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  1. Abstract. For more than a century, estuarine exchange flow has been quantified by meansof the Knudsen relations which connect bulk quantities such as inflow andoutflow volume fluxes and salinities. These relations are closely linked toestuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which usessalinity coordinates to calculate these bulk quantities, allows an exactformulation of the Knudsen relations in realistic cases. There are howevernumerical issues, since the original method does not converge to the TEF bulkvalues for an increasing number of salinity classes. In the present study,this problem is investigated and the method of dividing salinities,described by MacCready et al. (2018), is mathematically introduced. Achallenging yet compact analytical scenario for a well-mixed estuarineexchange flow is investigated for both methods, showing the properconvergence of the dividing salinity method. Furthermore, the dividingsalinity method is applied to model results of the Baltic Sea to demonstratethe analysis of realistic exchange flows and exchange flows with more thantwo layers.

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