# Improving the predictive equation for dispersion in estuaries

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## Abstract

Dispersion is often hard to incorporate in analytical salt intrusion models. The analytical models of Savenije (1986) and Kuijper & Van Rijn (2011) are quite similar and use a predictive equation for the dispersion in the estuary mouth. The biggest difference between the two models is the Van der Burgh K for which Kuijper and Van Rijn stated that it should be equal to 0.5. The main goal of this research is to improve the applicability of the analytical salt models. The two models were applied to 72 measurements in 27 estuaries. Both models gave reasonable results, but Savenije's model gave in general a slightly better fit. The differences were found in especially the tail of the curve, what indicates that K is probably not equal to 0.5. Linear regressions were carried out in order to derive new possible predictive equations for the dispersion coefficient. Several existing dimensionless ratios were combined in different regressions. Another regression technique, genetic programming, confirmed that a linear combination of the log of the dimensionless ratios is correct. The linear regressions were carried out for both models and for the estuary mouth and the inflection point, where the shape of the estuary changes. Many of the derived equations showed however more or less comparable results. The significance of the different terms was tested to see if each term contributed significantly. In this way it was already possible to reduce the number of possible new predictive equations. The same selection of equations was applied to the salt models. Eventually a choice of a new predictive equation was made based on the regressions, the local applications and the applications in the salt models. The horizontal to vertical tidal range and a friction term should be added to the Richardson number to get an improved predictive equation. The applicability of the analytical models will also increase by starting the calculation from the more clearly defined inflection point. A disadvantage of the new equation is especially the friction term, because friction is often not known a priori. The hydraulic model of Cai et al. (2012) was used to test if friction and depth could be estimated with just a minimum of information. It was possible to use these equations to make a "quick and dirty" estimate of these parameters. The new proposed approach is therefore as follows: - Determine the location of the inflection point based on information about the geometry - Estimate hydraulic parameters, also with help of the equations of Cai et al. (2012) - Determine the dispersion coefficient with the new predictive equations - Determine the salt distribution with the model of Savenije (1986) or Kuijper & Van Rijn (2011)