Review of atmospheric turbulence over cities

Transcription

1 Q. J. R. Meteorol. SOC. (2000), 126, pp Review of atmospheric turbulence over cities By M. ROTH* National University of Singapore, Singapore (Received 22 October 1998; revised 20 September 1999) SUMMARY This paper provides a comprehensive, critical review of turbulence observations over cities. More than fifty studies are analysed with their experimental conditions summarized in an appendix. The main results are based on 14 high-quality experiments which met criteria based on stringent experimental requirements. The observations are presented as non-dimensional statistics to facilitate comparison between urban studies and work conducted over other rough, inhomogeneous surfaces. Wake production associated with bluff bodies, and the inhomogeneous distribution of sources and sinks of scalars, result in a roughness sub-layer which for the studies reviewed extends to about 2.5 to 3 times the height of the buildings. It is shown that within this region the basis of several traditional micrometeorological approaches to describe the turbulent exchange is in doubt. There are strong similarities to flow over plant canopies, and many of the turbulence characteristics can be interpreted in the framework of a plane mixing layer. Future field observations should concentrate on the turbulent exchange near the top and within the urban canopy as well as within the urban boundary layer. KEY WORDS: Mixing-layer analogy Roughness sub-layer Urban boundary layer Urban turbulence 1. INTRODUCTION Turbulence research has traditionally focused on the structure of the turbulent boundary layer over relatively smooth and homogeneous surfaces. In the atmosphere the underlying surface, however, is almost always rough, and in recent years the interests and efforts of boundary-layer researchers have been increasingly directed towards problems of surface-atmosphere interaction over complex surfaces. At the base of such research lies the fundamental difficulty that the well-established homogeneous surfacelayer relationships, used to describe the mean and turbulence properties, collapse in regions of inhomogeneity because several assumptions underlying their derivation are invalid. Comprehensive field studies of atmospheric turbulence over rough and inhomogeneous environments in general are difficult to accomplish and as a result limited in scope. Nevertheless, a consistent picture of flow and scalar transfer is emerging, based on carefully conducted observations over a wide range of complex surfaces such as crops and forests (e.g. Kaimal and Finnigan 1994) and from rough-wall wind-tunnel studies (e.g. Raupach et al. 1991). Based on these results, Raupach et al. (1996) argue that the turbulence and motions near the top of a vegetation canopy are patterned on a plane mixing-layer (see below), which differs in several ways from turbulence in the surface layer. Similar understanding of the urban atmosphere is not available. The main motive for studying turbulent flow in the urban atmosphere is, of course, to understand the processes governing the exchanges of momentum, heat and mass between the urban surface and the atmosphere, and the effects on energy and water balance studies. Apart from this basic interest, there are several crucially important real world applications of such knowledge. At the top of the list is the need to understand and model the dispersion of pollutants, which strongly depends on meteorological conditions. Further, a good understanding of urban wind dynamics is needed to estimate wind loads on urban structures. Progress towards better knowledge of turbulence in the urban atmosphere has been slow, mainly because of two factors. First: given the inherent experimental difficulties, observational studies have primarily been confined to a specific aspect of turbulence * Corresponding address: Department of Geography, National University of Singapore, 1 Arts Link, Kent Ridge, Singapore

2 942 M. ROTH which reflects a particular set of urban morphology and surface fetch conditions. Such work takes little note of the three-dimensionality of the urban atmosphere and is difficult to generalize to other localities. Second: because of the absence of a suitable framework for the analysis and presentation of turbulence over rough terrain in general, comparison of published data from sites with different surface characteristics is difficult. The objective of this review is threefold. First, to explore the turbulence mechanisms found in the urban boundary layer and to discuss the implications for observational studies (section 2). Second, to examine historical developments in urban turbulence over the last five decades, and to provide a comprehensive list of the studies within this time period combined with a critical evaluation of them (section 3 and appendix). Third, to organize the basic observed properties of urban turbulence into a coherent body of information so as: (i) to present the results in such a way that they can be compared amongst themselves and with studies from other rough surfaces, and to provide the necessary background for a discussion of the turbulent transfer (sections 4 and 5); and (ii) to identify problem areas, and clarify the research which remains to be done (section 6). Apart from these considerations specific to urban environments, it is hoped that this review will be discussed in the context of the role of land-air exchanges and local atmospheric environments over a wide range of surfaces (urban, forests, agricultural, etc.). The urban observations will be interpreted within the framework of the mixinglayer analogy proposed by Raupach et al. (1996), which predicts many aspects of the behaviour of canopy turbulence. A mixing layer forms when two co-flowing streams with different velocities mix (e.g. flow within and above a canopy). Because of instabilities associated with the characteristic strong inflection in the mean velocity profile, turbulence characteristics (e.g. normalized standard deviations, ratios of eddy diffusivities, turbulent kinetic energy balance or turbulent length-scales) in a plane mixing layer are different from those in a boundary layer. 2. URBAN TURBULENCE AND BOUNDARY-LAYER STRUCTURE (a) General features The dominant environmental controls on urban turbulence are the high roughness (buildings, trees and other large structures) of the urban surface (for definition see Voogt and Oke 1997) and the urban heat island (e.g. Oke 1995). When the aerodynamically rough and inhomogeneous surface interacts with the airflow, the following processes (which are usually less explicit over more homogeneous rural surfaces) modify the turbulent transfer and hence turbulence structure. (1) An intense shear layer is formed near the top of the canopy, whose turbulence properties differ in systematic ways from those in the overlying surface layer. Mean kinetic energy of the flow is converted into turbulent kinetic energy and results in high turbulence intensities. (2) Wake difision (Thom et al. 1975), i.e. mixing generated by turbulent wakes behind individual roughness elements, efficiently mixes and diffuses momentum, heat, moisture or any other scalar quantity. The size of these eddies is related to the dimensions of the wake-shedding roughness elements. They are important in sparse canopies; however, if small (relative to the canopy height) they will contribute little to vertical transfer but are still significant in dissipating turbulent energy. (3) Form drag due to bluff-bodies, i.e. pressure differences across individual roughness elements (illustrated by the case where the windward face of a building is under

3 REVIEW OF TURBULENCE OVER CITIES 943 increased pressure but the leeward face under suction), augments the transport of momentum to the surface and has no analogue in the transport of heat or mass. (4) Sources and sinks of momentum and scalars such as heat and water vapour are organized in three-dimensional arrays and not necessarily collocated. The spatial fields of heat and mass within the intervening spaces are the products of local warm/cold spots and moisture patterns. Differential heatinghooling of sunlithhaded surfaces as well as dry/wet surfaces lead to the development of discrete and localized heat and mass plumes which, together with the wakes and vortices of canyon flows, result in a complex system of energy and mass transport to add spatial and temporal inhomogeneities. (5) The extreme heterogeneity of urban surfaces, usually at all length-scales, makes definition of a uniform fetch impossible: local advection is the norm rather than the exception. (6) It is possible that the regularity or structure in the surface contributes to organized (coherent) motions manifested in e.g. sweeps and ejections or ramp structures in signals. (7) Increased mechanical mixing at the urban surface results in enhanced mixedlayer-surface-layer interaction and in combination with the urban heat-island effect may lead to larger boundary-layer heights. (8) Atmospheric stability near the surface is generally reduced owing to the presence of the urban heat island and increased shear production. Given the complexity of the urban system, it is not reasonable to expect traditional micrometeorological theories such as profile methods (e.g. Oke 1987) or general similarity schemes such as the Monin-Obukhov similarity (MOS) framework (Monin and Obukhov 1954) to apply in the urban context. Because of the absence of a unifying method for turbulent transfer, much of the recent work has focused on testing the applicability of previously mentioned concepts and identifying possible departures. (b) Vertical structure of the urban boundary layer To understand the processes listed in (a) in detail, it is convenient to define a number of layers each characterized by its own set of scaling properties. The focus is on differences, contrasting with homogeneous boundary-layer development usually described in textbooks (e.g. Garratt 1992). The regions identified in Table 1 are based on a simple classification first proposed by Oke (1976) which recognizes the urban canopy layer (UCL) and urban boundary layer (UBL) respectively. Expanding on this simple two-layer model the roughness sub-layer (RSL) is defined in analogy to frameworks used in the interpretation of flows over plant canopies. Other layers are as conventionally defined. The depth of the RSL, z*, is the subject of much debate. Unfortunately, the available urban observations do not lend themselves to a more detailed exploration of this important issue. It is, therefore, necessary to borrow from work over tall vegetation and rough-wall wind-tunnel studies. The z* values in Table 2 are obtained from gradient and eddy correlation measurements (ideally observed simultaneously) and the subsequent evaluation of the flux-gradient relationships. The criterion for an observed RSL effect is the deviation of the measured non-dimensional vertical profile function from that derived over ideal terrain (e.g. Dyer 1974). It appears that the length-scales relevant to z* are the horizontal spacing (D) of the dominant roughness elements, their height (zh), the aerodynamic roughness length (to) and, to a lesser extent, the zero-plane displacement height (Zd). Most authors conclude that the transfer of heat is affected more strongly than that of momentum, which will be the case if the respective source/sink

4 944 M. ROTH Region TABLE 1. CHARACTERISTICS OF URBAN BOUNDARY-LAYER REGIONS Characteristics Urban boundary layer (UBL) Ground to top of boundary layer Portion of planetary boundary layer whose characteristics are affected by the presence of the urban area. Local to mesoscale phenomenon. Includes all other layers. Urban canopy [ayer (UCL) Ground level to about roof level produced by microscale effects of site characteristics. Dynamic and thermal processes are dominated by the immediate surroundings. Flow and scalar structure are generally very complex. Most clearly pronounced in areas of high building density, but may be discontinuous in less developed suburban areas. Roughness sub-layer (RSL) Ground to z, Also called the transition layer, interfacial layer or wake layer; includes UCL. Mechanically and thermally influenced by length-scales associated with the roughness. Because of wake diffusion and differential sourcedsinks of momentum and scalars, momentum and heat transfers are dissimilar, and therefore Reynold s analogy may not be valid (Roth and Oke 1995). As a result of local-scale advection, the turbulence field is often not horizontally uniform, even in a time average, and must be considered three-dimensional (e.g. Ching 1985; Schmid et al. 1991). Constant-jlu layer (CFL) z, to -0. lz, Also called the inertial sub-layer. Mean profiles obey semi-logarithmic laws or their diabatic extensions and MOS applies. Very little is known about it in urban areas, in part due to the height restrictions of measurement towers which, due to the existence of a RSL with dimensions of tens of metres, often do not extend into the CFL. The vertical extent of the urban CFL is also determined by the development of an infernal boundary layer which responds to mesoscale land-use changes in upwind surface characteristics. It is possible that under unstable conditions the depth of the RSL exceeds the potential depth of the CFL and no such layer exists (Oke et al. 1989). Mixed layer (ML) -0. IZ, to z; Little is known about urban MLs, but turbulence properties are probably independent of the surface roughness. It is topped by an entrainment layer which may be substantial because of enhanced coupling between the rough and warm urban surface and the ML (Roth and Oke 1995) and the relatively larger availability of turbulent kinetic energy (TKE) (e.g. Eaton and Dirks 1977). distributions do not match (see above). The vertical extent of the roughness sublayer further depends on atmospheric stability, generally being higher for unstable stratification (e.g. Garratt 1980). Although simplistic, it is instructive to calculate z* as a function of the most readily available parameter, zh. With a few exceptions the values of z*/zh reported in Table 2 generally correspond well with those from Raupach et al. (1991) from a review of atmospheric and laboratory boundary layers over rough surfaces. For wind (momentum) they found z* values as low as 2 zh in the case of closely spaced canopies, increasing to about 5zH over rough vegetated surfaces. It is possible that these limiting values are larger for temperature (heat). (c) Methodology Applicability of standard boundary-layer theory and observational methods to the urban system has been discussed by Oke et al. (1989). The large size of the roughness elements, and the considerable horizontal and vertical spatial variability of the sources and sinks, pose spatial and temporal sampling problems which need to be considered in observational studies. It helps to formulate a set of criteria for the design of urban turbulence studies (Table 3) similar to those of Wieringa (1993) and Grimmond and Oke (1999). Some of them are discussed in the following.

