Boundary-Layer Meteorology

, Volume 151, Issue 2, pp 373–387 | Cite as

Intercomparison of Methods for the Simultaneous Estimation of Zero-Plane Displacement and Aerodynamic Roughness Length from Single-Level Eddy-Covariance Data

  • Alexander Graf
  • Anneke van de Boer
  • Arnold Moene
  • Harry Vereecken
Research Note


We applied three approaches to estimate the zero-plane displacement \(d\) through the aerodynamic measurement height \(z\) (with \(z = z_{m}- d\) and \(z_{m}\) being the measurement height above the surface), and the aerodynamic roughness length \(z_{0}\), from single-level eddy covariance data. Two approaches (one iterative and one regression-based) were based on the universal function in the logarithmic wind profile and yielded an inherently simultaneous estimation of both \(d\) and \(z_{0}\). The third approach was based on flux–variance similarity, where estimation of \(d\) and consecutive estimation of \(z_{0}\) are independent steps. Each approach was further divided into two methods differing either with respect to the solution technique (profile approaches) or with respect to the variable (variance of vertical wind and temperature, respectively). All methods were applied to measurements above a large, growing wheat field where a uniform canopy height and its frequent monitoring provided plausibility limits for the resulting estimates of time-variant \(d\) and \(z_{0}\). After applying, for each approach, a specific data filtering that accounted for the range of conditions (e.g. stability) for which it is valid, five of the six methods were able to describe the temporal changes of roughness parameters associated with crop growth and harvest, and four of them agreed on \(d\) to within 0.3 m most of the time. Application of the same methods to measurements with a more heterogeneous footprint consisting of fully-grown sugarbeet and a varying contribution of adjacent harvested fields exhibited a plausible dependence of the roughness parameters on the sugarbeet fraction. It also revealed that the methods producing the largest outliers can differ between site conditions and stability. We therefore conclude that when determining \(d\) for canopies with unknown properties from single-level measurements, as is increasingly done, it is important to compare the results of a number of methods rather than rely on a single one. An ensemble average or median of the results, possibly after elimination of methods that produce outliers, can help to yield more robust estimates. The estimates of \(z_{0}\) were almost exclusively physically plausible, although \(d\) was considered unknown and estimated simultaneously with the methods and results described above.


Aerodynamic roughness length Barley Eddy covariance Sonic anemometer Sugarbeet Wheat Zero-plane displacement 



This study was enabled by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the project “Links between local scale and catchment scale measurements and modelling of gas exchange processes over land surfaces” (GR2687/3-1 and SCHU 2350/2-1). Additional synergies were provided by the Helmholtz investment initiative TERENO (instrument availability) and the DFG Collaborative Transregional Research Centre 32 “Patterns in Soil–Vegetation–Atmosphere–Systems”, particularly subproject C3, which provided their canopy-height measurements for comparison and densification of our own observations. We would like to thank Martin Lennefer, University of Bonn, and Bernhard Pospichal, now University of Leipzig, for assistance in the set-up and regular maintenance of the stations, and Dirk Schüttemeyer, University of Bonn (now European Space Agency) for support in the set-up as well as helpful comments on the manuscript. We are indebted to the three anonymous reviewers for suggestions that helped to greatly improve the manuscript.


