt}. Finally, for 1≤m≤3, we find an explicit upper bound for the time to equilibrium t_e, by showing that q(t) differs from the equilibrium outflow r by a quantity of the form c e^{-pt}.
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2011
Settore MAT/05 - Analisi Matematica
Pavone, M. (2011). The overland flow equation for constant rainfall excess: an evaluation of runoff volume and time to equilibrium. BOLLETTINO DI MATEMATICA PURA E APPLICATA, IV, 11-23.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/76327`