Boundary-Layer Meteorology

, Volume 107, Issue 2, pp 401–427

Improvement of the K-profile Model for the Planetary Boundary Layer based on Large Eddy Simulation Data

  • Y. Noh
  • W. G. Cheon
  • S. Y. Hong
  • S. Raasch
Article

Abstract

Modifications of the widely used K-profile model of the planetary boundary layer (PBL), reported by Troen and Mahrt (TM) in 1986, are proposed and their effects examined by comparison with large eddy simulation (LES) data. The modifications involve three parts. First, the heat flux from the entrainment at the inversion layer is incorporated into the heat and momentum profiles, and it is used to predict the growth of the PBL directly. Second, profiles of the velocity scale and the Prandtl number in the PBL are proposed, in contrast to the constant values used in the TM model. Finally, non-local mixing of momentum was included. The results from the new PBL model and the original TM model are compared with LES data. The TM model was found to give too high PBL heights in the PBL with strong shear, and too low heights for the convection-dominated PBL, which causes unrealistic heat flux profiles. The new PBL model improves the predictability of the PBL height and produces profiles that are more realistic. Moreover, the new PBL model produces more realistic profiles of potential temperature and velocity. We also investigated how each of these three modifications affects the results, and found that explicit representation of the entrainment rate is the most critical.

