Analysing and Predicting Streamwise Velocity Fluctuations in Nonstationary Atmospheric Surface Layers Using the ARMA-GARCH Model

Obtaining reliable statistical results from nonstationary data remains a big challenge in understanding the atmospheric surface layer (ASL). This work employs autoregressive moving average (ARMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models to analyze and predict nonstationary streamwise velocities of the ASL data obtained from the Qingtu Lake Observation Array site in Minqin District, Gansu Province, China. The ARMA process captures temporal autocorrelation, and the GARCH process describes the varying turbulent kinetic energy induced by the mean flow. The ARMA-GARCH model allows for estimating instantaneous variance and correlation for short intervals, which is advantageous over a direct moving average by avoiding an artificially defined averaging window. In addition, we use the phase space spanned by the GARCH coefficients to characterize ASL flows for clear-air and sand-laden situations, and find that sand enhances temporal correlation. We predict the velocity fluctuation by combining an empirical linear relation between the GARCH process and the mean velocity. Even though the current simple model only captures the second-order statistics, it helps extract information from nonstationary data and benefits ASL modelling.