Abstract
Accurate prediction of global horizontal irradiance (GHI) is essential for optimizing solar energy utilization. Satellite-based datasets often overestimate GHI, leading to errors that hinder reliable solar resource assessment. This study presents a sequential modeling approach combining newly developed empirical models with artificial neural networks (ANN) to reduce errors in satellite-derived GHI for four cities in Pakistan: Bahawalpur, Islamabad, Lahore, and Peshawar. First 6 empirical models were developed for each city, and then the output of the best model for each city was incorporated into the ANN model. Ground-measured data from the Energy Sector Management Assistance Program (ESMAP) and satellite data from NASA’s Prediction of Worldwide Energy Resources (POWER) database were used. Using meteorological parameters such as temperature, humidity, precipitation, clearness index, and day number, empirical models were formulated, and their outputs fed into ANN models. The sequential Empirical-ANN (SE-ANN) model achieved mean absolute percentage errors (MAPE) ranging from 5.86% in Bahawalpur to 17.09% in Lahore, outperforming satellite data, which achieved a maximum MAPE of 25.30%. Root mean square errors (RMSE) and Mean absolute error (MAE) decreased significantly, with values as low as 0.43 kWh/m2/day and 0.29 kWh/m2/day in Bahawalpur compared to 1.07 kWh/m2/day for satellite data. The sequential model has reduced the MAPE in satellite data by 36.95% in Peshawar, 36.7% in Lahore, and 31.6% in Bahawalpur. For Islamabad, the Empirical model M6 performed best, reducing the MAPE by 17.6%. The R2 values for the model range from 0.78 in Lahore to 0.93 in Bahawalpur. The results indicate that the SE-ANN model provides a more accurate and cost-effective alternative to pure satellite or empirical models, improving GHI prediction reliability in data-scarce regions and supporting better solar energy system planning and management.
Keywords: Solar irradiation, Empirical models, Artificial Neural Network (ANN), Sequential model, Satellite data error mitigation
Subject terms: Climate sciences, Engineering, Environmental sciences
Introduction
Energy demand has increased significantly over the past decade1. The limited supply of fossil fuels and the increasing concerns over climate change are accelerated by the emissions from burning these fuels. The researchers are exploring new ways to use renewable energy resources efficiently2. Among renewable energy sources, solar energy is the most promising, as it is readily available worldwide. About 
W of solar energy reaches the Earth’s surface, and utilizing only 1% of this energy, it can generate 4 times more energy than the world’s demand. The most crucial factor in solar energy applications is solar irradiance on a horizontal surface, as it is the fundamental parameter that determines the availability of solar energy. Solar irradiance is fundamental for assessing available solar energy, calculating optimal angles for solar collectors, and estimating solar gain for buildings. For this reason, those interested have long been engaged in developing models to estimate solar irradiance in all its components: DNI, direct beam, sky-diffuse, ground-reflected, Albedo, and view factors3–5. But because of its intermittent nature, it is challenging to use efficiently6,7.
Solar irradiation can be measured directly with pyranometers, but this is almost impossible due to high costs and other challenges. Also, satellite databases are available for nearly all locations worldwide, but satellite data have overestimated GHI at most locations8,9. To overcome the expenses and challenges involved in the physical measurement of solar irradiation and to avoid errors present in the satellite data, researchers have developed methods such as empirical, analytical, and Artificial Intelligence (AI) based models10,11. Empirical models establish correlations between meteorological parameters and GHI and have been widely used in previous decades due to their low computational cost. Based on the inputs used, solar irradiation prediction models can be divided into three categories: sunshine-based models, modified sunshine-based models, and non-sunshine-based models. The modified sunshine-based models have shown promising results across all three methods, but using sunshine as an input parameter limits the model’s applicability to areas where stations record sunshine data12–16. Temperature and other meteorological models have been developed because meteorological stations can easily measure this data17,18,8,11.
