*4.4. Balances of Water and Sediment Fluxes*

Using the simulation results (see Video S1 for details), the spatial distributions of water and sediment fluxes in the Yangtze Estuary are sketched, as shown in Figure 11. The horizontal circulations of the water and the sediment fluxes are quantitatively analyzed as follows.

**Figure 11.** Sketch of the spatial distributions of water and sediment fluxes in Yangtze Estuary.

For a spring tide, the ebbtide *CSWF* at the entrance cross-section of the South Branch (SE) comprises three parts. Water flux, which intrudes upstream of cross-section SE from the South Branch during the floodtide duration, returns during the ebbtide duration and contributes to the first part (31.41 × 10<sup>8</sup> m<sup>3</sup>/day). Inflow runoff from Datong (16.31 × 10<sup>8</sup> m<sup>3</sup>/day) contributes to the second part. The water spillover from the North Branch (0.6 × 10<sup>8</sup> m<sup>3</sup>/day) contributes to the third part, accounting for 1.24% of the ebbtide *CSWF* at cross-section SE. The ebbtide *CSSF* at the entrance cross-section of the South Branch (SE) also comprises three parts. Sediment flux, which intrudes upstream of cross-section SE from the South Branch during the floodtide duration, returns during the ebbtide duration, and contributes to the first part (85.76 × 10<sup>4</sup> t/day). Sediment input at Datong is 18.39 × 10<sup>4</sup> t/day and it evolves to 25.35 × 10<sup>4</sup> t/day at cross-section XLJ after a long-distance adjustment of erosion and deposition, which contributes to the second part. The sediment spillover from North Branch (30.89 × 10<sup>4</sup> t/day) contributes to the third part, accounting for 21.75% of the ebbtide *CSSF* at cross-section SE.

For a neap tide, the water spillover from the North Branch reduces to 0.46 × 10<sup>8</sup> m<sup>3</sup>/day, accounting for 1.39% of the *CSWF* at cross-section SE during the ebbtide duration. At the same time, the sediment spillover from the North Branch reduces to 7.88 × 10<sup>4</sup> t/day, accounting for 18.46% of the *CSSF* at cross-section SE during the ebbtide duration.
