Footprint Evaluation for Flux and Concentration Measurements for an Urban-Like Canopy with Coupled Lagrangian Stochastic and Large-Eddy Simulation Models

A footprint algorithm, based on a Lagrangian stochastic (LS) model embedded into a parallelized large-eddy simulation (LES) model, is used for the evaluation of flux and concentration footprints of passive scalars in flow in and above an urban-like canopy layer of a neutrally stratified 440m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$440 \hbox { m}$$\end{document} deep boundary layer. The urban-like canopy layer is realized by an aligned array of cuboids whose height H is 40m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$40\hbox { m}$$\end{document}. The canopy flow involves strong small-scale inhomogeneities although it is homogeneous at the large scale. The source height is 1m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\hbox { m}$$\end{document} (0.025H) above the ground in the street canyons, roughly mimicking traffic emissions. Footprints are evaluated for four heights from 0.25H to 2.5H, and for up to eight different horizontal sensor positions per measurement height, comprising sensor positions inside as well as outside of the street canyon that extend perpendicular to the mean wind direction. The LES-LS footprints are compared with footprints estimated by a conventional model (Kormann and Meixner, in Boundary-Layer Meteorol 99:207–224, 2001). It becomes evident that the local heterogeneity of the flow has a considerable impact on flux and concentration footprints. As expected, footprints for measurements within and right above the canopy layer show complex and completely different footprint shapes compared to the ellipsoidal shape obtained from conventional footprint models that assume horizontal homogeneity of the turbulent flow as well as the sources of passive scalars. Our results show the importance of street-canyon flow and turbulence for the vertical mixing of scalar concentration.