Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model


The spatial peak surface shear stress \({\tau _S^{\prime\prime}}\) on the ground beneath vegetation canopies is responsible for the onset of particle entrainment and its precise and accurate prediction is essential when modelling soil, snow or sand erosion. This study investigates shear-stress partitioning, i.e. the fraction of the total fluid stress on the entire canopy that acts directly on the surface, for live vegetation canopies (plant species: Lolium perenne) using measurements in a controlled wind-tunnel environment. Rigid, non-porous wooden blocks instead of the plants were additionally tested for the purpose of comparison since previous wind-tunnel studies used exclusively artificial plant imitations for their experiments on shear-stress partitioning. The drag partitioning model presented by Raupach (Boundary-Layer Meteorol 60:375–395, 1992) and Raupach et al. (J Geophys Res 98:3023–3029, 1993), which allows the prediction of the total shear stress τ on the entire canopy as well as the peak \({(\tau _S ^{\prime\prime}/\tau )^{1/2}}\) and the average \({(\tau _S^{\prime}/\tau )^{1/2}}\) shear-stress ratios, is tested against measurements to determine the model parameters and the model’s ability to account for shape differences of various roughness elements. It was found that the constant c, needed to determine the total stress τ and which was unspecified to date, can be assumed a value of about c = 0.27. Values for the model parameter m, which accounts for the difference between the spatial surface average \({\tau _S^{\prime}}\) and the peak \({\tau _S ^{\prime\prime}}\) shear stress, are difficult to determine because m is a function of the roughness density, the wind velocity and the roughness element shape. A new definition for a parameter a is suggested as a substitute for m. This a parameter is found to be more closely universal and solely a function of the roughness element shape. It is able to predict the peak surface shear stress accurately. Finally, a method is presented to determine the new a parameter for different kinds of roughness elements.

This is a preview of subscription content, access via your institution.


A f :

Roughness element frontal area

A :

Effective shelter area

C R :

Roughness element drag coefficient

C S :

Surface drag coefficient

R 2 :

Coefficient of determination

Re h  = U h h/ν:

Roughness element Reynolds number

S :

Total surface area per roughness element


Exposed surface area per roughness element

U δ :

Free stream velocity

\({\langle U_i \rangle}\) :

Spatiotemporally-averaged velocity inside the canopy

U h :

Mean velocity at top of roughness elements

V :

Effective shelter volume

a :

\({\tau _S ^{\prime\prime}/\tau _S^{\prime}}\) peak mean stress ratio

a i :

Fit parameters

b :

Roughness element width

b i :

Fit parameters

c, c i , c′ and c′′:

Constants of proportionality

h :

Roughness element height

m :

Parameter defining relation between \({\tau _S ^{\prime\prime}}\) and \({\tau _S^{\prime}}\)

u * = (τ /ρ)1/2 :

Friction velocity

u τ :

Skin friction velocity

\({-\overline {u^{\prime}w^{\prime}}}\) :

Kinematic Reynolds stress

z 0 :

Aerodynamic roughness length

βC R /C S :

Roughness element to surface drag coefficient ratio

λA f /S :

Roughness density

\({\nu \approx 1.5\times 10^{-5} {m}^{2} {s}^{-1}}\) :

Kinematic viscosity of air

\({\Phi}\) :

Force on single roughness element

ρ :

Air density

σ :

Ratio of roughness element basal to frontal area

\({\tau = \rho u_*^2}\) :

Total shear stress on entire canopy

τ R :

Shear stress acting on roughness elements

τ S :

Spatial average surface shear stress on area S

τ S (x, y):

Local surface shear stress

\({\tau _S^{\prime}}\) :

Spatial average surface shear stress on area S

\({\tau _S ^{\prime\prime}}\) :

Spatial peak surface shear stress


  1. Arya SPS (1975) A drag partition theory for determining the large-scale roughness parameter and wind stress on the Arctic pack ice. J Geophys Res 80: 3447–3454

    Article  Google Scholar 

  2. Bagnold R (1941) The physics of blown sand and desert dunes. Meghuen, London 265 pp

  3. Brown S, Nickling WG, Gillies JA (2008) A wind tunnel examination of shear stress partitioning for an assortment of surface roughness distributions. J Geophys Res. doi:10.1029/2007JF000790

  4. Burri K, Gromke C, Graf F (2011a) Mycorrhizal fungi protect the soil from wind erosion: a wind tunnel study. Land Degrad Dev. doi:10.1002/ldr.1136

  5. Burri K, Gromke C, Lehning M, Graf F (2011b) Aeolian sediment transport over vegetation canopies: a wind tunnel study with live plants. Aeolian Res 3: 205–213

    Article  Google Scholar 

  6. Clifton A, Lehning M (2008) Improvement and validation of a snow saltation model using wind tunnel measurements. Earth Surface Process Landf 33: 2156–2173. doi:10.1002/Esp.1673

    Article  Google Scholar 

  7. Clifton A, Ruedi JD, Lehning M (2006) Snow saltation threshold measurements in a drifting-snow wind tunnel. J Glaciol 52(179): 585–596

