Articles | Volume 21, issue 7
Research article
04 Jul 2017
Research article |  | 04 Jul 2017

The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

Zhilin Zhang and Hubert H. G. Savenije

Abstract. The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1∕2 < K < 2∕3 for density-driven mixing which falls within the feasible range of 0 < K < 1. In addition, we developed a one-dimensional predictive equation for the dispersion of salinity as a function of local hydraulic parameters that can vary along the estuary axis, including mixing due to tide-driven residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

Short summary
An estuary is where fresh water rivers meet the salty open sea. This mixture of salty fresh water leads to a varying water quality. There a model works well showing how far the salty water can travel, with an empirical parameter that needs to be calibrated every time. This paper provides a possible solution for this parameter to make the model predictive. Also, the model was improved by considering 2-D exchange flow. This new model was supported by observations in 18 estuaries around the world.