Calculation of Surface Fluxes under Convective Conditions by Turbulence Closure Models

Lech Łobocki Department of Environmental Engineering, Warsaw University of Technology, Warsaw, Poland

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Abstract

A method of deriving new relationships between near-surface turbulent fluxes and vertical differences of wind speed and potential temperature between two levels in the atmospheric surface layer from simplified second-order turbulence closure models is presented. The paper aims at a coherent treatment of fair-weather conditions and the asymptotic free-convection limit. The traditionally used representation of wind and temperature profiles is modified to reflect the three-sublayer structure of the surface layer in accordance with recent proposals; this leads to a generalization of the profile method. The modification suggests a new framework for the analysis of empirical data gathered in statically unstable fair-weather conditions. A general formulation of the problem involves a set of integral equations, which is solved numerically; with this aim, a new “convective” vertical coordinate transformation suitable for the computation of the upper part of the profile is proposed. Two popular turbulence closure models are used to calculate flux–finite difference relationships in the atmospheric surface layer. Approximated forms of the resulting universal functions are proposed for practical applications, based on the results of numerical integration.

The main goals of the paper are to show the formalism of deriving the free-convection-safe surface flux calculation algorithms from turbulence closure models; to explore the implications for the convective boundary layer scaling and for the construction of surface layer algorithms, coming from the analysis of the model; and to provide additional criteria for evaluating and developing turbulence closure models, based on analysis of their properties at free convection.

The paper results in a new formulation of flux-profile relationships. The near-free-convection part of the profile is described in terms of heat flux, height, and the Monin–Obukhov parameter ζ; matches smoothly to the classic Monin–Obukhov solution; and transforms asymptotically, with vanishing shear, into a purely free convection regime.

A generalization of the method for application to a horizontally homogeneous, quasi-steady-state, shear-free, convective boundary layer, leads to results comparable to the predictions of the convection-induced stress regime theory despite the different approach taken here.

Corresponding author address: Dr. Lech Łobocki, Institute of Environmental Engineering Systems, Warsaw University of Technology, Nowowiejska 20, 00-653 Warsaw, Poland.

Lech.Lobocki@is.pw.edu.pl

Abstract

A method of deriving new relationships between near-surface turbulent fluxes and vertical differences of wind speed and potential temperature between two levels in the atmospheric surface layer from simplified second-order turbulence closure models is presented. The paper aims at a coherent treatment of fair-weather conditions and the asymptotic free-convection limit. The traditionally used representation of wind and temperature profiles is modified to reflect the three-sublayer structure of the surface layer in accordance with recent proposals; this leads to a generalization of the profile method. The modification suggests a new framework for the analysis of empirical data gathered in statically unstable fair-weather conditions. A general formulation of the problem involves a set of integral equations, which is solved numerically; with this aim, a new “convective” vertical coordinate transformation suitable for the computation of the upper part of the profile is proposed. Two popular turbulence closure models are used to calculate flux–finite difference relationships in the atmospheric surface layer. Approximated forms of the resulting universal functions are proposed for practical applications, based on the results of numerical integration.

The main goals of the paper are to show the formalism of deriving the free-convection-safe surface flux calculation algorithms from turbulence closure models; to explore the implications for the convective boundary layer scaling and for the construction of surface layer algorithms, coming from the analysis of the model; and to provide additional criteria for evaluating and developing turbulence closure models, based on analysis of their properties at free convection.

The paper results in a new formulation of flux-profile relationships. The near-free-convection part of the profile is described in terms of heat flux, height, and the Monin–Obukhov parameter ζ; matches smoothly to the classic Monin–Obukhov solution; and transforms asymptotically, with vanishing shear, into a purely free convection regime.

A generalization of the method for application to a horizontally homogeneous, quasi-steady-state, shear-free, convective boundary layer, leads to results comparable to the predictions of the convection-induced stress regime theory despite the different approach taken here.

Corresponding author address: Dr. Lech Łobocki, Institute of Environmental Engineering Systems, Warsaw University of Technology, Nowowiejska 20, 00-653 Warsaw, Poland.

Lech.Lobocki@is.pw.edu.pl

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  • Abdella, K., and N. McFarlane, 1997: A new second-order turbulence closure scheme for the planetary boundary layer. J. Atmos. Sci.,54, 1850–1867.

  • Beljaars, A. C. M., 1995: The parameterization of surface fluxes in large-scale models under free convection. Quart. J. Roy. Meteor. Soc.,121, 255–270.

