# Optimal Operation Model of Drainage Works for Minimizing Waterlogging Loss in Paddy Fields

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## Abstract

**:**

## 1. Introduction

## 2. Model Development

#### 2.1. Assumptions

- Ignore the duration it takes to open and close a specific drainage work, and all drainage works are scheduled once only for one waterlogging event.
- All drainage works only have two states—fully open and fully closed—the sluice is opened with opening height above the water surface or the pumping station is in operation at the rated flow, respectively. For the pump station with gate, the pump was launched only when the gate was closed. A pump station with multiple pumps is considered as one work.
- The flow rate and power consumption of a specific pump station are assumed to be constant and are calculated according to the rated value.

#### 2.2. Objective Functions and Calculation Formula

^{2}; ${A}_{i}$ is the area of the paddy field in unit $i$, hm

^{2}; $K$ is the number of drainage pumping stations; $P\left(j\right)$ is rated power of the drainage pumping station $j$, kWh; $\eta \left(j\right)$ is working efficiency coefficient of drainage pumping station $j$, %;$\delta $ is price of electricity, yuan/$\mathrm{kW}\xb7\mathrm{h}$; $T\left(j\right)$ is the running time of the pumping station $j$, h.

#### 2.2.1. Waterlogging Loss Estimation

^{2}; $CR{P}_{a}$—the planting area of crop $k$ in cell $i$, hm

^{2}; mm is loss coefficient of crop $k$ at different growth stages; $C{P}_{k}$ is unit price of crop $k$, yuan/kg; ${F}_{k}$ is yield of crop $k$ per unit area in average years, kg/m

^{2}; $D{C}_{k}$ is yield reduction rate of crop $k$ per unit area (as a percentage of average annual yield), %.

#### 2.2.2. Waterlogging Process Simulation

#### 2.3. Constraint Conditions

^{2}—for nodes without storage capacity, its value can be considered as 0; ${Z}_{i}^{j}$ is the water level of node $i$ in river $j$, m; ${Z}_{i}$ is average water level of node $i$, m.

^{3}/s;${Z}_{u}$ is upstream water level of overflow structure, m; ${Z}_{d}$ is downstream water level of overflow structure, m; ${Z}_{0}$ is floor elevation of overflow structure, m; $B$ is overcurrent width of overflow structure, m.

## 3. Model Solving by Using Genetic Algorithm

#### Genetic Algorithm

## 4. Result and Discussion

#### 4.1. Study Area

^{2}, composed of independent polders such that there is no water exchange between them. Therefore, this study only selects a specific agricultural field, Longben Polder, as the object to study the operation mode of drainage work.

^{2}, of which the cultivated area accounts for 90%. It is high in the south and low in the west, and the flow direction of the whole area is from south to north. The drainage system is composed of embankment, drainage ditch, barrier pond, river course, and gate station. There are eight pumping stations and four culverts in the research area, which are combined into seven stations according to the location of the pumping stations, including one inner drainage station and six outer drainage stations. The map of the study area and drainage system is shown in Figure 4.

#### 4.2. Calibration and Vertification

#### 4.3. Model Application

^{2}, occurred in a small part located at the eastern part of the study area. In Figure 8b, the reduction of average loss per km

^{2}was 13,670~166,530 yuan, which showed different decreases compared with the original operation in other regions. We found the most significant improvement in units with high vulnerability. By adopting the optimized scheme, the total yield loss of rice decreased by 35.4% to 1.589 million yuan, compared with 2.459 million yuan in local practice. The effect was very significant. The total of yield losses and operating costs of pump stations was 2,196,300 yuan, which decreased by about 33.8% compared with the original loss.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the operation rules of drainage works. $x$ is time; $y$ is the serial number of the drainage work.

**Figure 2.**Structure of the two-layer tank model. R represents the outflow of side hole, p represents the outflow of bottom hole, S represents water depth of the tank, and E means evaporation.

**Figure 4.**Study area map and drainage system generalization. (0)–(6) presrnts serial number of pump Station: (0). Heping, (1). Kouhe, (2). Nijia, (3). Hongqi, (4). Jiangmahe, (5). Zhongshihe, (6). Lvyanghe.

**Figure 6.**Process of rainfall and river water level change in Gaoyou Irrigation Area. (

**a**) Rain fall Event1(from 3:00 on 13 August to 3:00 on 18 August 2014) (

**b**) Rain fall Event2 (from 10:00 on 9 August to 2:00 on 21 August 2015).

**Figure 7.**Working flowchart of pumping stations in Rainfall Event 2. (

**a**) Original operation and (

**b**) optimized operation. Black represents gates and red represents pumps. Serial number of pump Station: P1—Heping, P2—Kouhe, P3—Nijia, P4—Hongqi, P5—Jiangmahe, P6—Zhongshihe, P7—Lvyanghe.

