Artificial Intelligence-Based Improvement of Empirical Methods for Accurate Global Solar Radiation Forecast: Development and Comparative Analysis

Abstract

Artificial intelligence (AI) technology has expanded its potential in environmental and renewable energy applications, particularly in the use of artificial neural networks (ANNs) as the most widely used technique. To address the shortage of solar measurement in various places worldwide, several solar radiation methods have been developed to forecast global solar radiation (GSR). With this consideration, this study aims to develop temperature-based GSR models using a commonly utilized approach in machine learning techniques, ANNs, to predict GSR using just temperature data. It also compares the performance of these models to the commonly used empirical technique. Additionally, it develops precise GSR models for five new sites and the entire region, which currently lacks AI-based models despite the presence of proposed solar energy plants in the area. The study also examines the impact of varying lengths of validation datasets on solar radiation models’ prediction and accuracy, which has received little attention. Furthermore, it investigates different ANN architectures for GSR estimation and introduces a comprehensive comparative study. The findings indicate that the most advanced models of both methods accurately predict GSR, with coefficient of determination, R², values ranging from 96% to 98%. Moreover, the local and general formulas of the empirical model exhibit comparable performance at non-coastal sites. Conversely, the local and general ANN-based models perform almost identically, with a high ability to forecast GSR in any location, even during the winter months. Additionally, ANN architectures with fewer neurons in their single hidden layer generally outperform those with more. Furthermore, the efficacy and precision of the models, particularly ANN-based ones, are minimally impacted by the size of the validation data sets. This study also reveals that the performance of the empirical models was significantly influenced by weather conditions such as clouds and rain, especially at coastal sites. In contrast, the ANN-based models were less impacted by such weather variations, with a performance that was approximately 7% better than the empirical ones at coastal sites. The best-developed models, particularly the ANN-based models, are thus highly recommended. They enable the precise and rapid forecast of GSR, which is useful in the design and performance evaluation of various solar applications, with the temperature data continuously and easily recorded for various purposes.

1. Introduction

Currently, because of the growing population and the limited availability of energy resources, there is a need to develop sustainable sources of renewable energy [1]. Solar energy represents the most plentiful and environmentally friendly kind of renewable energy [2,3]. The precise and reliable knowledge of solar radiation is the first stage in assessing solar energy availability [4,5,6,7]. Additionally, it is a necessary component for various solar energy applications [8]. Measurements of solar radiation necessitate the use of costly devices like Pyranometers. This form of estimation is the most accurate way to determine solar radiation for a given place. Due to the expensive cost and the need for instrument maintenance and calibration, this method is not appropriate for many countries, especially developing ones [9]. Since solar radiation measurements are inaccessible in many places, numerous models have been proposed to predict solar radiation [9,10,11]. These models are presented to forecast solar radiation using various methodologies, such as using empirical-based techniques, AI-based techniques like artificial neural networks, time series-based techniques, and satellite image-based techniques, which are based on employing different forms of data such as using meteorological parameters and geographical data [12,13]. Numerous studies have been carried out to examine the usefulness of various solar models in calculating solar radiation in various places. Generally, models that depend on meteorological parameters are the most often studied and utilized models globally. These models are empirically based and rely on common meteorological parameters such as relative humidity, sunshine data, and temperature, which is the most extensively used parameter to predict GSR [14,15].

Regarding the empirical technique, Angström [16] suggested the principle model, which utilized sunshine information, to forecast GSR. After that, Prescott [17] improved Angström’s model [14], which has since been the one most often used to predict GSR in different places throughout the world [14]. A study of improving GSR prediction by comparing sunshine-based models with other meteorological-based models was carried out by İrfan Uçkan1 and Kameran Mohammed Khudhur [18]. The study estimated and compared GSR, which was calculated using three newly developed models and 24 models selected from the literature. The result showed that the other meteorological-based models performed better than sunshine-based models at the three selected sites. Additionally, the newly developed models in their study outperformed the other models at different sites. Dehkordi et al. [19] calibrated and validated Angström–Prescott’s model coefficients [17] via different optimization methods at six weather stations in Iran’s arid and semi-arid areas. In addition, they enhanced it by including other meteorological variables, relative humidity, and temperature. Their findings showed that the Angström–Prescott model [17] performed better in terms of accuracy and error than upgraded models at the selected stations. Perdinan [20] assessed various methods of computing daily solar radiation to use it as an input to crop process models. Similarly, Kaplan [21] attempted to build a new GSR forecast model utilizing the simulated annealing technique (SAA). The SAA GSR forecasting model showed good performance when it was compared with other common forecasting methods in the literature. According to the statistical error statistics, the estimated GSR data using the innovative SAA-GSR forecast model closely matches the measured meteorological values. Kamil et al. [22] assessed the performance of GSR models on horizontal ground in all-sky climates. Similarly, for 51 locations in the Brazilian state of Minas Gerais, Cunha et al. [23] set out to calibrate and statistically evaluate the efficacy of fifteen temperature-based GSR models. Bautista-Rodrıguez et al. [24] aimed to give a technical tool for the design and execution of solar energy-generating projects by proposing a physical–mathematical method depending on the traditional Angstrom–Prescott model, which allows the designer to simulate GSR on the Earth’s surface to maximize the utilization of this source in a particular geographical region. KUMAR et al. [25] proposed a new empirical model to evaluate the monthly average values of GSR at eighteen Indian sites with different weather conditions. Gouda et al. [26] tried to fill gaps in the literature by analyzing contemporary prediction models and dividing them into several categories based on their inputs, as well as compiling a complete collection of approaches for categorizing China into solar regions. Blal et al. [27] studied the link between solar radiation and the climatology of the desert area under different climatic circumstances, where four GSR models were chosen and investigated using a four-year period. The findings revealed that model M4 performed the best, with a coefficient of determination, R², equal to 0.87. In Iran, Khorasanizadeh and Sepehrnia [28] proposed a study that uses long-term climatic and solar data from eight main territories in Iran with five different weather types to broaden the awareness of solar energy values and mitigate the lack of studies on solar radiation exergy. They evaluated five empirical models and identified the most accurate one for each province. In China, Feng et al. [29] introduced a unique empirical model for reliably forecasting GSR at the national level and then compared it with another nineteen models which have been widely indicated within the literature. Their findings indicated that the newly suggested model (C4) had the greatest overall forecasting performance of the models, and it may be suggested as the best one for forecasting GSR in China. The issue of evaluating and comparing the performance of different models for estimating solar radiation was investigated by Teke et al. [30], where about 90 articles were reviewed and the best models were identified. Teyabeen et al. [31] addressed the challenge of calculating monthly averaged daily horizontal global sun radiation. Climate data from the twelve main cities in Libya were analyzed to construct seven alternative empirical models. The results showed that sunshine duration-based models are more precise than air temperature-based models, and the quadratic regression model performed best across all selected sites.

On the other hand, artificial intelligence, AI, is considered one of the most recent advancements in the computer science field. Since AI methods like machine learning (ML) and deep learning (DL) can identify both the immutable structure and nonlinear properties in solar data, they are currently being extensively reported to have competitive forecasting accuracy. The most popular AI techniques include artificial neural networks, ANNs; fuzzy logic, FL; support vector machine, SVM; expert systems, ESs; genetic algorithms, GAs; extreme learning machines, ELMs; and different Hybrid Systems, HSs, which are composites of two or multiple of the aforementioned techniques. These AI algorithms provide several benefits; for example, AI typically has effective feature extraction and nonlinear mapping functions; AI algorithms also have better compatibility and can be conveniently integrated into different PV power prediction cases; and AI can accomplish a predetermined level of inference that aids in the realization of a high degree of intelligence for solar predictor variables. Therefore, AI technologies have been successfully used to estimate PV power and solar radiation [32,33].

For example, Viscondi and Alves-Souza [33] introduced a thorough comparison of the three commonly utilized ML techniques to estimate solar radiation, ANN, SVM, and ELM, intending to achieve the best estimation of daily radiance in the São Paulo, Brazil, area. According to their results, the three developed models achieved good prediction, where the SVM technique generated a smaller root mean square error (RMSE). Faisal et al. [34] suggested an approach for predicting solar radiation using Neural Networks, where weather parameters from five distinct Bangladeshi regions were utilized. The approach uses various weather information gathered the day before to predict radiation amounts for any day. Using these data, three distinct networks—Gated Recurrent Unit (GRU), Recurrent Neural Network (RNN), and long short-term memory (LSTM)—were trained. The results illustrated that the GRU network provided the most accurate prediction among all developed models with a mean absolute percentage error, MAPE, equal to 19.28%. Rocha and Santos [35] proposed two ML prediction algorithms for horizontal GSR and direct normal radiation: the first utilizes extreme gradient boosting (XGBoost), while the second uses a hybrid CNN-LSTM model that combines a convolutional neural network (CNN) with an LSTM network. The obtained results showed that the suggested models had improved RMSE values for both models. Similarly, a study developing a generalized XGBoost model to estimate daily GSR for places in China with no previous data was conducted by Qiu et al. [36]. In India, Husain and Khan [37] investigated six ML algorithms to estimate GSR using just temperature data as an entry parameter for the various climatic regions, including SVM, XGBoost, Gaussian process regression (GPR), multi-layer perception (MLP), random forest (RF), and k-nearest neighbours (KNN). Additionally, the effectiveness of these models was compared to several empirical-based models. The results reveal that ML-based models outperform empirical-based models in general; however, the empirical-based models outperform ML-based models in a few climatic regions. The best ML-based models are KNN and XGBoost. As a result, they strongly advise using models that rely on temperature parameters to forecast GSR in Indian regions in which just data on air temperature are accessible. Based on two AI techniques—the KNN and ANN methods—Jagadeesh and Subbaiah [38] proposed two models developed by Python, a programing language, for solar irradiance prediction.

