A reduced order with data assimilation model: Theory and practice

Numerical simulations are extensively used as a predictive tool to better understand complex air flows and pollution transport on the scale of individual buildings, city blocks and entire cities. Fast-running Non-Intrusive Reduced Order Model (NIROM) for predicting the turbulent air flows has been proved to be an efficient method to provide numerical forecasting results. However, due to the reduced space on which the model operates, the solution includes uncertainties. Additionally, any computational methodology contributes to uncertainty due to finite precision and the consequent accumulation and amplification of round-off errors. Taking into account these uncertainties is essential for the acceptance of any numerical simulation. In this paper we combine the NIROM method with Data Assimilation (DA), the main question is how to incorporate data (e.g. from physical measurements) in models in a suitable way, in order to improve model predictions and quantify prediction uncertainty. Here, the focus is on the prediction of nonlinear dynamical systems (the classical application example being weather forecasting). DA is an uncertainty quantification technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. The Reduced Order Data Assimilation (RODA) model we propose in this paper achieves both efficiency and accuracy including Variational DA into NIROM. The model we present is applied to the pollutant dispersion within an urban environment.