  • Berkowicz, R., and L. P. Prahm, 1982: Evaluation of the profile method for estimation of surface fluxes of momentum and heat. Atmos. Environ.,16, 2809–2819.

  • Bernstein, A. B., 1966: A new dimensional approach to the problem of flux-gradient relationships near the ground. Quart. J. Roy. Meteor. Soc.,92, 560–566.

  • Betchov, R., and A. M. Yaglom, 1971: Comments on the theory of similarity as applied to turbulence in an unstably stratified fluid. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana,7, 1270–1279.

  • Brutsaert, W., 1982: Evaporation into the Atmosphere. D. Reidel, 299 pp.

  • Businger, J. A., 1966: Transfer of heat and momentum in the atmospheric boundary layer. Proc. Arctic Heat Budget and Atmospheric Circulation, Santa Monica, CA, RAND Corporation, 305–332.

  • Businger, J. A., 1973a: A note on free convection. Bound.-Layer Meteor.,4, 323–326.

  • Businger, J. A., 1973b: Turbulent transfer in the atmospheric surface layer. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 67–100.

  • Businger, J. A., 1988: A note on the Businger-Dyer profiles. Bound.-Layer Meteor.,42, 145–151.

  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci.,28, 181–189.

  • Carl, D. M., T. C. Tarbell, and H. A. Panofsky, 1973: Profile of wind and temperature from towers over homogeneous terrain. J. Atmos. Sci.,30, 788–794.

  • Deardorff, J. W., 1970: Convective velocity and temperature scales for the unstable planetary boundary layer and for Raleigh convection. J. Atmos. Sci.,27, 1211–1213.

  • Deardorff, J. W., 1973: Three-dimensional numerical modeling of the planetary boundary layer. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 271–311.

  • Delage, Y., and C. Girard, 1992: Stability functions correct at the free convection limit and consistent for both the surface and Ekman layers. Bound.-Layer Meteor.,58, 19–31.

  • Donaldson, C. duP., 1973: Construction of a dynamic model of the production of atmospheric turbulence and the dispersal of atmospheric pollutants. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 313–392.

  • Dyer, A. J., 1967: The turbulent transport of heat and water vapour in an unstable atmosphere. Quart. J. Roy. Meteor. Soc.,93, 501–508.

  • Dyer, A. J., and B. B. Hicks, 1970: Flux-gradient relationships in the constant-flux layer. Quart. J. Roy. Meteor. Soc.,96, 715–721.

  • Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996: Bulk parameterization of air-sea fluxes for Tropical Ocean Global Atmosphere–Coupled Ocean Atmosphere Response Experiment. J. Geophys. Res.,101, 3747–3764.

  • Garratt, J. R., R. J. Francey, I. C. McIlroy, A. J. Dyer, I. Helmond, E. F. Bradley, and O. T. Denman, 1979: The international turbulence comparison experiment (Australia, 1976)—Micrometeorological support data. CSIRO, Division of Atmospheric Physics Tech. Paper 37, 23 pp. [Available from CSIRO, Aspendale, Victoria 3195, Australia.].

  • Godfrey, J. S., and A. C. M. Beljaars, 1991: On the turbulent fluxes of buoyancy, heat and moisture at the air-sea interface at low wind speeds. J. Geophys. Res.,96 (C12), 22 043–22 048.

  • Golitsyn, G. S., and A. A. Grachev, 1986: Free convection of multi-component media and parameterization of air-sea interaction at light winds. Ocean-Air Int.,1, 57–78.

  • Grachev, A. A., C. W. Fairall, and S. S. Zilitinkevich, 1997: Surface layer scaling for free-convection induced stress regime. Bound.-Layer Meteor.,83, 423–439.

  • Holtslag, A. A. M., and A. P. van Ulden, 1983: A simple scheme for daytime estimates of the surface fluxes from routine weather data. J. Climate Appl. Meteor.,22, 517–529.

  • Kader, B. A., and V. G. Perepelkin, 1989: Effect of the unstable stratification on wind and temperature profiles in the surface layer. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana,25, 787–795.

  • Kader, B. A., and A. M. Yaglom, 1990: Mean fields and fluctuation moments in unstably stratified turbulent boundary layers. J. Fluid Mech.,212, 637–662.

  • Kaimal, J. C., and J. C. Wyngaard, 1990: The Kansas and Minnesota experiments. Bound.-Layer Meteor.,50, 31–47.

  • Kolmogorov, A. N., 1941: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Compt. Rend. Akad. Nauk SSSR,30, 301–305.

  • Kondo, J., and S. Ishida, 1997: Sensible heat flux from the earth’s surface under natural convective conditions. J. Atmos. Sci.,54, 498–509.