An artificial neural network model was proposed by Benatiallah et al. [39] to forecast the daily GSR in three places in south-west Algeria: Bechar, Tindouf, and Naâma. The outcomes demonstrated that the Cascade-forward Neural Network, CFNN, and feed-forward neural network, FFNN, models provided a substantially superior prediction of daily GSR in the selected locations over a five-year period. Kaushika et al. [40] provided an ANN model based on a direct method that takes into account the relationship properties of different components of solar radiation: diffuse, direct, and global solar radiation. Their results showed that the ANN model estimation demonstrates excellent agreement with data, with an overall mean biassed error, MBE, and RMSE for GSR of −0.194% and 5.19%, respectively. Halima et al. [41] investigated three methods (ANN, GA-ANN, and ANFIS) for predicting daily GSR in the south of Algeria: Ouargla, Adrar, and Bechar. The suggested hybrid GA-ANN model, which uses genetic algorithm-based optimization, was created to improve the ANN model. The GA-ANN and ANFIS models outperformed the sole ANN-based model, with GA-ANN being better suited for predicting at all sites and performing the best. Yadav et al. [42] presented a study utilizing WEKA software (Waikato Environment for Knowledge Analysis) deployed to 26 Indian sites with varying weather conditions to determine the most affected input factors for solar radiation forecasting in ANN-based models. The results demonstrate that WEKA recognizes temperature (ambient, minimum, and maximum), sunshine period, and altitude as the most important input factors in solar radiation forecasting, whereas longitude and latitude are the least influential parameters. Yadav and Chandel [43] proposed reviewing ANN-based approaches to discover viable approaches for solar radiation forecasting that are present in the literature and to determine research needs. According to their findings, ANN algorithms estimate solar radiation more precisely than traditional methods. The study of reviewing the development of artificial neural-based models for solar radiation prediction was performed by Choudhary et al. [44]. According to the study, models based on ANNs are much more accurate than other methods. In [45], an evaluation of works published between 2017 and 2022 comparing AI and empirical approaches for forecasting solar irradiation was conducted. The review found that AI approaches are more accurate than empirical ones.

Generally, models that depend on sunshine parameters perform better than other meteorological-based models. Sunshine knowledge, in contrast, is not as widely accessible as other meteorological parameters, like temperature parameters, which are collected at traditional meteorological stations. Therefore, it is difficult to use sunshine-based GSR models in places where sunshine data are unavailable [46]. Since most weather stations around the world lack sunshine information, numerous meteorological parameters, including maximum temperature, ambient temperature, minimum temperature, relative humidity, and cloud cover, have been investigated and proposed for GSR estimation. Hassan et al. [46] proposed many new empirical models based on temperature data to forecast GSR as a substitute for the frequently employed sunshine-based models. The findings display that the best model from these newly suggested temperature-based models (Hassan et al. [46] Model 6) provides an accurate GSR forecast at different sites. Similarly, Husain and Khan [43] investigated several ML and empirical solar radiation models, and they highly recommend utilizing temperature parameters to predict GSR in locations where only air temperature data are available.

In this view, in this work, different temperature-based GSR models are constructed based on the commonly utilized approaches in machine learning techniques, ANNs, and classical methods (empirical models) to predict GSR using just temperature data as the entry parameter. The performance of these established models, which are machine learning-based, is also matched with one of the top empirical models. In addition, solar radiation models are developed for several sites as well as the whole region (the Suez Canal zone), which lacks AI-based models despite the existence of different proposed solar energy projects in this region. NREA, Ministry of Electricity, Egypt, proposes different locations around Egypt which have solar energy potential for PV installations, such as “ZAAFRANA Solar Park”, which is located in the studied region (the Suez Canal zone). Assessing solar radiation estimates is a vital initial phase in determining the viability and efficacy of such solar energy application activities. Accordingly, the observed GSR data from the researched sites for a 37-year period are utilized to create and assess the proposed models in this paper. Some of the innovations and contributions of this work include the following:

▪

Development of precise global solar radiation models for the studied locations as well as the whole region, which presently lack AI-based models, despite the presence of multiple proposed solar energy plants in the region.

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Investigating different ANN architectures in GSR estimation, where ANNs’ performance is investigated and tested using different neuron numbers (five, ten, and fifteen neurons) within the hidden layer.

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Examination of the impact of varying lengths of the validation data set on solar radiation models’ prediction and accuracy.

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Assessment of the proficiency of ANN-based solar models in GSR forecasting in five new cities, particularly coastal ones, where no ANN-based models are proposed or developed at these sites.

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Carrying out of a thorough comparison study that provides useful knowledge for designers and engineers as well as for any potential solar energy application at the studied locations:

⮚

The best local and general models have been compared together.

⮚

The obtained results from the two validation data sets, the short data set (Single Year) and the long data set (Three-Year Average), are compared to each other to assess the effect of varying lengths of validation data set on models’ efficacy.

⮚

The performance of the ANN technique is compared to the performance of the traditional method (empirical technique)

▪

The present work also deals with the issue of a lack of weather stations, which restricts the use of radiation measurement equipment at the research site.

The efficacy of the constructed models is assessed and compared to GSR data recorded at the five specified locations. Additionally, the generalization of the proposed models is evaluated for the Suez Canal zone and the five researched cities, namely Port Said, El Kantara, Ismailia, Fayid, and Suez. These selected cities are scattered over the Suez Canal zone, as shown in Figure 1, and their geographical information is listed in

Table 1. Geographical data for the chosen places.

#	Site Name	Longitude. E	Latitude. N
1	Port Said	32°18′	31°15′
2	El Kantara	32°18′	30°51′
3	Ismailia	32°16′	30°35′
4	Fayid	32°18′	30°18′
5	Suez	32°33′	29°58′

. In addition, the most popular metrics are calculated to assess prediction accuracy [14,47]. The most precise of these generated models is identified. Furthermore, the suggested models, ANN-based models and empirical-based models, are developed and validated using two distinct validation data sets (Single Year, Three-Year Average).

For more clarification, Figure 2 shows the general flow chart of the work and its various phases, such as data processing, model development, evaluating models’ performance, performance comparison, prediction technique comparison, and, finally, the concluding key aspects of the work. The remainder of this paper is arranged as follows: The GSR models are described in Section 2.1 and Section 2.2. Then, Section 2.3 presents more information about the used indicators for evaluating models’ performance and accuracy. Data collection and extra-terrestrial solar radiation calculation methods are explained in Section 2.4. Section 3 introduces both experimental results and a discussion of the studied models, including performance comparison for the local and general models using different validation data sets (Long Period: 2018–2020, Single Year: 2018), followed by a comprehensive comparative analysis between the ANN approach and the empirical approach for global solar radiation prediction. Finally, the conclusion is presented in Section 4.

2. Materials and Methods

2.1. Artificial Neural Network-Based Approach

2.1.1. ANNs’ Basic Concept

Generally, the basic component of our brains is neurons. They make it possible to integrate previous knowledge into the current situation. ANNs are an AI component ideally suited for various applications such as pattern identification, nonlinear function prediction, and simulations. ANNs are considered one of the superior techniques for solving complex and ambiguous issues. It learns from previous instances and can deal with distorted and partial data. Once it is trained, it can conduct estimates at an excellent rate, which makes it an effective modelling tool—especially for system modelling. ANNs may be distinguished by their structures, activation functions, and training algorithms. Generally, ANNs’ structure describes neurons’ relationship. ANN architecture is composed of input and output layers and at least one hidden layer. Figure 3 displays the primary ANN design. The ANN’s layers are linked by a communication connection known as weights, which keeps their influence at the moment of information transmission. The training algorithms are responsible for determining these weights. In general, ANNs can be classified into different types such as supervised, unsupervised, and semi-supervised based on the used learning method. The activation functions determine how a neuron’s output and input are related depending on the degree of input activity. ANNs’ prediction methodology includes several phases. Firstly, the input and output parameters must be determined. Next is the data separation phase, where the data are divided into two different sets, a training set and a testing set. After that, ANN models are built and training parameters are selected. Following this, the developed ANN models are trained and various error indicators are calculated to evaluate the developed models’ performance. Finally, the model with the minimum errors is chosen [44,49].

2.1.2. ANN-Based Forecasting Models

ANNs are an excellent tool for estimating solar radiation. They outperform fuzzy, nonlinear, and linear models in prediction accuracy. When estimating solar radiation using ANNs, the input and output parameters are chosen initially. In general, whereas the output parameter of an ANN model is hourly, daily, monthly, or yearly average solar radiation, the input parameters are one or more parameters like sunshine hours, minimum air temperature, average air temperature, maximum air temperature, relative humidity, etc. [44]. As mentioned above, an ANN-based model is a model wherein the output parameters are calculated from the input ones through the use of fundamental functions or connections.

Considering this, a neural network with feed-forward back-propagation (BP) was employed in this study. This type of neural network, in general, is made up of many layers of neurons which are linked together. There may be one or more hidden layers among the input layer and the output layer, which are referred to as the first and last layers of the network, respectively. The network outcome, $y_i$, could be represented as

$$y_i={\sum }_{j=1}^n{w}_{i,j}\ast x_{i,j}+b_i$$

(1)

where $x_{i,j}$ represents the signal that is received from the $j\mathrm{t}\mathrm{h}$ neuron at the input level. $w_{i,j}$ represents the weight of the link that is directed from neuron $j$ to neuron $i$ at the hidden level, and $b_i$ indicates neuron $i$’s bias. Each $y_i$ is computed, and then it is modified using an activation function.

