The refinement of a meteorological preprocessor for the urban environment. Ari Karppinen, Sylvain M. Joffre and Jaakko Kukkonen

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1 Int. J. Environment and Pollution, Vol. 14, No. 1-6, The refinement of a meteorological preprocessor for the urban environment Ari Karppinen, Slvain M. Joffre and Jaakko Kukkonen Finnish Meteorological Institute, Air Qualit Research, Sahaajankatu 0 E, FIN 00810, Helsinki, Finland Abstract: The meteorological preprocessor used routinel at the Finnish Meteorological Institute (FMI) has been modified in order to better represent urban conditions. We have re-evaluated the roughness length, introduced the ero-displacement height and divided the surface laer into a roughness sublaer and an inertial sublaer. The friction velocit and Monin-Obukhov length are evaluated using an empiricall developed exponential Renoldsstress profile in the roughness sublaer. The effect of these modifications has been studied b computing the dispersion parameters used in the urban dispersion modelling sstem UDM-FMI and comparing the revised parameters with the previous model computations. Kewords: meteorological preprocessor, urban environment, dispersion Reference to this paper should be made as follows: Karppinen, A., Joffre, S. M. and Kukkonen, J. (000) The refinement of a meteorological preprocessor for the urban environment, Int. J. Environment and Pollution, Vol. 14, No. 1-6, pp Introduction Short-range atmospheric dispersion models require input data on the state of the atmospheric boundar laer. These models need estimates of at least the mean plume transport velocit, the lateral and vertical components of turbulent energ, the vertical stabilit parameter and the mixing depth. Not all of these parameters are routinel observed, and it is therefore necessar to estimate them in terms of the routinel observed variables, using a so-called meteorological preprocessor. The meteorological preprocessor applied in combination with the regulator atmospheric dispersion models in Finland (Karppinen et al., 1997) was originall designed for rural areas onl. This paper describes the modifications of the meteorological preprocessor in order to account for urban conditions. The atmospheric surface laer is divided into two parts: a roughness sublaer of height * and an inertial sublaer. Monin-Obukhov similarit laws are expected to be valid onl in the inertial sublaer (Rotach, 1996). Close to the ground surface, the local Renolds stress profile is used to recalculate the relevant turbulence parameters. The ke parameter in order to characterise vertical turbulence, the Monin-Obukhov length, can be assumed to be equal to the depth of the mechanicall well-mixed laer Copright 000 Inderscience Enterprises td.

2 A. Karppinen, S. M. Joffre and J. Kukkonen (for instance, Stull, 1988); this can be identified as the roughness sublaer. In stable conditions we therefore set the minimum value for to be equal to * ( * min ). The influence of these modifications has been analsed b computing the dispersion parameters used in the UDM-FMI dispersion modelling sstem, and comparing the revised parameters with the previous "non-urban" model computations. Description of the meteorological pre-processor The meteorological pre-processing model is based on the method developed originall b van Ulden and Holtslag (1985). This method evaluates the turbulent heat and momentum fluxes in the atmospheric boundar laer (AB) from snoptic weather observations. The parameteriation of the AB height is based on boundar laer scaling, utiliing meteorological sounding data. The four main scaling parameters of this method are: the roughness height o, the friction velocit u *, the temperature scale θ * and the boundar laer height i. The friction velocit u * determines the shear production of turbulent kinetic energ at the surface. According to surface-laer similarit theor, the wind speed U () is related to u * b u * o U ( ) ln ψ m + ψ m. (1) k o The influence function ψ m can be evaluated from (van Ulden and Holtslag, 1985): 1 / 4 ψ m for unstable stratification ( < 0) () m 17 1 exp ( 0.9 ) ψ for stable stratification ( > 0) (3) The Monin-Obukhov length is defined b the velocit and temperature scales as T u* k gθ (4) where T is the air temperature at the height of m, and k is the von Karman constant. The scaling temperature θ * can be written in terms of the turbulent kinematic heat flux at the surface Q o and the friction velocit, i.e.: θ * - Q o / u *. The mixing height h is defined as the mean height to which turbulence extends verticall. In unstable conditions, scalar quantities (eg. temperature, moisture) are generall well-mixed up to this height.

3 The refinement of a meteorological preprocessor for the urban environment 3 3. The dispersion parameters The turbulence dispersion parameters in the UDM-FMI dispersion model (Karppinen et al., 1998) are written in terms of the turbulence intensities as (Hanna, 1985): σ t i σ i t f x, f x, σ v i U σ w i U ( ) ( ),, f f [ 1+ B x] 1 1 [ 1+ B x] (5) where i and i are the lateral and vertical turbulence intensities, f and f are functions of the downwind distance x, σ v and σ w are the standard deviations of the turbulent velocit fluctuations in the lateral and vertical direction, and U () is the average wind speed at height. In this paper we investigate onl the effect of urban scaling on the parameters σ v and σ w, although in the modelling sstem the parameter B also is a function of the roughness length and Monin-Obukhov length (and therefore stabilit) as follows: 0, B pq, , p q 0.5,( unstable) 0.5 < p p q q <.0,( neutral).0,( stable) where the dimensionless stabilit parameter p q is calculated from : (6) p q ( ) o + [ ln( )] o exp o This equation represents a functional relationship between Monin-Obukhov length and roughness length o for various Pasquill stabilit classes (Karppinen et al., 1998). In equation (5) for unstable situations B 0, which means that f 1. The standard deviations of the turbulent velocit fluctuations σ v and σ w for point and area sources are evaluated at the average dispersion height H eff as follows. In stable conditions ( > 0), (7) H u.0 1 eff v i σ and σ w H u eff i (8)

