Statistical models for mapping solar irradiation across southern Thailand using meteorological and satellite data

A statistical model is developed to calculate the monthly average daily solar irradiation on the ground by considering cloud fraction and temperature. Cloud fraction data were gathered from 29 meteorological stations throughout southern Thailand and from the Aura satellite. Average temperature values were collected from the FLDAS model, through the utilization of interpolation techniques. In addition, solar irradiation data from ground-based pyranometers was collected for 2014 to 2023 from the Songkhla meteorological center to serve as the basis for the modeling (R² = 0.70–0.84). The data from the developed model and the measured data were in good agreement, with a Root Mean Square Deviation (RMSD) score of 6.84%–9.37% (Mean Absolute Percent Error, RMSE-observations of the Standard Deviation Ratio, Nash-Sutcliffe Efficiency, and Peak Irradiance to Noise scores were also very good). Solar irradiation estimated from data acquired by the GLDAS model was in reasonable agreement with the model estimate, with RMSD score of 20.93%. The model was utilized to generate solar irradiation maps for southern Thailand, using kriging, IDW, Spline, Trend, KIB, DIW, LPI, and RBF estimation techniques. The map, which was similar to maps derived from a more complex model, showed that solar irradiation in the region is mainly influenced by mountains, and the southeast and northwest monsoons, which cause dense cloud cover.

1 Introduction

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.

2 Measuring devices and acquisition of information

2.1 Ground-based data

2.1.1 Global solar irradiation data

A statistical model is proposed that aggregates solar irradiation data from observations taken from 08:30 to 16:30 (Pyranometer, CM11 from Kipp&Zonen) at the solar measurement station at the Songkhla southern meteorological center (7.20°N, 100.60°E) in Thailand. Statistical data acquired from 2014 to 2023 were used to establish the model. In addition, solar irradiation data over the same 10-year period was collected from four stations of the Department of Alternative Energy Development and Efficiency (DEDE) of Thailand. The stations are located in Trang Province (7.51°N, 99.62°E), Phuket Province (8.13°N, 98.30°E), Ranong Province (9.95°N, 98.63°E) and Prachuap Khiri Khan Province (11.83°N, 99.81°E). The data from the four additional stations were used to verify the accuracy of the model. Figure 1 shows the locations of the five meteorological stations. It can be seen that there are seas to the east and west of all the stations, namely, the Gulf of Thailand to the east and the Andaman Sea to the west.

Figure 1

Figure 1. The maps show the locations of the solar radiation measuring stations ( ) and the positions of the meteorological stations ( ): I) Thailand, and II) the Southern region of Thailand.

2.1.2 Cloud fraction

Cloud fraction or $\stackrel{—}{C}/{\mathrm{C}}_0$ represents the proportion of the sky covered by clouds to the total sky area in a particular time frame, extends from 0 (entirely clear sky) to 1 (completely overcast sky) (Jia et al., 2024; Svennevik et al., 2024).

2.1.3 Extraterrestrial solar radiation (${\stackrel{—}{H}}_0$)

The daily extraterrestrial solar radiation is calculated using Equations 1, 2 is the calculation for the monthly average daily extraterrestrial solar radiation based on the celestial sphere principle proposed by Iqbal, 1983. The equation utilizes the following variables: ${\mathrm{E}}_0$ is a factor that compensates for the variation in the Earth–Sun distance [-], ${\mathrm{I}}_{\mathrm{s}\mathrm{c}}$ is the constant of daily solar radiation, ${\mathrm{\omega }}_{\mathrm{s}}$ is the sunset hour angle (in degrees), $\mathrm{\delta }$ is the angle of solar declination (which varies between −23.50^o to 23.50^o), $\mathrm{\varphi }$ is the angle of latitude (in degrees) and $\gamma$ is the day angle (in radians). Figure 2 shows a yearly extra-atmospheric solar radiation map that was created using the ArcGIS 10.8 software (Geographic Information System) and employs a color scale similar to those in the article by Roca-Fernández et al., 2025.

