Estimation of Solar Radiation with Consideration of Terrestrial Losses at a Selected Location—A Review

Abstract

The United Nations has set an ambitious goal to achieve net zero carbon emissions by 2050. This objective requires shifting towards green and renewable energy sources instead of conventional fossil fuels to address the global energy crisis without emitting greenhouse gases. While the energy radiated by the sun is one of the most abundant sources of energy available, its efficient and optimal use remains a significant challenge. To facilitate solar-energy-based applications, estimating the amount of solar energy available is crucial. Empirical and soft computing is the most-used method to estimate solar energy. This paper aims to analyze the existing techniques used in various models for estimating and predicting the quantity and quality of solar radiation using readily available data. Additionally, the study aims to identify the most appropriate techniques for developing prediction models using available explanatory variables. To fully harness the potential of solar energy, it is necessary to limit the terrestrial loss of solar radiation by minimizing the harmful effects of anthropogenic factors that reduce the quantity and quality of solar radiation in the area. This paper provides valuable insights to identify opportunities to maximize the potential of solar energy in different locations.

1. Introduction

This section of the paper explains the necessity of green energy sources and the rest of the paper. In the present scenario, the emission of greenhouse gases increases by leaps and bounds due to various human activities. The climatic conditions during the preindustrial period were suitable for human beings. In the preindustrial period, humans did not start using fossil fuels to fulfill their energy demands. As per the report published in the Bulletin of the American Meteorological Society (BAMS), the better “starting line” for the preindustrial period is 1720–1800. It is assumed that the concentration of greenhouse gases in the atmosphere was significantly less in the preindustrial period [1]. The primary cause of greenhouse gas emissions is the combustion of fossil fuels. Due to this, the difficulties faced by human beings are the increment of the average surface temperature, sinkage of glaciers and rise in sea levels, and many others. Li Berlin and HaneKlaus Nil [2] discussed in detail how the combustion of fossil fuels and urbanization increase the CO₂ emission in China. China is accepting this level of CO₂ emission to maintain its economic growth. We can obtain better climate conditions by limiting the emission of greenhouse gases. The energy demand and average earth surface temperature will drop simultaneously if the emission of greenhouse gases decreases exponentially. Suppose the ambient temperature range lies in the suitable range so the fan can replace A.C. to obtain a good comfort level in the living areas. Similarly, we can remove the room heater for a good comfort level. In more detail, it is explained in the Draft of the energy policy of India how to obtain energy conservation and efficiency [3].

In the previous paragraph, it is found that there is a strong requirement to stop the consumption of fossil fuels [4]. At the same time, the question arises of how to meet energy demand. The use of green energy sources can fulfill both criteria. The growth of energy demand in India is explained with the help of Figure 1.

India’s energy consumption is explained with the help of Figure 2. The production of energy using green energy sources emits a low amount of greenhouse gases.

To fulfill energy demand and low levels of greenhouse emission, the Government of India (GoI) has set a deadline of March 2022 to achieve the target of 175 gigawatts (GW) of grid-connected renewable electricity. The generation of electricity by different energy sources is depicted with the help of Figure 3.

The numerical magnitude of GoI’s plans to accomplish its goal is explained with the help of

Table 1. Sectors of installation of renewable energy.

Type of Renewable Energy	Capacity
Solar	100 GW
Wind	60 GW
Biomass	10 GW
Small hydro	5 GW

.

The Ministry of New and Renewable Energy (MNRE) also aims for 1 GW of Geothermal capacity by 2022. The other endeavors of GoI are explained in more detail in reference [5].

A similar scenario exists in all the developing countries of the world. They are facing a problem providing a clean cooking facility to all households, which has been delayed; this is explained in the World Energy Outlook in October 2020 [6].

The energy radiated by the sun is the major energy source freely available everywhere on earth. It has been found by calculation that if solar energy is converted efficiently, then all the world’s energy demand can be met by only solar energy. The earth’s surface receives annually approximately 4 million exajoules (1 Exajoules $={10}^{18}\mathrm{J}$) of solar energy. The solar radiation received on the earth’s surface has little contribution to the global energy supply [7].

Extra-terrestrial radiation (radiation outside the Earth’s atmosphere) that reaches the Earth’s surface meets the atmosphere. The atmosphere has many gases and suspended particles of various sizes. This composition causes absorption, scattering, reflection, refraction, and many other processes, diminishing the amount of solar radiation reaching the Earth’s surface. For the reliable generation of electricity, we must know the value of gaseous composition and suspended particles of the atmosphere for that location. So, measuring the air quality index and its component is necessary to know the amount of solar radiation in the territory.

It is estimated that the collective set up capacity of photovoltaic (PV) could reach 22% of global electricity generation in 2050 [8]. This large-scale electricity production by PV array must have better reliability and continuous generation. So, before establishing a solar farm or maximum utilization of solar energy, it is necessary to know the quantity and quality of solar radiation available in that area; it will help the investors to assess the investment cost of the SPV system.

The consistent measurement and recording of global and diffuse solar radiation do not exist in many developing countries. The reason is its high cost and difficulty installing and maintaining measuring instruments such as pyranometers. In India, there are 46 stations available for the measurement of solar radiation under the India Meteorological Department (IMD); out of them, 5 are defunct, 39 measure Global Solar Radiation (GSR), and 23 measure diffuse solar radiation [9].

So, the different methods suggest estimating and predicting radiation at any location without measuring the radiation. The advantage of this method is that the cost of installation and maintenance of the measurement setup can be diminished.

The variation in incident irradiance on the PV array produces voltage and frequency fluctuation in the generated electricity by the PV panels. To avoid a costly storage system and reliable grid operation/integration, it is necessary to know the advanced effect of this random variable on the PV output power. Apart from solar radiation, the other random parameters are mostly meteorological variables. Dust accumulation on solar panels affects the yield of electrical power generated. To counteract this negative effect, it is essential to estimate the dust deposition rate on solar panels [10].

The application of solar radiation estimation is not limited to the SPV system, but it is critical in various applications, as given below:

• To enhance the crop yield and reduce the risk factor associated with crop growth. Apart from this, long-term solar radiation data are used to maximize the utilization of agriculture sectors, for example, crop drying and drying process of agriculture products.
• Tourism and healthcare.
• To calculate the cooling load of the building and living area.

The above discussion shows that solar radiation estimation plays a critical role in different sectors. Various models have been developed from time to time to estimate solar radiation. In the beginning, the empirical model was developed with the help of recorded variables and statistical/mathematical approaches. Later, a few other models were developed with the advancement of computer science and machine learning approaches. Nowadays, it is preferable to estimate solar radiation with the help of hybrid models. Each method has its advantages, limitations, challenges, and accuracy. The empirical model has a simple mathematical relation but cannot handle nonlinearity and multiple input variables. The soft-computing approaches handle the incapability of empirical models; however, these approaches require knowledge of various software and involve high computational costs. Multiple explanatory variables do not need to give more accurate results. The optimum number of the data set and variables give good results. Knowledge of the software is not required to develop empirical models, but with the help of a dedicated software package, the empirical models can develop conveniently. In this work, various approaches are compared in different conditions. Apart from this, it is demonstrated how to select a suitable approach for an available data set of explanatory variables. The performance of the models varies as the scale of the predicted variable is changed. For example, empirical models are accurate for predicting monthly averaged solar radiation, while it performs poorly when predicting daily or hourly solar radiation. For predicting hourly or daily solar radiation soft computing method performed well. If the data (input and output) are poorly defined, i.e., insufficient data points, missing value, and presence of outliers, the soft computing method performs well, while empirical methods give the worst results.

Section 2 of this paper explains various empirical methods with explanatory variables used to estimate solar radiation. Section 2 also explains the chronological order of the empirical methods. Apart from this, Section 2 covers the drawbacks and complexity of the empirical methods. The different researchers compare soft computing-based models with empirically based models. The properties of the soft-computing approach were utilized by different researchers for the development of a highly accurate estimation model of solar radiation. Section 3 contains the definition and application of soft computing in brief. Section 3 divides into various sub-sections. Section 3.1 covers the selection of input variables for the soft computing models and the artificial neural network (ANN) methods for the variable selections. Section 3.2 cover the computational intelligence methods for the estimation of solar radiation. Section 3.2 discusses the chronological order of different soft computing methods developed by different authors.

Section 4 of this paper covers the effect of anthropogenic substances on solar radiation. This section covers the various factors incorporated into the estimation model of solar radiation to obtain highly accurate results, e.g., air pollution index (API) and its components. The losses in radiation due to these anthropogenic factors have been explained in terms of loss of revenue, efficiency, etc., and are discussed in this section. Section 5 explains the critical finding. The critical findings were obtained after a detailed study of the available literature and research papers. The purpose of critical findings is to demonstrate the challenges obtained by different research observed during the development of estimators. The critical finding also demonstrates the possible solution to these challenges as suggested by different researchers.

