# Global Sensitivity Analysis of a Water Quality Model in the Three Gorges Reservoir

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}[27]. 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 the 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 [28,29].

^{2}, a length of 33 km, and an annual average discharge of 7.5 m

^{3}s

^{−1}. After impoundment of the TGR, a 7-km-long bay was formed, which was influenced by TGR regulation, which ranges the water level from 145 m to 175 m. Hereafter, this area is called Caotang Bay (CB) in this paper. The CB’s average depth is 18.39 m when the TGR is at the lowest level in the summer (up to 145 m). The CB’s average depth is 33.54 m and its maximum depth is 70 m when the TGR is at the highest level in the winter (up to 175 m).

## 3. Materials and Methods

#### 3.1. Tributary Bay Water Quality Model

_{Q}is the stream runoff, V

_{P}is the direct precipitation, V

_{G}is the groundwater, V

_{O}is the set of other inflows, such as sewage, V

_{in}is the hydrographically driven advective inflow, V

_{out}is the advective outflow of water from the system, and V

_{E}is the evaporation. In this study, precipitation, groundwater, other inflows, and evaporation are smaller than 5% of V

_{Q}, so we assume V

_{P}= V

_{G}= V

_{O}= V

_{E}= 0.

#### 3.2. Global Sensitivity Analysis

_{i}is the variance contribution of individual parameter X

_{i}to the total variance, V

_{ij}is a part of the total variance caused by the interactions between X

_{i}and X

_{j}, and V

_{12…k}is the variance due to the interactions between all parameters. Using this variance decomposition, the first-order sensitivity S

_{i}and the total sensitivity index S

_{ti}are given as (see notations in Table 2):

#### 3.3. Design of Numerical Experiments

#### 3.4. Initial Conditions

^{−1}; detritus: 0.24 mmolC L

^{−1}; dissolved oxygen: 9.11 mg L

^{−1}; nitrate: 1.76 mg L

^{−1}; ammonium: 0.08 mg L

^{−1}; phosphate: 0.11 mg L

^{−1}; and dissolved silicon: 8.16 mg L

^{−1}. The physical and biological state variables were assumed to be vertically and horizontally homogenous in the numerical domain.

## 4. Results

#### 4.1. Simulation Result for the Water Quality Model

^{−1}and the RMSE of DO is 1.92 mg L

^{−1}. The parameter sensitivity will be analyzed in the following section.

#### 4.2. Parameter Sensitivity Temporal Variation for Chlorophyll-a

_{ti}) for chlorophyll-a.

_{0}(maximum phytoplankton growth rate), T

_{1}(lower optimum temperature for algal growth), K

_{p}(phosphate half saturation constant for algal), and μ

_{1}(phytoplankton linear mortality rate). Although none of these parameters can be classified as an important parameter according to Table 3, the summation over these four parameters explains around 82% of chlorophyll-a variance. The remaining parameters are irrelevant during this season. These indicate that the algae growth in summer is a combined effect of several factors instead of one key factor. In the early autumn, it is the same as in the summer, while in the middle and later autumn, T

_{1}becomes a very important parameter. In winter and spring, T

_{1}and μ

_{1}become very important parameters alternatively.

#### 4.3. Parameter Sensitivity Temporal Variation for DO

_{1}, μ

_{1}, b

_{p}(Phytoplankton basal respiration rate), and r

_{DET}(Detritus remineralization rate). The summation over these four parameters explains around 93% of DO concentration variance. The remaining parameters are irrelevant during this period. During the rest of the year, T

_{1}and μ

_{1}become very important parameters alternatively.

_{ti}is seldom equal to 1, because the summation of the sensitivity indices is a measure of model additivity [8].

## 5. Discussion

#### 5.1. Ecological Implication from Parameter Sensitivity for Chlorophyll-a

_{0}, T

_{1}, K

_{p}, and μ

_{1}) have a greater influence compared with other parameters, which indicates that the TGR tributary bay is similar to other water bodies and has difference with them as well. A GSA on Lake Dianchi [42], which is a shallow lake with an average depth of 5.2 m in China, shows that the max growth rate of algae, the basal respiration rate, the chlorophyll-a induced light extinction coefficient, and the lower bound of optimal temperature for algae have an important influence on Chlorophyll-a. These indicate that there are sufficient nutrient or no nutrient limits in Lake Dianchi. A GSA on the Paso de las Piedras Reservoir [43], which is a shallow reservoir with an average depth of 8.2 m in Argentina, shows that the most important parameters for phytoplankton are the organic phosphorus mineralization rate, phytoplankton death and respiration, and the background light attenuation coefficient. These indicate that there are also no nutrient limits due to organic phosphorus mineralization in the Paso de las Piedras Reservoir. Therefore, light is not an important parameter in the TGR compared with shallow lakes and reservoirs.

#### 5.2. Ecological Implication from Parameter Sensitivity for DO

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{3}, NH

_{4}, PO

_{4}and Si are phytoplankton, detritus, dissolved oxygen, nitrate, ammonium, phosphate, and dissolved silicon, respectively. Superscript represents the biochemistry process, subscript represents the related variables. gpp, mor, exc, res, rmn, denit, nit and upt represent gross primary production, respiration, excretion, mortality, remineralization, denitrification, nitrification and uptake.