${\mathrm{H}}_0=\frac{24}{\mathrm{\pi }}{\mathrm{I}}_{\mathrm{s}\mathrm{c}}{\mathrm{E}}_0\left[\frac{\mathrm{\pi }}{180}{\mathrm{\omega }}_{\mathrm{s}}\left(\sin \mathrm{\delta }\sin \mathrm{\varphi }\right)+\left(\cos \mathrm{\delta }\cos \mathrm{\varphi }\sin {\mathrm{\omega }}_{\mathrm{s}}\right)\right](1)$

Equation 2 calculates the monthly average daily extraterrestrial solar irradiation obtained from Equation 1. The author uses the variables in Equations 3–6 to calculate extraterrestrial solar irradiation (in Equation 1).

${\stackrel{—}{\mathrm{H}}}_0=\frac{1}{\mathrm{N}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}}{\mathrm{H}}_{0,\mathrm{i}}(2)$

Equation 3 from Spencer (1971).

${\mathrm{E}}_0=1.000110+0.034221\cos \gamma +0.001280\sin \gamma +0.000719\cos 2\gamma +0.000077\sin 2\gamma (3)$

Equation 4 δ from Cooper (1969).

$\begin{array}{l}\mathrm{\delta }=0.006918+0.399912\cos \gamma +0.070257\sin \gamma -0.00675\cos 2\gamma +0.000907\sin 2\gamma \\ -0.002697\mathrm{c}\text{os}3\gamma +0.00148\sin 3\gamma \end{array}(4)$

Equations 5, 6 from Iqbal (1983).

${\mathrm{\omega }}_{\mathrm{s}}={\cos }^{-1}\left[-\tan \mathrm{\varphi }\tan \mathrm{\delta }\right](5)$

$\gamma =\frac{2\mathrm{\pi }\left({\mathrm{d}}_{\mathrm{n}}-1\right)}{365}(6)$

Figure 2

Figure 2. Annual extraterrestrial solar irradiation map for southern Thailand.

2.2 Satellite data

The satellite data utilized was the daily cloud fraction data from the OMI/Aura satellite (OMT03e v3), covering the period from 1 January 2014 to 31 December 2023 at a spatial resolution of 0.25 latitude x 0.25 longitude (Gadde et al., 2009; Liang et al., 2018). The average temperature data were implemented from the FLDAS (Famine Early Warning Systems Network Land Data Assimilation System) model (NOAH01 C GL v1), covering 2014–2023 at a resolution of 0.10 × 0.10. Figure 3 displays a comparison of cloud fractions derived from ground-based and satellite data. Traditionally, analyses rely solely on ground-based data. However, the availability of such data is limited. Consequently, satellite-derived data are incorporated using a polynomial equation.

Figure 3

Figure 3. Correlation between monthly average daily cloud fractions derived from ground-based data and satellite data.

2.3 Statistical analysis

The performance and precision of the model were assessed (Table 1) using the following statistical parameters (Equations 7–14): Root Mean Square Deviation (RMSD) (%), Mean Bias Deviation (MBD) (%), Root Mean Square Error (RMSE) (MJ/m²), Mean Bias Error (MBE) (MJ/m²), Mean Absolute Percent Error (MAPE) (-), RMSE-observations of the Standard Deviation Ratio (RSR) (-), Nash-Sutcliffe Efficiency (NSE) (-), and Peak Irradiance to Noise (PIN) (-), calculated as follows.

Table 1

Table 1. Performance evaluation criteria for the statistical parameters of the prediction model.

RMSD (Wattan and Janjai, 2016):

$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{D}=\frac{\sqrt{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}\right)}^2}{\mathrm{N}}}}{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}}{\mathrm{N}}}\mathrm{x}100(7)$

MBD (Wattan and Janjai, 2016):

$\mathrm{M}\mathrm{B}\mathrm{D}=\frac{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}\right)}{\mathrm{N}}}{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}}{\mathrm{N}}}\mathrm{x}100(8)$

RMSE (Willmott and Matsuura, 2005):

$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\frac{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}\right)}^2}}{\mathrm{N}}(9)$

MBE (Willmott and Matsuura, 2005):

$\mathrm{M}\mathrm{B}\mathrm{E}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}\right)}{\mathrm{N}}(10)$

MAPE (Hyndman and Koehler, 2006):

