Probability density functions of the stream flow discharge in linearized diffusion wave models

This article considers stream flow discharge moving through channels subject to the lateral inflow and described by a linearized diffusion wave equation. The variability of lateral inflow is manifested by random fluctuations in time, which is the only source of uncertainty as to flow discharge quantification. The stochastic nature of stream flow discharge is described by the probability density function (PDF) obtained using the theory of distributions. The PDF of the stream flow discharge depends on the hydraulic properties of the stream flow, such as the wave celerity and hydraulic diffusivity as well as the temporal correlation scale of the lateral inflow rate fluctuations. The focus in this analysis is placed on the influence of the temporal correlation scale and the wave celerity coefficient on the PDF of the flow discharge. The analysis demonstrates that a larger temporal correlation scale causes an increase of PDF of the lateral inflow rate and, in turn, the PDF of the flow discharge which is also affected positively by the wave celerity coefficient.