A New Harmonic Regression Approach to Interpret and Predict Estuarine Salinity Variation

Abstract

In this paper, we introduce a physics-inspired harmonic regression model to capture the nonstationary salinity dynamics at monitoring stations in well-mixed estuarine systems. Building on existing hybrid harmonic regression approaches, which modify the classical harmonic analysis to cope with nonstationary signals to predict tidal water levels, our model captures tidal and subtidal salinity variations using a simplified analytical salt intrusion model. The harmonic regression model was tested in the well-mixed Ems and Scheldt estuaries using data sets spanning 2–4 years, explaining 87.4%–96.4% of the observed salinity variance at upstream stations. A key finding is that storm surge effects typically have longer wavelengths than the estuary's length scale, which justifies using a linear relation between vertical and horizontal excursions. In alluvial estuaries, where the system widens, unsteadiness of the river discharge shows to be increasingly important for more downstream stations. The model quantifies the characteristic response time of salinity to variation in discharge. Based on a critical evaluation of the model equations, we offer a physical interpretation of the optimized parameters. Specifically, we discuss the Van der Burgh constant, which is an empirical coefficient commonly used in salt intrusion models. Our findings reveal that the Van der Burgh coefficient scales with the spatial scales of dispersion and advection, relative to changes in channel geometry.