Typically, one of the bounded monotonic functions—like the common sigmoid functions—are usually used as the activation function. In this work, the developed ANN-based models are MLP networks with one hidden layer, as demonstrated in Figure 4, where the weight tuning is performed by the Levenberg–Marquardt (LM) algorithm. For the output tier, a linear activation function, “PURELIN”, is used. For network training, the ‘‘TRAINLM’’ algorithm is used, while the “TANSIG” transfer function is used in the hidden layer and it is defined as [51,52]

$$f\left(x\right)={\displaystyle \frac{2}{1+\exp (-2x)}}-1$$

(2)

In general, the activation function outcome for a neuron in a given layer becomes an input for the next layer. In contrast, the activation function of the last layer produces the model’s final outcome. Back-propagation is the term given to the process of determining the errors for hidden layers by recursively calculating the error for the output layer. The Generalized Delta Rule (GDR), a back-propagation network’s learning technique, is utilized to optimize the neurons’ weights during the learning process. The architecture of the ANN network influences its training. For instance, a network that is too large is not particularly effective during training, and overfitting could cause the network’s generalization capacity to deteriorate. However, a network that is too tiny may never converge. Thus, the feed-forward back-propagation technique with one hidden layer was employed in this research, taking into account the peculiarities of the current work and combining the training outcomes of networks with various hidden layers. Neurons in the back-propagation method exhibit saturated nonlinear properties. This generally indicates that if there is a significant variance between the neuron’s input and the threshold value, the neuron’s output is going to be either the largest or the lowest value. To avoid this problem, the network’s input values must be controlled; therefore, all input values were normalized between 0 and 1 using Equation (3) and then restored to their original values following the simulation process [51,53]. Common sigmoid functions like “TANSIG” and “LOGSIG” are frequently used as the hidden layers’ transfer functions. Using sigmoid transfer functions in the output tier could restrict the output data range, but using linear activation functions in the output tier, such as the “PURELIN” transfer function, can tackle the difficult issues.

$$X_{norm}={\displaystyle \frac{X-X_{min}}{X_{max}-X_{min}}}$$

(3)

In fact, determining the hidden layer’s neuron numbers is a difficult challenge. There is currently no mathematically justified way to determine the number of hidden nodes. A network with an excessive number of neurons will take longer to train and reduce its capacity for prediction and generalization. However, using too few neurons may not capture the link between the next value and the previous one, resulting in an inadequate model [51,54]. Therefore, the current study developed and investigated several ANN architectures, based on the different neurons’ numbers in the single hidden layer (5, 10, and 15 neurons). The designed ANN-based models, MLP-type models, were trained to forecast GSR as a function of extra-terrestrial solar radiation and air temperature. Furthermore, because the bias and weights of the ANN network were initialized at random, we chose the most efficient results from 10 runs. The developed ANN models used the most common learning rate (0.01) and were trained by the neural network toolbox within MATLAB (2021a) using the first subset of the data (1 January 1984–31 December 2017).

In general, the developed ANN architecture in this work was selected because single-hidden-layer feed-forward ANNs have been demonstrated to be universal approximators capable of approximating any continuous representation [55,56]. Furthermore, MLP has been recognized for its effectiveness since it is one of the quicker learning algorithms that is frequently used [57]. Furthermore, feed-forward neural network models are being researched because they are easy to use and can represent measurable functions with high precision, especially when suited to weather forecasting [58,59]. Additionally, a single-hidden-layer feed-forward neural network’s ability to solve a variety of regression issues has been proven [60]. Additionally, MLP models outperform other machine learning (ML) methods in predicting global irradiation, including the adaptive neuro-fuzzy inference system (AN-FIS) and support vector machines (SVM) algorithms [44,61]. Recently, deep learning (DL) techniques are being used more and more by researchers to create forecasting models because they can draw out important information from vast amounts of data. The DL approaches, in general, are a subset of a wider family of ML approaches that rely on ANNs with representation-based learning and have gained importance in a number of industries [62]. In order to solve complicated problems, both ML and DL techniques pull pertinent information from vast amounts of data. Although DL approaches are able to predict GSR better than ML approaches, the difference is not very large. In comparison to DL-based algorithms, ML-based algorithms utilize less data and compute more quickly, and ANNs show an effective approach for accurate GSR prediction [63,64].

2.2. Empirical-Based Approach

The established solar radiation models typically depend upon linear and nonlinear relationships. They show a relationship between incoming solar radiation and other meteorological variables such as relative humidity, cloud, temperature (average, maximum, or minimum), and sunshine duration [65]. Overall, temperature-dependent GSR models are among the best solar models since temperature information is easily accessible as compared to other weather variables, and it has been collected very simply and regularly for various aims [66].

Novel temperature-based solar radiation models were developed by Hassan et al. [46] as an alternative to the widely used one, sunshine-based models. The outcomes demonstrated that the most precise model among these new temperature-based models offered accurate forecasts for GSR at different locations. Additionally, this top model surpasses the two top sunshine-based models within the literature. Recently, it has shown excellent performance when it is utilized to estimate GSR at new locations with different conditions regardless of the used validation datasets [15,67]. This model is represented as follows:

Model 1 [46]:

$${\displaystyle \raisebox{1ex}{$G$}\!\left/ \!\raisebox{-1ex}{$G_0$}\right.}=a T^b G_0+c$$

(4)

where a, b, and c stand for the empirical coefficients, while $T$,$G_0$, and $G$ are the values of monthly average daily ambient air temperature (°C), extra-terrestrial solar radiation on horizontal ground (MJ/m² day⁻¹), and GSR on a horizontal plane (MJ/m² day⁻¹), respectively.

2.3. Performance Comparison Metrics

The proficiency of the established models in this work was tested and assessed using the most commonly used metrics, including Correlation Coefficient (r), coefficient of determination (R²), mean absolute percentage error (MAPE), Mean Percentage Error (MPE), Mean Bias Error (MBE), Mean Absolute Bias Error (MABE), and root mean square error (RMSE) [9,14,46,68]. The acceptable ranges for the MPE, MAPE, RMSE, MBE, and MABE are within ±10%, while r and R² are between 0 and 1 (0 ≤ $r$ and $R^2$ ≤ 1), and their perfect values are near unity [69,70,71,72]. These metrics’ equations are given as

$$r={\displaystyle \frac{{\sum }_{i=1}^n(G_{i.m }-\overline{G_m})(G_{i.c }-\overline{G_c})}{{\left[{\sum }_{i=1}^n{(G_{i.m }-\overline{G_m})}^2{\sum }_{i=1}^n{(G_{i.c }-\overline{G_c})}^2\right]}^{1/2}}}$$

(5)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(G_{i.m}-{ G}_{i.c})}^2}{{\sum }_{i=1}^n{(G_{i.m }-\overline{G_m})}^2}}$$

(6)

$$MABE={\displaystyle \frac{1}{n}} {\sum }_{i=1}^n\left|(G_{i.c}-G_{i.m})\right|$$

(7)

$$MBE={\displaystyle \frac{1}{n}} {\sum }_{i=1}^n(G_{i.c}-G_{i.m})$$

(8)

$$MAPE={\displaystyle \frac{1}{n}} {\sum }_{i=1}^n\left|\left({\displaystyle \frac{G_{i.c}-G_{i.m}}{G_{i.m}}}\right)\times 100\right|$$

(9)

$$MPE={\displaystyle \frac{1}{n}} {\sum }_{i=1}^n\left({\displaystyle \frac{G_{i.c}-G_{i.m}}{G_{i.m}}}\right)\times 100$$

(10)

$$RMSE={\left[{\displaystyle \frac{1}{n}} {\sum }_{i=1}^n{(G_{i.c}-G_{i.m})}^2\right]}^{1/2}$$

(11)

$$e=\left({\displaystyle \frac{G_{i,c}-G_{i,m}}{G_{i,m}}}\right)\times 100$$

(12)

where $G_{i.m}$ and $G_{i.c}$ are the $i$th observed and estimated values, and $\overline{G_c}$ and $\overline{G_m}$ are the average values of the estimated and observed values, where $n$ represents the number of observations.

$R^2$ values provide information about the quality of fit among anticipated and observed values. The values of $r$ and $R^2$ vary between zero and one, where the highest figure being the desired one. MBE statistics give information regarding the long-term model’s competence. The negative figures of the MBE indicate underestimation, while the positive ones indicate overestimation, and the tiny figures represent the ideal values. The RMSE value remains positive and provides information about the short-term model’s performance. Smaller RMSE values indicate that the model is accurate, whilst zero figures reflect the best value. The agreement between the measured and forecasted values of $G$ for each month is represented by the relative percentage error (e), Equation (12), with optimal values ranging from −10 to +10 (%) [9,14,46].

2.4. Data Description

In order to create and test the suitability of the developed models for forecasting the monthly average daily GSR on horizontal ground at the chosen areas as well as across the Suez Canal’s entire region, we utilized the collected observation of ambient air temperature and GSR for 37 years, from 1 January 1984 to 31 December 2020. These records were obtained from the Surface Meteorology and Solar Energy section of the NASA website, which has been used and employed in a variety of research studies [9,11,73,74,75].

For studying climate and climatic processes, the NASA climatic data set offers long-term observations of weather information acquired from satellite measurements. The major characteristics of the NASA data set are that they are globally spread and continuous in time. Additionally, it demonstrates sufficient precision, when compared to common ground observations, to be a trustworthy source of information. As a result, it can be used and utilized with confidence in situations when there are few or no ground observations. Despite the fact that ground observations are frequently regarded as more reliable than satellite-based observations, the necessary weather parameters for this work were collected from NASA records. The choice was made due to two factors. The NASA data set has all the necessary meteorological parameters for all locations under consideration, which was the initial justification. The second factor had to do with how accurate ground-based measurements are likely to be, which is debatable. This is typically due to the fact that on-site datasets lack information on measurement errors resulting from operations mistakes, data shortages, or calibration deviation [76,77].

In contrast, declination angle values, extra-terrestrial solar radiation values, and the monthly average daily values for all these variables were generated using in-house software written in C# programing language [78]. Extra-terrestrial radiation, often known as $G_0$, is the solar radiation quantity outside the Earth’s atmosphere and it is described as follows [79,80]:

$$G_o={\displaystyle \frac{24\times 3600 G_{sc}}{\pi }} k\left[\left({\displaystyle \frac{\pi \omega }{180}}\right)\sin \left(L\right)\sin \left(\delta \right)+\cos \left(L\right)\cos \left(\delta \right)\cos \left(\omega \right)\right]$$

(13)

$G_{sc}$ represents the solar constant ($G_{sc}$ = 1367 W/m²) [81,82]; k represents the Earth’s orbit eccentricity correlation factor; and $\omega$, $L$, and δ are the hour angle at sunset, the latitude angle, and the declination angle with degree, respectively. They are given as follows [83]:

$$\omega ={\cos }^{-1}[-\tan \left(L\right)\tan (\delta \left)\right]$$

(14)

$$\delta =23.45 sin\left[{\displaystyle \frac{360}{365}}(284+N)\right]$$

(15)

$$k=\left[1+0.033\cos \left({\displaystyle \frac{360 N}{365}}\right)\right]$$

(16)

$N$ is the numbered day of the year (starting from the first of January).