2. Empirical Models for Estimating Solar Radiation with their Input Variables

The goal of studying various empirical models is a critical finding. A correlation equation was created based on the experimental results to describe the model’s behavior. The empirical model is the term coined for this newly developed model. This section of the paper examines the various empirical methods for predicting solar radiation. However, dynamical modeling is used to predict large-scale solar radiation [11].

The first estimate of global solar radiation was made using sunshine duration by Angstrom [12]. World Meteorological Organization (WMO) suggested a better definition of sunshine duration in 2003 as the period in which solar irradiance crosses the cut-off of 120 W/m² in a single day. In cloud-free conditions, this duration is equivalent to the solar irradiance level shortly after sunrise or before sunset. Prescott used the Angstrom model to calculate the monthly average daily global radiation (MJ/m²-day) on a horizontal surface from the monthly average daily total insolation on an extra-terrestrial horizontal surface using Equation (1) below.

$$\frac{H}{H_0}=a+b\frac{S}{S_0}$$

(1)

where $H$ is the monthly average global radiation on a horizontal surface, $S$ is the monthly average daily bright sunshine hours, $S_0$ is the maximum possible monthly average daily sunshine hours or the day length, $H_0$ is the monthly average daily extraterrestrial irradiation, $a$ and $b$ are empirical constants.

The monthly average global solar radiation in P.D.R. Yemen is estimated and compared with the measured value at six stations/towns of P.D.R. Yemen by Gadhi et al. [13]. Their results reveal that for the towns of Aden, Seiyun, Lahej, Fiyush, and Al-Sufal, the percentage difference between computed and measured values is less than 13.8%. However, the percentage difference value is very high for the station Mukiras because the data available for that location are very small. They use no statistical indicator or relative measure to improve the strength and clarity of understanding of the results.

Safi et al. [14] used a different strategy based on the lost solar component. The difference between extra-terrestrial radiation and daily global radiation recorded on the Earth’s surface is the lost solar component. Lost solar component data are categorized as non-Gaussian and non-stationarity. The selected location has the longitude $8^{°}{02}^{\prime }$ W and latitude ${31}^{°}{32}^{\prime }$ N with an elevation of 463 m.

The analysis was compared with the predicted result based on the clearness index and found that the lost solar component model is better. The result is summarized using

Table 2. Performance comparison of lost solar component and clearness index.

Parameter	Methods	Magnitude
NMBE	Lost solar component	2.28%
	clearness index	11.87%
NRMSE	Lost solar component	0.16%
	clearness index	0.28%
t-statistics	Lost solar component	1.75
	clearness index	2.93

. The approach is used for the conversion of the random system and its information into a non-Gaussian and non-stationarity system, and this information is used in some other fields. Fabrice Poirion used the same approach as Irmela Zentner [15] to construct the probabilistic model for time or space-dependent natural hazards.

The performance comparison of the two methods based on NMBE and NRMSE is explained with the help of Figure 4. Figure 4 more clearly depicts the performance comparison. In Figure 4, mean bias error and RMSE are normalized, and both have the unit Kw/m². The t-statistics are depicted in Figure 5. The smaller value of t shows better model performance. The t-statistics were calculated for modeling daily solar radiation with unit Kw/m².

The graphical comparison of t-statistics explains with the help of Figure 5.

Even with a pocket calculator, Kaplains S.K. [16] provides two new easy ways to estimate hourly global solar radiation on a horizontal surface. The author performed this study to achieve the goal of better sizing solar thermal or solar power systems and simultaneously managing both solar energy sources and power load. Comparisons are made between the expected global solar hourly radiation values, estimates from two current packages, and the measured solar radiation for Greece’s two largest cities. The geographical coordinates (latitude/longitude) in degrees of the location of Athens and Thessaloniki are 37.98381 N/23.727539 E, and 40.640266 N/22.939524 E, respectively. The climate condition of Athens is a hot-summer Mediterranean climate, while Thessaloniki has a cold semi-arid climate with Mediterranean and humid subtropical influences. Each city has different climate conditions.

The multilinear regression and multi-nonlinear regression equation were used to estimate solar radiation with more than one variable that had been taken together. The global solar radiation is estimated using the multilinear model created by Falayi et al. [17], with the independent input variable as single or multi variables. These variables are sunshine duration, mean daily temperature, maximum and minimum daily temperature ratio, and relative humidity. The authors used relative measures: correlation coefficient (R), coefficient of determination (R²), mean bias error (MBE), root mean squared error (RMSE), and MPE to compare the performance of various models. The objective of this study is to predict the data of monthly daily global solar radiation on the horizontal surface for better utilization of solar energy-based applications in Iseyin, southwest Nigeria. The geographical coordinates (latitude/longitude) in degrees of the location Iseyin 7.98 N/3.6 E. The climate condition of Iseyin is tropical climate.

Ahmed Taha and Hussein Tawfik [18] developed a computer model to estimate Hourly values of solar radiation using the metrological variable. These metrological variables are sunshine duration, cloud cover, maximum and minimum, and daily mean of ambient temperature. They calculated the correlation coefficient and mean bias error and plotted the residual hourly solar radiation distribution as a function of measured data.

The grid-connected solar PV system needs unfluctuating power in terms of voltage and frequency. If we estimate the hourly global solar radiation I (h; nj), at any hour (h) in a day nj, we can reliably generate power and size solar energy plants. The hourly profile of the intensity of the global solar radiation, I (h; nj), at any hour (h) in a day nj at a site is suggested by Kaplanis S. and Kaplani E. [19]. One, two, or three morning measurements of the worldwide solar radiation in a day nj, provided by the vast data bank of previously recorded data, are needed by a model that forecasts hourly global solar radiation I (h;nj).

Ahmad M. Jamil and Tiwari G.N. [20] discussed 62 empirical models for estimating the GSR with the performance evaluation matrix MPE, RMSE, and MBE. They are categorized into four groups. Group I (linear model): The regression equation of this model is a first-order equation derived from Angstrom-type regression equations. The empirical constant was obtained from the analysis. Group II (Polynomial Model): A second, third, and more significant order polynomial has been proposed by some researchers as a means of estimating the modified Angstrom type relation (MADGR). Group III (Angular Model): By altering the original Angstrom-type equations, the angular model is derived. Group IV: The regression equation of this model was obtained by modifying the Angstrom-type equation, including the term logarithmic, nonlinear, and exponential.

The quick estimation of short-duration (hourly) solar radiation was estimated by Al- Rawahi N.Z., Zurigat Y.H., and Al-Azri N.A. [21] for calculating the cooling load for the building and solar collector performance. The predicted hourly solar radiation compared with the ground station data at the Seeb Meteorological station in Oman. The solar collector collects the maximum solar radiation at a tilt angle of about 25 degrees. The Seeb Meteorological station in Oman can collect the data for the calculation of hourly solar.

Ituen, Eno. E., et al. [22], in their paper “Relative humidity”, the highest temperature and the sunshine hours at Uyo, Nigeria’s Niger Delta, are used to forecast global solar radiation. They develop many regression equations and compare them based on correlation coefficient, MBE, RMSE, and MPE. Among them, a more accurate regression equation was discovered by using recorded values of air temperature, relative humidity, and sunshine hours for Uyo, a city in Nigeria’s Niger Delta, from 1991 to 2007.

Marwal V.K. et al. [23] used bright sunshine hours duration data for Jaipur and developed six regression equations. They compare these equations based on the following relative measures: regression coefficient, MBE, and RMSE. They determined that cubic regression had the lowest RMSE and MBE values, as well as the highest correlation coefficient value. While the logarithmic has a lower correlation coefficient and greater RMSE and MBE values when all six regression equations are used, respectively.

To estimate the monthly average daily global solar radiation on a horizontal surface for certain diverse climate cities in Iran, Bagheri Tolabi Hajar et al. [24] created a MATLAB software based on imperialist competitive algorithms. The author uses the imperialist competitive algorithm (ICA) to estimate the experimental coefficient of the Angstrom model. They compared their result calculated using the statistical regression techniques (SRT) and found that the accuracy of ICA is higher than the SRT.

Almorox Javier et al. [25] estimate daily global solar radiation from the measured temperature at Canada de Luque, Cordoba, Argentina. With temperature as an input parameter, they compare five models for global solar radiation prediction. The performance of these five models was compared based on relative measures such as R², RMSE, MBE, MAPE, and mean percentage error (MPE).

The convenient and simple model was developed by Khorasanizadeh Hossein et al. [26] for the enriched region of solar radiation of the world and in Iran for the city of Birjand. Without using any geographical and metrological variables, they developed a model that predicts daily global solar radiation on a horizontal surface and monthly mean global solar radiation on a horizontal surface based on the day of the year. The developed model performs well compared to the temperature-based model, but its performance is minutes lower than the sunshine duration-based model. So, the day-of-the-year-based model (DYB) can be ranked second for Birjand. The city of Birjand is located in eastern Iran and is the capital of South Khorasan province.

