Moment Evolution of the Outflow-Rate from Nonlinear Conceptual Reservoirs

The temporal evolution of moments of outflow-rate is investigated in a stochastically perturbed nonlinear reservoir due to precipitation. The detailed stochastic behaviour of outflow is obtained from the numerical solution of a nonlinear stochastic differential equation with multiplicative noise. The time-development of first two moments is studied for various choices of parameters. Using Stratonovich interpretation, it turns out that the mean outflow-rate is above that given by the deterministic solution. Based on the set of 9000 simulation runs, 90 % confidence intervals for the mean evolution of outflow-rate are computed. The effect of stochastic perturbations with finite correlation time is investigated