Abstract
Numerical simulations are widely 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. To improve prediction for air flows and pollution transport, we propose a Variational Data Assimilation (VarDA) model which assimilates data from sensors into the open-source, finite-element, fluid dynamics model Fluidity. VarDA is based on the minimization of a function which estimates the discrepancy between numerical results and observations assuming that the two sources of information, forecast and observations, have errors that are adequately described by error covariance matrices. The conditioning of the numerical problem is dominated by the condition number of the background error covariance matrix which is ill-conditioned. In this paper, a preconditioned VarDA model is presented, it is based on a reduced background error covariance matrix. The Empirical Orthogonal Functions (EOFs) method is used to alleviate the computational cost and reduce the space dimension. Experimental results are provided assuming observed values provided by sensors from positions mainly located on roofs of buildings.
Highlights
Introduction and MotivationNumerical simulations are widely 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
The condition in Formula (33) allows us to properly assimilate observed data even if the problem is solved in a reduced dimension space, i.e., by alleviating the computational cost
Numerical issues faced in developing a Variational Data Assimilation (VarDA) algorithm include the ill-conditioning of the background covariance matrix and the choice of the regularization parameter
Summary
Numerical simulations are widely 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. Big Data Mining and Analytics, December 2018, 1(4): 297–307 with which they are combined Those which have gained acceptance as powerful methods in the last ten years are the variational DA approaches[2,3] based on the minimization of a function which estimates the discrepancy between numerical results and observations assuming that the two sources of information, forecast and observations, have errors that are adequately described by error covariance matrices. The most popular DA software, which implements a VarDA model, is used to fix the regularization parameter equal to one It means that the forecasted and the observed data have the same weight. The necessity to run DA in real-time mandates a proper choice of numerical algorithms to regularize the ill posed problem, to compute the minimum as well as to introduce preconditioning
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