Simulation data from a quasi-geostrophic 1-layer model pde model with observations and stream function field and it's observations which are satellite tracks.

These two datasets are used for demostration of the learning capabilities of 4DVarNet, a deeplearning model for data assimilation. They contain ground truth data in terms of stream function, voriticty and observations. The Quasi-Geostrophic (QG) model offers a more realistic and challenging alternative over simple and chaotic ODE based models such as Lorenz-63 and Lorenz-96. As a PDE-based model, the QG system captures essential features of large-scale geophysical fluid dynamics while remaining computationally tractable. It serves as a model of intermediate complexity, bridging the gap between toy models and full-scale numerical weather prediction systems. In the QG model, the vorticity field is the fundamental dynamical variable, evolving under nonlinear advection and forcing, and governed by conservation laws. Observations, however, are typically taken in the streamfunction space, which is related to vorticity through an elliptic inversion (a form of diagnostic relationship). This setup introduces a realistic observation operator and offers a natural framework for exploring the performance of data assimilation techniques in the presence of model and observation noise. The QG model is thus particularly well-suited for testing advanced machine learning and deep learning methods for data assimilation.