3. Results and Discussion

The observed data of ambient temperature and GSR are divided into three subsets and summed to obtain the monthly average daily values. The first subset (1 January 1984–31 December 2017) is used to develop models, and it was adjusted as trainRatio: 70%, valRatio: 15%, and testRatio: 15% when training the developed ANN-based models. For accurate GSR prediction, this study developed and investigated several ANN architectures, based on the different neuron numbers in the single hidden layer (5, 10, and 15 neurons). These developed ANN-based models (MLP-type models) were trained to estimate GSR as a function of ambient air temperature and extra-terrestrial solar radiation. Because the ANN’s bias and weights were chosen at random, we selected the best efficient outcomes from 10 runs. For each of the five selected locations, the best ANN-based model from the three developed ANN architectures was selected, indicating the number of the iteration in which the best performance was obtained. The validation method, on the other hand, made use of two distinct validation data sets. The first is a three-year average of data from January 2018 to December 2020. The second validation data set, from January to December 2018, is the average data for one year, 2018. These two validation data sets will be used to evaluate and validate the constructed models in this study. Additionally, they will be utilized to examine how modifying the length or duration of the validation data set affects the effectiveness and accuracy of the models (using average data from three years and average data from one year, respectively). The suggested models’ predictions are compared to observed values of the monthly average daily GSR, and the most frequent statistical indicators, RMSE, MBE, MPE, MAPE, MABE, $e$, $r$, and $R^2$, are obtained using Equations (5)–(12).

The sections that follow describe and analyze the validation findings achieved using each validation data set (validation data set 1: three-year data average, validation data set 2: single-year data average). For each validation data set, the gained findings of the local models are described first, followed by the results of the general models that developed for that whole region (Suez Canal zone), and then a comparison between the local and general models is offered. Additionally, a performance comparison between the prediction of the best ANN-based models and the empirical technique at the five selected sites is presented and discussed. Finally, the outcomes of these two validation data sets (data set 1 and data set 2) are compared and analyzed to examine the impact of varying lengths of validation datasets on models’ prediction and accuracy. For more clarification, Figure 2 exhibits the main stages with their steps as mentioned before.

3.1. Validation Using Long-Term Data (Using the Data from the Succeeding Longer Years of 2018–2020)

This validating data set employed the average data from three years, from 1 January 2018 to 31 December 2020. The measured data for all used parameters as well as the extra-terrestrial solar radiation data in each city were averaged to obtain the monthly mean values. The most accurate ANN-based models from the three ANN architectures that were built, using the local data in each city, are recognized for each site, along with the iteration number that achieved the greatest performance, as seen in

Table 2. The proposed ANN-based models (local and general) from the three developed ANN architectures, along with the iteration number from ten runs that achieved the greatest performance during model building, at the selected sites using a developing data set (January 1984–December 2017).

Site	Local Models		General Models
	Model Type	Iteration No.	Model Type	Iteration No.
Port Said	Model_5N	8	Model_5N	10
	Model_10N	10	Model_10N	5
	Model_15N	10	Model_15N	10
El Kantara	Model_5N	8	Model_5N	10
	Model_10N	10	Model_10N	5
	Model_15N	10	Model_15N	10
Ismailia	Model_5N	9	Model_5N	10
	Model_10N	10	Model_10N	5
	Model_15N	4	Model_15N	10
Fayid	Model_5N	9	Model_5N	10
	Model_10N	10	Model_10N	5
	Model_15N	10	Model_15N	10
Suez	Model_5N	10	Model_5N	10
	Model_10N	10	Model_10N	5
	Model_15N	3	Model_15N	10

N refers to the neuron numbers within the single hidden layer of the ANN model.

. The prediction of the models is compared against the observed data in each city, where all performance metrics (MPE, MAPE, MBE, MABE, RMSE, $e$,$r$, and $R^2$) of the established models are calculated using Equations (5)–(12) and presented in

Table 3. Performance indicators for the locally developed ANN-based models at the selected locations using validation data set 1 (Long Period, January 2018–December 2020).

Type	Site	Model	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$	Rank
Local Models	Port Said	Model_5N	3.65490	0.40327	0.92969	5.35676	0.84151	0.99535	0.97856	2
		Model_10N	1.92217	0.11361	0.84811	4.41988	0.73673	0.99463	0.98215	1
		Model_15N	3.60763	0.36405	1.14504	6.11046	1.03554	0.99087	0.96747	3
	El Kantara	Model_5N	2.24654	0.22460	0.78356	3.79819	0.66934	0.99854	0.98359	1
		Model_10N	2.15237	0.20589	0.81524	4.07256	0.73167	0.99711	0.98224	2
		Model_15N	2.37725	0.27635	1.02763	4.27861	0.79210	0.99122	0.97178	3
	Ismailia	Model_5N	2.14154	0.20317	0.84457	3.90937	0.71149	0.99695	0.98094	1
		Model_10N	3.55581	0.47516	0.91382	4.68668	0.80093	0.99814	0.97768	2
		Model_15N	1.57824	0.04712	1.55105	5.73291	1.08472	0.97052	0.93571	3
	Fayid	Model_5N	2.35806	0.26666	0.77417	3.71788	0.66071	0.99796	0.98398	2
		Model_10N	2.54464	0.30327	0.76652	3.79592	0.66428	0.99825	0.98430	1
		Model_15N	1.98925	0.18159	0.81653	3.81238	0.70567	0.99710	0.98218	3
	Suez	Model_5N	4.61072	0.69807	1.12449	5.50349	0.95460	0.99667	0.96418	1
		Model_10N	5.26722	0.81045	1.22514	5.99275	1.02269	0.99821	0.95748	2
		Model_15N	4.55418	0.65296	1.28840	6.10674	1.11445	0.99322	0.95298	3

. According to the findings, the most accurate model in each city is identified by comparing the acquired performance indicators of the three developed ANN architectures, and it has the highest $R^2$ value [46,69,70,74,84]. The most superior one from the three investigated ANN architectures in each city is highlighted in bold as shown in Table 3.

According to the comparison with the GSR’s observed data in each city, all models perform well in GSR estimation, and their statistical errors (MPE, MAPE, MBE, MABE, and RMSE) are within the acceptable limits, ±10%, and have coefficient of determination ($R^2$) values ranging from 93% to 98%. It is also noted that the developed models with five or ten neurons in their single hidden layer, Model_5N and Model_10N, always have the best proficiency compared with the ANN model with fifteen neurons in its single hidden layer. While Model_5N and Model_10N performed well, Model_15N experienced a slight decline in its performance, such as in Ismailia and Suez, with $R^2$ values equal to 93% and 95%, respectively. This slight slip in $R^2$ values may be returned to different climatic conditions, especially at coastal locations such as Suez city, which is located very close to the Red Sea, as seen in Figure 1 [69,85].

Focusing on the best local models, all models have excellent performance with high $R^2$ values. While the value of $R^2$ in Suez city is larger than 0.96%, it exceeds 0.98% in the four remaining cities, which indicates good fitting between the estimated and observed values. Additionally, the values of the remaining statistical errors are within the accepted range of ±10%; for example, MPE, MBE, and RMSE values range from 1.92 to 4.61 (%), from 0.11 to 0.69 (MJ m⁻² day⁻¹), and from 0.76 to 1.12 (MJ m⁻² day⁻¹), respectively. It is also noted that the proficiencies for two models, Model_5N and Model_10N, are close to each other. While the ANN model with 10 neurons in its single hidden layer (Model_10N) provided the best performance in Port Said and Fayid, the other one, which has 5 neurons in its single hidden layer (Model_5N), gave the best accuracy in the remaining cities, El Kantra, Ismailia, and Suez. For more explanation, the best models’ predictions are compared to the observed GSR data at the five selected locations and represented in Figure 5. Similarly, Figure 6 displays the performance indicator graph of the best local ANN-based models at the five selected sites using validation data set 1 (Long Period, 2018–2020).

For the general models, on the other hand, all measured data for the used parameters ($T$, $G$, and $G_0$) in the five selected cities of the Suez Canal zone (as shown in Figure 1) are averaged and utilized to assess the generalizability capacity of the three developed ANN architectures over the whole Suez Canal area. The estimation of the general ANN-based models is compared against the observed data of the five cities.

Table 4. Performance indicators for the general ANN-based models, which are developed for the whole Suez Canal zone, at the selected locations using validation data set 1 (Long Period, January 2018–December 2020).

Type	Site	Model	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$	Rank
General Models (Suez Canal Zone)	Port Said	Model_5N	2.22622	0.11679	0.89560	4.89941	0.79687	0.99580	0.98010	1
		Model_10N	1.10850	-0.09991	0.95111	5.22469	0.86057	0.99447	0.97756	2
		Model_15N	2.26700	0.11408	1.19298	6.66175	1.05889	0.98611	0.96469	3
	El Kantara	Model_5N	1.70379	0.15432	0.67046	3.35007	0.61371	0.99857	0.98799	2
		Model_10N	2.19621	0.27324	0.65596	3.22489	0.56519	0.99848	0.98850	1
		Model_15N	3.29598	0.44940	0.91358	4.51385	0.79933	0.99667	0.97770	3
	Ismailia	Model_5N	1.70379	0.15432	0.67046	3.35007	0.61371	0.99857	0.98799	2
		Model_10N	2.19621	0.27324	0.65596	3.22489	0.56519	0.99848	0.98850	1
		Model_15N	3.29598	0.44940	0.91358	4.51385	0.79933	0.99667	0.97770	3
	Fayid	Model_5N	2.07041	0.24630	0.69588	3.48560	0.64340	0.99749	0.98706	1
		Model_10N	2.37430	0.31167	0.70841	3.30568	0.58208	0.99771	0.98659	2
		Model_15N	3.54005	0.50269	0.96939	4.76469	0.85463	0.99559	0.97489	3
	Suez	Model_5N	1.81652	0.20719	0.79294	3.56140	0.70421	0.99509	0.98219	2
		Model_10N	1.87895	0.22070	0.68448	3.23424	0.60953	0.99798	0.98673	1
		Model_15N	2.20825	0.26389	0.82541	3.80005	0.72465	0.99624	0.98070	3

summarizes the performance indicators obtained for general models’ prediction at every site. According to the obtained finding in Table 4, all general models have excellent GSR predictions with good performance metrics in the acceptable ranges (±10%), and $R^2$ is larger than 96%, which refers to the goodness of fit between the models’ prediction and the observed data. Moreover, it is noted that these general models performed well in the coastal cities, like Suez city, when they are compared with the local models, where $R^2$ is improved by about 3% (increased from 95% to 98%). More so, the best general models provided high prediction accuracy, with $R^2$ values exceeding 98%, as well as MPE, MBE, and RMSE values ranging from 1.8 to 2.2 (%), from 0.11 to 0.27 (MJ m⁻² day⁻¹), and from 0.65 to 0.89 (MJ m⁻² day⁻¹), respectively. Also, Model_5N and Model_10N had approximately the same performance. Figure 6 shows the statistical indicator graph of the general models at the selected locations using validation data set 1 (Long Period, 2018–2020). Similarly, the general models’ forecast is compared against the observed data at the selected locations and presented in Figure 5.

