Enhancing Agricultural Sustainability Through Intelligent Irrigation Using PVT Energy Applications: Implementing Hybrid Machine and Deep Learning Models

Abstract

This research focuses on developing an intelligent irrigation solution for agricultural systems utilising solar photovoltaic-thermal (PVT) energy applications. This solution integrates PVT applications, prediction, modelling and forecasting as well as plants’ physiological characteristics. The primary objective is to enhance water management and irrigation efficiency through innovative digital techniques tailored to different climate zones. In the initial phase, the performance of PVT solutions was evaluated using ANSYS Fluent software R19.2, revealing that scaled PVT systems offer optimal efficiency for PV systems, thereby optimising electrical production. Subsequently, a comprehensive approach combining integral feature selection (IFS) with machine learning (ML) and deep learning (DL) models was applied for reference evapotranspiration (ETo) prediction and water needs forecasting. Through this process, 301 optimal combinations of predictors and best-performing linear models for ETo prediction were identified. Achieving R² values exceeding 0.97, alongside minimal indicators of dispersion, the results indicate the effectiveness and accuracy of the elaborated models in predicting the ETo. In addition, by employing a hybrid deep learning approach, 28 best models were developed for forecasting the next periods of ETo. Finally, an interface application was developed to house the identified models for predicting and forecasting the optimal water quantity required for specific plant or crop irrigation. This application serves as a user-friendly platform where users can input relevant predictors and obtain accurate predictions and forecasts based on the established models.

1. Introduction

As per the United Nations Environment Program’s (UNEP) annual report in 2000 [1], freshwater scarcity has been identified as the second most significant environmental challenge of the 21st century by scientists and political leaders. The demand for water is not only linked to ensuring access to drinking water for the population but also plays a critical role in supporting agriculture, tourism, and various industrial and agro-food sectors [2,3]. Consequently, water resources are central to systems of interaction that experience mounting pressures and conflicts among users.

Global climate trends have shown significant deviations from historical norms in recent years, including increased solar radiation intensity, elevated temperatures, and reduced precipitation levels. These changes contribute to various environmental challenges, such as droughts, climate change, floods, and the emergence or exacerbation of health risks. While some of these impacts are natural, a considerable portion can be attributed to human activities, particularly the extensive use of non-renewable energy sources over the past two centuries [4]. Furthermore, projections indicate that the global average air temperature will continue to rise in the coming decades due to increased anthropogenic CO₂ emissions [5]. This ongoing warming is expected to disrupt both regional and global hydrological cycles, leading to alterations in precipitation patterns and increased water-related stress [6,7].

The Mediterranean region (including Morocco) is considered a global “hot point” regarding climate variability and change. According to forecasts made by the MAGICC model [8], it has been concluded that warming in the southern Mediterranean region is estimated to be at 3 °C by 2050 and 5 °C by 2100, while precipitation will decrease from 10 to 30% by 2050 and from 20 to 50% by 2100. These changes should put additional pressure on water management and, therefore, on agricultural production. Several studies [2,9,10,11] have deduced that regions with low and irregular productivity levels will be the ones most affected by the damage of climate change. A warming of 2 °C could lead to a permanent reduction of 4–5% of the annual per capita incomes in Africa and South Asia [12].

The impact of climate change will also affect the quantity and variability of water supplies [13,14] because changes in mean temperatures, even small ones, imply an increase in the frequency of extreme climatic conditions, namely drought and floods [15]. The increase in temperatures, the decrease in precipitation, and the increase in its variability imply a delay and a reduction in growth periods, as well as an acceleration of soil degradation and the loss of productive land [16]. These changes are expected to put additional pressure on agricultural production, although increasing atmospheric CO₂ concentrations could potentially improve the photosynthesis process by up to 30% [17].

At the same time, the issues of greenhouse gas (GHG) emissions and the depletion of fossil fuels are ending conventional agricultural practices. With the infiltration of renewable technologies, the agriculture sector aims to feed the growing population in a more sustainable manner. Considering all the renewable energy sources, solar energy is among the most adaptable sources for farm applications. Over the years, solar PVT energy applications have been employed to supply the required power for various agricultural applications, including water pumping and irrigation, saltwater desalination, crop drying, and greenhouse cultivation [18]. However, emerging PV technology over water bodies through floating solar panels can resolve the challenge of substantial land requirements and additionally lead to operation of the panels at low temperatures, improving the energy generation efficiency and insulating water bodies to account for a reduction in evaporation loss [19].

Evapotranspiration (ET) serves as a fundamental link between the water needs of plants and the surrounding environment, playing a pivotal role in the growth, development, and survival of agricultural crops [20]. Understanding the intricate connection between ET and plant water needs is essential for optimising irrigation practices, conserving water resources, and enhancing agricultural sustainability. Water resource management requires more investigation in response to ET partitioning and water use efficiency [21].

