Boundary-Layer Meteorology

, Volume 157, Issue 2, pp 191–217 | Cite as

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

  • Antti HellstenEmail author
  • Sofia-M. Luukkonen
  • Gerald Steinfeld
  • Farah Kanani-Sühring
  • Tiina Markkanen
  • Leena Järvi
  • Juha Lento
  • Timo Vesala
  • Siegfried Raasch


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 \(440 \hbox { m}\) deep boundary layer. The urban-like canopy layer is realized by an aligned array of cuboids whose height H is \(40\hbox { m}\). The canopy flow involves strong small-scale inhomogeneities although it is homogeneous at the large scale. The source height is \(1\hbox { m}\) (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.


Concentration footprint Flux footprint Lagrangian stochastic model Large-eddy simulation Urban canopy 



This study was supported by the German Science Foundation (DFG) under grants RA 617/13-1, RA 617/23-1, and by the German Academic Exchange Service (DAAD), by the Finnish Centre of Excellence in Atmospheric Science – From Molecular and Biological Processes to the Global Climate (project 272041), EU project InGOS Integrated non-CO2 greenhouse gas observation system and ICOS 271878, ICOS-Finland 281255 and ICOS-ERIC 281250 and grant number 138328 funded by the Academy of Finland, and by the European Research Council funded project “Atmospheric planetary boundary layers: Physics, modelling and role in the earth system” (PBL-PMES) (Grant agreement number 227915) and by the CityClim project funded by the Academy of Finland (Grant number 277664). The final computations have been performed on the Cray XC-40 supercomputer of the Center of Scientific Computing (CSC Oy) in Espoo, Finland. CSC is warmly acknowledged for providing us the necessary parallel computing capacity. Preparatory simulations were partly carried out on the IBM Regatta P690 series of the Norddeutscher Verbund für Hoch- und Hochstleistungsrechnen (HLRN) in Hannover/Berlin, Germany and partly on Sun Fire x4600 Cluster Tsubame at the Global Scientific Information and Computing Center of the Tokyo Institute of Technology. Mr. Jin Zhang is acknowledged for modifying the particle boundary condition algorithm of the PALM model for non-flat topographies. Three anonymous reviewers helped improve the manuscript and provided different viewpoints to the problem.


