Observational verification of urban surface roughness parameters derived from morphological models

Transcription

1 METEOROLOGICAL APPLICATIONS Meteorol. Appl. 16: (29) Published online 3 October 28 in Wiley InterScience ( DOI: 1.12/met.19 Observational verification of urban surface roughness parameters derived from morphological models Gang Liu, Jianning Sun* Weimei Jiang Department of Atmospheric Sciences, Nanjing University, Nanjing 2193, China ABSTRACT: This study focuses on how to verify the aerodynamic roughness parameters in an urban area by using observational data collected in the roughness sub-layer. Anemometrical observations were made in the downtown area of Nanjing, China, in summer winter. Data were collected using both slow fast response anemometers mounted on a 36 m tower. The friction velocity was observed just above the top of the urban canopy layer, which is at the height of 19.7 m, while the mean wind speed was observed at a relatively low level that is generally thought to be in the roughness sub-layer, of which the top usually ranges from 2 to 5 times the height of the urban canopy layer. The results of the measurements show that the dimensionless friction velocities (normalized by the mean wind speed at an upper level) maintain approximately a constant (.2) the fluctuations are small (±.2) in a period of 21 days. The results imply that the similarity relation for the mean wind profile is still valid that the effect of stratification is negligibly small in the urban roughness sub-layer. Based on the measurement results, the logarithmic wind profile was applied to verify the aerodynamic roughness parameters empirically derived from four morphological models: the rule of thumb (Rt) method, the Bottema (Ba) method, the Macdonald (Ma) method the Raupach (Ra) method. The results show that they are not very different from each other. The good performance of the Rt method may be due to the fact that the distribution of buildings in the study area is regular. The Ba Ra methods are likely to be better since they can give reasonable estimates of roughness parameters. Evidence indicates that the Ma method underestimates the roughness length. Copyright 28 Royal Meteorological Society KEY WORDS urban area; roughness parameters; dimensionless friction velocity; morphological model Received 23 April 28; Revised 12 August 28; Accepted 15 September Introduction In recent years urban boundary layer research has received more attention, as people have realized that urbanization has impacts on weather climate (Changnon, 1992; Martilli, 22; Kalnay Cai, 23; Shepherd Burian, 23; Lim et al., 25; Best, 26). Studies on the urban boundary layer have been carried out through various approaches including observational experiment, physical modelling numerical simulation. Among these, numerical simulation is conducted extensively due to its many advantages. In numerical simulation of urban areas the two aerodynamic parameters (the roughness length, z, the zero-plane displacement, z d ) are essential to represent properly the impacts of urban areas on weather climate. However, so far, the determination of z z d in urban areas has often been inadequate for use in numerical models (Grimmond Oke, 1999). Cities are the roughest of the underlying surfaces under the atmospheric boundary layer, which thus make the airflow over them more complex (Grimmond Oke, * Correspondence to: Jianning Sun, Department of Atmospheric Sciences, Nanjing University, Nanjing 2193, P. R. China. jnsun@nju.edu.cn 1999). According to their wind tunnel work, Hussain Lee (198) distinguished three general city flow regimes: isolated flow, in which roughness elements are far apart act as individual wake generators; wake interference flow, in which the spacing is close enough that the wakes reinforce each other; skimming flow, in which the density of packing is so great that the main flow skips over the top of the elements. Accurate knowledge of the aerodynamic characteristics of cities is important to describe, model forecast the behaviour of urban winds turbulence at all scales. Methods to determine z z d can be generalized in to two classes of approaches (Grimmond Oke, 1999): 1. morphological (or geometric) methods that relate aerodynamic parameters to measures of surface morphology,, 2. anemometric methods that use field observations of wind turbulence to solve for the aerodynamic parameters included in the theoretical relations derived from logarithmic wind profile (namely, the Monin-Obukhov similarity theory, hereinafter the MOS theory). Copyright 28 Royal Meteorological Society

