## Fourier analysis-based air temperature movement analysis and forecast

Climate change and climate variability have become issues of global concern. Conventional Fourier analysis is the most common analysis method in the frequency domain. In this study, an evaluation model using limited terms of Fourier series is introduced to describe yearly air temperature movement by month and daily air temperature by hour. Then a forecast method based on the Fourier analysis in the least-square sense is proposed that incorporating with the least-square method, the Fourier-series model is extended to forecast that predict future temperature movements based on limited previous observation values. The forecast model is built by finding its optimum Fourier coefficients in the least-square sense based on the previous observed temperature movements. Experiments including yearly and daily air temperature evaluation and forecast at several observation stations in China, yield satisfied results agreeing well with actual observation values. Experimental results demonstrate that the Fourier evaluation model evaluates the annual and the daily air temperature movements most closely by about 5-term and 11-term Fourier series, respectively. The forecast model predicts both the annual and daily air temperature movements most fit with about 4-term Fourier series. Result analysis indicates workability and effectiveness of the proposed.