Abstract
Abstract. For more than a century, estuarine exchange flow has been quantified by means of the Knudsen relations which connect bulk quantities such as inflow and outflow volume fluxes and salinities. These relations are closely linked to estuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which uses salinity coordinates to calculate these bulk quantities, allows an exact formulation of the Knudsen relations in realistic cases. There are however numerical issues, since the original method does not converge to the TEF bulk values 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. A challenging yet compact analytical scenario for a well-mixed estuarine exchange flow is investigated for both methods, showing the proper convergence of the dividing salinity method. Furthermore, the dividing salinity method is applied to model results of the Baltic Sea to demonstrate the analysis of realistic exchange flows and exchange flows with more than two layers.
Highlights
The Total Exchange Flow (TEF) analysis framework calculates time-averaged net volume and mass transport between enclosed volumes of the ocean and ambient water masses, sorted by salinity classes
Lorenz et al.: Numerical issues of the Total Exchange Flow (TEF) analysis framework such that Qc can be obtained via integration of qc in salinity space: Smax
Similar to the dependency of the TEF bulk values on I in the oscillating exchange flow in Sect. 2, we investigate the dependency of the TEF bulk values on the temporal resolution of the exchange flow
Summary
The Total Exchange Flow (TEF) analysis framework calculates time-averaged net volume and mass transport between enclosed volumes of the ocean and ambient water masses, sorted by salinity classes. The TEF analysis framework provides one consistent calculation method for these bulk values, which for this case describe the net exchange flow. MacCready et al (2018) showed how the bulk concept can be used to estimate the volume-integrated average mixing M (defined as the rate of reduction of the net salinity variance due to mixing) in estuaries: M ≈ sinsoutQr , i.e. the volume-integrated average mixing in an estuary is approximated by the product of inflow and outflow salinity with the estuarine freshwater supply This mixing estimate by MacCready et al (2018) approximates the TEF-based exact formulations developed by Burchard et al (2018b).
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