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Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

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Abstract

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.

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References

  • 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: 2666–2689

    Article  Google Scholar 

  • Baldocchi DD, Falge E, Gu L, Olson R, Hollinger D, Running S, Anthoni P, Bernhofer C, Davis K, Fuentes JD, Goldstein A, Katul G, Law BE, Lee X, Malhi Y, Meyers T, Munger JW, Oechel W, Pilegaard K, Schmid HP, 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: 2415–2435

    Article  Google Scholar 

  • Beare RJ, Cortes MAJ, Cuxart J, Esau I, Golaz C, Holtslag AAM, Khairoutdinov M, Kosovic B, Lewellen D, Lund T, Lundquist J, McCabe A, Macvean MK, Moene A, Noh Y, Poulos G, Raasch S, Sullivan PP (2006) An intercomparison of large-eddy simulations of the stable boundary-layer. Boundary-Layer Meteorol 118: 247–272

    Article  Google Scholar 

  • Cai X, Zhang R, Li Y (2006) A large-eddy simulation and Lagrangian stochastic study of heavy particle dispersion in the convective boundary layer. Boundary-Layer Meteorol 120: 413–435

    Article  Google Scholar 

  • Cai XH, Leclerc MY (2007) Forward-in-time and backward-in-time dispersion in the convective boundary layer: the concentration footprint. Boundary-Layer Meteorol 123: 201–218

    Article  Google Scholar 

  • de Roode SJ, Duynkerke PG, Jonker HJJ (2004) Large Eddy simulation: how large is large enough? J Atmos Sci 61: 403–421

    Article  Google Scholar 

  • Deardorff JW (1980) Stratocumulus-topped mixed layers derived from a three-dimensional model. Boundary- Layer Meteorol 18: 495–527

    Article  Google Scholar 

  • Drobinski P, Carlotti P, Redelsperger JL, Banta RM, Masson V, Newsom RK (2007) Numerical and experimental investigation of the neutral atmospheric surface layer. J Atmos Sci 64: 137–156

    Article  Google Scholar 

  • Finn D, Lamb B, Leclerc MY, Horst TW (1996) Experimental evaluation of analytical and Lagrangian surface-layer flux footprint models. Boundary-Layer Meteorol 80: 283–308

    Google Scholar 

  • Finnigan J (2004) The footprint concept in complex terrain. Agric For Meteorol 127: 117–129

    Article  Google Scholar 

  • Foken T, Leclerc MY (2004) Methods and limitations in validation of footprint models. Agric For Meteorol 127: 223–234

    Article  Google Scholar 

  • Garratt JR (1990) The internal boundary layer—a review. Boundary-Layer Meteorol 50: 171–203

    Article  Google Scholar 

  • Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, Cambridge, p 316

    Google Scholar 

  • Gash JHC (1986) A note on estimating the effect of a limited fetch on micrometeorological evaporation measurements. Boundary-Layer Meteorol 35: 409–414

    Article  Google Scholar 

  • Grant A (1992) The structure of turbulence in the near-neutral atmospheric boundary-layer. J Atmos Sci 49: 226–239

    Article  Google Scholar 

  • Hadfield MG (1994) Passive scalar diffusion from surface sources in the convective boundary layer. Boundary- Layer Meteorol 69: 417–448

    Article  Google Scholar 

  • Haenel HD, Grünhage L (1999) Footprint analysis: a closed analytical solution based on height-dependent profiles of wind speed and eddy viscosity. Boundary-Layer Meteorol 93: 395–409

    Article  Google Scholar 

  • Horst TW, Weil JC (1992) Footprint estimation for scalar flux measurements in the atmospheric surface layer. Boundary-Layer Meteorol 59: 279–296

    Article  Google Scholar 

  • Horst TW, Weil JC (1994) How far is far enough—the fetch requirements for micrometeorological measurement of surface fluxes. J Atmos Oceanic Technol 11: 1018–1025

    Article  Google Scholar 

  • Horst TW, Weil JC (1995) Corrigenda: How far is far enough—the fetch requirements for micrometeorological measurements of surface fluxes. J Atmos Oceanic Technol 12: 447

    Article  Google Scholar 

  • Inagaki A, Letzel MO, Raasch S, Kanda M (2006) Impact of surface heterogeneity on energy imbalance: a study using LES. J Meteorol Soc Jpn 84: 187–198

    Article  Google Scholar 

  • Kanda M, Inagaki A, Letzel MO, Raasch S (2004) LES study of the energy imbalance problem with eddy covariance fluxes. Boundary-Layer Meteorol 110: 381–404

    Article  Google Scholar 

  • Kemp JR, Thomson DJ (1996) Dispersion in stable boundary layers using large-eddy simulation. Atmos Environ 30: 2911–2923