2 26 G. LIU ET AL. Morphological methods have the advantage that the values can be determined from the database of the distribution of roughness elements. Based on a Geographic Information System (GIS), a detailed database of urban surface elements can easily be obtained, the values of z z d can then be calculated for any direction surrounding the site of interest. However, these methods have the disadvantage that most are based on empirical relations derived from wind tunnel experiments that concern idealized flows over simplified arrays of roughness elements. In these simulations the flow is often relatively constant in direction, typically normal to the face of the elements, the array is often regularly spaced. These conditions differ from those in real cities, where wind direction is ever changing, even if the street pattern is relatively regular, the size shape of individual roughness elements (buildings trees) is variable. The performances of morphological methods in real cities need to be examined. Wind-based methods have the advantage that the characteristics of the surface do not need to be specified. Grimmond Oke (1999) reviewed more than 5 studies that provide anemometrically-based estimates of roughness parameters in cities. Unfortunately, only a few studies were found to be acceptable. Grimmond et al. (1998) analysed the roughness parameters of urban areas derived from wind observations. The values of z were derived from both slow-response fast-response anemometry, while the z d values were only derived from fast response anemometry. The results were not satisfactory Grimmond et al. found there was no clear best choice of anemometric methods to determine roughness parameters. Actually, there exists inherent disadvantage in the anemometric methods they employed. To calculate z, z d needs to be known, while the formula to estimate z d has empirical coefficients. It is possible to fit the values to obtain the coefficients using the observed data, but in order to do this a value of z d must be assigned. This is a circular argument which only generates the initially assigned value of z d. On the other h, it is difficult to find a satisfactory measurement site in a developed city to collect high-quality data. Grimmond Oke (1999) reviewed a series of morphological models compared the values to the in situ measurement results. They found there was poor statistical agreement between even the highest-quality measurements morphological estimates of roughness parameters for cities. How to verify the values derived from the morphological methods seems problematic needs to be investigated further. Previous studies show that there are so many uncertainties associated with current methods that the roughness parameters of the urban surface cannot be estimated accurately. This situation stimulates investigators to do more detailed work to improve knowledge of the aerodynamic characteristics of cities, since the roughness parameters should be incorporated in studies of urban diffusion in mesoscale models of airflow urban climate. In our opinion, z d should be estimated from morphological models since the logarithmic wind profile is not sensitive to it, z can then be estimated from anemometrical methods. This approach was employed in the study of urban surface roughness parameters in Beijing (Al- Jiboori Hu, 25). The problem is how to verify the accuracy of the estimated roughness parameters in a proper way. For this purpose anemometrical observation data were collected in a densely built-up area of Nanjing, China, in the summer winter, to examine the morphological estimates of roughness parameters. The aims of this study are (1) to determine whether the MOS theory for the shear profile of wind speed is applicable to the urban surface layer, especially the roughness sublayer, (2) to investigate how to verify the roughness parameters derived from morphological models. 2. Methodology 2.1. Monin-Obukhov similarity (MOS) theory Although the applicability of the MOS theory is still questioned, it is often used in modelling the turbulent transfer statistics in urban boundary layers. Recently, Moriwaki Ka (26) analysed the shear profiles of momentum heat using the data measured above an urban canopy. They proposed a scaling velocity u = ( u w ) 1/2,whereu is friction velocity u w is momentum flux, at roof level, which is equivalent to surface friction velocity. The results showed that the mean wind speed profile in the urban surface layer (including the roughness sub-layer) followed a conventional stratified logarithmic profile when it is scaled by the surface friction velocity. That is: u = 1 [ ( z zd ln