Using Non-Homogeneous Gaussian Regression to incorporate heteroscedasticity when post-processing air temperature forecasts by Bayesian Model Averaging

Raw forecasts, be they weather or hydrological, suffer from the inevitable errors stemming from either model structures or initial conditions estimation. With forecasting being a critical component in addressing challenges in flood control, reservoir and hydropower operation, and other fields related to the environment, energy and public safety, improving forecasting skill is increasingly necessary. Post-processing methods can help in this regard and can help improve forecast accuracy and reliability. Non-Homogeneous Gaussian Regression (NGR) and Bayesian Model Averaging (BMA) are the two most commonly used methods when it comes to post-processing probabilistic forecasts, and they have shown to be similarly efficient in many studies. For case studies where there are several distinct forecasts for one single observation, NGR risks losing information on uncertainty by aggregating the forecasts even though it accounts for heteroscedasticity. BMA, on the other hand, evaluates distinct model components and utilizes them accordingly, while assuming all the forecasts are alike in their under/overdispersion. This work introduces a mixed NGR-BMA approach for calibrating air temperature forecasts with lead-times of 1-10 days where the forecasts are first processed with NGR and then corrected once more by BMA according to a priori information on the skill of model components. This way, the upsides of each method is maintained through post-processing. The results generally show that the higher the lead-time, the more the proposed method outperforms either BMA or NGR taken individually.