**Figure 8.**Distribution and process of flooding water depth and reduction in water level for the optimized scheme. (

**a**) Inundated water depth in Rainfall Event 1. (

**b**) Inundated water depth for optimized scheme in Rainfall Event 2. (

**c**) Reduction in inundated water depth compared with local practice in Rainfall Event 2.

**Figure 9.**The distribution of paddy losses before and after optimization of Rainfall Event 2. Number in black represents serial number of field and blue represent paddy loss. (

**a**) Distribution of flooding losses in original operation. (

**b**) Distribution of flooding losses after optimization. (1)–(22) represents numbers of fields.

Stage | Function |
---|---|

Tillering stage | $D{C}_{rice}=2.738{H}^{4.385}{T}^{1.462}$ |

Booting stage | $D{C}_{rice}=36.909{H}^{2.084}{T}^{0.437}$ |

Heading stage | $D{C}_{rice}=48.038{H}^{3.407}{T}^{0.300}$ |

Layer | Parameter/Unit | Optimal Value | Describe of Parameter | Outflow Formula |
---|---|---|---|---|

First | ${h}_{11}/m$ | 0.047 | the height of upper hole—represents the water storage capacity of the rice field | ${P}_{1}={\beta}_{1}{S}_{1}$ ${\mathrm{R}}_{21}$, ${\mathrm{R}}_{22}$ is calculated by the weir width of the broad-crested weir overflow formula. |

${h}_{12}/m$ | 0.0 | the height of lower hole—reflects the infiltration of the ridge of the paddy field | ||

${b}_{1}/{m}^{-1}$ | 0.000014 | weir width of broad-crested weir overflow formula | ||

${\mathsf{\beta}}_{1}$ | 0.008 | outflow coefficient of infiltration hole | ||

Second | ${\alpha}_{21}$ | 0.41 | outflow coefficient of upper hole | ${R}_{21}={\alpha}_{21}\left({S}_{2}-{h}_{21}\right)$ ${R}_{22}={\alpha}_{22}\left({S}_{2}-{h}_{22}\right)$ ${P}_{2}={\beta}_{2}{S}_{2}$ |

${\alpha}_{22}$ | 0.019 | outflow coefficient of lower hole | ||

${h}_{21}/m$ | 0.50 | height of upper hole—equal to soil water storage depth corresponding to the soil saturation capacity | ||

${h}_{22}/m$ | 0.40 | height of lower hole—equivalent to the soil water storage depth corresponding to field moisture capacity | ||

${b}_{2}/{m}^{-1}$ | 0.00076 | weir width of broad-crested weir overflow formula | ||

${\beta}_{2}$ | 0.032 | outflow coefficient of infiltration hole |

**Table 3.**Occurrence probability distribution parameters of rainfall and design rainfall with different return period.

Factor | Time | ||||
---|---|---|---|---|---|

1 h | 3 h | 6 h | 24 h | ||

Parameter | EX ^{1} (mm) | 40.96 | 63.14 | 81.13 | 110.00 |

Cv | 0.35 | 0.36 | 0.39 | 0.41 | |

Cs/Cv | 2.66 | 2.33 | 2.77 | 2.93 | |

Design rainfall | P1% (mm) | 83.25 | 127.44 | 172.06 | 250.46 |

P2% (mm) | 76.96 | 119.31 | 162.65 | 228.41 | |

P5% (mm) | 67.68 | 105.12 | 140.95 | 196.10 |

^{1}: EX is average rainfall, Cv is coefficient of variation and Cs is coefficient of skew.

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**MDPI and ACS Style**

Liu, Z.; Xiong, Y.; Xu, J.; Yang, S.; Jiang, Z.; Liu, F. Optimal Operation Model of Drainage Works for Minimizing Waterlogging Loss in Paddy Fields. *Water* **2021**, *13*, 2811.
https://doi.org/10.3390/w13202811

**AMA Style**

Liu Z, Xiong Y, Xu J, Yang S, Jiang Z, Liu F. Optimal Operation Model of Drainage Works for Minimizing Waterlogging Loss in Paddy Fields. *Water*. 2021; 13(20):2811.
https://doi.org/10.3390/w13202811

**Chicago/Turabian Style**

Liu, Zhenyang, Yujiang Xiong, Juzeng Xu, Shihong Yang, Zewei Jiang, and Fangping Liu. 2021. "Optimal Operation Model of Drainage Works for Minimizing Waterlogging Loss in Paddy Fields" *Water* 13, no. 20: 2811.
https://doi.org/10.3390/w13202811