The radiation emitted by our Sun has a direct impact on all life, every climate, and all activities on Earth (Samuel Chukwujindu, 2017; Wang et al., 2024). Therefore, most processes in the atmosphere and on the surface of the Earth are directly or indirectly influenced by solar radiation (Zekai, 2008). To evaluate meteorological, hydrological, and ecological processes, photosynthesis, agricultural and industrial production, and the growth and use of energy, it is necessary to measure global solar radiation (Asaf et al., 2013; Paulescu et al., 2016; Wang et al., 2016). Solar power is gradually assuming a more significant place among global energy sources, driven by technological advances in the use of solar energy for more economical power generation. For instance, it is estimated that solar and wind power will contribute approximately 48% of power generate globally by 2040 (Babatunde et al., 2023; Tsanova, 2019). According to available statistics, the capacity of solar power plants grew by approximately 100% between 2009 and 2015 (Malinowski et al., 2017).

In order to measure solar irradiance at the surface of the Earth, networks of pyranometers have been installed across the world, but the density of the installations in parts of these networks, especially within developing countries, is still comparatively low (Department of Alternative Energy Development and Efficiency, 2009). Although pyranometers are relatively uncomplicated, their efficiency is highly dependent on the density of the network.

Estimating solar irradiation based on meteorological characteristics such as cloud cover and temperature is therefore a useful approach to counteract an inadequate network density (Yakoubi et al., 2021). In fact, cloud cover is considered to be the most accurate indicator of solar irradiance (Polo, 2015; Polo et al., 2011; Wacker et al., 2015). The significance of solar irradiance has inspired numerous studies throughout the world (Agrawal et al., 2025; Attya et al., 2025; Bai et al., 2025; Bounoua et al., 2024; Obiwulu et al., 2022).

Model development for assessing solar irradiation can be classified into four main types: statistical, empirical, semi-empirical, and physical models. Each type has different principles and restrictions. Statistical models employ statistical techniques to analyze data relationships, such as linear regression and multiple linear regression, which are suitable for temporal data with distinct trends. Empirical models are based on actual observations, such as the Angstrom model, which uses cloud fraction as the main variable. Although simple, it has limitations in accuracy in variable weather conditions. Semi-empirical models combine physics principles with empirical data to increase the accuracy of the estimation without relying on complete data as physics models. Physical models use physics concepts to simulate the movement and scattering of atmospheric solar radiation, such as models that use sky photography to estimate radiation. These models are highly accurate but require a lot of data and computational resources (Bamisile et al., 2022; Garniwa et al., 2021). However, in the case of Thailand, surface solar irradiation has been developed and mapped using a variety of techniques, For instance, Janjai et al., 2013 used a physical model to calculate solar radiation using a satellite approach, and Chanalert et al., 2022 employed a semi-empirical model involving atmospheric variables to map the global solar radiation.

Statistical model-based estimation is a widely used technique to assess and evaluate the solar energy at an area of interest before decisions are made to invest in solar-powered equipment or devices (Da Silva et al., 2017). As a consequence, an assortment of statistical models have been constructed to predict solar irradiation using meteorological parameters, such as cloud cover, temperature (Hassan et al., 2016), and relative humidity (Li et al., 2015). Many investigations have demonstrated that the best performing models are sunshine-based, followed by cloud-based and temperature-based models (Li et al., 2013). Therefore, in this work, we propose a statistical model for calculating solar irradiation across southern Thailand that integrates ground-based data and satellite data.

Figure 4 shows comparisons of solar irradiation calculated from surface data acquired from pyranometers, and solar radiation data from the GLDAS (Global Land Data Assimilation System model) model (shortwave radiation, NOAH025 3H v2.1), at a spatial resolution of 0.25^ox0.25^o (b). Furthermore, Table 2 displays the performance scores in terms of RMSD (%) and MBD (%) from five stations in southern Thailand. The RMSD between the ground-based solar irradiation data and the data from the GLDAS model was 20.93% (Figure 5).

Table 3 shows a comparison of solar irradiation between the measured data (581 for all stations) and the model data of Okundamiya et al., 2016, Black, J.N., 1956, Bădescu, 2008; Yakoubi et al., 2021. The RMSD values range from 9.33% to 41.46%.

Table 4 shows coefficients, t-stat values, p-value and R ² values. The t-stat values show the goodness of fit of the data for the same number of samples, and indicate, whether there is a strong or weak correlation (Malinowski et al., 2017). The coefficient of determination (R ²) measures how much the independent variable can explain the variance in the dependent variable (Adhikari, 2022). Values were obtained by using the STATISTICA v10 program, according to the methods of Charuchittipan et al. (2018) and Choosri et al. (2017). Table 4 shows that the R ² values were relatively high, that t-statistic values associated with a , b , c and d had an absolute value greater than 2, and that the obtained p-values were low.

