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Application of a large-eddy simulation database to optimisation of first-order closures for neutral and stably stratified boundary layers

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Atmospheric Boundary Layers

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Abstract

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located.

The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.

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References

  • Andren A and Moeng C-H (1993). Single-point Closures in a neutrally stratified boundary Layer. J. Atmos Sci 50: 3366–3379

    Article  Google Scholar 

  • Ayotte KW, Sullivan PP, Andrén A, Doney SC, Holtslag AAM, Large WG, McWilliams JC, Moeng C-H, Otte MJ, Tribbia JJ and Wyngaard JC (1996). An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations. Boundary-Layer Meteorol 79: 131–175

    Article  Google Scholar 

  • Ballard SP, Golding BW and Smith RNB (1991). Mesoscale model experimental forecasts of the Haar of Northeast Scotland. Mon Wea Rev   119(9): 2107–2123

    Article  Google Scholar 

  • Beare RJ, MacVean MK, Holtslag AAM, Cuxart J, Esau I, Golaz JC, Jimenez MA, Khairoudinov M, Kosovic B, Lewellen D, Lund TS, Lundquist JK, McCabe A, Moene AF, Noh Y, Raasch S and Sullivan P (2006). An intercomparison of large eddy simulations of the stable boundary layer. Boundary-Layer Meteorol 118(2): 247–272

    Article  Google Scholar 

  • Blackader AK (1962). The vertical distributions of wind and turbulent exchange in neutral atmosphere. J Geophys Res 67: 3095–3120

    Google Scholar 

  • Brown RA (1972). On the inflection point instability of a stratified ekman boundary layer. J Atmos Sci 29(5): 850–859

    Article  Google Scholar 

  • Businger JA, Wyngaard JC, Izumi Y and Bradley EF (1971). Flux-profile relationships in the atmospheric surface layer. J Atmos Sci 28: 181–189

    Article  Google Scholar 

  • Businger JA (1988). A note on the businger-dyer profiles. Boundary-Layer Meteorol 42: 145–151

    Article  Google Scholar 

  • Cassano JJ, Parish TR and King JC (2001). Evaluation of turbulent surface flux parameterizations for the stable surface layer over Halley, Antarctica. Mon Wea Rev 129: 26–46

    Article  Google Scholar 

  • Cuxart J, Holtslag AAM, Beare RJ, Bazile E, Beljaars A, Cheng A, Conangla L, Freedman MEkF, Hamdi R, Kerstein A, Kitagawa H, Lenderink G, Lewellen D, Mailhot J, Mauritsen T, Perov V, Schayes G, Steeneveld GJ, Svensson G, Taylor P, Weng W, Wunsch S and Xu K-M (2006). Single Column model intercomparison for the stably stratified atmospheric boundary layer. Boundary-Layer Meteorol 118(2): 273–303

    Article  Google Scholar 

  • Deardorff JW (1972). Parameterization of the planetary boundary layer for use in general circulation models. Mon Wea Rev 100: 93–106

    Article  Google Scholar 

  • Derbyshire SH (1999). Boundary layer decoupling over cold surfaces as a physical boundary instability. Boundary-Layer Meteorol 90: 297–325

    Article  Google Scholar 

  • Djolov GD (1973) Modeling of the interdependent diurnal variation of meteorological elements in the boundary layer. Ph.D. Thesis, Univ. of Waterloo, Waterloo, Ont., Canada, 127 pp

    Google Scholar 

  • Esau I (2004). Simulation of ekman boundary layers by large eddy model with dynamic mixed subfilter closure. J Environ Fluid Mech 4: 273–303

    Article  Google Scholar 

  • Esau I and Zilitinkevich SS (2006). Universal dependences between turbulent and mean flow parameters in stably and neutrally stratified planetary boundary layers. Nonlin Proces Geophys 13: 122–144

    Google Scholar 

  • Fedorovich E, Conzemius R, Esau I, Chow FK, Lewellen DC, Moeng, C-H, Pino D, Sullivan PP, Vila J (2004) Entrainment into sheared convective boundary layers as predicted by different large eddy simulation codes. Paper P4.7., 16th Symposium on Boundary Layers and Turbulence, Amer Meteorol Soc, January 2004, pp 1–14