u κ z ) ( )] z zd ψ m L (1) u = ( u w z= ) 1/2 (2) where κ, the von Karman constant, equals.4; z is the height above ground level; is the mean building height; L is the Monin-Obukhov length; ψ m is an empirical function that is associated with atmospheric stability (Businger et al., 1971; modified after Högström, 1988). In this study, the shear stress u w was measured at the level just a few metres above the mean building height, the horizontal wind speeds were measured at three levels. The lowest level is at about z/ = 1.5. Since at this level z (z = z z d ) is much smaller in comparison with the Monin-Obukhov length, it is assumed that the effect of ψ m can be neglected (ψ m ). This above assumption appears reasonable is supported by the measurement data. The observation results in Figure 2 (Section 4) show that there are no indications of significant diurnal seasonal variations of the values of u /u, the mean values show that they are not influenced obviously by stratification conditions. Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

3 OBSERVATIONAL VERIFICATION OF URBAN ROUGHNESS PARAMETERS 27 This result supports the argument that turbulence is dominantly produced by the mechanical process in the urban roughness sub-layer when the wind speed is not very small, thus it is reasonable to assume that the turbulence statistics behave well in terms of near-neutral stratification conditions. In addition, this assumption is also supported by the other urban measurement data. In Figure 4 of Moriwaki Ka (26), it can be seen that the logarithmic curve for neutral conditions almost coincides with the two others for stable unstable conditions at the lower height. In other words, the differences of the turbulence statistics between the three stratification conditions are very small in the lower part of the urban roughness sublayer. This is the second reason for the assumption that the effect of the stability term in Equation (1) can be neglected. It is preferred to use the dimensionless friction velocity, it can be expressed as follows: u / ( ) z1 z d = κ ln (3) u 1 z Here u 1 is the mean wind speed at the first level of three levels of mean wind speed measurement z 1 is the height of the first level. If z d z are estimated from morphological models, the dimensionless friction velocity can be calculated according to the above equation, then the values can be compared to the observationallyobtained counterparts. This is the verification method for the estimated roughness parameters. The problem is whether this method is applicable. Some researchers think similarity theory is valid in the roughness sub-layer above forests (Simpson et al., 1998) while some think it is still valid above the urban canopy layer (Moriwaki Ka, 26), but the validity of the MOS theory in the urban roughness sub-layer has yet to be verified conclusively. To our knowledge, the similarity theory describes the balance of interactions between mean airflow turbulence. The steadier the turbulence statistics, the clearer the relations between the mean airflow turbulence. That s why the MOS theory performs best under convective conditions does not perform satisfactorily under stable conditions, especially when the stratification of atmosphere is strong the turbulence is more intermittent (Stull, 1988). However, the mechanical turbulence in the urban surface layer is generally strong enough unless the wind speed is very small, since the airflow is continually perturbed by the roughness elements. So the turbulence in the urban roughness sub-layer is generally statistical the relationship between the mean airflow turbulence can be well established. With this point of view in mind, it is inferred that the MOS theory is still valid in the urban roughness sub-layer the proposed method is applicable Morphological models The most common morphological approach is a simple rule of thumb (Rt), which holds that z d z are simply related to the height of the elements: Rt d is z d = f d (4) Rt is z = f (5) where f d f are empirical coefficients derived from observation. Based on their review, Grimmond Oke (1999) suggested that the values should be determined according to the element density flow regime in the urban area. Considering the characteristics of the measurement site, values of f d.7 f.1 are considered acceptable. The methods associated with height plan aerial fraction λ P = A P /A T, where A P is the plan area of elements A T is the total surface area of the fetch, are often used to determine z z d. Bottema (1995) presents a method (Ba) explicitly intended for use in urban areas for situations where the airflow