Suthar M. et al. [27] further used the multilinear and nonlinear regression equations to compare the model results with input variables.

Table 3. Demonstration of the best results obtained from the Exp.-quadratic model.

Independent Variable	Type of Model	RMSE	MBE	MABE	MPE	MAPE	R
Sunshine, API, latitude (φ1) and longitude (φ2)	Exp.-quadratic	3.08	0.6	2.3	0.004	0.1342	0.3790

demonstrates the best results obtained from the different models having various input variables, while the other model has a lower value than the demonstrated results of Table 3.

Suthar M. et al. [27] model is depicted in Figure 6. Figure 6 shows the model’s superiority compared to other models developed by the authors.

In the above-discussed empirical models, the authors [17] use the first-order regression equation to establish the relationships among the data available for estimating solar radiation. Similarly, the other authors use different empirical models to develop the regression equation for estimating solar radiation. In all the methods, variables are related to response variables by statistical methods or mathematical equations.

3. Estimation of Solar Energy Using a Soft-Computing Approach

The difficulty associated with empirical modeling is the presence of measurement noise. So, before establishing a regression equation, there is a need to pre-process data. The purpose of pre-processing data is to find outliers and irrelevant data points in both (attribute and target variables). Another difficulty is finding the best regression equation from the actual data. The selection of inclusive variables and their order take a lot of time and effort. However, the inclusion of the variables is decided by the relative measure adjusted R². Selecting the order and type of regression equation requires a lot of effort and developer skills. Sometimes decisions are stuck among the accuracy, complexity, and coefficient of determination. The advantages of soft-computing methods are that they can overcome both the difficulty associated with the empirical methods. Soft computing is the branch of engineering that deals with computational intelligence—human decision-making tasks can be performed with the help of a soft-computing approach. So, the actual intended operation is performed by the techniques rather than human beings.

This section aims to reveal the existing soft-computing methods and their pros and cons used in solar radiation estimation. What is the necessity of new methods that may not have been utilized till now for solar radiation estimation?

Computational intelligence is similarly used as a stand-in for the human mind. The techniques that come under the umbrella of soft computing are ANN, fuzzy logic, GA, wisdom-based expert system (WES), probabilistic reasoning (PR), evolutionary computing (EC), neural computing (NC), machine learning (ML), etc. Apart from these, all the new computational intelligence methods come under soft computing [28]. The role of the soft-computing method is to establish the regression equation for solar radiation and other independent variables of regression equations. Machine learning can analyze vast amounts of data and identify specific trends and patterns humans would miss. The accuracy and efficiency of ML methods have been improved after gaining experience. Machine learning methods are the most widely used for developing prediction models among all the soft-computing methods. A data set of target and attribute variables is used to develop regression equations for a prediction model. The best regression equation can be developed with the help of suitable learning methods. In machine learning, there are five types of learning methods. These are supervised, unsupervised, reinforcement, deep, and deep reinforcement. Advantages and disadvantages of the soft-computing method ANN, fuzzy, and EA are given in

Table 4. Advantages and disadvantages of ANN, fuzzy, and evolutionary algorithms/GA.

	ANN	Fuzzy	Evolutionary Algorithms/GA
Advantages	Capability to learn and adapt	Rules are used to represent knowledge.	Organized random search
	Capability to tolerate faults	Capability to tolerate faults	Offers several solutions
	Model-free technique	Expertise is necessary
	Data from the past (numerical) is required for training.	Intellectual aptitude
Disadvantages	Inherent operation is not known (Black box approach)	No learning capability	Convergence is a slow near-optimal solution
	It can only handle quantitative data.	It can only handle qualitative data.
	No reasoning capability

.

Sometimes it is impossible to obtain good results with a single soft-computing approach; thus, we combine two more soft-computing approaches to boost the results. This approach is called the hybrid soft-computing approach/methods or algorithms. In hybrid soft-computing algorithms, knowledge of the system allows us to embody the mathematical model and clearly explain the related problem. A complex problem model requires techniques that can explain the problem more clearly. Now, we obtain the optimal solution by using the second technique. In brief, we can conduct the optimal solution search by integrating each advantage. For example, an adaptive neuro-fuzzy inference system (ANFIS) is a hybrid soft-computing technique (HSCT) in which NNs are used to tune a fuzzy logic controller (FLC).

Next, we discuss how these methods are utilized in solar radiation prediction. After studying this section, the researcher can know how to select a better one.

3.1. Estimation of Solar Radiation Using an Artificial Neural Network

The ANN is one of the alternative methods of prediction/estimation of solar radiation over the conventional method. ANN comes into existence when nonlinearity exists among the attributes and target variables. It can also perform a selection of variables and data sorting etc., simultaneously.

ANN can solve unknown input for which it was not trained. Many variables are there in ANN. Any change can create a new model. All the networks of ANN variations exist due to their different inputs and forms of measured output. The flow chart of solar radiation estimation using ANN can be summarized below in Figure 7.

ANN was successfully applied for the estimation of solar radiation by many authors and researchers. These are discussed one by one in these sections. Yadav A.K. and Chandel S.S. [29] discussed various methods to explain the application of ANN in solar radiation estimation in their review paper. They classify and compare the ANN model based on output quantity or desired profile for which solar radiation is measured. They classify the ANN methods for GSR, daily solar radiation (DSR), and short-term solar radiation. They explain the input variables for ANN models and suggest the requirement of geographical and metrological variables and their possible combinations for better estimation. They explain the possible input combination with the help of another research.

Alam et al. [30], for the estimation of solar radiation in the form of monthly mean, hourly, and daily diffuse, use the data of the Indian Metrological Department for IMD stations located in the cities: Chennai, Vishakhapatnam, Pune, Nagpur, Mumbai, Ahmedabad, Jodhpur, Kolkata, Port Blair, and New Delhi. They observed that the ANN model with input combination from S. N. (serial number) 1–8 shown in

Table 5. Input variable and short form.

S.N.	Input Variable	Short Form
01	Latitude	Lat
02	Longitude	Long
03	Altitude	Alt
04	Time	Time
05	Air temperature	At
06	Relative humidity	Rh
07	Wind speed	Ws
08	Net long wavelength	Lw
09	Months of the year	Moy
10	Rainfall	Rf

with their short-form having mean squared error (MSE) is 10⁻⁵ for summer.

The ANN model with different architecture and the same input combination having MSE is 10⁻⁴ for rainy. In winter, the ANN model with different architecture and the same input combination except S.N. 07 having MSE is 10⁻⁵. They developed a varied model from the possible input combination of Table 5; they found that the maximum RMSE is 8.8%. In the paper, they tabulate all the models and found that the prediction of hourly and daily diffuse radiation has better accuracy than the empirical models.

Authors [29] discussed two methods to select the input variables to obtain good results: one is the automatic relevance determination (ARD) method, and the other is niching genetic algorithm (NGA) and their combination. They compare the ARD and NGA methods to select more critical parameters related to the ANN model for solar radiation prediction.

Kumar S. and Kaur T. [31] use ANN to select input variables and obtain a more accurate estimate of solar radiation quantity. They explained the 12 architectures of the ANN model and observed a minimum MAPE of 12.15 and a correlation coefficient of 0.78 and 0.74 during training and testing the data set with the architecture 5-48-15-1. They applied the analysis by using a five-input variable to 50 architectures of ANN. Then, they defined the selection criteria for selecting an input. The absolute weight value associated with each network’s input parameters ranks the input variables. The input with the highest weight considers a high rank and is more critical for estimating solar radiation. The value obtained by all 50 networks is tabulated in

Table 6. The rank of input parameters.

Parameters	Number of Networks
	Rank 1	Rank 2	Rank 3	Rank 4	Rank 5	Final Rank (Majority Rule)
Atmospheric pressure	10	8	20	9	3	3
Clearness index	7	10	8	15	10	4
Precipitation	5	2	12	11	20	5
Temperature	20	12	4	9	5	1
Relative humidity	8	18	6	6	12	2

, shown below.

They observed that the input variable temperature was at rank 1 in 20 networks, relative humidity was at rank 2 in 18 networks, atmospheric pressure was at rank 3 in 20 networks, clearness index was at rank 4 in 15 networks, and precipitation was at rank 5 in 20 networks. They found the final rank of the input variable by applying the majority vote rule, which is also shown in Table 6. The above-discussed analysis applies to the satellite data obtained for the Chamba region in Himachal Pradesh, India. The geographical coordinate of Chamba lies in between 32°11′–33°13′ N and longitude 75°49′–77°3′ E with an altitude of 996 m above sea level. Based on the result, they concluded or observed that temperature, relative humidity, and atmospheric pressure are more relevant parameters for solar radiation estimation.