ET directly reflects the combined effects of climatic factors, soil properties, and vegetation characteristics on water loss from the soil-plant-atmosphere continuum. It represents the total amount of water vapour transferred from the land surface to the atmosphere, integrating the influence of solar radiation, temperature, humidity, wind speed, and vegetation cover on water fluxes [22]. In agricultural settings, where water availability is often a limiting factor for crop growth, accurately estimating ET provides valuable insights into the timing and quantity of irrigation required to meet the water demands of crops [23]. ET is generally obtained by ground-based observations and model simulations. Compared with these models, machine learning (ML) and deep learning (DL) methods can directly, through prediction or forecasting, estimate ET from the provided data [24]. ML and DL models facilitate real-time ET forecasting and decision support systems for agricultural water management. By leveraging vast amounts of data from various sources, including meteorological observations, satellite imagery, soil moisture measurements, and vegetation indices, ML and DL models can provide accurate and timely predictions and forecasting of ET at different spatial and temporal scales [25].

Numerous ML-based and DL methods have been explored in the literature to approximate real ET values under varying climate conditions and crop characteristics. The authors of [26] suggested a combination forecasting model for estimating directly expected irrigation water. The authors of [27] employed measured ET as a predictor variable to facilitate land surface temperature (LST) modelling and forecasting. The authors of [23] employed a combination of decomposition techniques, feature selection methods, and ML approaches, including filter-based empirical mode decomposition (TVF-EMD), the tree-Boruta feature selection algorithm, a bidirectional recurrent neural network (Bi-RNN), a multilayer perceptron neural network (MLP), random forests (RFs), and extreme gradient boosting (XGBoost), are used to forecast weekly evapotranspiration. Their findings, with R² values ranging between 0.87 and 0.92, emphasised the superiority of the TVF-BiRNN model in weekly ET prediction. In [25], the performance of random forest (RF) and long short-term memory (LSTM) neural networks was compared in calculating and forecasting the daily ET for three crops. Their results, with R² values ranging from 0.5 to 0.7, indicated low performance accuracy. The authors of [28] proposed an XGBoost model to predict daily weather variables and subsequent ET at 51 weather stations across China. They reported R² values between 0.56 and 0.85 for ET predictions. The authors of [29] introduced novel hybrid ML approaches for reference evapotranspiration (ETo) forecasting, utilising a multilayer perceptron-random forest (MLP-RF) stacked model and XNV. Their method achieved forecasting of ET 60 days ahead, with high-performance accuracy assessed by the Kling–Gupta (KGE) efficiency and mean absolute percentage error (MAPE), yielding values of 0.98 and 8.356%, respectively. The authors of [30] forecasted future reference evapotranspiration (ETO) values using a recurrent LSTM neural network optimised by the Coronavirus Optimization Algorithm. They reported an average R² value of 0.7194. The authors of [31] conducted a comparative study of 10 ML methods for predicting evapotranspiration across large surfaces, where neural networks demonstrated the most favourable outcomes, with R² values ranging between 0.69 and 0.73. The authors of [32] found the N-BEATS model to be the top-performing model for ETo time series forecasting among a set of statistical, ML, and DL models, with an R² value close to one. The authors of [33] assessed LSTM and nonlinear autoregressive network with exogenous inputs (NARX) models for short-term (1–7 days ahead) actual ET prediction, reporting R² values in the range of 0.82–0.91 for both models.

In this context, accurate prediction and monitoring of ET are crucial in guiding decision-making processes related to irrigation scheduling, water resource management, and crop yield optimisation. By integrating advanced modelling techniques, remote sensing technologies, and on-site measurements, researchers and practitioners can enhance our understanding of the complex interactions between ET and plant water needs. Through interdisciplinary approaches that bridge the gap between hydrology, agronomy, and climatology, we can develop innovative solutions to address the challenges of water scarcity, climate variability, and food security facing agricultural systems worldwide [34].

In recent years, growing attention has been directed toward integrated resource management frameworks that address the interconnections between water, energy, and food systems, particularly in the context of sustainable agriculture and irrigation [35]. Water-energy microgrids have emerged as localised, decentralised systems that combine renewable energy sources (e.g., photovoltaic or photovoltaic-thermal systems) with advanced water distribution technologies to optimise energy use and water delivery for agricultural applications. These microgrids enhance system resilience, reduce dependence on fossil fuels, and support precision irrigation strategies in off-grid or resource-constrained environments.

The water-energy-food (WEF) nexus also provides a holistic perspective for managing competing demands and interdependencies among essential resources. Nexus-based management systems aim to improve efficiency, sustainability, and policy coordination across sectors, particularly in regions vulnerable to climate change and resource scarcity. By aligning irrigation technologies with energy-efficient and environmentally conscious practices, WEF-based approaches contribute to long-term agricultural productivity and ecosystem preservation [36,37].

