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Characterization and Parametrization of Reynolds Stress and Turbulent Heat Flux in the Stably-Stratified Lower Arctic Troposphere Using Aircraft Measurements

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Abstract

Aircraft measurements are used to characterize properties of clear-air turbulence in the lower Arctic troposphere. For typical vertical resolutions in general circulation models, there is evidence for both downgradient and countergradient vertical turbulent transport of momentum and heat in the mostly statically stable conditions within both the boundary layer and the free troposphere. Countergradient transport is enhanced in the free troposphere compared to the boundary layer. Three parametrizations are suggested to formulate the turbulent heat flux and are evaluated using the observations. The parametrization that accounts for the anisotropic nature of turbulence and buoyancy flux predicts both observed downgradient and countergradient transport of heat more accurately than those that do not. The inverse turbulent Prandtl number is found to only weakly decrease with increasing gradient Richardson number in a statistically significant way, but with large scatter in the data. The suggested parametrizations can potentially improve the performance of regional and global atmospheric models.

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References

  • Aliabadi AA, Staebler RM, de Grandpré J, Zadra A, Vaillancourt PA (2016a) Comparison of estimated atmospheric boundary layer mixing height in the Arctic and Southern Great Plains under statically stable conditions: experimental and numerical aspects. Atmos-Ocean 54:60–74

  • Aliabadi AA, Thomas JL, Herber A, Staebler RM, Leaitch WR, Law KS, Marelle L, Burkart J, Willis M, Abbatt JPD, Bozem H, Hoor P, Köllner F, Schneider J, Levasseur M (2016b) Ship emissions measurement in the Arctic from plume intercepts of the Canadian coast guard Amundsen icebreaker from the Polar 6 aircraft platform. Atmos Chem Phys Discuss 1–37. doi:10.5194/acp-2015-1032

  • Aliabadi AA, Staebler RM, Sharma S (2015) Air quality monitoring in communities of the Canadian Arctic during the high shipping season with a focus on local and marine pollution. Atmos Chem Phys 15(5):2651–2673

    Article  Google Scholar 

  • Bélair S, Mailhot J, Strapp JW, MacPherson JI (1999) An examination of local versus nonlocal aspects of a TKE-based boundary layer scheme in clear convective conditions. J Appl Meteorol 38:1499–1518

    Article  Google Scholar 

  • Bougeault P, Lacarrere P (1989) Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon Weather Rev 117:1872–1890

    Article  Google Scholar 

  • Cho JYN, Newell RE, Anderson BE, Barrick JDW, Thornhill KL (2003) Characterizations of tropospheric turbulence and stability layers from aircraft observations. J Geophys Res Atmos 108:8784

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

  • Deardorff JW (1966) The counter-gradient heat flux in the lower atmosphere and in the laboratory. J Atmos Sci 23:503–506

    Article  Google Scholar 

  • Deardorff JW (1972a) Theoretical expression for the countergradient vertical heat flux. J Geophys Res Atmos 77:5900–5904

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dehghan A, Hocking WK, Srinivasan R (2014) Comparisons between multiple in-situ aircraft turbulence measurements and radar in the troposphere. J Atmos Sol-Terr Phy 118:64–77

    Article  Google Scholar 

  • Delage Y (1997) Parameterizing sub-grid scale vertical transport in atmospheric models under statically stable conditions. Boundary-Layer Meteorol 82:23–48

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Geernaert GL, Larsen SE, Hansen F (1987) Measurements of the wind stress, heat flux, and turbulence intensity during storm conditions over the North sea. J Geophys Res Oceans 92:13,127–13,139

    Article  Google Scholar 

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

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

    Article  Google Scholar 

  • Han Z, Zhang M, An J (2009) Sensitivity of air quality model prediction to parameterization of vertical eddy diffusivity. Environ Fluid Mech 9:73–89

    Article  Google Scholar 

  • Hocking W (1999) The dynamical parameters of turbulence theory as they apply to middle atmosphere studies. Earth Planets Space 51:525–541

    Article  Google Scholar 

  • Iida O, Nagano Y (2007) Effect of stable-density stratification on counter gradient flux of a homogeneous shear flow. Int J Heat Mass Tran 50:335–347

    Article  Google Scholar 

  • Inoue J, Kawashima M, Fujiyoshi Y, Wakatsuchi M (2005) Aircraft observations of air-mass modification over the sea of Okhotsk during sea-ice growth. Boundary-Layer Meteorol 117:111–129

    Article  Google Scholar 

  • Kennedy PJ, Shapiro MA (1980) Further encounters with clear air turbulence in research aircraft. J Atmos Sci 37:986–993

    Article  Google Scholar 

  • Kim J, Mahrt L (1992) Simple formulation of turbulent mixing in the stable free atmosphere and nocturnal boundary layer. Tellus 44A:381–394

    Article  Google Scholar 

  • Komori S, Nagata K (1996) Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification. J Fluid Mech 326:205–237