K-profile model Large eddy simulation (LES) Non-local mixing Planetary boundary layer (PBL) PBL model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdella, K. and McFarlane, N.: 1997, 'A New Second-Order Closure Scheme for the Planetary Boundary Layer', J. Atmos. Sci. 54, 1850–1867.Google Scholar
  2. Asselin, R.: 1972, 'Frequency Filter for Time Integrations', Mon. Wea. Rev. 100, 487–490.Google Scholar
  3. Ayotte, K. W., Sullivan, P. P., Andrén, A., Doney, S. C., Holtslag, A. A., Large, W. G., McWilliams, J. C., Moeng, C. H., Otte, M. J., Tribbia, J. J., and Wyngaard, J. C.: 1996, 'An Evaluation of Neutral and Convective Planetary Boundary-Layer Parameterizations Relative to Large Eddy Simulations', Boundary-Layer Meteorol. 79, 131–175.Google Scholar
  4. Ball, F. K.: 1960, 'Control of Inversion Height by Surface Heating', Quart. J. Roy. Meteorol. Soc. 44, 2823–2838.Google Scholar
  5. Brown, A. R.: 1996, 'Evaluation of Parameterization Schemes for the Convective Boundary Layer Using Large-Eddy Simulation Results', Boundary-Layer Meteorol. 81, 167–200.Google Scholar
  6. Brown, A. R. and Grant, A. L. M.: 1997, 'Non-Local Mixing of Momentum in the Convective Boundary Layer', Boundary-Layer Meteorol. 84, 1–22.Google Scholar
  7. Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, 'Flux-Profile Relationships in the Atmospheric Surface Layer', J. Atmos. Sci. 28, 181–189.Google Scholar
  8. Chrobock, G., Raasch, S., and Etling, D.: 1992, 'A Comparison of Local and Non-Local Turbulence Closure Methods for the Case of a Cold Air Outbreak', Boundary-Layer Metorol. 58, 69–90.Google Scholar
  9. Deardorff, J. W.: 1966, 'The Counter Gradient Heat Flux in the Lower Atmosphere and in the Laboratory', J. Atmos. Sci. 23, 503–506.Google Scholar
  10. Deardorff, J. W.: 1979, 'Prediction of Convective Mixed-Layer Entrainment for Realistic Capping Inversion Structure', J. Atmos. Sci. 36, 205–236.Google Scholar
  11. Deardorff, J. W.: 1980, 'Stratocumulus-Capped Mixed Layers Derived from a Three-Dimensional Model', Boundary-Layer Meteorol. 18, 495–527.Google Scholar
  12. Deardorff, J. W., Willis, G. E., and Stockton, B. H.: 1980, 'Laboratory Studies of the Entrainment Zone of a Convective Mixed Layer', J. Fluid Mech. 100, 41–64.Google Scholar
  13. Driedonks, A. G. M.: 1982, 'Models and Observations of the Growth of the Atmospheric Boundary Layer', Boundary-Layer Meteorol. 23, 283–306.Google Scholar
  14. Frech, M and Mahrt, L.: 1995, 'A Two-Scale Mixing Formulation for the Atmospheric Boundary Layer', Boundary-Layer Meteorol. 73, 91–104.Google Scholar
  15. Holtslag, A. A. M. and Boville, B. A.: 1993, 'Local Versus Non-Local Boundary Layer Diffusion in a Global Climate Model', J. Climate 6, 1825–1842.Google Scholar
  16. Holtslag, A. A. M. and Moeng, C. H.: 1991, 'Eddy Diffusivity and Countergradient Transport in the Convective Boundary Layer', J. Atmos. Sci. 48, 1690–1698.Google Scholar
  17. Hong, S. Y. and Pan, H. L.: 1996, 'Non-Local Boundary Layer Vertical Diffusion in a Medium-Range Forecast Model', Mon. Wea. Rev. 124, 2322–2339.Google Scholar
  18. Lenschow, D. H., Wyngaard, J. C., and Pennell, W. T.: 1980, 'Mean Field and Second Moment Budget in a Baroclinic, Convective Boundary Layer', J. Atmos. Sci. 37, 1313–1326.Google Scholar
  19. Lock, A. P.: 1998, 'The Parameterization of Entrainment in Cloudy Boundary Layers', Quart. J. Roy. Meteorol. Soc. 124, 2729–2753.Google Scholar
  20. Lock, A. P., Brown, A. R., Bush, M. R., Martin, G. M. and Smith, R. N. B.: 2000, 'A New Boundary Layer Mixing Scheme. Part I: Scheme Description and Single-Column Model Tests', Mon. Wea. Rev. 128, 3187–3199.Google Scholar
  21. Lüpkes, C. and Schlünzen, K. H.: 1996, 'Modeling the Arctic Convective Boundary-Layer with Different Turbulence Parameterizations', Boundary-Layer Meteorol. 79, 107–130.Google Scholar
  22. Mahrt, L., Hearld, R. C., Lenschow, D. H., Stankov, B. B., and Troen, I.: 1979, 'An Observational Study of the Nocturnal Boundary Layer', Boundary-Layer Meteorol. 17, 247–264.Google Scholar
  23. Mellor, G. L. and Yamada, T.: 1982, 'Development of a Turbulence Closure Model for Geophysical Fluid Problems', Rev. Geophys. Space Phys. 20, 851–875.Google Scholar
  24. Moeng, C. H. and Sullivan, P. P.: 1994, 'A Comparison of Shear and Buoyancy-Driven Planetary Boundary Layer Flows', J. Atmos. Sci. 51, 999–1022.Google Scholar
  25. Panofsky, H. M. and D4utton, J. A.: 1984, Atmospheric Turbulence: Models and Methods for Engineering Applications, Wiley & Sons, 397 pp.Google Scholar
  26. Piacsek, S. A. and Williams, G. P.: 1970, 'Conservation Properties of Convection Difference Schemes', J. Appl. Meteorol. 9, 856–861.Google Scholar
  27. Raasch, S. and Etling, D.: 1991, 'Numerical Simulation of Rotating Turbulent Thermal Convection', Beitr. Phys. Atmosph. 64, 185–199.Google Scholar
  28. Raasch, S. and Etling, D.: 1998, 'Modelling Deep Ocean Convection: Large Eddy Simulation in Comparison with Laboratory Experiments', J. Phys. Oceanog. 28, 1786–1802.Google Scholar
  29. Raasch, S. and 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.Google Scholar
  30. Raasch, S. and Schröter, M.: 2001, 'PALM-A Large Eddy Simulation Model Performing on Massively Parallel Computers', Z. Meteorol. 10, 363–372.Google Scholar
  31. Schröter, M., Bange, J., and Raasch, S.: 2000, 'Simulated Airborne Flux Measurements in a LES Generated Convective Boundary Layer', Boundary-Layer Meteorol. 95, 437–465.Google Scholar
  32. Sorbjan, Z.: 1996, 'Numerical Study of Penetrative and “Solid Lid” Nonpenetrative Convective Boundary Layers', J. Atmos. Sci. 53, 101–112.Google Scholar
  33. Stull, R. B.: 1976, 'The Energetics of Entrainment across a Density Interface', J. Atmos. Sci. 33, 1260–1267.Google Scholar
  34. Stull, R. B.: 1984, 'Transilient Turbulence Theory. Part I: The Concept of Eddy Mixing across Finite Distances', J. Atmos. Sci. 41, 3351–3367.Google Scholar
  35. Stull, R. B.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.Google Scholar
  36. Therry, G. and Lacarrére, P.: 1983, 'Improving the Eddy Kinetic Energy Model for Planetary Boundary Layer Description', Boundary-Layer Meteorol. 25, 63–88.Google Scholar
  37. Troen, I. and Mahrt, L.: 1986, 'A Simple Model of the Atmospheric Boundary Layer: Sensitivity to Surface Evaporation', Boundary-Layer Meteorol. 37, 129–148.Google Scholar
  38. vanZanten, M. C., Duynkerke, P. G., and Cuijpers, W. M.: 1999, 'Entrainment Parameterization in Convective Boundary Layers', J. Atmos. Sci. 56, 813–828.Google Scholar
  39. Vogelezang, D. H. P. and Holtslag, A. A. M.: 1996, 'Evaluation and Model Impacts of Alternative Boundary-Layer Height', Boundary-Layer Meteorol. 81, 245–269.Google Scholar
  40. Wetzel, P. J.: 1982, 'Toward Parameterization of the Stable Boundary Layer', J. Appl. Meteorol. 21, 7–13.Google Scholar
  41. Wittich, K. P. and Roth, R.: 1984, 'A Case Study of Non-Local Wind and Temperature Profiles over the Inhomogeneous Terrain of Northern Germany with Some Considerations of Turbulent Fluxes', Boundary-Layer Meteorol. 28, 169–186.Google Scholar
  42. Zeman, O. and Tennekes, H.: 1977, 'Parameterization of the Turbulent Kinetic Energy Budget at the Top of the Daytime Boundary Layer', J. Atmos. Sci. 34, 111–123.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Y. Noh
    • 1
  • W. G. Cheon
    • 1
  • S. Y. Hong
    • 1
  • S. Raasch
    • 2
  1. 1.Department of Atmospheric SciencesYonsei UniversitySeoulKorea
  2. 2.Institute of Meteorology and ClimatologyUniversity of HannoverGermany

Personalised recommendations