4 4 A. Karppinen, S. M. Joffre and J. Kukkonen and in unstable conditions ( < 0), 3 / i Heff σ v u * k i σ 1 /.., and / 3 / 3 H eff H eff H * 1.54 i eff exp w u k i i i 1/ (9) These equations can be derived based on Wratt (1987), Ara (1984) and Caughe et al.(1979); as presented b Karppinen et al. (1998). 4. Modifications in order to allow for urban conditions In order to allow for the influence of urban conditions, we have re-evaluated the roughness height o and introduced the ero-displacement height d, using a computational method discussed b Rotach (1997). The quantities o and d were determined for the Helsinki metropolitan area. We have also divided the surface laer into a roughness sublaer and an inertial sublaer. In stable conditions, we have used the height of the roughness sublaer * as a lower limit for the Monin-Obukhov length, as can be interpreted as the depth of the mechanicall well-mixed laer. It is therefore plausible to assume that the Monin- Obukhov length * min, since the roughness sublaer height * is the height, at which the urban roughness elements are generating a more intense turbulence b definition. 5. Application to the Helsinki metropolitan area The roughness length and ero-displacement height are evaluated b utiliing an estimate of the proportion of built-up area: A R /A 15 %. This value is based on the roughness element densit and the average building height h of 10 m in the Helsinki metropolitan area (Cit of Helsinki, 1997). Using these values in the formula of Counihan (1971), estimates can be obtained for the roughness length and displacement height: o d 0. h ( m). These values are similar with the roughness length estimates reported commonl for suburban areas (e.g. Seinfeld & Pandis, 1998). The following computations are based on these estimates for o and d. A more accurate estimate of the displacement height and roughness length, based on measurements from a meteorological mast, ielded similar values for o as the abovementioned. However, based on the mast measurements, the displacement height was reestimated to be d 6 m; this value is better in agreement with corresponding estimates in the literature (e.g. Stull, 1988). This revised value of d would correspond to the

5 The refinement of a meteorological preprocessor for the urban environment 5 proportion A R /A 50 %, which is reasonable, if one takes into account the combined effect of buildings, trees and other obstacles in the area. Utiliing wind measurements from the Helsinki-Vantaa airport, we can estimate the friction velocit in the inertial sublaer (Rotach, 1997), ielding u IS * 1.08 u *, where the friction velocit of the non-urban computations is denoted b u * and the subscript IS refers to inertial sublaer. The height of the roughness sublaer can be determined b several methods (e.g., Raupach, 1993). We have adopted the value * 30 m, which is in the range from 3 to 5 times the average building height. Using the exponential Renolds stress profile, suggested b Rotach (1993), and requiring that u * ( * IS ) 0.99 u *, we obtain u IS ' 3 *( ') u1' u3 '( ') u* (1 e ) (10) where is the elevation from the ero-displacement level d. We assume that the turbulent heat flux is constant throughout the roughness sublaer (Rotach, 1997). The profiles of the Monin-Obukhov length and temperature scale in the roughness sublaer can now be computed using equation (4). However, in stable conditions, if the computed Monin-Obukhov length is less than the lower limit of, we appl the min -value for, and recompute the values of the friction velocit and temperature scale. 6. Comparison of dispersion parameters for urban and rural conditions Figures 1 and show the ratios of the re-evaluated (urban) and original (rural) dispersion parameters. Figures 1 and correspond to unstable, and neutral and stable atmospheric stratification, respectivel. The results are based on meteorologicall preprocessed data in the Helsinki Metropolitan Area in The effective source height is assumed to be low ( 3 m), compared with the mixing height, as the change in dispersion parameters affects mainl the concentrations near the ground level.. In unstable conditions, the urban vertical dispersion parameters are approximatel half of the corresponding rural values, at an effective dispersion height near the eroplane displacement. Clearl, the urban roughness elements give rise to enhanced turbulence above the roof top level and one would therefore expect the urban dispersion parameters to be larger within this laer, compared with the corresponding non-urban parameters. However, the introduction of the displacement height and the exponentiall decreasing Renolds stress result numericall in clearl smaller values of turbulence parameters in the laer between roof top level and displacement height. This effect can be seen to be consistent with the generall accepted picture of turbulent flow changing to laminar flow close to a surface. In this case we can consider the urban roughness sublaer as a laer within which the spatial average of Renolds stress increases from ero to its value in the inertial sublaer (Rotach, 1993).