    Google Scholar 

  • Galmarini S, Beets C, Duynkerke PG and Vilà-Guerau de Arellano J (1998). Stable nocturnal boundary layers: a comparison of one-dimensional and large-eddy simulation models. Boundary-Layer Meteorol 88: 181–210

    Article  Google Scholar 

  • Holt T and Raman S (1988). A review and comparative evaluation of multi-level boundary layer parameterizations for first order and turbulent kinetic energy closure schemes. Rev Geophys 26: 761–780

    Google Scholar 

  • Holtslag AAM and Moeng C-H (1991). Eddy diffusivity and countergradient transport in the convective atmospheric boundary layer. J Atmos Sci 48: 1690–1698

    Article  Google Scholar 

  • Holtslag AAM and Boville B (1993). Local versus nonlocal boundary-layer diffusion in a global climate model. J Climate 6: 1825–1842

    Article  Google Scholar 

  • Högström U (1988). Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary-Layer Meteorol 42: 55–78

    Article  Google Scholar 

  • Lane DE, Somerville R and Iacobellis SF (2000). Sensitivity of cloud and radiation parameterizations to changes in vertical resolution. J Climate 13: 915–922

    Article  Google Scholar 

  • Liu Y and Key J (2003). Detection and analysis of clear-sky, low-level atmospheric temperature inversions with MODIS. J Atmos Ocean Tech 20: 1727–1737

    Article  Google Scholar 

  • Louis J-F (1979). A parametric model of vertical eddy fluxes in the atmosphere. Boundary-Layer Meteorol 17(2): 187–202

    Article  Google Scholar 

  • Mahrt L and Vickers D (2003). Formulation of turbulent fluxes in the stable boundary Layer. J Atmos Sci 60: 2538–2548

    Article  Google Scholar 

  • Moeng C-H and Wyngaard JC (1989). Evaluation of turbulent transport and dissipation closures in second-order modeling. J Atmos Sci 46: 2311–2330

    Article  Google Scholar 

  • Nakanishi M (2001). Improvement of the mellor–Yamada turbulence closure model based on large-eddy simulation data. Boundary-Layer Meteorol 99: 349–378

    Article  Google Scholar 

  • Nieuwstadt FTM (1984). The turbulent structure of the stable nocturnal boundary layer. J Atmos Sci 41: 2202–2216

    Article  Google Scholar 

  • Nikuradze J (1933). Strömungsgesetze in Rauhen Rohren. Forsch Arb Ing-Wes 361, Ausgabe B, Band 4: 2–22

    Google Scholar 

  • Noh Y, Cheon WG, Hong SY and Raasch S (2003). The improvement of the K-profile model for the PBL using LES. Boundary-Layer Meteorol. 107: 401–427

    Article  Google Scholar 

  • Overland JE and Guest PS (1991). The arctic snow and air temperature budget over sea ice during winter. J Geophys Res 96: 4651–4662

    Google Scholar 

  • Poulos GS, Blumen W, Fritts DC, Lundquist JK, Sun J, Burns SP, Nappo C, Banta R, Newsom R, Cuxart J, Terradellas E, Balsley B and Jensen M (2002). CASES-99: a comprehensive investigation of the stable nocturnal boundary layer. Bull Amer Meteorol Soc 83: 555–581

    Article  Google Scholar 

  • Roeckner E, Brokopf R, Esch M, Giorgetta M, Hagemann S, Kornblueh L, Manzini E, Schlese U and Schulzweida U (2006). Sensitivity of simulated climate to horizontal and vertical resolution in the ECHAM5 Atmosphere Model. J Climate 19(16): 3771–3791

    Article  Google Scholar 

  • Tjernstrom M, Zagar M, Svensson G, Cassano JJ, Pfeifer S, Rinke A, Wyser K, Dethloff K, Jones C, Semmler T and Shaw M (2005). Modelling the arctic boundary layer: an evaluation of six ARCMIP regional-scale models with data from the SHEBA project. Boundary-Layer Meteorol 117: 337–381

    Article  Google Scholar 

  • Thorpe AJ and Guymer TH (1977). The nocturnal jet. Quart J Roy Meteorol Soc 103: 633–653

