Distributions-oriented wind forecast verification by a hidden Markov model for multivariate circular-linear data

Winds from the North-West quadrant and lack of precipitation are known to lead to an increase of PM10 concentrations over a residential neighborhood in the city of Taranto (Italy). In 2012 the local government prescribed a reduction of industrial emissions by 10% every time such meteorological conditions are forecasted 72 h in advance. Wind forecasting is addressed using the Weather Research and Forecasting (WRF) atmospheric simulation system by the Regional Environmental Protection Agency. In the context of distributions-oriented forecast verification, we propose a comprehensive model-based inferential approach to investigate the ability of the WRF system to forecast the local wind speed and direction allowing different performances for unknown weather regimes. Ground-observed and WRF-forecasted wind speed and direction at a relevant location are jointly modeled as a 4-dimensional time series with an unknown finite number of states characterized by homogeneous distributional behavior. The proposed model relies on a mixture of joint projected and skew normal distributions with time-dependent states, where the temporal evolution of the state membership follows a first order Markov process. Parameter estimates, including the number of states, are obtained by a Bayesian MCMC-based method. Results provide useful insights on the performance of WRF forecasts in relation to different combinations of wind speed and direction.