    Article  Google Scholar 

  8. Clifton A, Manes C, Ruedi JD, Guala M, Lehning M (2008) On shear-driven ventilation of snow. Boundary-Layer Meteorol 126: 249–261

    Article  Google Scholar 

  9. Crawley DM, Nickling WG (2003) Drag partition for regularly-arrayed rough surfaces. Boundary-Layer Meteorol 107: 445–468

    Article  Google Scholar 

  10. Gillies JA, Nickling WG, King J (2002) Drag coefficient and plant form response to wind speed in three plant species: burning Bush (Euonymus alatus), Colorado Blue Spruce (Picea pungens glauca.), and Fountain Grass (Pennisetum setaceum). J Geophys Res. doi:10.1029/2001JD001259

  11. Gillies JA, Nickling WG, King J (2007) Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer. Boundary-Layer Meteorol 122: 367–396

    Article  Google Scholar 

  12. Gromke C, Ruck B (2008) Aerodynamic modelling of trees for small-scale wind tunnel studies. Forestry 81: 243–258

    Article  Google Scholar 

  13. Gromke C, Manes C, Walter B, Lehning M, Guala M (2011) Aerodynamic roughness length of fresh snow. Boundary-Layer Meteorol. doi:10.1007/s10546-011-9623-3

  14. 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 Earth Surf 113: F03024

    Article  Google Scholar 

  15. Irwin HPAH (1981) A simple omnidirectional sensor for wind-tunnel studies of pedestrian-level winds. J Wind Eng Ind Aerodyn 7: 219–239

    Article  Google Scholar 

  16. King J, Nickling WG, Gillies JA (2006) Aeolian shear stress ratio measurements within mesquite-dominated landscapes of the Chihuahuan Desert, New Mexico, USA. Geomorphology 82: 229–244

    Article  Google Scholar 

  17. Lyles L, Allison BE (1975) Wind erosion: uniformly spacing nonerodible elements eliminates effects of wind direction variability. J Soil Water Conserv 30: 225–226

    Google Scholar 

  18. Marshall JK (1971) Drag measurements in roughness arrays of varying density and distribution. Agric Meteorol 8: 269–292

    Article  Google Scholar 

  19. Musick HB, Gillette DA (1990) Field evaluation of relationships between a vegetation structural parameter and sheltering against wind erosion. Land Deg Rehabil 2: 87–94

    Article  Google Scholar 

  20. Musick HB, Trujillo SM, Truman CR (1996) Wind-tunnel modelling of the influence of vegetation structure on saltation threshold. Earth Surf Process Landf 21: 589–605

    Article  Google Scholar 

  21. Raupach MR (1992) Drag and drag partition on rough surfaces. Boundary-Layer Meteorol 60: 375–395

    Article  Google Scholar 

  22. Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44: 1–25

    Article  Google Scholar 

  23. Raupach MR, Gillette DA, Leys JF (1993) The effect of roughness elements on wind erosion threshold. J Geophys Res 98: 3023–3029

    Article  Google Scholar 

  24. Schlichting H (1936) Experimental investigations of the problem of surface roughness. NASA technical memorandum 823, Washington, DC

  25. Shao Y, Yang Y (2005) A scheme for drag partition over rough surfaces. Atmos Environ 39: 7351–7361

    Article  Google Scholar 

  26. Shao Y, Yang Y (2008) A theory for drag partition over rough surfaces. J Geophys Res 113: F02S05

    Article  Google Scholar 

  27. Walter B, Gromke C, Lehning M (2009) The SLF boundary layer wind tunnel—an experimental facility for aerodynamical investigations of living plants. In: 2nd international conference on wind effects on trees, Freiburg, Germany

  28. Walter B, Gromke C, Leonard K, Clifton A, Lehning M (2012a) Spatially resolved skin friction velocity measurements using Irwin sensors: a calibration and accuracy analysis. J Wind Eng Ind Aerodyn. doi:10.1016/j.jweia.2012.02.018

  29. Walter B, Gromke C, Leonard K, Manes C, Lehning M (2012b) Spatio-temporal surface shear stress variability in live plant canopies and cube arrays. Boundary-Layer Meteorol. doi:10.1007/s10546-011-9690-5

  30. Wolfe SA, Nickling WG (1996) Shear stress partitioning in sparsely vegetated desert canopies. Earth Surf Process Landf 21: 607–619

    Article  Google Scholar 

  31. Wooding RA, Bradley EF, Marshall JK (1973) Drag due to regular arrays of roughness elements of varying geometry. Boundary-Layer Meteorol 5: 285–308

    Article  Google Scholar 

  32. Wyatt VE, Nickling WG (1997) Drag and shear stress partitioning in sparse desert creosote communities. Can J Earth Sci 34: 1486–1498

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Benjamin Walter.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Walter, B., Gromke, C. & Lehning, M. Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model. Boundary-Layer Meteorol 144, 217–241 (2012).

Download citation


  • Boundary-layer flow
  • Drag partitioning
  • Irwin sensor
  • Shear-stress ratio
  • Vegetation canopy
  • Wind tunnel