The present study builds on this paradigm by integrating machine and deep learning-based forecasting models with photovoltaic-thermal systems to support intelligent irrigation decisions, positioning our work within the broader landscape of smart water-energy management for sustainable agriculture.

In this study, a model for intelligent irrigation with PVT energy will be elaborated upon and proposed for the first time. When the literature was examined, no study was found for intelligent irrigation systems with PVT energy. Within this research, we will combine top-performing modelling, predicting, and forecasting techniques with PVT applications to deliver precise irrigation water estimates for sustainable agriculture. In the initial stage, we evaluated 13 common ML models to predict ETo, considering variables such as precipitation (P), temperature (T), relative humidity (RH), solar irradiance (H), wind speed (Ws), and wind direction (Wd). The top-performing ML model from this stage was combined with an integral feature selection (IFS) method to determine the most effective combinations of predictors for ETo predictions. Subsequently, in the second stage, we employed a Deep NARMAX model to identify optimal formulas for forecasting future ETo periods. By leveraging these two stages and utilising a specific equation, we accurately predicted and forecasted the quantity and quality of water required to irrigate specific plants or crops across diverse weather conditions. Concurrently, we conducted simulations and assessments of various configurations for PVT systems using Ansys Fluent. Through this process, we identified the most efficient configuration and determined the PVT delivered temperature under different climatic conditions. Finally, we developed an interface application using GUIDE MATLAB 2023a to integrate the identified models for predicting and forecasting the optimal water quantity and quality needed to irrigate specific plants or crops. This user-friendly platform allows users to input relevant predictors and obtain precise predictions and forecasts based on the established models.

The rest of the sections of this paper can be ordered as follows: Material and Methods, including data description, the locations considered, the model evaluation criteria, the PVT solution, the ML and DL models, the IFS approach, and the research methodology are summarized in Section 2. The results and discussions are given in Section 3, while the conclusions are listed in Section 4.

2. Material and Methods

2.1. Data and Statistical Analysis

2.1.1. Local Weather Information

The research was conducted using data sourced from locally implemented stations across 11 sites in Morocco. These locations experience a temperate climate characterised by long, hot summers and short, mild winters. The variables provided by each station include the ETo (mm), P (mm), T (MIN, AVR, and MAX in °C), RH (MIN, AVR, and MAX as percentages), H (kWh/m²), wind speed Ws (km/h), and wind direction Wd (degrees).

Table 1. The chosen locations, corresponding periods, and average values for the provided data.

Period	Location	Latitude (Degrees)	Longitude (Degrees)	Altitude (m)	Average Evapotranspiration (mm)	Average Precipitation (mm)	Average Solar Radiation Intensity (kWh/m2/day)	Average Ambient Temperature (°C)	Average Humidity (%)	Average Wind Speed (m/s)
2016–2020	AIT AMIRA	30.17	−9.48	84	4.03	0.09	5.82	17.53	76.93	20.03
2015–2020	AIT MELLOUL	30.33	−9.50	21	3.54	0.24	4.86	18.34	79.91	13.34
2015–2020	AOULOUZ	30.70	−8.15	735	3.84	0.10	4.66	19.38	59.93	14.52
2016–2020	KENITRA	34.30	−6.60	14	1.89	1.02	2.33	17.06	81.74	14.10
2018–2020	RIBAT-LKHEIR	34.05	−6.76	75	4.56	1.03	5.86	16.09	61.42	12.80
2016–2020	SIDI SLIMAN	34.26	−5.92	37	3.73	0.79	4.79	17.86	73.32	13.02
2016–2020	SOUK LARBAA	33.97	−6.61	37	4.27	0.99	5.99	18.04	73.81	12.52
2019–2020	TAFILALET—ARREFOUD	31.43	−4.23	813	6.15	0.14	6.75	25.58	24.96	7.40
2019–2020	TAFILALET—GOULMIMA	31.69	−4.95	1024	6.29	0.22	6.84	23.42	28.49	9.97
2016–2020	TEMSIA	30.36	−9.41	48	4.21	0.41	5.99	18.09	80.51	14.31
2015–2020	TAROUDANT	30.46	−8.86	30	4.53	0.18	5.66	19.02	65.52	16.56

summarises the average values for each variable, along with information regarding the measurement period and geographical coordinates of each site.

Table 2. The variables employed in this work: inputs and output variables.

Input	Variable
Input1	P (mm)
Input2	Tmin (°C)
Input3	Tavr (°C)
Input4	Tmax (°C)
Input5	Rhmin (%)
Input6	Rhavr (%)
Input7	Rhmax (%)
Input8	H (kW/m2)
Input9	Ws (km/h)
Input10	Wd (degrees)
Output	ETo (mm)

summarises the predictor variables employed for predicting and forecasting ETO.

