Since the weather is chaotic, forecasts aim to predict the distribution of future states rather than make a single prediction. Recently, multiple data driven weather models have emerged claiming breakthroughs in skill. However, these have mostly been benchmarked using deterministic skill scores, and little is known about their probabilistic skill. Unfortunately, it is hard to fairly compare AI weather models in a probabilistic sense, since variations in choice of ensemble initialization, definition of state, and noise injection methodology become confounding. Moreover, even obtaining ensemble forecast baselines is a substantial engineering challenge given the data volumes involved. We sidestep both problems by applying a decades-old idea -- lagged ensembles -- whereby an ensemble can be constructed from a moderately-sized library of deterministic forecasts. This allows the first parameter-free intercomparison of leading AI weather models' probabilistic skill against an operational baseline. The results reveal that two leading AI weather models, i.e. GraphCast and Pangu, are tied on the probabilistic CRPS metric even though the former outperforms the latter in deterministic scoring. We also reveal how multiple time-step loss functions, which many data-driven weather models have employed, are counter-productive: they improve deterministic metrics at the cost of increased dissipation, deteriorating probabilistic skill. This is confirmed through ablations applied to a spherical Fourier Neural Operator (SFNO) approach to AI weather forecasting. Separate SFNO ablations modulating effective resolution reveal it has a useful effect on ensemble dispersion relevant to achieving good ensemble calibration. We hope these and forthcoming insights from lagged ensembles can help guide the development of AI weather forecasts and have thus shared the diagnostic code.

We present a parsimonious deep learning weather prediction model on the Hierarchical Equal Area isoLatitude Pixelization (HEALPix) to forecast seven atmospheric variables for arbitrarily long lead times on a global approximately 110 km mesh at 3h time resolution. In comparison to state-of-the-art machine learning weather forecast models, such as Pangu-Weather and GraphCast, our DLWP-HPX model uses coarser resolution and far fewer prognostic variables. Yet, at one-week lead times its skill is only about one day behind the state-of-the-art numerical weather prediction model from the European Centre for Medium-Range Weather Forecasts. We report successive forecast improvements resulting from model design and data-related decisions, such as switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U-Net, and introducing gated recurrent units (GRU) on each level of the U-Net hierarchy. The consistent east-west orientation of all cells on the HEALPix mesh facilitates the development of location-invariant convolution kernels that are successfully applied to propagate global weather patterns across our planet. Without any loss of spectral power after two days, the model can be unrolled autoregressively for hundreds of steps into the future to generate stable and realistic states of the atmosphere that respect seasonal trends, as showcased in one-year simulations. Our parsimonious DLWP-HPX model is research-friendly and potentially well-suited for sub-seasonal and seasonal forecasting.