Machine learning (ML) models are often called AI models, and no explicit algorithms can represent them19. In standalone models, previous studies have confirmed the supremacy of ANN over other methods like empirical, physical, and numerical methods, and also over other ML methods developed across the globe in standalone models2,6,20–23. Compared to standalone models, the hybrid model has produced more accurate results for GHI predictions. Among hybrid models, combinations of CNN-SLSTM, numerical models combined with regression models, and ANN models combined with evolutionary algorithms have been used for GHI prediction13,24,25. The literature confirms that the developed models’ prediction outclasses the satellite data in terms of accuracy11,8,26,27. The literature review shows that empirical models and ML models have been widely used to predict GHI. Additionally, a few studies have improved the accuracy of satellite data to date. The lack of a combination of the two most widely used and effective methods creates a significant research gap. Using two different datasets, i.e., ground-measured and satellite, for diverse climate locations can result in the development of a model that can be used for any location in the region. This study aims to mitigate the errors present in the NASA Prediction of Worldwide Energy Resources data for four cities across Central and Northern Pakistan using sequential empirical and ANN models.
Methodology
Materials and methods
Six empirical models are developed using MATLAB R2025a on a Core i7 11th-generation laptop. Table 1 shows the developed empirical models. The model inputs were selected on a tick-and-trial basis. Inputs for models, including 
, 
, 
etc. are downloaded from the NASA Power Data Viewer28, whereas the target data is downloaded from ESMAP (Way et al.). The best ANN model is selected from a previous study incorporating the same data11, with the modification that the output of the empirical model is fed instead of 
.
Table 1.
Newly developed empirical models.
| Name | Model |
|---|---|
| M1 |
 +
|
| M2 |  |
| M3 |  |
| M4 |  |
| M5 |  |
| M6 |  |
Data collection
The ground-measured data for Bahawalpur, Islamabad, Lahore, and Peshawar were downloaded from the Energy-Sector-Management-Assistance-Program (ESMAP) website29. ESMAP recorded data for nine locations across Pakistan for two years (2015-2017). In contrast, the satellite data were downloaded from the NASA Prediction of Worldwide Energy Resources (Power)28. The Esmap data is available in 10-minute intervals, resulting in 240 samples per day, which are converted to a daily format using MS Excel. Figure 1 shows the map prepared in ArcGIS Pro 2.9.530 for the cities under study.
Fig. 1.
Geographical locations of study sites (Map Prepared using ArcGIS Pro 2.9.530).
Data preprocessing
The downloaded data sometimes contains missing values, outliers, and NAN values that need to be removed. The gaps created by the removal of missing values then need to be filled using interpolation. Also, the data is sometimes not in the required format, so it is converted to another format. Figure 2 depicts the data preprocessing. In the last stage, the data is normalized to values between 0 and 1 using Equation 1.
 |
1 |
Fig. 2.
Data preprocessing.
Input selection
Eleven input parameters were used in this study using the NASA Power Data Viewer. Latitude (L), Longitude (Lon), Altitude (H), Satellite GHI (Gsat), day number (D), relative humidity (RH), absolute humidity (AH), maximum temperature (Tmax), minimum temperature (Tmin), Precipitation (Prec) and clarity index (Kt) are the input parameters.
Development of an empirical model
An empirical model is created from observations rather than theoretical frameworks or fundamental principles31. These models are useful for systems when theoretical models are difficult, insufficient, or unavailable, as they use statistical or mathematical methods to model correlations between variables. The developed empirical models are shown in Table 1.
Development of SE-ANN model
The output GHI from the best empirical model is fed to the ANN model, in combination with the other input variables. The best ANN model is selected from the11 and tested for all four cities. The data was split into training and testing datasets by 70/30 ratio. For each city, four datasets, each incorporating different seasonal data as test datasets, were created,these datasets ensure the k-fold cross-validation. Inputs for the ANN models include L, Lon, H, D, Tmax, Tmin, RH, AH, Kt, Prec, and the output of the Empirical model G. The ANN incorporates one hidden layer with neurons ranging from 1:60 being tested, which transfer the information to the output layer, which contains one neuron.
Model selection
Based on the available data and the study’s goal, model selection involves choosing the best mathematical or statistical model from a group of candidates. The objective for empirical models is often to identify the model with the lowest MAPE errors.