Figure 1 illustrates the level of correlation among all the analysed variables, including both the predictors and the output variable. A notable strong correlation was evident between ETo and H, followed by Tmax and Tmoy (average temperature). A less-strong correlation was observed with Tmin, while a negative moderate correlation was indicated by the RH. However, the other variables showed no significant correlation with ETo.

2.1.2. Evapotranspiration and Water Need Computing

Crop water requirements are determined based on the maximum evapotranspiration estimated from the ETo. The water needs for a particular crop can be calculated as a function of evapotranspiration ETc, obtained by multiplying the ETo by a specific coefficient (Kc) corresponding to the crop type and its growth stage, as expressed in Equation (1):

$$\mathrm{E}\mathrm{T}\mathrm{c}=\mathrm{K}\mathrm{c}\times \mathrm{E}\mathrm{T}\mathrm{o}$$

(1)

For a given condition, the crop water requirements can be expressed as follows:

$$\left\{\begin{array}{c}\mathrm{Bn}=\mathrm{ETc} – \mathrm{Pe} – \mathrm{DS} \mathrm{if} \mathrm{ETc}>\mathrm{PE}\hfill \\ \mathrm{Bn}=0 \mathrm{if} \mathrm{ETc}<\mathrm{PE}\hfill \end{array}\right.$$

(2)

where Bn is the crop’s net water requirement; DS is the change in soil moisture (mm); and PE is the effective precipitation during the crop growth period, which takes the values

$$\left\{\begin{array}{c}\mathrm{PE}=0.8\mathrm{P} \mathrm{if} \mathrm{P}>75 \mathrm{mm}/\mathrm{month}\hfill \\ \mathrm{PE}=0.6\mathrm{P} \mathrm{if} \mathrm{P}<75 \mathrm{mm}/\mathrm{month}\hfill \end{array}\right.$$

(3)

2.1.3. Evaluation Criteria and Statistical Indices

Several widely used statistical performance metrics were employed to evaluate the performance of the machine learning (ML) and deep learning (DL) models considered in this study. The mathematical formulations of these indices are presented in Equations (4)–(9). For a comprehensive explanation of each metric, readers are referred to [38]:

• Mean absolute percentage error (MAPE):

  $$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{100}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\displaystyle \frac{{\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}^{\prime }}{{\mathrm{y}}_{\mathrm{i}}}}\right|$$

  (4)
• Root mean square error (RMSE):

  $$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}^{\prime }\right)}^2}$$

  (5)
• Coefficient of determination (R²):

  $${\mathrm{R}}^2=1-{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}^{\prime }\right)}^2}{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\overline{{\mathrm{y}}_{\mathrm{i}}}\right)}^2}}$$

  (6)
• Standard deviation (σ):

  $$\mathsf{\sigma }=\sqrt{{\displaystyle \frac{\mathrm{n}}{\mathrm{n}-1}}\left({\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}^2-{\mathrm{M}\mathrm{B}\mathrm{E}}^2\right)}$$

  (7)
• Mean bias error (MBE):

  $$\mathrm{M}\mathrm{B}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i}}^{\mathrm{n}}\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}^{\prime }\right)$$

  (8)

Here, n denotes the number of data points, $y_i$ represents the observed (actual) values, ${y’}_i$ is the predicted or forecasted values, and $\overline{y_i}$ is the mean of the observed data.

Lower values for the MAPE, RMSE, MBE, and σ indicate better model performance. A coefficient of determination (R²) value close to 1 signifies high predictive accuracy, with higher R² values indicating improved model performance. Finally, the models were ranked using a performance score (φ), as defined in Equation (9), where higher values of φ correspond to poorer performance:

$$\mathsf{\phi }=\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}\left(\mathrm{M}\mathrm{B}\mathrm{E}\right)+\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}\left(\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\right)+\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}\left(\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}\right)+\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}\left(\mathsf{\sigma }\right)+\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}\left({\mathrm{R}}^2\right)$$

(9)

2.2. Hybrid ML and DL Models

In this section, we present the components of a hybrid modelling framework that combines ML and DL approaches for predicting and forecasting reference evapotranspiration (ETo) in future periods. The proposed hybrid model integrates three key elements: (1) the best-performing ML model identified from a comparative analysis of 13 ML algorithms, (2) an integral feature selection (IFS) technique, and (3) a deep nonlinear autoregressive moving average with exogenous inputs (NARMAX) model. Each component is briefly introduced below. For comprehensive explanations and implementation details, readers are referred to the cited literature.

2.2.1. Machine Learning Models

The AI-based models we employed in this work are summarised in

Table 3. A brief description of the AI-based models employed in this work.

