Application Of The Weierstrass–Mandelbrot Function To The Simulation Of Atmospheric Scalar Turbulence: A Study For Carbon Dioxide

The statistical simulation of atmospheric carbon dioxide based on time series analysis plays an important role in the development of refined carbon emission assessment and traceability. A new statistical method based on the random Weierstrass–Mandelbrot function is proposed to simulate the high-Reynolds-number and high-Péclet-number scalar turbulence in the atmospheric flow. In this paper, we focus on the carbon dioxide, which is the most important scalar for the global climate changes. The new statistical method is used to simulate the time series of carbon dioxide concentrations in the high-frequency inertial subrange. Results show that the simulated power spectral densities are almost the same as the observed ones in the inertial subrange. Compared with the Gaussian distribution, the simulated probability density functions are more similar to the observed ones with the skewness characteristic. More importantly, the fractal characteristics of the time series that cannot be simulated by traditional methods in the meteorological engineering can also be well simulated by the new method.