# Relative Performance of 1-D Versus 3-D Hydrodynamic, Water-Quality Models for Predicting Water Temperature and Oxygen in a Shallow, Eutrophic, Managed Reservoir

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Study Methods

#### 2.1. Study Sites and Artificial Mixing Systems

#### 2.2. The 1-D Model

#### 2.3. The 3-D Model

## 3. Numerical Tests

## 4. Results and Discussion

#### 4.1. Year 2014 and 2015 Simulations

_{field}and v

_{sim}are respectively the field measurement and simulated data of the variable of interest, and n is the total number of field data points.

#### 4.2. Qualitative Comparison of Simulated Temperature and DO Profiles of 2014 and 2015

#### 4.3. Quantitative Comparison of Simulated Temperature and DO Profiles of Year 2014 and 2015

#### 4.4. Quantitative Analysis of the Predicted Thermal Structures

#### 4.5. Comparison of GLM-AED2 and Si3D-AED2 with EM

#### 4.6. Performance of Si3D-AED2

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Bathymetry contours of Falling Creek Reservoir (FCR) and field data collection sites. The locations of the side stream supersaturation (SSS) system (short white line) and the epilimnion mixing (EM) system (long white line) are also shown.

**Figure 2.**Comparisons of the one-dimensional (1-D, sediment module on, top row) and three dimensional (3-D) model temperature results (middle row) with field data (bottom row). (

**a**) Temperature plot of 2014. (

**b**) Temperature plot of 2015.

**Figure 3.**Comparisons of the 1-D (sediment module on, top row) and 3-D model DO results (middle row) with field data (bottom row). (

**a**) Dissolved oxygen (DO) plot of 2014. (

**b**) DO plot of 2015.

**Figure 4.**Profiles of the RMSEs of the temperature (left) and DO (right) RMSEs of the 1-D and 3-D models for 2014 and the mixed period of 2015.

**Figure 5.**Comparison of the simulated temperature and field data for EM15 at FCR50 (year 2015). The time of the field data collection is indicated by black inverse triangles on the plot of the field data.

**Figure 6.**Comparison of the simulated temperature and field data for EM16–3 at FCR50. The time of the field data collection is indicated by black inverse triangles on the plot of the field data.

**Table 1.**Information about the operation of the oxygenation system in the years 2014 and 2015 and the corresponding simulation periods.

Year | Field Campaign DoY | Oxygenation Settings | Simulation Period (DoY) | ||
---|---|---|---|---|---|

DoY | Oxygen Flow Rate (kg/day) | Water Flow Rate (L/min) | |||

2014 | 121–310 | 126–154 | 20 | 208 | 121–273 |

180–210 | 20 | ||||

230–273 | 25 | ||||

2015 | 90–331 | 125–152 | 15 | 90–331 |

**Table 2.**The Si3D-AED2 and GLM-AED2 simulation dates, the EM operation periods and the corresponding flow rates in the years 2015 and 2016.

Year | Name | Simulation DoY | EM Period DoY | Time | Flow Rate (L/min) |
---|---|---|---|---|---|

2015 | EM15 | 146–154 | 151 | 12:00–15:00 | 708 |

153 | 12:00–15:00 | ||||

2016 | EM16–1 | 147–153 | 150 | 12:00–18:00 | 708 |

EM16–2 | 172–183 | 178 | 12:00–19:00 | 425 | |

19:00–24:00 | 283 | ||||

179 | 0:00–12:00 | ||||

EM16–3 | 202–213 | 206 | 12:00–17:00 | 227 | |

17:00–24:00 | 708 | ||||

207 | 0:00–12:00 | ||||

12:00–24:00 | 340 | ||||

208 | 0:00–12:00 |

**Table 3.**The root mean square errors (RMSEs) of the predicted temperatures (in °C) at different depths for 2014 and 2015. The lower RMSEs between the 1-D and 3-D model results for both stratified and mixed conditions are shown in bold.

