Machine Learning for Reference Evapotranspiration Estimation with Limited Meteorological Data

Table of Contents

1 Introduction

Reference evapotranspiration (ETo) estimation is crucial for irrigation planning and water resource management, particularly in drought-prone regions like Morocco. The FAO-56 Penman-Monteith equation, while accurate, requires extensive meteorological data including temperature, humidity, solar radiation, and wind speed, making it impractical for regions with limited sensor infrastructure.

Traditional empirical equations such as Hargreaves-Samani, Romanenko, and Jensen-Haise offer simplified approaches but suffer from performance variability across different climatic conditions. This research addresses these limitations by exploring machine learning models that can achieve accurate ETo estimation with minimal input parameters.

2 Methodology

2.1 Data Collection and Preprocessing

Meteorological data from multiple stations in the Meknes region were collected, including temperature, humidity, solar radiation, and wind speed measurements. Data preprocessing involved handling missing values, normalization, and temporal alignment across different stations.

2.2 Machine Learning Models

Three machine learning models were implemented and compared:

• XGBoost: Gradient boosting framework known for high performance and efficiency
• Support Vector Machine (SVM): Effective for regression tasks with limited data
• Random Forest (RF): Ensemble method robust to overfitting

2.3 Experimental Setup

Two validation scenarios were implemented:

• Scenario 1: Random split of all available data
• Scenario 2: Training on one station, validation on another (spatial cross-validation)

3 Results and Discussion

3.1 Performance Comparison

All machine learning models outperformed traditional empirical equations in both validation scenarios. XGBoost demonstrated the highest accuracy with R² values exceeding 0.92, followed closely by Random Forest and SVM.

3.2 Feature Importance Analysis

Temperature and solar radiation emerged as the most critical features across all models. The analysis revealed that with just these two parameters, machine learning models could achieve 85-90% of the performance obtained with full parameter sets.

4 Technical Implementation

4.1 Mathematical Formulations

The standard FAO-56 Penman-Monteith equation serves as the benchmark:

$$ET_0 = \frac{0.408\Delta(R_n - G) + \gamma\frac{900}{T + 273}u_2(e_s - e_a)}{\Delta + \gamma(1 + 0.34u_2)}$$

Where $\Delta$ is the slope of vapor pressure curve, $R_n$ is net radiation, $G$ is soil heat flux, $\gamma$ is psychrometric constant, $T$ is air temperature, $u_2$ is wind speed, $e_s$ is saturation vapor pressure, and $e_a$ is actual vapor pressure.

4.2 Code Implementation

import xgboost as xgb
from sklearn.ensemble import RandomForestRegressor
from sklearn.svm import SVR
import numpy as np

class EToEstimator:
    def __init__(self, model_type='xgb'):
        if model_type == 'xgb':
            self.model = xgb.XGBRegressor(
                max_depth=6,
                learning_rate=0.1,
                n_estimators=100,
                objective='reg:squarederror'
            )
        elif model_type == 'rf':
            self.model = RandomForestRegressor(
                n_estimators=100,
                max_depth=10,
                random_state=42
            )
        elif model_type == 'svm':
            self.model = SVR(kernel='rbf', C=1.0, epsilon=0.1)
    
    def train(self, X_train, y_train):
        self.model.fit(X_train, y_train)
    
    def predict(self, X_test):
        return self.model.predict(X_test)

# Feature selection: temperature and solar radiation only
features = ['temp_max', 'temp_min', 'solar_rad']
target = 'ETo_FAO56'

5 Future Applications

The research demonstrates significant potential for practical implementation in several areas:

• Smart Irrigation Systems: Integration with IoT-based irrigation controllers for real-time water management
• Climate Change Adaptation: Improved water resource planning in drought-prone regions
• Agricultural Technology: Development of mobile applications for small-scale farmers
• Water Policy: Data-driven decision support for water allocation and pricing

Future research directions include transfer learning across different climatic zones, integration with satellite data, and development of edge computing solutions for remote areas.

6 References

1. Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and drainage paper 56.
2. Landeras, G., Ortiz-Barredo, A., & López, J. J. (2008). Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country. Agricultural Water Management, 95(5), 553-565.
3. Maestre-Valero, J. F., Martínez-Alvarez, V., & González-Real, M. M. (2013). Evaluation of SVM and ELM for daily reference evapotranspiration estimation in semi-arid regions. Computers and Electronics in Agriculture, 89, 100-106.
4. López-Urrea, R., Martín de Santa Olalla, F., Fabeiro, C., & Moratalla, A. (2006). Testing evapotranspiration equations using lysimeter observations in a semiarid climate. Agricultural Water Management, 85(1-2), 15-26.
5. Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., ... & Bengio, Y. (2014). Generative adversarial nets. Advances in neural information processing systems, 27.

7 Expert Analysis