For performance validation, they use the same methodology, i.e., a model with fewer input variables, for the Hamirpur District. The geographical coordinate of Hamirpur lies in between 31°25′–31°52′ N and longitude 76°18′–76°44′E with an altitude of 738 m above sea level. To estimate solar radiation, they consider only three more relevant input variables: temperature, relative humidity, and atmospheric pressure. They estimate radiation and compare it with the reference or existing model for the same locations. The comparison of results is shown in

Table 7. Comparison of results of ANN model and references.

ANN Model	Inputs to ANN	MAPE	Network
Present study model after implementing connection weight approach	T, RH, P	13.02	3-48-15-1
Yadav and Chandel [32]	T, Tmin, Tmax, H, SH, CI, ER, Lat and Long	35.04	…
Kumar S. and Kaur T. [33]	T, RH, P, PT, S	16.45	5-16-1

.

The performance evaluation was performed on the value of MAPE, and the result shows that the ANN model performs better than the existing model for the exact location. The model requires only three input variables which gives more accurate results. The author used ground station solar radiation data from the National Institute of Technology Hamirpur, Himanchal Pradesh (HP), India’s Centre for Energy and Environment, and the remaining data were from satellites. So, we can conclude that the connection weight approach can be used to find the most relevant input parameter for solar radiation estimation and complex locations where no metrological station is available. The meaning of complex location is where it is difficult to establish a metrological station and complex to calibrate the instruments.

The purpose of Section 3.1 is to show the importance of ANN in solar radiation prediction. References [29,30,31] show how both operations performed simultaneously with the help of ANN. Reference [27] demonstrates how only three variables can give more accurate results than empirical/existing models developed for the exact locations.

3.2. Computational Intelligence Techniques for Solar Radiation Estimation

In the previous section, we discussed the techniques through which we select the optimal number of parameters because the easiness of the estimation depends on the readily available data of variables used in solar radiation estimation. This section discusses the year-wise soft computing techniques for using solar radiation estimation.

3.2.1. Years (1990–1999)

The literature survey found that in 1998 Al- Alawi S.M., and Al-Himani H.A. [34] used a computational intelligence technique to estimate solar radiation. They suggest how to assume a missing value, find false data, and remove false values. They consider eight input variables for calculating solar radiation in the form of global solar radiation for Seeb sites. These inputs are location, month, mean pressure, mean temperature, mean vapor pressure, mean relative humidity, mean wind speed, and mean sunshine hours (SH). This ANN model with different location and different months has an accuracy near about 93% and MAPE 7.30. While the ANN model tested for the whole year for each month at Seeb sites, the accuracy was obtained at 95% with a MAPE of 5.43%.

In the same year, 1998, Mohandes M et al. [35] used ANN to estimate GSR in Saudi Arabia. They used four input variables, latitude, longitude, altitude, and Sunshine duration, for their ANN model. The MAPE magnitude for the stations Tabuk, Al-Ula, Unayzah, Shaqra, Dawdami, Yabrin, Turabah, Heifa, Kwash, and Najran is 10.7, 6.5, 14.6, 10.5, 13.4, 10.1, 16.4, 11.3, 19.1, and 13.5, respectively. Both models can be compared and summarized with the help of

Table 8. Comparison of two models at Seeb at Oman and different 10 locations in Saudi Arabia.

Authors	No. of Inputs	Data Durations/Points	MAPE	Multilayer Feedforward Architecture	Training TECHNIQUES
Al-Alawi S.M. et al. [34]	08	06 year	5.43, 7.30	Not define	B P algorithms
Mohandes M. et al. [35]	04	10 year/372	6.5–19.1	4,10,1	B P algorithms

.

3.2.2. Years (2000–2009)

In the next decade, the work suggested by Sfetsos A. et al. [36] for forecasting hourly solar radiation with the help of artificial intelligence techniques. They suggest estimating hourly solar radiation by using single variable and multivariable input for their models. The authors explain how to consider input variables for the ANN model because the trial-and-error method takes much time to select input variables for time series solar radiation forecasting. The linear model may use some statistical parameters to find the relevant variable or lags. They suggest sensitivity analysis techniques for selecting input variables for the nonlinear ANN model. They use a linear, radial basis function (RBF), Elman, ANFIS, and feedforward networks to forecast solar radiation. Training algorithms used for the networks are Levenberg–Marquardt (LM) and backpropagation (BP). They show that the RMSE between the LM and BP training algorithms is 1.06% for the single variable and 11.5% for the many variable cases. The descending order of accuracy is feedforward, ANFIS, RBF, Elman, linear network, and their approaches.

Sözen Adnan et al. [37] estimate solar potential in Turkey using ANN. They used 17 metrological and geographical data stations to train (11) and test (6) to develop the ANN model. In areas of Turkey without a metrological station, they utilize this approach to calculate the solar potential. Scaled conjugate gradient (SCG), Pola–Ribiere conjugate gradient (CGP), Levenberg–Marquardt (LM), and logistic sigmoid transfer function are the training methods for ANN models. The activation function is the logistic sigmoid transfer function. For the testing stations, the highest mean absolute percentage error of the ANN model was found to be less than 6.7 percent, and the absolute fraction of variance value was found to be about 99.8937 percent; for the training station, the corresponding values were found to be 2.45 and 99.99658 percent. In their paper, the authors compare their different ANN models for cities in Turkey. The authors used the term RMS rather than RMSE, but both are identical. The results can be understood with the help of the number of hidden neurons, absolute fraction of variance, root mean squared (RMS) (%), max error (%), MAPE (%), and coefficient of variation as a percentage (COV) for different cities.

Takagi–Sugeno (TS) fuzzy system used by Iqdour R. and Zeroual A. [38] for a nonlinear model of GSR prediction at location Marrakesh, Morocco. Takagi–Sugeno (TS) fuzzy system converts the nonlinear model into a linear part using a set of if-then rules. The authors show that this model performs well compared to other models based on the lost solar component and clearness index using higher-order statistics. The values of RMSE observed by them for their model in the training and validation phase are 0.76 and 0.82. The parameter of higher-order statistics is normalized root mean squared error (NRMSE), normalized mean bias error (NMBE), and t statistics. The value of NRMSE, NMBE, and t statistics for the TS fuzzy model are 13.87%, 0.44%, and 0.61, while the rest two models, i.e., lost solar component and clearness index, have the values of 16%, 2.28%, 1.75, 28%, 11.87%, and 2.93 respectively.

To draw a solar map for the country of Spain, Hontoria L. et al. [39] use a multilayer perceptron network. Two approaches were used to draw the solar radiation map, one for a small region and another for a large region. Data for training and validation are used for the places where the metrological station is available. They developed seven MLPs (multilayer perceptron) and compared their performance with the help of the relative measure mean relative variance (MRV). They successfully map solar radiation for Spain, a different climate zone, with the help of only seven metrological station data. The author suggests that MLPs can map solar radiation. At the same time, classical methods cannot generate solar radiation series for places without data for solar radiation. So, MLP is better than the classical method for mapping the solar radiation series.

The ANN technique, such as a multilayer feedforward network with backpropagation learning algorithms used by Elminir Hamdy K. et al. [40] to predict the solar radiation component at Helwan, Aswan monitoring station in Egypt. These components are (i) infrared, (ii) ultraviolet, and (iii) global solar radiation. They use relative measures to judge the performance analysis: RMSE, MBE, and correlation coefficient. Temperature, relative humidity, wind speed, and wind direction were used to train the network. The highest correlation coefficient value for all solar components explains with the help of

Table 9. Value of correlation coefficient for all solar components.

Solar Radiation Component	Month	Magnitude
I.R.	August	0.995
U.V.	October	0.992
Global	June	0.998

for the Helwan monitoring station.

The researcher employs hybrid models to lower the number of input variables in the study. One of them was developed by combining the feedforward network (ANN) with backpropagation learning algorithms and the library of Markov transition matrices (MTM) approach [41]. This hybrid model (ANN-MTM) produced a time sequence of daily GSR data for Algeria. The model inputs only geographical data, i.e., latitude, longitude, altitude of the given location, and an 8% maximum prediction error was obtained. The developed model has accuracy and is accepted by the designer for their application, such as stand-alone photovoltaic power (SAPVP) system sizing. The model outperforms established techniques such as AR, ARMA, Markov chain, and MTM while using fewer input variables and less simulation time. In the ANN (MLP)–MTM technique, the first model was used to produce a monthly average of data on global solar radiation based on geographic coordinates, and the second model was used to produce a series of daily solar radiation values based on a monthly average of the clearness index. Both blocks are connected in a cascade.