5 ~~ ~ REVIEW OF TURBULENCE OVER CITIES 945 TABLE 2. ROUGHNESS SUB-LAYER HEIGHTS (MEASURED FROM GROUND) FROM LABORATORY AND FIELD EXPERIMENTS Reference z* formula Surface Variable (stability) Z*/ZH Sadeh etal. (1971) wind-tunnel wind, momentum (neutral) 23 (model forest) natural wind log-profile (neutral) 5-10 Tennekes (1973); Townsend (1976) Pasquill (1974) Mulhearn and Finnigan (1978) Garratt ( 1978) Raupach et al. (1980) Garratt ( 1980) Garratt (1980) Raupach and Legg (1984) Fazu and Schwerdtfeger (1989) natural wind-tunnel (random) natural (savannah) wind-tunnel (regular) natural (savannah) natural (savannah) wind tunnel (strips) natural (trees) region of wake effects wind (neutral) momentum (neutral) momentum (neutral) sensible heat (near neutral) wind (neutral) wind (unstable) wind (unstable); zo = 0.4 m wind (unstable); zo = 0.9 m temperature (unstable) sensible heat (neutral) momentum (neutral) Raupach et nl. (1991)' (2-5)z~ natural, artificial wind, momentum (neutral) TABLE 3. CRITERIA USED TO ASSESS AND SCREEN STUDIES Criterion Measure of acceptance Fetch Flat; homogeneous surface morphology; satisfying 9. (1); XF 2 1Ooz,; or FSAM. Immediate surroundings of site Vertical or horizontal distance to nearest buildings close enough for lowest sensors to measure integrated urban influence, but not so close that individual anomalous areas or building wakes affect the data. Estimation of zo and Zd Credible measurement or estimation based on surface cover in fetch, in line with recommendations by Grimmond and Oke (1998). Slenderness of supporting Minimal interference from supporting structure; XT > 1Sd~ for opentower and exposure of lattice structures (e.g. Kaimal and Finnigan 1994). Installation on the instruments upwind side of the supporting structure. Setting of tower (surface vs. Unobstructed surface setting or tall tower on building which is not roof-top) significantly higher than surrounding roughness elements. Instrumentation EC approach using fast-response sensors; generally: T, > 2 Hz, T, > 15' (longer for larger heights and covariances, e.g. Wyngaard 1973). Documentation Explicit and comprehensive description of experimental details such as: site characteristics (e.g. spatial variability within fetch, distance from sensors to nearest buildings); atmospheric stability during observations; and instrumentation. FSAM-flux source area model (see Schmid 1994); EC-eddy correlation; qdistance between sensor and tower; &-lateral dimension of tower; T,-sampling rate in Hz; T,-averaging time in minutes. See. text for further explanations.

6 946 M. ROTH Measurement systems for turbulence properties must be located in the constantflux layer (CFL), i.e. above z*, to produce results which are fully representative of the underlying surface. However, it was noted above that the vertical extent of the CFL may be reduced owing to the slow development of an internal boundary layer (IBL), in which case one-dimensional scaling would become inappropriate. Field observations can only be generalized if the observations are within that part of the IBL where near-equilibrium adaptation of the fluxes to the downwind roughness occurs, which is below about 0.1 times the height of the IBL. Wieringa (1993) presents the following equation for the estimation of the fetch, XF, necessary to ensure that a particular observation level is still in the equilibrium layer and therefore fully adapted to an upwind surface characterized by zo: where zs is the height of the sensor above ground, and z, = zs - Zd is the efective height. Wieringa shows that (1) generally agrees well with the common rule of thumb, that fetches should be about 100 times the height of the observation level for neutral conditions. Because of the absence of suitable measurements, it is not known how well (1) performs over the high-roughness surfaces characteristic of urban environments. Nevertheless, it is probably a good first estimate of the required fetch at a given height. Surface cover in urban areas is often extremely heterogeneous, and point measurements below z* may not be representative of the mean CFL fluxes. In such cases it is important to estimate the size and locations of sources and sinks contributing to a turbulent-flux measurement. Models based on a reverse-plume diffusion approach have been used to estimate the source area influencing a measurement at a certain point (Schuepp et al. 1990; Schmid and Oke 1990; Horst and Weil 1992). For example, Schmid and Oke (1990) demonstrate the importance of the flow characteristics in determining the elliptical shape of the upwind source area. Using a version of the model for scalar fluxes (FSAM; Schmid 1994) Roth and Oke (1995) show the strong effect of stability on the size and location of the source area. Using typical values measured at a suburban site in Vancouver, Canada, they show that, for an instrument at z; = 19 m, the size of the source area and the distance of the maximum strength to the measurement location decreases by a factor of about 5 from near neutral to moderately unstable conditions. Thus with increasing instability the sources and sinks in the immediate vicinity of the site become increasingly important. As is true for all rough surfaces, accurate knowledge of the aerodynamic characteristics of cities is essential to describe and model the behaviour of urban winds and turbulence. Grimmond et al. (1 998) and Grimmond and Oke ( 1999) have reviewed methods to determine zo and Zd. They conclude that, if observations are available, turbulence-based approaches should be favoured over those involving multi-level profiles of anemometers. Grimmond and Oke present a detailed and critical analysis of morphometric methods which can be used in the absence of measurements. Although not completely satisfactory, first-order estimates can also be obtained from typical tabulated values (e.g. Grimmond and Oke 1999; Table 8). Of the two basic approaches to the measurement of turbulence properties, the eddy correlation method is favoured. Flux-gradient methods require constancy of fluxes with height and similarity of all transfer coefficients (eddy diffusivities), which cannot be assumed in the urban atmosphere (Roth and Oke 1995). To obtain spatially averaged turbulence properties within the RSL it is necessary to average many individual point

7 REVIEW OF TURBULENCE OVER CITIES 941 measurements. Remote-sensing methods, such as scintillation measurements, are potentially feasible and promising ways to obtain spatially averaged quantities. Applying MOS, Thiermann and Grass1 (1992) use the dissipation range of the turbulence spectra to determine the momentum and sensible-heat fluxes. As will be shown, the similarity constants used in the MOS framework are different for the urban case, so this will probably require modification to the scintillation method. Remote sensors, such as sodars, are also sometimes used in UBL research (Melling and List 1980; Casadio et af. 1996; Dupont et af. 1999). In the absence of appropriate urban data, the turbulence properties are inferred from back- and forward-scattered signals using relationships derived from the boundary layer over homogeneous terrain. Again the success of these methods depends on how well UBL turbulence can be described by empirical relationships derived over flat and homogeneous surfaces. 3. SUMMARY OF URBAN STUDIES (a) Histo rica f perspective Arguably the first observation of a turbulence property in the urban atmosphere dates back more than 100 years. Taylor (1918) used profiles of temperature measurements from the newly completed Eiffel tower in Paris to indirectly demonstrate that the diffusivity of heat is larger over a city than a rural surface. The first documented direct measurement of urban turbulence was probably performed in October 1946 from a tower at the Central Meteorological Observatory located in the centre of Tokyo next to the Imperial Palace (Shiotani and Yamamoto 1950). The stream-wise velocity fluctuations were measured at several heights using hot-wire anemometers. Unfortunately, the fast response time of the sensor could not be matched by the recording equipment and, furthermore, individual data points had to be extracted manually from the chart recorder. Hogstrom et al. (1982) in Uppsala, Sweden are the only others to use hot-wire anemometry in the city. Gill propeller anemometers were mainly employed during the following 40 years, eventually being succeeded by the almost exclusive use of sonic anemometer-thermometers during the 1990s. The field observations reviewed show that work from the early 1950s until the early 1970s was mainly concerned with mean properties of the flow and temperature. Many of these studies were carried out in the UBL using balloons (Agnell et af. 1974), tall TV towers (Soma 1964; Yamamoto and Shimanuki 1964; Arakawa and Tsutsumi 1967, 1976; Helliwell 1971; Wamser and Muller 1977), or even helicopters (McCormick and Kurfis 1966) as instrument platforms. Throughout this period emphasis was on the large-scale aspects of the flow, i.e. modifications of urban-scale compared to rural upwind reference data, and possible effects on the difision of air pollutants. In contrast, Japanese work during this period concentrated on the properties of turbulence in high winds. There was clearly a need for such knowledge for use in the design of tall buildings considering the high occurrence of taifuns (intense tropical cyclones) in the region. In particular peak wind velocities and the vertical distribution of wind gusts gained considerable attention. Unlike the more enterprising earlier experiments, more recent work has focused on the atmosphere closer to the surface, which is accessible through standard micrometeorological towers. The emphasis shifted toward atmosphere-surface interaction at smaller scales, including the measurement of fluxes and other turbulence quantities. In particular, the intra-urban variability of surface fluxes (especially heat) and surfacelayer studies of turbulence have received some attention (e.g. Ramsdell 1975; DuchCne- Marullaz 1975; Clarke et af. 1978,1981,1982,1985,1987; Hogstrom etaf. 1982; Steyn

8 948 M. ROTH 1982; Uno et al. 1988, 1992; Yersel and Goble 1986; Roth et af. 1989; Rotach 1993a,b, 1995; Wang 1992; Roth 1993; Roth and Oke 1993, 1995; Oikawa and Meng 1995, 1997; Xu et al. 1997; Feigenwinter et al. 1999). Investigation of the UBL has received less attention. The most comprehensive work to date has been within the framework of the METROMEX (e.g. Changnon 1981), and the Regional Air Pollution Study (RAPS; e.g. Schiermeier 1978) conducted in St. Louis in the 1970s. Using aircraft, turbulence properties and fluxes were measured at three heights during a few summer days in a convective UBL (e.g. Eaton and Dirks 1977; Ackerman and Hildebrand 1978; Hildebrand and Ackerman 1984; Godowitch etal. 1981; Ching etal. 1983; Ching 1985; Godowitch 1986; Westcott 1989). Remote-sensing techniques, such as sodars, have been used in a few experiments to probe the UBL with emphasis on the vertical distribution of the vertical-velocity variance (Melling and List 1980; Casadio et al. 1996; Dupont et af. 1999). A novel approach, which involved a specially constructed turbulence sonde attached to a kytoon, provides the only observations within a nocturnal UBL (Uno et af. 1988, 1992). To summarize this brief historical excursion, it is clear that, although the instrumentation has become increasingly more sophisticated, the same, generally, does not apply to the nature of the experiments. With a few notable exceptions, observations are usually restricted to particular aspects of urban turbulence, and often are measured at only one point in space. This clearly reflects the limitations set by the experimental difficulties encountered in cities. For example, the measurements usually have to be performed from already existing towers which are restricted in height, and the surroundings may not provide adequate fetch. (b) Evaluation of studies One objective of this review is to summarize all the existing work on field observations of urban turbulence (see appendix). Only studies for which the original publications could be traced were selected. A critical review needs to restrict its scope to high-quality experimental results. That way it should be possible to extract results of universal (in the urban sense) validity. Therefore, the overall quality and value of the individual studies was assessed using the criteria discussed above (Table 3). Not included in Table 3 is the relative height of the observations with respect to that of the buildings (zs/zh), which would obviously be another important measure if one were only interested in those measurements, say, taken above the roughness sub-layer. Unfortunately most studies failed to meet one or more of these objective criteria. A common problem is the lack of sufficient description of the site. Only 8 studies (S76, V78, V86, W86, 286, V89, S92, B95; see appendix for codes) report Zd values based on one of the above recommended approaches. The situation is slightly better for 7-0, adding another 10 to the previous 8 studies (L67, 072, H73, A79, U79, L89, N90, L94, C95, M95). Some of the early studies evaluated zo based on neutral wind profile data without allowing for Zd (K60, T63, L66, S73, N74, N90). The mean height of the roughness (mainly buildings) within the fetch is another important parameter often not directly given in the original publication (P18, T46, F66, L66, 071, 072, V71, H73, S73, W78, L79, L80, T80, T83,185, B86, T90, A91). In order to extract as much usable data as possible, it was in some cases necessary to work with sub-sets of the originally reported observations from e.g. selected wind direction sectors whose surface characteristics could be clearly deduced (F65, F66, M69, N74, U79, R94a). FSAM was used to estimate the surface cover in the source areas, which led to the rejection of some data which were influenced by non-urban morphologies near the sites (the lowest two observation levels in N74 and for unstable conditions in S92). Insufficient information

