Modeling and forecasting monthly movement of annual average solar insolation based on the least-squares Fourier-model

• Introduce a finite Fourier-series model for evaluating monthly movement of annual average solar insolation.
• Present a forecast method for predicting its movement based on the extended Fourier-series model in the least-squares.
• Shown its movement is well described by a low numbers of harmonics with approximately 6-term Fourier series.
• Predict its movement most fitting with less than 6-term Fourier series.

Solar insolation is one of the most important measurement parameters in many fields. Modeling and forecasting monthly movement of annual average solar insolation is of increasingly importance in areas of engineering, science and economics. In this study, Fourier-analysis employing finite Fourier-series is proposed for evaluating monthly movement of annual average solar insolation and extended in the least-squares for forecasting. The conventional Fourier analysis, which is the most common analysis method in the frequency domain, cannot be directly applied for prediction. Incorporated with the least-square method, the introduced Fourier-series model is extended to predict its movement. The extended Fourier-series forecasting model obtains its optimums Fourier coefficients in the least-square sense based on its previous monthly movements. The proposed method is applied to experiments and yields satisfying results in the different cities (states). It is indicated that monthly movement of annual average solar insolation is well described by a low numbers of harmonics with approximately 6-term Fourier series. The extended Fourier forecasting model predicts the monthly movement of annual average solar insolation most fitting with less than 6-term Fourier series.