Boundary-Layer Meteorology

, Volume 147, Issue 3, pp 401–419 | Cite as

Similarity Scaling Over a Steep Alpine Slope

  • Daniel F. NadeauEmail author
  • Eric R. Pardyjak
  • Chad W. Higgins
  • Marc B. Parlange


In this study, we investigate the validity of similarity scaling over a steep mountain slope (30–41\(^\circ \)). The results are based on eddy-covariance data collected during the Slope Experiment near La Fouly (SELF-2010); a field campaign conducted in a narrow valley of the Swiss Alps during summer 2010. The turbulent fluxes of heat and momentum are found to vary significantly with height in the first few metres above the inclined surface. These variations exceed by an order of magnitude the well-accepted maximum 10 % required for the applicability of Monin–Obukhov similarity theory in the surface layer. This could be due to a surface layer that is too thin to be detected or to the presence of advective fluxes. It is shown that local scaling can be a useful tool in these cases when surface-layer theory breaks down. Under convective conditions and after removing the effects of self-correlation, the normalized standard deviations of slope-normal wind velocity, temperature and humidity scale relatively well with \(z/\varLambda \), where \(z\) is the measurement height and \(\varLambda (z)\) the local Obukhov length. However, the horizontal velocity fluctuations are not correlated with \(z/\varLambda \) under all stability regimes. The non-dimensional gradients of wind velocity and temperature are also investigated. For those, the local scaling appears inappropriate, particularly at night when shallow drainage flows prevail and lead to negative wind-speed gradients close to the surface.


Drainage flow Downslope flow Flux divergence  Flux–gradient relationships Flux–variance relationships Local similarity  Mountain winds Surface layer 



The authors are grateful to all the collaborators at the Laboratory of Environmental Fluid Mechanics at EPFL who helped with the field campaign, and in particular to Hendrik Huwald. The authors would also like to thank Alain Rousseau from the Institut National de la Recherche Scientifique. This work was funded by the Swiss National Foundation under grant 200021-120238 and by the Office of Naval Research Program Award # N00014-11-1-0709, Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program.


