Boundary-Layer Meteorology

, 141:301 | Cite as

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

  • Daniel F. Nadeau
  • Eric R. Pardyjak
  • Chad W. Higgins
  • Harinda Joseph S. Fernando
  • Marc B. Parlange
Article

Abstract

A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition sub-periods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t−2 (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.

Keywords

Afternoon transition Curve fitting Decay of convective turbulence Early evening transition Sensible heat flux Surface layer Turbulent kinetic energy 

References

  1. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Publications, New York, p 1046Google Scholar
  2. Acevedo OC, Fitzjarrald DR (2001) The early evening surface-layer transition: temporal and spatial variability. J Atmos Sci 58: 2650–2667CrossRefGoogle Scholar
  3. Basu S, Vinuesa JF, Swift A (2008) Dynamic LES modeling of a diurnal cycle. J Appl Meteorol Climatol 47: 1156–1174CrossRefGoogle Scholar
  4. Beare RJ, Edwards JM, Lapworth AJ (2006) Simulation of the observed evening transition and nocturnal boundary layers: large-eddy simulation. Q J Roy Meteorol Soc 132: 81–99CrossRefGoogle Scholar
  5. Beyrich F, Mengelkamp HT (2006) Evaporation over a heterogeneous land surface: EVA_GRIPS and the LITFASS-2003 experiment—an overview. Boundary-Layer Meteorol 121: 5–32CrossRefGoogle Scholar
  6. Beyrich F, Leps JP, Mauder M, Bange J, Foken T, Huneke S, Lohse H, Ldi A, Meijninger W, Mironov D, Weisensee U, Zittel P (2006) Area-averaged surface fluxes over the LITFASS region based on eddy-covariance measurements. Boundary-Layer Meteorol 121: 33–65CrossRefGoogle Scholar
  7. Bou-Zeid E, Higgins CW, Huwald H, Meneveau C, Parlange MB (2010) Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier. J Fluid Mech 665: 480–515CrossRefGoogle Scholar
  8. Brazel AJ, Fernando HJS, Hunt JCR, Selover N, Hedquist BC, Pardyjak E (2005) Evening transition observations in Phoenix, Arizona. J Appl Meteorol 44: 99–112CrossRefGoogle Scholar
  9. Brown AR, Cederwall RT, Chlond A, Duynkerke PG, Golaz JC, Khairoutdinov M, Lewellen DC, Lock AP, MacVean MK, Moeng CH, Neggers RAJ, Siebesma AP, Stevens B (2002) Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land. Q J Roy Meteorol Soc 128: 1075–1093CrossRefGoogle Scholar
  10. Caughey SJ, Wyngaard JC, Kaimal JC (1979) Turbulence in the evolving stable boundary-layer. J Atmos Sci 36: 1041–1052Google Scholar
  11. Cheng YG, Parlange MB, Brutsaert W (2005) Pathology of Monin-Obukhov similarity in the stable boundary layer. J Geophys Res Atmos 110: D06101. doi:10.1029/2004jd004923 CrossRefGoogle Scholar
  12. Cole GS, Fernando HJS (1998) Some aspects of the decay of convective turbulence. Fluid Dyn Res 23: 161–176CrossRefGoogle Scholar
  13. Comte-Bellot G, Corrsin S (1971) Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated ‘isotropic’ turbulence. J Fluid Mech 48: 273–337CrossRefGoogle Scholar
  14. De Silva IPD, Fernando HJS (1994) Oscillating grids as a source of nearly isotropic turbulence. Phys Fluids 6: 2455–2464CrossRefGoogle Scholar
  15. Deardorff JW (1970) Preliminary results from numerical integrations of unstable planetary boundary layer. J Atmos Sci 27: 1209–1211CrossRefGoogle Scholar
  16. Dolas PM, Ramchandran R, Sen Gupta K, Patil SM, Jadhav PN (2002) Atmospheric surface-layer processes during the total solar eclipse of 11 August 1999. Boundary-Layer Meteorol 104: 445–461CrossRefGoogle Scholar
  17. Emanuel KA (1994) Atmospheric convection. Oxford University Press, New York, p 580Google Scholar
  18. Fernando HJS (2002) Turbulence in stratified fluids. In: Grimshaw R (ed) Environmental stratified flows, vol III. Kluwer Academic Publishers, Norwell, 296 ppGoogle Scholar
  19. Girard-Ardhuin F, Benech B, Campistron B, Dessens J, Jacoby-Koaly S (2003) Remote sensing and surface observations of the response of the atmospheric boundary layer to a solar eclipse. Boundary-Layer Meteorol 106: 93–115CrossRefGoogle Scholar