Performance evaluation using statistical metrics
The MAPE, RMSE, R2, and MAE have been widely used and are considered sufficient for validating the accuracy11,8. To confirm accuracy, statistical metrics, including R2,MAPE, MAE and RMSE, were used. The equations for the MAPE, RMSE, R2, and MAE are given below. The unit of MAPE is %, while the unit of RMSE, MAE, is the same as the GHI, which is kWh/
and the R2 has no unit32,33are as follows.
 |
2 |
 |
3 |
 |
4 |
 |
5 |
Comparison with satellite data
To verify the model’s effectiveness in reducing errors in the satellite data, the predicted data will be compared with satellite data in the last phase.
Assumptions, limitations, and uncertainties
The climatic conditions of Lahore, Islamabad, Bahawalpur, and Peshawar represent various climatic conditions across Pakistan, so it is assumed that the empirical models and SE-ANN model are applicable to all climates in the country. The study is limited to mitigating errors in Global Horizontal irradiation in the above-mentioned cities. The large errors in the GHI data for Lahore and Peshawar may affect the results.
Results and discussion
Using satellite data inputs, six empirical models shown in Table 1 are developed and tested for each location. The results of all the empirical models are compared with both the ground and satellite data. The output of the best model was fed to the ANN model with other satellite data input variables. The results of the sequential models are then compared with the ANN models’ results in11,34 and the empirical models developed in the study to confirm that the sequential models outperform the ANN and Empirical models. The satellite data errors are given in Table 2. Table 2 shows that satellite data MAPE ranges from 8.5% in Bahawalpur to 25.30% in Lahore. The same data was used by11 to predict ground-measured data, with MAPE ranging from 6.36% in Bahawalpur to 16.49% in Lahore. The RMSE value ranges from 0.46 kWh/m2
in Bahawalpur to 1.07 kWh/
in Lahore. At the same time, the11 RMSE values range from 0.43kWh/
in Bahawalpur to 0.77kWh/m2
in Lahore.
Table 2.
Satellite and Nawab et al. statistical evaluation11.
Empirical models - sequential empirical-ANN model
Six empirical models, each with different meteorological parameters, are developed and tested across all four cities. Table 3 shows the empirical models with coefficients determined by regression analysis.
Table 3.
Empirical models with calculated coefficients.
| Name | Model | |
|---|---|---|
| Bahawalpur | M1 |
 +
|
| M2 |  |
|
| M3 |  |
|
| M4 |  |
|
| M5 |  |
|
| M6 |  |
|
| Lahore | M1 |
 +
|
| M2 |  |
|
| M3 |  |
|
| M4 |  |
|
| M5 |  |
|
| M6 |  |
|
| Islamabad | M1 |
 +
|
| M2 |  |
|
| M3 |  |
|
| M4 |  |
|
| M5 |  |
|
| M6 |  |
|
| Peshawar | M1 |
 +
|
| M2 |  |
|
| M3 |  |
|
| M4 |  |
|
| M5 |  |
|
| M6 |  |
The results of empirical models are shown in Table 4. The empirical models have reduced the error present in satellite data. The M1, M6, and M5 models outperformed the others for Bahawalpur, Lahore, Islamabad, and Peshawar, respectively. The models’ R2 values for Bahawalpur range from 0.906 to 0.920; for Lahore, the range was 0.663 to 0.732. For Islamabad and Peshawar, the range was 0.935 to 0.939, and 0.849 to 0.854. For Bahawalpur, the MAPE is reduced to 6.13% from 8.57%, and the results are also better than those of the ANN models used in11. For Lahore, the MAPE error is 18.53%, which is lower than that of satellite data. The range of MAE for all cities were 0.29kWh/
to 0.335kWh/
, 0.656 to 0.732kWh/
(Lahore), 0.310 to 0.325kWh/
(Islamabad), 0.483 to 0.488kWh/
(Peshawar).
Table 4.
