Topological Digital Twins: A Reduced-Order Framework for the Analysis and Forecasting of Convective Systems

We propose an exploratory framework based on Topological Digital Twins (TDTs) for the monitoring and short-term forecasting of spatial dynamical systems. The approach represents the system through a reduced state built from topological descriptors obtained via persistent homology. These descriptors capture features such as connected components, cycles, and large-scale structure. The framework combines three components: an observation operator mapping spatial fields to a low-dimensional state, a reduced dynamical model evolving this state in time, and a data assimilation step aimed at improving robustness. This construction maps persistence diagrams to a finite-dimensional Euclidean space. This makes the model tractable but does not preserve the full algebraic structure of the original topological objects. We provide theoretical results supporting the stability of the representation under perturbations of the input field. The method is illustrated on a bow-echo convective system observed over Corsica on 18 August 2022, where the reduced state captures the main structural organization of the system over time. A comparison with standard nowcasting methods shows complementary behavior: pixel-based approaches provide better local accuracy, while the TDT framework better preserves the global spatial structure, as reflected by Wasserstein distances and persistence-based comparisons. Additional tests also indicate that the topological observables remain stable under small perturbations of the input field. The present study is based on a single case and should be understood as a proof of concept, rather than as a definitive validation. Future work will focus on validation on larger datasets and on the use of more advanced dynamical models.