    Article  Google Scholar 

  • Kondo J, Kanechika O, Yasuda N (1978) Heat and momentum transfers under strong stability in the atmospheric surface layer. J Atmos Sci 35:1012–1021

    Article  Google Scholar 

  • Leaitch WR, Korolev A, Aliabadi AA, Burkart J, Willis M, Abbatt JPD, Bozem H, Hoor P, Köllner F, Schneider J, Herber A, Konrad C, Brauner R (2016) Effects of 20-100 nanometre particles on liquid clouds in the clean summertime Arctic. Atmos Chem Phys Discuss 1–50. doi:10.5194/acp-2015-999

  • Lenschow DH, Li XS, Zhu CJ, Stankov BB (1988) The stably stratified boundary layer over the Great Plains. Boundary-Layer Meteorol 42:95–121

    Article  Google Scholar 

  • Lenschow DH, Mann J, Kristensen L (1994) How long is long enough when measuring fluxes and other turbulence statistics? J Atmos Ocean Technol 11:661–673

    Article  Google Scholar 

  • Lovejoy S, Tuck AF, Hovde SJ, Schertzer D (2007) Is isotropic turbulence relevant in the atmosphere? Geophys Res Lett 34:L15802

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mahrt L, Vickers D (2005) Boundary-layer adjustment over small-scale changes of surface heat flux. Boundary-Layer Meteorol 116:313–330

    Article  Google Scholar 

  • Makar PA, Nissen R, Teakles A, Zhang J, Zheng Q, Moran MD, Yau H, diCenzo C (2014) Turbulent transport, emissions and the role of compensating errors in chemical transport models. Geosci Model Dev 7:1001–1024

    Article  Google Scholar 

  • Mellor GL (1973) Analytic prediction of the properties of stratified planetary surface layers. J Atmos Sci 30:1061–1069

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ohya Y (2001) Wind-tunnel study of atmospheric stable boundary layers over a rough surface. Boundary-Layer Meteorol 98:57–82

    Article  Google Scholar 

  • Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Rotta JC (1951) Statistische theorie nichthomogener turbulenz. Z Phys 129:547–572

    Article  Google Scholar 

  • Stull RB (2003) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Taylor GI (1938) The spectrum of turbulence. Proc R Soc A164:476–490

    Google Scholar 

  • Ueda H, Mitsumoto S, Komori S (1981) Buoyancy effects on the turbulent transport processes in the lower atmosphere. Q J R Meteorol Soc 107:561–578

    Article  Google Scholar 

  • Willis GE, Deardorff JW (1976) On the use of Taylor’s translation hypothesis for diffusion in the mixed layer. Q J R Meteorol Soc 102:817–822

    Article  Google Scholar 

  • Yamada T, Mellor G (1975) A simulation of the Wangara atmospheric boundary layer data. J Atmos Sci 32:2309–2329

    Article  Google Scholar 

  • Zilitinkevich S, Calanca P (2000) An extended similarity theory for the stably stratified atmospheric surface layer. Q J R Meteorol Soc 126:1913–1923

Download references

Acknowledgments

The authors acknowledge the assistance of M. Wasey (ECCC), A. Elford (ECCC(ECCC)), M. Gehrman (AWI), C. Konrad (AWI), and J. Burkart (University of Toronto) for recovering and processing of the dataset. Expert reviews of the manuscript by J. de Grandpré, S. Bélair, and P. Makar (ECCC) are appreciated. We are grateful for scientific advice from J. Abbatt (University of Toronto) and R. Leaitch (ECCC), from the executive committee of the NETCARE Project. Our greatest appreciation goes to the editors E. Fedorovich and J. R. Garratt and anonymous reviewers of the manuscript who provided detailed comments along with key literature and suggestions to improve the quality of this manuscript. We thank the Nunavut Research Institute and the Nunavut Impact Review Board for licensing the study. Logistical support in Resolute Bay was provided by the Polar Continental Shelf Project (PCSP) of Natural Resources Canada. Funding for this work was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada under the CCAR NETCARE project, the Alfred Wegener Institute (AWI), and Environment and Climate Change Canada (ECCC).

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Correspondence to Amir A. Aliabadi.

Appendix 1: Flight and Radiosonde Schedule for the NETCARE 2014 Campaign

Appendix 1: Flight and Radiosonde Schedule for the NETCARE 2014 Campaign

See Tables 4 and 5.

Table 4 Flight schedule for the NETCARE 2014 campaign; only research flights listed (5–15); test and ferry flights excluded (1–4, 16–19)
Table 5 Radiosonde schedule and estimated boundary-layer height (\(Z_i\)) for the NETCARE 2014 campaign

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Aliabadi, A.A., Staebler, R.M., Liu, M. et al. Characterization and Parametrization of Reynolds Stress and Turbulent Heat Flux in the Stably-Stratified Lower Arctic Troposphere Using Aircraft Measurements. Boundary-Layer Meteorol 161, 99–126 (2016). https://doi.org/10.1007/s10546-016-0164-7

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  • DOI: https://doi.org/10.1007/s10546-016-0164-7

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