# Bivariate Gaussian models for wind vectors in a distributional regression framework

## TL;DR

This paper introduces a novel probabilistic post-processing method for wind vectors using bivariate Gaussian models within a distributional regression framework, improving forecast accuracy by modeling all distribution parameters simultaneously.

## Contribution

The study presents a new method that models all wind vector distribution parameters jointly, including correlation, with flexible regression splines, and incorporates ensemble forecast data for enhanced accuracy.

## Key findings

- Improved predictive skill for wind vectors across various terrains.
- Rotation-allowing model outperforms baseline in all tested sites.
- Small benefits observed from modeling correlation in alpine valleys.

## Abstract

A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are simultaneously modeled, namely the means and variances for both wind components and also the correlation coefficient between them employing flexible regression splines. To capture a possible mismatch between the predicted and observed wind direction, ensemble forecasts of both wind components are included using flexible two-dimensional smooth functions. This encompasses a smooth rotation of the wind direction conditional on the season and the forecasted ensemble wind direction. The performance of the new method is tested for stations located in plains, mountain foreland, and within an alpine valley employing ECMWF ensemble forecasts as explanatory variables for all distribution parameters. The rotation-allowing model shows distinct improvements in terms of predictive skill for all sites compared to a baseline model that post-processes each wind component separately. Moreover, different correlation specifications are tested and small improvements compared to the model setup with no estimated correlation could be found for stations located in alpine valleys.