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Theoretical models of the height of the atmospheric boundary layer and turbulent entrainment at its upper boundary

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Abstract

The planetary boundary layer (PBL), which directly interacts with the underlying surface, differs significantly in its nature from the low-turbulent stably stratified free atmosphere. Fluctuations of the Earth’s surface heat balance immediately affect the PBL and assimilate there owing to the effective mechanism of turbulent heat transfer. In this case the upper boundary of the PBL plays the role of a cover, preventing the direct penetration of thermal effects and contaminants into an overlying atmospheric layer. In view of this, air pollution is especially dangerous when associated with shallow PBL. In addition, local peculiarities of climate change are mainly determined by the PBL height due to the high sensitivity of thin stably stratified PBLs to the thermal effects. Deep convective PBLs are not very sensitive to weak thermal effects, but they significantly affect the formation of convective cloudiness and the climate system as a whole by means of the turbulent entrainment of the thermal energy, humidity, aerosols, and other admixtures through the upper boundary. The PBL height and turbulent entrainment must be calculated when simulating and forecasting air pollution, abnormal frosts and heat, and other hazardous phenomena. In this paper we discuss the state-of-the-art knowledge in the area of PBL height simulation and suggest a new model of turbulent entrainment for convective PBLs.

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References

  1. S. S. Zilitinkevich and I. N. Esau, “Planetary Boundary Layer Feedbacks in Climate System and Triggering Global Warming in the Night, in Winter and at High Latitudes,” Geogr. Environ. Sustainabil. 1(2), 20–34 (2009).

    Google Scholar 

  2. I. Esau and S. Zilitinkevich, “On the Role of the Planetary Boundary Layer Depth in the Climate System,” Adv. Sci. Res. 4, 63–69 (2010).

    Article  Google Scholar 

  3. N. N. Zubov, Arctic Ice (Izd. Glavsevmorputi, Moscow, 1945) [in Russian].

    Google Scholar 

  4. A. Baklanov, “Parameterisation of SBL Height in Atmospheric Pollution Models,” in Air Pollution Modeling and Its Application XV, Ed. by C. Borrego and G. Schayes (Kluwer Academic/Plenum Publishers, New York, 2002), pp. 415–424.

    Google Scholar 

  5. S. Zilitinkevich, A. Baklanov, J. Rost, et al., “Diagnostic and Prognostic Equations for the Depth of the Stably Stratified Ekman Boundary Layer,” Q. J. R. Meteorol. Soc. 128(579), 25–46 (2002).

    Article  Google Scholar 

  6. S. Zilitinkevich and A. Baklanov, “Calculation of the Height of the Stable Boundary Layer in Practical Applications,” Boundary-Layer Meteorol., 1993, vol. 63, pp. 65–96. 105 (3), 389–409 (2002).

    Article  Google Scholar 

  7. S. S. Zilitinkevich and I. N. Esau, “On Integral Measures of the Neutral Barotropic Planetary Boundary Layer,” Boundary-Layer Meteorol., 1993, vol. 63, pp. 65–96. 104 (3), 371–379 (2002).

    Article  Google Scholar 

  8. S. S. Zilitinkevich and I. N. Esau, “The Effect of Baroclinicity on the Equilibrium Depth of Neutral and Stable Planetary Boundary Layers,” Q. J. R. Meteorol. Soc. 129(595), 3339–3356 (2003).

    Article  Google Scholar 

  9. S. Zilitinkevich, I. Esau, and A. Baklanov, “Further Comments on the Equilibrium Height of Neutral and Stable Planetary Boundary Layers,” Q. J. R. Meteorol. Soc. 133(622), 265–271 (2007).

    Article  Google Scholar 

  10. S. Zilitinkevich and P. Calanca, “An Extended Similarity Theory for the Stably Stratified Atmospheric Surface Layer,” Q. J. R. Meteorol. Soc. 126(566), 1913–1923 (2000).

    Article  Google Scholar 

  11. S. S. Zilitinkevich, “Third-Order Transport due to Internal Waves and Non-Local Turbulence in the Stably Stratified Surface Layer,” Q. J. R. Meteorol. Soc. 128(581), 913–925 (2002).

    Article  Google Scholar 

  12. I. N. Esau, “Parameterization of a Surface Drag Coefficient in Conventionally Neutral Planetary Boundary Layer,” Ann. Geophys. 22, 3353–3362 (2004).

    Article  Google Scholar 

  13. S. S. Zilitinkevich and I. N. Esau, “Resistance and Heat-Transfer Laws for Stable and Neutral Planetary Boundary Layers: Old Theory Advanced and Re-Evaluated,” Q. J. R. Meteorol. Soc. 131(609), 1863–1892 (2005).

