In this article, the coupled equations describing the transient groundwater flow and stream flow fluctuations are solved based on the Fourier-Stieltjes integral representation, where the lateral inflow term in the stream flow perturbation equation connects the process of groundwater flow to that of stream flow. The closed-form solutions describing the variability in groundwater flow specific discharge and stream flow discharge are developed to quantify the influence of the variability in temporally correlated recharge in an unconfined aquifer on the stream flow discharge. We found from the closed-form solutions that the temporal correlation scale and the variance of recharge fields influence the variability in groundwater flow specific discharge and the stream flow discharge positively. In addition, the hydraulic diffusivity coefficient takes the role of reducing the variability in stream flow discharge.
- Diffusion waves
- Stochastic analysis
- Stream-aquifer system
- Temporally correlated groundwater recharge
- Variance of stream flow discharge