PBDW: a non-intrusive Reduced Basis Data Assimilation Method and its application to outdoor Air Quality Models

The challenges of understanding the impacts of air pollution require detailed information on the state of air quality. While many modeling approaches attempt to treat this problem, physically-based deterministic methods are often overlooked due to their costly computational requirements and complicated implementation. In this work we apply a non-intrusive reduced basis data assimilation method (known as PBDW state estimation) to air quality case studies with the goal of rendering methods based on parameterized partial differential equations (PDE) realistic in applications requiring quasi-real-time approximation and correction of model error in imperfect models. Reduced basis methods (RBM) aim to compute a cheap and accurate approximation of a physical state using approximation spaces made of a suitable sample of solutions to the problem. One of the keys of these techniques is the decomposition of the computational work into an expensive one-time offline stage and a low-cost parameter-dependent online stage. Traditional RBMs require modifying the assembly routines of the computational code, an intrusive procedure. We propose a less intrusive reduced method using data assimilation for measured pollution concentrations. In case studies presented in this work, the method allows to correct for unmodeled physics and treat cases of unknown parameter values, all while significantly reducing online computational time.