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Outlier Problem in Evaluating Similarity Functions in the Stable Atmospheric Boundary Layer

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Abstract

The gradient-based similarity approach removes turbulent fluxes as governing parameters and replaces them with vertical gradients of mean wind speed and potential temperature. As a result, the gradient Richardson number, Ri, appears as a stability parameter instead of the Monin–Obukhov stability parameter z/L (L is the Obukhov length). The gradient-based scaling is more appropriate for moderate and very stable conditions when the gradients are large and their errors are relatively small whereas z/L becomes ambiguous in these conditions because turbulent fluxes are small. However, the gradient-based formulation is faced with a problem related to the influence of Ri outliers: outliers with high values of Ri can exist in conditions that are really near-neutral. These outliers are mapped into the very stable range in plots in which Ri is the independent variable and may lead to spurious dependencies for bin-averaged data (spurious bin-averaging). This effect is quite large for functions that are steep for the gradient-based scaling. The present study uses the Surface Heat Budget of the Arctic Ocean (SHEBA) data to examine the problem and proposes two methods, conditional analysis and independent binning, to limit the influence of outliers on bin-averaging. A disadvantage of the conditional analysis is associated with eliminating outliers based on criteria that could be considered as subjective. The independent bin-averaging method does not have this disadvantage, but the scatter of the bin-averaged points is higher than for the conditional analysis, rendering data analysis and interpretation difficult.

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References

  • Andreas EL (2009) Relating the drag coefficient and the roughness length over the sea to the wavelength of the peak waves. J Phys Oceanogr 39(11): 3011–3020

    Article  Google Scholar 

  • Andreas EL (2010) Reply. J Phys Oceanogr 40(11): 2563–2568

    Article  Google Scholar 

  • Andreas EL, Hicks BB (2002) Comments on “Critical test of the validity of Monin–Obukhov similarity during convective conditions”. J Atmos Sci 59: 2605–2607

    Article  Google Scholar 

  • Andreas EL, Claffey KJ, Jordan RE, Fairall CW, Guest PS, Persson POG, Grachev AA (2006) Evaluations of the von Kármán constant in the atmospheric surface layer. J Fluid Mech 559: 117–149

    Article  Google Scholar 

  • Andreas EL, Horst TW, Grachev AA, Persson POG, Fairall CW, Guest PS, Jordan RE (2010a) Parametrizing turbulent exchange over summer sea ice and the marginal ice zone. Q J Roy Meteorol Soc 136(649B): 927–943

    Article  Google Scholar 

  • Andreas EL, Persson POG, Jordan RE, Horst TW, Guest PS, Grachev AA, Fairall CW (2010b) Parameterizing turbulent exchange over sea ice in winter. J Hydrometeorol 11(1): 87–104

    Article  Google Scholar 

  • Baas P, Steeneveld GJ, van de Wiel BJH, Holtslag AAM (2006) Exploring self-correlation in flux–gradient relationships for stably stratified conditions. J Atmos Sci 63(11): 3045–3054

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fairall CW, Bradley EF, Hare JE, Grachev AA, Edson JB (2003) Bulk parameterization of air–sea fluxes: updates and verification for the COARE algorithm. J Clim 16(4): 571–591

    Article  Google Scholar 

  • Grachev AA, Fairall CW, Persson POG, Andreas EL, Guest PS (2005) Stable boundary-layer scaling regimes: the SHEBA data. Boundary-Layer Meteorol 116(2): 201–235

    Article  Google Scholar 

  • Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2007a) SHEBA flux–profile relationships in the stable atmospheric boundary layer. Boundary-Layer Meteorol 124(3): 315–333

    Article  Google Scholar 

  • Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2007b) On the turbulent Prandtl number in the stable atmospheric boundary layer. Boundary-Layer Meteorol 125(2): 329–341

    Article  Google Scholar 

  • Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2008) Turbulent measurements in the stable atmospheric boundary layer during SHEBA: ten years after. Acta Geophys 56(1): 142–166

    Article  Google Scholar 

  • Hicks BB (1978) Comments on “The characteristics of turbulent velocity components in the surface layer under convective conditions” by H.A. Panofsky et al. Boundary-Layer Meteorol 15(2): 255–258

    Article  Google Scholar 

  • Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurements. Oxford University Press, New York, 289 pp

  • Klipp CL, Mahrt L (2004) Flux–gradient relationship, self-correlation and intermittency in the stable boundary layer. Q J Roy Meteorol Soc 130(601): 2087–2103

    Article  Google Scholar 

  • Lange B, Johnson HK, Larsen S, Højstrup J, Kofoed-Hansen H, Yelland MJ (2004) On detection of a wave age dependency for the sea surface roughness. J Phys Oceanogr 34(6): 1441–1458