9 REVIEW OF TURBULENCE OVER CITIES 949 on the atmospheric stability further reduced the acceptable observations (F65, M69, G88). In summary, of the 53 studies reviewed only 14 (marked by an asterisk next to their code in the appendix) are sufficiently documented and reliable to be included for further consideration. The results presented in sections 4 and 5 are mainly from those few experiments which passed all or most of the experimental requirements, although many of the studies which did not pass the criteria reported statistics which were in qualitative agreement with the results below. 4. RESULTS OF INTEGRAL STATISTICS The statistics reported in the following two sections are presented as a function of effective height normalized by roughness length (zl/zo), and height above ground normalized by the average height of the roughness (zs/zh) respectively. The former is a natural choice based on the wind profile equation, and relates the statistics to a measure of surface roughness, but it also requires accurate estimation of Zd and zo which many studies fail to report. It follows that only very few data are available for presentation in this format. The latter is more important from a practical point of view and also easier to derive, but is only a crude estimate of the site roughness and does not account for the spacing and density of roughness elements. However, since ZH is probably the single most important determinant of roughness it is an elementary and widely used parameter. Because of the absence of any other suitable conceptual approach for the presentation of data over rough and inhomogeneous surfaces, the results are given within the MOS framework, although they are usually not from a homogeneous surface layer. Further, MOS is of interest and merit in evaluating the applicability of similarity laws in rough environments. MOS is also implied in some of the micrometeorological approaches to measuring turbulence properties. Experimental data for the horizontal wind components from the homogeneous surface layer are usually less supportive of the similarity prediction, and it is often argued and observed that they scale better with mixed-layer variables. Nevertheless, MOS has been applied consistently to all variables presented below. Observations here termed neutral refer to Iz;/LI or for a few cases to IzL/LI 6 0.1; where the Obukhov length L = Tui/(kgT,), - here u* is the friction velocity, T* the surface-layer temperature scale (= -w T /u*, where the overbar denotes a time average), T the mean air temperature, k the von Kmhn constant (= 0.4) and g the acceleration due to gravity. This definition of neutral is wide on the stable side which, however, should not have a significant impact since the vast majority of the data were from unstable conditions. The results in this and the following section are compared to reference data observed over flat, homogeneous surfaces with low roughness which are designated as ideal. The turbulent statistics are non-dimensionalized by local (measured at the same position and height) values of scaling parameters, which renders the flow dynamically similar everywhere or locally invariant (if the scale of turbulence is small enough to permit rapid flow adjustment). Various urban statistics presented in local scaling have previously shown good agreement with reference data (e.g. Hogstrom et al. 1982; Roth 1993, Roth and Oke 1993). Other possibilities would have been scaling with values measured at the average height of the roughness (as suggested by e.g. Kaimal and Finnigan (1994) for plant canopies) or in the CFL. Neither approach is feasible for this study because the appropriate values are not usually available.

10 950 M. ROTH UJU UJU Figure 1. Variation of u*/u for neutral conditions with non-dimensional heights (a) z:/zg and (b) ZJZH. The line in (a) is based on the log-profile of Eq. (3) and the line in (b) is an empirical fit, see Eq. (5). The symbol codes are listed in the appendix. See text for further details. (a) Drug coeficient The intense turbulence created over rough surfaces can be expressed through the drag coefficient, CD, which is required for many practical purposes, such as relating the momentum flux to the mean wind profile, and the parametrization of the surface stress in numerical models. The non-dimensional form of the wind shear in the surface layer is: 4m = (kz;/u*)(au/az), (2) with U the mean wind speed. Integration of (2) for neutral stability (& = 1) results in the following expression for the drag coefficient: CD = (u*/ui2 = k2/{ln(zs/zo)l2. Note that for a given height and wind speed, CD increases with increasing surface roughness. The few urban observations available follow the theoretical prediction of (3) very well, and imply a logarithmic wind profile under neutral conditions (Fig. l(a)). These observations are supported by the only reliable direct measurement of 4m for a city by Rotach (1993b). His data show large scatter below zi/zo * 7, but relatively good agreement with data from ideal surfaces above, suggesting local equilibrium between the momentum flux and the wind gradient. As a consequence the turbulent exchange coefficient for momentum given by its logarithmic value: (3) Km = ku*zl(#m)-', (4) should also remain unchanged. This behaviour is consistent with observations from closed forest canopies, which show little deviation of & from their logarithmic values at several heights above the tree tops under neutral and near-neutral conditions

11 REVIEW OF TURBULENCE OVER CITIES 95 1 (e.g. Shuttleworth 1989). In contrast Garratt (1978) found that over a scattered, open, Savannah-type canopy the eddy diffusivity was increased by a factor of almost two. Corresponding urban data for the transfer of heat and water vapour are not available, but it is appropriate to note that observations over the forest sites suggest an increase of the diffusion coefficients by between 2 and 5 from neutral to moderately unstable (z;/l M -0.6) stratification. The mixing-layer analogy successfully describes the behaviour of momentum and heat diffusivities over plant canopies, and provides a partial explanation of the deviations from surface-layer values. As more data become available, it should be possible to test the utility of this framework in interpreting eddy diffhivities in urban environments. As expected, variability of data points is larger when plotted against zs/zh, especially for non-dimensional heights less than about 3 (Fig. l(b)). The square root of the drag coefficient is approximated by the empirical fit: c,!,'* = u,/u = I exp{-0.946(zs/z~)}. (5) (b) Normalized standard deviations (i) Standard deviations of velociv. The normalized velocity standard deviations are defined as Ai = a i/u* (i = U, U, w), (6a) where cr is the standard deviation and u, u and w are the longitudinal, transverse and vertical wind velocity respectively. Neutral values of Ai as a function of zl/zo or zs/zh are summarized in Fig. 2. The ratios of all three velocity components are relatively constant with height at z'/zo > 25 and zs/zh > 2.5. The generally larger W86 values for A,, at zl/zo > 20 or zs/zh > 2.2 are all from the same south-westem arc of this site whereas the rest are from the north-west. The corresponding Zi (see below for definition) values are also clearly larger (Fig. 7(a)-(d)). Based on the information available it is not possible to conclude what caused these unusually high ratios and they are therefore included in the present analysis. Much of the scatter closer to the surface is understandable in terms of differences in surface morphology of real cities and reflects the three-dimensional nature of the RSL. Given these data it is not possible to conclude if the ratios increase or decrease when approaching the surface. The average values for Au, A, and A, from all values plotted in Fig. 2 are 2.40, 1.91 and 1.27 respectively (Table 4). For measurements in undisturbed flow (say zs/zh > 2.5) the respective ratios are 2.32, 1.81 and The variability seen below this limit is reflected in the larger standard deviations of the corresponding averages for zs/zh < 2.5. The urban averages are very similar to the rural reference data, with differences of less than 10%. There is some debate whether the normalized standard deviations are a function of surface roughness. For example several authors report decreasing values of Ai with increasing zo (e.g. DuchCne-Marullaz 1979; Clarke et al. 1982; Yersel and Goble 1986). A similar trend cannot be confirmed by the summarized observations (Fig. 3) or in linear fits applied to the data (not shown). It is found that for unstable conditions (e.g. Panofsky and Dutton 1984; De Bruin et al. 1993) Ai = ai { 1 - bi (z;/l)}"j in which ai, bi and ci are constants. (6b) is confirmed for A, over ideal surfaces with ci = 1/3 as predicted by MOS in the limit of free convection. The urban observations (6b)

12 952 M. ROTH hz hz 2 l t i u Figure 2. Variation of A, = uu/ut (top row), A, = uv/u* (middle row) and A, = u,,,/u* (bottom row) for neutral conditions with non-dimensional heights z;/zo (left column) and ZJZH (right column). The key to the symbols is given in frame (0, the corresponding codes being listed in the appendix. See text for further details.

13 REVIEW OF TURBULENCE OVER CITIES 953 I I... I... k ;... i A U79 (zjz~ 0 WE6 (4% m zb8 H V89 (4% V... = 2.1, 7.1) = ) a ) I 2.6)... S92 (4% = ) 1 i"t "i I + i m 3 m b; o Figure 3. =0 Variation of A, = CJ,/U* (top), A, = uv/u+ (middle) and A, = u,,,/u* (bottom) for neutral conditions with ZO. The code for each symbol is given in the appendix. See text for further explanation. increase for -zl/l > O.l(Au,,) and -zl/l > 0.6(Au) (Fig. 4). The results for Au,u are similar to the rural results by Arya and Sundararajan (1976) and McBean (1971) which also find a definite increase with increasing instability. The predicted 1/3 slope is approached by most studies for A,. In particular V78, V89 and B95 show similarity behaviour for -zl/l > 0.6, -zi/l > 0.4 and -z;/l > 0.8 respectively, whilst the data from S76 approach this slope only at larger instabilities (Fig. 4(c)). The urban

14 954 M. ROTH (ZJZH = 5.6) - - S76 (ZJG = 3.2) S76 (24% = 2.8) X V76 (zj+ = 2.8) X 266 (zj ZH 1.5) W V89 (zj+ = 2.6) V 592 (zj+ = 2.6) 0 B95 (zj ZH = 1.5) (ZJq = B95 (ZJG = 3.2) ZJ L 10 Figure 4. Normalized standard deviations of u (top), u (middle) and w (bottom) plotted against zt/l. Thick, solid light and dark lines are reference data based on an empirical model (Binkowski 1979) and a fit to an empirical model (Eq. (6b). Table 5) respectively. Symbol codes are listed in the appendix. See text for further details.

15 REVIEW OF TURBULENCE OVER CITIES 955 TABLE 4. SUMMARY OF Ai FOR NEUTRAL STABILITY FROM SELECTED URBAN STUDIES AND REFERENCE RESULTS N74 S76 u79 W V89 S92 B S O S O Urban averages Zs/ZH > f f f 0.26 Zs/ZH > f f f0.07 Z~/ZH < f f f 0.34 Counihan (1975) Rural Panofsky and Dutton (1984) references 2.39 f f f 0.03 results show little variation for -zh/l -= 0.1 and on average are close to the expected mean value (Table 4). The most prominent differences when compared to the reference data (Binkowski 1979) are the initially decreasing ratios with increasing instability in particular for A, which result in a minimum close to but not at neutral, and the generally lower urban ratios for all three wind components at moderate to large instabilities (-zl/l > 0.2). Because of this peculiar shape, (6b) could only be fitted to values at -zi/l > 0.05 (Table 5). cw was set to 1/3 because of the observational support, but c,,~ was treated as a free constant. The neutral limits should be taken from Table 4 which includes a more comprehensive dataset. It is often observed that the statistics of u and v scale better with mixed-layer variables. Given the lack of appropriate observations and the wide scatter of the data it is not possible to conclude to what extent this is also true in the urban case (Fig. 5). The ratios are again systematically lower compared to the reference when plotted as a function of zi/ L.