  • Łobocki, L., 1992: On integration of a turbulence closure model on a sparse vertical grid. Preprints, 10th Symp. on Turbulence and Diffusion, Portland, OR, Amer. Meteor. Soc., 94–97.

  • Łobocki, L., 1993: A procedure for the derivation of surface layer bulk relationships from simplified second-order closure models. J. Appl. Meteor.,32, 126–138.

  • Mellor, G. L., 1973: Analytic prediction of the properties of stratified planetary surface layers. J. Atmos. Sci.,30, 1061–1069.

  • Mellor, G. L., and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci.,31, 1791–1806.

  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys.,20, 851–875.

  • Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the surface layer of the atmosphere. Tr. Geofiz. Inst., Akad Nauk SSSR,24, 1963–1967.

  • Monin, A. S., and A. M. Yaglom, 1971: Statistical Fluid Mechanics: Mechanics of Turbulence. MIT Press.

  • Nickerson, E. C., and V. E. Smiley, 1975: Surface layer and energy budget parameterizations for mesoscale models. J. Appl. Meteor.,14, 297–300.

  • Obukhov, A. M., 1946: Turbulence in an atmosphere with a non-uniform temperature. Tr. Inst. Teor. Geofiz., Acad. Nauk SSSR,1, 95–115.

  • Panofsky, H. A., 1963: Determination of stress from wind and temperature measurements. Quart. J. Roy. Meteor. Soc.,89, 85–94.

  • Panofsky, H. A., H. Tennekes, D. A. Lenschow, and J. C. Wyngaard, 1976: The characteristics of turbulent velocity components in the surface layer under convective conditions. Bound.-Layer Meteor.,11, 355–361.

  • Paulson, C. A., 1970: The mathematical representation of wind and temperature profiles in the unstable atmospheric surface layer. J. Appl. Meteor.,9, 857–861.

  • Prandtl, L., 1932: Meteorologische Anwendung der Strömungslehre. Beitr. Phys. Atmos.,19, 188–202.

  • San Jose, R., J. L. Casanova, R. E. Viloria, and J. Casanova, 1985: Evaluation of the turbulent parameters of the unstable surface boundary layer outside Businger’s range. Atmos. Environ.,19, 1555–1561.

  • Santoso, E., and R. B. Stull, 1998: Wind and temperature profiles in the radix layer: The bottom fifth of the convective boundary layer. J. Appl. Meteor.,37, 545–558.

  • Schemm, C. E., and F. B. Lipps, 1976: Some results of a simplified three-dimensional numerical model of atmospheric turbulence. J. Atmos. Sci.,33, 1021–1041.

  • Schumann, U., 1988: Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer. Bound.-Layer Meteor.,44, 311–326.

  • Sellers, W. D., 1962: A simplified derivation of the diabatic wind profile. J. Atmos. Sci.,19, 180–181.

  • Sorbjan, Z., 1997: Comments on “A convective transport theory for surface fluxes.” J. Atmos. Sci.,54, 576–578.

  • Stull, R. B., 1993: Review of non-local mixing in turbulent atmospheres: transilient turbulence theory. Bound.-Layer Meteor.,62, 21–96.

  • Stull, R. B., 1994: A convective transport theory for surface fluxes. J. Atmos. Sci.,51, 3–22.

  • Stull, R. B., 1997: Reply. J. Atmos. Sci.,54, 579.

  • Sykes, R. I., D. S. Henn, and W. S. Lewellen, 1993: Surface-layer description under free-convection conditions. Quart. J. Roy. Meteor. Soc.,119, 409–421.

  • Taylor, P. A., and Y. Delage, 1971: A note on finite-difference schemes for the surface and planetary boundary layers. Bound.-Layer Meteor.,2, 108–121.

  • Tennekes, H., 1970: Free convection in the turbulent Ekman layer of the atmosphere. J. Atmos. Sci.,27, 1027–1034.

  • Wyngaard, J. C., 1973: On surface-layer turbulence. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 101–149.

  • Yamada, T., 1979: PBL similarity profiles determined from a level-2 turbulence-closure model. Bound.-Layer Meteor.,17, 333–351.

  • Zilitinkevich, S. S., 1971: On the turbulence and diffusion in free convection. Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana,7, 1263–1269.

  • Zilitinkevich, S. S., 1973: Shear convection. Bound.-Layer Meteor.,3, 416–423.

  • Zilitinkevich, S. S., 1994: A generalized scaling for convective shear flows. Bound.-Layer Meteor.,70, 51–78.

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