In developing countries such as India, the IMD has developed 46 solar radiation measurement stations. Out of forty-six, five are defunct, 39 measure GSR and 21 measure direct solar irradiance [9]. In that case, there are some alternate methods to estimate direct solar irradiance. A method for selecting input variables to model direct solar radiation using GSR data was developed by López G. [42]. They learned about the more relevant input parameters using the automatic relevance determination (ARD) method. They found more relevance between the input variable’s clearness index and relative air mass. This approach reduces the necessity of a large amount of data for the isolated locations because there is no need for separation of data sets in training, testing, and validation data set.

Alam Shah et al. [30] developed an ANN model that estimates beam solar radiation at an Indian location using the Reference Clarity Index (RCI) estimate beam solar radiation. The ANN model has the input variable of S.N. 1, 2, 3, and 9 from Table 5, apart from its mean duration of sunshine hours, relative humidity ratio, and rainfall ratio, incorporated to calculate RCI as an output variable. The six Indian location data were used for training, and five Indian locations of different latitudes and longitude used for testing. The RCI is defined as

$$\mathrm{RCI}=\frac{{\mathrm{H}}_{\mathrm{b}\mathrm{m}}}{{\mathrm{H}}_{\mathrm{b}\mathrm{h}}}$$

(2)

where ${\mathrm{H}}_{\mathrm{b}\mathrm{m}}$ = reference monthly mean daily beam solar radiation at normal incidence ${\mathrm{H}}_{\mathrm{b}\mathrm{h}}$ = monthly mean daily beam solar radiation computed using Hottel’s clear day model.

The estimated value is compared with the help of the measured value obtained from the various station of IMD in different parts of India. They cover the maximum climate zone of India except for the hilly region of North and Punjab. The computation of RCI takes place using MATLAB Neural Toolbox function ‘TRAINLM.’ The authors observed that the maximum RMSE is 2.79% in Mumbai, and the minimum error is 1.65% in Vishakhapatnam.

An ANN model was suggested by Elminir K. Hamdy et al. [43] to calculate and forecast diffuse fraction (K_D) on an hourly and daily basis. The input variables of the ANN model are GSR, longwave atmospheric emission, air temperature, relative humidity, and atmospheric pressure, and the output variable is K_D. The ANN model obtained a better result compared with the two regression equations. The authors employed skewness and kurtosis indices to examine the symmetry between the computed and observed data. Bulut and Büyükalaca [44] estimate daily global radiation using the trigonometric function in Turkey. They used a single independent variable with ten years of data for training and testing the model. The model has an accuracy that matches the requirement of the applications.

Mishra Anuradha et al. [45] used RBF and MLP networks to estimate direct solar radiation for eight sites in India with inputs such as latitude, longitude, mean sunshine per hour length, relative humidity ratio, and month. RBF is found to perform poorly when compared to MLP. They observed that RMSE for RBF ranges from 7–29%, while MLP RMSE range is 0.8–5.4%.

Mubiru J. et al. [46] have developed a method for estimating the monthly global average daily solar radiation at Uganda sites based on the ANN architecture of feedforward backpropagation. ANN model has L.M. training algorithms with the relative measure MAPE. The ANN model takes as inputs the yearly average of sunshine hours, cloud cover, relative humidity, rainfall, latitude, longitude, and altitude.

Moustris K. et al. [47] employ hourly data on air temperature, relative humidity, sunshine duration, cloud octals, and latitude to develop an MLP to predict the missing mean, maximum, and minimum global and diffuse solar irradiance hourly data for Greek regions. To check the linearity among the measured and estimated values, the author used a correlation coefficient with a 99% confidence level (p < 0.01). It shows good agreement between a measured value and a predicted value.

Rehman S. and Mohandesand M. [48] estimate the future value of GSR with the help of MLP networks and backpropagation learning algorithms. The inputs of the MLP network are the combination of measured air temperature and relative humidity, and the output is global solar radiation (GSR). The performance of the network and others summarize with the help of

Table 10. Summary of the performance of the models.

Input Combination	Architecture	Data Utilize	AMPE	Order of Error
Daily maximum air temperature, Day of the year	24 hidden neurons and one output neuron	1462 days for training, 240 days for testing	10.3%	medium
Daily mean air temperature, Day of the year	32 hidden neurons and one output neuron	1462 days for training, 240 days for testing	11.8%	highest
Daily mean air temperature, Day of the year, Daily mean relative humidity	24 hidden neurons and one output neuron	1462 days for training, 240 days for testing	4.49%	lowest

.

It is concluded from Table 10 that the selection of input plays an essential role in the accurate estimation of solar radiation. The authors [48] do not cover the hilly region of India such as J&K, Uttarakhand, and Himanchal Pradesh. The study or methods performed by Bosch J.L. et al. were made for the complex terrain of Spain. The station altitude varies from 1000 to 1700 m. Bosch J.L. et al. [49] explain the methods to estimate GSR for this complex terrain. The authors estimate solar radiation in two steps. First, one selects the input variable for the estimation model using ARD methods. After selecting the variable, they developed an MLP model with an RMSE of 6.0% and MBE of 0.2%. In this study, the author obtained GSR values from one radiometric station and compared them with the estimated value.

To forecast solar radiation for 12 Turkish cities, Şenkal Ozan and Kuleli Tuncay [50] created an ANN and physical model. Latitude, longitude, altitude, month, mean diffuse radiation, and mean beam radiation are all inputs to the network. They used nine cities’ data for training and three cities for testing the neural network. Its performance comparison can be summarized with the help of

Table 11. Summary of the performance comparison.

Model	Phase	RMSE
MLP	Training	54 W/m2
Physical	Training	64 W/m2
MLP	Testing	91 W/m2
Physical	Testing	125 W/m2

.

Benghanem M. and others [51] use the ANN model for estimating daily global solar radiation. The variables utilized for the modeling are global irradiation, diffuse irradiation, air temperature, relative humidity, and data of duration from 1998 to 2002 were taken from the NREL website. They use various combinations of input variables to create six ANN models (air temperature, relative humidity, sunshine duration, and day of the year). Each model’s output is the daily global solar radiation. The highest correlation coefficient value, or 97.65 percent, is obtained among all six models using sunshine duration and air temperature as inputs to ANN.

Fadare D.A. [52] used the MATLAB neural toolbox to create a standard multi-layered feedforward with a backpropagation network (ANN model) to predict Nigeria’s solar energy radiation. For 195 Nigerian cities, national aeronautics and space administration (NASA) geo-satellite data were used to collect geographical and metrological information. The various architecture was designed, and the estimated value compared with the actual mean monthly global solar radiation intensities better correlation coefficient value for training, testing, and whole data were 0.978, 0.971, and 0.956, respectively.

Azadesh A. et al. [53] created an ANN model for estimating solar radiation in various Iranian cities. They omit two variables from the study because they have a positive, intense correlation with other input variables. These two variables are location and month. They considered only seven input variables and developed various MLPs for the different cities of Iran. The activation function for the first layer was linear, all hidden layers were sigmoid, and the last one was linear with backpropagation learning algorithms. A relevance approach is applied for pruning the input from the network. In pruning, a decision to eliminate an input variable decided by the number of epochs below a particular threshold value connection is cut for that input. The MLP model for city BandarAbbas with structure 7-6-2-1 has MAPE is 0.03.

3.2.3. Years (2010–2019)

Rahimikhoob A. [54] created a model to estimate GSR in a semi-arid environment using an artificial neural network and air temperature data. This paper explains how daily global solar radiation (DGSR) modeling is possible using ANN techniques and readily available data. The comparison results show that, in general, the ANN model outperformed the calibrated Hargreaves and Samani models.

Şenkal O. et al. [55] developed a generalized regression neural network (GRNN) model to estimate solar radiation. They used metrological satellite data and geographical data for two cities in Turkey. The performance evaluation can be summarized with the help of

Table 12. Summary of the performance evaluation.

S.N.	Station	R	RMSE%	COV	MAPE
01	Adana	99.75	0.0144	0.0075	0.0260
02	İzmir	99.26	0.1381	0.0131	0.1013

. The predicted value from the ANN was compared with the measured value of solar radiation at Adana and İzmir stations in Turkey.

Mehleri E.D. et al. [56,57] predicted global solar radiation on tilted surfaces making use of horizontal surface solar radiation, extraterrestrial radiation, solar zenith angle, and solar inclination angle on the tilted plane, and the RBF network in Athens [56,57]. The coefficient of determination (R²) was found to be 0.96, which shows a fair prediction with the help of the model.

An adaptive α model was created by A. Melit et al. [58] to forecast hourly global, diffuse, and direct solar radiation. The advantage of this model is that we can add or omit the input variable as per their availability, i.e., a model can give the liberty to select the input variable to predict the desired quantity. The author took two inputs at a time and obtained the best result with a correlation coefficient (R) value of 96.65%. Air temperature and sunshine duration acted as these two inputs. However, an adaptive α model is less accurate than the feedforward neural network model (FFNN). The performance was compared based on the value of the correlation coefficient.

