# Deep Machine Learning for Forecasting Daily Potential Evapotranspiration in Arid Regions, Case: Atacama Desert Header

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Foundations of Evapotranspiration

#### Potential Evapotranspiration

- $E{T}_{0}$ = reference evapotranspiration (mm/day).
- γ* = modified psychometric constant (mbar/°C).
- ${e}_{s}-{e}_{a}$ = saturation vapor pressure deficit (mb).
- ${e}_{s}$ = saturation vapor pressure (mb).
- ${u}_{2}$ = wind speed at 2 m from the surface (m/s).
- L = latent heat of vaporization (cal/g).
- ∆ = slope of the saturation pressure curve.
- γ = psychrometric constant (mbar/°C).
- ${R}_{n}$ = net radiation on the crop surface (cal/cm
^{2}day). - T = average temperature (°C).
- G = density of soil heat flux (cal/cm
^{2}).

- $E{T}_{0}$ = reference evapotranspiration.
- ${T}_{max}$ = maximum temperature °C.
- ${T}_{min}$ = minimum temperature °C.
- ${R}_{s}$ = solar radiation extraterrestrial in (MJ/m
^{2}day).

- $ET$ = reference evapotranspiration.
- $SR$ = solar radiation (MJ/m
^{2}day). - ${T}_{max}$ = maximum temperature °C.
- ${T}_{min}$ = minimum temperature °C.
- ${\alpha}_{1}$ = is a coefficient that is calculated as follows:

- ET = reference evapotranspiration.
- RH = is the percentage relative humidity.
- T = average temperature °C.

## 3. Theoretical Foundations of Artificial Neural Networks

#### 3.1. Artificial Neural Networks and Multilayer Perceptron

- $\widehat{y}$ = exit.$g$ = non-linear activation function.
- ${w}_{0}$ = bias (weights).
- $\sum}_{i=1}^{m}{x}_{i}{w}_{i$ = linear combination of inputs.

#### 3.2. Multi-Layer Perceptron

#### 3.3. Optimization

- W = new position for the parameters that are closest to the minimum.
- n = learning ratio

## 4. Materials and Methods

#### 4.1. Data Description

#### 4.2. KDD (Knowledge Discovery from Data)

^{2}) and evapotranspiration (mm), which were measured and recorded every 30 min. In the selection phase, we transformed the time and date variables and addressed the Null values. In the transformation phase, we performed average aggregation tasks in the case of temperature, humidity, wind speed, atmospheric pressure, radiation, and summation aggregation in the case of precipitation and evapotranspiration; grouping this especially with the date information, to have the data organized at a daily level.

#### 4.3. The Data Science and Its Application in Hydrology

#### 4.4. Study Area

#### 4.5. Used Approaches

#### 4.6. Method Applied to Avoid Prediction

#### 4.7. Performance Measures of Predict Models

## 5. Results and Discussion

#### 5.1. Results

#### 5.1.1. Data Pre-Processing Results

#### 5.1.2. Applied Methods Results

#### 5.2. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**ETo forecasting approaches: (

**a**) Direct approach; (

**b**) Indirect approach; adapted from Torres et al. (2011) [7].

**Figure 6.**Comparison of the 300-day ETo prediction using a neural network with the actual data (Direct approach).

**Figure 7.**Blue color, original data; red color, predicted data. The figure shows the prediction for 300 days, using neural networks, of Maximum Temperature (°C), Minimum Temperature (°C), Wind Speed (km/hr), Moisture (%), Pressure (hPa), and Evapotranspiration (mm).

**Figure 8.**ETo calculated using the Penman-Monteith, Hargreaves-Samani, Ritchie, and Turc equations for 300 days, using climate variables predicted with neural networks compared with the actual data.

**Figure 9.**Comparison of the ETo as compared to the application of the Penman-Monteith, Hargreaves-Samani, Ritchie, and Turc equations.

Name | Ref. | Equation |
---|---|---|

Penman-Monteith equation | [25] | (1) |

Hargreaves-Samani equation | [22] | (2) |

Ritchie equation | [23] | (3) |

Turc equation | [24] | (4) |

(5) |

Indicator | Neural Network | Penman-Monteith | Hargreaves-Samani | Ritchie | Turc |
---|---|---|---|---|---|

MAE | 0.033 | 0.586 | 0.467 | 0.749 | 0.104 |

MSE | 0.002 | 0.411 | 0.285 | 0.632 | 0.016 |

RMSE | 0.043 | 0.641 | 0.534 | 0.795 | 0.128 |

RAE | 0.016 | 0.230 | 0.192 | 0.285 | 0.046 |

R-Squared | 0.998 | 0.550 | 0.689 | 0.309 | 0.982 |

t-7 | t-6 | t-5 | t-4 | t-3 | t-2 | t-1 | t |
---|---|---|---|---|---|---|---|

−0.32 | −0.32 | −0.33 | 0.35 | −0.35 | −0.36 | −0.36 | 0.35 |

−0.32 | −0.33 | −0.35 | 0.35 | −0.36 | −0.36 | −0.35 | 0.36 |

−0.33 | −0.35 | −0.35 | 0.36 | −0.36 | −0.35 | −0.36 | 0.36 |

−0.35 | −0.35 | −0.36 | 0.36 | −0.35 | −0.36 | −0.36 | 0.36 |

−0.35 | −0.36 | −0.36 | 0.35 | −0.36 | −0.36 | −0.36 | 0.37 |

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**MDPI and ACS Style**

Pino-Vargas, E.; Taya-Acosta, E.; Ingol-Blanco, E.; Torres-Rúa, A.
Deep Machine Learning for Forecasting Daily Potential Evapotranspiration in Arid Regions, Case: Atacama Desert Header. *Agriculture* **2022**, *12*, 1971.
https://doi.org/10.3390/agriculture12121971

**AMA Style**

Pino-Vargas E, Taya-Acosta E, Ingol-Blanco E, Torres-Rúa A.
Deep Machine Learning for Forecasting Daily Potential Evapotranspiration in Arid Regions, Case: Atacama Desert Header. *Agriculture*. 2022; 12(12):1971.
https://doi.org/10.3390/agriculture12121971

**Chicago/Turabian Style**

Pino-Vargas, Edwin, Edgar Taya-Acosta, Eusebio Ingol-Blanco, and Alfonso Torres-Rúa.
2022. "Deep Machine Learning for Forecasting Daily Potential Evapotranspiration in Arid Regions, Case: Atacama Desert Header" *Agriculture* 12, no. 12: 1971.
https://doi.org/10.3390/agriculture12121971