Water level outputs from SRM at 13 sample stations are used as the system state ⁠. Similar to the previous application of the hypothetical bay experiment, the two KFs are also coupled with the trained LM. These water levels are simulated through the LM at these 13 stations individually, with a 1 hour forecast horizon, which is consistent with the numerical model output interval. The optimal embedding parameters used are shown in Table 4. The measured water levels at six observed stations (West Coast, Tanjong Changi, Langkawi, Kelang, Tioman, and Getting) are considered as six variables of the observed vector ⁠. The linear observation function H is used in both two-SKF and one scenario of UKF. As described in Figure 1, based on the system driven by LM at each time step, the information from both observations and numerical model are combined to construct the Kalman gain according to Equations (7) and (19). Based on these Kalman gains, the scheme further corrects the model state, which will be the initial state for the next time step:where, x, y is the system state and observation as indicated in Equations (10) and (11); the water level output from SRM simulation at all the stations of interest; the measured water level at monitoring stations; H the linear observation transformation function.