Abstract
Given incident logarithmic profiles of wind and pollutant concentration above a rough, absorbing surface, the three-dimensional distribution of pollutant concentration over a hill of gentle slope is determined from a linearized model. The model is applied in neutrally stratified flow, without chemistry, and is integrated using spectral methods in the horizontal and a finite-difference scheme in the vertical. This approach allows for flexibility in choosing a closure scheme and a variety of surface boundary conditions. This was not possible in the analytic approach of Padro (1987) who added pollutant concentration and flux to the MS3DJH/1 model of Walmsley et al. (1980). The present model requires as input the turbulent kinetic energy, E, dissipation, ε, and the perturbation vertical velocity, w, from the three-dimensional boundary-layer flow model of Beljaars et al. (1987), hereinafter referred to as MSFD, The latter model also supplies wind velocity perturbations at the upper boundary, as input to upper boundary conditions on the pollutant flux perturbations.
The present study describes applications of the model to idealized terrain features: isolated two- and three-dimensional hills and ridges and an infinite series of ridges. (Application to real terrain, however, presents no difficulties.) Comparisons were made with different (though uniform) surface roughnesses. Tests were performed to examine the effect of upstream terrain features in the periodic domain and to illustrate the importance of the vertical resolution of the output for interpreting results from the sinusoidal terrain case.
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References
Beljaars, A. C. M., Walmsley, J. L., and Taylor, P. A.: 1987, ‘A Mixed Spectral Finite-Difference Model for Neutrally Stratified Boundary-Layer Flow over Roughness Changes and Topography’, Boundary-Layer Meteorol. 38, 273–303.
Hanjalic, K. and Launder, B. E.: 1972, ‘A Reynolds Stress Model of Turbulence and its Application to Thin Shear Flows’, J. Fluid Mech. 52, 609–638.
Hunt, J. C. R. and Simpson, J. E.: 1982, ‘Atmospheric Boundary Layers over Non-Homogeneous Terrain’, in E. J. Plate (ed.), Engineering Meteorology, Elsevier, Amsterdam.
Jackson, P. S. and Hunt, J. C. R.: 1975, ‘Turbulent Flow over a Low Hill’, Quart. J. Roy. Meteorol. Soc. 101, 929–955.
Karpik, S. R.: 1988, ‘An Improved Method for Integrating the Mixed Spectral Finite Difference (MSFD) Model Equations’, Boundary-Layer Meteorol. 43, 273–286.
Launder, B. E.: 1975, Prediction Methods for Turbulent Flows, Von Karman Institute, Rhode-St-Genese, Belgium.
Mason, P. J. and King, J. C.: 1985, ‘Measurements and Predictions of Flow and Turbulence over an Isolated Hill of Moderate Slope’, Quart. J. Roy. Meteorol. Soc. 111, 617–640.
Mason, P. J. and Sykes, R. I.: 1979, ‘Flow over an Isolated Hill of Moderate Slope’, Quart. J. Roy. Meteorol. Soc. 105, 383–395.
Mickle, R. E., Cook, N. J., Hoff, A. M., Jensen, N. O., Salmon, J. R., Taylor, P. A., Tetzlaff, G., and Teunissen, H. W.: 1988, ‘The Askervein Hill Project: Vertical Profiles of Wind and Turbulence’, Boundary-Layer Meteorol. 43, 143–169.
Padro, J.: 1987, ‘Boundary-Layer Pollutant Concentrations over Complex Terrain’, Boundary-Layer Meteorol. 38, 17–28.
Panofsky, H. A. and Dutton, J. A.: 1984, Atmospheric Turbulence: Models and Methods for Engineering Applications, John Wiley, New York, 397 pp.
Pielke, R. A.: 1984, Mesoscale Meteorological Modelling, Academic Press, Orlando, Florida, 612 pp.
Taylor, P. A., Walmsley, J. L., and Salmon, J. R.: 1983, ‘A Simple Model of Neutrally Stratified Boundary-Layer Flow over Real Terrain Incorporating Wavenumber-Dependent Scaling’, Boundary-Layer Meteorol. 26, 169–189.
Walmsley, J. L. and Padro, J.: 1990, ‘Shear Stress Results from a Mixed Spectral Finite-Difference Model: Application to the Askervein Hill Project Data’, Boundary-Layer Meteorol. 51, 163–172.
Walmsley, J. L., Salmon, J. R., and Taylor, P. A.: 1982, ‘On the Application of a Model of Boundary-Layer Flow over Low Hills to Real Terrain’, Boundary-Layer Meteorol. 23, 17–46.
Walmsley, J. L., Taylor, P. A., and Keith, T.: 1986, ‘A Simple Model of Neutrally Stratified Boundary-Layer Flow over Complex Terrain with Surface Roughness Modulations (MS3DJH/3R)’, Boundary-Layer Meteorol. 36, 157–186.
Walmsley, J. L., Taylor, P. A., and Salmon, J. R.: 1989, ‘Simple Guidelines for Estimating Wind Speed Variations due to Small-Scale Topographic Features — An Update’, Climatol. Bull. 23, 3–14.
Yamada, T.: 1977, ‘A Numerical Experiment on Pollutant Dispersion in a Horizontally-Homogeneous Atmospheric Boundary Layer’, Atmos. Environ. 11, 1015–1024.
Zeman, O, and Jensen, N. O.: 1987, ‘Modification of Turbulence Characteristics in Flow over Hills’, Quart. J. Roy. Meteorol. Soc. 113, 55–80.
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Padro, J., Walmsley, J.L. A mixed spectral finite-difference model for pollutant concentrations over a hill. Boundary-Layer Meteorol 51, 343–363 (1990). https://doi.org/10.1007/BF00119673
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DOI: https://doi.org/10.1007/BF00119673