Search results for "Overland flow equation"
showing 2 items of 2 documents
On the solutions of the differential overland flow equation
2010
In this paper we study the overland flow equation for an arbitrary positive value of the rating exponent m. We write the general solution of the equation and generalize the series solution given in [1] and [2]. Finally, we show how the five solutions presented in [5] are actually a special case of a general formula valid for any rational m≥1.
The overland flow equation for constant rainfall excess: an evaluation of runoff volume and time to equilibrium
2011
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}.