Model	Description	Key Features and Highlights	Reference
Artificial Neural Networks (ANNs)	ML models inspired by the brain, composed of layers of interconnected neurons. Include input, hidden, and output layers.	Inspired by biology, uses backpropagation. Suited for various tasks.	[39]
Decision Trees (DTs)	Hierarchical models with nodes representing decisions based on feature values. Simple and interpretable.	Used for classification, regression, rule extraction, and anomaly detection.	[40]
Support Vector Machine (SVM)	Supervised algorithm that finds a hyperplane to separate classes with maximum margin.	Effective in high-dimensional spaces; used for classification and regression.	[41]
Extreme Learning Machine (ELM)	Neural network with a single hidden layer; weights from input to hidden layer are random. Fast training.	Faster alternative to traditional training; random weights in a hidden layer.	[42]
Extreme Gradient Boosting (XGBoost)	Gradient boosting ensemble algorithm that sequentially adds trees to correct errors.	High accuracy and efficiency; widely used in ML competitions.	[43]
Random Forest (RF)	Ensemble method of decision trees using bagging and random feature selection.	Robust, handles high-dimensional data; used in many domains.	[44]
Tree Bagger (TreeBag)	Ensemble of bagged decision trees trained on bootstrap samples.	Reduces variance and improves prediction through averaging.	[45]
Generalised Linear Regression (GLR)	Extends linear regression to handle non-normal response variables using a link function.	Flexible for different distributions; suitable for generalised tasks.	[46]
Gaussian Process Regression (GPR)	Non-parametric probabilistic model defining a distribution over functions for regression.	Models uncertainty; predictions are probabilistic.	[47]
Linear Regression (LR)	Predicts a continuous outcome from one or more input variables using a linear approach.	Simple, interpretable, and widely used historically and across disciplines.	[48]
Generalised Additive Model (GAM)	Extends GLMs to include nonlinear additive effects for each predictor.	Captures nonlinear relationships while maintaining interpretability.	[49]
Kernelised Ridge Regression (KRR)	Combines ridge regression with kernel trick to handle nonlinearity.	Regularisation + kernel transformation; suited for nonlinear regression.	[50]
Linear Ridge Regression (LRR)	Linear regression with L2 regularisation. Has a closed-form solution for model coefficients.	Controls overfitting; analytically solvable.	[51]

.

2.2.2. Integral Feature Selection Method

In [38], a novel approach was introduced within the integral variable selection (IVS) framework, aiming to accurately identify the optimal combinations of predictor variables for modelling, prediction, and forecasting tasks. This method systematically evaluates and compares all possible combinations of input variables to determine the most effective subset that yields the highest prediction accuracy for the target variable (objective function).

The total number of possible input combinations is calculated using the binomial coefficient, known as the “n choose k” formula. The cumulative number of combinations across all subset sizes is given by

$$\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{b}={\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{n}}^{\mathrm{p}}={\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\displaystyle \frac{\mathrm{n}!}{\left(\mathrm{n}-\mathrm{k}\right)!\mathrm{k}!}},$$

(10)

where n is the total number of available input variables and k is the number of variables selected in each subset. This exhaustive approach ensures a comprehensive search for the optimal predictor set, enhancing the reliability of the model performance.

2.2.3. Deep NARMAX Model

The Deep NARMAX model is an advanced extension of the classical nonlinear autoregressive moving average with exogenous inputs (NARMAX) model, traditionally used for modelling and forecasting complex dynamic systems [52]. By integrating principles from deep learning, particularly deep neural networks, the Deep NARMAX framework significantly enhances the modelling capacity of conventional NARMAX, making it highly suitable for complex nonlinear systems across various domains, including environmental sciences.

The conventional NARMAX model predicts the future values of a target variable by utilising its historical observations along with recent values of other relevant predictor variables. A discrete-time nonlinear system with input u and output y can be described as follows [53]:

$$\left\{\begin{array}{c}x\left(\mathrm{t}+1\right)=f\left(\mathrm{x}\left(\mathrm{t}\right),\mathrm{u}\left(\mathrm{t}\right),\mathrm{w}\left(\mathrm{t}\right)\right)\\ y\left(\mathrm{t}\right)=h\left(\mathrm{x}\left(\mathrm{t}\right),\mathrm{e}\left(\mathrm{t}\right)\right) \end{array}\right.$$

(11)

where w(t) represents process noise (associated with the system weights) and e(t) denotes measurement noise (model error).

In the present study, we adapted the traditional NARMAX structure to perform multi-step-ahead forecasting of reference evapotranspiration (ETo). The proposed Deep NARMAX model constructs and evaluates multiple NARMAX models using lagged values of ETo and other relevant predictor variables at time steps t − 1, t − 2, t − 3, etc. to predict the output at time t, as described in Equation (12). These predicted ET₀ values are subsequently employed to forecast pollutant concentrations (ozone and PM) for upcoming time steps through an iterative procedure:

$$\mathrm{y}\left(\mathrm{t}\right)=\mathrm{F}\left(\mathrm{y}\left(\mathrm{t}-1\right),\dots ,\mathrm{y}\left(\mathrm{t}-\mathrm{n}\right),\mathrm{u}\left(\mathrm{t}\right),\dots ,\mathrm{u}\left(\mathrm{t}-\mathrm{k}\right),\mathrm{e}\left(\mathrm{t}-1\right),\dots ,\mathrm{e}\left(\mathrm{t}-\mathrm{r}\right)\right)+\mathrm{e}\left(\mathrm{t}\right)$$

(12)

In this equation, y(t) denotes the predicted output at time t, u(t) represents the set of predictor variables at time t, and e(t) is the model’s error term. The function F is a nonlinear mapping defined over the past values of both the output and input variables, capturing the dynamics of the system.

