Wind input data for urban dispersion modelling - CiteSeerX

Wind input data for urban dispersion modelling Mathias W. Rotach1), Ekaterina Batchvarova2), Ruwim Berkowicz3), Josef Brechler4), Zbynek Janour5), Petra Kastner-Klein1), Doug Middleton6), Viktor Prior7), Christian Sacré8), Cecilia Soriano9) 1) 2) 3) 4) 5) 6) 7) 8) 9)

Swiss Federal Institute of Technology, Institute for Climate Research National Istitute of Meterology and Hydrology, Bulgaria Danish National Environmental Research Institute, Department of Atmospheric Environment Charles University, Dept. of Meteorology and Env. Protection, Prague Institute of Thermomechanics, AS CR, Prague UK Met. Office, Bracknell Instituto de Meteorologia, Lisbon CSTB Service Aerodynamique et Environnement Climatique, Nantes Universitat Politecnica de Catalunya (UPC), Barcelona

1 Introduction The present contribution aims at summarising the work of working group 1 within COST 715 (‘Meteorology Applied to Urban Air Pollution’), which is concerned with the urban wind field. It therefore reflects the present state of this working group’s efforts rather than describing final or definitive results. In view of the COST action’s over-all focus we are particularly concerned with the estimation, parameterisation or description of wind statistics (mean wind speed and velocity variances) which are relevant for applications in dispersion modelling. The focus of the present contribution lies on the question: if somebody has to run any type of dispersion model over an urban area and observations are available i) from a nearby rural station (e.g., the city’s airport) or ii) from one particular site over the city of interest, how can these observations be used to estimate the wind statistics at any desired location within the urban area. Obviously, this is a formidable task and essentially requires all aspects of the urban wind field to be known and understood. This is clearly not the case at present. We will try, therefore, to set out the problem, refer to the available information and knowledge and also point out the gaps in our understanding. 2 The structure of the urban boundary layer Both in the vertical and in the horizontal, the urban boundary layer has a characteristic structure (Fig. 1) that has to be taken into account when dealing with the interpretation and estimation of wind data from urban areas. Based on this type of conceptual layout, it is suggested that (at least) the following four1 topics have to be taken into account: 1) The profile of mean wind speed and velocity statistics in the roughness sublayer (RS) including the canopy. 2) Conditions in the remaining part of the Urban Boundary Layer (UBL): unstable stratification (Urban Mixed Layer) and stable stratification (Urban Stable Boundary Layer) 3) Direct statistical and/or physically based relations between ‘rural‘ and corresponding urban parameter values

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These are – among others – the working areas of WG1 within COST 715.

4) Spatial inhomogeneity: i) growth of the UBL from the ’edge’ of a city and ii) change from one to another city ‘quarter‘ In the present contribution we focus on topics 1) and 3), well realising that the remaining two are of vital interest and their treatment will deserve much of our attention in the near future. This essentially means that we assume for the moment that our location within the city (where wind information is both desired or available) is situated far enough from the ‘edge’ of the city and from any major change in city structure to allow for assuming that a ‘local equilibrium’ of the flow has already established. Due to the large size of the roughness elements, the urban boundary layer has a more structured layering than boundary layers over smoother surfaces. In particular, the surface layer (SL), i.e. the ‘lowest‘ atmospheric layer over relatively smooth surfaces, is split up into the inertial sublayer (IS) and the roughness sublayer (RS) and the latter contains the so-called canopy layer (Fig. 1). Due to the large vertical extension of an urban RS (Rotach, 1999), an in situ observation over an urban surface is very likely to stem from within the roughness sublayer and thus, when attempting to find wind information at another location (another height at the same site, another site), it is necessary to take the roughness sublayer’s flow and turbulence structure into account. The same is true if remote information (e.g., from an airport) is used to estimate the profile of wind speed and turbulence statistics at a particular site within a city. The height of the RS, z* , is crucial as a length scale for the RS flow (see below) and – of course – determines the vertical extension of its applicability. However, it is not very well known nor investigated. Grimmond and Oke (1999) cite a number of estimates in the context of urban studies. They are all in the range given by Raupach et al. (1991), viz. z* = 2 –5 h

(1)

where h denotes the average building (or rather: roughness element) height. Here, it is suggested to use the lower limit (i.e., z* = 2 h) for typical European cities for the following reasons: •

In the present context we will use (or interpret) z* mainly as the height of the maximum Reynolds stress (see below) 2. The available full-scale data suggest that Reynolds stress has its maximum in the range 1.5h < z < 2.5h.

•

In wind tunnel studies maximum Reynolds stress is observed around z=2h (Rafailidis 1997, regular array, flat roofs) and sometimes significantly lower (Kastner-Klein et al 2000 – ‘real array' of Nantes; Rafailidis 1997 – regular array, slanted roofs).