16 956 M. ROTH TABLE 5. EMPIRICAL CONSTANTS FOR Ai = ail1 - bi(z;/l)]'i EVALUATED BETWEEN 0.05 < -Z:/L < 6.2 (U, U, W) AND 0.02 < -Z;/L < 5 (T) FOR ALL VALUES AND AT Zs/ZH > 2.5 ONLY (IN BRACKETS) PLOTTED IN FIGS. 4 AND 6 u 1.98 (1.88) 0.33 (0.15) 0.56 (0.94) u 1.64 (1.52) 2.84 (3.34) 0.30 (0.31) w 1.12 (1.15) 2.48 (2.09) 0.33 (0.33) T (-4.10) 24.4 (65.0) (-0.33) zi / L Figure 5. Normalized standard deviations of u and u plotted against zi/l. Light solid line is an empirical fit to aircraft data over Oceans and rural tower data by Panofsky et al. (1977) of the form U,,,~/U* = I12 + O.~(-Z~/L)]'/~. Symbol codes are listed in the appendix. See text for further details. A possible explanation for the departure of the urban data from the accepted forms follows from the evaluation of all terms in the turbulent kinetic energy (TKE) budget. It has been previously noted that the near-neutral and slightly unstable nondimensional dissipation values for TKE are also systematically smaller compared to empirical homogeneous surface-layer data (Clark et al. 1982; Roth and Oke, 1993). Clarke et al. (1987) show that at their suburban site more energy was produced locally than was dissipated, which resulted in a large residual component of TKE probably due to vertical transport, flux divergence, pressure transport and, possibly, horizontal advection. As Roth and Oke (1993) note, it seems reasonable to suppose that large and organized horizontal and vertical structures in the urban environment as well as transfer of energy through pressure-velocity interactions will result in increased transport of

17 REVIEW OF TURBULENCE OVER CITIES 957 A I I 1 I ZJ L Figure 6. As Fig. 4 but for T. The light solid and dashed lines are empirical fits to curd data by Wyngaard et al. (1971) and De Bruin et al. (1993) of the forms -ut/t* =0.95(-~:/L)-'/~ and -q/t* =2.9(1-28.4~;/L)-'/~ respectively. The dark solid line is a fit to an empirical model (Eq. 6@), Table 5). Symbol codes ace listed in the appendix. See text for further details. locally produced TKE away from the surface. The relatively efficient momentum transfer observed at a suburban location (Roth 1993) indirectly supports this hypothesis. (ii) Standard deviations of scalars. Dimensional considerations show that in the limit of free convection normalized standard deviations of scalars are a function of (-z;/l)-'j3 (e.g. Hill 1989). The variation of the standard deviation of temperature normalized by T* with stability is shown in Fig. 6. Urban ratios follow the reference data surprisingly well at most zs/zh, with a tendency to slightly larger values. Large variations are expected at near neutral stability (the two reference functions also differ in their limiting value at neutral), where the heat flux becomes close to zero, but production of temperature fluctuations does not cease. The - 1 /3 slope predicted by MOS is followed by S76, V89 and the data from the two lower levels of B95 for -zl/l > 0.3. Equation (6b) which also applies in the case of temperature (De Bruin et al. 1993) has been fitted to the urban observations using CT = 1/3 and excluding B95 at zs/zh = 3.2 (Table 5). The latter data are consistently larger, possibly due to temperature inhomogeneities in the relatively large source area. Only one urban study reports similar data for humidity. Roth (1993) shows that at a suburban site (V89) the normalized humidity standard deviations are generally larger than rural reference data, do not follow the -1/3 similarity prediction and are marked by considerable scatter. This result is explained by a combination of generally low transfer efficiency of moisture, low A, and the influence of mixed-layer processes near the surface (Roth 1993).

18 958 M. ROTH (c) Turbulence intensity The rate of production of turbulence, and its intensity defined as Zi =ai/u (i = u, V, w), (7) are functions of the Reynolds stresses and the mean velocity profile of the flow. Zj depends on the height of observation, the surface roughness and stability. It is generally observed that, for a given height, Zi is up to twice as much over an urban surface than a corresponding rural reference value (e.g. Bowne and Ball 1970). This is not so much a result of increasing ai, but due to retardation of the flow close to the roughness. Whilst the wind profile is strongly sheared, especially close to the canopy, ai here vary randomly with height (N74,286, S92 and B95). The estimated variation of Zi as a function of zi and zo in the CFL, under neutral conditions can be derived from (3) by substituting u* with the observed urban values of the Ai, viz. ai/u = kaj(ln(zl/zo))-'. (8) The urban observations follow the shape of (8) quite well (Fig. 7(a), (c) and (e)). The variability observed is also a result of the variability of the particular Ai value used (Table 4: 'urban averages' for zs/z~ > 2.5). If the respective neutral values of the individual studies were used in (8) agreement would be better. The unusually large values of for W86 have already been noted. At lower zi/zo, the turbulence intensities show increased variability around the theoretical prediction, especially for I,. I, tends to smaller values compared to (8). Given the lack of data in this range it cannot be concluded whether the good correspondence at the lowest levels of the 286 and S92 values is merely accidental. Similar to the profiles of CA'2 (Fig. I), the turbulence intensities show less organization close to the canopy when plotted against zs/zh (Figs. 7(b), (d) and (0). Roughness effects and differences in surface morphology introduce large variations which can be close to a factor of 2 for a given ratio at nondimensional heights zs/zh < 3. The urban Zi observations in the range 0.8 < zs/zh < 6.3 are approximated by the following empirical relationships: I, = u ~/U = exp{-0.943(zs/zh)} I, = Dv/U = k exp{-0.563(zs/z~)} I, = a,/ U = exp{-0.634(zs/z~)). (9a) (9b) (9c) Effects of atmospheric stratification on Zi are shown in Fig. 8. There is a tendency for ratios to increase on the unstable side close to neutral. The V89 data also suggest an increase at larger instabilities. As expected, data from individual sites are ordered roughly according to zs/zh (or zi/zo). The urban results in Fig. 8 are compared with the MOS prediction: li = Ai (zl/l)kiln(zk/zo) - $ m(~k/l)}-', which is obtained by substitution of (7) into the integrated form of (2). +m(zl/l) is the correction to the logarithmic wind profile for diabatic conditions (e.g. Paulson 1970) and Ai (zi/l) is obtained using parametrizations of data from the homogeneous surface layer (Binkowski 1979). The urban observations are clearly larger in comparison with the rural reference curve evaluated at Z ~/ZO = 450 which corresponds to the height of the V89 data but assuming low roughness (zo = 0.05 m). (10)

19 REVIEW OF TURBULENCE OVER CITIES n " O"/U " /U 7 I I I u /u u /u I I 80 - (e) I I I ow /U u /u W Figure 7. Variation of uu/u (top row), u,/u (middle row) and (~,,,/ll (bottom row) for neutral conditions with non-dimensional heights Z:/ZO (left column) and ZJZH (right column). The light solid lines in (a), (c) and (e) are based on theory (Eq. (8)) and the dark solid lines in (b), (d) and (f) are empirical fits (Eq. (9)). Symbol codes are listed in the appendix. See text for further details.

20 M. ROTH 0.51 :: I I! I I -1.o zs'/ L Figure 8. Turbulence intensity plotted against z!jl for (a) a,/u and (c) a,/u. Light solid lines are MOS predictions (Eq. (10)). See appendix for interpretation of symbol codes, and text for further details. (d) Mixing-layer similarity Mixing-layer similarity (Willis and Deardorff 1974) implies that under convective conditions the standard deviations of velocity and temperature, normalized using the

21 REVIEW OF TURBULENCE OVER CITIES h l 4 I I ?... i... : L ;.+ i 1 (a) 1.a cr 2/ W,2 W */T? T Figure 9. Normalized standard deviations presented in mixing-layer coordinates of (a) w and (b) T. Light solid, and dashed light lines are fits to reference data, Eqs. (13) and (14), and free convection predictions, Eqs. (15) and (16). respectively. See appendix for interpretation of symbol codes, and text for further details. scaling velocity, w*, and scaling temperatures, T*: w* = ((g/~wlel)ozi} /~ should be unique functions of zs/zi. The validity of mixed-layer scaling has been confirmed in boundary layers over oceans (Lenschow et az. 1980), and rural surfaces (Kaimal et uz. 1976; Caughey and Palmer 1979). The following functions from Sorbjan (1989) provide good fits to above mentioned datasets and are used as the reference: O:/W: = (ZS/Z~)~/~(~ - zs/z~)~/~ (~s/~i)~/~(1 - zs/z~)~/~ (13) CT;/T: = 2(1 - ZS/Z~)~/~(Z~/Z~)-~ ~ (zs/~j)~ ~(l - z S / Z ~ ) - ~ / ~. (14) Close to the surface (zs/zi < 0.15) data are shown to follow the free-convection predictions rewritten in mixed-layer notation (e.g. Caughey and Palmer 1979): Profiles of urban standard deviations of vertical velocity and temperature (all from convective, mostly afternoon conditions) normalized by mixed-layer variables are plotted in Fig. 9. The urban cri/wi ratios are in agreement with the reference functions close to the surface and in the upper part of the boundary layer (Fig. 9(a)). Similar to

22 962 M. ROTH the rural data reported by Kaimal et al. (1976), the urban results show only a small decrease near the inversion base. The observations suggest that the urban ratios reach a peak closer to the ground (zs/ti 0.2 to 0.4) compared to the reference (zs/zi % 0.4 to 0.5). Considering the lack of corresponding data for temperature, it is not possible to conclude whether the slightly larger ratios close to the surface and other deviations from the reference are real features or not (Fig. 9(b)). The relatively good agreement between the individual studies is surprising given that the sensors used to measure the turbulence quantities included aircraft gust-probes (S75a, S76a, P79a), Doppler sodars (T75a, R94a) and 3-D sonic anemometers (S84), and that zi varied greatly, being m (S84), 350 m (R94a), m (T75a), 1000 m (S75a, P79a) and m (S76a). It should be noted that calculation of w, requires knowledge of the surface heat flux (1 1). This quantity is usually not measured directly, but obtained from the vertical-velocity variance profile and by interpolation of the resulting heat-flux profile to the surface. This procedure is prone to errors, but in the absence of appropriate research it is not possible to conclude to what extent and in which way it would affect the results summarized in Fig. 9. In the lower part of the convective UBL, ow itself can be between 20% (Godowitch et al. 1981) and 50% (Godowitch 1986) higher than data measured over nearby rural areas. The success of mixed-layer scaling for the statistics of w may be due to a corresponding increase in the sensible-heat flux at the surface often observed in urban areas (e.g. Ching 1985), and possibly also due to larger zi (doming of the UBL). 5. RESULTS OF (C0)SPECTRA AND TURBULENCE LENGTH-SCALES (a) Theoretical background To better understand the discussion of the following results it is helpful to briefly review the main characteristics of energy spectra. (Co)spectra show the behaviour of time- and length-scales of turbulence, and enable a visual inspection of the energy distribution as a function of frequency. The energy densities (which equal the (co)variance when integrated over the full range of frequencies measured) are commonly plotted against a non-dimensional frequency: with n the natural frequency, which collapses the (co)spectra measured in the CFL under identical stability conditions. Taking the frequency at the spectral density with the largest magnitude (fm or fh, defined as the peak on a log(ns) vs. log(f) plot where S is the spectral energy density) a peak wavelength can be defined by virtue of Taylor s hypothesis as: Three major spectral regions can generally be identified which are: (i) the energycontaining range (low-frequency range); (ii) the inertial subrange (high-frequency range); and (iii) the dissipation range (which marks the drop-off to zero at the highfrequency end of the spectrum, and is not further considered here). The energycontaining range, where energy is produced by buoyancy and shear, has its own characteristic length which is related to A,. The inertial subrange separates the energycontaining and dissipation ranges. Using the second Kolmogorov hypothesis (e.g.

