Boundary-Layer Meteorology

, Volume 153, Issue 1, pp 117–139 | Cite as

Modelling Small-Scale Drifting Snow with a Lagrangian Stochastic Model Based on Large-Eddy Simulations

  • C. D. Groot Zwaaftink
  • M. Diebold
  • S. Horender
  • J. Overney
  • G. Lieberherr
  • M. B. Parlange
  • M. Lehning


Observations of drifting snow on small scales have shown that, in spite of nearly steady winds, the snow mass flux can strongly fluctuate in time and space. Most drifting snow models, however, are not able to describe drifting snow accurately over short time periods or on small spatial scales as they rely on mean flow fields and assume equilibrium saltation. In an attempt to gain understanding of the temporal and spatial variability of drifting snow on small scales, we propose to use a model combination of flow fields from large-eddy simulations (LES) and a Lagrangian stochastic model to calculate snow particle trajectories and so infer snow mass fluxes. Model results show that, if particle aerodynamic entrainment is driven by the shear stress retrieved from the LES, we can obtain a snow mass flux varying in space and time. The obtained fluctuating snow mass flux is qualitatively compared to field and wind-tunnel measurements. The comparison shows that the model results capture the intermittent behaviour of observed drifting snow mass flux yet differences between modelled turbulent structures and those likely to be found in the field complicate quantitative comparisons. Results of a model experiment show that the surface shear-stress distribution and its influence on aerodynamic entrainment appear to be key factors in explaining the intermittency of drifting snow.


Drifting snow Lagrangian stochastic model Large-eddy simulations Particle tracking Saltation Surface shear stress 



We thank Katherine Leonard and Roland Meister for their contribution to the drifting snow measurements at Weissfluhjoch Versuchsfeld. This project is funded by the Swiss National Science Foundation. We thank the reviewers for useful comments.


