Description:
<jats:p>The Fokker‐Planck equation is used to describe the evolution through time of the probability density function of storage levels between the boundaries of a finite reservoir. Analytical solutions for the equilibrium density function are obtained under the assumption that potential storage displacements are independent stationary Gaussian random variables. The potential storage displacement represents the change in storage that would occur during a unit time interval in a reservoir of infinite capacity. Results show that the storage density function is a mixed truncated exponential distribution with mass concentrations on the lower and upper boundaries corresponding to the steady state probability that the reservoir is empty or full, respectively. Parameters of the equilibrium storage density function are computed from the reservoir capacity and the mean and variance per unit time of the potential storage displacement. A dimensionless parameter, analogous to a Peclet number, identifies conditions for which the finite reservoir effectively behaves as one with semi‐infinite capacity. Analytical solutions from the diffusion approximation show excellent agreement with independent estimates of the storage distribution function obtained using probability matrix methods, Monte Carlo simulation, and numerical methods.</jats:p>