23 REVIEW OF TURBULENCE OVER CITIES 963 Champagne et al. 1977), it can be shown that the energy density in this region should be proportional to the wave number to the -5/3 power. This law is translated into the -2/3 power law when the energy densities are multiplied by the natural frequency and plotted against f or f I. The same law holds for temperature (Corrsin 1951), and the exponent is -4/3 for cospectra (Wyngaard and Cot6 1972). If local isotropy exists in the inertial subrange the v and w spectral levels are R = 4/3 times those of u. The (co)spectral energy densities can be normalized in two ways. First, normalization by the respective (co)variance is simple, and is therefore the preferred approach in most studies and is the one adopted below. Second, presentation within the MOS framework yields additional information on the stability dependence of the energycontaining range (e.g. Kaimal et ul. 1972). MOS scaling, however, requires the computation of the dissipation rates, which is only possible through a detailed analysis of the highest frequencies (within the inertial subrange). Only three studies which present their (co)spectra within the MOS framework passed the selection criteria (S76, U79 and V89). Roth and Oke (1993) present a comprehensive and detailed analysis of all important atmospheric variables and fluxes measured under unstable conditions at zs/zh = 2.6 during V89, which also includes the spectral correlation coefficients, coherence spectra and phase-angle spectra. Their observations show all the major characteristics expected from MOS scaling; specifically, the (co)spectra collapse in the inertial subrange and display the required -2/3 (-4/3) slope (which is also observed in S76 and U79). As predicted, the spectra exhibit a systematic variation with zi/l at the low-frequency end, which is most pronounced for w, but also seen to a lesser extent in other (co)spectra. The most pronounced difference from data from the homogeneous surface layer is the lower non-dimensional energy dissipation rates for unstable stratification, which are also observed in S76. Of particular interest is how the urban (co)spectra depart from the shapes and scaling relationships developed for the reference data, which are rural observations from the Kansas and Minnesota experiments (Kaimal et al. 1972; Kaimal 1978) and measurements over crops (Anderson and Verma 1985). The following discussion concentrates on three characteristics: (i) the overall (co)spectral shape; (ii) the position of the spectral peaks; and (iii) (co)spectral slopes and isotropy in the inertial subrange. (b) Velocity spectra and length-scales (i) Neutral strutijcution. Frequency-weighted velocity spectra measured under neutral conditions at different non-dimensional height ratios are plotted in Fig. 10. The urban u and w data are compared to empirical formulae based on the Kansas experiment (Kaimal et al. 1972; also Hgjstrup 1981 for w) of the form: ns,(n)/u: = losf /(l + 33 f f ) 513 f 513 nsw(n)/us = 2f Il + 5.3(f ) 1, and substituting u* with the similarity predictions given by De Bruin et al. (1993): D,/u* = 2.39( 1-3zb/L) l3 (19) (20) ow/u* = 1.25(1-3z:/L) l3. (22) The right-hand sides (r.h.s.) of (21) and (22) are chosen to equal A, and Aw, as suggested by Panofsky and Dutton (1984) (Table 4), in the neutral limit (i.e. zi/l = 0). The overall shapes of the urban spectra are remarkably similar to the reference for both u (Fig. 10(a)) and w (Fig. 10(b)). The higher values at the high-frequency end (f > 8)

24 964 M. ROTH.:/ oc b \ 0.01 I,, P = nz, /U Figure 10. Normalized spectra for neutral conditions measured at different non-dimensional heights of (a) u, and (b) w, plotted against f on a log-log plot. The light solid lines in (a) and (b) are a model based on the Kansas data (Eqs. (19x22)); the light dashed line in (a) is a rural reference from Anderson and Verma (1985). See appendix for interpretation of symbol codes, and text for further details. for B95 in this and all subsequent figures are probably not real, but reflect aliasing of potential energy contained above the Nyquist frequency. The somewhat irregular behaviour of the S92 data (Fig. 10(a)) is caused by the small number of individual mns. Whereas the u-spectra are within the region given by the reference curves, the w-spectra are consistently displaced towards lower frequencies. Although not plotted (because they are only normalized within MOS) the same is true for the neutral w-spectra from U79 and V89. The non-dimensional peak frequencies as a function of normalized height are plotted in Fig. 11. The results from the studies with multi-level observations generally show an internally consistent increase of the peak frequency with increasing height for all three velocity components (Fig. 1 l(a), (d) and (g)) in particular below zs/zh 3. Note that the values for N74 are not directly measured peak frequencies, but are computed from a longitudinal length-scale derived from the autocorrelation function. The absolute magnitudes are therefore different; this is, however, irrelevant for the purpose of the

25 REVIEW OF TURBULENCE OVER CITIES 965 Figure 11. Variation with height normalized as Zs/Zh of spectral peak frequencies of (top row) u, (middle row) u, and (bottom row) w, for neutral, unstable and stable conditions (from left to right). Shaded areas show range of measured peak frequencies from the Kansas data (Kaimal et al. 1972). Low- and high-frequency limits correspond to -2 4 z:/l < -0.1 (unstable), -0.1 < z:/l < 0.1 (neutral) and 0.1 < zi/l < 1 (stable) respectively. See appendix for interpretation of symbol codes, and text for further details.

26 966 M. ROTH present comparison, and the focus should be on the relative change with height. There is some variability amongst the u and u data but they generally fall within the rural limits (shaded areas in Fig. 11). This is not the case for w whose peak frequency is systematically lower than the reference at all heights. This, and the fact that the spectra do not collapse onto a single curve, suggests that traditional MOS scaling alone cannot explain the behaviour of the urban results below approximately zs/zh < 3 where additional lengths-scales may become important. A shift to lower frequencies would be expected when element (hence wake) lengths-scales are important, rather than the height above ground. Figure 12 shows the associated peak wavelengths normalized by the mean height of the roughness elements. The number of studies plotted is larger than on Fig. 11 because the zero-plane displacement length is not needed to calculate Am. The neutral u and u references are based on the Kansas neutral limits on the positive side (z;/l = O+) in the surface layer computed as: The behaviour of the peak wavelength for w can be expressed as follows (Kaimal and Finnigan 1994): Aw,m = zk( ~i/li)-' 0 < Z: 6 -L (23c) A.w,m z~i(o.55 + Z;/L)-' 0 6,z: < L. (234 Based on the studies with directly determined Zd values in Fig. 12, Zd/ZH = 0.5, which is the same as suggested by Grimmond and Oke (1999) for low- and medium-density cities, and is the value used to calculate Z; in (23). The neutral w range (Fig. 12(g)) corresponds to -0.1 < zh/l < 0.1. The peak wavelengths of the horizontal wind velocities seem shifted towards larger scales (Fig. 12(a) and (d)) when compared to the reference. This is because (23a) and (23b) represent the neutral limit from the positive side only. Unstable spectra do not follow surface-layer scaling, and it is not possible to calculate a corresponding unstable limit. As shown in the frequency domain, the observations are in good agreement with the Kaimal data (Figs. ll(a) and (d)). It was already noted above that urban vertical length-scales, hw,m, are generally larger than reference data (Fig. 12(g)). Also plotted are wind-tunnel (strips and rods), crop (corn) and forest (representing open canopies) data summarized by Kaimal and Finnigan (1994). In these environments the position of the spectral peak is invariant with height when normalized by the height of the canopy, and quickly increases above the canopy top, consistent with the Kaimal surface-layer relationships. Kaimal and Finnigan (1994) explain this rapid transition as a consequence of the large-scale inactive horizontal motions well above the roughness sublayer which modulate the production of the canopy-scale eddies. The latter are crucial to the transfer of momentum and scalars, and are dynamically linked to the height-scale of the roughness elements. This fits the physical picture for the dominant eddy structure in a plant canopy suggested by the mixing-layer analogy. According to Raupach et al. (1996) three ranges of eddy-scales can be distinguished relative to a vertical length-scale Ls (which is roughly of the order of ZH or less) characteristic of the active canopy turbulence associated with strong vertical transfer. First, at the largest scale the boundary layer is dominated by eddies much larger than Ls, scaling with Zi, and which are practically horizontal near the surface and therefore contribute little to the vertical transfer in

27 REVIEW OF TURBULENCE OVER CITIES lo00 LLYJ lo lo00 I..,..,.,I... I..,& 1... I... I... Figure 12. As for Fig. 11 but for wavelength of spectral peak normalized by height of roughness elements. Shaded areas are based on Kansas data (Kaimal et al. 1972) calculated using Eqs. (23c), (23d), and (25). Light solid lines in (a) and (d) are neutral limits on positive side from Eqs. (23a), (23b) and (25). Thin solid lines in (a), (d) and (9) are canopy layer data summarized by Kaimal and Finnigan (1994) (see text).

28 968 M. ROTH canopies. Second, the active canopy-scale eddies are of the order of Ls, and originate from instabilities of the kind found in mixing-layer turbulence associated with the inflection observed in the mean wind profile near the top of canopies. Third, fine-scale turbulence at scales much less than Ls is created by e.g. wake shedding and contributes little to the vertical transfer; however, it is important in dissipating turbulent energy. This representation may need to be modified when the spacing of canopy elements approaches zh as will be the case in sparse canopies such as urban areas. In this case the flow field becomes three-dimensional on the scale of Ls itself, leading to additional complications. In particular, both wake enhancement and mixing-layer instability might be important in the vertical transport, which could explain some of the variability seen in the present data. This is supported by recent field and wind-tunnel measurements of uniformly thinned forests (Novak et ul. 2000), which show that variation in tree density adds a modulation to the mixing-layer analogy and wake production is important within sparse canopies. The importance of D as a scaling length is demonstrated by the A,,,,/z~ data of W78S and S92 near the top of the canopy. Although measured at similar zs/zh the values are different (Fig. 12(a)). W78S is a relatively high-density urban surface (zh/d% 1-3) with wake interference or skimming flow, and the dominant morphological lengthscale would be of the order of the height of the roughness. On the other hand, S92 is representative of an open, low-density residential neighbourhood (zh/d x 0.25) which would be characteristic of an isolated-flow rkgime. Here the roughness inter-element spacing should become important and is likely to result in an increase of the peak wavelength. By contrast, the studies summarized by Kaimal and Finnigan are all from relatively dense canopies. (ii) Unstuble/stuble strut$cution. Unstable velocity spectra at several heights within and above the canopy are summarized in Fig. 13. Stabilities of individual studies are for: V78, very unstable; V86, mean zi/l = -0.75; 286, slightly unstable; V89, mean zl/l = -0.62; and B95, zi/l < The faster than expected roll-off at the highfrequency end, observed for V78, is caused by the relatively low response time of the sensor used (see appendix). Similar to their neutral spectra, the unstable horizontal wind components for B95 move towards higher frequencies with increasing height (Fig. 13(a) and (b)). u and v data from V78, V86 and V89, which are from similar non-dimensional ratios (zs/zh = 2.6 to 2.8), agree very well with each other, but are closest to B95 measured at the lowest level (zs/zh = 1.5). These studies have overall shapes which are very similar to the surface-layer prediction from Kaimal (1978). Unlike the v-spectra, the peaks of the u-spectra tend to be slightly shifted towards higher frequencies (Fig. 1 l(b) and (e)). This, and the faster roll-off at the low-frequency end (Fig. 13(a)), is consistent with the concept of a shift towards smaller (relative to zi) scales of energy-producing eddies in the wake of upstream buildings. There is a point of inflexion at around f z 0.1 (more prominent for u) which marks the transition region between the energycontaining eddies at the low-frequency end and the energy-dissipating eddies at the highest frequencies, and agrees with the idea that the low-frequency and high-frequency parts of surface-layer horizontal wind spectra obey different scaling regimes (e.g. Kaimal 1978). Differences between individual studies are probably the result of different stabilities, but also, as noted above, may be due to variability in urban morphologies (packing of buildings) which is not accounted for in the simple zs/zh ratio. Using f as the scaling parameter collapses the V78, V86, V89 and B95 w-spectra measured at 1.5 < Z JZH < 3.2 (Fig. 13(c)). Besides an insignificant shift towards lower

29 REVIEW OF TURBULENCE OVER CITIES \!?= nc be \ 0.1 \.,..\ I \..... :..- \ %.. ". \ '. * I\ P = nz,'/u Figure 13. Normalized spectra for unstable conditions measured at different non-dimensional heights of (a) u, (b) u, and (c) w, plotted against f' on a log-log plot. The thick, light solid lines in (a) and (b) are a model based on the Minnesota data (Kaimal 1978) evaluated at zk/l = - 1; the thick, light dashed and dotted lines in (c) are a model based on the Kansas data (see Eq. 24) (Hfhjstrup 1981), evaluated at z:/l = -1 and respectively. See appendix for interpretation of symbol codes, and text for further details.. \- 1

