Post-processing typically takes the outputs of a Numerical Weather Prediction (NWP) model and applies linear statistical techniques to produce improve localized forecasts, by including additional observations, or determining systematic errors at a finer scale. In this pilot study, we investigate the benefits and challenges of using non-linear neural network (NN) based methods to post-process multiple weather features -- temperature, moisture, wind, geopotential height, precipitable water -- at 30 vertical levels, globally and at lead times up to 7 days. We show that we can achieve accuracy improvements of up to 12% (RMSE) in a field such as temperature at 850hPa for a 7 day forecast. However, we recognize the need to strengthen foundational work on objectively measuring a sharp and correct forecast. We discuss the challenges of using standard metrics such as root mean squared error (RMSE) or anomaly correlation coefficient (ACC) as we move from linear statistical models to more complex non-linear machine learning approaches for post-processing global weather forecasts.

Heat waves are projected to increase in frequency and severity with global warming. Improved warning systems would help reduce the associated loss of lives, wildfires, power disruptions, and reduction in crop yields. In this work, we explore the potential for deep learning systems trained on historical data to forecast extreme heat on short, medium and subseasonal timescales. To this purpose, we train a set of neural weather models (NWMs) with convolutional architectures to forecast surface temperature anomalies globally, 1 to 28 days ahead, at $\sim200~\mathrm{km}$ resolution and on the cubed sphere. The NWMs are trained using the ERA5 reanalysis product and a set of candidate loss functions, including the mean squared error and exponential losses targeting extremes. We find that training models to minimize custom losses tailored to emphasize extremes leads to significant skill improvements in the heat wave prediction task, compared to NWMs trained on the mean squared error loss. This improvement is accomplished with almost no skill reduction in the general temperature prediction task, and it can be efficiently realized through transfer learning, by re-training NWMs with the custom losses for a few epochs. In addition, we find that the use of a symmetric exponential loss reduces the smoothing of NWM forecasts with lead time. Our best NWM is able to outperform persistence in a regressive sense for all lead times and temperature anomaly thresholds considered, and shows positive regressive skill compared to the ECMWF subseasonal-to-seasonal control forecast after two weeks.