Regarding local and general models’ comparison, the performance of the best local and general models is compared relying on the result of the validation process using validation data set 1 (2018–2020). It is worthy of note that while the performances for Model_5N and Model_10N are almost the same in the five locations, the general models improved the prediction in Suez city by about 2% ($R^2$ increased from 96% to 98%). In addition, Model_5N and Model_10N always have more accurate performances compared with Model_15N. For more clarification, the results of performance comparison for the best models (local and general) in the five selected cities are illustrated together in Figure 5, and their statistical indicator graphs are also demonstrated jointly in Figure 6. Furthermore, the relative percentage error ($e$) is computed, using Equation (12), for these best models (local and general) during the whole year and summarized in

Table 5. Relative error,$e$, for the best ANN models (local and general) at the selected locations using validation data set 1 (Long Period, January 2018–December 2020).

Type	Month	Port Said (Model_10N)	El Kantara (Model_5N)	Ismailia (Model_5N)	Fayid (Model_10N)	Suez (Model_5N)
Local Models	January	1.4	5.7	6.4	9.3	8.3
	February	6.7	6.2	5.5	6.0	12.2
	March	5.5	3.0	4.8	2.7	4.5
	April	3.3	0.0	−0.1	−0.6	2.9
	May	1.1	0.2	1.2	1.1	2.2
	June	−1.8	−2.9	−2.9	−2.8	−0.9
	July	−3.0	−3.8	−5.3	−3.9	−2.2
	August	−5.8	−2.7	−2.3	−0.2	−2.2
	September	−4.4	1.6	1.0	2.0	0.9
	October	0.5	2.0	0.9	3.5	4.6
	November	5.4	5.4	4.9	3.4	7.7
	December	14.2	12.2	11.7	10.0	17.4
General Models (Suez Canal Zone)		(Model_5N)	(Model_10N)	(Model_10N)	(Model_5N)	(Model_10N)
	January	5.1	5.4	5.4	3.3	5.6
	February	5.6	5.1	5.1	5.3	5.4
	March	5.3	3.4	3.4	3.8	1.6
	April	3.3	2.4	2.4	2.1	2.0
	May	0.4	−1.3	−1.3	1.9	1.2
	June	−2.8	−3.6	−3.6	−2.7	−4.2
	July	−4.2	−0.3	−0.3	−2.7	−1.4
	August	−5.3	−0.3	−0.3	−2.1	−1.7
	September	−3.7	−0.6	−0.6	−1.0	−0.8
	October	0.4	3.7	3.7	2.6	2.8
	November	7.5	3.4	3.4	3.5	3.6
	December	15.1	9.2	9.2	10.9	8.5

.

In general, what stands out from the table is that the relative error value of the local models is within the acceptable range of ±10% for all months, except for Suez city in February and Port Said, El Kantara, Ismailia, and Suez in December, during which it exceeded the limit. This may be explained by different weather conditions, such as clouds and rain, particularly in winter months or at coastal sites [46,69,74,85]. On the other hand, the general models’ relative error is better than those of the local models, where it is in the accepted boundary during the year except for December in Port Said and Fayid. While it reached 15.1% at Port Said, it slightly surpasses the range at Fayid at 10.9%. Furthermore, the majority of the general models’ relative errors are within acceptable limits compared with the local ones. This might be interpolated by the averaging process for the observed data of the five selected locations, which leads to better values for the used parameters ($T$, $G$, and $G_0$). For more clarification, the relative error graphs of the best ANN models (local and general) are displayed in Figure 7.

3.2. Validation Using Neighbouring Year (i.e., Using the Data in 2018 for Validation)

When it comes to the second data set, validation data set 2 (Single Year, 2018), a similar procedure as with validation data set 1 is followed. To begin, the monthly average values are calculated by averaging the observed data of all variables for a single year, from 1 January 2018 to 31 December 2018. The predictions of the models are then compared against the observed data, and all performance metrics are calculated for both local and general models at each site, as shown in

Table 6. Performance indicators for the ANN-based models (local and general) at the selected locations using validation data set 2 (Single Year, January 2018–December 2018).

Type	Site	Model	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$	Rank
Local Models	Port Said	Model_5N	2.23881	0.16004	0.73494	4.13855	0.63993	0.99736	0.98682	1
		Model_10N	0.54890	-0.08165	0.74252	3.31423	0.59720	0.99548	0.98655	2
		Model_15N	-0.05539	-0.30909	1.02216	4.58919	0.87105	0.99670	0.97451	3
	El Kantara	Model_5N	1.91737	0.18452	0.79110	3.75218	0.70187	0.99615	0.98298	1
		Model_10N	2.56215	0.31626	0.93584	4.19557	0.77972	0.99275	0.97618	2
		Model_15N	2.53084	0.31061	1.14735	4.94496	0.94551	0.98632	0.96419	3
	Ismailia	Model_5N	2.38853	0.28405	0.94852	4.32869	0.83579	0.99241	0.97553	1
		Model_10N	3.84825	0.52777	1.10227	5.35620	0.94103	0.99228	0.96695	2
		Model_15N	2.19189	0.21263	1.31003	5.59356	1.08920	0.98004	0.95332	3
	Fayid	Model_5N	2.16554	0.24301	0.86331	3.82517	0.71419	0.99402	0.97973	2
		Model_10N	2.46797	0.29213	0.85560	4.02212	0.73455	0.99516	0.98009	1
		Model_15N	1.85009	0.18039	0.90241	3.86167	0.75382	0.99295	0.97785	3
	Suez	Model_5N	4.52488	0.74273	1.10459	5.39579	0.99335	0.99420	0.96529	1
		Model_10N	6.02530	0.97575	1.37355	6.73833	1.18131	0.99448	0.94633	2
		Model_15N	4.97716	0.72684	1.53231	7.18430	1.37926	0.98398	0.93320	3
General Models (Suez Canal Zone)	Port Said	Model_5N	1.00481	-0.10090	0.84267	4.16739	0.68918	0.99659	0.98267	1
		Model_10N	1.61809	0.00738	0.86085	4.62802	0.74703	0.99552	0.98192	2
		Model_15N	1.79198	-0.03430	1.09332	6.01821	0.95618	0.99217	0.97083	3
	El Kantara	Model_5N	2.32779	0.32902	0.83957	3.54344	0.67904	0.99333	0.98083	2
		Model_10N	2.38929	0.32548	0.78656	3.50812	0.64196	0.99531	0.98317	1
		Model_15N	4.64530	0.64718	1.24316	5.99219	1.02980	0.99172	0.95796	3
	Ismailia	Model_5N	2.32779	0.32902	0.83957	3.54344	0.67904	0.99333	0.98083	2
		Model_10N	2.38929	0.32548	0.78656	3.50812	0.64196	0.99531	0.98317	1
		Model_15N	4.64530	0.64718	1.24316	5.99219	1.02980	0.99172	0.95796	3
	Fayid	Model_5N	2.72405	0.40201	0.89906	3.94340	0.75313	0.99285	0.97801	1
		Model_10N	2.96009	0.42316	0.90638	4.13992	0.75621	0.99413	0.97765	2
		Model_15N	4.89683	0.69868	1.30289	6.20925	1.07373	0.99039	0.95383	3
	Suez	Model_5N	3.07131	0.47601	1.11636	4.68751	0.94479	0.98756	0.96455	1
		Model_10N	3.62559	0.57856	1.19167	5.09772	1.00837	0.98720	0.95960	2
		Model_15N	4.78915	0.72645	1.34822	6.43214	1.20408	0.98866	0.94829	3

, where the best models are recognized and highlighted in bold.

Focusing on the local models, the revealed outcomes illustrate that all developed models have good GSR estimation and their statistical errors are within the accepted limits of ±10%, where $R^2$ ranges between 93% and 98%. While the performance of Model_5N is much closer to the performance of the best model, Model_10N, in Fayid city, its performance is ranked first in the remaining four cities. Additionally, it is noted that the performance for the remaining two modes, Model_10N and Model_15, is slightly decreased in Suez city. This drop in the models’ performance can be interpreted as different weather conditions in the coastal cities, as mentioned before [69,85]. Additionally, the best models provide an excellent GSR estimation with $R^2$ ranging from 96% to 98%. On the other hand, the general models show good performance with $R^2$ values between 94% and 98%. In addition, the performance of Model_10N is still slightly lower than the performance of the other model. Generally, the best general models have excellent forecasts with $R^2$ > 96%, and they have approximately the same performance as the local models. Of more interest is that the prediction of the models (local and general) and their performance indicators in the five cities are graphed and illustrated in Figure 8 and Figure 9.

Furthermore, the relative error values were computed for all models (local and general), and they are within the acceptable ranges (±10%) except for some, especially in the winter season. For example, in December, the relative error values of the best models in El Kantara, Ismailia, and Fayid marginally exceeded the limit. Similarly, in February in Suez city, it slimly surpasses the ranges for both models; the best local and the best general models have values of 11.7% and 12.8%, respectively, which may be explained by different weather in winter months, such as rain and winds.

Table 7. Relative error,$e$, for the best ANN models (local and general) at the selected locations using validation data set 2 (Single Year, January 2018–December 2018).

