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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

hydrology and earth system sciences

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