## 5 Results and Discussion
### Spatial Variation of Residuals Currents (Direction of Residual Currents)  
Tidal hydraulics and entrance dynamics along with bank erosion and water quality are dominant issues with high priorities that need to be addressed for Currimumdi Lake. The hydrodynamic and residual transport patterns emerging from tidal motion have important consequences for the transport of sediments, water quality and bank erosion; thus, an accurate estimation of residual currents is very important in this setting.  
A previously developed tidal rating curve was used to predict a long time series of discharges by measuring the water level at a gauging station. This relationship was  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Free-Run** & **Base-Test** & **Set-Up I** & **Set-Up II** \\  & **No Assimilation** & **DA with Lagrangian** & **DA with Eulerian** & **DA with Lagrangian** \\  & & **Data** & **Data** & **\& Eulerian Data** \\ \hline RMSE (m/s) & 0.07 & 0.05 & 0.059 & 0.043 \\ \hline R\({}^{2}\) & 0.56 & 0.95 & 0.92 & 0.97 \\ \hline Improvement (\%) & & 28 & 16 & 39 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of the data assimilation performance (RMSE).  
Figure 9: Scatter plots of modelled versus observed velocity (m/s) for Lagrangian (Base-Test), Eulerian (Set-Up I) and Lagrangian and Eulerian (Set-Up II) assimilation.  
validated by investigating the correlation between the predicted and observed discharge, along with examining the comparison between model outputs using observed and predicted discharge boundary conditions [31]. The residual currents were derived from tidal velocities during 8-day, 4-day, 2-day and 1-day periods in which full tidal cycles prevailed. These non-tidal currents driven by wind are important in estuaries because they are the principal means of transport for dissolved and suspended matter [45; 46]. In addition, the lack of consistent current measurements in these areas begs the need for accurate current estimations. The effect of DA on the direction of residual currents in terms of RMSD is shown in Figure 10. While the assimilation window is kept constant at 3 h, the time window of residual velocity changes. A significant difference between the model without assimilation and Set-Up II for time windows of 1, 2, 4, and 8 days was observed (Figure 10a-d, respectively). The deviation is particularly larger in the 1-day window of residual velocity and especially in shallow sections of the lake mostly driven by wind (close to downstream boundary) and the section where drifters made their way through as expected from DA performance analysis results. Given that the assimilation period is constant, as the time window of residual velocity increases, the deviation between model results without assimilation and Set-Up II decreases, which shows the effect of the ratio of residual velocity period to assimilation period on the DA performance (Figure 11).  
Figure 10: _Cont._  
Figure 11: The effect of residual velocity time window on averaged root mean square error.  
Figure 10: Residual velocity calculated for: (**a**) 1-day, (**b**) 2-day, (**c**) 4-day and (**d**) 8-day periods; the assimilation window is 3 h in all cases.