Behrang M.A. et al. [59] developed an ANN model to predict the daily global solar radiation using five metrological variables and the day of the year as input and daily GSR as an output. The six-input variables are used in different input combinations, and MLP and RBF networks utilize them to predict the daily GSR. Using the MATLAB 2007 software’s neural network toolbox, they create MLP and RBF networks. They compare the result from both the model previously developed ANN and conventional GSR prediction (CGSRP) models. The proposed MLP-5 has a MAPE of about 5.21%, which shows better results when compared with the CGSRP-5 models and other ANN models; however, one of the MLP (ANN) models for Saudi Arabia has a MAPE of 4.49%. The paper shows the comparative study of the potential available in different ANN models.

The reliable operation of a grid-connected solar PV system depends on the accurate estimation of solar irradiance incidents on the solar plates for each hour of the day. Mellit and Pavan [60] apply the ANN techniques to forecast solar irradiance for 24 h at Trieste, Italy. The mean daily solar irradiance, mean daily air temperature, and the day of the month are the input variables in the created MLP architecture. The output layer gives the next day’s 24 h data. The authors developed an experimental setup for data recording/collection. They use a calibrated reference cell for measuring solar irradiance PT100 temperature sensor for measuring air temperature, and a data logger for recording these data with a time scale of 10 min. The model was trained and tested using the recorded data. The authors use four-day data for the performance comparison. The best value was obtained for MAE (%), MBE (%), and R (%) for the date 21 May 2009, and its magnitude was 2.75, 7.31, and 94.14, respectively. However, the lowest RMSE (%) value was on 20 May, and its magnitude was 32.98, which shows a minor deviation in measured and forecasted values.

Lazzús Juan A. et al. [61] developed a neural network model for estimating GSR for the city of La Serena (Chile) using metrological data. The data were obtained from the metrological station. The feedforward neural network mode has four input neurons and one output. These include air and soil temperatures, wind speed, relative humidity, and air temperature. The predicted value of GSR is compared with the measured value of the metrological station and the other models discussed by the authors in the paper. Good accuracy was obtained from the proposed model. The author also explains when and where we use ANN techniques for solar radiation prediction.

Rodrigurez et al. [62] developed an ANN model to estimate GSR using geographical and satellite data. The proposed method avoids the necessity of ground measurement. The developed model has a good forecast capability of GSR. The input variables for the MLP feedforward NN are latitude, longitude (geographical), day of the year, total cloud cover, surface temperature, total column water vapor, and total column ozone (ERA-Interim data set). In contrast, the output variables are only one daily global solar radiation. The data set of daily GSR on the horizontal surface was recorded by the Andalusian Regional Office of Agriculture and Fishing. The statical scores used in the study for the performance analysis of the ANN model are MBE, RMSE, relative root mean square error, and correlation coefficient. The proposed MLP feedforward NN has the value of RMSE and a correlation coefficient of 16.4% and 94%, respectively. The author also explains the seasonal variation in the statistical score. Koca et al. [63] invented an MLP network (5-8-1) to estimate global solar radiation for Anatolia’s Mediterranean region. The ground station data of solar radiation and metrological variables were taken from the Turkish State Metrological Service. The relative measures used for the performance evaluation are root mean squared error (RMSE), COV, and R². The different MLPs were developed using different input combinations, and relative measures were calculated for each. The authors show that the maximum value of R² shows the input variable selection for the estimator. The maximum and minimum values of RMSE were 6.9% and 3.58%. Lu et al. [64] used multi-functional transport satellite (MTSAT) data to estimate daily global solar radiation. The daily clearness index is an output variable of the model with daytime, mean air mass, and surface altitude as different input combinations. The proposed model compares with the model that incorporates surface altitude. The higher correlation value was obtained with the input variables in the proposed model. A model was created by Rahoma et al. [65] to forecast the time series of solar radiation over the Egyptian plain. According to the authors, the proposed Takagi–Sugeno (TS) model has an accuracy of approximately 96% and an RMSE of less than 6%. Khatib et al. [66] develop various models for estimating global and diffuse solar radiation on five main sites in Malaysia. They develop a linear model, nonlinear model, fuzzy logic model, and ANN model for the estimation of global solar radiation. The author‘s relative measure for the GSR estimation used by different cities is MAPE, RMSE, RMSE (%), MBE, and MBE (%). They use long-term data for the training of ANN. The data for 1975–2004 are used for training purposes, and the testing data for 2005 were considered. The average value for relative measures for various methods and sites can be summarized with the help of

Table 13. The average value for relative measures for various methods.

Model	MAPE	RMSE	RMSE (%)	MBE	MBE (%)
Linear	8.13	0.44	9.32	−0.014	−0.30
Non-Linear	6.93	0.41	8.73	−0.013	−0.31
Fuzzy logic	6.71	0.42	8.80	0.019	0.32
ANN	5.38	0.35	7.37	−0.019	−0.42

.

Among all the developed estimation models, the author’s ANN model performs well, which can be shown with the help of

Table 14. The model performance of various models.

Model	MAPE	RMSE	RMSE (%)	MBE	MBE (%)
Linear	4.35	0.146	5.22	0.003	0.094
Non-Linear	3.74	0.136	4.85	0.003	0.090
ANN	1.53	0.056	2.01	−0.0009	−0.062

.

For the 41 sites, Ouammi et al. [67] created an ANN model to estimate the yearly and monthly solar irradiation. Solar irradiation data used by the authors were taken from the photo voltaic graphical information system (PVGIS) database. The analysis was carried out with the help of data for the duration of 1998–2010, and the inputs of the network are in the normalized form. They use the satellite observation of reflected solar radiation to remove the uncertainty due to overlying clouds in estimating solar radiation data. The proposed method shows the lowest error of magnitude of 0.14% while the maximum error of magnitude of 4%.

Khatib et al. [68] developed a method to predict Malaysia’s global solar and diffuse radiation. The first step of the method is to generate the value of the sky clearness index (K_T) using a feedforward multilayer perceptron network (FFMLP) with backpropagation learning algorithms by using the input variables latitude, longitude, day number, and sunshine ratio. The 28-weather station recorded data were used for training (23) and testing (5). In the second part of the paper, the generated value of the sky clearness index (K_T) is used to predict global solar radiation and diffuse radiation by the various equations suggested by the authors. The suggested equations have a lower MAPE value than the other conventional equations. In this study, the magnitude of the relative measures of MAPE, MBE, and RMSE is 5.92%, 1.46%, and 7.96%, respectively.

Hasni et al. [69] developed an ANN model with the network training performed by using Levenberg–Marquardt (LM) feedforward backpropagation algorithms. The input variables for the ANN model are month, day, hour, temperature, relative humidity, and measured hourly GSR as an output. Data were used for the training from 2 February to 31 May 2011 (approximately 81%) for training and June 2011 (approximately 19%) data for testing. The value of the relative measures, i.e., RMSE, MAE, and R² for the performance evaluation, were 0.0840, 2.999, and 0.998, respectively, for the training phase, while for the testing phase; these values were 0.1720, 2.9971, and 0.9999 respectively.

Rumbayan et al. [70] developed a map of solar radiation potential for Indonesia. They theoretically use the ANN method to theoretically calculate GSR at a different site in Indonesia. After that, with the help of a GIS (geographic information system) tool, they map the whole country. In developing the model that has been taken from the NASA websites. The nine input variables were used to develop the model, while the output is only GSR. The authors consider obtained data of GSR from the NASA website as the measured variable while the value generated by the ANN model is a predicted value. They developed various models, among them the best one with the architecture 9-11-1 having the correlation coefficient (R) = 0.93 and MAPE = 3.29%. The values of MAPE for the test cities of Jakarta, Samarinda, Manado, Ambon, and Bengkulu are 4.9%, 1.2%, 2.7%, 4.5%, and 3.5%, respectively. The values of the metrological variable’s average temperature, average humidity, average sunshine duration, average wind speed, and average precipitation were taken from the NASA website. The other parameters are static for a particular site. The proposed method suggests estimating solar radiation for remote locations and locations where no ground station is available.

According to Rehman et al. [71], estimating DSR and DNR (direct normal radiation) can be achieved by inputting GSR, ambient temperature, the day of the year, and relative humidity into a radial basis function neural network. The most effective RBF network architecture for parameter prediction in Al-Hasa was found to have 40 hidden neurons and a spread of 0.1. The most effective RBF network for parameter prediction in Al-Jouf had 50 hidden neurons and a spread of 0.1.