30 970 M. ROTH frequencies, the urban observations compare very well with a spectral model developed by Hprjstrup (198 1) based on the Minnesota results (Kaimal 1978) of the form: and substituting for u* with (22). The 286 wind velocities within and just above a high-density urban canopy are significantly shifted towards higher frequencies and resemble neutral observations (Fig. 13(c)). However, processes other than stability have to account for this shift because the data are from slightly unstable conditions (M. Rotach 1998, personal communication). Similar transfer of energy to smaller scales close to the canopy (zs/zh < 2) is observed in the M69 data (Fig. 12(b), (e) and (h)). This abrupt change, observed just above the roughness elements (most prominent for u and u), reflects the transition between two flow regimes as noted above in connection with the neutral data. The difference in scales is larger in the case of unstable stratification, because the flow also responds to thermal plumes which scale with the height of the boundary layer. Measurements taken below the mean height of the roughness show the most pronounced changes, which include the disappearance of a well-defined peak and distribution of spectral densities over a wide range of frequencies (0.02 < f < 0.4). The energy transfer near the top and within the canopy is apparently due to eddies with a wide range of length-scales, about (0.5-10)zH. The failure of z: as a single scaling length (the spectra do not collapse) is further demonstrated by the 286 u and u data measured at the same non-dimensional height ratio. The observations from over the canyon (zs/zh = 1.3%) are clearly different from those measured over the adjacent roof-top (zs/zh = 1.3%) and resemble the data from within the canyon. This example suggests that under unstable conditions canopy-layer turbulence includes eddies with sizes that correspond to thermal plumes/downdraughts which are linked to the heat sources/sinks of the urban surface. This could also be true for the horizontal velocity components, because they depend on large (boundary-layer-scale) thermal plumes in the surface layer. Only very few urban measurements from stable conditions are available for analysis. This is not surprising considering the rough nature of the surface, heat released from storage at night and the additional heat input from anthropogenic sources, which result in near-neutral or slightly unstable stratification even on clear nights. Peak frequencies are consistently shifted towards lower values (larger scales) at all heights (Fig. I 1 (c), (f) and (i) and Fig. 12(c), (fj and (i), respectively) compared to reference data, which are again from Kaimal et al. (1972) using (23d) and: evaluated for 0.1 < zk/l < I. L, m = Lm/5 = L.m/2, (25) (c) Scalar spectra and length-scales Spectral information on scalars is very scarce, and even spectra of the most readily measured variable, temperature, have only been published on few occasions. The overall shapes and peaks of the V86 and V89 data correspond well to each other and to the rural reference from Anderson and Verman (1985) (Fig. 14). The B95 observations on the other hand show less energy at larger scales, and the observations from the top level (zs/zh = 3.2) are different in shape and location of the peak (Fig. 15(a) and (d)). A possible reason for this may be advection from areas with different thermal surface characteristics (which would also imply that the flow was not fully adjusted to

31 REVIEW OF TURBULENCE OVER CITIES.,(.....I...,..(..... I.., b : - \ 0.01 V88 (4/+ 265) A - V88 (4/+ = 26)... v88 (4/+ 17) (4/+ 3 2) (4/ ) 1 i (4/+ - 15) 0 ZE6(4/+= 165) o a 6 (4zn = 1 35r) - ZSe(tr'+ - 13%) A zes(4/+=091) I...,.,.I... I f' = nz,'/u Figure 14. Normalized temperature spectra for unstable conditions measured at different non-dimensional heights. The thick, light solid line is a rural reference from Anderson and Verma (1985) representing slightly unstable conditions. See appendix for interpretation of symbol codes, and text for further details. the underlying surface). It should be noted that only V86 and V89 measure temperature directly by using fast-response thermocouples, whereas both 286 and B96 derive temperature from sonic wind speeds (see appendix). Similar to their velocity components, the peaks of 286 temperature spectra are shifted towards higher frequencies. This suggests an increasingly important role of the w component in contributing to fluctuations in T, or a transition from a flow regime which is dominated by boundarylayer scales at larger heights to one that responds to canopy-layer plumes closer to the roughness. The flat appearance of the spectra within the canyon (zs/zh = 0.91) indicates the absence of a preferred length-scale, and production of energy over a range of eddy sizes. Measurements of urban humidity spectra are extremely rare and the only observations are from V89. Because of the absence of a well-defined low-frequency peak (Fig. 4(b) in Roth and Oke 1993), the data suggest that even close to the canopy the transfer of humidity is modulated by large-scale structures. This can be expected over the rough urban surface which is likely to produce well-developed interaction between the surface and the upper portion of the UBL (Roth and Oke 1995). (d) Cospectra and length-scales Figure 16 shows momentum and heat-flux cospectra from unstable conditions. The reference (Anderson and Verma 1985) for u w and w T is for neutral and slightly unstable conditions, respectively. The most obvious feature of the urban uw data is their jagged appearance at all frequencies (Fig. 16(a)). The peaks of V86, V89 and B95 are all slightly shifted towards lower frequencies compared to the reference which is, however, also due to differences in stabilities. The urban peak frequencies still fall within the lower range of the expected region (Fig. 15(b)). Similar to the u-spectra (Fig. 13(a)) the uw data show a marked roll-off at the low-frequency end, which results in a relatively

32 972 M. ROTH Figure 15. Variation with height normalized as Zs/Zh of (top row) spectral peak frequencies, and (bottom row) peak wavelength, normalized by height of roughness elements of T, uw and wt (from left to right) for unstable conditions. Shaded areas are as in Fig. 11. See appendix for interpretation of symbol codes, and text for further details. well-defined peak. The observations from 286 are again shifted towards smaller scales, while the cospectra within the canyon essentially lose their significance. Agreement between individual heat-flux cospectra and the reference is excellent, with the exception of 286 which is again shifted towards higher frequencies (Fig. 16(b)). Peak frequencies also correspond well with reference data (Fig. 15(c)). V89 is the only study which presents humidity-flux cospectra. The observations closely resemble those for heat flux, but are marked by more variability at the lowfrequency end (Fig. 6(b) in Roth and Oke 1993). Despite the absence of a peak in the corresponding humidity spectra, the flux cospectra show a relatively organized low-frequency roll-off, which is attributed to steep low-frequency roll-off found in the w-spectra and the low vertical wind-humidity correlations found at large scales (Roth and Oke 1993).

33 REVIEW OF TURBULENCE OVER CITIES , r f 3 \ 0.01 ; t A urn "1 rn Figure 16. Normalized cospectra for unstable conditions measured at different non-dimensional heights of (a) uw, and (b) wt, plotted against f' on a log-log plot. The thick, light solid lines in (a) and (b) are a rural reference from Anderson and Verma (1985) representing near neutral (a) and slightly unstable (b) conditions. See appendix for interpretation of symbol codes, and text for further details. (e) Mixed-layer vertical velocity length-scale Very few spectral data from the UBL have been published. Observations of vertical velocity peak wavelength are presented in Fig. 17. The reference of the form: Aw,m = 1.8zj(l - e-4zk/zi e8zk/zi) for 0.lZj < < zj, (26) has been derived by Caughey and Palmer (1979). The small number and variation of the data points reinforces the need for more high-quality UBL research before any conclusions can be drawn. (f) Spectral slopes and isotropy in the inertial subrange The three conditions for the existence of an inertial subrange of surface layer spectra are: -2/3 power law; vanishing cospectral levels; and isotropy which implies that S,(n) = Sw(n) = RSu(n) where R = 4/3 (Kaimal and Finnigan 1994). The urban data

34 974 ti- \ N@ 1.o M. ROTH I I I I \o - m S76a P79S I I I I I Figure 17. Variation with height normalized as zs/zi of the vertical velocity peak wavelength. The light solid line is a rural reference (E.q. (26)). See appendix for interpretation of symbol codes, and text for further details. on the -2/3 slope are inconsistent (Figs. 10, 13, 14 and 16). At approximately f' > 2 the neutral and unstable velocity and unstable temperature data measured during S76 (not shown), U79 (not shown), V86 and V89 and S92 (all at zs/zh > 2.5) roll off as f '-*I3. Between 1.5 < zs/zh < 3.2 the neutral and unstable u observations for B95 also generally show the classic -2/3 slope, however, the roll-off is less for the unstable u and T and the neutral w components (except, surprisingly, at the lowest level). The neutral U79 observations (not shown) at ZJZH = 1.8 have slightly smaller u and steeper u and w slopes compared with the theoretical prediction. Because of the relatively slow sampling rate (1 Hz) it is not possible to comment on the high-frequency slopes of the 286 data. The u w cospectra roll-off rate is generally less than the prediction (Fig. 16(a)), which is the same as observed for the B95 wt data (Fig. 16(b)). On the other hand, the V86 and V89 w T cospectra follow the -4/3 power law. Comparison of the urban data with observations from other rough surfaces remains inconclusive. Within the canopy layer u and w spectral levels are often increased due to wake production which is a source of energy. This occurs at the expense of the u fluctuations because the drag term is quadratic in the total velocity (3) and therefore is much more efficient at extracting energy from the u-fluctuations than from u and w (Kaimal and Finnigan 1994). Few studies report velocity spectra to sufficiently high frequency to be able to comment on the 4/3 ratio (all are based on S,(n)/S,(n)). In U79 the 4/3 ratio is approached for f' > 4 at zs/zh = 6.3; however, R is only about 1.06 at zs/z" = 1.8. Ri % is obtained in V89 for f' > 1 at zs/z~ = 2.6. Neutral, slightly unstable and unstable observations from B95 generally fall short of the prediction, with R % 1.2 at the top two levels (zs/zh = 2.1 and 3.2) and 1.3 at the lowest level (zs/z~ = 1.5) for f > 3, with the exception of the unstable data which are between 1 and 1.1 at the lowest level. R is less than unity in the case of 286 at zs/z~ = No such urban data are available from zs/zh < 1, however R varies between less than 1 and 1.7 in forest and corn canopies (Kaimal and Finnigan 1994), which demonstrates that large departures

35 REVIEW OF TURBULENCE OVER CITIES 975 from classical isotropy theory are possible within the canopy layer, and possibly just above. 6. CONCLUSIONS This paper has attempted to combine micrometeorological studies of atmospheric turbulence over cities and place them into a single framework. The results are based on a few high-quality studies which met criteria based on stringent experimental requirements. For neutral conditions the main findings are as follows: 0 Integral statistics agree well with the log-profile prediction in the case of CD but are lower for Zi. 0 Average values of Ai are very similar to reference data, but show increased variability below z* M (2.5 to 3)zH. The same range for z* is supported by the spectral results, and is suggested as the upper limit of the roughness sub-layer of urban canopies. 0 The shapes of the velocity spectra show good agreement with reference data. Only close to and within the canopy of a densely built area is there a shift towards higher frequencies and the disappearance of a well-defined peak. The result that fh,, is shifted towards lower values at all heights, indicates that most of the vertical transport is due to eddies produced by element wakes at length-scales comparable to zh rather than much smaller. 0 Variability of the data is decreased when non-dimensional statistics are plotted against zl/zo instead of zjzh. Whilst ZH is a useful first-order approximation of the roughness of a site, the actual surface roughness parameters are probably better suited to describe the transfer of turbulent quantities. The greatest differences to reference data are observed under unstable conditions: 0 Because of reduced wind speed in the city, Zi(zt/L) is systematically larger than rural data. 0 A, exhibits a peculiar decrease with increasing instability close to neutral, unlike Au3w which remains fairly constant. At greater instabilities A,,u,w increases and the slope approaches 1/3 in the case of A,. 0 Au,u,w(Ar) is generally smaller (slightly larger) at near neutral to unstable stratification. 0 Spectra are only clearly affected by individual roughness characteristics close to and within the canopy. The w T cospectra are surprisingly well-behaved, and agree with reference data in their shape and location of the peak. On the other hand, u w cospectra are ill-defined with large variability. It is clear that more high-quality momentum flux data are needed. There are a number of implications from the present review: (1) The basis of several micrometeorological approaches is in doubt. The gradient method is suspect because the difisivities of heat and moisture are different. Scintillation methods rely on MOS, which is not followed by all variables. The same is true for remote sensing of the UBL (e.g. using sodar) which relies on traditional convective boundary-layer theory. (2) Existing air quality and dispersion models, which calculate dispersion parameters based on homogeneous-surface-layer assumptions, or make crude corrections to the stability to account for the increased roughness of the city, are flawed. Such models