$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|\frac{{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}}{{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}}\right|}{\mathrm{N}}\mathrm{x}100(11)$

RSR (D. N. Moriasi et al., 2007):

$\mathrm{R}\mathrm{S}\mathrm{R}=\frac{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}{{\mathrm{S}\mathrm{T}\mathrm{D}\mathrm{E}\mathrm{V}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}}=\frac{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}\right)}^2}}{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}}{\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{mean},\mathrm{i}}\right)}^2}(12)$

NSE (D. N. Moriasi et al., 2007):

$\mathrm{N}\mathrm{S}\mathrm{E}=1-\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l},\mathrm{i}}\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}-{\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n},\mathrm{i}}\right)}^2}(13)$

PIN (Temporal-Neto et al., 2025):

$\mathrm{P}\mathrm{I}\mathrm{N}=20{\log }_{10}\frac{1360}{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}(14)$

2.4 The model

The statistical model to calculate solar irradiation was developed by using the following equations with the collected 10-year data from the Songkhla southern meteorological center and the solar irradiance model associated with average cloud cover and average temperature.

Okundamiya et al., 2016.

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.7506-0.6455\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}(15)$

Black, J.N., 1956.

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.803-0.340\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}-0.458{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^2(16)$

Bădescu, 2008.

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.2382+2.0385\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}-3.60377{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^2+1.5722{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^3(17)$

Yakoubi et al., 2021.

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.654-0.268\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}+0.004{\stackrel{—}{\mathrm{T}}}_{\mathrm{m}}(18)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.625\left[1-\exp \left(-15.158\frac{{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{-2.103}}{{\mathrm{T}}_{\mathrm{m}}}\right)\right](19)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.611\left[1-\exp \left(-823.506{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{1.559}\right)\right](20)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.643+0.226{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{0.5}-0.832{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{1.5}+0.423{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{2.5}(21)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=\left(0.779-0.396\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right){\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{0.039}(22)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.552{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{-0.164}(23)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=15.451{\left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)}^{-0.007}-14.941(24)$

$\frac{\stackrel{—}{\mathrm{H}}}{{\stackrel{—}{\mathrm{H}}}_0}=0.033\log \left(\frac{\stackrel{—}{\mathrm{C}}}{{\mathrm{C}}_0}\right)+0.542(25)$

In the above equations, $\stackrel{—}{\mathrm{H}}$ = monthly average daily solar irradiance [MJ/m²].

${\stackrel{—}{\mathrm{H}}}_0$ = monthly average daily extraterrestrial solar radiation [MJ/m²].

$\stackrel{—}{\mathrm{C}}$ = monthly average daily cloud cover (there are values from 0 to 10).

${\mathrm{C}}_0$ = maximum cloud cover (equal to 10).

${\stackrel{—}{\mathrm{T}}}_{\mathrm{m}}$ = monthly average daily temperature [°Celsius].

2.5 The interpolation methods

There are two fundamental types of interpolation techniques (Fung et al., 2022; Tayyab et al., 2023).

2.5.1 Stochastic methods

Kriging is employed to assess missing points based on spatial autocorrelation between available data points.

2.5.2 Deterministic methods

Inverse Distance Weighting (IDW): Uses a weight inversely proportional to distance. Points that are closer have a greater influence.

Spline: Produces a smooth curve through data points. Applies different degrees of polynomials.

Trend: Predicts unknown points by employing a global polynomial.

Kernel Interpolation with Barrier (KIB): Applies kernel smoothing with consideration of physical barriers in the landscape. This method provides better accuracy in environments where such barriers influence the spatial continuity.

Diffusion Interpolation with Barrier (DIB): Utilizes the use of a diffusion equation that takes into account local barriers.

Local polynomial interpolation (LPI): polynomials for specific groups of neighboring points.

Radial Basis Function (RBF): Implement a function that depends on the distance from the focal point. Appropriate for unevenly distributed data.

3 Result and discussion

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).

Figure 4

Figure 4. The plots compare solar irradiation calculated from pyranometer data and GLDAS model data.

Table 2

Table 2. The performance comparison in terms of RMSD (%) and MBD (%).

