# Water Residence Time in a Typical Tributary Bay of the Three Gorges Reservoir

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[19]. Its annual flow is 951.3 km

^{3}. The TGD, located at the end of the upper Yangtze River, is 185 m high. Construction began in 1998 and was completed in 2003. The TGR is currently one of the largest reservoirs in the world, with a capacity of 39.3 billion m

^{3}over a length of 663 km and an average width of 1.1 km [20,21].

## 2. Model Setup

#### 2.1. Study Area

^{2}, a length of 31.4 km, and an annual average discharge of 2.54 m

^{3}/s which is much lower than that of the Yangtze River’s ~11,000 m

^{3}/s. After the impoundment of the TGR, a 6-km-long bay was formed, which was influenced by TGR regulation, which can modify the water level from 145 m to 175 m. Hereafter, this area is called Zhuyi Bay (ZB) in this paper. The ZB’s average depth is 36.23 m and its maximum water depth is 80 m when the TGR is at the highest level in the winter (up to 175 m). The wind over ZB is weak with an annual mean wind speed of 1.5 m/s.

#### 2.2. Hydrodynamic Model

#### 2.3. Diagnosing RT by the Adjoint Method

## 3. Results

#### 3.1. Validation of the Hydrodynamic Model

#### 3.2. Annual Mean RT of ZB

^{2}/s. For the average water depth of 20 m, the timescale of vertical mixing is about 1.5 days, which is much smaller than that of the horizontal transport. Therefore, the annual mean RT exhibits little vertical variability.