  1. Albertson JD, Parlange MB (1999) Surface length scales and shear stress: implications for land-atmosphere interaction over complex terrain. Water Resour Res 35(7):2121–2132CrossRefGoogle Scholar
  2. Alfredsson PH, Johansson AV, Haritonidis JH, Eckelmann H (1988) The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys Fluids 31(5):1026–1033CrossRefGoogle Scholar
  3. Anderson RS, Haff PK (1991) Wind modification and bed response during saltation of sand in air. Acta Mech Suppl 1:21–51CrossRefGoogle Scholar
  4. Araoka K, Maeno N (1981) Dynamical behaviour of snow particles in the saltation layer. In Proceedings of 3rd symposium on polar meteorology and glaciology. Memoirs of Nationa Institute of Polar Research, vol 19, Tokyo, pp 253–263Google Scholar
  5. Baas ACW (2008) Challenges in aeolian geomorphology: investigating aeolian streamers. Geomorphology 93(1–2):3–16CrossRefGoogle Scholar
  6. Baas ACW, Sherman DJ (2005) Formation and behavior of aeolian streamers. J Geophys Res 110:F03011Google Scholar
  7. Bagnold RA (1941) The physics of blown sand and desert dunes. Methuen, London, 265 ppGoogle Scholar
  8. Bou-Zeid E, Meneveau C, Parlange M (2005) A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys Fluids 17(2):025105CrossRefGoogle Scholar
  9. Butterfield GR (1998) Transitional behaviour of saltation: wind tunnel observations of unsteady winds. J Arid Environ 39:377–394CrossRefGoogle Scholar
  10. Butterfield GR (1999) Application of thermal anemometry and high-frequency measurement of mass flux to aeolian sediment transport research. Geomorphol 29:31–58Google Scholar
  11. Chester S, Meneveau C, Parlange MB (2007) Modeling turbulent flow over fractal trees with renormalized numerical simulation. J Comput Phys 225(1):427–448CrossRefGoogle Scholar
  12. Clifton A, Lehning M (2008) Improvement and validation of a snow saltation model using wind tunnel measurements. Earth Surf Process Landf 33:2156–2173CrossRefGoogle Scholar
  13. Clifton A, Rüedi J-D, Lehning M (2006) Snow saltation threshold measurements in a drifting snow wind tunnel. J Glaciol 39:585–596CrossRefGoogle Scholar
  14. Davidson PA (2004) Turbulence: an introduction for scientists and engineers. Oxford University Press, New York, 657 ppGoogle Scholar
  15. Deardorff JW (1972) Numerical investigation of neutral and unstable planetary boundary layers. J Atmos Sci 29:91–115CrossRefGoogle Scholar
  16. Déry SJ, Yau MK (2001) Simulation of blowing snow in the canadian arctic using a double-moment model. Boundary-Layer Meteorol 99:297–316CrossRefGoogle Scholar
  17. Diebold M, Higgins C, Fang J, Bechmann A and Parlange M (2013) Flow over hills: a large-eddy simulation of the bolund case. Boundary-Layer Meteorol 148(1):177–194Google Scholar
  18. Doorschot JJJ, Lehning M (2002) Equilibrium saltation: mass fluxes, aerodynamic entrainment, and dependence on grain properties. Boundary-Layer Meteorol 104(1):111–130CrossRefGoogle Scholar
  19. Doorschot JJJ, Lehning M, Vrouwe A (2004) Field measurements of snow-drift threshold and mass fluxes, and related model simulations. Boundary-Layer Meteorol 113(3):347–368CrossRefGoogle Scholar
  20. Ellis JT, Sherman DJ, Farrell EJ, Li B (2012) Temporal and spatial variability of aeolian sand transport: implications for field measurements. Aeolian Res 3(4):379–387CrossRefGoogle Scholar
  21. Gauer P (1999) Blowing and drifting snow in Alpine Terrain: a physically-based numerical model and related field measurements, Eidg. Institut für Schnee- und Lawinenforschung, Mitteilungen Nr 58, 128 ppGoogle Scholar
  22. Germano M, Piomelli U, Moin P, Cabot WH (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3(7):1760–1765CrossRefGoogle Scholar
  23. Gordon M, Biswas S, Taylor PA, Hanesiak J, Albarran-Melzer M, Fargey S (2010) Measurements of drifting and blowing snow at Iqaluit, Nunavut. Canada during the STAR project. Atmos-Ocean 48(2):81–100CrossRefGoogle Scholar
  24. Groot Zwaaftink CD, Mott R, Lehning M (2013) Seasonal simulation of drifting snow sublimation in Alpine terrain. Water Resour Res 49:1581–1590CrossRefGoogle Scholar
  25. Guala M, Manes C, Clifton A, Lehning M (2008) On the saltation of fresh snow in a wind tunnel: profile characterization and single particle statistics. J Geophys Res 113:F03024Google Scholar
  26. Hardalupas Y, Horender S (2001) Phase Doppler anemometer for measurements of deterministic spray unsteadiness. Part Part Syst Charact 18(4):205–215CrossRefGoogle Scholar
  27. Kok JF, Renno NO (2009) A comprehensive numerical model of steady state saltation (COMSALT). J Geophys Res 114:D17204CrossRefGoogle Scholar
  28. Lehning M, Löwe H, Ryser M, Raderschall N (2008) Inhomogeneous precipitation distribution and snow transport in steep terrain. Water Resour Res 44(7):W07404CrossRefGoogle Scholar
  29. Lenaerts JTM, van den Broeke MR (2012) Modeling drifting snow in Antarctica with a regional climate model: 2. Results. J Geophys Res 117:D05109Google Scholar
  30. Lieberherr G (2010) Modeling snow drift in the turbulent boundary layer. MSc Thesis, EPFL, Lausanne, 36 ppGoogle Scholar
  31. Lilly DK (1967) The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM scientific computing symposium on environmental sciences. IBM Form No. 320–1951, White Plains, pp 195–209Google Scholar
  32. Mann GW, Anderson PS, Mobbs SD (2000) Profile measurements of blowing snow at Halley Antarctica. J Geophys Res 105(D19):24491–24508CrossRefGoogle Scholar
  33. Moeng CH (1984) A large-eddy simulation model for the study of planetary boundary-layer turbulence. J Atmos Sci 41:2052–2062CrossRefGoogle Scholar
  34. Nemoto M, Nishimura K (2004) Numerical simulation of snow saltation and suspension in a turbulent boundary layer. J Geophys Res 109:D18206CrossRefGoogle Scholar