  1. Al-Jiboori MH, Xu YM, Qian YF (2002) Local similarity relationships in the urban boundary layer. Boundary-Layer Meteorol 102:63–82CrossRefGoogle Scholar
  2. Andreas EL, Hill RJ, Gosz JR, Moore DI, Otto WD, Sarma AD (1998) Statistics of surface-layer turbulence over terrain with metre-scale heterogeneity. Boundary-Layer Meteorol 86:379–408CrossRefGoogle Scholar
  3. Banta RM (1985) Late-morning jump in TKE in the mixed layer over a mountain basin. J Atmos Sci 42:407–411CrossRefGoogle Scholar
  4. Brooks IM, Rogers DP (2000) Aircraft observations of the mean and turbulent structure of a shallow boundary layer over the Persian Gulf. Boundary-Layer Meteorol 95:189–210CrossRefGoogle Scholar
  5. Brutsaert W (2005) Hydrology: an introduction. Cambridge University Press, Cambridge, UK, 605 ppGoogle Scholar
  6. Brutsaert W, Kustas WP (1987) Surface water vapor and momentum fluxes under unstable conditions from a rugged-complex area. J Atmos Sci 44:421–431CrossRefGoogle Scholar
  7. Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux–profile relationships in the atmospheric surface layer. J Atmos Sci 28:181–189CrossRefGoogle Scholar
  8. Cheng YG, Parlange MB, Brutsaert W (2005) Pathology of Monin–Obukhov similarity in the stable boundary layer. J Geophys Res-Atmos 110:D06101. doi: 10.1029/2004jd004923
  9. de Franceschi M, Zardi D, Tagliazucca M, Tampieri F (2009) Analysis of second-order moments in surface layer turbulence in an Alpine valley. Q J R Meteorol Soc 135:1750–1765CrossRefGoogle Scholar
  10. Drennan WM, Kahma KK, Donelan MA (1999) On momentum flux and velocity spectra over waves. Boundary-Layer Meteorol 92:489–515CrossRefGoogle Scholar
  11. Dyer AJ (1974) A review of flux–profile relationships. Boundary-Layer Meteorol 7:363–372CrossRefGoogle Scholar
  12. Foken T (2006) 50 years of the Monin–Obukhov similarity theory. Boundary-Layer Meteorol 119:431–447CrossRefGoogle Scholar
  13. Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, Cambridge, UK, 316 ppGoogle Scholar
  14. Geissbuhler P, Siegwolf R, Eugster W (2000) Eddy covariance measurements on mountain slopes: the advantage of surface-normal sensor orientation over a vertical set-up. Boundary-Layer Meteorol 96:371–392CrossRefGoogle Scholar
  15. Grachev A, Andreas E, Fairall C, Guest P, Persson P (2007) On the turbulent Prandtl number in the stable atmospheric boundary layer. Boundary-Layer Meteorol 125:329–341CrossRefGoogle Scholar
  16. Grisogono B, Kraljevic L, Jericevic A (2007) Notes and correspondence—the low-level katabatic jet height versus Monin–Obukhov height. Q J R Meteorol Soc 133:2133–2136CrossRefGoogle Scholar
  17. Grubisic V, Doyle JD, Kuettner J, Mobbs S, Smith RB, Whiteman CD, Dirks R, Czyzyk S, Cohn SA, Vosper S, Weissmann M, Haimov S, De Wekker SFJ, Pan LL, Chow FK (2008) The terrain-induced rotor experiment—a field campaign overview including observational highlights. Bull Am Meteorol Soc 89:1513–1533CrossRefGoogle Scholar
  18. Hicks BB (1981) An examination of turbulence statistics in the surface boundary layer. Boundary-Layer Meteorol 21:389–402CrossRefGoogle Scholar
  19. Högström U, Bergström H, Alexandersson H (1982) Turbulence characteristics in a near neutrally stratified urban atmosphere. Boundary-Layer Meteorol 23:449–472CrossRefGoogle Scholar
  20. Holtslag AAM, Nieuwstadt FTM (1986) Scaling the atmospheric boundary-layer. Boundary-Layer Meteorol 36:201–209CrossRefGoogle Scholar
  21. Kader BA, Yaglom AM (1990) Mean fields and fluctuation moments in unstably stratified turbulent boundary-layers. J Fluid Mech 212:637–662CrossRefGoogle Scholar
  22. Khanna S, Brasseur JG (1997) Analysis of Monin–Obukhov similarity from large-eddy simulation. J Fluid Mech 345:251–286CrossRefGoogle Scholar
  23. Klipp CL, Mahrt L (2004) Flux–gradient relationship, self-correlation and intermittency in the stable boundary layer. Q J R Meteorol Soc 130:2087–2103CrossRefGoogle Scholar
  24. Krishnan P, Kunhikrishnan PK (2002) Some characteristics of atmospheric surface layer over a tropical inland region during southwest monsoon period. Atmos Res 62:111–124CrossRefGoogle Scholar
  25. Lenschow DH, Wyngaard JC, Pennell WT (1980) Mean-field and 2nd-moment budgets in a baroclinic, convective boundary-layer. J Atmos Sci 37:1313–1326CrossRefGoogle Scholar
  26. Lenschow DH, Mann J, Kristensen L (1994) How long is long enough when measuring fluxes and other turbulence statistics. J Atmos Ocean Technol 11:661–673CrossRefGoogle Scholar
  27. Mahrt L (1998) Stratified atmospheric boundary layers and breakdown of models. Theor Comput Fluid Dyn 11:263–279CrossRefGoogle Scholar
  28. Mahrt L (1999) Stratified atmospheric boundary layers. Boundary-Layer Meteorol 90:375–396CrossRefGoogle Scholar