#### 3.3. Seasonal Variation of RT

## 4. Discussion

#### 4.1. Relationship between RT and TGR Regulation

#### 4.2. Influences of Dynamic Processes on the RT

#### 4.3. The Potential Relationship between RT and Algal Blooms in the Tributary

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Acronym | Full Name |

TGR | Three Gorges Reservoir |

TGD | Three Gorges Dam |

ZB | Zhuyi Bay |

RT | Residence time |

## References

- De Brauwere, A.; de Brye, B.; Blaise, S.; Deleersnijder, E. Residence time, exposure time and connectivity in the Scheldt Estuary. J. Mar. Syst.
**2011**, 84, 85–95. [Google Scholar] [CrossRef] - Lucas, L.V.; Thompson, J.K.; Brown, L.R. Why are diverse relationships observed between phytoplankton biomass and transport time? Limnol. Oceanogr.
**2009**, 54, 381–390. [Google Scholar] [CrossRef] - McLusky, D.S.; Elliott, M.; Elliott, M. The Estuarine Ecosystem: Ecology, Threats and Management; Oxford University Press: Oxford, UK, 2004. [Google Scholar]
- Wolanski, E.; Elliott, M. Estuarine Ecohydrology: An Introduction; Elsevier: Amsterdam, The Netherlands, 2015. [Google Scholar]
- Delhez, É.J.M.; Wolk, F. Diagnosis of the transport of adsorbed material in the Scheldt Estuary: A proof of concept. J. Mar. Syst.
**2013**, 128, 17–26. [Google Scholar] [CrossRef] - Andutta, F.P.; Ridd, P.V.; Deleersnijder, E.; Prandle, D. Contaminant exchange rates in estuaries—New formulae accounting for advection and dispersion. Prog. Oceanogr.
**2014**, 120, 139–153. [Google Scholar] [CrossRef] - Bolin, B.; Rodhe, H. A note on the concepts of age distribution and transit time in natural reservoirs. Tellus
**1973**, 25, 58–62. [Google Scholar] [CrossRef] - Zimmerman, J.T.F. Mixing and flushing of tidal embayments in the western dutch wadden sea part I: Distribution of salinity and calculation of mixing time scales. Neth. J. Sea Res.
**1976**, 10, 149–191. [Google Scholar] [CrossRef] - Takeoka, H. Fundamental concepts of exchange and transport time scales in a coastal sea. Cont. Shelf Res.
**1984**, 3, 311–326. [Google Scholar] [CrossRef] - Delhez, E.J.M.; Campin, J.-M.; Hirst, A.C.; Deleersnijder, E. Toward a general theory of the age in ocean modelling. Ocean Model.
**1999**, 1, 17–27. [Google Scholar] [CrossRef][Green Version] - Delhez, É.J.M. On the concept of exposure time. Cont. Shelf Res.
**2013**, 71, 27–36. [Google Scholar] [CrossRef] - Nixon, S.W.; Ammerman, J.W.; Atkinson, L.P.; Berounsky, V.M.; Billen, G.; Boicourt, W.C.; Boynton, W.R.; Church, T.M.; Ditoro, D.M.; Elmgren, R.; et al. The fate of nitrogen and phosphorus at the land-sea margin of the north atlantic ocean. Biogeochemistry
**1996**, 35, 141–180. [Google Scholar] [CrossRef] - Dettmann, E.H. Effect of water residence time on annual export and denitrification of nitrogen in estuaries: A model analysis. Estuaries
**2001**, 24, 481–490. [Google Scholar] [CrossRef] - Crump, B.C.; Hopkinson, C.S.; Sogin, M.L.; Hobbie, J.E. Microbial biogeography along an estuarine salinity gradient: Combined influences of bacterial growth and residence time. Appl. Environ. Microbiol.
**2004**, 70, 1494–1505. [Google Scholar] [CrossRef] - Delesalle, B.; Sournia, A. Residence time of water and phytoplankton biomass in coral reef lagoons. Cont. Shelf Res.
**1992**, 12, 939–949. [Google Scholar] [CrossRef] - Lucas, L.V.; Koseff, J.R.; Cloern, J.E.; Monismith, S.G.; Thompson, J.K. Processes governing phytoplankton blooms in estuaries. I: The local production-loss balance. Mar. Ecol. Prog. Ser.
**1999**, 187, 1–15. [Google Scholar] [CrossRef] - Lucas, L.V.; Koseff, J.R.; Monismith, S.G.; Cloern, J.E.; Thompson, J.K. Processes governing phytoplankton blooms in estuaries. II: The role of horizontal transport. Mar. Ecol. Prog. Ser.
**1999**, 187, 17–30. [Google Scholar] [CrossRef] - Valiela, I.; McClelland, J.; Hauxwell, J.; Behr, P.J.; Hersh, D.; Foreman, K. Macroalgal blooms in shallow estuaries: Controls and ecophysiological and ecosystem consequences. Limnol. Oceanogr.