  1. Andren A, Brown A, Graf J, Mason P, Moeng C, Nieuwstadt F, Schumann U (1994) Large-eddy simulation of a neutrally stratified boundary layer: a comparison of four computer codes. Q J R Meteorol Soc 120:1457–1484CrossRefGoogle Scholar
  2. Aubinet M, Vesala T, Papale D (eds) (2012) Eddy covariance. A practical guide to measurement and data analysis. Springer, Dordrecht, 438 ppGoogle Scholar
  3. Avissar R, Schmidt T (1998) An evaluation of the scale at which ground-surface heat flux patchiness affects the convective boundary layer using large-eddy simulations. J Atmos Sci 55:2666–2689CrossRefGoogle Scholar
  4. Baldocchi D, Falge E, Gu L, Olson R, Hollinger D, Running S, Anthoni P, Bernhofer C, Davis K, Fuentes J, Goldstein A, Katul G, Law B, Lee X, Malhi Y, Meyers T, Munger J, Oechel W, Pilegaard K, Schmid H, Valentini R, Verma S, Vesala T, Wilson K, Wofsy S (2001) FLUXNET: a new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapour and energy flux densities. Bull Am Meteorol Soc 82:2415–2435CrossRefGoogle Scholar
  5. Beare R, Cortes M, Cuxart J, Esau I, Golaz C, Holtslag A, Khairoutdinov M, Kosovic B, Lewellen D, Lund T, Lundquist J, McCabe A, Macvean M, Moene A, Noh Y, Poulos G, Raasch S, Sullivan P (2006) An intercomparison of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol 118:247–272CrossRefGoogle Scholar
  6. Cai X, Leclerc M (2007) Forward-in-time and backward-in-time dispersion in the convective boundary layer: the concentration footprint. Boundary-Layer Meteorol 123:201–218CrossRefGoogle Scholar
  7. Cai X, Chen J, Desjardins R (2010) Flux footprints in the convective boundary layer: large-eddy simulation and Lagrangian stochastic modelling. Boundary-Layer Meteorol 137:31–47CrossRefGoogle Scholar
  8. Castillo M, Inagaki A, Kanda M (2011) The effects of inner- and outer-layer turbulence in a convective boundary layer on the near-neutral inertial sublayer over an urban like surface. Boundary-Layer Meteorol 140:453–469CrossRefGoogle Scholar
  9. Christen A, Coops N, Crawford BRK, Liss K, Olchovski I, Tooke TR, van der Laan M, Voogt JA (2011) Validation of modeled carbon-dioxide emissions from an urban neighborhood with direct eddy-covariance measurements. Atmos Environ 45:6057–6069CrossRefGoogle Scholar
  10. Coceal O, Thomas T, Castro I, Belcher S (2006) Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol 121:491–519CrossRefGoogle Scholar
  11. Deardorff J (1970) Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection. J Atmos Sci 27:1211–1213CrossRefGoogle Scholar
  12. Deardorff J (1980) Stratoculumus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18:495–527CrossRefGoogle Scholar
  13. Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32:519–571CrossRefGoogle Scholar
  14. Flesch T (1996) The footprint for flux measurements, from backward Lagrangian stochastic models. Boundary-Layer Meteorol 78:399–404CrossRefGoogle Scholar
  15. Flesch T, Wilson J, Yee E (1995) Backward-time Lagrangian stochastic dispersion models, and their application to estimate gaseous emissions. J Appl Meteorol 34:1320–1332CrossRefGoogle Scholar
  16. Foken T, Leclerc M (2004) Methods and limitations in validation of footprint models. Agric For Meteorol 127:223–234CrossRefGoogle Scholar
  17. Hanna S, Tehranian S, Carissimo B, MacDonald R, Lohner R (2002) Comparisons of model simulations with observations of mean flow and turbulence within simple obstacle arrays. Atmos Environ 36:5067–5079CrossRefGoogle Scholar
  18. Hellsten A, Zilitinkevich S (2013) Role of convective structures and background turbulence in the dry convective boundary layer. Boundary-Layer Meteorol 149:323–353CrossRefGoogle Scholar
  19. Horst T, Weil J (1992) Footprint estimation for scalar flux measurements in the atmospheric surface layer. Boundary-Layer Meteorol 59:279–296CrossRefGoogle Scholar
  20. Inagaki A, Kanda M (2008) Turbulent flow similarity over an array of cubes in near-neutrally stratified atmospheric flow. J Fluid Mech 615:101–120CrossRefGoogle Scholar
  21. Inagaki A, Letzel M, Raasch S, Kanda M (2006) Impact of surface heterogeneity on energy imbalance: a study using LES. J Meterol Soc Jpn 84:187–198CrossRefGoogle Scholar
  22. Kanda M, Inagaki A, Letzel M, Raasch S (2004) LES study of the energy imbalance problem with eddy covariance fluxes. Boundary-Layer Meteorol 110:381–404CrossRefGoogle Scholar
  23. Korman R, Meixner F (2001) An analytical footprint model for non-neutral stratification. Boundary-Layer Meteorol 99:207–224CrossRefGoogle Scholar
  24. Kotthaus S, Grimmond C (2012) Identification of micro-scale anthropogenic \({\rm CO}_{2}\), heat and moisture sources—processing eddy covariance fluxes for a dense urban environment. Atmos Environ 57:301–316CrossRefGoogle Scholar