Empirical statistical evaluation.
| City | Model | MAPE (%) | RMSE (kWh/ 
|
R2 | MAE (kWh/
|
|---|---|---|---|---|---|
| Bahawalpur | M1 | 6.13 | 0.419 | 0.920 | 0.290 |
| M2 | 6.90 | 0.447 | 0.919 | 0.330 | |
| M3 | 6.73 | 0.448 | 0.915 | 0.323 | |
| M4 | 6.96 | 0.451 | 0.906 | 0.335 | |
| M5 | 6.73 | 0.448 | 0.911 | 0.326 | |
| M6 | 6.73 | 0.447 | 0.91 | 0.324 | |
| Lahore | M1 | 18.99 | 0.830 | 0.716 | 0.678 |
| M2 | 20.70 | 0.925 | 0.647 | 0.732 | |
| M3 | 18.75 | 0.842 | 0.707 | 0.663 | |
| M4 | 20.71 | 0.926 | 0.646 | 0.727 | |
| M5 | 18.54 | 0.837 | 0.711 | 0.656 | |
| M6 | 18.53 | 0.837 | 0.711 | 0.660 | |
| Islamabad | M1 | 7.50 | 0.418 | 0.939 | 0.313 |
| M2 | 7.70 | 0.431 | 0.935 | 0.320 | |
| M3 | 7.62 | 0.427 | 0.937 | 0.31 | |
| M4 | 7.86 | 0.434 | 0.935 | 0.325 | |
| M5 | 7.44 | 0.420 | 0.939 | 0.312 | |
| M6 | 7.40 | 0.419 | 0.939 | 0.310 | |
| Peshawar | M1 | 12.84 | 0.653 | 0.854 | 0.485 |
| M2 | 12.90 | 0.666 | 0.849 | 0.486 | |
| M3 | 12.93 | 0.663 | 0.850 | 0.488 | |
| M4 | 12.90 | 0.666 | 0.849 | 0.485 | |
| M5 | 12.75 | 0.653 | 0.854 | 0.484 | |
| M6 | 12.75 | 0.653 | 0.854 | 0.483 |
Similarly, for Islamabad, the MAPE is reduced from 8.99% to 7.40%, and for Peshawar, the MAPE is 12.75% compared to 18.35% in the satellite data and 11.75% in11. Fig. 3 compares predicted, satellite, and measured data. The empirical model-predicted data are much closer to the measured data than to the satellite data.
Fig. 3.
Comparison of the Empirical model-predicted GHI and satellite GHI with the ground-measured GHI.
The output of the best empirical model for each city, in combination with other meteorological parameters such as Latitude, Longitude, Height, Day number, maximum and minimum temperatures, relative and absolute humidities, clearness index, and precipitation are fed to the ANN model. The results of the sequential Empirical-ANN models are shown in Table 5. Figure 4 shows the comparison of predicted GHI and satellite GHI with the ground-measured GHI. The predicted GHI is much closer to the measured GHI than the satellite GHI. The MAPE of the SE-ANN model ranges from 5.86% in Bahawalpur to 17.09% in Lahore. The RMSE values of the SE-ANN model range from 0.43kWh/
in Bahawalpur to 0.82kWh/
in Lahore. The lowest MAE value for the model was 0.29kWh/
, and the highest value was 0.66kWh/
in Lahore. The R2 values were 0.916 (Bahawalpur), 0.718 (Lahore), 0.93 (Islamabad), and 0.85 (Peshawar).
Table 5.
Sequential empirical-ANN model statistical evaluation.
| City | MAPE (%) | RMSE (kWh/ ) |
R2 | MAE (kWh/ ) |
|---|---|---|---|---|
| Bahawalpur | 5.86 | 0.4338 | 0.916 | 0.29 |
| Lahore | 16.0 | 0.8246 | 0.78 | 0.66 |
| Islamabad | 7.82 | 0.4503 | 0.93 | 0.33 |
| Peshawar | 11.55 | 0.6541 | 0.85 | 0.47 |
Fig. 4.
Comparison of SE-ANN predicted GHI and satellite GHI with the ground-measured GHI.
