Hydraulics of Stream Flow Routing with Bank Storage

Bank storage is a process in which volumes of water are temporarily retained by alluvial stream banks during storm events and gradually released to partially sustain baseflow. This process has important hydrologic and ecological implications. In this paper, analytical solutions are developed for routing stream flow, lateral stream-aquifer interactions, and aquifer storage. In effect, the stream-flow routing Muskingum method is modified for bank storage. The analysis is based on one-dimensional lateral groundwater flow in semiinfinite homogeneous unconfined aquifers, which are in contact with streams through semipervious bed sediments. Impulse response and unit step response functions are derived for the stream-aquifer system, using Laplace transformations. These response functions relate stream outflow, stream-aquifer flow, bank storage, and cumulative reach discharge volume to discrete-time inflow hydrographs through convolution integrals. The impulse response function decreases with increasing aquifer hydraulic conductivity at earlier times, but increases with the conductivity and persists at later times. The unit step response function decreases with aquifer conductivity uniformly in time. The dependence of stream flow and bank storage on aquifer hydraulic conductivity, streambed leakance, stream width, and aquifer diffusivity is investigated. The analysis is extended to discrete input data, and modification of the methodology to route discrete-time inflow hydrographs of general form is achieved, using discrete-time kernels. The presented analysis establishes the time domain for validity of the analytical solutions in terms of the Muskingum parameters and an aquifer-related parameter.