is not perpendicular to buildings. It requires information on height area of roughness elements: APb + (1 p)a Pt Ba d is z d = A T Ba is z = ( z d ) exp (.4 (.5 Cdb W yib ib + )).5 C dt W yit it /A T.6 (6) (7) where the subscript b refers to buildings, t refers to trees, p is a coefficient to allow for porosity of trees. Bottema (1995) assigns a value of.8 to C db (the drag coefficient for buildings), C dt (the drag coefficient for trees) is set equal to C db (1 p). The horizontal dimensions of the roughness elements are W. Since there are fewer trees than buildings in the study area around the measurement site, the height of trees is much lower than that of buildings, the contribution of trees is not considered in this study. Another kind of morphological method that considers height frontal area index (λ F ) is also commonly used to estimate z z d. The frontal area index, which combines mean height, breadth, density of roughness elements, is defined as (Raupach, 1992): λ F = W y ρ el (8) where W y is the mean breadth of roughness elements perpendicular to the wind direction, ρ el is the density number (n) of roughness elements per unit area (ρ el = n/a T ). Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

4 28 G. LIU ET AL. Macdonald et al. (1998) present a new derivation that starts from fundamental principles some simple assumptions. This method (Ma) yields values of z d z as follows: Ma d is z d = 1 + α λ P (λ P 1) (9) Ma is z ( = { exp 1 z d ) [.5β C D κ 2 ( 1 z ) ] }.5 d λ F (1) where α is an empirical coefficient, C D is a drag coefficient (1.2), κ is von Karman constant, β is a correction factor for drag coefficient. The two empirical coefficients (α β) have to be set apriori. Macdonald et al. (1998) provide a graphical sensitivity analysis that demonstrates responses to changes in their values. They calibrated their equations using wind tunnel data recommended that for staggered arrays of cubes α = 4.43 β = 1.. These coefficients are the values used here. Raupach (1994) used his previous analytic treatment of drag drag partition on rough surface (Raupach, 1992) to derive expressions for z d z as a function of height frontal area index (Raupach, 1994, 1995): where Ra d is z d = 1 + exp[ (c d12λ F ).5 ] 1 (c d1 2λ F ).5 (11) Ra is z = (1 z d ) exp( κ U u + ψ h ) (12) [ u U = min (c S + c R λ F ).5, ( u U ) max ] (13) ψ h is the roughness sub-layer influence function, U u are the large scale wind speed the friction velocity; c S c R are drag coefficients for the substrate surface at height in the absence of roughness elements, of an isolated roughness element mounted on the surface, respectively, c d1 is a free parameter. The values specified by Raupach (1994) are c S =.3, c R =.3, (u /U) max =.3, ψ h =.193, c d1 = 7.5. Since the measurement of U was conducted in the roughness sub-layer, the effect of ψ h is not considered in this study. The morphological models considered here are far from exhaustive. Grimmond Oke (1999) have reviewed nine models. They suggested that the Ba, Ma Ra methods are the best, so verification in the present research focuses on these, which are applied to estimate the roughness parameters Fetch Roth (2) reviewed atmospheric turbulence over cities, concluded that the extreme heterogeneity of urban surfaces, usually at all scales, makes the definition of a uniform fetch (or a source area) impossible, while the results from integral statistics suggest the existence of strong similarities between turbulent flows over cities plant canopies. Thus, local fetches are used in the present study. Based on the methods proposed by Schmid (1994), used by Grimmond Oke (1999), the source areas for the study are estimated. The parameters are as follows: the flux concentration contribution level P = 9%; the non-dimensional height z ref /z = 8.25, where z ref is the difference between the sensor height z d ; the lateral turbulence parameter σ v /u = 2., where σ v is the horizontal crosswind stard deviation of the wind speed fluctuations; the stratification is in neutral condition (z ref /L = ). However, the results show that the source area seems to be underestimated: the radial distance is approximately 2 m; the lateral distance is less than 1 m. Since Schmid s method is thought to be applicable to source areas for scalar fluxes, the concept of fetch is thought to be more suitable for the estimation of source areas for momentum fluxes. If the approach for the internal boundary layer is introduced the methods to compute the fetch are employed to estimate the influence upwind distance, the distance is approximately 1 1 times the relative height