Figure 5

Figure 5. Comparison between solar irradiation data from pyranometers (${\stackrel{—}{H}}_{measure}$) and solar radiation data (${\stackrel{—}{H}}_{satellite}$) from GLDAS model.

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 3

Table 3. Comparison of the performance of solar irradiation and that of other models.

Table 4 shows coefficients, t-stat values, p-value and R² 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 (R²) 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 R² values were relatively high, that t-statistic values associated with $\mathrm{a}$, $\mathrm{b}$, $\mathrm{c}$ and $\mathrm{d}$ had an absolute value greater than 2, and that the obtained p-values were low.

Table 4

Table 4. The coefficients of the adjusted model and the statistical variables.

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.

Table 5

Table 5. RMSD (%) and MBD (%) of the estimations of each model of solar irradiation at five sun monitoring stations in southern Thailand.

Table 6

Table 6. Test performances of the proposed solar irradiation model.

To test the performance of the solar irradiation model, the study used data from five sun monitoring stations. The results obtained from the model (${\stackrel{—}{\mathrm{H}}}_{\mathrm{mod}\mathrm{e}\mathrm{l}}$) and the pyranometer measurements (${\stackrel{—}{\mathrm{H}}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}}$) 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.

Figure 6

Figure 6. Comparison between the solar irradiation calculated from the model (${\stackrel{—}{H}}_{\mathrm{mod}el}$) and the pyranometer values (${\stackrel{—}{H}}_{measure}$): (a) model 1, (b) model 2, (c) model 3, (d) model 4, (e) model 5, (f) model 6, (g) model 7, (h) model 8, (i) model 9, (j) model 10, (k) model 11, (l) model 12, (m) model 13, (n) model 14, and (p) model 15.

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.

Figure 7

Figure 7. The monthly temperature map from the FLDAS model (2014–2023) for southern Thailand.

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.

Figure 8

Figure 8. The scale shows the yearly cloud fraction map in southern Thailand.

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 ${\stackrel{—}{\mathrm{H}}}_0$, $\stackrel{—}{\mathrm{C}}$, and ${\stackrel{—}{\mathrm{T}}}_{\mathrm{m}}$ were used to provide an overview of the long-term solar potential of the southern region, as shown in Figures 9–13.

Figure 9

Figure 9. Monthly average daily solar irradiation map (kriging) of southern Thailand.

Figure 10

Figure 10. The yearly solar irradiation map for southern Thailand (kriging).

Figure 11

Figure 11. Seasonal average solar irradiation (kriging) maps for summer and rainy.

Figure 12

Figure 12. Annual solar irradiation map (kriging) for southern Thailand compiled from estimates derived from (A) model 1, (B) model 4, (C) model 5, (D) model 6, (E) model 8, (F) model 9, (G) model 12, (H) model 13, and (I) model 14.

Figure 13

Figure 13. Annual solar irradiation maps of southern Thailand compiled from estimates derived from IDW, Spline, Trend, KIB, DIB, LPI, and RBF.

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.

4 Conclusion

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.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

RS: Investigation, Validation, Writing – review and editing, Software, Methodology, Resources, Data curation, Visualization, Conceptualization, Writing – original draft, Supervision. TP: Writing – original draft, Project administration, Visualization, Formal Analysis, Supervision, Methodology, Writing – review and editing, Investigation, Software, Data curation, Funding acquisition, Conceptualization, Resources, Validation. AK: Data curation, Conceptualization, Writing – review and editing, Formal Analysis, Software, Methodology, Supervision. SK: Conceptualization, Data curation, Writing – review and editing, Resources. OT: Investigation, Validation, Supervision, Writing – review and editing, Writing – original draft.

Funding

The authors declare that financial support was received for the research and/or publication of this article. Rusmadee Sabooding was supported by a Graduate Fellowship (Research Assistant) from the Faculty of Science, Prince of Songkla University, Contract no. 1-2567-02-036, and this research work was partially supported by Chiang Mai University.

Acknowledgements

The authors thank the Atmospheric Physics Laboratory, Department of Physics, Faculty of Science, Silpakorn University, for providing solar radiation data.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Generative AI was used in the creation of this manuscript.

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