Bernoulli-Langevin wind Speed model for Simulation of storm events

Abstract

We present a simple nonlinear dynamics Langevin model for predicting the wind speed profile during storm events typically accompanying extreme low pressure situations. It is based on a 2nd degree Bernoulli equation with -correlated Gaussian noise. Transition between increasing and decreasing wind speed are formally described by the sign change of the controlling rate parameter or time constant. This approach is similar to a simplified laser model using a non-equilibrium 2nd-order phase transition analogy for the incoherent to coherent transition of light emission. The analytical solution of the Bernoulli model is successfully tested by fitting of two historical wind profiles (low pressure situations “Xaver” and “Christian”, 2013) taken from METAR weather data at Hamburg airport, with a logistic approximation to the dynamic model (i.e. with constant rate coefficients k). Simulations with the corresponding Bernoulli-Langevin equation with a time dependent sinusoidal rate ansatz k(t) of period T (= storm duration) and -correlated force according to empirical speed variance demonstrate the potential for realistic speed profile and time series modeling and prediction. Instationary speed fluctuations are estimated with a stationary Fokker-Planck approximation.