of the instruments (the sensor height of the instruments minus the mean height of the buildings, about 1 m in the study). The more stable the stratification, the larger the distance. Taking into account that the turbulence is so strong in the urban roughness sub-layer unless the wind speed is very small, a compromise value of 5 times is taken, i.e. the influence upwind distance is 5 m. In order to match the radial distance, the lateral distance is extended to 15 m, which means that both the radial lateral distances approximately increase by the same magnitude. Consequently, the fetches are set in a circle with a radius of 5 m centred on the observation site (Figure 1). The single fetch is defined as an ellipse Figure 1. Aerial photograph of the study area. The centre of the circle is the observation site marked S. The radius of the circle is 5 m. S Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

5 OBSERVATIONAL VERIFICATION OF URBAN ROUGHNESS PARAMETERS 29 according to the wind direction the lengths of the major minor axis of each fetch are 5 15 m respectively. Beginning with the direction due east as 9, the major axes of the fetches are set anticlockwise with the interval of 15 in turn. Thus there are 24 fetches in total numbered The near endpoint of each fetch is the centre of the circle (the observation site). The fetch corresponding to the anemometrical observation is determined by the averaged wind direction during the measurement, which should deviate from the direction of the major axis by an angle less than Measurement site data processing The atmospheric boundary layer field observation campaign was carried out twice in Nanjing. The durations were from 17 to 27 July 25 (summer) from 17 February to 6 March 26 (winter). The observation site in the urban area was on the rooftop of a building (32.4 N, E), the orientation of which is nearly the due north south direction. The height of the building is 22 m. The observation yard is the flat rooftop made of cement concrete materials, the area of which is 2 m 1 m. Typical residence business districts are within the radius of 1 km around the observation site. Buildings st densely in the districts the mean height of the buildings within the 5 m radius around the observation site is 19.7 m (Figure 1). The buildings streets occupy about 7% of the total surface area. In situ investigations were carried out to collect information about the height orientation of each building in the study area. For the study area, a GIS (Geographic Information System) has been developed from aerial photographs field surveys. The length, width coordinate information of the buildings were obtained through the GIS following the procedures described by Grimmond Souch (1994). The radiation, turbulence, temperature mean wind were observed at the urban site. The threedimensional wind speed fluctuations, virtual temperature, water vapour carbon dioxide content in the air were measured with an ultrasonic anemometer (CSAT3, Campbell Scientific Inc., Logan, Utah, USA) CO 2 /H 2 O analyser (LI-75, Licor, Lincoln, Nebraska, USA), 2.2 m above the building rooftop. The data from the observation equipment were collected stored by a data logger (CR5, Campbell Scientific Inc., Logan, Utah, USA) with a sampling frequency of 1 Hz. There is a 36 m tower on the building rooftop. A set of mean wind temperature observation systems (vane anemometer: Model122, R. M. Young, Traverse City, Michigan, USA; temperature humidity: HMP45C, Campbell Scientific Inc., Logan, Utah, USA; data logger: CR1X, Campbell Scientific Inc., Logan, Utah, USA) was installed on the tower. Mean wind speed, wind direction, temperature, humidity pressure were measured at heights of 8.5, 15.2, 27.7 m above the building rooftop with a sampling frequency of.5 Hz. During the two observation periods, data of 8 days in total were missing or incorrect. These data were removed in the calculations all calculations were performed, conclusions obtained, without these missing or incorrect data. The mean wind speed u was calculated over a period of 1 min through the mean wind observation data. The friction velocity u was calculated according to Equation (2) over a period of 1 min through the time series of the turbulent wind speed fluctuations. The dimensionless friction velocity was then calculated. 