    Article  Google Scholar 

  • Troen I and Mahrt L (1986). A simple model of the atmospheric boundary layer: sensitivity to surface evaporation. Boundary-Layer Meteorol 37: 129–148

    Article  Google Scholar 

  • Uttal T, Curry JA, Mcphee MG, Perovich DK, Moritz RE, Maslanik JA, Guest PS, Stern H, Moore JA, Turenne R, Heiberg A, Serreze MC, Wylie DP, Persson OG, Paulson CA, Halle C, Morison JH, Wheeler PA, Makshtas A, Welch H, Shupe MD, Intrieri JM, Stamnes K, Lindsey RW, Pinkel R, Pegau WS, Stanton TS and Grenfeld TC (2002). Surface heat budget of the arctic ocean. Bull Amer Meteorol Soc 83: 255–275

    Article  Google Scholar 

  • Viterbo P, Beljaars ACM, Mahouf J-F and Teixeira J (1999). The representation of soil moisture freezing and its impact on the stable boundary layer. Quart J Roy Meteorol Soc 125: 2401–2426

    Article  Google Scholar 

  • Weng W and Taylor PA (2003). On modelling the one-dimensional atmospheric boundary layer. Boundary-Layer Meteorol 107(2): 371–400

    Article  Google Scholar 

  • Xu D and Taylor PA (1997). On turbulence closure constants for atmospheric boundary-layer modelling: neutral stratification. Boundary-Layer Meteorol 84: 267–287

    Article  Google Scholar 

  • Yague C, Viana S, Maqueda G and Redondo JM (2006). Influence of stability on the flux-profile relationships for wind speed and temperature for the stable atmospheric boundary Layer. Nonlin Proces Geophys 13: 185–203

    Google Scholar 

  • Zilitinkevich SS (2002). Third-order transport due to internal waves and non-local turbulence in the stably stratified surface layer. Quart J Roy Meteorol Soc 128: 913–925

    Article  Google Scholar 

  • Zilitinkevich SS and Esau I (2002). On integral measures of the neutral barotropic planetary boundary Layers. Boundary-Layer Meteorol 104(3): 371–379

    Article  Google Scholar 

  • Zilitinkevich SS and Esau I (2003). The effect of baroclinicity on the depth of neutral and stable planetary boundary Layers. Quart J Roy Meteorol Soc 129: 3339–3356

    Article  Google Scholar 

  • Zilitinkevich SS and Esau I (2005). Resistance and heat transfer laws for stable and neutral planetary boundary layers: old theory, advanced and re-evaluated. Quart J Royal Meteorol Soc 131: 1863–1892

    Article  Google Scholar 

  • Zilitinkevich SS, Esau I (2007) Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer. Boundary-Layer Meteorol (this issue)

    Google Scholar 

  • Zilitinkevich SS, Esau I and Baklanov A (2007). Further comments on the equilibrium height of neutral and stable planetary boundary layers. Quart J Roy Meteorol Soc 133: 265–271

    Article  Google Scholar 

  • Zilitinkevich SS, Elperin T, Kleeorin N, Rogachevskii I (2007b) Energy- and Flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes. Boundary-Layer Meteorol (this issue)

    Google Scholar 

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Authors and Affiliations

  1. G.C. Rieber Climate Institute, Nansen Environmental and Remote Sensing Centre, Thormohlensgt, 47, Bergen, 5006, Norway

    Igor N. Esau

  2. Bjerknes Centre for Climate Research, Bergen, Norway

    Igor N. Esau & Øyvind Byrkjedal

  3. Geophysical Institute, University of Bergen, Bergen, Norway

    Øyvind Byrkjedal

Authors
  1. Igor N. Esau
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  2. Øyvind Byrkjedal
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Correspondence to Igor N. Esau .

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Editors and Affiliations

  1. Danish Meteorological Institute, Copenhagen, Denmark

    Alexander Baklanov

  2. Department of Geophysics, University of Zagreb, Zagreb, Croatia

    Branko Grisogono

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Esau, I.N., Byrkjedal, Ø. (2007). Application of a large-eddy simulation database to optimisation of first-order closures for neutral and stably stratified boundary layers. In: Baklanov, A., Grisogono, B. (eds) Atmospheric Boundary Layers. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74321-9_5

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