Turbulent Schmidt number for source term estimation using Bayesian inference

Publication date: 15 November 2017
Source:Building and Environment, Volume 125
Author(s): Fei Xue, Xiaofeng Li, Ryozo Ooka, Hideki Kikumoto, Weirong Zhang
Source term estimation (STE) addresses the retrieval of emission source information, including location and strength, based on available information. STE can be viewed as an assimilation process of the observed concentration data measured by a sensor network and the predicted concentration data provided by a dispersion model. When considering emissions in complex urban areas, computational fluid dynamics (CFD) approaches are generally used to provide building-resolving results; however, the value of a key parameter, the turbulent Schmidt number $S{c}_t$, has remained an arbitrary choice. Therefore, it is important to investigate the role of $S{c}_t$ in STE problems and determine its optimum value for the purpose of obtaining better estimation results. In this paper, the impact of $S{c}_t$ on STE problems is examined, and Bayesian inference is used to improve estimation accuracy by treating $S{c}_t$ as an extra unknown parameter. A wind tunnel experiment with a constant point tracer source in an urban-like geometry is used for demonstration. The results show that $S{c}_t$ has a major impact on estimation. Larger $S{c}_t$ values shift the estimated location towards the upwind direction and decrease the estimated strength. Compared with a conventional estimation method performed by using a pre-assigned value of $S{c}_t=0.7$, treating $S{c}_t$ as an unknown improves point estimates, while the uncertainty increases since the proposed method introduces an extra unknown parameter. For source strength, more improvement in point estimates and a larger increase in uncertainty are shown due to its greater sensitivity of $S{c}_t$ compared with the source location.