Sumithira and Kumar [72] developed an adaptive neuro-fuzzy inference system (ANFIS) model that can forecast monthly global solar radiation over Tamil Nadu (India). Authors combine ANN and fuzzy systems to obtain more accurate methods for estimating monthly global solar radiation. The authors use the data from the automatic weather station at Tamilnadu Agricultural University (TNAU). In the proposed model, hybrid soft computing and Sugeno fuzzy inference systems have been used. The data set consists of 204 (17 × 12) and 168 (14 × 12) samples for training and testing, and these data sets cover all 31 (17 + 14) districts of Tamil Nadu. The MBE, RMSE, and R2 values for the developed model are −1.031, 0.0078, and 0.9898, respectively. Notton et al. [73] hourly horizontal global irradiation was used to calculate the hourly global irradiation on a tilted plane. They developed three ANN models that can estimate the amount of hourly global irradiation on a 45°, 60°, and β° plane. Declination, hour, zenith angle, hourly extraterrestrial horizontal irradiation, hourly horizontal global irradiation, and one additional inclination angle used for β inclination are the inputs for the ANN model.

The five-year data have been taken to train and test the developed ANN model. The accuracy of the optimal configuration is around 6% for the NRMSE or relative root mean square error (RRMSE) and around 3.5% for the relative mean absolute error (RMAE). Although NRMSE and RRMSE are the same here, two different notations are used so that readers do not confuse while they study the paper of Notton et al. [73]. The proposed method shows a better result than the earlier used empirical equations.

Yacef et al. [74] apply their analysis in Al-madinah (Saudi Arabia) using ground station data from 1998 to 2002. The Bayesian technique provides the opportunity to choose the ideal number of hidden units using the evidence framework.

Niching Genetic algorithm was suggested by Will et al. [75] as a solution to the issue of choosing variables for solar radiation estimation. The study’s overall purpose is to omit input variables from the analysis so that very few variables are sufficient for predicting solar radiation. Yıldız et al. [76] compare two ANN models used for solar radiation estimation. The first is based on input variables (i) latitude, (ii) longitude, (iii) altitude, (iv) month and metrological land surface temperature. The second was developed by using all variables of the first model to replace metrological land surface temperature with satellite land surface temperature. The correlation coefficient (R) for the first ANN model is 80.41%, while for the second one is 82.37%, respectively.

Bhardwaj et al. [77] estimate solar radiation by combing the two approaches for better results for estimated solar radiation quantity. This study aims to achieve a goal by combining the techniques when a single technique does not provide sufficient solutions. The purpose is to use the hidden Markov model (HMM) and the generalized fuzzy model (GFM). The role of continuous density HMM with the Pearson R model in the proposed work for shape-based clusters from the input metrological parameters while the role of GFM to accurately estimate solar radiation. This paper uses weather and solar radiation data from the comprehensive weather monitoring station in Gurgaon, India. The geographical coordinates (latitude/longitude) in degrees of Gurgaon, Haryana, India is 28.457523 N/77.026344 E. The location is situated in a hot semi-arid climate. The 15 sets of various input variables were applied to the model to estimate solar radiation so that the sole effect of each variable on the output could be identified. After training and testing the model with the considered data, it is observed that sunshine duration is the prime parameter in solar radiation estimation. The next order of the variables is temperature, relative humidity, atmospheric pressure, and wind speed, as per their importance. The best-performing model did not have wind speed, while the sunshine duration was incorporated. The best value of the relative measure, i.e., RMSE, MAPE, and R for the proposed model, were 7.9124, 3.0089, and 0.9921, respectively. Dahmani K et al. [78] developed a method that helped to address missing tilted solar radiation data by analyzing horizontal radiation inputs. When the ANN is sufficiently trained, this approach can obviate the need for an inclined pyrometer.

For time horizons ranging from 15 min to two hours, Pedro HTC and Coimbra CFM [79] developed an ANN and k-nearest neighbors (KNN) optimizer to predict global solar irradiance. The result was superior to other straightforward forecasting methods.

In order to forecast global irradiance, Gutierrez-Corea F-V et al. [80] developed various architectures and parameters of ANN based on MLPNN (multilayer perceptron neural network) with BP algorithms. Data from nearby weather stations were utilized as input for the forecast, covering the period between 1 and 6 h.

For forecasting solar power, Sivaneasan B et al. [81] created an ANN model that was connected to triple-layer BP and a fuzzy pre-processing method. It performed better than solo ANN, ANN-fuzzy combined, and ANN fuzzy with an error correction factor. An LSTM model for day-ahead solar irradiance prediction from weather data were created by Qing X and Niyu Y [82]. It performs better than multilayer FFNN-BPNN (back propagation neural network algorithm) models, linear least square regression (LLSR), Levenberg–Marquardt (LM), and persistence models.

3.2.4. Years (2020–till Now)

Alskaif Tarek et al. [83] study suggests how many metrological variables are required for accurate PV output power estimation using ML techniques with ground station data. This study was performed to show the effect of various input variables on PV output power in different climatic conditions. The first case uses metrological and PV output power data for the exact locations. In the second case, weather station data and PV data from the 10 households near the weather station. The geographical coordinates (latitude/longitude) in degrees of the location Austin are 30.267 N/−97.715942 W with a humid subtropical climate region. The city Utrecht has the coordinates (latitude/longitude) in degree 52.1551 N/5.387200 E with oceanic climate conditions. Each city has its different climate conditions.

The techniques for selecting data are suggested by Xiao Mingzhong et al. [84] in their publication. For the investigation, metrological data from 97 stations between 1993 and 2016 were combined with the observed daily solar radiation. According to the findings, direct solar radiation showed a more pronounced concave-shaped association with relative sunshine duration than global solar radiation. For diffuse solar energy, however, an inverted U-shaped connection was discovered.

According to a study by Mohammadi Babak and Aghashariatmadari Zahra [85], the hybrid SVR (support vector regression)-KHA (krill-herd algorithm) model is more flexible and has minimal inaccuracy while simulating the nonlinear and complicated system. It is successfully applied to the estimation of solar radiation.

Kumar Deepak [86] explains the method of obtaining solar radiation data with the help of satellite data. These satellite data were obtained from the NREL website as open-source archive data. Kumar Deepak suggests the good spatial and temporal distribution of solar irradiance over the grid of 10 Km × 10 Km for the many states of south India.

In this section, various soft computing methods were used by different authors compared with other methods. It is found after the study of this section that soft computing methods perform well than the other methods.

4. Anthropogenic Substances and Solar Radiation

An effect or thing that results from human activity is called anthropogenic. This section discusses the objects that reduce the quantity of solar radiation that incident on the earth’s surface. Anthropogenic substances have a lot of harmful effects on human health. According to the World Health Organization (WHO), only the ambient particulate matter was responsible for approximately 30 lakhs of premature death. The readily measured value of this anthropogenic substance for some other purpose is considered here for evaluating the harmful effect on solar energy applications and its role in estimating solar energy. In highly densely populated area, especially in India and China, these anthropogenic substances severely affect solar energy-based applications. So, the effect of this anthropogenic substance is discussed here for maximum utilization in terms of efficiency and minimum loss of revenue and reliability of solar-energy-based appliances/applications.

The Nobre Andre M. et al. [87] study suggests the methods of acquiring data for clear sky conditions using filters so that the effect of particulate matter using standard pollutant Index (PSI) is estimated how attenuation in Irradiance affects PV power generation using a different type of PV system.

The proposed relationship between observed global solar radiation quantities, sunshine hours, and the air pollution index (API) for Indian cities was made by Suthar M. et al. [27]. They establish several other regression models (e.g., linear, quadratic, exp-linear, and exponential quadratic) to find the general regression equation for most of the cities of India.

Peters I. M. et al. [88] explain the quantitative relationship between particulate matter PM_2.5 and solar irradiance incidents on the Earth’s surface. PM_2.5 is the major factor responsible for the haze. The objective of this study is to show the effect of haze in Urban areas as well as on human life. They use ground station data for both air pollution and solar insolation. They proved that insolation received by Si PV panels dropped by 200 kWh m⁻². They show that only Delhi had approximately 200 lakhs USD in revenue loss in a year. It shows the very severe effect of air pollution on solar radiation. The geographical coordinates (latitude/longitude) in degrees of the location Delhi, capital of India, is 28.644800 N/77.216721 E. The climate of Delhi is an overlap between monsoon-influenced humid subtropical and semi-arid, with high variation between summer and winter temperatures and precipitation.

Fan Junilang et al. [89] suggest the support vector machine (SVM) technique for the regression of global and diffuse solar radiation prediction with air pollution parameters as an independent variable. This study aims to demonstrate the effect of heavy urban air pollution on global and diffuse solar radiation. The data used in this study are ground station data. The Beijing–Tianjin–Hebei (BTH) region has a semi-arid climate zone.

Yao WX et al. [90] suggest estimating GSR with the help of SVM with an extra input AQI (air quality index). In this paper, the various model with or without AQI has been taken. The best model is SVM with AQI.

Authors Peters I. M. et al. [88] show how solar radiation is affected by air pollution. Peters I. M. et al. [91] show the gain in solar radiation due to a drastic reduction in air pollution. This drastic reduction in air pollution occurs during the lockdown period due to the COVID-19 pandemic in Delhi (the capital of India). They selected Delhi because Delhi is the most air-polluted city in India and the world. The great change in input variables demonstrates a significant change in solar radiation.