Type	Month	Port Said (Model_10N)	El Kantara (Model_5N)	Ismailia (Model_5N)	Fayid (Model_10N)	Suez (Model_5N)
Local Models	January	9.6	7.4	7.9	10.6	8.7
	February	8.5	4.6	4.4	4.9	11.7
	March	1.9	0.3	2.8	1.6	3.4
	April	0.4	−1.1	−1.3	−1.3	3.9
	May	1.4	3.9	5.5	4.6	6.4
	June	−0.7	−3.0	−3.2	−3.1	−0.7
	July	−3.2	−3.9	−5.5	−4.0	−2.4
	August	−5.0	−2.9	−1.6	−0.9	−2.1
	September	−2.4	2.1	3.2	1.8	2.1
	October	4.8	1.8	4.1	3.5	5.8
	November	3.0	3.1	0.5	0.6	5.8
	December	8.7	10.9	11.8	11.3	11.8
General Models (Suez Canal Zone)		(Model_5N)	(Model_10N)	(Model_10N)	(Model_5N)	(Model_10N)
	January	5.5	7.1	7.1	4.6	2.6
	February	6.7	2.9	2.9	7.2	12.8
	March	0.0	3.8	3.8	3.7	3.8
	April	−0.5	−0.1	−0.1	0.9	3.4
	May	1.7	3.7	3.7	7.3	8.0
	June	−3.0	−4.4	−4.4	−2.8	−2.7
	July	−4.8	−0.5	−0.5	−2.8	−3.8
	August	−5.5	−1.4	−1.4	−1.7	−3.2
	September	−4.7	1.2	1.2	0.5	0.4
	October	−0.4	6.6	6.6	3.8	2.9
	November	3.0	−0.3	−0.3	1.4	3.2
	December	14.1	10.1	10.1	10.5	9.5

summarizes the relative error values ($e$) for the best ANN models (local and general) in the five selected sites using validation data set 2 (Single Year, January 2018–December 2018). For more clarification, the relative errors for the best local and general models are shown in Figure 10.

3.3. Performance Comparison for ANNs and Empirical Techniques

As mentioned above, Hassan et al. [46] proposed a novel empirical-based GSR model, which provides good GSR estimation when it is compared to the other empirical ones. Therefore, the first subset, which was used to train the ANN-based models (1 January 1984–31 December 2017), will also be employed to build the empirical-based models using regression analysis [14,70,86]. The values of empirical coefficients that match the observed data in selected cities were obtained and are summarized in

Table 8. Empirical coefficients of the local and general empirical-based model for the selected locations and the Suez Canal zone as a whole.

Location	a	b	c
Port Said	0.00034	0.84062	0.50640
El Kantara	0.00101	0.51049	0.47280
Ismailia	0.00101	0.51062	0.47281
Fayid	0.00089	0.53876	0.48038
Suez	0.00099	0.49708	0.50472
Suez Canal Zone General Model	0.00076	0.58719	0.48948

. Similarly, the general coefficients for the entire region of the Suez Canal zone were also computed and are represented in Table 8, after averaging the observed data of the used parameters at the five selected sites. Then, the developed empirical models (local and general) will be validated using the same validation data sets (data set 1: Long Period data set 2018–2020, data set 2: Single Year data set 2018) to compare their performance with the performance of the best-developed ANN-based models. Thus, the prediction of these empirical-based models is compared against the observed data at the selected locations, where all performance indicators are computed and summarized in

Table 9. Performance indicators of the local and general empirical-based models for the selected locations and the Suez Canal zone using validation data set 1 (Long Period, January 2018–December 2020).

Type	Site	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$
Local Models	Port Said	9.3092	1.6925	1.7998	9.3092	1.6925	0.9975	0.9196
	El Kantra	−5.6514	−1.0118	1.1207	5.6514	1.0118	0.9979	0.9664
	Ismailia	−5.6512	−1.0118	1.1207	5.6512	1.0118	0.9979	0.9664
	Fayid	−5.6506	−1.0151	1.1219	5.6506	1.0151	0.9979	0.9664
	Suez	−4.4699	−0.8082	0.9823	4.8015	0.8989	0.9971	0.9727
General Models (Suez Canal Zone)	Port Said	6.7679	1.1712	1.3275	6.7679	1.1712	0.9954	0.9563
	El Kantra	−4.1394	−0.6977	0.8606	4.3170	0.7461	0.9982	0.9802
	Ismailia	−4.1394	−0.6977	0.8606	4.3170	0.7461	0.9982	0.9802
	Fayid	−4.3220	−0.7255	0.8973	4.5274	0.7814	0.9981	0.9785
	Suez	−6.4757	−1.2098	1.3175	6.5420	1.2279	0.9976	0.9508

and

Table 10. Performance indicators of the local and general empirical-based models for the selected locations and the Suez Canal zone using validation data set 1 (Single Year, January 2018–December 2018).

Type	Site	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$
Local Models	Port Said	10.5113	1.8491	2.0009	10.5113	1.8491	0.9949	0.9023
	El Kantra	−5.3352	−0.9423	1.1776	6.0551	1.1312	0.9950	0.9623
	Ismailia	−5.3350	−0.9423	1.1776	6.0549	1.1312	0.9950	0.9623
	Fayid	−5.3578	−0.9508	1.1799	6.0634	1.1360	0.9950	0.9621
	Suez	−3.6626	−0.6399	1.0303	4.8051	0.9390	0.9927	0.9698
General Models (Suez Canal Zone)	Port Said	7.8331	1.3024	1.4987	7.8331	1.3024	0.9935	0.9452
	El Kantra	−3.7947	−0.6218	0.9672	4.7566	0.8741	0.9952	0.9746
	Ismailia	−3.7947	−0.6218	0.9672	4.7566	0.8741	0.9952	0.9746
	Fayid	−4.0050	−0.6557	1.0015	4.9680	0.9084	0.9951	0.9727
	Suez	−5.6395	−1.0325	1.2968	6.3898	1.2306	0.9932	0.9522

.

Focusing on validation data set 1 (Long Period, 2018–2020), it can be noted that the developed local empirical models have good GSR estimation, where all performance indicators are within acceptable ranges. Whereas the local formula of the model performed well with $R^2$ values larger than 96% at four sites, it marginally declined at the fifth site, Port Said city, with an $R^2$ equal to 0.9196%. This decline in the model’s proficiency can be interpreted as the varied weather in this coastal city, which is located very near the Mediterranean Sea, as seen in Figure 1. On the other hand, the general empirical formulas made excellent predictions at El Kantara, Ismailia, and Fayid. Additionally, while its prediction accuracy is slightly decreased by about 2%, $R^2$ slipped from 97% to 95%; at Suez city, its prediction is improved by about 4%, $R^2$ increased from 91% to 95% at Port Said. This may be interpreted as the averaging process for the observed data of the selected sites leading to improved values of parameters T, G, and G₀ at Port Said city, and vice versa at Suez city. The prediction of the local and general formulas of the empirical model and the observed data at the five selected cities can be seen in Figure 11, and their performance indicators can also be seen in Figure 12.

On the other hand, the obtained results from validation data set 2 (Single Year, 2018) show that all performance indicators for all developed empirical models (local and general) are within the acceptable limits (±10%) except for the MAPE of the local model at Port Said city, which is slimly over the range (10.5%). The local and general formulas provide good GSR forecasts with $R^2$ > 95% except for Port Said, where they are between 0.9023% and 0.9452%. As mentioned before, generally at the coastal locations—like Port Said—models’ estimation is affected by the weather conditions at these sites, especially in the winter season [46,69,74,85]. Similarly, it is noted that the general formula in Port Said city improves the GSR prediction by about 4%. For more clarification, the prediction of the local and general formulas of the empirical model and the observed data in the five selected cities are demonstrated in Figure 13, and their performance indicators are represented in Figure 14.

More so, the prediction and the performance of the best ANN-based models are compared with those of the empirical models in the five chosen cities using the same validation datasets (Long Period: 2018–2020, and Single Year: 2018), as demonstrated in

Table 11. Performance comparison for the best local and general models for both techniques (ANN and empirical) at the five selected sites using validation data set 1 (Long Period, 2018–2020).

Site	Model Type	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$	Rank
Port Said	ANN–Local	1.9222	0.1136	0.8481	4.4199	0.7367	0.9946	0.9822	1
	Empirical–Local	9.3092	1.6925	1.7998	9.309	1.6925	0.9975	0.9196	4
	ANN–Canal Zone	2.2262	0.1168	0.8956	4.8994	0.7969	0.9958	0.9801	2
	Empirical–Canal Zone	6.7679	1.1712	1.3275	6.7679	1.1712	0.9954	0.9563	3
El Kantara	ANN–Local	2.2465	0.2246	0.7836	3.7982	0.6693	0.9985	0.9836	2
	Empirical–Local	−5.6514	−1.0118	1.1207	5.6514	1.0118	0.9979	0.9664	4
	ANN–Canal Zone	2.1962	0.2732	0.6560	3.2249	0.5652	0.9985	0.9885	1
	Empirical–Canal Zone	−4.1394	−0.6977	0.8606	4.3170	0.7461	0.9982	0.9802	3
Ismailia	ANN–Local	2.1415	0.2032	0.8446	3.9094	0.7115	0.9970	0.9809	2
	Empirical–Local	−5.6512	−1.0118	1.1207	5.6512	1.0118	0.9979	0.9664	4
	ANN–Canal Zone	2.1962	0.2732	0.6560	3.2249	0.5652	0.9985	0.9885	1
	Empirical–Canal Zone	−4.1394	−0.6977	0.8606	4.3170	0.7461	0.9982	0.9802	3
Fayid	ANN–Local	2.5446	0.3033	0.7665	3.7959	0.6643	0.9982	0.9843	2
	Empirical–Local	−5.6506	−1.0151	1.1219	5.6506	1.0151	0.9979	0.9664	4
	ANN–Canal Zone	2.0704	0.2463	0.6959	3.4856	0.6434	0.9975	0.9871	1
	Empirical–Canal Zone	−4.3220	−0.7255	0.8973	4.5274	0.7814	0.9981	0.9785	3
Suez	ANN–Local	4.6107	0.6981	1.1245	5.5035	0.9546	0.9967	0.9642	3
	Empirical–Local	−4.4699	−0.8082	0.9823	4.8015	0.8989	0.9971	0.9727	2
	ANN–Canal Zone	1.8789	0.2207	0.6845	3.2342	0.6095	0.9980	0.9867	1
	Empirical–Canal Zone	−6.4757	−1.2098	1.3175	6.5420	1.2279	0.9976	0.9508	4

and

Table 12. Performance comparison for the best local and general models for both techniques (ANN and empirical) at the five selected sites using validation data set 2 (Single Year, 2018).