**1997**, 42, 1105–1118. [Google Scholar] [CrossRef][Green Version] - Chen, C.; Li, J.; Shen, H.; Wang, Z. Yangtze river of China: Historical analysis of discharge variability and sediment flux. Geomorphology
**2001**, 41, 77–91. [Google Scholar] [CrossRef] - Nilsson, C.; Reidy, C.A.; Dynesius, M.; Revenga, C. Fragmentation and flow regulation of the world’s large river systems. Science
**2005**, 308, 405. [Google Scholar] [CrossRef] - Yang, S.L.; Zhang, J.; Dai, S.B.; Li, M.; Xu, X.J. Effect of deposition and erosion within the main river channel and large lakes on sediment delivery to the estuary of the yangtze river. J. Geophys. Res. Earth Surf.
**2007**, 112, 111–119. [Google Scholar] [CrossRef] - Wu, J.; Huang, J.; Han, X.; Xie, Z.; Gao, X. Three-gorges dam—Experiment in habitat fragmentation? Science
**2003**, 300, 1239–1240. [Google Scholar] [CrossRef] [PubMed] - Shen, G.; Xie, Z. Three Gorges Project: Chance and challenge. Science
**2004**, 304, 681. [Google Scholar] [CrossRef] - Stone, R. Three Gorges Dam: Into the unknown. Science
**2008**, 321, 628–632. [Google Scholar] [CrossRef] [PubMed] - Fu, B.-J.; Wu, B.-F.; Lü, Y.-H.; Xu, Z.-H.; Cao, J.-H.; Niu, D.; Yang, G.-S.; Zhou, Y.-M. Three Gorges Project: Efforts and challenges for the environment. Prog. Phys. Geogr.
**2010**, 34, 741–754. [Google Scholar] [CrossRef] - Xu, X.; Tan, Y.; Yang, G. Environmental impact assessments of the Three Gorges Project in China: Issues and interventions. Earth Sci. Rev.
**2013**, 124, 115–125. [Google Scholar] [CrossRef][Green Version] - Holbach, A.; Norra, S.; Wang, L.; Yijun, Y.; Hu, W.; Zheng, B.; Bi, Y. Three Gorges Reservoir: Density pump amplification of pollutant transport into tributaries. Environ. Sci. Technol.
**2014**, 48, 7798–7806. [Google Scholar] [CrossRef] [PubMed] - Zhao, Y.; Zheng, B.; Wang, L.; Qin, Y.; Li, H.; Cao, W. Characterization of mixing processes in the confluence zone between the Three Gorges Reservoir mainstream and the daning river using stable isotope analysis. Environ. Sci. Technol.
**2016**, 50, 9907–9914. [Google Scholar] [CrossRef] - Cheng, Y.; Wang, Y.; Zhou, H.; Dang, C. The influence of the Three Gorges Reservoir regulation on a typical tributary heat budget. Environ. Earth Sci.
**2018**, 77, 764. [Google Scholar] [CrossRef] - Cheng, Y.; Wang, Y.; Zhou, H.; Hu, M.; Jiang, R.; Bao, Y.; Dang, C. Heat budget contribute rate in the Three Gorges Reservoir tributary bay between mainstream and tributary using stable isotope analysis. Water Supply
**2019**, 19, 553–564. [Google Scholar] [CrossRef] - Wang, L.; Cai, Q.; Tan, L.; Kong, L. Phytoplankton development and ecological status during a cyanobacterial bloom in a tributary bay of the Three Gorges Reservoir, China. Sci. Total Environ.
**2011**, 409, 3820–3828. [Google Scholar] [CrossRef] - Liu, L.; Liu, D.; Johnson, D.M.; Yi, Z.; Huang, Y. Effects of vertical mixing on phytoplankton blooms in xiangxi bay of Three Gorges Reservoir: Implications for management. Water Res.
**2012**, 46, 2121–2130. [Google Scholar] [CrossRef] - Yang, Z.; Cheng, B.; Xu, Y.; Liu, D.; Ma, J.; Ji, D. Stable isotopes in water indicate sources of nutrients that drive algal blooms in the tributary bay of a subtropical reservoir. Sci. Total Environ.
**2018**, 634, 205–213. [Google Scholar] [CrossRef] [PubMed] - Cheng, Y.; Li, Y.; Ji, F.; Wang, Y. Global sensitivity analysis of a water quality model in the Three Gorges Reservoir. Water
**2018**, 10, 153. [Google Scholar] [CrossRef] - Zhou, Z.; Li, X.; Chen, L.; Li, B.; Liu, T.; Ai, B.; Yang, L.; Liu, B.; Chen, Q. Macrobenthic assemblage characteristics under stressed waters and ecological health assessment using ambi and m-ambi: A case study at the xin’an river estuary, yantai, China. Acta Oceanol. Sin.
**2018**, 37, 77–86. [Google Scholar] [CrossRef] - Li, H.; Li, Z.; Li, Z.; Yu, J.; Liu, B. Evaluation of ecosystem services: A case study in the middle reach of the heihe river basin, northwest China. Phys. Chem. Earth Parts A/B/C
**2015**, 89–90, 40–45. [Google Scholar] [CrossRef] - Liu, Z.; Lin, L.; Xie, L.; Gao, H. Partially implicit finite difference scheme for calculating dynamic pressure in a terrain-following coordinate non-hydrostatic ocean model. Ocean Model.
