Abstract
A method based on the principle of the Method of Weighted Residuals for evaluating the roughness-length (z 0) and zero-plane displacement (d) is presented. This method not only can minimize errors involved during the calculation process but can also smooth and re-distribute the already minimized error in a most favourable manner via using appropriate weighting functions. With the inclusion of d in addition to z 0, formulae for wind and temperature profiles in the surface layer are presented by:% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGvbGaeyypa0% ZaaSaaaeaacaWG1bWaaSbaaSqaaiaacQcaaeqaaaGcbaGaam4Aaaaa% daWadaqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiaadQhacqGHsi% slcaWGKbaabaGaamOEamaaBaaaleaacaaIWaaabeaaaaaakiaawIca% caGLPaaacqGHRaWkcqaHipqEaiaawUfacaGLDbaaaaa!43FC!\[U = \frac{{u_* }}{k}\left[ {\ln \left( {\frac{{z - d}}{{z_0 }}} \right) + \psi } \right]\]and% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH4oqCcqGHsi% slcqaH4oqCdaWgaaWcbaGaaGimaaqabaGccqGH9aqpcqaH4oqCdaWa% daqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiaadQhacqGHsislca% WGKbaabaGaamOEamaaBaaaleaacaaIWaaabeaaaaaakiaawIcacaGL% PaaacqGHRaWkcqaHipqEdaWgaaWcbaacbmGaa8hvaaqabaaakiaawU% facaGLDbaaaaa!485A!\[\theta - \theta _0 = \theta \left[ {\ln \left( {\frac{{z - d}}{{z_0 }}} \right) + \psi _T } \right]\]where ψ and ψ T are the ‘integrated diabetic influence functions’' for velocity and temperature profiles respectively.
Analytical expressions for both ψ and ψ T as functions of wind shear or, implicitly in terms of the Richardson number have been derived.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lettau, H. H. and Stearns, C. R.: 1969, ‘Studies of Effects of Boundary Modification in Problems of Small Area Meteorology’, ECOM 66-G24-F, United States Army Electronics Command, Atmospheric Sciences Laboratory, Fort Huachuca, Arizona.
Lo, A. K.: 1977, ‘Boundary Layer Flow over a Gentle Curvilinear Topography with a Sudden Change in Surface Roughness’, Quart. J. Roy. Meteorol. Soc. 103, 199–209.
Monin, A. S. and Obukhov, A. M.: 1954, ‘Dimensionless Characteristics of Turbulence in the Surface Layer’, Akad. SSR. Geofis. Trudy 24, 151–163.
Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics, (John L. Lumley, ed.), The MIT Press, 769 pp.
Mukammal, E. I.: 1968, ‘Comparison of Pine Forest Evapotranspiration Estimated by Energy Budget, Aerodynamic, and Priestley Method’, (unpublished report).
Paulson, C. A.: 1970, ‘The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer’, J. Appl. Meteorol. 9, 857–861.
Peterson, E. W., Kristenson, L., and Su, C. C.: 1976, ‘Some Observations and Analysis of Wind over Nonuniform Terrain’, Quart. J. Roy. Meteorol. Soc. 102, 857–869.
Stearns, C. R.: 1970, ‘Determining Surface Roughness and Displacement Height’, Boundary-Layer Meteorol. 1, 102–111.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lo, A.K. An analytical-empirical method for determining the roughness length and zero-plane displacement. Boundary-Layer Meteorol 12, 141–151 (1977). https://doi.org/10.1007/BF00121969
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00121969