Site	Model Type	MPE	MBE	RMSE	MAPE	MABE	$\mathit{r}$	${\mathit{R}}^2$	Rank
Port Said	ANN–Local	2.2388	0.1600	0.7349	4.1386	0.6399	0.9974	0.9868	1
	Empirical–Local	10.5113	1.8491	2.0009	10.511	1.8491	0.9949	0.9023	4
	ANN–Canal Zone	1.0048	−0.1009	0.8427	4.1674	0.6892	0.9966	0.9827	2
	Empirical–Canal Zone	7.8331	1.3024	1.4987	7.8331	1.3024	0.9935	0.9452	3
El Kantara	ANN–Local	1.9174	0.1845	0.7911	3.7522	0.7019	0.9962	0.9830	2
	Empirical–Local	−5.3352	−0.9423	1.1776	6.0551	1.1312	0.9950	0.9623	4
	ANN–Canal Zone	2.3893	0.3255	0.7866	3.5081	0.6420	0.9953	0.9832	1
	Empirical-Canal Zone	−3.7947	−0.6218	0.9672	4.7566	0.8741	0.9952	0.9746	3
Ismailia	ANN–Local	2.3885	0.2841	0.9485	4.3287	0.8358	0.9924	0.9755	2
	Empirical–Local	−5.3350	−0.9423	1.1776	6.0549	1.1312	0.9950	0.9623	4
	ANN–Canal Zone	2.3893	0.3255	0.7866	3.5081	0.6420	0.9953	0.9832	1
	Empirical–Canal Zone	−3.7947	−0.6218	0.9672	4.7566	0.8741	0.9952	0.9746	3
Fayid	ANN–Local	2.4680	0.2921	0.8556	4.0221	0.7346	0.9952	0.9801	1
	Empirical–Local	−5.3578	−0.9508	1.1799	6.0634	1.1360	0.9950	0.9621	4
	ANN–Canal Zone	2.7241	0.4020	0.8991	3.9434	0.7531	0.9929	0.9780	2
	Empirical–Canal Zone	−4.0050	−0.6557	1.0015	4.9680	0.9084	0.9951	0.9727	3
Suez	ANN–Local	4.5249	0.7427	1.1046	5.3958	0.9934	0.9942	0.9653	2
	Empirical–Local	−3.6626	−0.6399	1.0303	4.8051	0.9390	0.9927	0.9698	1
	ANN–Canal Zone	3.0713	0.4760	1.1164	4.6875	0.9448	0.9876	0.9645	3
	Empirical–Canal Zone	−5.6395	−1.0325	1.2968	6.3898	1.2306	0.9932	0.9522	4

. On the one hand, we compared the performances of both techniques, the ANN and empirical models, using validation data set 1 (2018–2020). Looking at the local models, the results show that the best ANN-based models perform about 2% better than empirical ones in El Kantara, Ismailia, and Fayid, with $R^2$ increased from 96% to 98%. Additionally, the best ANN-based model in Port Said city surpasses the empirical one by about 7%, with the performance increasing from 91% to 98%. These findings indicate that ANN has the ability to predict GSR with high accuracy even at the coastal sites. On the contrary, in Suez city, the local empirical-based model performs better than the local ANN-based one by about 1%. Regarding the general models, the findings show that the two techniques have almost the same performance in El Kantara, Ismailia, and Fayid, with $R^2$ values of about 98%. Nevertheless, in the two remaining cities, Port Said and Suez, ANN-based models surpass the empirical ones by about 3%, with $R^2$ values higher than 98%.

On the other hand, the best models from both techniques are also compared together using validation data set 2 (2018). Looking at the local models, similar to the obtained results from validation data set 1, the best ANN-based models perform better than the empirical ones with about 2% improvement in the same cities (El Kantara, Ismailia, and Fayid). In addition, whereas both techniques have the same performance in Suez city ($R^2$ > 96%), the ANN model outperforms the empirical one by approximately 8% ($R^2$ increased from 90% to 98%). Regarding the general models, while ANN’s prediction accuracy is greater than that of the empirical model by about 1% at El Kantara, Ismailia, and Suez, it exceeded 4% at Port Said, increasing from 94% to 98%. In Fayid city, both methods have almost the same proficiency with $R^2$ values larger than 98%.

Overall, it can be noted that ANN-based models predict GSR with high accuracy, ranging from 96% to 98%, even at coastal locations, and all other indicators have good values within the acceptable ranges, which demonstrates that ANN is a powerful tool in GSR forecasting. For more explanation, the prediction of the best local and general models and the observed data in the five selected cities is clarified in Figure 11 and Figure 13, and their performance indicators are represented in Figure 12 and Figure 14. Furthermore, the relative error values of empirical-based models are computed and compared with those of the best ANN-based models and summarized in

Table 13. Relative error comparison for the best local and general models for both techniques (ANN and empirical) at the five selected sites using validation data set 1 (Long Period, 2018–2020).

Site	Model Type	January	February	March	April	May	June	July	August	September	October	November	December
Port Said	ANN–Local	1.4	6.7	5.5	3.3	1.1	−1.8	−3.0	−5.8	−4.4	0.5	5.4	14.2
	Empirical–Local	12.2	13.5	11.7	11.7	10.9	7.6	7.7	6.3	5.4	6.7	4.4	13.5
	ANN–Canal Zone	5.1	5.6	5.3	3.3	0.4	−2.8	−4.2	−5.3	−3.7	0.4	7.5	15.1
	Empirical–Canal Zone	10.7	12.1	10.4	10.3	8.4	4.4	3.9	2.4	1.9	3.6	1.9	11.4
El Kantara	ANN–Local	5.7	6.2	3.0	0.0	0.2	−2.9	−3.8	−2.7	1.6	2.0	5.4	12.2
	Empirical–Local	−9.9	−5.8	−3.0	−1.8	−0.2	−3.6	−2.6	−4.0	−5.9	−7.6	−13.3	−10.0
	ANN–Canal Zone	5.4	5.1	3.4	2.4	−1.3	−3.6	−0.3	−0.3	−0.6	3.7	3.4	9.2
	Empirical–Canal Zone	−8.3	−4.4	−1.8	−0.6	1.1	−2.2	−1.1	−2.4	−4.3	−5.9	−11.6	−8.2
Ismailia	ANN–Local	6.4	5.5	4.8	−0.1	1.2	−2.9	−5.3	−2.3	1.0	0.9	4.9	11.7
	Empirical–Local	−9.9	−5.8	−3.0	−1.8	−0.2	−3.6	−2.6	−4.0	−5.9	−7.6	−13.3	−10.0
	ANN–Canal Zone	5.4	5.1	3.4	2.4	−1.3	−3.6	−0.3	−0.3	−0.6	3.7	3.4	9.2
	Empirical–Canal Zone	−8.3	−4.4	−1.8	−0.6	1.1	−2.2	−1.1	−2.4	−4.3	−5.9	−11.6	−8.2
Fayid	ANN–Local	9.3	6.0	2.7	−0.6	1.1	−2.8	−3.9	−0.2	2.0	3.5	3.4	10.0
	Empirical–Local	−9.8	−5.8	−3.1	−1.9	−0.2	−3.7	−2.7	−4.0	−6.0	−7.6	−13.2	−9.8
	ANN–Canal Zone	3.3	5.3	3.8	2.1	1.9	−2.7	−2.7	−2.1	−1.0	2.6	3.5	10.9
	Empirical–Canal Zone	−8.7	−4.6	−2.0	−0.7	1.2	−2.2	−1.1	−2.5	−4.5	−6.2	−12.0	−8.6
Suez	ANN–Local	8.3	12.2	4.5	2.9	2.2	−0.9	−2.2	−2.2	0.9	4.6	7.7	17.4
	Empirical–Local	−8.2	−3.8	−4.4	0.0	2.0	−2.2	−2.5	−4.0	−4.4	−6.4	−10.6	−9.1
	ANN–Canal Zone	5.6	5.4	1.6	2.0	1.2	−4.2	−1.4	−1.7	−0.8	2.8	3.6	8.5
	Empirical–Canal Zone	−11.1	−6.7	−7.0	−2.4	0.4	−3.5	−3.6	−5.1	−5.8	−8.3	−12.9	−11.8

and

Table 14. Relative error comparison for the best local and general models for both techniques (ANN and empirical) at the five selected sites using validation data set 2 (Single Year, 2018).

Site	Model Type	January	February	March	April	May	June	July	August	September	October	November	December
Port Said	ANN–Local	9.6	8.5	1.9	0.4	1.4	−0.7	−3.2	−5.0	−2.4	4.8	3.0	8.7
	Empirical–Local	17.2	16.9	8.5	9.7	15.6	8.4	7.9	6.4	5.5	7.9	4.4	17.7
	ANN–Canal Zone	5.5	6.7	0.0	−0.5	1.7	−3.0	−4.8	−5.5	−4.7	−0.4	3.0	14.1
	Empirical–Canal Zone	15.4	15.3	6.9	7.9	12.7	5.0	4.0	2.6	1.9	4.8	2.0	15.6
El Kantara	ANN–Local	7.4	4.6	0.3	−1.1	3.9	−3.0	−3.9	−2.9	2.1	1.8	3.1	10.9
	Empirical–Local	−7.2	−7.6	−6.2	−3.2	4.3	−3.3	−2.5	−3.7	−5.2	−6.6	−13.9	−9.0
	ANN–Canal Zone	7.1	2.9	3.8	−0.1	3.7	−4.4	−0.5	−1.4	1.2	6.6	−0.3	10.1
	Empirical–Canal Zone	−5.5	−6.1	−4.9	−2.0	5.8	−1.9	−1.0	−2.1	−3.6	−4.9	−12.2	−7.2
Ismailia	ANN–Local	7.9	4.4	2.8	−1.3	5.5	−3.2	−5.5	−1.6	3.2	4.1	0.5	11.8
	Empirical–Local	−7.2	−7.6	−6.2	−3.2	4.3	−3.3	−2.5	−3.7	−5.2	−6.6	−13.9	−9.0
	ANN–Canal Zone	7.1	2.9	3.8	−0.1	3.7	−4.4	−0.5	−1.4	1.2	6.6	−0.3	10.1
	Empirical–Canal Zone	−5.5	−6.1	−4.9	−2.0	5.8	−1.9	−1.0	−2.1	−3.6	−4.9	−12.2	−7.2
Fayid	ANN–Local	10.6	4.9	1.6	−1.3	4.6	−3.1	−4.0	−0.9	1.8	3.5	0.6	11.3
	Empirical–Local	−7.2	−7.4	−6.2	−3.4	4.2	−3.3	−2.6	−3.7	−5.3	−6.7	−13.8	−8.9
	ANN–Canal Zone	4.6	7.2	3.7	0.9	7.3	−2.8	−2.8	−1.7	0.5	3.8	1.4	10.5
	Empirical–Canal Zone	−6.1	−6.2	−5.1	−2.1	5.8	−1.8	−1.0	−2.1	−3.8	−5.3	−12.6	−7.7
Suez	ANN–Local	8.7	11.7	3.4	3.9	6.4	−0.7	−2.4	−2.1	2.1	5.8	5.8	11.8
	Empirical–Local	−7.6	−1.4	−5.2	0.8	6.1	−2.2	−2.8	−3.9	−3.6	−5.9	−10.5	−7.9
	ANN–Canal Zone	2.6	12.8	3.8	3.4	8.0	−2.7	−3.8	−3.2	0.4	2.9	3.2	9.5
	Empirical–Canal Zone	−10.5	−4.1	−7.5	−1.4	4.5	−3.4	−3.8	−5.1	−5.0	−7.8	−12.8	−10.7

. The relative errors for the empirical and ANN models are in the acceptable range (±10%) except for some months, but, in general, the ANNs’ values are better than those of the empirical ones. While the relative error values of the empirical models are exceeded in one or more winter months (November, December, and January), the ANN values are exceeded in approximately one month, in Dec. The reason for this can be interpreted as different weather conditions in the winter season, such as rain, clouds, and wind. Whereas there is a slight effect on the ANNs’ performance due to these different conditions, there is a considerable effect on the empirical models’ performance.

