*3.3. Calibration and Validation Tests of STM*

The sediment-capacity coefficient, *K,* is also calibrated using the spring-tide condition from 2012/12/14 0:00 to 2012/12/16 0:00. At the upstream boundary, the river discharge and the sediment concentration are respectively 19,000 m<sup>3</sup>/s and 0.112 kg/m3. The parameter *K* is calibrated as 0.11–0.08 from Datong to Jiangyin, 0.07–0.04 from Jiangyin to Xuliujing, 0.05–0.02 for the North and the South Branches. Similar to the calibrated *nm*, the calibrated *K* in coast sea regions of the Yangtze Estuary (0.07–0.02) also appears to be smaller than that of inland rivers (0.1–0.2), but approaches the values (about 0.07) reported by [32].

Using the aforementioned distribution of *K*, the STM is then verified by simulating a full spring neap tide process in the Yangtze Estuary on 6–16 December 2012. The histories of the simulated sediment concentration are generally observed to agree with field data, with minor amplitude errors (see Figure 6). The mean absolute relative errors in simulated sediment concentrations are generally less than 20%.

**Figure 6.** Comparisons of simulated sediment concentration histories and field data at survey locations. (**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.

On the one hand, Zhang's formula [21], used to evaluate the sediment-carrying capacity, does not involve an incipient velocity (the critical velocity at which sediment particles begin to move from a rest state). Hence, the sediment-carrying capacity calculated by Zhang's formula [21] is always sensitive to the velocity. In neap-tide periods, the calculated sediment-carrying capacity is closely related to the velocity of the flow, so the history of the simulated depth-averaged sediment concentration closely follows the tidal process. On the other hand, in the survey of field data, the depth-averaged sediment concentration is evaluated by using the measurements at different heights in a vertical line. However, during neap tides, the vertical distribution of sediment concentration is strongly nonuniform, and a grea<sup>t</sup> number of the transported sediment gathers in the bottom layers of the flow. The high concentration at bottom layers is often not caught or improperly measured because of the sensibility problem or the inaccurate vertical location of instruments. The vertical distribution of sediment concentration during spring-tide periods is much more uniform than that during neap-tide periods. It is easier to obtain the accurate sediment concentrations which can achieve a good representation of the value of the measured vertical line. This may explain that the data around day 343 (neap-tide periods) is poorly approximated and that around day 349 is fairly well reproduced in Figure 6a–c.

The topographical data of December 2011 and November 2013 are then employed to verify the module of bed evolution, where a simulation of 2-year unsteady flow, nonuniform sediment transport, and fluvial process from 2011/12/1 to 2013/11/30 in the Yangtze Estuary is carried out. During the 731 days, the total quantities of the runoff and the inflow sediment are respectively 17,947 × 10<sup>8</sup> m<sup>3</sup> and 2.854 × 10<sup>8</sup> tons. The daily river discharge and sediment concentration are imposed at the upstream boundary, while the seaward open boundaries are forced by tide levels of one-hour intervals. The measured topographical data in December 2011 is used to set the initial topography. The elevations of the nodes in the area of reclamations (or regulations) are modified to be consistent with the design, and the cells there are set to be non-erodible. Then, the model steps forward to November 2013 to ge<sup>t</sup> the final topography.

The simulated riverbeds at selected cross-sections of the North Branch (see Figure 3) are compared with those measured in November 2013, as shown in Figure 7. Generally, the simulated topographies at most cross-sections agree with field data. The reach, where cross-section CS5 is located, is narrowed by a project named "Xincun Sand regulation" which was launched during 2011–2013. In this reach, the flow is gathered, and the flow intensity is stronger than that in the original wider channel. As a result, the shallow sand is erased by the gathered flow after the time of the simulation. However, on the one hand, the disturbances from the projects of reclamations and regulations, launched in the North Branch during 2011–2013, may not be fully considered in the simulation. On the other hand, the present model does not have a module for simulating bank failures. Due to these disadvantages, the simulated riverbed evolutions at some cross-sections deviate from the field data. The North Branch experienced mild erosion form December 2012 to November 2013 in the simulation, which is consistent with the field. The erosion quantity of sediment is 5128.1 × 10<sup>4</sup> tons in the simulation, and has an error of +11.1% relative to field data.

**Figure 7.** Comparisons of the simulated riverbed evolutions and field data at cross-sections. (**a**) at CS2, (**b**) at CS5, (**c**) at CS7, (**d**) at CS9.

