Improving Deep Learning Weather Prediction Using the HEALPix Mesh

The successful deep learning weather prediction (DLWP) model of Weyn et al. (2021) is significantly improved by shifting its grid structure from the cube sphere to the Hierarchical Equal Area Pixelization (HEALPix) mesh, which is used extensively in astronomy. This is an easy-to-refine equal-area mesh whose cells lie along lines of constant latitude. The HEALPix mesh has unique properties that make it better suited for CNNs in weather forecasting applications than the cube sphere or alternative grid structures. Further improvements were obtained by refining the convolution neural network architecture and by introducing gated recurrent units.

The model remains parsimonious, using only seven 2D shells of prognostic data with an effective grid spacing of roughly 100 km. The model simulates realistic weather patterns at 3-hour time resolution while being recursively stepped forward over a full annual cycle. At short time scales, the diurnal 2-m temperature cycle is well resolved by the 3-hour time step and requires no special boundary-layer parameterization (see figure).

Compared to the accuracy of the ECMWF IFS as configured for subseasonal-to-seasonal (S2S) forecasting, at 1-week forecast lead times the model is approximately 1 day behind in RMSE and 1.5 days behind in ACC. These statistics can be substantially improved by applying a multi-model ensemble strategy to a single initial state.

Figure caption: Four-day forecast (solid lines) of diurnal cycles over the Amazon (green) and Australian desert (red) and adjacent oceans, initialized at 00 UTC 12 March 2018. Dashed lines are ERA5 reanalysis. The model correctly captures the larger diurnal signal over the desert without using geo-specific training data or CNN kernels.