4. Results discussion Figure 2 is the temporal variation of the observationallyobtained friction velocity at the first level (i.e. z = 3.5 m). The data of the mean wind speed with values less than l m s 1 have already been removed. It is shown in the figure that the mean value stard deviation of the friction velocities keep.2 ±.2 both in summer winter. The patterns of the temporal variations of friction velocity at the second third levels (i.e. z = m) are almost the same as at the first level, while the stard deviations are slightly decreased (the results are not shown). Moreover, there are no indications of significant diurnal seasonal variations of the friction velocities, the mean values show that they are not influenced obviously by stratification conditions. This result supports the argument that the turbulence is dominantly produced by the mechanical process in the urban roughness sub-layer when the wind speed is not very small. According to Equation (3), the friction velocities should only depend on height, so long as the observation period is not very short. It can be expected that the thermal effect will increase with height above the roughness sub-layer (Figure 4 of Moriwaki Ka, 26). However, as compared in Figure 3, when the wind speed is small the fluctuations of friction velocity increase significantly the statistical characteristic becomes unsteady. This might explain the existence of relatively large fluctuations in the first day of Figure 2(b). Although the data with mean wind speed less than 1 m s 1 have already been removed, the strong oscillations of mean wind speed still influence the statistical characteristic of the flow, which is similar to the situation under stable stratification conditions. Figure 4 shows the results of the surface roughness parameters calculated with the morphological models in each fetch. It can be seen that each fetch has a different z d z. The variation of roughness parameters is induced by different wind direction, can be interpreted as the heterogeneity of distributions of roughness elements. It can also be seen that the differences between the roughness parameters derived from the four morphological models are not very small. On average, the Rt approach estimates the highest z d, the Ba approach estimates the lowest z d, while the Ba approach estimates the highest z, the Ra approach estimates the lowest z. The values of z over z d are calculated shown in Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

6 21 G. LIU ET AL. (a) / 12 24/ 12 24/ 12 24/ 12 24/ 12 24/ 12 24/ (b) / 12 24/ 12 24/ 12 24/ 12 24/ 12 24/ 12 24/ Figure 2. The temporal variation of the hourly-averaged dimensionless friction velocity obtained from the observations. The mean wind speed at the 1st level (z = 3.5 m) was used. (a) LST 17 July to 24 July 25 (LST = UTC + 8). The mean value stard deviation are.2 ±.2; (b) 21 February to LST 28 February 26. The mean value stard deviation are.2 ±.2. Figure 5. The biggest values are from the Ba approach, the smaller values are from the Rt approach. For the existing buildings, the mean height is fixed. It can be thought empirically that when z d is relatively large, z should be relatively small, since less of the buildings above z d are portioned to the roughness elements. This situation is consistent with the relationship of z d z described in Equation (3). In this context, the Ra approach gives acceptable middle values, while the Ma approach seems to have underestimated z. Figure 6 is the comparison between the observational results morphological results. All the friction velocities were calculated according to their corresponding fetches. For the observationally-obtained friction velocities, the mean wind speed at the first level (i.e. z = 3.5 m) was used. In each fetch their mean value stard deviation were calculated through all the friction velocities within the same fetch (i.e. within a certain range of wind directions). The morphologically-obtained friction velocities were calculated with Equation (3) in each fetch. Figure 6 indicates that in most of the fetches the morphological results are in good agreement with the observed results. The overall differences between them are small. Most of the morphological results fall into the range of the stard deviations of the observed results. It proves that Equation (3) is valid applicable as long as the wind speed is not smaller than 1 m s 1 the observation period is not shorter than 1 week. The dimensionless friction velocities obtained from different morphological methods are not very different. Their deviations from the observed results are listed in Table I. Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

