Abstract. Near-surface winds over complex terrain generally feature a large variability at the local scale. Forecasting these winds requires high-resolution numerical weather prediction (NWP) models, which drastically increase the duration of simulations and hinder them in running on a routine basis. Nevertheless, downscaling methods can help in forecasting such wind flows at limited numerical cost. In this study, we present a statistical downscaling of WRF (Weather Research and Forecasting) wind forecasts over southeastern France (including the southwestern part of the Alps) from its original 9 km resolution onto a 1 km resolution grid (1 km NWP model outputs are used to fit our statistical models). Downscaling is performed using convolutional neural networks (CNNs), which are the most powerful machine learning tool for processing images or any kind of gridded data, as demonstrated by recent studies dealing with wind forecast downscaling. The previous studies mostly focused on testing new model architectures. In this study, we aimed to extend these works by exploring different output variables and their associated loss function. We found that there is no one approach that outperforms the others in terms of both the direction and the speed at the same time. Finally, the best overall performance is obtained by combining two CNNs, one dedicated to the direction forecast based on the calculation of the normalized wind components using a customized mean squared error (MSE) loss function and the other dedicated to the speed forecast based on the calculation of the wind components and using another customized MSE loss function. Local-scale, topography-related wind features, which were poorly forecast at 9 km, are now well reproduced, both for speed (e.g., acceleration on the ridge, leeward deceleration, sheltering in valleys) and direction (deflection, valley channeling). There is a general improvement in the forecast, especially during the nighttime stable stratification period, which is the most difficult period to forecast. The result is that, after downscaling, the wind speed bias is reduced from −0.55 to −0.01 m s−1, the wind speed MAE is reduced from 1.02 to 0.69 m s−1 (32 % reduction) and the wind direction MAE is reduced from 25.9 to 15.5∘ (40 % reduction) in comparison with the 9 km resolution forecast.