3.4. Validation Data Set Comparison

It is more interesting to compare the obtained results from both validation data sets, validation data set 1 (Long Period: 2018-2020) and validation data set 2 (Single Year: 2018). The outcomes of this comparison can offer several valuable pieces of information; for instance, one can understand the impact of changing the length of the validation data set on models’ proficiency and precision and identify the most accurate, reliable, and stable technique at different locations that have different climatic factors. Thus, the revealed findings from both validation data sets, as demonstrated above in Table 11 and Table 12, are compared with each other (local and general), and the obtained relative error results in are compared in Table 13 and Table 14.

Focusing on ANN-based models, the results of validation dataset (Long Period: 2018-2020; and Single Year: 2018) comparison for the best local models show that there are almost no big differences in models’ performance with $R^2$ values that are approximately the same. Additionally, the difference between values of RMSE, MABE, and MAPE range from 0.01 to 0.11 (MJ m⁻² day⁻¹), from 0.03 to 0.12 (MJ m⁻² day⁻¹), and from 0.04 to 0.28 (%), respectively. Similarly, this range of difference remains little for the general ANN-based models, where RMSE, MABE, and MAPE are from 0.05 to 0.43 (MJ m⁻² day⁻¹), from 0.07 to 0.33 (MJ m⁻² day⁻¹), and from 0.07 to 1.4 (%), respectively. For more clarification, the impact of varying lengths of validation data sets on ANN-based models’ prediction and accuracy is displayed in Figure 15.

Looking at empirical-based models, similar to ANN-based models, the outcomes of validation datasets are compared and the range of difference is obtained; RMSE is from 0.02 to 0.17 (MJ m⁻² day⁻¹), MABE is from 0.02 to 0.12 (MJ m⁻² day⁻¹), and MAPE is from 0.4 to 1.0 (%). Overall, it can be noted that the difference range is still small, and $R^2$ values are almost the same except for coastal sites; there is a difference of about 1(%) in the models’ efficacy. For more explanation, the impact of varying lengths of validation datasets on empirical-based model prediction and accuracy is illustrated in Figure 16.

Regarding relative errors for both techniques (empirical and ANN), the results of the validation data set comparison reveal that the relative errors of ANN-based models that exceed ranges ± 10%, especially in the winter months, are improved when ANN models are validated with validation data set 2 (Single Year, 2018). For example, the values of local ANN-based models at Port Said, El Kantara, and Suez in December improved compared with the values which were obtained from validation data set 1 (Long Period, 2018–2020); the values decreased from 14.2, 12.2, and 17.4 to 8.7, 10.9, and 11.8, respectively. This may be due to the process of averaging the data in validation data set 1 (2018–2020) leading to this difference in the ANNs’ relative error values. In contrast, the relative error value of local empirical-based models, that exceed limits ± 10%, at the coastal sites is increased when they are validated by validation data set 2 (Single Year, 2018). This can be interpreted as the process of averaging data leading to improved values of some entry parameters (such as temperature) of the empirical-based model, especially at coastal sites like Port Said city.

Of more interest is the estimation of electrical power production using Photovoltaic (PV) systems in the Suez Canal zone: Figure 17 shows the monthly average of the observed and calculated daily GSR over the Suez Canal zone during 2018. The calculated values were obtained based on the general empirical-based model, using the general empirical coefficients as stated in Table 8. Based on these results, the annual average energy per day from solar radiation over the Suez Canal zone is about 21 MJ/m², with an average daily solar radiation of 243 W/m². This reflects a total annual solar energy of 2129 kW·h/m². If a Photovoltaic (PV) system is installed to generate electrical power with a panel efficiency of 15% and a performance ratio of 0.75, the expected annual production of electrical energy is about 240 kW/m². This reflects an average daily electricity production of 0.6558 kW·h/m², with an average daily production of electrical power of 27.33 W/m² (27.33 MW/Km²). Based on these calculations, one Gigawatt of actual electrical power can be produced by installing a PV system with an area of 37 km². This is compared with the data available for Benban solar park, which is still under construction near Aswan, south of Egypt (24°27′21.6″ N 32°44′20.4″ E), and can be considered the largest solar PV installation worldwide [87,88]. The nameplate planned capacity for Benban solar park is 1465 MW with a site area of about 37 Km², a capacity factor of 0.26, and a site resource of about 2472 kW.hr/m² based on the data from Solar Atlas of Egypt 2018 [89]. The actual produced electrical power based on the site area, resources, and 0.75 performance ratio is about 1.16 GW.

Based on these results, the expected electrical power generation for the Suez Canal zone is consistent with the data for Benban solar park. The higher produced power for the Benban site is due to the higher solar resources of 2472 kW·h/m² compared with the average solar resources of 2129 kW·h/m² for the Suez Canal zone.

NREA, Ministry of Electricity, Egypt, proposes different locations around Egypt which have solar energy potential for PV installations. One of these sites is ZAAFRANA, which is located in the region of the Suez governorate as a part of the Suez Canal zone. As shown in Figure 18, the Zaafrana site consists of four locations A, B, C, and D, with different area ranges between 8 and 80 km². Based on the calculation of the actual electrical power that can be produced by PV installations in the Suez Canal zone, locations A, B, C, and D can produce about 2186, 2076, 223.8, and 236.6 MW of electrical power, as listed in

Table 15. The available area and expected actual production of electrical power for the different four locations of the Zaafrana site in the SCZ.

Location	Area (km2)	Actual Electrical Power (MW)
A	80	2186
B	76	2076
C	8.19	223.8
D	8.66	236.6

. The total available area for all four locations is about 178.85 km², which can produce about 4.67 GW of electrical power. Based on these results, the Zaafrana site with its four locations can produce more than four times the actual electrical power produced by Benban solar park. As Zaafrana is very close to the SCZONE, it can be considered the most sustainable source of renewable energy which can support the future power demand for different industrial zones in the Suez Canal zone.

In general, based on the above discussion, the findings demonstrate that the proposed models in this work performed well in GSR forecasting with good performance indicators values. Also, AI algorithms have the ability to provide superior, rapid, and more applicable forecasts than any other method; ANN is an effective tool in forecasting GSR with high accuracy—especially at coastal sites—at any time. Therefore, the best-developed models in this work are the recommended solar radiation model to predict GSR with high accuracy at the studied locations specifically or the whole Suez Canal zone.

4. Conclusions

The potential for AI technology in environmental and renewable energy applications has expanded tremendously in recent times, with ANNs being the most widely used technique. Solar energy is now considered one of the attractive sources of clean energy for supplying a major amount of the demanded energy in the world. Thus, the first step in figuring out solar energy availability is obtaining accurate information about solar radiation. Additionally, it is recognized as an essential element in different solar applications. With the shortage of solar measurement in many locations across the globe, various solar radiation methods are developed to forecast GSR. Thus, in this study, temperature-based GSR models are developed using a commonly employed technique in ML-based approaches, ANNs, to forecast GSR using only ambient air temperature. These established models are compared with the performance of the most commonly used technique, the empirical method (Hassan et al. [46], Equation (4)). We also propose accurate GSR models for five new cities (particularly coastal ones) and the entire region, which presently lacks AI-based models, despite the presence of multiple proposed solar energy plants in the region (the Suez Canal zone, Egypt). Furthermore, the impact of varying lengths of the validation data set on solar radiation models’ prediction and accuracy is assessed, which has received little attention. In addition, we investigate different ANN architectures for GSR prediction and present a comprehensive comparative study. To achieve these goals, the observed GSR data for 37 years at the five chosen sites are used to establish and validate the developed models in this work. Moreover, the developed models’ generalization potential is also evaluated and examined in the five studied Egyptian sites, namely, Suez, Fayid, Ismailia, El Kantara, and Port Said.

The results indicate that both the empirical model and ANN techniques yielded highly accurate predictions of GSR, with R² ranging between 96% and 98%. The empirical models, which comprise both local and general formulas, displayed a similar level of performance at non-coastal sites. In contrast, the ANN-based models, both local and general, exhibited a high level of accuracy in predicting GSR in any weather condition, even in the winter months. Interestingly, ANN models with fewer neurons in their single hidden layer showed better performance as compared to those with larger numbers. Moreover, the accuracy and precision of the models, especially the ANN-based models, were minimally affected by the size of the validation datasets. Additionally, while the difference in weather conditions, such as clouds and rain, has a significant effect on the performance of empirical models, particularly at coastal sites, it only slightly affects ANN-based models, where ANN models outperform empirical models by approximately 7% at coastal sites. When it comes to the relative error, it is worth noting that while the relative error values of the empirical-based models tend to exceed the limits of ±10% at coastal sites when validated by the short validation data set (2018), the relative error values of ANN-based models improve when validated with the same data set. Additionally, the relative error values of the empirical models tend to be exceeded in one or more winter months, such as November, December, and January. In contrast, the ANNs’ relative error values are only exceeded in one month, which is December. Consequently, the best-developed models, particularly ANN-based ones, are recommended for precise and swift GSR forecasting, which can be used in the design and performance evaluation of various solar applications. The primary benefit of this approach in the current investigation is that temperature data are continuously and effortlessly recorded for various purposes.