  35. Nield JM, Wiggs GFS (2011) The application of terrestrial laser scanning to aeolian saltation cloud measurement and its response to changing surface moisture. Earth Surf Process Landf 36(2):273–278CrossRefGoogle Scholar
  36. Nieuwstadt FTM, Brost RA (1986) The decay of convective turbulence. J Atmos Sci 43(6):532–546CrossRefGoogle Scholar
  37. Nishimura K, Hunt JCR (2000) Saltation and incipient suspension above a flat particle bed below a turbulent boundary layer. J Fluid Mech 417:77–102CrossRefGoogle Scholar
  38. Nishimura K, Nemoto M (2005) Blowing snow at Mizuho station Antarctica. Philos Trans Roy Soc 363(1832):1647–1662CrossRefGoogle Scholar
  39. Overney J (2006) Lagrangian stochastic modeling of heavy particle trajectories in atmospheric turbulence. MSc Thesis, EPFL, Lausanne, 55 ppGoogle Scholar
  40. Pomeroy JW, Marsh P, Gray DM (1997) Application of a distributed blowing snow model to the arctic. Hydrol Proc 11(11):1451–1464CrossRefGoogle Scholar
  41. Porté-Agel F, Meneveau C, Parlange MB (2000) A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J Fluid Mech 415:261–284CrossRefGoogle Scholar
  42. Raupach MR (1991) Saltation layers, vegetation canopies and roughness lengths. Acta Mech Suppl 1:83–96CrossRefGoogle Scholar
  43. Rice MA, Willetts BB, McEwan IK (1995) An experimental study of multiple grain-size ejecta produced by collisions of saltating grains with a flat bed. Sedimentol 42(4):695–706CrossRefGoogle Scholar
  44. Sato T, Higashiura M (1997) Characteristics of blowing snow fluctuation. In: Izumi M et al (eds) Snow engineering: recent advances. Balkema, Rotterdam, 650 ppGoogle Scholar
  45. Sato T, Uematsu T, Kaneda Y (1997) Application of random walk model to blowing snow. In: Izumi M et al (eds) Snow engineering: recent advances. Balkema, Rotterdam, 650 ppGoogle Scholar
  46. Schmidt RA (1982) Vertical profiles of wind speed, snow concentration, and humidity in blowing snow. Boundary-Layer Meteorol 23:223–246CrossRefGoogle Scholar
  47. Schneiderbauer S, Prokop A (2011) The atmospheric snow-transport model: SnowDrift3D. J Glaciol 57(203):526–542CrossRefGoogle Scholar
  48. Shao Y, Li A (1999) Numerical modelling of saltation in the atmospheric surface layer. Boundary-Layer Meteorol 91:199–225CrossRefGoogle Scholar
  49. Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic experiment. Mon Weather Rev 91(3):99–164CrossRefGoogle Scholar
  50. Soldati A (2005) Particles turbulence interactions in boundary layers. Z Angew Math Mech 85(10):683–699CrossRefGoogle Scholar
  51. Sterk G, Jacobs AFG, Van Boxel JH (1998) The effect of turbulent flow structures on saltation sand transport in the atmospheric boundary layer. Earth Surface Process Landf 23:877–887CrossRefGoogle Scholar
  52. Stout JE, Zobeck TM (1997) Intermittent saltation. Sedimentology 44:959–970CrossRefGoogle Scholar
  53. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht, 666 ppGoogle Scholar
  54. Sturm M, Stuefer S (2013) Wind-blown flux rates derived from drifts at arctic snow fences. J Glaciol 59(213):21–34CrossRefGoogle Scholar
  55. Sugiura K, Maeno N (2000) Wind-tunnel measurements of restitution coefficients and ejection number of snow particles in drifting snow: Determination of splash functions. Boundary-Layer Meteorol 95(1):123–143CrossRefGoogle Scholar
  56. Sugiura K, Nishimura K, Maeno N, Kimura T (1998) Measurements of snow mass flux and transport rate at different particle diameters in drifting snow. Cold Reg Sci Technol 27(2):83–89CrossRefGoogle Scholar
  57. Sundsbø PA, Hansen EWM (1997) Modelling and numerical simulation of snow drift around snow fences. In: Izumi M et al (eds) Snow engineering: recent advances. Balkema, RotterdamGoogle Scholar
  58. Thomson DJ (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180:529–556CrossRefGoogle Scholar
  59. Tong D, Huang N (2012) Numerical simulation of saltating particles in atmospheric boundary layer over flat bed and sand ripples. J Geophys Res 117:D16205CrossRefGoogle Scholar
  60. Vinkovic I (2005) Dispersion et mélange turbulents de particules solides et de gouttelettes par une simulation des grandes échelles et une modélisation stochastique lagrangienne. PhD thesis, Ecole centrale de LyonGoogle Scholar
  61. Vinkovic I, Aguirre C, Ayrault M, Simoëns S (2006) Large-eddy simulation of the dispersion of solid particles in a turbulent boundary layer. Boundary-Layer Meteorol 121(2):283–311CrossRefGoogle Scholar
  62. Vionnet V, Guyomarc’h G, Martin E, Durand Y, Bellot H, Bel C, Puglièse P (2013) Occurrence of blowing snow events at an alpine site over a 10-year period: observations and modelling. Adv Water Resour 55:53–63CrossRefGoogle Scholar
  63. Weil JC, Sullivan PP, Moeng CH (2004) The use of large-eddy simulations in Lagrangian particle dispersion models. J Atmos Sci 61:2877–2887CrossRefGoogle Scholar
  64. Wilson JD (2000) Trajectory models for heavy particle in atmospheric turbulence: comparison with observations. J Appl Meteorol 39:1894–1912CrossRefGoogle Scholar
  65. Winstral A, Marks D (2002) Simulating wind fields and snow redistribution using terrain-based parameters to model snow accumulation and melt over a semi-arid mountain catchment. Hydrol Proc 16(18):3585–3603CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • C. D. Groot Zwaaftink
    • 1
    • 2
  • M. Diebold
    • 2
  • S. Horender
    • 1
    • 3
  • J. Overney
    • 2
  • G. Lieberherr
    • 2
  • M. B. Parlange
    • 2
  • M. Lehning
    • 1
    • 2
  1. 1.WSL Institute for Snow and Avalanche Research SLFDavosSwitzerland
  2. 2.School of Architecture, Civil and Environmental EngineeringEPFLLausanneSwitzerland
  3. 3.Leibniz Institute for Tropospheric Research (TROPOS)LeipzigGermany

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