Stream aquifer interactions: analytical solution to estimate stream depletions caused by stream stage fluctuations and pumping wells near streams

Abstract

This dissertation is composed of three parts of contributions. Systems of a fully penetrating pumping well in a confined aquifer near a fully penetrating stream with and without streambeds are discussed in Chapter II. In Chapter III, stream-aquifer systems with a fully penetrating pumping well in a confined aquifer between two parallel fully penetrating streams with and without streambeds are discussed. Stream depletion rates in Chapter II are solved using Laplace and Fourier transform methods, and stream depletion rates in Chapter III are solved using the potential method. Chapter II presents analytical solutions in the Laplace domain for general stream depletion rates caused by a pumping well and caused by stream stage fluctuations. For seasonal case, the stream stage is a function of time. For an individual flood wave, the stream stage is a function of time and distance along the stream. Semi-analytical solutions of seasonal stream depletion rates in time domain, using a cosine function to simulate stream stage fluctuations, are presented. The stream depletion rate caused by pumping is solved analytically, while the stream depletion rate caused by stream stage fluctuations is solved numerically. Various parameters affecting stream depletion rates, such as flood period and streambed, are analyzed. For a short-term case, the pumping rate is assumed to be constant, and a Gaussian function is used as an example of floodwaves. This part is solved using the same method as used in the seasonal case. Early time and late time approximations of the stream depletion rates are also presented. This approximation leads to an interesting finding that the stream depletion rate caused by seasonal stream stage fluctuations can be neglected if the stream aquifer system has a long time to equilibrate. In Chapter III, analytical stream depletion rates caused by a pumping well between two parallel streams with and without streambeds are presented. In this chapter, stream stage is assumed to be constant. Capture zone delineations were analyzed in the case without streambed. For the case with streambed, streambed conductance, which is an important factor controlling stream depletion, is analyzed. All solutions discussed in this dissertation can be used to predict stream depletion rates and to estimate parameters controlling stream depletion rates, which is crucial for water management. In addition to the stream depletion, the derived semi-analytical solutions in the Laplace-Fourier domain can also be used to predict drawdown in the aquifer near the stream. The derived solutions may also be used inversely to find the streambed and aquifer parameters if the stream stage fluctuation can be well described.