# Modeling of Mixed Crop Field Water Demand and a Smart Irrigation System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Field Water Balance Method

#### 2.2. Crop Evapotranspiration

^{−1}); ${\mathrm{R}}_{\mathrm{n}}$ is the net radiation at the crop surface ($\mathrm{MJ}\xb7{\mathrm{m}}^{-2}\xb7{\mathrm{d}}^{-1}$); $\mathrm{G}$ is the heat flux of soil ($\mathrm{MJ}\xb7{\mathrm{m}}^{-2}\xb7{\mathrm{d}}^{-1}$); $\mathrm{T}$ is the mean daily temperature at 2-m height (°C); ${\mathrm{U}}_{2}$ is the measured wind velocity at 2 m height ($\mathrm{m}\xb7{\mathrm{s}}^{-1})$; ${\mathrm{e}}_{\mathrm{s}}$ is the saturation vapor pressure ($\mathrm{kPa}$); ${\mathrm{e}}_{\mathrm{a}}$ is the actual vapor pressure ($\mathrm{kPa}$); ${\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}$ is the vapor pressure deficit ($\mathrm{kPa}$); $\Delta $ is the gradient of saturated vapor pressure ($\mathrm{kPa}\xb7{\xb0\mathrm{C}}^{-1}$); $\mathsf{\gamma}$ is psychrometric the constant of humidity ($\mathrm{kPa}\xb7{\xb0\mathrm{C}}^{-1}$).

#### 2.3. Irrigation Water Demand

#### 2.4. Percolation Calculation

#### 2.4.1. Vertical Percolation

_{t}can be obtained as in Equation (14):

#### 2.4.2. Lateral Seepage

#### 2.5. Field Surface Runoff Calculation

_{D}is continuous rainfall in D days (mm), according to the Xi-Zhou rainfall station with a 10-year return period, which is 294.5 $\mathrm{mm}\xb7{\mathrm{d}}^{-1}$; and H is the height of the ridge (mm).

## 3. System Dynamic Model: VENSIM

#### 3.1. Study Area Overview

#### 3.2. Model Establishment

- Level: Also called accumulated amount, the accumulation of flow inside the system, which indicates the variable’s situation in a moment, for example, field storage; integral calculus in mathematics.
- Rate: Also called rate amount, which implies the in or out storage flow. The value is obtained by function calculation; differential calculus in mathematics.
- Auxiliary: Its main function is to describe the relation between Level and Rate, and makes the system structure more clear. Another function is that of test value or test function.
- Arrow: It is used to connect auxiliary and flow formula.

#### 3.3. Model Verification

^{2}) was used as a criterion. Based on the field station setting limitations, the discharge data was available during the experimental period ranges from 17 April 2015 to 6 May 2015. The discharge of the observed and simulated shows good fit in similarity with the coefficient of correlation R

^{2}equals 0.83 (Figure 13).

## 4. Results and Discussion

#### 4.1. Scenario 1: 30% Reduction of Planned Irrigation Water

#### 4.2. Scenario 2: 50% Discount of Planned Irrigation Water

- The target ponding depth is 5 cm for the 1st day to 20th day cropping period. Blocks 1–3 reach this depth within 11 days, while block 4 reaches the target depth on the 34th day. The irrigation started in a sequence from upstream to downstream and reduces the issue of lack of water. The upstream fields receive the targeted depth irrigation and then transfer the water to downstream fields. The simulation results of targeted water depth of blocks 1–4 are shown in Figure 21, Figure 22, Figure 23 and Figure 24.
- The water depth of block 5 dropped below the saturated soil moisture curve on the 6th day due to lack of water. On the 21st day, the field storage turns lower than field capacity and the vertical percolation stopped. Up to the 29th day, the decrease in field storage continued and reached to the wilting point, also stopping the evapotranspiration, as shown in Figure 25.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 13.**The comparison between observed and simulated discharge (CMD: Cubic Meters per Day, R

^{2}: coefficient of correlation).

**Figure 14.**Irrigation, discharge, and rainfall simulation result of 30% reduction of planned irrigation water during the first crop season.

**Figure 15.**Simulation of block 1 under 30% reduction of planned irrigation water during the first crop season.

**Figure 16.**Simulation of block 2 under 30% reduction of planned irrigation water during the first crop season.

**Figure 17.**Simulation of block 3 under 30% reduction of planned irrigation water during the first crop season.

**Figure 18.**Simulation of block 4 under 30% reduction of planned irrigation water during first crop season.

**Figure 19.**Simulation of block 5 under 30% reduction of planned irrigation water during the first crop season.

**Figure 20.**Irrigation, discharge, and rainfall simulation result for 50% reduction of the planned irrigation water during first crop season.

