Analysis of optimal atmospheric predictability using machine learning-based forecasting models

With the development of highly skillful, machine learning-based weather prediction models over the last 2-3 years, many new possibilities have emerged. These include applications, such as downscaling, temporal interpolation, or generating climate storylines, but also a wide range of scientific questions can be (re)examined with the models. One of these is the study of predictability limits by leveraging the full differentiability of the models. For instance, Vonich and Hakim (2024) demonstrated that optimizing initial conditions using the pre-trained GraphCast model significantly reduces forecasting error, even when used with another machine learning-based forecasting model. While this suggests that the improvement in the initial conditions is not only due to compensation in model error, it remains currently unclear to which extent the initial conditions are enhanced by physically meaningful features.

In our work, we aim to address this shortcoming. As a first step, we analyze whether optimized initial conditions can be identified for a broad range of cases by assessing the forecast skill of the model for a larger set of examples. We evaluate the improvement of the forecasts for several variables dependent on the number of optimization steps, the forecast lead time, and for different models. Subsequently, we consider case studies over Europe and compare the optimized initial conditions with data from independent, high quality datasets, in particular local reanalyses and conventional observations. In this way, we examine if the optimized states are physically better aligned with reference data than the original ERA5 initial conditions. To better understand which of the features in the optimized initial conditions lead to the improved forecast, we analyze the null space of the given machine learning-based weather prediction models. This allows us to obtain insight into the information that is exploited by the models for a forecast. 

Our work will shed light on the intrinsic predictability limits of weather forecasts and also how MLWP can provide forecasts that outperform equation-based weather prediction models.