7 OBSERVATIONAL VERIFICATION OF URBAN ROUGHNESS PARAMETERS 211 (a).7 (b) (c) Figure 3. The temporal variation of the 1-min-averaged dimensionless friction velocity obtained from the observations. The mean wind speed at the 1st level (z = 3.5 m) was used. The black dots represent the mean wind speed is less than 1 m s 1 ; the circles represent the mean wind speed is not less than 1 m s 1. (a) LST 21 February 26 (LST = UTC + 8); (b) LST 27 February 26; (c) LST 5 March 26. There are no values where the solid line is missed, since the mean wind speed as the denominator is very close to zero z z d z /z d Fetch (n) Fetch (n) Figure 4. The z d z values of the urban area calculated with the morphological methods. Fetch is based on wind direction. The grey fonts represent z d ; the black fonts represent z.( : the Rt method; : the Ba method; : the Ma method; +: the Ra method). The biases of the Rt, Ba Ra approaches are almost the same. This situation is due to the correlation of estimated values, in which larger z d accompanies smaller z, they complement each other in calculation of friction Figure 5. Values of z over z d. Fetch is based on wind direction. ( :the Rt method; : the Ba method; : the Ma method; +: the Ra method). velocity according to Equation (3). That is to say, the logarithmic method cannot distinguish which is the better one between Rt, Ba Ra. However, the Ma approach produces the largest bias. Since the logarithmic method is more sensitive to z than to z d this result supports the argument that the Ma approach underestimates the z. Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

8 212 G. LIU ET AL % % % Fetch (n) Figure 6. The observationally-obtained dimensionless friction velocities compared to the morphologically-obtained counterparts. Fetch is based on wind direction. The periods are July 17 23, 25 26, 25; February 17, March 4 5, 26 (LST = UTC + 8). (ž: the observed values; : the Rt method; : the Ba method; : thema method; +: the Ra method). Table I. Mean absolute bias between the observationallyobtained dimensionless friction velocities the morphologically-obtained counterparts Figure 7. The frequency distributions of the wind directions. The radial coordinate is frequency; the azimuthal coordinate is fetch number. The periods are July 17 23, 25 26, 25; February 17, March 4 5, 26 (LST = UTC + 8) Morphological model Rt Ba Ma Ra Mean absolute bias ymo y ob Note: The mean absolute bias is N. Here y mo is the morphological value; y ob is the mean observational value; the summator represents the summation over all active fetches; N is the total of active fetches (N = 23, since no wind blew from the 7th fetch). Probability Distribution (%) According to Figure 6, in most of the fetches the mean value of the observationally-obtained friction velocities is less than.2, but in Figure 2 the mean value is equal to.2. Figure 7 shows the fetches where the frequencies are among the largest, i.e. where the frequencies of the wind directions are larger than 1%, are 1, 2, In these fetches, the mean value of the observationallyobtained dimensionless friction velocities is very close to.2 (Figure 6). Thus it is not strange that in Figure 2 the mean value of the dimensionless friction velocities is equal to.2. The proportion of the dimensionless friction velocities that are between to the total samples is close to 7% (Figure 8), so it is reasonable reliable that the mean value of the dimensionless friction velocities is equal to Summary A densely built-up urban area was divided into 24 fetches, four morphological methods were applied in each fetch to obtain the zero-plane displacement (z d )the roughness length (z ). The turbulence mean wind data in the urban roughness sub-layer were used to calculate the observational Figure 8. The probability distributions of the dimensionless friction velocities. The periods are July 17 23, 25 26, 25; February 17, March 4 5, 26 (LST = UTC + 8). dimensionless friction velocities. The friction velocities do not demonstrate significant diurnal seasonal variation characteristics. Their mean value over a long time remains constant, the stard deviation is small, indicating the friction velocities are steady not significantly changing with the time. Based on the observations the similarity theory in the urban roughness sub-layer, a simple dynamical method is proposed to verify the morphological estimates of z d z, with which the calculated dimensionless friction velocities are directly compared to the observational data. Unlike some recent methods (e.g. Martano, 2), there are no priori constants or undecided parameters in this method. Compared to previous studies, in which the method was applied in the inertial sub-layer limited to neutral conditions (Grimmond et al., 1998; Rooney, 21), there is no restriction assumption on stratification conditions in the present study. Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met