  29. Marques EP, Sa LDA, Karam HA, Alvala RCS, Souza A, Pereira MMR (2008) Atmospheric surface layer characteristics of turbulence above the Pantanal wetland regarding the similarity theory. Agric For Meteorol 148:883–892CrossRefGoogle Scholar
  30. Martins CA, Moraes OLL, Acevedo OC, Degrazia GA (2009) Turbulence intensity parameters over a very complex terrain. Boundary-Layer Meteorol 133:35–45CrossRefGoogle Scholar
  31. Monin AS, Obukhov AM (1954) Basic laws of turbulent mixing in the ground layer of the atmosphere. Trudy Inst Theor Geofiz An SSSR 151:163–187 in RussianGoogle Scholar
  32. Nadeau DF, Pardyjak ER, Higgins CW, Huwald H, Parlange MB (2012) Flow during the evening transition over steep alpine slopes. Q J R Meteorol Soc. doi: 10.1002/qJ1985
  33. Nieuwstadt FTM (1984) The turbulent structure of the stable, nocturnal boundary-layer. J Atmos Sci 41:2202–2216CrossRefGoogle Scholar
  34. Nordbo A, Järvi L, Haapanala S, Moilanen J, Vesala T (2012) Intra-city variation in urban morphology and turbulence structure in Helsinki, Finland. Boundary-Layer Meteorol. doi: 10.1007/s10546-012-9773-Y
  35. Panofsky HA, Dutton JA (1984) Atmospheric turbulence. Models and methods for engineering applications. Wiley, New York, 397 ppGoogle Scholar
  36. Panofsky H, Tennekes H, Lenschow D, Wyngaard J (1977) The characteristics of turbulent velocity components in the surface layer under convective conditions. Boundary-Layer Meteorol 11:355–361CrossRefGoogle Scholar
  37. Park MS, Park SU (2006) Effects of topographical slope angle and atmospheric stratification on surface-layer turbulence. Boundary-Layer Meteorol 118:613–633CrossRefGoogle Scholar
  38. Perlik M, Messerli P, Batzing W (2001) Towns in the Alps: urbanization processes, economic structure, and demarcation of European functional urban areas (EFUAs) in the Alps. Mt Res Dev 21:243–252CrossRefGoogle Scholar
  39. Ramana MV, Krishnan P, Kunhikrishnan PK (2004) Surface boundary-layer characteristics over a tropical inland station: seasonal features. Boundary-Layer Meteorol 111:153–175CrossRefGoogle Scholar
  40. Rannik Ü (1998) On the surface layer similarity at a complex forest site. J Geophys Res-Atmos 103:8685–8697Google Scholar
  41. Rotach MW, Zardi D (2007) On the boundary-layer structure over highly complex terrain: key findings from MAP. Q J R Meteorol Soc 133:937–948CrossRefGoogle Scholar
  42. Rotach MW, Andretta M, Calanca P, Weigel AP, Weiss A (2008) Boundary layer characteristics and turbulent exchange mechanisms in highly complex terrain. Acta Geophys 56:194–219CrossRefGoogle Scholar
  43. Shao YP, Hacker JM (1990) Local similarity relationships in a horizontally inhomogeneous boundary-layer. Boundary-Layer Meteorol 52:17–40CrossRefGoogle Scholar
  44. Sorbjan Z (1988) Local similarity in the convective boundary layer. Boundary-Layer Meteorol 45:237–250CrossRefGoogle Scholar
  45. Tamagawa I (1996) Turbulent characteristics and bulk transfer coefficients over the desert in the HEIFE area. Boundary-Layer Meteorol 77:1–20CrossRefGoogle Scholar
  46. Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, New York, 355 ppGoogle Scholar
  47. Wilczak J, Oncley S, Stage S (2001) Sonic anemometer tilt correction algorithms. Boundary-Layer Meteorol 99:127–150CrossRefGoogle Scholar
  48. Wood CR, Lacser A, Barlow JF, Padhra A, Belcher SE, Nemitz E, Helfter C, Famulari D, Grimmond CSB (2010) Turbulent flow at 190 m height above London during 2006–2008: a climatology and the applicability of similarity theory. Boundary-Layer Meteorol 137:77–96CrossRefGoogle Scholar
  49. Xu Y, Chaofu Z, Zhongkai LI, Wei Z (1997) Turbulent structure and local similarity in the tower layer over the Nanjing area. Boundary-Layer Meteorol 82:1–21CrossRefGoogle Scholar
  50. Yusup YB, Daud WRW, Zaharim A, Talib MZM (2008) Structure of the atmospheric surface layer over an industrialized equatorial area. Atmos Res 90:70–77CrossRefGoogle Scholar
  51. Zhang HS, Chen JY, Park SU (2001) Turbulence structure in unstable conditions over various surfaces. Boundary-Layer Meteorol 100:243–261CrossRefGoogle Scholar
  52. Zhong L, Ma Y, Su Z, Lu L, Ma W, Lu Y (2009) Land–atmosphere energy transfer and surface boundary layer characteristics in the Rongbu Valley on the northern slope of Mt. Everest. Arct Antarct Alp Res 41:396–405CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Daniel F. Nadeau
    • 1
    • 4
    Email author
  • Eric R. Pardyjak
    • 2
  • Chad W. Higgins
    • 3
  • Marc B. Parlange
    • 1
  1. 1.School of Architecture, Civil and Environmental EngineeringÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Department of Mechanical EngineeringUniversity of UtahSalt Lake CityUSA
  3. 3.Department of Biological and Ecological EngineeringOregon State UniversityCorvallisUSA
  4. 4.Institut National de la Recherche Scientifique, Centre Eau, Terre et EnvironnementQuebecCanada

Personalised recommendations