The results showed that for Bahawalpur, Peshawar, and Lahore, the SE-ANN model is more accurate than empirical and ANN models prepared by Nawab et al11. For Islamabad, the Emprical model predictions are more precise, followed by the ANN model. The results showed that Sequential models can result in more accurate predictions11,8. The model has the best results as compared to Nawab et al.11, as their model error reduction ranges from 6.36% to 16.49%, while our range is 5.86 to 16%. Also, the ANN model in8 reduced error by 35.8% in Peshawar, 10.2% in Islamabad, while our model reduced the error by 36.95% and 17.6% for the same locations. The study also confirms that satellite GHI and the clearness index are the most effective parameters. At the same time, the RH, AH, and D have minimal effect on accuracy. The effectiveness of the clearness index may be due to the close link between clearness and GHI. When the sky is clear, the GHI value is high, and vice versa. This linear connection is the reason for its effectiveness. Also, the satellite GHI has the same pattern as ground-measured GHI but has different values due to errors. The results also confirmed that the model can reduce the error by a proportion, with most cities showing error reductions of 35% to 40%. So the cities where errors are high in number, the model error will be high. Such as in Lahore, the satellite error is 25.3%, and the model error is 16%, while for Bahawalpur, the satellite error is 8.57% and the model error is 5.86%. So the variation in satellite error affects model outputs. The uncertainty analysis shows that the higher error in satellite GHI results in a high number of statistical errors.
Conclusion
This study investigated empirical models and the sequential empirical model to mitigate errors in satellite data for four cities across central and northern Pakistan. The empirical models incorporate 6 different combinations of maximum and minimum temperature, relative humidity, absolute humidity, satellite GHI, clearness index, and day number. The inputs for the ANN models include L, Lon, H, D, Tmax, Tmin, RH, AH, KT, Prec, and the output of the Empirical model. The results are also compared with ANN models developed using the same data. The result confirms that sequential models achieve higher accuracy than ANNs and empirical models alone, as sequential model predictions have fewer errors in three out of four cities. The sequential model has improved the R2 in satellite data by 12.58%% in Peshawar, 48.57% in Lahore, 35.69% in Bahawalpur and 0.65% in Islamabad. The MAPE, MAE and RMSE were reduced by 36.97, 31.68% and 22.84 in Peshawar, 36.77%, 19.21% and 23.26% in Lahore, 31.70%, 35.69% and 23.33% in Bahawalpur, 36.77%, 19.21% and 23.26% in Islamabad.For Islamabad, the Empirical model M6 performed best, reducing the MAPE by 17.6%. The study also confirms that satellite GHI and the clearness index are the most effective parameters. At the same time, the relative humidity, absolute humidity, and the incorporation or removal of day numbers from the model have minimal effect on accuracy. Also, incorporating aerosol data and other parameters can yield more accurate results. In future work, combinations of other methods, such as analytical and physical methods, with AI methods can be evaluated. Also, the testing of the existing model for predictions of GHI on a tilted surface can be carried out.
Acknowledgement
Sincerely, thank you to the Solar Thermal and Sustainable Technology Group, under the Sustainable Resources, Nature and Smart Living Cluster, University Research Group (KPU), and the Solar Energy Research Institute, Universiti Kebangsaan Malaysia, for their invaluable support and guidance throughout this project.
Author contributions
Shaqeeb Ahmad: review & editing, Writing – original draft, Validation, Methodology, Investigation, Data curation, Conceptualization. Adnan Ibrahim: Writing – review & editing, Validation, Supervision, Project administration, Funding acquisition, Conceptualization. Sharul Sham Dol: Writing – review & editing, Validation, Supervision, Project administration, Funding acquisition, Conceptualization. Faisal Nawab: Validation, Methodology, Data curation. Shoaib Ahmad: Writing – review & editing, and Validation. Norasikin Binti Ahmad Ludin: Writing – review & editing, Validation, Supervision, Project administration, Conceptualization.
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Data availability
The datasets generated and/or analysed during the current study are available from the corresponding author, upon reasonable request.
Declarations
Competing interest
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets generated and/or analysed during the current study are available from the corresponding author, upon reasonable request.