  20. Goulart A, Degrazia G, Rizza U, Anfossi D (2003) A theoretical model for the study of convective turbulence decay and comparison with large-eddy simulation data. Boundary-Layer Meteorol 107: 143–155CrossRefGoogle Scholar
  21. Goulart A, Bodmann B, de Vilhena M, Soares P, Moreira D (2010) On the time evolution of the turbulent kinetic energy spectrum for decaying turbulence in the convective boundary layer. Boundary-Layer Meteorol 138: 61–75CrossRefGoogle Scholar
  22. Grant ALM (1997) An observational study of the evening transition boundary-layer. Q J Roy Meteorol Soc 123: 657–677CrossRefGoogle Scholar
  23. Higgins CW, Meneveau C, Parlange MB (2007) The effect of filter dimension on the subgrid-scale stress, heat flux, and tensor alignments in the atmospheric surface layer. J Atmos Ocean Technol 24: 360–375CrossRefGoogle Scholar
  24. Kang HS, Chester S, Meneveau C (2003) Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation. J Fluid Mech 480: 129–160CrossRefGoogle Scholar
  25. Kleissl J, Kumar V, Meneveau C, Parlange MB (2006) Numerical study of dynamic Smagorinsky models in large-eddy simulation of the atmospheric boundary layer: validation in stable and unstable conditions. Water Resour Res 42: W06D10. doi:10.1029/2005wr004685 CrossRefGoogle Scholar
  26. Kumar V, Kleissl J, Meneveau C, Parlange MB (2006) Large-eddy simulation of a diurnal cycle of the atmospheric boundary layer: atmospheric stability and scaling issues. Water Resour Res 42: W06D09. doi:10.1029/2005WR004651 CrossRefGoogle Scholar
  27. Kumar V, Svensson G, Holtslag AAM, Meneveau C, Parlange MB (2010) Impact of surface flux formulations and geostrophic forcing on large-eddy simulations of diurnal atmospheric boundary layer flow. J Appl Meteorol Climatol 49: 1496–1516CrossRefGoogle Scholar
  28. Metzger M, Holmes H (2008) Time scales in the unstable atmospheric surface layer. Boundary-Layer Meteorol 126: 29–50CrossRefGoogle Scholar
  29. Nieuwstadt FTM, Brost RA (1986) The decay of convective turbulence. J Atmos Sci 43: 532–546CrossRefGoogle Scholar
  30. Pardyjak ER (2001) Atmospheric boundary layer dynamics in regions of complex terrain. PhD thesis, Arizona State UniversityGoogle Scholar
  31. Pardyjak ER, Monti P, Fernando HJS (2002) Flux Richardson number measurements in stable atmospheric shear flows. J Fluid Mech 459: 307–316CrossRefGoogle Scholar
  32. Pardyjak ER, Fernando HJS, Hunt JCR, Grachev AA, Anderson J (2009) A case study of the development of nocturnal slope flows in a wide open valley and associated air quality implications. Meteorol Z 18: 85–100CrossRefGoogle Scholar
  33. Pino D, Jonker HJJ, de Arellano JVG, Dosio A (2006) Role of shear and the inversion strength during sunset turbulence over land: characteristic length scales. Boundary-Layer Meteorol 121: 537–556CrossRefGoogle Scholar
  34. Ramamurthy P, Pardyjak ER (2010) Understanding the behavior of carbon dioxide and surface energy fluxes in the semi-arid Salt Lake Valley Utah USA. Atmos Environ 45: 73–84CrossRefGoogle Scholar
  35. Sorbjan Z (1997) Decay of convective turbulence revisited. Boundary-Layer Meteorol 82: 501–515CrossRefGoogle Scholar
  36. Sorbjan Z (2007) A numerical study of daily transitions in the convective boundary layer. Boundary-Layer Meteorol 123: 365–383CrossRefGoogle Scholar
  37. Strang EJ, Fernando HJS (2001) Entrainment and mixing in stratified shear flows. J Fluid Mech 428: 349–386CrossRefGoogle Scholar
  38. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, The Netherlands, p 666Google Scholar
  39. Stull RB (2000) Meteorology for scientists and engineers. Brooks/Cole Thomson, Pacific Grove, p 502Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Daniel F. Nadeau
    • 1
  • Eric R. Pardyjak
    • 2
  • Chad W. Higgins
    • 1
  • Harinda Joseph S. Fernando
    • 3
  • Marc B. Parlange
    • 1
  1. 1.School of Architecture, Civil and Environmental EngineeringÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Department of Mechanical EngineeringUniversity of UtahSalt Lake CityUSA
  3. 3.Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA

Personalised recommendations