2.3. Methodologies

2.3.1. Methodology for Predicting and Forecasting of ETo

The proposed methodology for predicting and forecasting reference evapotranspiration (ETo) is outlined in the flowchart below (see Figure 2).

The methodology is structured into five main stages:

• Data Preprocessing: The process begins with loading the complete dataset, which is divided into training (70%) and testing (30%) subsets. Preprocessing steps include normalisation of the data and the application of an autonomous anomaly detection technique to identify and remove anomalous data points, thereby enhancing model reliability and accuracy.
• Machine Learning Model Evaluation: Thirteen machine learning (ML) models are trained and evaluated to determine their effectiveness in predicting and forecasting ETo. This comparative analysis is essential for identifying the most suitable ML model based on prediction performance metrics.
• Hybrid IFS-ML Model Implementation: A hybrid model combining integral feature selection (IFS) with the best-performing ML model is employed to identify the most informative predictor variables. This step involves an exhaustive search across all possible combinations of input features, systematically eliminating irrelevant or redundant combinations and retaining only those that yield the highest predictive accuracy.
• Deep NARMAX Model Integration: The optimal predictor combinations derived from the hybrid IFS-ML model are then fed into a Deep NARMAX model. This integration leverages the strengths of both ML-based feature selection and deep NARMAX’s nonlinear dynamic modelling capability to perform multi-step-ahead forecasting of ETo. Model parameters and forecasting formulas are iteratively refined and adapted during this stage.
• Application Development and Deployment: Finally, the entire predictive framework is encapsulated into a user-friendly application designed to facilitate efficient and accessible ETo prediction and forecasting. This step involves deploying the trained models into an interactive environment for real-time or batch predictions.

2.3.2. Solar Photovoltaic-Thermal Simulation Using ANSYS Fluent

Solar photovoltaic-thermal (PVT) systems refer to PV systems integrated with a cooling network. Typically, this cooling is achieved by circulating a designated fluid (water in this study). The water circulated within the PVT system can be used for irrigation, mainly through an underground irrigation system. The water delivered to the crops must maintain an optimal temperature and quantity. These parameters may vary depending on the design of the pumping system and prevailing climatic conditions.

The PVT system proposed for water irrigation was simulated using ANSYS Fluent 19.2. Initially, the simulation focused on the PV system alone, considering two different irradiance values (800 W/m² and 1000 W/m²) to demonstrate their impact on the output power generated. Subsequently, two scenarios were tested for equipping the PV system with a cooling network—scaled PVT and coiled PVT—with both utilising water as the flowing fluid. ANSYS Fluent has been widely employed in previous research to investigate water flow within PV panels for two primary purposes: cooling the PV panel and generating water with various temperatures [54,55].

3. Results and Discussion

3.1. PVT Solutions

The proposed system involves circulating water through the PVT system before delivering it to the crops. Additionally, the electricity generated from the PVT can power the pump used in the irrigation process. This integrated approach represents a novel endeavour.

Based on ANSYS Fluent simulations, we analysed the temperature distribution of a specific PV module without a cooling-equipped network, considering two solar irradiance values: 800 W/m² and 1000 W/m² (see Figure 3). The results indicate that the temperature within the PV module ranged from 51.895 °C to 53.523 °C for insolation of 800 W/m² and from 59.368 °C to 61.403 °C for insolation of 1000 W/m². Notably, the PV panel was completely exposed to solar radiation in this simulation. These results show that high irradiance levels can significantly elevate the temperature of the PV panel, consequently reducing the efficiency of the PV system. Hence, we investigated the same PV panel under similar irradiances with two cooling options: scaled PVT and coiled PVT. Figure 4 demonstrates the temperature distribution for scaled PVT (a) at 800 W/m² solar irradiance and (b) at 1000 W/m² solar irradiance. As a result, the PV panel temperature could decrease by approximately 14 °C and 15 °C for 800 W/m² and 1000 W/m² solar irradiance, respectively. This significant reduction in temperature undoubtedly enhances the effectiveness of the PV system and increases the electricity produced for pumping and irrigation purposes.

With the scaled PVT solution, the PV panel temperature varied between 26.747 °C and 40.963 °C for 800 W/m² solar flux and between 26.51 °C and 44.672 °C for 1000 W/m² solar flux. This indicates an improvement in PV efficiency of approximately 7.32% and 10.02% for both irradiances, as summarised in

Table 4. Performance comparison of PV modules with and without cooling system.