6 6 A. Karppinen, S. M. Joffre and J. Kukkonen Unstable horiontal disp Unstable vertical disp Ver Unstable horiontal disp Ver Unstable vertical disp Height (m) Figure 1. The ratio of urban and rural dispersion parameters in unstable conditions Extr. Stable Ver Stable Stable Neutral Height (m) Figure. The ratio of urban and rural dispersion parameters in stable and neutral conditions

7 The refinement of a meteorological preprocessor for the urban environment 7 In neutral conditions, the variation of the curve is similar, compared with the unstable cases. However, in stable conditions the imposed limit of the Monin-Obukhov length substantiall changes the situation. In extremel stable conditions, the urban dispersion parameters exceed the corresponding rural values with a large margin; the ke factors influencing this ratio are stabilit and height of the roughness sublaer. Figure 3 shows the effect of the modified dispersion parameters on the computed concentration distribution. The highest concentrations, which commonl correspond to extremel stable situations, are lower and more realistic in the new (urban) calculations. The concentrations in the range from 10 to 70 µg/m 3, which tpicall correspond to neutral or unstable situations, are onl marginall higher in the urban calculations. NO concentrations at Töölö New calculations (µg/m 3 ) Old calculations (µg/m 3 ) Figure 3. The calculated cumulative NO concentration distributions at the monitoring station of Töölö, Helsinki in Figure 4 shows that the effect of the model modifications on monthl average concentrations is fairl small.

8 8 A. Karppinen, S. M. Joffre and J. Kukkonen µg/m 3 55 NO concentrations at Töölö monitoring station Old calculations New calculations Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov Dec Figure 4. The calculated monthl average NO concentrations at the monitoring station of Töölö, Helsinki Conclusions The meteorological preprocessor developed at our institute has been modified in order to better represent urban conditions. We have re-evaluated the roughness length, introduced the ero-displacement height and divided the surface laer into a roughness sublaer and an inertial sublaer. The friction velocit (Renolds stress) and Monin-Obukhov length are re-evaluated using an empiricall developed exponential Renolds-stress profile in the roughness sublaer. The influence of these modifications has been investigated, b computing the dispersion parameters used in the UDM-FMI dispersion modelling sstem, and comparing the revised parameters with the corresponding previous "non-urban" parameters. These modifications can have a substantial influence on the computed concentrations for the ground level or near the ground level sources (e.g., traffic). The reevaluated friction velocit and dispersion parameters result in clearl lower concentrations in stable atmospheric stratification, and slightl higher concentrations in neutral and unstable atmospheric stratification, respectivel.

9 The refinement of a meteorological preprocessor for the urban environment 9 8. References Ara, S. P. S., Parametric relations for the atmospheric boundar laer. Boundar-aer Meteor. 30, Counihan, J., 1971, Wind tunnel determination of the roughness lengths as a function of the fetch and the roughness densit of three-dimensional roughness elements, Atmos. Environ, 5, Caughe, S. J., Wngaard, J. C. and Kaimal, J. C., Turbulence in the evolving stable boundar laer. J. Atmos. Sci., 36, Cit of Helsinki, Statistical Centre: Statistics of the Helsinki metropolitan area in 1996 (in Finnish), Edita O, Helsinki. Hanna, S. R., Air qualit modelling over short distances. In: Houghton, D.D. (ed.). Handbook of applied meteorolog, Chapter 5. Universit of Wisconsin, Wisconsin. Härkönen, J., Valkonen, E., Kukkonen, J., Rantakrans, E., Jalkanen,. and ahtinen, K., An operational dispersion model for predicting pollution from a road. Intern. J. Environ. and Poll. 5, Nos. 4-6, Karppinen, A., Joffre, S. and Vaajama, P., Boundar laer parametriation for Finnish regulator dispersion models. Intern. J. Environ. and Poll. 8, Nos. 3-6, Karppinen, a., Kukkonen, J., Nordlund, G., Rantakrans, E. and Valkama, I., A dispersion modelling sstem for urban air pollution. Finnish Meteorological Institute, Publications on Air Qualit 8. Helsinki, 58 p. Rotach, M. W., 1991, Turbulence within and above an urban canop, ETH Diss. 9439, 40 pp. Published as ZGS, Heft 45, Verlag GGIETH, Zürich. Rotach, M. W., 1993, Turbulence close to a rough urban surface Part I: Renolds Stress. Boundar aer Meteorol., 65, 1-8. Rotach, M. W., 1997, Towards a Meteorological Preprocessor for Dispersion Models in the Urban Environment. Intern. J. Environ. and Poll. 8, Nos. 3-6, Seinfeld, J. H. and Pandis, S. N., Atmospheric Chemistr and Phsics, John Wile & Sons, New York. Stull, R. B., 1988, An Introduction to Boundar aer Meteorolog, Kluwer Academic Publishers, Boston, MA. van Ulden, A. P. and Holtslag A. A. M., Estimation of Atmospheric Boundar aer Parameters for Diffusion Applications. J. Clim Appl. Meteor., 4, Wratt, D. S., An experimental investigation of some methods of estimating turbulence parameters for use in dispersion models. Atmos. Environ. 1,