# Employing Data Mining Algorithms and Mathematical Empirical Models for Predicting Wind Drift and Evaporation Losses of a Sprinkler Irrigation Method

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Site

#### 2.2. Procedures for Sprinkler Tests

_{d}is the coefficient of discharge (C

_{d}= 0.98) according to findings from experiments performed by Playán et al. [39] and Ouazaa et al. [40]. By monitoring the flow rate in the field, Playán et al. [39] obtained the coefficient of discharge of the RC130-BY sprinkler for a range of working pressures. The nozzle orifice’s area is A, the acceleration due to gravity is g (measured in m/s

^{2}), the working pressure is P (measured in kPa), and q is a constant [41,42,43]. For this study, q was taken to be equal to 0.50. In each set test, the irrigation water depth (ID) released by the sprinkler was estimated using Equation (2):

^{2}). The proportion of the irrigation water depth (ID) released by the sprinkler that was not collected in the pluviometers was employed to obtain the percentage of WDEL during each test [18,44,45]. The WDEL were calculated using Equation (3):

_{CC}is the average water depth measured by the pluviometers.

#### 2.3. WDEL Mathematical Empirical Models

_{a}and e

_{s}are the actual vapor pressure of the air and the saturation vapor pressure, respectively, kPa; T is the air dry-bulb temperature, °C; and RH is the relative humidity of the air, %. The same meteorological and operating conditions were simulated for WDEL using the mathematical empirical models of Yazar [19], Trimmer [20], Tarjuelo et al. [11], and Playán et al. [18]. Table 2 lists the investigated empirical equations, where WDEL are expressed as a percentage (%), D is the primary nozzle diameter expressed in millimeters, $\mathsf{\Delta}\mathrm{e}$ is the vapor pressure deficit expressed in kPa, P is the working pressure expressed in kPa, and W is the wind speed expressed in meters per second.

#### 2.4. Details of the Data Mining Algorithms

#### 2.5. Multilayer Perceptron

_{ij}is the input from unit i to j, w

_{ji}is the weight from unit i to j, α is the learning rate, and δ

_{j}is the error discovered at unit j. The weights are adjusted using training examples, and this procedure is repeated a certain number of cycles or until the inaccuracy is negligible or cannot be lowered. The weight update at the n

^{th}iteration of the backpropagation is made partially dependent on the amount of weight changed in the (n − 1)

^{th}iteration in order to increase the performance of the backpropagation process. A constant termed the momentum term (β) controls how much the (n − 1)

^{th}iteration contributes; however, it is increased to produce a quicker convergence. Equation (7) provides the new rule applied for the weight update at the n

^{th}iteration.

#### 2.6. REPTree

#### 2.7. Prediction Performance of Fitted Models

_{i}is the value of WDEL observed in field experiments, $\overline{\mathrm{Y}}$ and $\widehat{\overline{\mathrm{Y}}}$ are the means of the observed and predicted WDEL values, and Nt is the number of data points in the testing data set.

## 3. Results and Discussion

#### 3.1. Wind Drift and Evaporation Losses (WDEL)

#### 3.2. Prediction of WDEL—Data Mining Models

^{2}). The points in this figure are sparsely distributed around the regression line (R

^{2}= 0.967), indicating that the values derived from the experimental data are either overestimated or underestimated. The distribution of points around the best fit line demonstrates the method’s great accuracy in estimating low WDEL values. Weka software version 3.6.13 was also used to create a REPTree model using the same data used to train the ANN model [47]. Figure 4 displays a scatter plot of the estimated WDEL values from the REPTree model against the values of the tested data that were actually observed. A proper agreement is indicated by the R

^{2}score of 0.943. When predicting low WDEL values, the distribution of points around the best fit line illustrates how inaccurate this method is; nevertheless, as WDEL increase, the amount of error diminishes.

#### 3.3. Mathematical Empirical Models for WDEL Simulations

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**An ANN model with one hidden layer to predict WDEL. Each connection is linked with a weight. Sigmoid units are employed as hidden and output units (number of epochs were 500, error per epoch was 0.0072431, learning rate was 0.3, and momentum was 0.2).

