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The concept of residual, i.e., tidally-averaged, flows through a multiple inlet system is reappraised. The evaluation of the residual through-flow depends on the time interval over which is integrated, in other words, on how one defines the tidal period. It is demonstrated that this definition is ambiguous and that different definitions (based on, e.g., high waters, slack tides, etc.) yield very different results for the residual, also in terms of their long-term statistical properties (median and standard deviation). A basin-wide applicable method of defining the tidal period, in terms of enclosed water volume, is analyzed. We compare the different methods on the basis of high-resolution model results for the Western Dutch Wadden Sea. The multitude of tidal constituents together with wind variability creates broad distributions for the residuals, with standard deviations much larger than the mean or median residual flows.

Calculating residual flows through a multiple-inlet system: the conundrum of the tidal period