## 2 Materials and Methods
### Hydrodynamic Model  
Hydrodynamic simulations were conducted using Delft3D FM, an open-source hydrodynamic model developed by Deltares, Netherlands. The model was run in depth-averaged 2D mode. The model solves the Navier-Stokes equations for an incompressible fluid, using the shallow water equations and the Boussinesq assumptions. To ensure that the model output is independent of the grid resolution, a grid independence test was carried out. Five different grids were constructed ranging from 25 m down to 2 m. The cross-sectional average velocity at the middle of the domain (Point C in Figure 1a) was used to test the mesh convergence. The results show that the average velocity was not sensitive to further refinement beyond a minimum grid size of 5 m. However, an increase in the minimum grid size caused an increase in the cross-sectional average velocity. Courant-Friedrichs-Lewy (CFL) condition for this model was (CFL \(\leq\) 1). A detailed model description can be accessed through the manual [29]. Modelling at Currimundi Lake used an unstructured grid with a spatial resolution of 5 m following the channel morphology; the time series of discharge obtained from an ADV and the water level obtained from a gauging station were used for upstream and downstream boundaries, respectively. The downstream boundary was forced with water level data obtained from the tidal gauge within the main channel and sampled at an interval of five minutes. Therefore, the diurnal, semi-diurnal and higher frequency tidal constituents are included in the boundary. The simulation time step was 1 min over the simulation period of 21 h plus a 21 h spin-up time for initial condition propagation. A spatially constant bottom friction was defined by applying [PERSON]'s coefficient \(n=0.025\) obtained through model calibration. The model calibration process is a pivotal prerequisite to the DA process because DA algorithms are mainly bias-blind [30] and erroneous parameters can lead to significant uncertainties in the DA process. The calibration of the hydrodynamic model was performed with two sets of data: Eulerian calibration using 70% of velocity measurements collected from a fixed-instrument (ADV) and Lagrangian calibration using 70% velocities from GPS-tracked drifters. Both calibrations used Root Mean Square Error (RMSE) and correlation (R\({}^{2}\)) between observed and simulated velocities and aimed to adjust the bed roughness coefficient through [PERSON]'s coefficient (\(n\)). The optimum Manning coefficient (\(n=0.025\)) attained through Lagrangian calibration was equivalent to that observed via Eulerian calibration. Thus, Lagrangian data has the potency to be used in hydrodynamic model calibration in such environments. After the calibration, modelled and observed velocities correlated very well (R\({}^{2}=0.94\)) and root mean square error was reasonably low (RMSE = 0.019 m/s), suggesting that the calibration successfully reduced systematic model errors. The calibrated model was then validated by comparing simulated velocities with 30% of the measurements for both Eulerian and Lagrangian velocities. The RMSE and R\({}^{2}\) values through this validation reflected a successful calibration of the model. The calibration and validation of the hydrodynamic model are presented in full detail in [28]. To investigate the effect of DA on the direction of residual currents in the main channel, we used our calibrated model to simulate the dynamics of Currimundi Lake for longer durations of one day, two days, four days and eight days. Upstream and downstream boundary forcings (i.e., discharge and water level) used in the hydrodynamic model for longer temporal simulations were obtained by developing a stage-discharge relationship and gauging station data measurements. Details of the tidal discharge rating curve used to predict flow discharge as well as calibration and validation of the model can be found in [31].