•

Using the concept as described here (Section 5) to simulate urban tracer dispersion experiments (Rotach 2000a), the assumption of z* = 2 h yields the best correspondence between observations and modelled results.

However, if the density of roughness elements is very low, one of the other expressions as discussed in Grimmond and Oke (1999) may be considered. 3. Flow and turbulence structure within the roughness sublayer It is beyond the scope of the present contribution to give a complete overview on this topic. For this see, e.g., Roth (2000) and Rotach (1999). Here, we mainly discuss the overall features and present some characteristic results. Boundary layer data from ‘near the surface’ are usually treated within the framework of Monin-Obukhov similarity theory (MOST), but over urban (i.e., very rough) surfaces, this is only 2

Rather than the height, where the influence of individual roughness elements on mean and/or turbulence profiles vanishes. –2–

justifiable within the IS. It is important to note that all the following considerations refer to spatial averages of the variables of interest. At some distance from the roughness elements the actual profile at a particular location will not strongly depart from such an average. However, when approaching the surface this is no longer true and more specific information may be required (see below). Based on observational evidence, at least two main departures from MOST have to be taken into account in the RS and are briefly outlined in the following.

Figure 1

Sketch of the urban boundary layer (modified after Oke1988)

3.1 Reynolds stress Reynolds stress is not ‘approximately constant with height’, as a basic assumption states for MOST. A conceptual sketch of the vertical distribution of Reynolds stress is given in Fig. 2. Based on full-scale data of Rotach (1993a), Oikawa and Meng (1995) and Feigenwinter et al. (1999), a parameterisation (Fig. 3) has been suggested by Rotach (2000a): b

 u (z)  π  *,l  = sin( Z) a,  IS  2  u* 

Z ≤1

(2)

where u*, l (z) = (−u' w '(z))1/2 is the local scaling velocity, u*IS is the friction velocity (evaluated in the inertial sublayer, see Fig.2), Z = z' / z' * is a non-dimensional height using z' = z − d and z' * = z * − d . The parameters a and b are fitted to the data of Fig. 3 to yield a=1.28 and b=3.0.

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Data from wind tunnel studies over regular arrays (Rafailidis 1997) and over a ‘real array’ (Kastner-Klein et al. 2000), confirm the general findings from the full-scale studies. However, they suggest that one single ‘curve’ as eq. (2) may not describe the vertical profile of Reynolds stress at any location. Full-scale conditions, i.e. variable height and distribution of roughness elements along with variable wind direction (changing the source area or footprint) seem to generally smoothen the profile.

Figure 2

Conceptual sketch of Reynolds stress in the neutral urban boundary layer. The solid line corresponds to a parameterisation according to de Haan and Rotach (1998), which slightly departs from the ‘standard’ linear profile (cf. the upper part of the figure) in that it assumes an approximately constant value when approaching the surface. (From Rotach 2000a).

3.2. Local scaling Due to the non-constant Reynolds stress within the urban RS the ‘traditional’ approach according to MOST (i.e., using the surface fluxes to derive scaling variables) cannot be adopted in order to obtain nondimensionalised turbulence statistics. Two alternatives are available in principle: i) replace the friction velocity as derived from the surface stress (MOST) by another velocity scale. A ‘candidate’ to derive such IS

IS

a velocity scale, could be the Reynolds stress from the inertial sublayer, u' w' , (Fig. 2). Indeed, u' w' reflects the over-all surface drag on the flow and should be used to describe the profile of mean wind speed in the IS. ii) the local value of Reynolds stress, u' w' (z), can alternatively be used to nondimensionalise velocity statistics. Rotach (1993b) has shown that this second approach is preferable in the upper part of the RS (i.e., above the roughness elements). In many other studies, the success of local scaling has been confirmed (Roth and Oke 1993, Oikawa and Meng 1995, Feigenwinter et al. 1999, Roth 2000). Fig 4 shows, as an example for the local scaling approach, the non-dimensional gradient of mean wind ( Φ m (z / L) = ∂u ∂z ⋅(kz u * ) , where k is the von Karman constant). In this case, even the same functional form as in the IS can be used provided the local momentum flux is employed to find the scaling velocity and the (local) Obukhov length L. Fig. 5 shows locally scaled velocity variances from various studies over urban areas (Roth 2000).

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Figure 3

Parameterised profile of (local) friction velocity, u* , as a function of non-dimensional height (solid line, eq. 2). The symbols refer to the full-scale data of Rotach (1993a), x; Oikawa and Meng (1995), * and Feigenwinter et al. (1999), o. Wind tunnel data after Rafailidis (1997), +, are shown for comparison parameterisation (only the ‘flat roof’ experiments with aspect ratio 1/2 shown). The latter are not employed to fit the parameters of the (from Rotach 2000a).

