Reconstruction of Tidal Discharges in the St. Lawrence Fluvial Estuary: The Method of Cubature Revisited

Abstract

AbstractKnowledge of tidal flows in rivers and estuaries is often scarce yet vital in determining flushing properties and sediment transport rates. While many rivers still remain ungauged, methodological difficulties often arise in gauged systems, resulting in short flow records compared to historical water level data. Notwithstanding, discharge reconstructions in estuaries are possible using indirect methods based on long‐term tidal data. In this paper, we revisit the method of cubature, integrating the continuity equation for discharges at different sections. The method consists in computing temporal changes in water volume from simultaneous tidal heights readings along the river and storage width estimations. These water balance estimates remain challenging to produce, because they require spatial interpolation of gappy tidal records and an accurate representation of inundated areas over time. Improvements on the method are made by using a 1‐D nonstationary tidal harmonic model that provides continuous tidal data along the estuary, with no temporal or spatial gaps. Second, a 2‐D finite element discretization is used to compute the time‐varying wetted surface area, relying on detailed topographic data over intertidal flats. The method is applied to the St. Lawrence fluvial estuary (SLFE) and validated against discharge data collected along nine cross sections of the river, reaching relative RMSE below 4% of the diurnal tidal discharge range at downstream locations and below 9% upstream. One year reconstructions conducted in the SLFE also show the potential of the method to reproduce the tidal discharge variability along the tidal‐river continuum, for a wide range of temporal scales.