The complexity of solving problems of air quality in urbanized areas lies in the disparity of spatiotemporal scales over which the phenomena take place. In particular, two of the most important scales include: (a) - an ‘urban scale' of a few tens of kilometers (a typical city size), where primary pollutions are emitted, and (b) - a ‘meso-scale' of a few hundreds of kilometers, where the secondary pollutions are formed and dispersed.

In order to determine average and turbulent transport and chemical transformations of pollutants, it is necessary to accurately predict major meteorological quantities such as wind, turbulent fluxes of momentum, heat and mass, temperature, pressure, and humidity. The effects of urban roughness must be parameterized because the horizontal size of the region is on the order of the mesoscale (100 km) and the difference-grid spacing minimized with respect to computational time consumption is generally within several hundred meters and, consequently, the structure of the urbanized surface of the city is difficult to resolve in details.

The two most important effects of an urbanized surface on the structure of air flow over it are: (a) drag on the incident air flow from buildings (because of pressure difference across roughness elements) and (b) differential heating of urbanized surfaces, which is able to generate the effect of an urban heat island.

In this study, a modified three-parameter model of turbulence for a thermally stratified planetary boundary layer (PBL) is developed. The model is based on tensor-invariant parameterizations for the pressure–strain and pressure–temperature correlations that are more complete than parameterizations used in the Mellor–Yamada model of level 3.0. Turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbolic algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence [1, 2]. The three-parameter E-epsilon-theta^2 model of thermally stratified turbulence is employed to obtain closed form algebraic expressions for the fluxes [3]. A computational test of a 24-hour PBL evolution is implemented for an idealized two-dimensional region. Comparisons of computed results with available observational data [4] and other numerical models show [1] that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized PBL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city.

Sample results

The urban-heat-island phenomenon and its associated circulation driven by the energy generated by anthropogenic sources are found to be most intense at nighttime under clear skies and weak ambient wind. The new three-parametric turbulence model developed for simulation of a turbulent urban-heat-island structure has high computational efficiency [1-3]. The numerical results are in good agreement with data of laboratory experiments [5].

The improved mesoscale model for the turbulent PBL is capable to reproduce the most important features of wind field above the city. Simulation results show that the thermal circulation caused by longitudinal temperature gradient between hotter air above city and colder air of its vicinities increases speed of wind aloft on a leeside [6], and the term of the longitudinal turbulent diffusion in the potential temperature equation acts to increase the daytime boundary layer height above the city.

One area of interest in the study of an urban boundary layer is related to the pollutant dispersion.  The modeling results of passive tracer diffusion emitted at ground level in the center of an urban area with a time variation typical of traffic emissions (high in the afternoon and low at night) are obtained. The concentrations computed by the model at the lowest level in the centre of the urban area are higher during the night than during the day, as expected. Moreover, the position and intensity of the peak downwind over the city are also different.

Aircraft measurements have revealed counter-gradient heat flows from about 150 m above the ground to about 350 and 1250 m, respectively. The occurrence of counter-gradient sensible heat flux is not predicted by simple K-theory for the turbulent heat flux [7]. The anisotropic algebraic expression for the vertical turbulent heat flux is derived using symbolic algebra. It includes the counter-gradient term [7], which makes it physical correct by taking into account non-local effects of the turbulent heat transport mechanism [2].

Acknowledgements

The author would like to thank the Russian foundation for Basic Research for financial support (grant # 03-05-64005, 06-05-64002).

References

1.    Kurbatskiy, A. F. and Kurbatskaya, L. I.  2006. Three-Parameter Model of Turbulence for the Atmospheric Boundary Layer over an Urbanized Surface. Izvestia. Atmospheric and Oceanic Physics. 42, 439-455.

2.    Kurbatskiy, A. F.  2007. Modeling and Simulation of Urban Boundary Layer over a Flat Terrain. Environmental Fluid Mechanics (submitted).

3.    Kurbatskii, A.F. 2001. Computational modelling of the penetrative convection above the urban heat island in a stably stratified environment. J. Appl. Meteor., 40, 1748-1761.

4.    Roth, M.  2000. Review of Atmospheric Turbulence over Cites. Quart. J. Roy. Meteor. Soc. 126, 941–990.

5.    Lu J., Araya S.P., Snyder W.H., Jr. Lawson R.E. 1997. A Laboratory Study of the Urban Heat Island in a Calm and Stably Stratified Environment. Part I: Temperature Field; Part II: Velocity Field, J. Appl. Meteor. 36, 1377-1402.

6.    Bornstein R. D. and Johnson D.S. 1977. Urban-Rural wind velocity differences. Atmospheric Environment. 11, 597-604.

7.    Deardorff, J. W. 1966. The counter-gradient heat flux in the lower atmosphere and in the laboratory. J. Atmos. Sci. 23, 503-506.