  1. Blyth EM, Dolman AJ, Wood N (1993) Effective resistance to sensible- and latent-heat flux in heterogeneous terrain. Q J R Meteorol Soc 119:423–442CrossRefGoogle Scholar
  2. de Bruin HAR, Moore CJ (1985) Zero-plane displacement and aerodynamic roughness length for tall vegetation, derived from a simple mass conservation hypothesis. Boundary-Layer Meteorol 31:39–49CrossRefGoogle Scholar
  3. de Bruin HAR, Verhoef A (1997) A new method to determine the zero-plane displacement. Boundary-Layer Meteorol 82:159–164CrossRefGoogle Scholar
  4. 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
  5. Foken T (2008) Micrometeorology. Springer, Heidelberg, 308 ppGoogle Scholar
  6. Garratt JR (1978) Flux profile relations above tall vegetation. Q J R Meteorol Soc 104:199–211CrossRefGoogle Scholar
  7. Garratt JR (1993) Sensitivity of climate simulations to land-surface and atmospheric boundary-layer treatments—a review. J Clim 6:419–449CrossRefGoogle Scholar
  8. Gao Z, Bian L (2004) Estimation of aerodynamic aerodynamic roughness length and zero-plane displacement of an urban surface from single-level sonic anemometer data. Aust Meteorol Mag 53:21–28Google Scholar
  9. Graf A, Schüttemeyer D, Geiß H, Knaps A, Möllmann-Coers M, Schween JH, Kollet S, Neininger B, Herbst M, Vereecken H (2010) Boundedness of turbulent temperature probability distributions, and their relation to the vertical profile in the convective boundary layer. Boundary-Layer Meteorol 134:459–486CrossRefGoogle Scholar
  10. Högström U (1988) Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary-Layer Meteorol 42:55–78CrossRefGoogle Scholar
  11. Holtslag AAM, de Bruin HAR (1988) Applied modelling of the nighttime surface energy balance over land. J Appl Meteorol 27:689–704CrossRefGoogle Scholar
  12. Harman IN, Finnigan JJ (2007) A simple unified theory for flow in the canopy and roughness sublayer. Boundary-Layer Meteorol 123:339–363CrossRefGoogle Scholar
  13. Hsieh C, Katul G, Chi T (2000) An approximate analytical model for footprint estimation of scalar fluxes in thermally stratified atmospheric flows. Adv Water Resour 23:765–772CrossRefGoogle Scholar
  14. Handorf D, Foken T, Kottmeier C (1999) The stable atmospheric boundary layer over an Antarctic ice sheet. Boundary-Layer Meteorol 91:165–186CrossRefGoogle Scholar
  15. Jacobs AFG, van Boxel JH (1988) Changes of the zero-plane displacement and aerodynamic roughness length of maize during the growing season. Agric For Meteorol 42:53–62CrossRefGoogle Scholar
  16. Kormann R, Meixner FX (2001) An analytical footprint model for non-neutral stratification. Boundary-Layer Meteorol 99:207–224CrossRefGoogle Scholar
  17. Kessomkiat W, Hendricks Franssen HJ, Graf A, Vereecken H (2013) Estimating random errors of eddy covariance data: an extended two-tower approach. Agric For Meteorol 171–172:203–219CrossRefGoogle Scholar
  18. Kendall MG, Stuart A (1958) The advanced theory of statistics: distribution theory, vol 1. Griffin, London, 431 ppGoogle Scholar
  19. Kustas WP, Choudhury BJ, Kunkel K, Gay LW (1989) Estimate of the aerodynamic roughness parameters over an incomplete canopy cover of cotton. Agric For Meteorol 46:91–105CrossRefGoogle Scholar
  20. Korres W, Reichenau TG, Schneider K (2013) Patterns and scaling properties of surface soil moisture in an agricultural landscape: an ecohydrological modelling study. J Hydrol 498:89–102CrossRefGoogle Scholar
  21. Lo AK (1976) An analytical-empirical method for determining the aerodynamic roughness length and zero-plane displacement. Boundary-Layer Meteorol 12:141–151CrossRefGoogle Scholar
  22. Lloyd CR, Gash JHC, Sivakumar MVK (1992) Derivation of the aerodynamic roughness parameters for a Sahelian savannah site using the eddy correlation technique. Boundary-Layer Meteorol 58:261–271CrossRefGoogle Scholar
  23. Massman WJ (1997) An analytical one-dimensional model of momentum transfer by vegetation of arbitrary structure. Boundary-Layer Meteorol 83:407–421CrossRefGoogle Scholar
  24. Moore CJ (1986) Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol 37:17–35CrossRefGoogle Scholar
  25. Martano P (2000) Estimation of surface aerodynamic roughness length and zero-plane displacement from single-level sonic anemometer data. J Appl Meteorol 39:708–715CrossRefGoogle Scholar
  26. Massman WJ (2000) A simple method for estimating frequency response corrections for eddy covariance systems. Agric For Meteorol 104:185–198CrossRefGoogle Scholar