    Article  Google Scholar 

  • Kim SW, Moeng CH, Weil JC, Barth MC (2005) Lagrangian particle dispersion modeling of the fumigation process using large-eddy simulation. J Atmos Sci 62: 1932–1946

    Article  Google Scholar 

  • Kljun N, Rotach MW, Schmid HP (2002) A three-dimensional backward Lagrangian footprint model for a wide range of boundary-layer stratifications. Boundary-Layer Meteorol 103: 205–226

    Article  Google Scholar 

  • Kljun N, Kormann R, Rotach MW, Meixner FX (2003) Comparison of the Lagrangian footprint model LPDM-B with an analytical footprint model. Boundary-Layer Meteorol 106: 349–355

    Article  Google Scholar 

  • Kljun N, Kastner-Klein P, Fedorovich E, Rotach MW (2004) Evaluation of a Lagrangian footprint model using data from a wind tunnel convective boundary layer. Agric For Meteorol 127: 189–201

    Article  Google Scholar 

  • Kosovic B, Curry JA (2000) A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J Atmos Sci 57: 1052–1068

    Article  Google Scholar 

  • Leclerc MY, Thurtell GW (1990) Footprint prediction of scalar fluxes using a Markovian analysis. Boundary- Layer Meteorol 52: 247–258

    Article  Google Scholar 

  • Leclerc MY, Shen SH, Lamb B (1997) Observations and large-eddy simulation modeling of footprints in the lower convective boundary layer. J Geophys Res Atmos 102: 9323–9334

    Article  Google Scholar 

  • Leclerc MY, Meskhidze N, Finn D (2003) Comparison between measured tracer fluxes and footprint model predictions over a homogeneous canopy of intermediate roughness. Agric For Meteorol 117: 145–158

    Article  Google Scholar 

  • Letzel MO, Raasch S (2003) Large-eddy simulation of thermally induced oscillations in the convective boundary layer. J Atmos Sci 60: 2328–2341

    Article  Google Scholar 

  • Letzel MO, Kanda M, Raasch S (2006) A new dimension of urban climate modelling with parallel large-eddy simulation. Preprints, 6th international conference on urban climate, Göteborg, Sweden, International Association for Urban Climate

  • Mahrt L (2008) The influence of transient flow distortion on turbulence in stable weak-wind conditions. Boundary-Layer Meteorol 127: 1–16

    Article  Google Scholar 

  • Moeng CH, Sullivan PP (1994) A comparison of shear-driven and buoyancy-driven planetary boundary-layer flows. J Atmos Sci 51: 999–1022

    Article  Google Scholar 

  • Nieuwstadt FTM, de Valk JPJMM (1987) A large-eddy simulation of buoyant and non-buoyant plume dispersion in the atmospheric boundary layer. Atmos Environ 21: 2573–2587

    Article  Google Scholar 

  • Pasquill F (1972) Some aspects of boundary layer description. Quart J Roy Meteorol Soc 98: 469–494

    Article  Google Scholar 

  • Patton EG, Sullivan PP, Moeng CH (2005) The influence of idealized heterogeneity on wet and dry planetary boundary layers coupled to the land surface. J Atmos Sci 62: 2078–2097

    Article  Google Scholar 

  • Piacsek SA, Williams GP (1970) Conservation properties of convection difference schemes. J Comp Phys 6: 392–405

    Article  Google Scholar 

  • Raasch S (2008) PALM group. [Available online at http://www.muk.uni-hannover.de/~raasch/PALM_group/]

  • Raasch S, Etling D (1998) Modeling deep oceanic convection: large-eddy simulation in comparison with laboratory experiments. J Phys Oceanogr 28: 1786–1802

    Article  Google Scholar 

  • Raasch S, Harbusch G (2001) An analysis of secondary circulations and their effects caused by small-scale surface inhomogeneities using large-eddy simulation. Boundary-Layer Meteorol 101: 31–59

    Article  Google Scholar 

  • Raasch S, Schröter M (2001) A large-eddy simulation model performing on massively parallel computers. Meteorol Z 10: 363–372

    Article  Google Scholar 

  • Rannik Ü, Aubinet M, Kurbanmuradov O, Sabelfeld KK, Markkanen T, Vesala T (2000) Footprint analysis for measurements over a heterogeneous forest. Boundary-Layer Meteorol 97: 137–166

