The Knudsen theorem and the Total Exchange Flow analysis framework applied to the Baltic Sea

The Knudsen theorem for estuarine exchange flow, based on mass conservation of water and salt, and its generalization with resolution in salinity coordinates, the Total Exchange Flow (TEF) analysis framework, are reviewed here. The former had been developed, and applied to quantify exchange flow between the North Sea and the Baltic Sea, more than a century ago. In this paper, the underlying short research paper published in 1900 by Martin Knudsen, originally written in German, is translated into English. Reaching far beyond the Knudsen relation in particular, the extensive scientific achievements of Martin Knudsen on the salinity of seawater are reviewed. Using the Knudsen theorem and the TEF analysis framework, validated multi-decadal (years 1949-2013) model simulations are analyzed in terms of exchange flow through straits of the Western Baltic Sea. When comparing the model results to the original findings of Martin Knudsen, it is impressive to see how relevant his analysis of ratios of averaged inflowing and outflowing water masses still is today, given that they were based on just a few salinity observations. The model-based long-term Knudsen and TEF analyses of exchange flow in the Western Baltic Sea reproduces the Major Baltic Inflows (MBIs) that have occurred since the 1950s. For the complex inflow years 2002/2003, with two baroclinic summer inflows and one barotropic winter inflow in between, the strong underestimation of the exchange flow by Eulerian analysis as compared to TEF analysis is demonstrated.