**Figure 3.**Scatter plot of estimated WDEL values using ANN model against observed values of testing data set.

**Figure 4.**Scatter plot of estimated WDEL values using REPTree model against observed values of testing data set.

**Table 1.**Spacing of collectors according to the ASAE Standard [38].

Sprinkler Throw Distance (m) | Maximum Collector Distance between Centers (m) |
---|---|

0.3–3 | 0.30 |

3–6 | 0.60 |

6–12 | 0.75 |

>12 | 1.50 |

Model | Empirical Equation |
---|---|

Trimmer [20] | $\mathrm{WDEL}=\left(1.98\times \mathrm{D}+0.22\u2206{\mathrm{e}}^{0.63}+3.6\times {10}^{-4}\times {\mathrm{P}}^{1.16}+0.14\times {\mathrm{W}}^{0.7}\right)$ |

Yazar [19] | $\mathrm{WDEL}=(0.003\times \mathrm{exp}\left(0.2\times \mathrm{W}\right)\times \left(10\times \u2206\mathrm{e}\times {10}^{0.59}\times {\mathrm{T}}^{0.23}\times {\mathrm{P}}^{0.76}\right)+0.2$ |

Tarjuelo et al. [11] | $\mathrm{WDEL}=\left(0.007\times \mathrm{P}+7.38\times \u2206{\mathrm{e}}^{0.5}+0.844\times \mathrm{W}\right)$ |

Playán et al. [18] | $\mathrm{WDEL}=\left(20.3+0.214\times {\mathrm{W}}^{2}-2.29\times {10}^{-3}\times {\mathrm{RH}}^{2}\right)$ |

**Table 3.**WDEL averaged across a range of working pressures, nozzle diameters, and environmental factors.

Nozzle Diameter | Actual Working Pressure | Wind Speed | Air Temperature | Air Relative Humidity | Vapor Pressure Deficit | WDEL |
---|---|---|---|---|---|---|

(mm) | (kPa) | (m/s) | (°C) | (%) | (kPa) | (%) |

4 | 188.1 | 0.82 | 14.93 | 57.11 | 0.73 | 11.60 |

4 | 286.6 | 1.07 | 19.12 | 47.89 | 1.16 | 14.85 |

4 | 379.4 | 1.27 | 21.59 | 40.56 | 1.54 | 18.49 |

Overall mean | 1.05 | 18.55 | 48.52 | 1.14 | 14.98 | |

4.5 | 191.3 | 0.92 | 15.17 | 59.44 | 0.70 | 11.17 |

4.5 | 287.5 | 1.87 | 17.97 | 51.33 | 1.02 | 14.17 |

4.5 | 384.5 | 2.85 | 24.89 | 38.44 | 1.95 | 17.94 |

Overall mean | 1.88 | 19.34 | 49.74 | 1.22 | 14.43 | |

5 | 190.4 | 0.87 | 10.83 | 59.22 | 0.53 | 10.61 |

5 | 287.3 | 1.82 | 14.73 | 49.11 | 0.86 | 13.68 |

5 | 379.8 | 2.58 | 16.71 | 35.67 | 1.23 | 16.25 |

Overall mean | 1.76 | 14.09 | 48.00 | 0.87 | 13.52 |

**Table 4.**Error statistics regarding WDEL estimation by the REPTree and ANN models using testing data set.

The Tested Model | RMSE (%) | MAE (%) |
---|---|---|

ANN | 0.771 | 0.600 |

REPTree | 0.679 | 0.544 |

**Table 5.**Observed and predicted WDEL values using different approaches under various climatic and operating conditions (testing data set).

D | P | W | T | RH | $\mathbf{\u2206}\mathbf{e}$ | Observed WDEL | Predicted WDEL | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Trimmer [20] | Yazar [19] | Tarjuelo et al. [11] | Playán et al. [18] | REPTree | ANN | |||||||

(mm) | (kPa) | (m/s) | (°C) | (%) | (kPa) | (%) | (%) | (%) | (%) | (%) | (%) | (%) |

4.5 | 193 | 1.20 | 15.40 | 56 | 0.77 | 12.44 | 1.99 | 3.75 | 8.84 | 13.43 | 12.104 | 11.91 |

4.5 | 288 | 1.98 | 19.11 | 49 | 1.13 | 14.65 | 3.99 | 8.16 | 11.53 | 15.64 | 15.638 | 14.63 |

4.5 | 195 | 0.47 | 14.30 | 64 | 0.59 | 9.20 | 1.35 | 2.49 | 7.42 | 10.97 | 8.885 | 9.18 |

5.0 | 272 | 1.43 | 14.63 | 51 | 0.82 | 12.51 | 2.43 | 5.23 | 9.78 | 14.78 | 13.473 | 12.30 |

4.5 | 194 | 1.18 | 14.50 | 58 | 0.69 | 12.00 | 1.90 | 3.49 | 8.50 | 12.89 | 11.037 | 11.42 |