**2016**, 106, 44–57. [Google Scholar] [CrossRef] - Munk, W.H. Note on the theory of the thermocline. J. Mar. Res.
**1948**, 7, 276–295. [Google Scholar] - Lin, L.; Liu, Z. Tvdal: Total variation diminishing scheme with alternating limiters to balance numerical compression and diffusion. Ocean Model.
**2019**, 134, 42–50. [Google Scholar] [CrossRef] - Fairall, C.W.; Bradley, E.F.; Rogers, D.P.; Edson, J.B.; Young, G.S. Bulk parameterization of air-sea fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment. J. Geophys. Res. Oceans
**1996**, 101, 3747–3764. [Google Scholar] [CrossRef] - Delhez, É.J.M.; Heemink, A.W.; Deleersnijder, É. Residence time in a semi-enclosed domain from the solution of an adjoint problem. Estuar. Coast. Shelf Sci.
**2004**, 61, 691–702. [Google Scholar] [CrossRef] - Delhez, E.J.M. Transient residence and exposure times. Ocean Sci.
**2006**, 2, 1–9. [Google Scholar] [CrossRef][Green Version] - Delhez, É.J.M.; Deleersnijder, É. The boundary layer of the residence time field. Ocean Dyn.
**2006**, 56, 139–150. [Google Scholar] [CrossRef] - De Brye, B.; de Brauwere, A.; Gourgue, O.; Delhez, E.J.M.; Deleersnijder, E. Water renewal timescales in the Scheldt Estuary. J. Mar. Syst.
**2012**, 94, 74–86. [Google Scholar] [CrossRef] - Zeng, H.; Song, L.; Yu, Z.; Chen, H. Distribution of phytoplankton in the Three-Gorge Reservoir during rainy and dry seasons. Sci. Total Environ.
**2006**, 367, 999–1009. [Google Scholar] [CrossRef] - Zhou, G.; Bi, Y.; Zhao, X.; Chen, L.; Hu, Z. Algal growth potential and nutrient limitation in spring in Three-Gorges Reservoir, China. Fresenius Environ. Bull.
**2009**, 18, 1642–1647. [Google Scholar] - He, Q.; Kang, L.; Sun, X.; Jia, R.; Zhang, Y.; Ma, J.; Li, H.; Ai, H. Spatiotemporal distribution and potential risk assessment of microcystins in the Yulin River, a tributary of the Three Gorges Reservoir, China. J. Hazard. Mater.
**2018**, 347, 184–195. [Google Scholar] [CrossRef] - Dai, H.; Mao, J.; Jiang, D.; Wang, L. Longitudinal hydrodynamic characteristics in reservoir tributary embayments and effects on algal blooms. PLoS ONE
**2013**, 8, e68186. [Google Scholar] [CrossRef] - Hagy, J.D.; Boynton, W.R.; Sanford, L.P. Estimation of net physical transport and hydraulic residence times for a coastal plain estuary using box models. Estuaries
**2000**, 23, 328–340. [Google Scholar] [CrossRef] - Shen, J.; Haas, L. Calculating age and residence time in the tidal york river using three-dimensional model experiments. Estuar. Coast. Shelf Sci.
**2004**, 61, 449–461. [Google Scholar] [CrossRef] - Scully, M.E. Wind modulation of dissolved oxygen in Chesapeake Bay. Estuaries Coasts
**2010**, 33, 1164–1175. [Google Scholar] [CrossRef] - Li, Y.; Li, M. Wind-driven lateral circulation in a stratified estuary and its effects on the along-channel flow. J. Geophys. Res. Oceans
**2012**, 117. [Google Scholar] [CrossRef][Green Version] - Du, J.; Shen, J. Water residence time in Chesapeake Bay for 1980–2012. J. Mar. Syst.
**2016**, 164, 101–111. [Google Scholar] [CrossRef] - Shen, J.; Lin, J. Modeling study of the influences of tide and stratification on age of water in the tidal James River. Estuar. Coast. Shelf Sci.
**2006**, 68, 101–112. [Google Scholar] [CrossRef] - Liu, Z.; Wang, H.; Guo, X.; Wang, Q.; Gao, H. The age of Yellow River water in the Bohai Sea. J. Geophys. Res. Oceans
**2012**, 117. [Google Scholar] [CrossRef][Green Version] - Wang, H.; Guo, X.; Liu, Z. The age of Yodo River water in the Seto Inland Sea. J. Mar. Syst.
**2019**, 191, 24–37. [Google Scholar] [CrossRef] - Li, J.; Yang, W.; Li, W.; Mu, L.; Jin, Z. Coupled hydrodynamic and water quality simulation of algal bloom in the Three Gorges Reservoir, China. Ecol. Eng.
**2018**, 119, 97–108. [Google Scholar] [CrossRef] - Ye, L.; Han, X.; Xu, Y.; Cai, Q. Spatial analysis for spring bloom and nutrient limitation in xiangxi bay of Three Gorges Reservoir. Environ. Monit. Assess.
**2007**, 127, 135–145. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Illustration of the domain of interest, with (