36 976 M. ROTH often underestimate concentrations (e.g. Olesen 1995; Rotach 1997). Further improvements will only be possible if the special nature of the turbulence exchange in the urban atmosphere is taken into account. (3) The results on integral statistics and spectra suggest the existence of strong similarities between turbulent flows over cities and plant canopies. This analogy has important implications in terms of flow dynamics and its consequences on statistics, spectra or turbulent length-scales, because plant turbulence shows many similarities to plane mixing-layer flows (Raupach et al. 1996). It has been shown that urban turbulence can be interpreted in the same framework, with possible modifications to take into account wake turbulence which becomes increasingly important in sparse canopies. To better understand the local atmospheric environment of cities, the following areas of research should be given emphasis over the coming years. First, the transfer processes (organized motions) near the top of and within the urban canopy, i.e. within the main region of momentum, heat and mass exchange. Second, the exchange at larger heights, to test the existence of a CFL. Third, since the early efforts in METROMEX, no study has focused on the turbulent structure of the daytime mixed layer. Consequently very little is known about the UBL. Raupach et al. (1991), for example, point out that even if the conditions at the surface are drastically altered by roughness, the main boundary-layer structure is not changed in any fundamental way. Based on the few results available, however, it is impossible to conclude to what extent standard mixed-layer approaches are applicable in the urban case. Very few urban-turbulence studies are sufficiently documented and reliable to warrant further analysis. Although obvious, it is necessary to again point out that all work should include a detailed description of the overall setting of the observation site and the characteristics of the fetch (average height of buildings, aerodynamic roughness length and zero-plane displacement height as a minimum). A photograph taken from the main observation site towards the fetch is also desirable. Further, it is essential that future field observations are made over surfaces with sufficiently simple structure or morphology for the results to be of general value. ACKNOWLEDGEMENTS I am grateful to many individuals for their help in sending me reports of their recent work and finding reference material. In particular, Mathias Rotach and Christian Feigenwinter provided valuable information and additional data. Many analyses have profited from discussions with Tim Oke. Financial support by the Swiss National Science Foundation (grant # ) and the National University of Singapore, Faculty of Arts and Social Sciences (Rp # ) is gratefully acknowledged. APPENDIX A summary of the physical and aerodynamic properties of turbulence studies over cities is shown in Table A. 1.

37 TABLE A.1. SUMMARY OF THE PHYSICAL AND AERODYNAMIC PROPERTIES OF TURBULENCE STUDIES OVER CITIES SORTED BY YEAR OF OBSERVATION Site characteristics Measurements Comments records [r] Code City - site ZH [ml ~0 [m]' zd [mil Fetch characteristics* zs [m] statistics sensors used (time of reported3 (sampling observation) frequency) Taylor(1918) PI8 Paris-Eiffel HDcitycentre da da n/a tower ( ) Shiotaniand T46 Tokyo-Centr. N: -20 N -6.5d N 14' MD Met. Obs. S: -12 S -2.5' S: 8.4' -4d SOma(1964) (summer 1946) K60 Kokubunji da (spring and autumn ) T60 Tokyo-Tokyo tower (196041) T63 Tokyo-Tokyo 274 tower (196043) 0.4a 2.32w 1.6Sa da LD with big open Spaces n/a HD n/a SameasT60 123,197,302 KH , 30.8, L cup anem.. u [lo']; 48.2 thennocouples AT [30'1 26, , n/a (da) 150 [60'1 25,35,45,55. Iu. u*, KM hot-wire anem. 6[lo'] 60 (I and 2 Hz) uu. /.. Su, cupanem. (0.5 Hz) 21 [lo'] CD. E Stable to neutral Near-neuaal, slightly unstable (cloudy); Original Zd Unstable, neutral, stable; no Q Near-neutral (strong winds, passages of taifuns) Unstable, neutral, stable McCormick and Kutds (1966) Bowne and Ball ( 1970) F65 Ft.Wayne.IN- -8 GT (autumn, winter 1%5/66) C66 Cincinnati,OH da (da) F66 Ft.Wayne.IN- -8 GT and othm (summer 1964, winter 1965/66) L66 London,ON Bell 1.3Iw n/a 6y 2.1a n/a NW-sector: LD n/a n/a n/a SameasF65 n/a MD; 2 to 4-storey houses, tall tnes 9, , u.u. ue 2-D Climet anem. (da) -19 [3d] KH,A resistance 21 therm. (W, helicopter sunphotometer soundings uu, Au,u.w. 3-D vector vanes for Ri, S, (8 Hz, 0.8 m) spectra) cou w [3o'l su 3-cup anem. 6 13dI (-1 Hz) < Ri c c Ri < WQ Winter, strong winds See note 1 following the table for meanings of alphabetical superscripts in these columns. *See note 2 for reference and definitions. 3~ note 3 for definitions of symb~ls not in the main text. 4Fmm Arakawa and Tsutsumi (1976). 9 m

38 ~~~~~~ ~ ~ ~ TABLEA.l. CONTINUED Site characteristics Measurements Comments ReferenHs) Code City-site ZH [m] zo [mil zd [mil Fetch characteristics* zs [ml statistics Sensors used records [r] (time of reported3 (sampling observation) frequency) Arakawaand T66 Tokyo-Tokyo 27 da n/a TsutsUmi ( tower ( ) 1976) Helliwell(l971) L67 London - Post e 20.7 Brook (1972) Angell et ul. (1974) Brook (1974) Nakano er al. (1974) Wamser and Miiller (1977) Office tower (winter 1967) M69 Melbourne- 16 n/a n/a Physics Dept. N: 10 RMIT (spring ) 071a OIrlahomaCity, 70 n/a n/a OL-various (<150) (autumn 1971) V71 Melbourne- da O.Sl.4 da Wctoria Dock (winter 71/72) 072 da Osaka-Osaka da 1.9 tower (winter 1971) H73 da Hamburg- n/a 0.78' NDR (summer 1973) RamsdeU(1975) S73 da Seattle, WA- LU: 12 LU:0.7a LUandK (1973/74) K-S: 35 (<W K-N: 12 DucMne- c2= N74* Nantes-CSTB a Marullaz (1975, (197477) 1979) Same as T60 HR MD and H D da LD - industrial docklands, inlets, mudflats HR Sector Ill: LD - industrial docklands, inlets LU: hfd - grass area hrst 150 m upwind of tower K-S: HR K-N: MD Sector D: MD - houses and blocks of <5-storey. open spaces and trees; grass area first 100 m upwind of tower 26,67,107, Gusts 3-cup fast response 47 Ida] 173,253 anem. (I Hz) 43.61, 195 tu cup anem. (5 s) 16.9 tu. CD, Su.u.w, 3-D Gill-type 23 sku, u. w1 anem. (1 Hz) 28.5 Kuu.v.w -400 W, sfress Tetroon , resistance them u*. CD. Ri, 2.3-D Gill-type 47.8,73.5, TKE, S,,.,,, anem., pt COUW. Sk. Ku, A (-1 Hz) 120 (25-125) %u,w. u*. KM da 50 E, Su. A,,,,,, SAT (10 Hz) 250 LU:6.9, 12.6, b,u.w.au,v.u, 3-DGill(2Hz) ; Su.w.v. Au.u.w K: 77, u*, CD, 1,. 2.3-D Gill (2 Hz) Au,v,w, Su, Au,w 115 [5'1 <24 120'1 32 flights [dal 120 [25'] 25 [-SO'] '1 LU: -37 "'1 K: 10 (31'1 Near-neutral (very high winds) Data biased towards strong winds; only N sector chosen; tower on top of 10 m bldg. Stable, unstable Generally unstable -1.6 c Ri < 1.5; no Zd -2.5 < zs f L (indirect through qh); 25 m tower on top of 70 m bldg. -25 [10-20'] < Ri < 0.025; moderate winds; original no Zd P s X

39 TABLE A.l. CONTINUED Site charactenshcs Measurements Comments Reference( s) records [r] Code City - site ZH [m] 20 [ml' Zd [m]' Fetch charactenshcs' zs Iml StahShCS Sensors used (hme of reported3 (sampling observahon) frequency) Ackeman and Hildehrand (1978); Hildebrand and Ackerman (1981, 1984); Westcott (1989) Melling and List ( 1980) Teunissen (1979) Schmeter (1978) Eaton and Dirks (1977). Auer (1981), Godowitch ef al. (1981); Ching ef a1 (1983); Ching (1 985). Godowitch (1986) S75a* St. Louis,MN n/a (summer 1975) T75a Toronto, ON - n/a U of T (July 1975-Nov. 1976) 076 Oaawa,ON- n/a Rocliff Stolport (spring 1976) U76a 5citiesin n/a Ukraine (summer 1976) S76a* StLouis,MN n/a (summer 1976) n/a n/a n/a n/a 1.29 n/a da n/a n/a n/a n/a HDandHR LD grass area first 300 m upwind of tower da MD and HD: 530% vegetation -300 u'w', W'T;, (-0.2 zi) w'q'. e'w', -650 Utr fju.v.w. (-0.45 zi) lu+ o,$/wi (-0.75 Zi) 0.k1.2 zi ow. o:/w: (z; = 35W30) Skw, Sw L.V.W. sw. Au.v,w ,200,300, nu. w Sv. w -550 Airplane gust 6 [-20 km] probe. pt-resistance them., refractometer (2 w Monostatic 13 [-@I Doppler echosonde 3-D SAT (20,4 >23 Hz), cup and [9', 15'1 vane-anem., pt resistance kthem. (-I Hz) 7 x [-3.5 km Airborne pressure (%")I; sensors, vanes and flight path pt resistance not known sensors (-I 1 Hz) n/a (da) n/a [da] Airplane gust km] Clear, afternoon, nearneutral (well mixed); surface heat flux from extrapolation Daytime, light winds, CBL Near-neutral, slightly unstable (afternoon, high winds) Near-neutral. unstable Noon and afternoon CBL; surface heat flux from extrapolation 0 m c P