Figure 4

Non-Dimensional gradient of wind speed averaged over bins of (local) stability. Data from Zürich, Switzerland. Triangles: 10m above roof level, plus: 5m above roof level (from Rotach 1993b). Note that the local Reynolds stress is used, for both, Φm and the Obukhov length, L. The solid line corresponds to the SL expression after Businger et al (1971), modified after Högström (1988).

3.3 Profile of mean wind speed The profile of mean wind speed can be deduced from the knowledge of the Reynolds stress profile (eq. 2) along with the concept of local scaling (Fig. 4). A detailed, step-by-step procedure how this is done can be found on the web site of COST 715, WG1 (http://www.geo.umnw.ethz.ch/research/cost715/cost715.html). Rotach (1993a) shows that on average this leads to an excellent correspondence between prediction and observation (his Fig. 7). In general the gradient is reported to be smaller than predicted by MOST as also found over other rough surfaces (Kaimal and Finnigan 1994). If a spatially averaged profile of mean wind speed is desired (as input for an urban-scale dispersion problem) this procedure is recommended. However, the closer the surface is approached the more important become the details of the surface structure. Therefore, if a wind speed profile at one specific location is required (e.g., the upwind side of a –5–

particular street canyon under normally approaching flow) the appropriate departure from the mean profile has to be found. Rotach (1995) discusses average profiles of mean wind speed for approaching flows parallel or normal to a street canyon as well as their sensitivity to stability. Fig. 6 gives an example from a ‘real array‘ wind tunnel study (Kastner-Klein et al. 2000). Much work remains to be done on the formal description of these various characteristic profiles.

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Locally scaled velocity variances (i.e., standard deviations) from various urban turbulence studies. For details see Roth (2000), from where the figure stems.

4 Practical considerations The observational evidence as briefly summarised in the previous section leads to some general suggestions for the estimation and retrieval of wind statistics within an urban RS (for details see the web site as mentioned in Section 3.3 and henceforth referred to as WEB). The first step is to use eq. (2) in IS

order to find either u*IS = sqrt(−u' w' ) from an observation of Reynolds stress within the RS, or to find the local scaling velocity from the friction velocity u*IS . WEB indicates a possibility to retrieve u*IS from a rural observation of Reynolds stress (e.g., at the airport) and also summarises the possibilities to estimate the –6–

necessary input variables to eq. (2) for a given urban surface structure. Once the profile of Reynolds stress is established, the non-dimensional gradient of mean wind speed (Fig. 4) in connection with local scaling can be used to find the mean wind speed at any desired level. If a mean wind observation is available at the site of interest a numerical integration (as detailed in WEB) of the non-dimensional gradient of mean wind yields an estimate at any other desired height. If no measurement at all is available, the procedure has to start in the inertial sublayer, where the mean wind speed can be inferred using MOST and u*IS . For neutral conditions, Fig. 5 gives a guideline for the locally scaled velocity variances. For non-neutral conditions it is suggested to use the empirical functions of Roth (2000) where again the locally scaled velocity variances are described as a function of (local) stability. 4

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Profiles of scaled mean wind speed at various sites over an urban surface. Data from a wind tunnel study (Kastner-Klein et al., 2000) under neutral stability. The numbers in the inlet refer to different positions, profile 13 is the approaching flow.

5 Applications 5.1 Relation between urban and rural wind speed For rural sites, a reference height for wind-speed observations (10m) is defined by WMO. For various reasons it would be desirable to have such a ‘urban reference height‘, but this can obviously not simply be z=10m as well. For example, such an (urban) standard reference height is necessary to compare observations from different cities. In order to find (possible) simple relations between rural and urban wind speed (for use in simple urban dispersion models when only a rural observation is available). WG1 of COST 715 has, as a working hypothesis, defined an urban reference level according to: zref ,u = d +10m , where d is the zero plane displacement. In Fig. 7 two urban-rural comparisons are shown (where both urban observations are not from this reference height). Obviously, there exists some relation between the wind speed at a rural site (reference level) and an urban site but the fitted slopes and intercepts are –7–

mainly characteristic for the site (and level) under consideration and also depend on wind direction (not shown) and other meteorological parameters. It is hoped3 that, if also at the urban site the wind speed is from an urban reference level, some more general relations can be found. 5.2 Urban-scale dispersion modelling Traditionally, dispersion models of all levels of sophistication, even when applied in urban areas do not take into account the turbulence structure of the roughness sublayer. Using a Lagrangian particle dispersion model Rotach (1997, 1999, 2000a) has compared two types of simulations: •

In the first type the lower portion of the boundary layer is parameterised according to MOST, therefore assuming that surface layer characteristics prevail down to the ground. Thus, these simulations correspond to what may be termed the ‘traditional’ practice for dispersion modelling even over urban surfaces. These simulations are referred to as 'non–urban' simulations. It should be noted that 'nonurban' does not mean rural, but rather emphasises the absence of an urban RS in the simulation.