    Article  Google Scholar 

  • Mahrt L (2008) The influence of transient flow distortion on turbulence in stable weak-wind conditions. Boundary-Layer Meteorol 127(1): 1–16

    Article  Google Scholar 

  • Mahrt L, Sun J, Blumen W, Delany T, Oncley S (1998) Nocturnal boundary-layer regimes. Boundary-Layer Meteorol 88: 255–278

    Article  Google Scholar 

  • Mauritsen T, Svensson G (2007) Observations of stably stratified shear-driven atmospheric turbulence at low and high Richardson numbers. J Atmos Sci 64(2): 645–655

    Article  Google Scholar 

  • Monin AS, Obukhov AM (1954) Basic laws of turbulent mixing in the surface layer of the atmosphere. Trudy Geofiz Inst Acad Nauk SSSR 24(151): 163–187

    Google Scholar 

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

    Article  Google Scholar 

  • Obukhov AM (1946) Turbulence in an atmosphere with a non-uniform temperature. Trudy Inst Teoret Geofiz Akad Nauk SSSR 1:95–115 (translation in: Boundary-Layer Meteorol (1971) 2:7–29)

    Google Scholar 

  • Pardyjak ER, Monti P, Fernando HJS (2002) Flux Richardson number measurements in stable atmospheric shear flows. J Fluid Mech 449(1): 307–316

    Google Scholar 

  • Persson POG, Fairall CW, Andreas EL, Guest PS, Perovich DK (2002) Measurements near the Atmospheric Surface Flux Group tower at SHEBA: near-surface conditions and surface energy budget. J Geophys Res 107(C10): 8045. doi:10.1029/2000JC000705

    Article  Google Scholar 

  • Sorbjan Z (1986) On similarity in the atmospheric boundary layer. Boundary-Layer Meteorol 34: 377–397

    Article  Google Scholar 

  • Sorbjan Z (1988) Structure of the stably-stratified boundary layer during the SESAME-1979 experiment. Boundary-Layer Meteorol 44: 255–260

    Article  Google Scholar 

  • Sorbjan Z (2006) Local structure of turbulence in stably-stratified boundary layers. J Atmos Sci 63(5): 1526–1537

    Article  Google Scholar 

  • Sorbjan Z (2008) Gradient-based similarity in the atmospheric boundary layer. Acta Geophys 56(1): 220–233

    Article  Google Scholar 

  • Sorbjan Z (2010) Gradient-based scales and similarity laws in the stable boundary layer. Q J Roy Meteorol Soc 136(650A): 1243–1254

    Google Scholar 

  • Sorbjan Z (2012) The height correction of similarity functions in the stable boundary layer. Boundary-Layer Meteorol 142(1): 21–31

    Article  Google Scholar 

  • Sorbjan Z, Grachev AA (2010) An evaluation of the flux–gradient relationship in the stable boundary layer. Boundary-Layer Meteorol 135(3): 385–405

    Article  Google Scholar 

  • Wyngaard JC, Coté OR (1972) Cospectral similarity in the atmospheric surface layer. Q J Roy Meteorol Soc 98: 590–603

    Article  Google Scholar 

  • Yagüe C, Viana S, Maqueda G, Redondo JM (2006) Influence of stability on the flux–profile relationships for wind speed, φ m , and temperature, φ h , for the stable atmospheric boundary layer. Nonlinear Process Geophys 13(2): 185–203

    Article  Google Scholar 

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Authors and Affiliations

  1. NOAA Earth System Research Laboratory/Cooperative Institute for Research in Environmental Sciences, University of Colorado, 325 Broadway, R/PSD3, Boulder, CO, 80305-3337, USA

    Andrey A. Grachev & P. Ola G. Persson

  2. NorthWest Research Associates, Inc., Lebanon, NH, USA

    Edgar L. Andreas

  3. NOAA Earth System Research Laboratory, Boulder, CO, USA

    Christopher W. Fairall

  4. Naval Postgraduate School, Monterey, CA, USA

    Peter S. Guest

Authors
  1. Andrey A. Grachev
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  2. Edgar L. Andreas
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  3. Christopher W. Fairall
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  4. Peter S. Guest
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  5. P. Ola G. Persson
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Correspondence to Andrey A. Grachev.

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Grachev, A.A., Andreas, E.L., Fairall, C.W. et al. Outlier Problem in Evaluating Similarity Functions in the Stable Atmospheric Boundary Layer. Boundary-Layer Meteorol 144, 137–155 (2012). https://doi.org/10.1007/s10546-012-9714-9

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  • DOI: https://doi.org/10.1007/s10546-012-9714-9

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