Physics-inspired adaptions to low-parameter neural network weather forecasts systems

Recently, there has been a surge of research on data-driven weather forecasting systems, especially applications based on convolutional neural networks (CNNs). These are usually trained on atmospheric data represented on regular latitude-longitude grids, neglecting the curvature of the Earth. We assess the benefit of replacing the standard convolution operations with an adapted convolution operation which takes into account the geometry of the underlying data (Spherenet convolution), specifically near the poles. Additionally, we assess the effect of including the information that the two hemispheres of the Earth have "flipped" properties - for example cyclones circulating in opposite directions - into the structure of the network. Both approaches are examples of physics-informed machine learning. The methods are tested on the WeatherBench dataset, at a resolution of $\sim1.4^{\circ}$ which is higher than many previous studies on CNNs for weather forecasting. For most lead times up to day +10 for 500 hPa geopotential and 850 hPa temperature, we find that using Spherenet convolution or including hemisphere-specific information individually lead to improvement in forecast skill. Combining the two methods typically gives the highest forecast skill. Our version of Spherenet is implemented flexibly and scales well to high resolution datasets, but is still significantly more expensive than a standard convolution operation. Finally, we analyze cases with high forecast error. These occur mainly in winter, and are relatively consistent across different training realizations of the networks, pointing to flow-dependent atmospheric predictability.