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**Figure 3.**Schematic of the water quality model in TGR. P, DET, DO, NO

_{3}, NH

_{4}, PO

_{4}and Si are phytoplankton, detritus, dissolved oxygen, nitrate, ammonium, phosphate, and dissolved silicon, respectively.

**Table 1.**The parameter values of the ecological water quality model applied in the Caotang Bay (CB).

Parameter | Description | Value | Unit | Selected to GSA (Y/N) |
---|---|---|---|---|

${r}_{0}$ | Maximum phytoplankton growth rate | 3.039 | day^{−1} | Y |

${T}_{1}$ | Lower optimum temperature for algal growth | 24 | °C | Y |

${T}_{2}$ | Upper optimum temperature for algal growth | 29 | °C | Y |

$KW$ | Light extinction coefficient for all absorption components (except algae) | 1 | m^{−1} | Y |

$KC$ | Factor for light extinction coefficient for algae | 0.01 | m^{−1} mmolC^{−1} | N |

${I}_{opt}$ | Optimum light intensity | 80.0 | W m^{−2} | Y |

${K}_{N{O}_{3}}$ | Nitrate half saturation constant for algae | 0.040 | mmolN m^{−3} | N |

${K}_{N{H}_{4}}$ | Ammonia half saturation constant for algae | 0.030 | mmolN m^{−3} | N |

${K}_{P}$ | Phosphate half saturation constant for algae | 0.285 | mmolP m^{−3} | Y |

${K}_{S}$ | Silica half saturation constant for algae | 1.16 | mmolSi m^{−3} | N |

${\mu}_{1}$ | Phytoplankton linear mortality rate | 0.335 | day^{−1} | Y |

${\mu}_{2}$ | Phytoplankton second order mortality rate | 0.001 | mmolC day^{−1} | Y |

${\alpha}_{P}$ | Phytoplankton excretion rate | 0.15 | day^{−1} | N |

${b}_{P}$ | Phytoplankton basal respiration rate | 0.2 | day^{−1} | Y |

${\gamma}_{P}$ | Phytoplankton active respiration rate | 0.1 | day^{−1} | N |

${O}_{cr}$ | Oxygen critical concentration for nitrification | 11.161 | mmolO_{2} m^{−3} | Y |

$dcr$ | Oxygen confinement factor for nitrification | 6.0 | -- | N |

${r}_{DET}$ | Detritus remineralization rate | 0.127 | day^{−1} | Y |

${T}_{scd}$ | Temperature confinement factor for remineralization | 20.0 | -- | N |

${T}_{hsr}$ | Reference temperature for remineralization | 13.0 | °C | N |

${r}_{nit}$ | Nitrification rate | 0.045 | day^{−1} | N |

${r}_{den}$ | Denitrification rate | 0.01 | mmolN m^{−3} day^{−1} | N |

${K}_{DET}$ | Detritus half saturation constant | 6.625 | mmolC m^{−3} | N |

${d}_{DN}$ | Denitrification ratio of detritus | 1.25 | -- | N |

${d}_{NN}$ | Ammonia release ratio for denitrification | 0.189 | -- | N |

${d}_{PN}$ | Phosphate release ratio for denitrification | 0.012 | -- | N |

${d}_{SN}$ | Silica release ratio for denitrification | 0.259 | -- | N |

${R}_{PC}$ | Redfield ratio P:C | 1:106 | -- | N |

${R}_{NC}$ | Redfield ratio N:C | 16:106 | -- | N |

${R}_{SC}$ | Redfield ratio Si:C | 22:106 | -- | N |

${m}_{CO}$ | Stoichiometric number of carbon to oxygen | 1 | mmolO_{2} mmolC^{−1} | N |

${m}_{NO}$ | Stoichiometric number of nitrogen to oxygen | 2 | mmolO_{2} mmolN^{−1} | N |

Symbol | Description |
---|---|

N | Sample size |

k | Number of factors |

X_{i} | Generic factor |

X | N × k matrix of input factors |

${X}_{~i}$ | N
× (k − 1) matrix of all factors but X_{i} |

${V}_{{X}_{i}}(\cdot )$, ${E}_{{X}_{i}}(\cdot )$ | Variance or mean of argument (·) taken over
X_{i} |

${V}_{{X}_{~i}}(\cdot )$, ${E}_{{X}_{~i}}(\cdot )$ | Variance or mean of argument (·) taken over all factors but
X_{i} |

Condition | Description |
---|---|

0.8 ≤ S_{ti} ≤ 1 | Very important |

0.5 ≤ S_{ti} < 0.8 | Important |

0.3 ≤ S_{ti} < 0.5 | Unimportant |

0 ≤ S_{ti} < 0.3 | Irrelevant |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/w10020153

**AMA Style**

Cheng Y, Li Y, Ji F, Wang Y.
Global Sensitivity Analysis of a Water Quality Model in the Three Gorges Reservoir. *Water*. 2018; 10(2):153.
https://doi.org/10.3390/w10020153

**Chicago/Turabian Style**

Cheng, Yao, Yajun Li, Fei Ji, and Yuchun Wang.
2018. "Global Sensitivity Analysis of a Water Quality Model in the Three Gorges Reservoir" *Water* 10, no. 2: 153.
https://doi.org/10.3390/w10020153