Mathematical models of temperature and precipitation forecasting using fractal and Fourier-analysis of meteorological series

The article presents a methodology for constructing statistical models that can be used to predict the temperature regime and precipitation for the upcoming month. Temperature and precipitation are predicted on a two-element scale (high or low parameter value). Within the framework of the considered examples, it was found that temperature is predicted better than precipitation, and recently the accuracy of forecasts tends to increase. The article also provides a detailed analysis of the model parameters, including their change in the annual cycle, trends in the dynamics of change over the past 80 years, and the correlation between climatic parameters. Along with the basic statistical functions of climatic indicators, the models contain fractal parameters (fractal index) and parameters of the discrete Fourier transform (amplitude and phase of the first harmonic). It was found that the fractal indices of monthly series of average daily temperatures is lower than those for monthly series containing daily temperature values.