*3.2. Calibration and Validation Tests of HDM*

Field data of spring neap tides during 6–16 December 2012 were used to calibrate parameters of the model and then validate its accuracy. In the hydrological survey, tidal levels were recorded at 14 fixed gauges from 6 December (the 340th day of 2012) to 16 December. The depth-averaged horizontal velocity was recorded from 8 December at 12:00 to 9 December at 21:00 for neap tides and from 14 December at 7:00 to 15 December at 13:00 for spring tides. Arrangements of the hydrological survey locations are shown in Figure 3. At the upstream boundary, the daily average river discharge at Station Datong gradually reduced from 22,000 to 18,700 m<sup>3</sup>/s during 6–16 December 2012.

**Figure 3.** Arrangements of hydrology survey locations in Yangtze Estuary.

In the simulations, the time step of the HDM is set to 90 s, while nine sub steps are used in the backtracking of the ELM. For a simulation of free-surface flows, the initial condition has a significant effect on the simulation of unsteady flows. In our simulations, the initial condition was determined by a preliminary simulation.

Manning's roughness coe fficient, *nm*, was calibrated using the spring-tide condition from 14 December at 0:00 to 16 December at 0:00. The inflow discharge was set to 19,000 m<sup>3</sup>/s. The *nm* of sub regions was adjusted so that the simulated tide-level histories would agree with field data. The *nm* was then corrected slightly so that the simulated velocity histories would agree with field data at the same time. The *nm* was finally calibrated as 0.022–0.021 from Station Datong to Jiangyin, 0.021–0.015 from Station Jiangyin to Xuliujing, and 0.014–0.011 for the North and South Branches. The *nm* in the North and South Branches was similar to the values reported in previous research [31,32].

Using the aforementioned distribution of *nm*, the histories of the simulated tidal levels and depth-averaged velocities were shown to agree well with field data. Generally, the mean absolute error in simulated tide levels was less than 0.15 m compared with the field data, while the mean absolute relative error in simulated velocity at survey positions was less than 10%. The accuracy of the model was then verified by simulating a full spring-neap tide process on 6–16 December 2012, and the simulation results are shown in Figures 4 and 5.

**Figure 4.** Comparisons of the simulated tide-level histories and field data. (**a**) at Station Xuliujing (XLJ), (**b**) at Station Qinglonggang (QLG), (**c**) at Station Lianxingang (LZG), (**d**) at Station Nanmen (NM), (**e**) at Station Hengsha (HS).

**Figure 5.** Comparisons of simulated histories of velocity with field data (negative velocity is landward velocity, which appears during the flood duration). (**a**) at Survey Point B1, (**b**) at Survey Point A1, (**c**) at Survey Point A3, (**d**) at Survey Point A5, (**e**) at Survey Point B7.
