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

## TL;DR

This paper introduces a Bayesian Markov model to evaluate the accuracy of wind forecasts by the WRF system, considering different weather regimes and their distributional characteristics.

## Contribution

It develops a novel mixture model for joint wind speed and direction data, incorporating regime changes and Bayesian inference for forecast verification.

## Key findings

- Insights into WRF forecast performance across wind regimes
- Effective modeling of multivariate circular-linear data
- Identification of distinct weather states affecting wind predictions

## Abstract

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 hours 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.