    Article  Google Scholar 

  • 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: 163–189

    Article  Google Scholar 

  • Rebmann C, Göckede M, Foken T, Aubinet M, Aurela M, Berbigier P, Bernhofer C, Buchmann N, Carrara A, Cescatti A, Ceulemans R, Clement R, Elbers JA, Granier A, Grünwald T, Guyon D, Havrankova K, Heinesch B, Knohl A, Laurila T, Longdoz B, Marcolla B, Markkanen T, Miglietta F, Moncrieff J, Montagnani L, Moors E, Nardino M, Durcival JM, Rambal S, Rannik Ü, Rotenberg E, Sedlak P, Unterhuber G, Vesala T, Yakir D (2005) Quality analysis applied on eddy covariance measurements at complex forest sites using footprint modelling. Theor Appl Climatol 80: 121–141

    Article  Google Scholar 

  • Schmid HP (2002) Footprint modeling for vegetation atmosphere exchange studies: a review and perspective. Agric For Meteorol 113: 159–183

    Article  Google Scholar 

  • Schmid HP, Oke TR (1990) A model to estimate the source area contributing to turbulent exchange in the surface layer over patchy terrain. Quart J Roy Meteorol Soc 116: 965–988

    Article  Google Scholar 

  • Schröter M, Bange J, Raasch S (2000) Simulated airborne flux measurements in a LES generated convective boundary layer. Boundary-Layer Meteorol 95: 437–456

    Article  Google Scholar 

  • Schuepp PH, Leclerc MY, MacPherson JI, Desjardins RL (1990) Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation. Boundary-Layer Meteorol 50: 355–373

    Article  Google Scholar 

  • Schumann U, Sweet RA (1988) Fast Fourier-transforms for direct solution of Poisson equation with staggered boundary-conditions. J Comp Phys 75: 123–137

    Article  Google Scholar 

  • Steinfeld G, Letzel MO, Raasch S, Kanda M, Inagaki A (2007) Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study. Boundary-Layer Meteorol 123: 77–98

    Article  Google Scholar 

  • Su HB, Leclerc MY (1998) Large-eddy simulation of trace gas footprints from infinite crosswind line sources inside a forest canopy. In: Proceedings of the 23rd conference on agricultural and forest meteorology. American Meteorological Society, Boston, pp 388–391

  • Sullivan PP, Horst TW, Lenschow DH, Moeng CH, Weil JC (2003) Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling. J Fluid Mech 482: 101–139

    Article  Google Scholar 

  • Thomson DJ (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180: 529–556

    Article  Google Scholar 

  • Valentini R, Matteucci G, Dolman AJ, Schulze ED, Rebmann C, Moors EJ, Granier A, Gross P, Jensen NO, Pilegaard K, Lindroth A, Grelle A, Bernhofer C, Grüwald T, Aubinet M, Ceulemans R, Kowalski AS, Vesala T, Rannik Ü, Berbigier P, Loustau D, Guomundsson J, Thorgeirsson H, Ibrom A, Morgenstern K, Clement R, Moncrieff J, Montagnani L, Minerbi S, Jarvis PG (2000) Respiration as the main determinant of carbon balance in European forests. Nature 404: 861–865

    Article  Google Scholar 

  • Vesala T, Kljun N, Rannik Ü, Rinne J, Sogachev A, Markkanen T, Sabelfeld K, Foken T, Leclerc MY (2008) Flux and concentration footprint modelling: state of the art. Environ Pollut 152: 653–666

    Article  Google Scholar 

  • Vinkovic I, Aguirre C, Ayrault M, Simoens S (2006) Large-eddy simulation of the dispersion of solid particles in a turbulent boundary layer. Boundary-Layer Meteorol 121: 283–311

    Article  Google Scholar 

  • Weil JC, Sullivan PP, Moeng CH (2004) The use of large-eddy simulations in Lagrangian particle dispersion models. J Atmos Sci 61: 2877–2887

    Article  Google Scholar 

  • Weil JC, Patton EG, Sullivan PP (2005) Lagrangian modeling of dispersion in the stable boundary layer. In: Extended abstracts, 17th symposium on boundary layers and turbulence. American Meteorological Society, San Diego, CA, USA

  • Willis GE, Deardorff JW (1976) A laboratory model of diffusion into the convective boundary layer. Quart J Roy Meteorol Soc 102: 427–445

    Article  Google Scholar 

  • Zagar N, Zagar M, Cedilnik J, Gregoric G, Rakovec J (2006) Validation of mesoscale low-level winds obtained by dynamical downscaling of ERA40 over complex terrain. Tellus 58: 445–455

    Google Scholar 

  • Zilitinkevich SS, Esau IN (2002) On integral measures of the neutral barotropic planetary boundary layer. Boundary-Layer Meteorol 104: 371–379

    Article  Google Scholar 

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Steinfeld, G., Raasch, S. & Markkanen, T. Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation. Boundary-Layer Meteorol 129, 225–248 (2008). https://doi.org/10.1007/s10546-008-9317-7

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