•

In the second type of simulations, a roughness sublayer is explicitly taken into account using the results from the field and wind tunnel studies as summarised in Section 3 to parameterise its turbulence structure. Consequently, the surface layer has two parts, an inertial sublayer and, immediately above the surface, a roughness sublayer. This second type of simulations is termed 'urban '. For a number of urban tracer experiments the comparison of the performance of these ‘urban‘ and ‘nonurban‘ simulations shows that, in general, the ‘urban‘ approach yields improved summary statistics under near-neutral and convective conditions (Rotach 2000a). In particular, the fractional bias (of the ‘non-urban‘ simulation) is reduced at the same time as the normalised mean square error is reduced and the correlation is increased. Thus the ‘urban‘ approach seems to take more of the physics of the actual dispersion process into account than does the ‘non-urban‘ approach. A sensitivity analysis (Rotach 2000b) shows that the largest impact of the RS turbulence can be expected for low sources and mechanically dominated conditions. It is worth noting that low sources are typical for urban environments (traffic, domestic heating) and that the rough urban surface tends to increase the mechanical portion of turbulence production. De Haan et al. (1998, 2000) use a similar approach in connection with an operational Gaussian multisource/multi-receptor dispersion model. In this case, not only an urban tracer experiment, but also yearly

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Comparison of mean wind speed at Barreiro (nearby Lisbon) (10m level) to that at an urban site in Lisbon. Level of urban observation: 32 m.

WG1 is presently working on a number of data sets to investigate this issue. –8–

averages for NOx and SO2 concentrations at 28 sites in the city of Zurich, Switzerland are simulated. A similar improvement due to the ‘urban‘ approach as described above for the Lagrangian particle model results (de Haan et al. 2000). Furthermore, this exercise may serve to estimate the over-all effect of the roughness sublayer turbulence on surface concentrations, based on a typical urban source distribution. It is found that the urban modification results in a 25–35% increase of the annual mean surface concentration as compared to the common practice (i.e., the ‘non-urban‘ approach). 20

Copenhagen, 1995 Airport - Kastrup (10 m) Urban - University building (30 m) Wind Speed (m/ s) Ur ban

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Comparison of mean wind speed at Kaastrup airport (10m level) to that at an urban site in Copenhagen. Level of urban observation: 30 m. Example of NE approaching flow.

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Oikawa, S. and Meng, Y.: 1995, ‘Turbulence Characteristics and Organized Motion in a Suburban Roughness Sublayer’, Boundary-Layer Meteorol., 74, 289–312. Oke, T. R. (1988): The urban energy balance. Progress in Physical Geography, 12, No. 4, 471–508 Rafailidis, S.: 1997, ‘Influence of building areal density and roof shape on the wind characteristics above a town’, Boundary-Layer Meteorol., 85, 255–271. Raupach, M.R; Antonia, R.A. and Rajagopalan, S.: 1991, ‘Rough-Wall Turbulent Boundary Layers‘, Appl. Mech. Rev., 44, 1–25. Rotach, M.W.: 1993a, 'Turbulence Close to a Rough Urban Surface Part I: Reynolds Stress', BoundaryLayer Meteorol., 65, 1-28. Rotach, M.W.: 1993b, 'Turbulence Close to a Rough Urban Surface Part II: Variances and Gradients', Boundary-Layer Meteorol., 66, 75-92. Rotach, M.W.: 1995, 'Profiles of Turbulence Statistics in and Above an Urban Street Canyon', Atmospheric Environ., 29, 1473-1486. Rotach, M.W.: 1997, 'The Turbulence Structure in an Urban Roughness Sublayer', in: Perkins, R.J. and Belcher, S.E. (Eds.): Flow and Dispersion through on Groups of Obstacles, Clarendon Press, Oxford, 249pp., 143-155. Rotach, M.W.: 1999, ‘On the Urban Roughness Sublayer’, Atmospheric Environ., 33, 4001-4008. Rotach, M.W.: 2000a, ‘Simulation of urban-scale dispersion Part I: Concept and validation’, subm. to Boundary-Layer Meteorol. Rotach, M.W.: 2000b, ‘Simulation of urban-scale dispersion Part II: sensitivity, subm. to Boundary-Layer Meteorol. Roth, M., and Oke, T. R. (1993): Turbulent transfer relationships over an urban surface. I: Spectral characteristics. Quart. J. Roy. Meteorol. Soc., 119, 1071–1104 Roth, M.: 2000, ‘Review of atmospheric turbulence over cities’, in press Quart. J. Roy. Meteorol. Soc.

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