## 3 Illustrative Simulation and Analysis  
In this study, we used four methods--i.e., linear regression, SVM, MLNN, and LSTM--to deduct local solar irradiance (GHI, MJ/m\({}^{2}\)). The models were trained using 70,090 hourly data points collected over eight years, consisting of temperature (\({}^{\circ}\)C), humidity ratio (g/kg), air pressure (mbar), wind velocity (m/s), wind direction (0-360\({}^{\circ}\)), amount of total cloud cover (0-10), amount of middle and low-layer cover (0-10) and were tested using 8760 hourly data points collected over one year. This study explores the accuracy of each model algorithm, and also evaluates how each weather parameter significantly impacts the local solar irradiance. We can estimate long-term solar irradiance without actual radiance sensors based on local weather data and variations. This study used four estimation methods, with weather parameters as the input data and solar irradiance as the output. Based on eight years of training data and one year of testing data, the solar irradiance values were estimated and evaluated by comparison with real values. The performances of the four models were also evaluated based on accuracy and error rate. The results of one-year (January-December) hourly prediction outputs compared with real values are shown in Figure 7. In general, compared to the linear regression and SVM methods, the two ANN models, MLNN and LSTM, exhibited significantly better performance and higher accuracy in deducing solar irradiance. The LSTM model especially showed higher accuracy than the other models. Figure 7 shows that the output of the two ANN models agreed well with the real data; however, the GHI values estimated by linear regression and SVM are even higher than zero during the nighttime. These two algorithms had overshot the estimation values at nighttime. Therefore, these two methods are not suitable for estimating solar irradiance because of their high error rates. Compared with other algorithms, LSTM had relatively overestimated the predicted values in daytime, however, it had good accuracy and the overestimating impact is small. The mean relative error and mean square error (MSE) results for each model are shown in Figure 8. The MSE results for the linear regression and SVM models were 0.3718 and 0.0932, respectively, and these models showed low accuracy and high error rates compared to those of the two ANN methods. The MLNN and LSTM models achieved MSE values of 0.0324 and 0.0221, respectively. The estimation MSE using LSTM showed a 31.7% increase in accuracy compared to MLNN. Thus, the two ANN models showed higher performance with good accuracy and stability when estimating local solar irradiance. Based on the results, the LSTM showed the best estimation performance out of the four models even though it had regularly overestimated in daytime. The ANN models showed significantly better estimation performance because having multiple layers between the input and output nodes allowed them to learn to activation functions and network configuration parameters to determine the best value and to minimize the error rate. Figure 9 presents how much each weather parameter impacts on the local solar irradiance, as determined using four prediction algorithms. Temperature and amount of total cloud cover (Tcc) significantly dominate the local solar irradiance because temperature variations represent seasonal changes, and the total cloud cover can directly affect how much solar irradiance can reach the ground surface. However, the linear regression method did not clearly show the impact factor of each parameter. The results obtained using MLNN and LSTM models indicated that four main parameters mainly affect the actual solar irradiance: temperature, amount of total cloud cover, amount of middle and low-layer cloud cover (MLcc), and the humidity ratio. Moreover, other parameters, including air  
pressure, wind velocity, and wind direction, could be neglected when considering the main environmental influences for estimating solar irradiance.