40 TABLE A.l. CONTINUED $! Site characteristics records [TI Measurements Comments Refcrcna(s) Code City-site ZH [ml zo [m]' Zd [m]' Fetch characteristics2 zs [ml statistics Sensors used (time of repod3 (sampling observation) frequency) ClarkeetOL S76* St Louis.MN- (1978, , 107, I ,1985, (summer and 1987) autumn 1976) Step (1980, V78* Vancouver, BC 1982) - Sunset (summer 1978) Jackson(1978) W78* Wellington (da) Coppin (I 979) A79 Addaide - Hills lndushies tower (autumn, spring 1977n8) Helmis et OL L79 London - UNv. (1983) college (autumn 1979) Greeohutetd P79a Philadelphia, ( 1984) PN (summer 1979) d 2b 105: LD 9.7 l.ld gb warehouses.light 11.1 I.7d gb industry 107: MD closely spaced 2-storey houses. large trees 11 1: MD: 2-storey houses, gardens, trees 8.5 OSb 3Sb LD single houses with gardeh trees N-10 N: 3.8" N:3.0"' N:MD: (1.2) inhomogeneous S: -40 S: n/a S:0.6m S: Hr I c; I@ MD:residential 0.(M.6d with some trees nla da nla Central city site n/a nla nla nla 31 E. Aw 24.1 ~ill. Au.v.w su,v,w 10.5, 18.7, 1.. Au.u,w 28.5,35,43.5, Sku. Ku. 54.5,62,69.5 Su 33.8 Au,w, CD (15, ) Su,w.~.q couw,wt. wq PhwT -50 "7. SAT (2 Hz); head them. (2 Hz) 3-D Gill anem. 62 [60'] (2.5 Hz) 2.3-D Gill anem. 38 I-35'1 (0.5 Hz) I-D Gill anen 21 [3-15'] (l-2hz; 1.2m),bead therm. (-1 Hz), hfra-red h ymn (20 Hz) Pt-wire~ (20 Hz) SO t-1'1 Airplane gust km] probe and others (40 Hz) -5 < z;/l < < zs/l < -0.2 Neutral, slightly unstable: original no zd < zs/l < Unstable, near-neutral, stable: tower 4 m above roof-top Afternoon and evening with scattered clouds F 3Cr 2 X HogstriimerOL U79* Uppsala- ( ); Grinby (G). Karlsson (1986) Upplandia (v) (autumn ) U: I5 Id.'' 8.7' U HD: 4-storey G: 8 OSd." 5.3' row apartments and Ships G: Md: 4-storey apartment blocks, open spaces c z;/l -= 0.07

41 REVIEW OF TURBULENCE OVER CITIES 98 1 c t! 2 i 2 C c - d Y ii 2 s $ v IA N

42 TABLE A.l. CONTINUED Site characteristics Measurements Comments Code City - site ZH [m] zo [ml' zd [m]' Fetch characteristics' zs [mi statistics Sensors used records [rl (time of reported' (sampling observation) frequency) Xuefnl. (1993) G88 wang (1992) L89 n/a LD grass area first Roth (1991, 1993); Roth and Oke (1993, 1995) V89* Guanzhou I5 Id (summer 1988) LanzhOU d (winter 1989) Vancouver, BC Sunset O.Sd (summer 1989) I@ 4.2b; gf n/a 3-D Gill-type anem. (I Hz) 50 m upwind of tower Same as V78 3-D SAT, thermocouple (10 Hz); 1-D.3-D SAT, thermocouples, Lya hygrom. (25 Hz) K '. -6 < zs/l c 3; 7 m less for tower on 28 m high specma] bldg [60'] -8 < zs/l c 0.7 (light winds); no Q '1-1.8 < zk/l c Xuelal. (1997) N90 Kalogiros and Helmis (1995) Oikawa (1993); Meng ef al. (1993); Oikawa and Meng ( 1995, 1997); Oikawa et nl. (1995) Batchvarova and Gryning (1998) Grimmond et al. (1998) T90 A9 1 Nanjing - NJU 8 0.6= (spring 1990) 0.63d Tokyo Shibuya (A, B) 30 n/a (1990) Athens - Lab n/a of Met. (winter and spring 1991) Sapporo b Ishikari (summer 1991, winter 1992) 6.2e n/a n/a MD. vicinity of tower is grass field HR mixed business and residential A:31 lu. su.0.w. B: 56 AU.U,W 3-D Gill-type anem., pt them (1 Hz) 3-D SAT (1 Hz) HD: near city centre R-wires (20 Hz), bead (wet) therm. (0.2 Hz) S92* 2.3b LD: single 2-storey 3-D SAT ( 10 Hz) A94 L94 Ahns - NOA, n/a n/a Marousi (sum 1994) Los Angeles, d CA - Arcadia (I 993/94) n/a n/a houses, gardens, some trees; grass area first 30 m upwind of tower -21 [W] -8 < zs/l < 8; original no Zd 50'000 All year including 2 [lo'] typhooos; 9-12 m tower on top of bldg. 120 [-2'] Unstable. near-neutral, stable (light winds); tower 4 m above mftop -70 (5 for -1 < z;/l < 0.08; spectra) turbulence profiles not [lo'] concurrent or CD located n/a 15 u*. w't'. Au,u,w 3-D SAT (da) n/a -1.9cz;fLc 1.8 MD 2-storey houses with large gardens. bees 32.8 AU 3-D SAT (10 Hz); wind sentry (0.2 Hz) % h, 7d 3 X

43 TABLE A.1. CONTINUED Site characteristics Measurements Comments Reference(s) Code City - site ZH [m] zo [m]' zd [m]' Fetch characteristics* zs [ml statistics Sensors used records Irl (time of reported3 (sampling observation) frequency) Duponteral. da P94a Paris - Jussieu 20 (1999) (winter ) Casadioetal. da R94a* Rome-UNv. 3&60 (1996) of Rome (summer 1994) Feigenwinter et al. B95* da Basel - BASTA 24 (1997, 1999) (summer-winter 1995-%) King and C95 Chicago, IL 8 I.32d Grimmond (summer 1995) (1997) GrimmondetnL 0Ad M95 Miami,K- 6.3 (1998) Dade county fairground (summer 1995) da HD near city centre da HR: near city centre 22f HR: mixed commercial, business, residential and open spaces da MD - single 1.5 and 2-storey houses, gardens, trees da LD - single 1 - and 2- storey houses, gardens, trees 300 (0.3-1 Zi) uw Doppler sodar (Remtech PA2) (50 m) zi; zi = we. q*, uw/w* Doppler sodar, 2oO-Mo Uq/q*. TKE, Sw R m lidar zi (33 Au.u,w.r. 3-D SAT (21 Hz) -75) su,",w,r. couw,wr 27 cou w 9 3-D SAT. Krypton J?uw.wT.wq hygrom. (10 w 41 U* I-D. 3-D SAT (10, 21 Hz), thermocouple, Krypton hygrom. (LO Hz) -260 [ZW] 6 [61'] Ai: 2000 [3W; spectra: 1300 [W'] 9 da [3d] Near-neutral, unstable; surface heat flux from extrapolation Night-lime, clear, light winds; surface heat flux from extrapolation Stable, neutral, unstable; 50 m tower on top of 24 m high bldg. -3 < zs/l < 0 Unstable, slightly stable Notes: Ia-from (neutral) wind profile plot without allowing for Zd; b-based on morphometric approach; '-neutral wind profiles, however, lowest levels most certainly affected by roughness; &neutral log-law assumpti00 and directly measured us; e*eutral wind profile; f-tvm method (Rotach, 1994); k--effective zo using Fiedler and F'anofsky (1972); '"-based on fit to power law but deemed unreliable by Jackson (1978); "-using measured u* at 35 m and neutral wind profile equation, assuming Zd =O; corrected to 'expected' value of 1.2 by author; P-estimated by author based on roughness classification scheme in Counihan (1975); q-including trees; *--constant fraction of ZH determined by respective author@); '-based on a relation between the roughness length and the geostmphic drag coefficient using Rossby number similarity (Kondo and Yamazawa 1986); "-modified to include neutral data over homogeneous urban fetch only; v-alculated, allowing for zd; w--see Counihan (1975); '-see Bottema (1996); Y-method of derivation unknown. *After Grimmond and Oke (1998) where available; otherwise from original references using urban density categories in Grimmond and Oke (Table 7); Lwlow density; MB-medium density; HDhigh density; HR-high rise. 3 ~ y as m in main ~ ~ text or MOW. Symbols: *Studies selected for detailed analysis; da-not available; SAT-sonic anemometer-thermometer; r-sampling time or distance; Ci-structure parameter; Co; --cospectra; Cohi-coherence spectra; K A,M,H~Y diffisivity of aerosol. momentum and heat; Kui-kurtosis; Phi-phase angle spectra; Ri-spectral correlation coefficient; Ri-Richardson number; Si-spectra; Skiskewness; ri-hear correlation coefficient; Ri-spectral correlation coefficient; e-water-vapour pressure; 03--0zone; EAissipation; Ai-peak wavelength; 0-wind direction angle; &-normalized dissipation; 4~,~-nondimensional profile of wind and temperature. 4From Arakawa and Tsutsumi (1976). 7J rn < el i z 0 m 0 rn 7J < G \o m W

44 984 M. ROTH Ackerman, B. and Hildebrand, P. H. Anderson, D. E. and Verma, S. B. Angel]. J. K., Hoecker, W. H.. Dickson, C. R. and Pack, D. H. Arakawa, H. and Tsutsumi, K. Arya, S. P. S. and Sundararajan, A. Auer, A. H. Batchvarova, E. and Gryning, S.-E. Binkowski, F. S. Bottema, M. Bowne, N. E. and Ball, J. T. Brook, R. R. Caughey, S. J. and Palmer, S. G. Casadio, S., Di Sarra, A., Fiocco, G., Fuii, D., Lena, F. and Rao, M. P. Champagne, F. H., Friehe, C. A,, LaRue, J. C. and Wyngaard, J. C. Changnon, S. E. (Editor) Ching, J. K. S. Ching, J. K. S., Clarke, J. F., Irwin, J. S. and Godowitch, J. M. Clarke, J. F., Ching, J. K. S., Binkowski, F. S. and Godowitch, J. M. Clarke, J. F., Ching, J. K. S. and Godowitch. J. M I REFERENCES Structure of the planetary boundary layer over a complex mesoregion. Final Report ATM , Illinois State Water Survey at University of Illinois, Urbana, Illinois 61801, USA Turbulence spectra of COz, water vapour, temperature and wind velocity fluctuations over a crop surface. Boundary-Layer Meteorol., 33, 1-14 Urban influence on a strong daytime air flow determined from tetroon flights. J. Appl. Meteorol., 12, Strong gusts in the lowest 250 m layer over the city of Tokyo. J. Appl. Meteorol., 6, Strong gusts in the lowest 250 m layer over the city of Tokyo. Pp in Proceedings of the 2nd USA-Japan research seminar on wind effects on structures. Eds. Ishizaki and Chiu, The University Press of Hawaii, USA An assessment of proposed similarity theories for the atmospheric boundary layer. Boundary-Layer Meteorol., 110, Urban boundary layer. Pp in METROMEX: A review and summary. Meteorological Monographs, Vol. 40. Ed. S. A. Changnon. American Meteorological Society, Boston, USA Wind climatology, atmospheric turbulence and internal boundarylayer development in Athens during the MEDCAPHOT- TRACE experiment. Amos. Environ., 32, A simple semi-empirical theory for turbulence in the atmospheric surface layer. Amos. Environ., 13, Aerodynamic roughness parameters for homogeneous building groups. Part 2: results. Document Sub-Meso #23, Equipe Dynamic de I Atmosphere Habitbe, Ecole Central de Nantes, France Observational comparison of rural and urban boundary layer turbulence. J. Appl. Meteorol., 9, The measurement of turbulence in a city environment. J. Appl. Meteorol., 11, A study of wind structure in an urban environment. Australian Government Publishing Service, Dept. of Sci., Bureau of Meteorol., 27 Some aspects of turbulence structure through the depth of the convective boundary layer. Q. J. R. Meteorol. SOC., 105, Convective characteristics of the nocturnal urban boundary layer as observed with Doppler sodar and Raman lidar. Boundary- Layer Meteorol., 79, Flux measurements, flux estimation techniques and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci., 34, METROMEX: a review and summary. Meteorological Monographys. Vol. 40. American Meteorological Society, Boston, USA Urban-scale variations of turbulence parameters and fluxes. Boundary-Layer Meteorol., 33, Relevance of mixed layer scaling for daytime dispersion based on RAPS and other field programs. Amos. Environ., 17, I Turbulent structure of the urban surface boundary layer. Pp in Proceedings of the 9th NATOECMS International technical meeting on air pollution modeling and its application. Toronto, Canada Spectral characteristics of surface boundary layer turbulence in an urban area. Pp in Roceedings of the fifth symposium on turbulence, diffusion and air pollution, Atlanta, Ga, March American Meteorological Society, Boston, USA An experimental study of turbulence in an urban environment. Technical Report US EPA, Research Triangle Park, N.C. USA

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