    Article  Google Scholar 

  14. V. W. Ekman, “On the Influence of the Earth’s Rotation on Ocean Currents,” Arkiv für matematik, astronomi och fysik 2(11), 1–52 (1905).

    Google Scholar 

  15. C. G. Rossby and R. B. Montgomery, “The Layer of Frictional Influence in Wind and Ocean Currents,” Pap. Phys. Oceanogr. Meteorol. 3(3), 1–101 (1935).

    Google Scholar 

  16. S. S. Zilitinkevich, “On the Determination of the Height of the Ekman Boundary Layer,” Boundary-Layer Meteorol., 1993, vol. 63, pp. 65–96. 3 (2), 141–145 (1972).

    Article  Google Scholar 

  17. S. J. Caughey, J. C. Wyngaard, and J. C. Kaimal, “Turbulence in the Evolving Stable Boundary Layer,” J. Atmos. Sci. 36(6), 1041–1052 (1979).

    Google Scholar 

  18. Atmospheric Turbulence and Air Pollution Modelling, Ed. by F. T. M. Nieuwstadt and H. Van Dop (D. Reidel, Dordrecht, 1982).

    Google Scholar 

  19. J. R. Holton, An Introduction to Dynamic Meteorology (Academic Press, New York, 1972).

    Google Scholar 

  20. J. W. Deardorff, “Parameterization of the Planetary Boundary Layer for Use in General Circulation Models,” Mon. Wea. Rev. 100(2), 93–106 (1972).

    Article  Google Scholar 

  21. A. K. Betts, “Non-Precipitating Cumulus Convection and Its Parameterization,” Q. J. R. Meteorol. Soc. 99(419), 178–196 (1973).

    Article  Google Scholar 

  22. D. J. Carson, “The Development of a Dry Inversion-Capped Convectively Unstable Boundary Layer,” Q. J. R. Meteorol. Soc. 99(421), 450–467 (1973).

    Article  Google Scholar 

  23. H. Tennekes, “A Model for the Dynamics of the Inversion above a Convective Boundary Layer,” J. Atmos. Sci. 30(4), 558–567 (1973).

    Article  Google Scholar 

  24. R. B. Stull, “Mixed-Layer Depth Model Based on Turbulent Energetics,” J. Atmos. Sci. 33(7), 1268–1278 (1976).

    Article  Google Scholar 

  25. S.-E. Gryning and E. Batchvarova, “Analytical Model for the Growth of the Coastal Internal Boundary Layer during Onshore Flow,” Q. J. R. Meteorol. Soc. 116(491), 187–203 (1990).

    Article  Google Scholar 

  26. E. Batchvarova and S. -E. Gryning, “Applied Model for the Growth of the Daytime Mixed Layer,” Boundary-Layer Meteorol., 1993, vol. 63, pp. 65–96. 56 (3), 261–274 (1991).

    Article  Google Scholar 

  27. P. Seibert, F. Beyrich, S.-E. Gryning, et al., “Review and Intercomparison of Operational Methods for the Determination of the Mixing Height,” Atmos. Environ. 34(7), 1001–1027 (2000).

    Article  Google Scholar 

  28. S. S. Zilitinkevich, Turbulent Penetrative Convection (Avebury Technical., Aldershot, 1991).

    Google Scholar 

  29. S. S. Zilitinkevich, “Comments on’ A Model for the Dynamics of the Inversion above a Convective Boundary Layer’,” J. Atmos. Sci. 32(5), 991–992 (1975).

    Article  Google Scholar 

  30. S. S. Zilitinkevich, “A Theoretical Model of Penetrating Turbulent Convection,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 23(6), 593–610 (1987).

    Google Scholar 

  31. Yu. I. Troitskaya, D. A. Sergeev, E. V. Ezhova, et al., “Self-Induced Internal Waves Excited by Buoyant Plumes in a Stratified Tank,” Dokl. Earth Sci. 419(5), 506–510 (2008).

    Article  Google Scholar 

  32. V. G. Bondur, Yu. V. Grebenyuk, E. V. Ezhova, et al., “Surface Manifestations of Internal Waves Investigated by a Subsurface Buoyant Jet: 1. The Mechanism of Internal-Wave Generation,” Izv. Atmos. Ocean. Phys. 45(6), 779–790 (2009).

    Article  Google Scholar 

  33. V. G. Bondur, Yu. V. Grebenyuk, E. V. Ezhova, et al., “Surface Manifestations of Internal Waves Investigated by a Subsurface Buoyant Jet: Part 2. Internal Wave Field,” Izv. Atmos. Ocean. Phys. 46(3), 347–359 (2010).