### *3.4. Sensitivity Study of Model Parameters and Coe*ffi*cients*

Generally, the accuracy of a simulation may be sensitive to the variation of model parameters and coe fficients, while simulation results vary with respect to them. The spring neap tide process in the Yangtze Estuary on 6–16 December 2012 is also used to perform the sensitivity studies of the main model parameters (e.g., Δ*t*) and coe fficients (e.g., *nm*, and *K*).

First, the sensitivity study of time steps is performed. On the one hand, the use of a large time step means low time resolution of cell update, which will reduce the accuracy of the simulations of strongly unsteady tidal flows, such as those in the Yangtze Estuary. On the other hand, the ELM used in the current model becomes very dissipative at small time steps, per [27,33,34]. According to the tests of real shallow water systems in [25,26,28], the time step of the current model is suggested to be equal

to or larger than 60 s, under a grid of moderate scale. Hence, the model is tested here on gradually reduced time steps which are sequentially 60, 75, 90, 100, and 120 s, to clarify the influence of time steps on the accuracy of solutions. Correspondingly, the number of substeps for the ELM backtracking (*N*bt) is, respectively, set to 6, 8, 9, 10, and 12.

Under di fferent time steps, the histories of the simulated tide level, survey-point velocity, and sediment concentration are shown in Figure 8, respectively (taking Station QLG and Survey Point A1 as examples). In a simulation of the adopted spring neap tide process, the mean absolute error in simulated tide levels is calculated to be 0.01–0.02 m, the mean absolute error in simulated survey-point velocities is 0.019–0.035 m/s, and the mean absolute error in simulated survey-point sediment concentrations is 2.8–3.5%, based on the simulated histories using di fferent Δ*ts*. Although minor di fferences are observed in the results of simulations using di fferent time steps, the accuracies of the HDM and the STM are both stable with respect to the time step. The suggested time step (90 s) is revealed to be proper.

**Figure 8.** Comparisons of the simulated histories and field data. (**a**) Tide-level histories at Station Qinglonggang (QLG), (**b**) velocity histories at Survey Point A1, and (**c**) sediment concentration histories at Survey Point A1.

Second, the sensitivity study of the coefficient of Manning's roughness (*nm*) is performed by changing the *nm* in the North and the South Branches which are considered as the most important regions in this case study. The distribution of the *nm*, obtained by the calibration test, is taken as the reference and is denoted by "original friction (nm)". The tests, with the *nm* being reduced (−0.001) and increased (+0.001), are denoted by "nm −0.001" and "nm +0.001", respectively.

Under different *nm*, the histories of the simulated tide level and survey-point velocity are, respectively, shown in Figure 9 (taking Station QLG and Survey Point A1 as examples). It is found that the smaller the *nm* of the North and South Branches are, the stronger the landward floodtide flow in these reaches will be (characterized by higher tidal levels and large velocities). It is obvious that the variation of water levels with respect to the *nm* is just opposite for the estuary tidal flows and for the inland river flows. The variation of the peak water level in Station QLG is +0.15 m when the *nm* is reduced by 0.001, and is −0.04 m when the *nm* is increased by 0.001. The variation of the peak velocity in Survey Point A1 is +0.12 m/s when the *nm* is reduced by 0.001, and is −0.25 m/s when the *nm* is increased by 0.001.

**Figure 9.** Comparisons of the simulated histories and field data. (**a**) Tide-level histories at Station Qinglonggang (QLG) and (**b**) velocity histories at Survey Point A1.

Third, the sensitivity study of the coefficient of sediment-carrying capacity (*K*) is performed by changing the *K* in the North and South Branches, which are considered as the most important regions in this case study. The distribution of the *K*, obtained by the calibration test, is taken as the reference and is denoted by "original coefficient". The tests, with the *K* being reduced (−0.002) and increased (+0.002), are denoted by "*K* −0.002" and "*K* +0.002", respectively.

Under different *K*, the histories of the simulated sediment concentration are shown in Figure 10 (taking Survey Point A1 as an example). It is found that the simulated sediment concentration increases with respect to *K*. The variation of the sediment concentration in Survey Point A1 is −0.33 kg/m<sup>3</sup> when the *K* is reduced by 0.002, and is +0.25 kg/m<sup>3</sup> when the *K* is increased by 0.002.

**Figure 10.** Comparisons of the histories of the simulated sediment concentration and field data (at Survey Point A1).
