Quaternion-valued short-term joint forecasting of three-dimensional wind and atmospheric parameters

This work introduces novel methodology for the simultaneous modelling and forecasting of three-dimensional wind field. This is achieved based on a quaternion wind model, which by virtue of its division algebra accounts naturally for the coupling between the three wind dimensions. To fully exploit the available second order statistics, we employ the newly developed augmented quaternion statistics and perform prediction based on the widely linear model. The proposed quaternion domain processing also facilitates the fusion of external atmospheric parameters, such as air temperature, yielding improved forecasts. Simulations for wind regimes with different dynamics and over a range of prediction horizons, together with the fusion of air temperature, support the approach.