Table 5 shows the model estimations for 2014–2023 in the form of RMSD (%) and MBD (%) at Songkhla meteorological center (SK), Prachuap Khiri Khan meteorological station (PG), Ranong meteorological station (RN), Phuket southern meteorological center (PK), and Trang meteorological station (TR). Overall, there was good consistency between the calculations, except for the Ranong station, where the solar irradiation estimated by the model was higher than the measured data. The results indicate that the statistical model can be used to estimate solar irradiation at every site in the Southern region of Thailand. Table 6 displays the results of the model performance test.

To test the performance of the solar irradiation model, the study used data from five sun monitoring stations. The results obtained from the model ( H — mod ⁡ e l ) and the pyranometer measurements ( H — m e a s u r e ) are compared in Figure 6. The test results were in good agreement, with an RMSD value of 6.84% and an MBD value of 1.07%. Chanalert et al. (2022) estimated solar irradiation using a semi-empirical model that included atmospheric parameters and found that the model estimation and measured data had an RMSD = 6.9% and an MBD = 1.0%. Earlier, Polo et al. (2011) estimated the solar radiation over India using satellite data. It was found that the solar irradiation calculated using the physical model from the satellite data and the ground measurements were reasonably consistent with each other. The RMSD value was approximately 12% and the MBD value was approximately 5%. Later, Polo (2015) used a satellite method to evaluate the solar irradiation across Spain. The global irradiation using a semi-empirical model obtained from the satellite data and the ground measurements had an RMSD of 11%. Therefore, the accuracy of the model proposed here is similar to the accuracy reported in the works mentioned above.

The average monthly temperature data for 2014–2023, acquired from the long-term FLDAS model at a spatial resolution of 0.10 latitude x 0.10 longitude, was collected and employed in an interpolation method to cover the entire area of southern Thailand. Figure 7 shows a map of the yearly average temperature.

The monthly average daily cloud fraction map in Figure 8 was compiled from data for 2014–2023 collected from 29 meteorological stations throughout the South region of Thailand. The ground-based data was combined with data from OMI/Aura satellites in order to obtain more cloud fraction data using polynomial equations.

The compilation of the monthly average daily solar irradiation map required the collection of variables covering the whole of southern Thailand. The cloud fraction was measured at 29 meteorological stations and calculated from Aura satellite data using the same estimation method. Average temperature data were obtained from the FLDAS model, using the same estimation method. Finally, various equations were used to calculate the solar irradiation across southern Thailand. The parameters of H — 0 , C — , and T — m were used to provide an overview of the long-term solar potential of the southern region, as shown in Figures 9–13.

The monthly solar irradiation map in Figure 9 shows that solar irradiation in the south of Thailand increases continuously during January and is highest in March–April before declining until the end of the year. However, the annual solar irradiation maps (Figures 10–13) indicate relatively low levels of solar irradiation in the mountain ranges. Moreover, due to the very dense rainclouds that form during the southwest monsoon (May–September) and the northeast monsoon (October–January), the region receives low levels of irradiation at these times (Charuchittipan et al., 2018). The yearly solar irradiation in southern Thailand ranged from 14 to 21 MJ/m² per year-day which is comparable to Agbo et al., 2023; Chanalert et al., 2022; Suwanwimolkul et al., 2024.

As seen in Figure 11, seasonal average solar irradiation maps over a 10-year period (2014–2023) are summer (February–March–April) and rainy (January–May–June–July–August–September–October–November–December). It can be seen that seasonal solar irradiation was higher and reached its maximum in the summer but was lower and reached its minimum in winter.

In addition, in this work, interpolation techniques were used to fill in the gaps between stations using ArcGIS 10.8 with Inverse Distance Weighting (IDW), Spline, Trend, Kernel Interpolation with Barriers (KIB), Diffusion Interpolation with Barriers (DIB), Local Polynomial Interpolation (LPI), and Radial Basis Functions (RBF), as shown in Figure 13.

In this article, a mathematical model was designed to calculate solar irradiation in southern Thailand. The solar irradiation values calculated using the model were compared with the solar irradiation values obtained from five ground observation stations during 2014–2023. The results demonstrated that the values were similar. The difference between the computed and measured values in Root Mean Square Deviation was between 6.84% and 15.67%. Therefore, the developed statistical model can calculate the monthly average daily solar irradiation accurately and is convenient to use, and it has found that the most appropriate models were non-linear models (models 12–15). The results showed that the distribution of solar irradiation in southern Thailand is mainly influenced by the mountainous areas of the region, the southwest monsoon, and the northeast monsoon. Most areas of southern Thailand receive a daily average solar irradiation of approximately 14–21 MJ/m²/year-day. This result demonstrates that the region has a relatively high solar potential, which can be applied in future solar applications.