  27. Mauder M, Foken T (2004) Documentation and instruction manual of the eddy covariance software package TK2. Arbeitsrgebnisse Univ, Bayreuth, Abt. Mikrometeorologie, Nr. 26Google Scholar
  28. Moene AF, Michels BI (2002) Estimation of the statistical error in large eddy simulation results, 15–19 July 2002, Wageningen. American Meteorological Society, Boston, p 3.12Google Scholar
  29. Monin AS, Oukhov AM (1954) Osnovnye zakonomernosti turbulentnogo peremesivanija v prizemnom sloe atmosfery (Basic laws of turbulent mixing in the atmosphere near the ground). Trudy Geofiz Inst AN SSSR 24(151):163–187Google Scholar
  30. Neftel A, Spirig C, Ammann C (2008) Application and test of a simple tool for operational footprint evaluations. Environ Pollut 152:644–652CrossRefGoogle Scholar
  31. Paulson CA (1970) The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J Appl Meteorol 9:857–861CrossRefGoogle Scholar
  32. Panofsky HA (1984) Vertical variation of roughness length at the Boulder atmospheric observatory. Boundary-Layer Meteorol 28:305–308CrossRefGoogle Scholar
  33. Panofsky HA, Tennekes H, Lenschow DH, Wyngaard JC (1977) The characteristics of turbulent velocity components in the surface layer under convective conditions. Boundary-Layer Meteorol 11:355–361CrossRefGoogle Scholar
  34. Prueger JH, Kustas WP, Hipps LE, Hatfield JL (2004) Aerodynamic parameters and sensible heat flux estimates for a semi-arid ecosystem. J Arid Environ 57:87–100CrossRefGoogle Scholar
  35. Raupach MR (1994) Simplified expressions for vegetation aerodynamic roughness length and zero-plane displacement as functions of canopy height and area index. Boundary-Layer Meteorol 71:211–216CrossRefGoogle Scholar
  36. Rotach MW (1994) Determination of the zero plane displacement in an urban environment. Boundary-Layer Meteorol 67:187–193CrossRefGoogle Scholar
  37. Schmid HP (1994) Source areas for scalars and fluxes. Boundary-Layer Meteorol 67:293–318CrossRefGoogle Scholar
  38. Schotanus P, Nieuwstadt FTM, de Bruin HAR (1983) Temperature-measurement with a sonic anemometer and its application to heat and moisture fluxes. Boundary-Layer Meteorol 26:81–93CrossRefGoogle Scholar
  39. Takagi K, Miyata A, Harazono Y, Ota N, Komine M, Yoshimoto M (2003) An alternative approach to determining zero-plane displacement, and its application to a lotus paddy field. Agric For Meteorol 115:173–181CrossRefGoogle Scholar
  40. Toda M, Sugita M (2003) Single level turbulence measurements to determine roughness parameters of complex terrain. J Geophys Res 108(D12):4363CrossRefGoogle Scholar
  41. Tsai JL, Tsuang BJ, Lu PS (2010) Measurements of aerodynamic roughness, Bowen ratio, and atmospheric surface layer height by eddy covariance and tethersonde systems simultaneously over a heterogeneous rice paddy. J Hydrometeorol 11:452–466CrossRefGoogle Scholar
  42. van Dijk A, Moene AF, de Bruin HAR (2004) The principle of surface flux physics: theory, practice and description of the ECPACK library. Internal report 2004/1. Meteorology and Air Quality Group, Wageningen University, Wageningen, The Netherlands, 99 ppGoogle Scholar
  43. van de Boer A, Moene AF, Schüttemeyer D, Graf A (2013) Sensitivity and uncertainty of analytical footprint models according to a combined natural tracer and ensemble approach. Agric For Meteorol 169:1–11CrossRefGoogle Scholar
  44. Weaver HL (1990) Temperature and humidity flux–variance relations determined by one-dimensional eddy correlation. Boundary-Layer Meteorol 53:77–91CrossRefGoogle Scholar
  45. Wieringa J (1993) Representative roughness parameters for homogeneous terrain. Boundary-Layer Meteorol 63:323–363CrossRefGoogle Scholar
  46. Wilczak JM, Oncley SP, Stage SA (2001) Sonic anemometer tilt correction algorithms. Boundary-Layer Meteorol 99:127–150CrossRefGoogle Scholar
  47. Zhang HS, Park SU (1999) Comments on ‘A new method to determine the zero-plane displacement’. Boundary-Layer Meteorol 91:135–139CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Alexander Graf
    • 1
  • Anneke van de Boer
    • 2
    • 3
  • Arnold Moene
    • 3
  • Harry Vereecken
    • 1
  1. 1.Agrosphere (IBG-3), Institute of Bio- and GeosciencesJülich Research CentreJülichGermany
  2. 2.Meteorological InstituteUniversity of BonnBonnGermany
  3. 3.Meteorology and Air Quality DepartmentWageningen UniversityWageningenThe Netherlands

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