4.0 | 186 | 0.80 | 16.90 | 56 | 0.85 | 13.08 | 2.17 | 3.41 | 8.77 | 13.26 | 13.473 | 11.45 |

5.0 | 388 | 2.57 | 16.81 | 36 | 1.23 | 16.76 | 5.57 | 12.10 | 13.06 | 18.75 | 15.683 | 16.03 |

5.0 | 189 | 0.93 | 10.51 | 60 | 0.51 | 11.01 | 1.26 | 2.47 | 7.37 | 12.24 | 11.037 | 9.80 |

4.5 | 299 | 1.89 | 17.50 | 52 | 0.96 | 13.81 | 3.77 | 7.35 | 10.92 | 14.87 | 13.473 | 13.86 |

5.0 | 195 | 0.95 | 11.24 | 59 | 0.55 | 11.23 | 1.33 | 2.68 | 7.63 | 12.52 | 11.037 | 10.05 |

4.0 | 379 | 1.30 | 22.10 | 41 | 1.57 | 18.50 | 6.18 | 9.91 | 13.00 | 16.81 | 18.204 | 17.98 |

4.0 | 376 | 1.28 | 20.50 | 40 | 1.45 | 18.18 | 5.86 | 9.21 | 12.59 | 16.99 | 18.204 | 17.79 |

4.0 | 290 | 1.02 | 19.10 | 53 | 1.04 | 13.40 | 3.59 | 5.80 | 10.42 | 14.09 | 13.473 | 12.71 |

4.0 | 285 | 0.87 | 19.46 | 49 | 1.15 | 14.50 | 3.53 | 5.84 | 10.65 | 14.96 | 15.683 | 13.20 |

4.5 | 190 | 0.52 | 14.70 | 62 | 0.64 | 9.96 | 1.40 | 2.62 | 7.65 | 11.56 | 8.885 | 9.52 |

5.0 | 379 | 2.43 | 16.32 | 34 | 1.23 | 16.10 | 5.26 | 11.35 | 12.87 | 18.92 | 15.638 | 16.19 |

Average | 13.58 | 3.22 | 5.99 | 10.06 | 14.54 | 13.50 | 13.00 | |||||

Minimum | 9.20 | 1.26 | 2.47 | 7.37 | 10.97 | 8.89 | 9.18 | |||||

Maximum | 18.50 | 6.18 | 12.10 | 13.06 | 18.92 | 18.20 | 17.98 | |||||

Standard deviation | 2.75 | 1.75 | 3.30 | 2.11 | 2.40 | 2.89 | 2.86 |

**Table 6.**Results of the index of agreement (d), correlation coefficient (r), and confidence index (c) tests for the different prediction methods in relation to observed WDEL using the testing data set.

Prediction Method | Index of Agreement | Correlation Coefficient | Confidence Index | Performance Based on Confidence Index |
---|---|---|---|---|

The model described by Trimmer [20] | 0.325 | 0.966 | 0.314 | Terrible |

The model described by Yazar [19] | 0.437 | 0.898 | 0.393 | Terrible |

The model described by the model described by Tarjuelo et al. [11] | 0.650 | 0.949 | 0.617 | Average |

Playán et al. [18] | 0.913 | 0.908 | 0.829 | Very good |

REPTree model | 0.984 | 0.971 | 0.956 | Optimal |

ANN model | 0.980 | 0.983 | 0.964 | Optimal |

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**MDPI and ACS Style**

Al-Dosary, N.M.N.; Maray, S.A.; Al-Hamed, S.A.; Aboukarima, A.M. Employing Data Mining Algorithms and Mathematical Empirical Models for Predicting Wind Drift and Evaporation Losses of a Sprinkler Irrigation Method. *Water* **2023**, *15*, 922.
https://doi.org/10.3390/w15050922

**AMA Style**

Al-Dosary NMN, Maray SA, Al-Hamed SA, Aboukarima AM. Employing Data Mining Algorithms and Mathematical Empirical Models for Predicting Wind Drift and Evaporation Losses of a Sprinkler Irrigation Method. *Water*. 2023; 15(5):922.
https://doi.org/10.3390/w15050922

**Chicago/Turabian Style**

Al-Dosary, Naji Mordi Naji, Samy A. Maray, Saad A. Al-Hamed, and Abdulwahed M. Aboukarima. 2023. "Employing Data Mining Algorithms and Mathematical Empirical Models for Predicting Wind Drift and Evaporation Losses of a Sprinkler Irrigation Method" *Water* 15, no. 5: 922.
https://doi.org/10.3390/w15050922