Solar Flux	${\mathit{\eta }}_{\mathit{e}\mathit{l}}$		Improvement Rate
	800 W/m2	1000 W/m2	800 W/m2	1000 W/m2
PV module	13.93%	13.37%	---	---
Scaled PVT	14.95%	14.71%	7.32%	10.02%
Coiled PVT	14.34%	14.67%	2.94%	9.72%

.

Figure 5 illustrates the temperature distribution for coiled PVT (a) at 800 W/m² solar irradiance and (b) at 1000 W/m² solar irradiance. In this scenario, the temperature within the PV panel varied between 19.398 °C and 51.378 °C for 800 W/m² irradiance and between 21.018 °C and 46.088 °C for 1000 W/m² irradiance. There was a reduction in temperature of approximately 2 °C and 15 °C for 800 W/m² and 1000 W/m², respectively. This indicates an enhancement in the PV efficiency of approximately 2.94% and 9.72% for both solar fluxes, as summarised in Table 4.

Based on the simulations and calculations, we observed a positive improvement rate, with a maximum value of approximately 10% for the scaled PVT module at 1000 W/m². A positive improvement rate indicates that the performance of the scaled PVT solution was more effective than that of the coiled PVT solution. Consequently, we can infer that scaled PVT collectors play a significant role in reducing PV panel temperatures, thereby increasing electrical efficiency compared with conventional PV collectors. Additional results are summarised in Table 4.

3.2. Correlation Between Variables

This subsection investigates the intricate relationships between ETo and the various meteorological variables in Table 2. The primary objective is to uncover and analyse the underlying interdependence and correlations between ETo and these influencing factors. Understanding these connections is vital for developing accurate models, enhancing prediction and forecasting capabilities, and supporting informed decision making in the context of sustainable agriculture.

Figure 6 highlights the main factors influencing ETo. Solar irradiance was the most significant meteorological parameter affecting ETo (R² = 0.89). Following this, Tmax and Tmoy exhibited notable importance (R² = 0.70 and R² = 0.67, respectively). Tmin demonstrated a moderate influence on ETo. Conversely, the correlation with precipitation, wind speed, and direction was weak, ranging between −0.23 and 0.13. Relative humidity showed negative and moderate correlations with ETo (R² between −0.44 and −0.55), indicating an inverse relationship between ETo and RH.

3.3. Best ML Models for Predicting ETo

In this subsection, we conduct a comparative analysis of 13 different ML models for ETo prediction, emphasising their prediction accuracy and suitability for agricultural applications. The results of the comparison are depicted in Figure 7. Each studied ML model demonstrated unique strengths and weaknesses in ETo prediction. During the training stage, the decision tree (DT) emerged as the best-performing model, whereas during the testing stage, the tree bagger (TreeBag) model outperformed the others. The R² values exceeded the level of confidence (R² = 0.95) and approached one, indicating the highest level of accuracy prediction achieved by the best-performing models.

3.4. Best Hybrid IFS-ML Models for Predicting ETo

In this subsection, we employ hybrid IFS-ML models to identify the optimal combinations of meteorological variables for predicting ETo with the highest possible correlation and accuracy. The ML model previously selected as the top performer from the testing stage is utilised here. The performance analysis was initially based on the values of R² (values superior to 0.95). Subsequently, all models are ranked based on the performance score φ, and the corresponding statistical indicators are summarised. In total, 1024 possible combinations were compared and assessed for predicting ETo.

The results obtained are presented in Figure 8 and Figure 9. A total of 301 best combinations of meteorological variables for predicting ETo were identified. Solar irradiance (H) emerged as the most crucial variable in all identified best combinations. This underscores the indispensability of H as a predictor in ETo modelling and prediction. The second most important variable was Tmax, present in 237 identified combinations. None of the combinations yielded ETo predictions based on just one or two input variables. Further insights can be gleaned from the same figures.

To further evaluate the best-found combinations, Figure 10 presents a Taylor diagram for visualising their performance. The Taylor diagram is widely utilised for ranking models based on their standard deviation (σ), RMSE, and R² values. A point closer to the left and downward corresponds to a model with better performance. As illustrated, the best-found combinations were plotted with the optimal values for indicators of dispersion and R². This suggests that these top models have the potential to predict ETo with nearly perfect correlation and minimal error.

Moreover, based on the best combinations of predictors identified here and utilising the least squares method, 301 linear formulas have been elaborated and summarised in Appendix A, alongside the corresponding statistical analysis.

3.5. Best Models for Forecasting ETo

Accurate forecasting of future ETo is essential for enabling proactive climate adaptation strategies and safeguarding agricultural sustainability. In this subsection, the optimal predictor combinations identified through prior feature selection processes are integrated into the Deep NARMAX framework to model and forecast upcoming periods of ETo. By harnessing the powerful nonlinear modelling capabilities of the Deep NARMAX architecture, the objective is to generate robust and reliable forecasts that effectively capture the complex dynamics among meteorological variables.

