On the effective resolution of AI weather models

In recent years, models based on artificial intelligence (AI) have become equally good or even slightly better at predicting the weather as standard operational models, which are based on solving physical equations. Although the grid size of the AI weather models is similar to that of to global operational models, it has been widely noted that forecasts from the AI models are overly smooth. This smoothness poses a potential issue for ensemble generation and for the simulation of extreme weather events, which are often caused by a superposition of multiple spatial scales. In this study, we develop a mathematical argument to better understand the reason for this low "effective resolution" of deterministic AI weather models. We find that an ideal, perfectly trained AI model follows the mean of the predictive distribution for the lead time interval which is used in its loss function during training. We demonstrate the consequences and limitations of this result with forecast data from various AI models, including Aurora, Pangu, GraphCast and GenCast.

We further demonstrate that a low effective resolution leads to better mean-square forecast error scores by reducing the double-penalty effect, especially at longer forecast lead time. To avoid this often unwanted effect, we suggest a spectral rescaling method for a fairer comparison of two models with different effective resolution. By applying this method to the AI forecasts and the ensemble and deterministic forecasts from the European Centre for Medium Range Weather Forecasting (ECMWF) we estimate to what extent the reported advantages of the AI models are only related to their smoothing. Our results will help users of AI forecasts to interpret their output correctly and guide AI developers in the design of loss function and training protocols.