An evaluation of analytical stream to groundwater exchange models: a comparison of gross exchanges based on different spatial flow distribution assumptions

Abstract. In this paper, a new method for estimating gross gains and losses between streams and groundwater is developed and evaluated against two existing approaches. These three stream to groundwater exchange (SGE) estimation methods are distinct in their assumptions on the spatial distribution of the inflowing and outflowing fluxes along the stream. The two existing methods assume that the fluxes are independent and in a specific sequence, while the third and newly derived method assumes that both fluxes occur simultaneously and uniformly throughout the stream. The analytic expressions in connection to the underlying assumptions are investigated through numerical stream simulations to evaluate the individual and mutual dynamics of the SGE estimation methods and to understand the causes for the differences in performance. The results show that the three methods produce significantly different results and that the mean absolute normalized error can have up to an order of magnitude difference between the methods. These differences between the SGE methods are entirely due to the assumptions of the SGE spatial dynamics of the methods, and the performance for a particular approach strongly decreases if its assumptions are not fulfilled. The assessment of the three methods through numerical simulations, representing a variety of SGE dynamics, shows that the method introduced, considering simultaneous stream gains and losses, presents overall the highest performance according to the simulations. As the existing methods provide the minimum and maximum realistic values of SGE within a stream reach, all three methods could be used in conjunction for a full range of estimates. These SGE methods can also be used in conjunction with other end-member mixing models to acquire even more hydrologic information as both require the same type of input data.