**Figure 21.**Simulation of block 1 under 50% reduction of planned irrigation water during first crop season.

**Figure 22.**Simulation of block 2 under 50% reduction of planned irrigation water during first crop season.

**Figure 23.**Simulation of block 3 under 50% reduction of planned irrigation water during first crop season.

**Figure 24.**Simulation of block 4 under 50% reduction of planned irrigation water during first crop season.

**Figure 25.**Simulation of block 5 under 50% reduction of planned irrigation water during first crop season.

Growth Days | Growth Stage | Growth Degree | Crop Season | |
---|---|---|---|---|

1st Crop | 2nd Crop | |||

— | Ground | — | — | — |

1~15 | Seedling | 185 | 0.92 | 1.01 |

16~30 | Early tillering | 381 | 1.00 | 1.11 |

31~45 | End of tillering | 589 | 1.00 | 1.11 |

46~60 | Early flowering | 808 | 1.13 | 1.23 |

61~75 | End of flowering | 1032 | 1.13 | 1.23 |

76~90 | Early ripening | 1259 | 0.89 | 0.93 |

91~105 | Middle of ripening | 1487 | 0.89 | 0.93 |

106~120 | End of ripening | 1715 | 0.89 | 0.93 |

Conveyance Loss (%) | Block 1 | Block 2 | Block 3 | Block 4 | Block 5 | |
---|---|---|---|---|---|---|

Sub-Block | ||||||

No. 1 | 8.15 | 13.15 | 20.23 | 21.16 | 28.5 | |

No. 2 | 8.15 | 13.15 | 20.23 | 24.93 | 28.5 | |

No. 3 | 10.45 | 11.9 | 22.01 | 24.93 | 29.33 | |

No. 4 | 10.45 | 11.9 | 22.01 | 33.33 | 29.33 | |

No. 5 | 11.71 | 19.08 | 22.85 | — | 30.38 | |

No. 6 | 11.71 | 19.08 | — | — | 30.38 | |

No. 7 | 12.74 | 21 | — | — | — | |

No. 8 | 12.74 | 21 | — | — | — |

Growth Stages | Seedling | Start of Tillering | End of Tillering | Young Panicle Differentiation | Young Panicle Formation | Booting Stage | Heading | Milk Ripe | Mature | Reaping | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|

The day after transplanting | 1 | 16 | 25 | 30 | 48 | 50 | 65 | 77 | 92 | 107 | 120 | 130 |

Date | 3/4 | 3/19 | 3/28 | 4/2 | 4/20 | 4/22 | 5/7 | 5/19 | 6/3 | 6/18 | 7/1 | 7/11 |

Ponding depth (cm) | 5 | 5 | 5 | 5 | 5 | 5 | 10 | 10 | 10 | 3 | 3 | 0 |

Symbol | Variable Definition | Component Description | Remark |
---|---|---|---|

Storage in the system | Storage | Initial value | |

Components | |||

Flow rate or storage rate | Flow Rate | Figures, tables, functions or logics are acceptable | |

Components | |||

The assistant variables between storage and flow | Auxiliary | ||

The connection of information and function in the system | Assistant | Connection | |

Components | |||

The system boundary | — | — |

**Table 5.**Simulation result of 30% reduction of planned irrigation water depth (mm) during the first crop season.

Block | 30% Discount of Planned Irrigation Water | Total Irrigated Water | Rainfall | Infiltration | Discharge | Crop Evapotranspiration | $\frac{\mathbf{Discharge}}{\mathbf{Rainfall}}$ | $\frac{\mathbf{Discharge}}{\left(\mathbf{Irrigated}\text{}\mathbf{water}\right)}$ |
---|---|---|---|---|---|---|---|---|

1 | 1003.2 | 762.1 | 675 | 537.2 | 858.8 | 336.3 | 1.272 | 1.127 |

2 | 756.6 | 675 | 535.9 | 336.3 | 1.135 | |||

3 | 732.7 | 675 | 533.5 | 336.3 | 1.172 | |||

4 | 704.5 | 675 | 528.4 | 336.3 | 1.219 | |||

5 | 624.7 | 675 | 513.4 | 336.3 | 1.374 |

**Table 6.**Simulation of 50% reduction of planned irrigation water depth (mm) during the first crop season.

Block | 50% Discount of Planned Irrigation Water | Total Irrigated Water | Rainfall | Infiltration | Discharge | Crop Evapotranspiration | $\frac{\mathbf{Discharge}}{\mathbf{Rainfall}}$ | $\frac{\mathbf{Discharge}}{\mathbf{Irrigated}\text{}\mathbf{water}}$ |
---|---|---|---|---|---|---|---|---|

1 | 716.6 | 761.5 | 675 | 537.3 | 516.0 | 336.3 | 0.764 | 0.678 |

2 | 740.7 | 675 | 534.7 | 336.3 | 0.697 | |||

3 | 703.7 | 675 | 528.3 | 336.3 | 0.733 | |||

4 | 558.0 | 675 | 498.4 | 336.3 | 0.925 | |||

5 | 366.6 | 675 | 420.4 | 325.5 | 1.408 |

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**MDPI and ACS Style**

Wu, R.-S.; Liu, J.-S.; Chang, S.-Y.; Hussain, F.
Modeling of Mixed Crop Field Water Demand and a Smart Irrigation System. *Water* **2017**, *9*, 885.
https://doi.org/10.3390/w9110885

**AMA Style**

Wu R-S, Liu J-S, Chang S-Y, Hussain F.
Modeling of Mixed Crop Field Water Demand and a Smart Irrigation System. *Water*. 2017; 9(11):885.
https://doi.org/10.3390/w9110885

**Chicago/Turabian Style**

Wu, Ray-Shyan, Jih-Shun Liu, Sheng-Yu Chang, and Fiaz Hussain.
2017. "Modeling of Mixed Crop Field Water Demand and a Smart Irrigation System" *Water* 9, no. 11: 885.
https://doi.org/10.3390/w9110885