9 OBSERVATIONAL VERIFICATION OF URBAN ROUGHNESS PARAMETERS 213 The four morphological methods recommended by Grimmond Oke (1999) are verified, the results show that they are not very different from each other. A good performance of the rule of thumb (Rt) method may be due to the fact that the distribution of buildings in the study area is regular. The Bottema (Ba) Raupach (Ra) methods are likely to be better since they can give reasonable estimates of roughness parameters. Evidence indicates that the Macdonald (Ma) method underestimates z. For further evaluation of morphological approaches, the proposed method needs more available data, which can cover a wide range of roughness parameters. Actually, the logarithmic method can only give the relationship between z z d. Sufficient data from different cities, with relatively large differences of z z d,can help determine whether the limited relationship is well obeyed or not, which could be the criterion of the accuracy of the estimated roughness parameters. Acknowledgements The research leading to this manuscript was supported by grants from the National Natural Science Foundation of China under Nos References Al-Jiboori MH, Hu F. 25. Surface roughness around a 325-m meteorological tower its effect on urban turbulence. Advances in Atmospheric Sciences 22: Best MJ. 26. Progress towards better weather forecasts for city dwellers: from short range to climate change. Theoretical Applied Climatology 84: Bottema M Parameterisation of aerodynamic roughness parameters in relation to air pollutant removal efficiency of streets. Air Pollution Engineering Management. Transactions on Ecology the Environment. Wessex Institute: Southampton, UK. Businger JA, Wyngaard JC, Izumi Y, Bradley EF Flux-profile relationships in the atmospheric surface layer. Journal of the Atmospheric Sciences 28: Changnon SA Inadvertent weather modification in urban areas: lessons for global climate change. Bulletin of the American Meteorological Society 73: Grimmond CSB, King TS, Roth M, Oke TR Aerodynamic roughness of urban areas derived from wind observations. Boundary Layer Meteorology 89: Grimmond CSB, Oke TR Aerodynamic properties of urban areas derived from analysis of surface form. Journal of Applied Meteorology 38: Grimmond CSB, Souch C Surface description for urban climate studies: A GIS based methodology. Geocarto International 9: Högström U Non-dimensional wind temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary Layer Meteorology 42: Hussain M, Lee BE A wind tunnel study of the mean pressure forces acting on large groups of low-rise buildings. Journal of Wind Engineering Industrial Aerodynamics 6: Kalnay E, Cai M. 23. Impact of urbanization l-use change on climate. Nature 423: Lim Y, Cai M, Kalnay E, Zhou L. 25. Observational evidence of sensitivity of surface climate changes to l types urbanization. Geophysical Research Letters 32: L22712, DOI: 1.129/25GL Macdonald RW, Griffiths RF, Hall DJ An improved method for estimation of surface roughness of obstacle arrays. Atmospheric Environment 32: Martano P. 2. Estimation of surface roughness length displacement height from single-level sonic anemometer data. Journal of Applied Meteorology 39: Martilli A. 22. Numerical study of urban impact on boundary layer structure: sensitivity to wind speed, urban morphology, rural soil moisture. Journal of Applied Meteorology 41: Moriwaki R, Ka M. 26. Flux-gradient profiles for momentum heat over an urban surface. Theoretical Applied Climatology 84: Raupach MR Drag drag partition on rough surfaces. Boundary Layer Meteorology 6: Raupach MR Simplified expressions for vegetation roughness length zero-plane displacement as functions of canopy height area index. Boundary Layer Meteorology 71: Raupach MR Corrigenda. Boundary Layer Meteorology 76: Rooney GG. 21. Comparison of upwind l use roughness length measured in the urban boundary layer. Boundary Layer Meteorology 1: Roth M. 2. Review of atmospheric turbulence over cities. Quarterly Journal of the Royal Meteorological Society 126: Schmid HP Source areas for scalars scalar fluxes. Boundary Layer Meteorology 67: Shepherd JM, Burian SJ. 23. Detection of urban-induced rainfall anomalies in a major coastal city. Earth Interactions 7: Simpson IJ, Thurtell GW, Neumann HH, Den Hartog G, Edwards GC The validity of similarity theory in the roughness sublayer above forests. Boundary Layer Meteorology 87: Stull R An Introduction to Boundary Layer Meteorology. Kluwer Academic Press: Dordrecht; 666. Copyright 28 Royal Meteorological Society Meteorol. Appl. 16: (29) DOI: 1.12/met