Son Junghoon et al. [92] suggest the effect of particulate matter (PM) and other metrological factors affecting solar PV power generation. They develop many models based on multiple regression techniques to predict power generation by solar PV systems. They compare the predicted value with the actual solar PV power generated by two solar PV power plants located in Korea. In this study, data from two power plants are used Y-PV (Yeongam Solar Power Plant) and E-PV (Eunpyeong Public Garage in Seoul). Their study shows the numerical reduction in solar PV systems due to suspended aerosols.

5. Critical Findings

The models are studied in detail but briefly discussed in Section 2, Section 3 and Section 4. Based on the study of discussed models, we observed many critical findings discussed next part of this section.

The empirical model is a simple and convenient way to develop a solar radiation estimation model. In empirical models, concise mathematical equations are used to find the value of dependent variables with the help of measured independent variables. Among the empirical models, the model developed with the help of sunshine duration is the most widely used.

An Assumption of Linear Regression Analysis

(i) The two variables should be in a linear relationship.

(ii) All the variables should be multivariate normal.

(iii) There should be no multicollinearity in the data.

(iv) There should be no autocorrelation in the data.

(v) There should be homoscedasticity among the data.

In linear regression analysis, two strategies are used. (a) Selection of variable’ (b) selection of order.

For a selection of variables, we use the following statistical indicators/methods.

(i) Adjusted $R^2;$ (ii) predicted $R^2$.

(iii) p-values for the predictors (iv) stepwise regression and the best sub-set regression.

(v) Check the accuracy and Uncertainty in the developed models.

Select the model with the best value discussed above for the regression model.

For the selection of order

i

Selection of order of equation based on residual plot, the shape of the residual plot decides the order of the equation.

ii

What is the suitable length of experimental data for empirical modeling?

iii

We transform the variable into a different form to avoid a higher-order regression equation.

In the literature review, Gouda Shaban G. et al. [93] found the most widely used variables in China’s empirical modeling. These are divided into three categories.

(i) Experimentally measured variables. (ii) Fixed variables. (iii) Combination of meteorological variables.

In (i), experimentally measured variables are meteorological variables. These are

(a) sunshine duration, (b) air temperature, (c) precipitation, (d) dew point/relative humidity, (e) fog, and (f) cloud cover.

In (ii) day of the year.

In (iii) combination of meteorological parameters.

The critical findings that are used to improvement of the performance of the empirical model are as follows:

i

Try to keep the polynomial equation’s order as low as possible.

ii

Apply transformation on row data to improve accuracy instead of jumping on the higher-order regression equation.

iii

If the first two conditions are not met, fit the models in increasing order, evaluating the statistical indicator at each stage. Discard the higher order if the magnitude of the statistical indicator does not change by a considerable amount between two consecutive orders.

Safi et al. [14] apply steps 1, 2, and 3 to find the order of the model. The graphical demonstration of the variable and its autocorrelation function shows the nature of the variable. If it is found to be non-stationary, then they convert them into linear variables. After converting it into a linear variable, we develop a linear model to predict future values. The daily clearness index and lost solar component were utilized by Safi et al. [14] to forecast daily global solar radiation. Safi et al. [14] use a backward differential operator to convert the selected variables into linear ones.

Improvement in accuracy and removal of measurement noise can occur if we shift the empirical techniques to soft computing techniques. The inclusion of soft computing techniques introduces decision-making capacity. So that without human interference, the identification of measurement noise is possible. The soft computing methods overcome the difficulties that occur in the empirical approach. These difficulties are measurement noise and proper regression equation if it is not of the first order.

Section 3.1 shows how ANN can handle the nonlinearity among the attributes and target variables. At the same time, the ANN suggests variable selection and data sorting so that the model’s complexity diminishes to certain levels.

Empirical methods are used to develop a concise mathematical relationship. The concise mathematical relation development depends on including the variables and their order. Safi et al. [14] show the method to identify the order of inclusive terms. Once we know the graphical relationship between the target and attribute variables, applying the transformation to the attribute is convenient so that the linear predictor equation develops. Safi et al. [14] used ACF to find the nature of the equation and suggest the method of conversion of the variables so that the developed equation has a simple form and gives more accurate prediction values.

Iqdour R. & Zeroual A. [38] developed the fuzzy system (Takagi-Sugeno) that performs better than the HOS model developed by Safi et al. [14]. Both paper authors use the same data sets. This result shows the superiority of the soft computing approach over the empirical approach.

In the Semi-arid region, the ANN model based on air temperature [54] performed well compared to the Hargreaves and Samani equation [94]. In India, 91 national parks and wildlife sanctuaries are located in semi-arid regions, which make up 37% of the nation’s total land area (970,530 km²). These 91 parks and wildlife sanctuaries total 15,302 km² or 2.8 percent of the nation’s biogeographical region. The acoustic pollution and combustion of fossil fuels are avoided entirely in national parks and wildlife sanctuaries. Green energy power generation systems with complete autonomy, such as solar photovoltaic systems, are good alternatives in these areas. So, as discussed in the previous point, solar radiation estimation by more readily available data is a good alternative in this area (No. 5).

To estimate solar radiation, a simplified and convenient model is preferred. The condition of underfitting and overfitting occurs in the model developed with the help of the soft computing approach. It can be overcome by adequately selecting inclusive variables and suitable data length. This study discusses various estimation techniques based on soft-computing techniques. The two desirable features in the models are optimum selections of variables and suitable data length of selected variables. The suitable data length for avoiding overfitting and underfitting is as follows:

• In data-driven models, data pre-processing is one of the ways to overcome the model complexity. Suitable data, after processing, apply as input to the prediction model. In data pre-processing, it is considered that selected data have almost all the information, i.e., repeated information covered a single time.
• In this study, we use ANN is explained by Lazzús Juan A. et al. [58]. They demonstrate that when the value of the correlation coefficient is less than 0.5 among the dependent and independent variables. In that case, the relationship that exists among the model variables is nonlinear. The nonlinear modeling methods, such as ANN, apply here to develop the regression equations.

Khatib et al. [66] develop various models for estimating global and diffuse solar radiation on five main sites in Malaysia. They establish a linear model, a nonlinear model, a fuzzy logic model, and an ANN model to estimate global solar radiation. The model performance comparison is shown in Table 12 and Table 13. In Table 12 and Table 13, the fuzzy logic and ANN model perform best, respectively. This shows better model development again with the help of the soft-computing approach.

The GSR prediction model developed for remote locations was suggested by Rumbayan et al. [70]. Remote locations are where it is challenging to establish a measurement station—a reasonable accuracy obtained by them in predicted values. The satellite data were collected from different sources. Which source is more reliable and provides highly accurate data is known in advance? It is possible by developing a correlation model between ground station data and satellite data.

The selection of relative measures (statistical indicators) is known to judge the model performance. The relative measure is based on the pattern of attributes and target variables.

The combination of two or more soft computing approaches provides better results. It could be understood with the example of SVR-KHA algorithms [85] discussed in the literature. So, more bio-inspired techniques/metaheuristics apply to develop better models and variable selections for the model.

The terrestrial loss occurs in solar radiation due to the presence of aerosols. So, including the air quality index and its variables in model development provide better results, as discussed in the literature. The density of aerosols depends on the location and time. Avoiding it degrades the system’s performance.

Suppose we want to develop a solar radiation model for a large area or map the solar radiation for the country. In that case, dividing the whole area into different climate zones is beneficial. The benefit of this scheme is explained by the authors [54].

6. Conclusions

In this paper, different solar radiation estimation techniques have been reviewed. One of the findings is that ‘sunshine duration’ is an essential variable of solar radiation estimation in empirical models. The review of various papers suggests that more accurate estimators are found to be nonlinear, and it was observed that empirical approaches could not handle this nonlinear relationship. Different authors handled this nonlinearity by using various soft-computing techniques. However, it was found that if the number of input variables increases, the estimators become more complex. In literature, two different approaches were utilized to handle this complexity. In the first approach, soft-computing techniques or any feature selection approaches were utilized to pick more relevant input variables, and then estimators were created for selected locations using these selected variables and soft-computing techniques. The second approach utilizes a hybrid soft-computing approach to pick input variables and estimates solar radiation, such as the Markov transition matrices (MTM) approach for variable selection, followed by solar radiation estimation using a generalized fuzzy model.

Furthermore, the review of various papers reveals that it is challenging to establish the solar measurement setup in hilly areas of high altitudes or complex terrain in Indian locations. Many researchers use satellite data to design solar radiation estimators for these world locations. Further, solar radiation estimators at the hilly area of high altitudes or complex terrain of Indian locations may be covered in future research as the solar potential of these locations has not been utilized yet.