  25. Kurbanmuradov O, Rannik Ü, Sabelfeld K, Vesala T (2001) Evaluation of mean concentration and fluxes in turbulent flows by Lagrangian stochastic models. Math Comput Simul 54:459–476CrossRefGoogle Scholar
  26. Letzel M, Raasch S (2003) Large-eddy simulation of thermally induced oscillations in the convective boundary layer. J Atmos Sci 60:2328–2341CrossRefGoogle Scholar
  27. Letzel M, Krane M, Raasch S (2008) High resolution urban large-eddy simulation studies from street canyon to neighbourhood scale. Atmos Environ 42:8770–8784CrossRefGoogle Scholar
  28. Markkanen T, Steinfeld G, Kljun N, Raasch S, Foken T (2009) Comparison of conventional Lagrangian stochastic footprint models against LES driven footprint estimates. Atmos Chem Phys 9:5575–5586CrossRefGoogle Scholar
  29. Markkanen T, Steinfeld G, Kljun N, Raasch S, Foken T (2010) A numerical case study on footprint model performance under inhomogeneous flow conditions. Meteorol Z 19:539–547CrossRefGoogle Scholar
  30. McDonald R, Griffiths R, Hall D (1998) An improved method for the estimation of surface roughness of obstacle arrays. Atmos Environ 32:1857–1864CrossRefGoogle Scholar
  31. Nordbo A, Järvi L, Haapanala S, Moilanen J, Vesala T (2013) Intra-city variation in urban morphology and turbulence structure in Helsinki, Finland. Boundary-Layer Meteorol 146:469–496CrossRefGoogle Scholar
  32. Pascheke F, Barlow J, Robins A (2008) Wind-tunnel modelling of dispersion from a scalar area source in urban-like roughness. Boundary-Layer Meteorol 126:103–124CrossRefGoogle Scholar
  33. Piacsek S, Williams G (1970) Conservation properties of convection difference schemes. J Comput Phys 6:392–405CrossRefGoogle Scholar
  34. Pope S (2008) Turbulent flows. Cambridge University Press, Cambridge 771 ppGoogle Scholar
  35. Raasch S, Schröter M (2001) PALM—a large-eddy simulation model performing on massively parallel computers. Meteorol Z 10:363–372CrossRefGoogle Scholar
  36. Rannik Ü, Markkanen T, Raittila J, Hari P, Vesala T (2003) Turbulence statistics inside and over forest: influence on footprint prediction. Boundary-Layer Meteorol 109:163–189CrossRefGoogle Scholar
  37. Schmid H (2002) Footprint modelling for vegetation atmosphere exchange studies: a review and perspective. Agric For Meteorol 113:159–183CrossRefGoogle Scholar
  38. Schröter M, Bange J, Raasch S (2000) Simulated airborne flux measurements in a LES generated convective boundary layer. Boundary-Layer Meteorol 95:437–456CrossRefGoogle Scholar
  39. Schumann U, Sweet R (1988) Fast-fourier-transforms for direct solution of Poisson equation with staggered boundary-conditions. J Comput Phys 75:123–137CrossRefGoogle Scholar
  40. Steinfeld G, Raasch S, Markkanen T (2008) Footprints in homogeneously and heterogeneously driven boundary layers derived from a Lagrangian stochastic particle model embedded into large-eddy simulation. Boundary-Layer Meteorol 129:225–248CrossRefGoogle Scholar
  41. Thomson D (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180:529–556CrossRefGoogle Scholar
  42. Vesala T, Kljun N, Rannik Ü, Rinne J, Sogachev A, Markkanen T, Sabelfeld K, Foken T, Leclerc M (2008) Flux and concentration footprint modelling: state of the art. Environ Pollut 152:653–666CrossRefGoogle Scholar
  43. Weil J, Horst T (1992) Footprint estimates for atmospheric flux measurements in the convective boundary layer. In: Schwartz S, Slinn W (eds) Precipitation scavenging and atmosphere–surface exchange. Hemisphere Publishing, Washington, D.C., pp 717–728Google Scholar
  44. Weil J, Sullivan P, Moeng C (2004) The use of large-eddy simulations in Lagrangian particle dispersion models. J Atmos Sci 61:2877–2887CrossRefGoogle Scholar
  45. Xie Z, Castro I (2006) LES and RANS for turbulent flows over arrays of wall-mounted obstacles. Flow Turbul Combust 76:291–312CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Antti Hellsten
    • 1
    Email author
  • Sofia-M. Luukkonen
    • 2
  • Gerald Steinfeld
    • 3
  • Farah Kanani-Sühring
    • 4
  • Tiina Markkanen
    • 1
  • Leena Järvi
    • 2
  • Juha Lento
    • 5
  • Timo Vesala
    • 2
  • Siegfried Raasch
    • 4
  1. 1.Finnish Meteorological InstituteHelsinkiFinland
  2. 2.Division of Atmospheric Sciences, Department of PhysicsUniversity of HelsinkiHelsinkiFinland
  3. 3.Institute of Physics, AG Turbulence, Wind Energy and Stochastics – TWISTOldenburgGermany
  4. 4.Institut für Meteorologie und KlimatologieLeibniz Universität HannoverHannoverGermany
  5. 5.CSC - IT Center for Science Ltd.EspooFinland

Personalised recommendations