Wind Speed Modeling by Nested ARIMA Processes

Wind speed modelling is of increasing interest, both for basic research and for applications, as, e.g., for wind turbine development and strategies to construct large wind power plants. Generally, such modelling is hampered by the non-stationary features of wind speed data that, to a large extent, reflect the turbulent dynamics in the atmosphere. We study how these features can be captured by nested ARIMA models. In this approach, wind speed fluctuations in given time windows are modelled by one stochastic process, and the parameter variation between successive windows by another one. For deriving the wind speed model, we use 20 months of data collected at the FINO1 platform at the North Sea and use a variable transformation that best maps the wind speed onto a Gaussian random variable. We find that wind speed increments can be well reproduced for up to four standard deviations. The distributions of extreme variations, however, strongly deviate from the model predictions.