**a**) the Yangtze River basin. (

**b**) the location of the Zhuyi Bay (ZB).

**Figure 4.**Comparison of the observed and simulated velocity profiles at site OBS for the 12 months in 2014. Blue circles denote simulation, and red circles denote observation.

**Figure 5.**Comparison of observed and simulated water temperature profiles at site OBS for the 12 months in 2014. Blue circles denote simulation, and red lines denote observation.

**Figure 6.**Vertical mean (

**a**), surface (

**b**), and bottom (

**c**) RT (days) averaged over 2014. The contour interval is five days. (

**d**) difference between the surface and bottom RT. Positive value denotes larger RT in surface layers. The contour interval is two days.

**Figure 7.**Vertical profile of the annual mean RT (days) along the deep channel section. The contour interval is five days.

**Figure 8.**Monthly variation of RT averaged over the entire Bay. Red lines denote medians of RT in the month, blue rectangles denote the first and third quartiles, dashed lines denote the upper and lower whiskers, and red crosses denote the outliers.

**Figure 13.**The observed water temperature difference between ZB and the Yangtze River. Positive value indicates that ZB temperature is higher than the Yangtze River. Negative value indicates that ZR temperature is lower than the Yangtze River.

Case | Tributary Discharge | Yangtze River Discharge | Local Winds | Baroclinic Forcing |
---|---|---|---|---|

0 | Yes | Yes | Yes | Yes |

1 | 0.5 times | Yes | Yes | Yes |

2 | Yes | 0.5 times | Yes | Yes |

3 | Yes | Yes | No | Yes |

4 | Yes | Yes | Yes | No |

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**MDPI and ACS Style**

Cheng, Y.; Mu, Z.; Wang, H.; Zhao, F.; Li, Y.; Lin, L.
Water Residence Time in a Typical Tributary Bay of the Three Gorges Reservoir. *Water* **2019**, *11*, 1585.
https://doi.org/10.3390/w11081585

**AMA Style**

Cheng Y, Mu Z, Wang H, Zhao F, Li Y, Lin L.
Water Residence Time in a Typical Tributary Bay of the Three Gorges Reservoir. *Water*. 2019; 11(8):1585.
https://doi.org/10.3390/w11081585

**Chicago/Turabian Style**

Cheng, Yao, Zheng Mu, Haiyan Wang, Fengxia Zhao, Yu Li, and Lei Lin.
2019. "Water Residence Time in a Typical Tributary Bay of the Three Gorges Reservoir" *Water* 11, no. 8: 1585.
https://doi.org/10.3390/w11081585