To demonstrate the performance of the top-performing Deep NARMAX configurations, Figure 11 presents the multi-step-ahead time series forecast of daily ETo. This illustration includes the predicted ETo values, corresponding prediction errors, as well as key performance indicators, such as RMSE and R² values. The most accurate model identified leveraged historical values of ETo at time steps t − 1 and t − 5, the minimum temperature at t − 5, and solar irradiance at t − 5. The statistical evaluation of this model indicates strong predictive performance, with error dispersion measures approaching zero and an R² value nearing unity, suggesting a high level of model accuracy.

Moreover, Appendix A provides a comprehensive set of elaborated forecasting formulas for the best-performing models and detailed statistical analyses. In total, 28 Deep NARMAX models were constructed and tested, utilising diverse combinations of historical time lags and meteorological predictors to forecast the next ETo period.

3.6. Application for Predicting and Forecasting ETo and Water Needs

Based on the best combination of meteorological variables discovered here and the best models developed for predicting and forecasting ETo, we created two applications: IntellIrrig and ClimForecast (see Figure 12). These applications cater to specific domains, with IntellIrrig focusing on agriculture, particularly intelligent irrigation, and ClimForecast targeting fields interested in atmospheric climate (meteorology). With IntellIrrig, users can determine the water requirement for a specific plant or crop at a given agricultural site by estimating the value of the reference evapotranspiration (ETo). On the other hand, ClimForecast enables users to predict and accurately forecast the most important meteorological parameters, such as solar radiation intensity, temperature, relative humidity, and wind speed.

To accurately estimate crop water requirements, the reference evapotranspiration (ETo) was first calculated using the ClimForecast application, incorporating key meteorological variables such as global solar radiation, air temperature, humidity, and wind speed. Subsequently, the IntellIrrig application was used to compute ETo and crop water requirements based on the type of crop and its water needs under various climatic conditions.

In addition, this study investigated the influence of ambient temperature on photovoltaic (PV) systems, and it proposes using photovoltaic-thermal (PVT) systems as an optimal solution. PVT systems offer the dual benefit of reducing the PV module temperature—thereby improving energy efficiency—and capturing thermal energy through a heat exchange fluid. This recovered heat can be used to irrigate crops with water at a controlled temperature, which is particularly advantageous for certain plants during cold seasons or in colder climates.

This integrated approach does not replace observed meteorological data when available but serves as a sensitivity analysis to explore how PVT-induced thermal modifications may affect local microclimates and, in turn, influence irrigation requirements. Finally, the irrigation demand is calculated by adjusting ETo with crop-specific coefficients and accounting for effective precipitation, aiming to provide more realistic and adaptive water management under combined energy–agriculture scenarios.

4. Conclusions

In this study, a comprehensive predictive framework combining hybrid machine learning (ML) and deep learning (DL) models was developed and applied to model, predict, and forecast reference evapotranspiration (ETo) as a basis for estimating crop water requirements under varying climatic conditions. The methodology included data preprocessing with anomaly detection, model comparison, integral feature selection, and Deep NARMAX forecasting model integration. The results demonstrated high prediction accuracy, particularly with the hybrid IFS-ML and Deep NARMAX models, outperforming traditional AI-based models in multi-step-ahead forecasting scenarios.

Based on the experimental results and performance analysis, the following conclusions are drawn:

• High Accuracy in ETo Prediction: Among the 13 evaluated models, the hybrid approach integrating feature selection with Deep NARMAX achieved superior forecasting performance, reduced prediction error, and improved reliability in capturing nonlinear temporal dependencies in ETo dynamics.
• Effective Feature Selection for Climate-Driven Forecasting: The integral feature selection method successfully identified the most relevant meteorological variables influencing ETo, enhancing model interpretability and reducing computational complexity without compromising accuracy.
• Potential for Intelligent Irrigation Integration: The proposed predictive model is a foundational component for intelligent irrigation systems. When coupled with real-time sensor data and photovoltaic-thermal (PVT) systems, this model can facilitate dynamic irrigation scheduling, improving water use efficiency in agriculture.
• Implications for Sustainable Agriculture: By incorporating PVT systems into the forecasting and irrigation pipeline, there is potential to utilise renewable energy for both electricity and thermal applications in agriculture. This integration supports sustainable practices by reducing fossil fuel dependence and improving overall system energy efficiency.
• Scalability across Climatic Zones: The framework’s modularity and data-driven nature make it adaptable to diverse agro-climatic regions, allowing for its application in water-scarce and humid environments with appropriate local calibration.

This study demonstrates the viability and accuracy of ML and DL approaches for ETo forecasting and supports their future use in automated, sustainable irrigation management systems.