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Summary: We study the interaction of a stream with a sloping unconfined aquifer that the stream is assumed to fully penetrate. The analysis applies to flow in a vertical section, considers the existence of a low-conductivity streambed layer and the flow in the aquifer to be induced by variations of the stream stage. Invoking the Dupuit assumption yields the 1-D Boussinesq equation, extended for a sloping base. The Boussinesq equation is linearised, the derived flow model is critiqued and an objective procedure for determining the linearisation level is developed. We solve the linear governing equation by the method of Laplace transform, with analytical inversion; the horizontal-aquifer case is treated in the zero-slope limit. The system response function is derived for the general case (sloping aquifer, sediment bed layer) and for several specific cases, and solutions are verified against known analytical results. Responses are contrasted for aquifers on positive, negative and zero slopes to step changes in the stage of streams with and without a sediment bed layer. The solutions give the aquifer stage and flow rate, the flow exchange rate at the stream–aquifer interface and the exchanged water volumes (bank storage/release). [Copyright &y& Elsevier]

Summary: We convolve the system response functions of the linearised 1D equation of Boussinesq (extended for slope, Dupuit approximation) derived in the companion paper of Akylas and Koussis [Akylas, E., Koussis, A.D., (submitted for publication). Response of sloping unconfined aquifer to stage changes in adjacent stream: I. Theoretical analysis and derivation of system response functions, J. Hydrol] and develop solutions for the interaction of a fully penetrating stream with a sloping unconfined aquifer, taking also into account a low-conductivity streambed layer. These solutions give the aquifer stage and flow rate, the flow exchange rate at the stream–aquifer interface and the exchanged water volumes (bank storage/release). The solutions are analytical, when the flow-inducing stream stage variations are common functions; otherwise, the convolution integral is evaluated numerically. Responses are compared for aquifers on positive, negative and zero base slopes to a wave-like change in the stage of the stream. Analytical and numerical convolution-derived solutions are used to model the interaction of Cedar River and its adjacent unconfined aquifer near Cedar Rapids, Iowa. In the model, the aquifer base is taken to be horizontal or inclined and the streambed clogged by a low-conductivity sediment layer; the model is verified against data not used in the calibration and is found to perform very well. [Copyright &y& Elsevier]