1-D | 3-D | |||||
---|---|---|---|---|---|---|

2014 * | 2015 | 2014 * | 2015 | |||

Stratified | Mixed | Stratified | Mixed | |||

0.1 m | 1.05 | 1.18 | 0.92 | 2.64 | 3.40 | 4.07 |

3.0 m | 1.68 | 2.39 | 1.06 | 1.64 | 1.64 | 3.25 |

6.0 m | 2.54 | 3.12 | 0.92 | 3.17 | 4.54 | 3.03 |

9.0 m | 2.45 | 1.42 | 1.36 | 1.20 | 3.84 | 3.21 |

Whole lake ** | 1.99 | 1.98 | 1.17 | 2.28 | 3.14 | 3.25 |

**Table 4.**The RMSEs of the predicted DO (in mmol/m

^{3}) at different depths for 2014 and 2015. Lower RMSEs between the 1-D and 3-D model results are shown in bold.

1-D | 3-D | |||||
---|---|---|---|---|---|---|

2014 * | 2015 | 2014 * | 2015 | |||

Stratified | Mixed | Stratified | Mixed | |||

0.1 m | 15.87 | 36.29 | 73.63 | 43.36 | 51.63 | 56.24 |

3.0 m | 78.71 | 130.04 | 48.34 | 38.51 | 70.42 | 57.91 |

6.0 m | 86.88 | 59.80 | 42.02 | 59.23 | 88.37 | 95.42 |

9.0 m | 103.25 | 143.63 | 64.93 | 95.95 | 153.58 | 163.59 |

Whole lake ** | 72.84 | 96.50 | 56.31 | 56.59 | 89.44 | 98.79 |

1-D | 3-D | Literature Range | |||||
---|---|---|---|---|---|---|---|

2014 * | 2015 | 2014 * | 2015 | ||||

Stratified | Mixed | Stratified | Mixed | ||||

Temperature | 0.072 | 0.081 | 0.11 | 0.084 | 0.12 | 0.12 | 0.037–0.12 |

DO | 0.29 | 0.29 | 0.18 | 0.24 | 0.23 | 0.32 | 0.054–0.33 |

**Table 6.**The RMSEs of the predicted thermocline depths and the metalimnion bottom depths for the entire stratified period of 2014 and 2015 from Si3D and GLM-AED2 simulations. The relatively lower RMSEs between the 1-D and 3-D model results are shown in bold.

Si3D-AED2 | GLM-AED2 | |||
---|---|---|---|---|

Year | 2014 | 2015 | 2014 | 2015 |

RMSE of the thermocline depth (m) | 1.7 | 1.2 | 1.7 | 3.0 |

RMSE of the metalimnion bottom depth (m) | 2.4 | 0.92 | 2.3 | 2.2 |

**Table 7.**RMSEs (in m) of simulated metalimnion bottom depths during the EM periods of 2015 and 2016.

EM15 | EM16–1 | EM16–2 | EM16–3 | Weighted Average | |
---|---|---|---|---|---|

GLM | 0.6 | 0.6 | 1 | 0.7 | 0.7 |

Si3D | 0.5 | 0.2 | 0.8 | 0.3 | 0.5 |

**Table 8.**The NMAEs of the temperature and DO of the 3-D model at FCR20, FCR30 and FCR45 for the 2014 simulation.

FCR20 | FCR30 | FCR45 | Average | |
---|---|---|---|---|

Temperature | 0.077 | 0.077 | 0.085 | 0.080 |

DO | 0.17 | 0.16 | 0.20 | 0.18 |

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**MDPI and ACS Style**

Man, X.; Lei, C.; Carey, C.C.; Little, J.C.
Relative Performance of 1-D Versus 3-D Hydrodynamic, Water-Quality Models for Predicting Water Temperature and Oxygen in a Shallow, Eutrophic, Managed Reservoir. *Water* **2021**, *13*, 88.
https://doi.org/10.3390/w13010088

**AMA Style**

Man X, Lei C, Carey CC, Little JC.
Relative Performance of 1-D Versus 3-D Hydrodynamic, Water-Quality Models for Predicting Water Temperature and Oxygen in a Shallow, Eutrophic, Managed Reservoir. *Water*. 2021; 13(1):88.
https://doi.org/10.3390/w13010088

**Chicago/Turabian Style**

Man, Xiamei, Chengwang Lei, Cayelan C. Carey, and John C. Little.
2021. "Relative Performance of 1-D Versus 3-D Hydrodynamic, Water-Quality Models for Predicting Water Temperature and Oxygen in a Shallow, Eutrophic, Managed Reservoir" *Water* 13, no. 1: 88.
https://doi.org/10.3390/w13010088