    Article  Google Scholar 

  34. V. G. Bondur, Yu. V. Grebenyuk, E. V. Ezhova, et al., “Surface Manifestations of Internal Waves Investigated by a Subsurface Buoyant Jet: 3. Surface Manifestations of Internal Waves,” Izv. Atmos. Ocean. Phys. 46(4), 482–491 (2010).

    Article  Google Scholar 

  35. O. A. Druzhinin and Yu. I. Troitskaya, “Auto-Generation of Internal Waves by a Fountain in a Stratified Fluid,” Izv. Akad. Nauk, Mekh. Zhidk. Gaza, no. 3, 147–158 (2010).

  36. S. N. Reznik and Yu. I. Troitskaya, “The Wave Resistance of a Localized Bottom Heterogeneity in a Stratified Shear Flow with a Critical Layer,” Izv. Atmos. Ocean. Phys. 32(1), 122–129 (1996).

    Google Scholar 

  37. Yu. I. Troitskaya, “The Viscous-Diffusion Nonlinear Critical Layer in a Stratified Shear Flow,” J. Fluid Mech. 233, 25–48 (1991).

    Article  Google Scholar 

  38. C. G. Knight, S. H. E. Knight, N. Massey, et al., “Association of Parameter, Software, and Hardware Variation with Large-Scale Behavior across 57.000 Climate Models,” Proc. Natl. Acad. Sci. USA 104(30), 12259–12264 (2007).

    Article  Google Scholar 

  39. W. A. Hoppel, R. V. Anderson, and J. C. Willett, “Atmospheric Electricity in the Planetary Boundary Layer,” in The Earth’s Electrical Environment, Ed. by E. P. Krider and R.G. Roble (National Academy Press, Washington, DC, 1986), pp. 149–165.

    Google Scholar 

  40. S. V. Anisimov, E. A. Mareev, and S. S. Bakastov, “On the Generation and Evolution of Aeroelectric Structures in the Surface Atmospheric Layer,” J. Geophys. Res. 104(D12), 14359–14368 (1999).

    Article  Google Scholar 

  41. S. V. Anisimov and E. A. Mareev, “Spectra of Electric Field Pulsations in the Near-Surface Atmosphere,” Dokl. Akad. Nauk 381(8), 975–980 (2001).

    Google Scholar 

  42. S. V. Anisimov, E. A. Mareev, N. M. Shikhova, et al., “Universal Spectra of Electric Field Pulsations in the Atmosphere,” Geophys. Rev. Lett. 29(24), 74–79 (2002).

    Article  Google Scholar 

  43. E. A. Mareev and O. V. Mareeva, “Nonlinear Electric-Field and Charge Structures in the Atmosphere,” Geomagn. Aeron. 39(6), 743–748 (1999).

    Google Scholar 

  44. E. A. Mareev, “Formation of Charge Layers in the Planetary Atmospheres,” Space Science Reviews 137(1–4) (2008). doi: 10.1007/s11214-008-9306-2

  45. S. V. Anisimov and E. A. Mareev, “Geophysical Studies of the Global Electric Circuit,” Izv. Phys. Solid Earth 44(10), 760–769 (2008).

    Article  Google Scholar 

  46. E. A. Mareev, “Advances and Prospects of Studies of the GLocal Electrical Circuit,” Usp. Fiz. Nauk 180(5), 527–534 (2010).

    Article  Google Scholar 

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Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 119017, Russia

    S. S. Zilitinkevich

  2. Lobachevskii State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

    S. S. Zilitinkevich, Yu. I. Troitskaya & E. A. Mareev

  3. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhni Novgorod, 603950, Russia

    S. S. Zilitinkevich, Yu. I. Troitskaya & E. A. Mareev

  4. Russian State Hydrometeorological University, Malookhtinskii pr. 98, St. Petersburg, 195196, Russia

    S. S. Zilitinkevich & S. A. Tyuryakov

  5. Finnish Meteorological Institute, p.b. 503, Helsinki, 00101, Finland

    S. S. Zilitinkevich & S. A. Tyuryakov

  6. Helsinki University, Helsinki, Finland

    S. S. Zilitinkevich

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  1. S. S. Zilitinkevich
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  2. S. A. Tyuryakov
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  3. Yu. I. Troitskaya
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  4. E. A. Mareev
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Correspondence to S. S. Zilitinkevich.

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Original Russian Text © S.S. Zilitinkevich, S.A. Tyuryakov, Yu.I. Troitskaya, E.A. Mareev, 2012, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2012, Vol. 48, No. 1, pp. 150–160.

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Zilitinkevich, S.S., Tyuryakov, S.A., Troitskaya, Y.I. et al. Theoretical models of the height of the atmospheric boundary layer and turbulent entrainment at its upper boundary. Izv. Atmos. Ocean. Phys. 48, 133–142 (2012). https://doi.org/10.1134/S0001433812010148

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