Numerical Study of Urban Impact on Boundary Layer Structure: Sensitivity to Wind Speed, Urban Morphology, and Rural Soil Moisture

Transcription

1 DECEMBER 2002 MARTILLI 1247 Numerical Study of Urban Impact on Boundary Layer Structure: Sensitivity to Wind Speed, Urban Morphology, and Rural Soil Moisture ALBERTO MARTILLI Air and Soil Pollution Laboratory, Swiss Federal Institute of Technology, Lausanne (EPFL), Lausanne, Switzerland (Manuscript received 9 June 2001, in final form 11 June 2002) ABSTRACT A mesoscale model with a detailed urban surface exchange parameterization is used to study urban influences on boundary layer structure. The parameterization takes into account thermal and mechanical factors, and it is able to reproduce the most important observed urban boundary layer features. A series of simulations is carried out on a 2D idealized domain to analyze the urban boundary layer sensitivity to wind speed, urban morphology, and rural soil moisture. The results show that, during the night, wind speed is correlated with inversion height, inversion depth, and inversion strength and that mean building height and street-canyon height-to-width ratio are correlated with inversion height but are anticorrelated with inversion depth and inversion strength. A reduction in rural soil moisture reduces inversion height and increases inversion strength. During daytime, differences between urban and rural boundary layers are strongly linked with wind speed and rural soil moisture. A factor analysis technique is used to evaluate the relative importance of thermal and mechanical urban factors in terms of their effects on boundary layer structure. The results show that, during the night, thermal factors are more important in the lower part of the urban boundary layer and mechanical factors are dominant in the upper part. Interactions between thermal and mechanical factors act to increase nocturnal boundary layer height. During the day, thermal factors play the most important role in modulating the PBL height evolution above the city. Interactions between thermal and mechanical factors act to reduce the daytime boundary layer height. Mechanical factors become important in the evening, when the turbulent kinetic energy produced by interactions between the airflow and buildings causes a delay in the decrease of PBL height. 1. Introduction A city is composed of low and high buildings, arrayed in blocks and intersected by streets. Such complex surfaces can strongly modify urban boundary layer structure. The two most important factors causing these modifications are as follows (Roth 2000). 1) Mechanical. Buildings induce drag (with a consequent sink of momentum) and increase the transfer of energy from large to small eddies (transformation of mean kinetic energy into turbulent kinetic energy). 2) Thermal. Buildings induce differential heating (cooling) of sunlit (shaded) surfaces, radiation trapping in street canyons, and a reduction in latent heat fluxes, which alter the sensible heat flux to the atmosphere. Both factors influence the structure of the urban boundary layer and pollutant dispersion as shown by several observational and numerical studies. Among the Corresponding author address: Alberto Martilli, Dept. of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC V6T 1Z4, Canada. amartilli@eos.ubc.ca first were Oke (1995) on the urban heat island (UHI), Uno et al. (1988) on the nocturnal urban boundary layer (UBL), and Rotach (1993a,b) on turbulent vertical profiles in the urban roughness sublayer (URS, from street level up to m). On the numerical side, Bornstein et al. (1993) simulated the effect of New York City on sea-breeze-front behavior and Saitoh et al. (1996) studied Tokyo s UHI. Because numerical models are widely used to investigate the link (which is highly nonlinear, especially if secondary pollutants are considered) between emission changes and air pollutant concentrations, a good representation of urban effects is crucial for such models. The aim of this paper, which focuses on mesoscale modeling, is 1) to describe an urban surface exchange parameterization (Martilli et al. 2002) and to show that is able to reproduce some of the most important observed UBL features and 2) to use the model to investigate the sensitivity of UBL structure to different parameters (e.g., wind speed, urban morphology, rural soil moisture). The domain used is flat and 2D. Two-dimensional simulations have been used widely in the past to study UBL structure (Bornstein 1975; Yoshikado 1992) because they allow an easy identification of the 2002 American Meteorological Society

2 1248 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 different mechanisms involved. The disadvantage is that three-dimensional features (e.g., flow circulating around a city) cannot be studied. However, this analysis focuses only on simulated UBL features that are also observed in experimental campaigns reported in the literature. The parameters chosen are typical of a midlatitude, midsize city in summertime. Because flat topography is assumed, results are valid in particular for cities far from complex topography (e.g., mountains, sea). Such topography can induce mesoscale circulation that may overcome urban effects. 2. Model a. Urban module In standard models, cities are represented using the same techniques adopted for rural areas [based on the Monin Obukhov similarity theory (MOST) and an energy balance at the surface] but with a higher roughness length and different soil thermal characteristics. However, field measurements (Rotach 1993a) have shown that MOST (which is based on the constant flux layer assumption) is not valid in the URS, the region in which pollutants are emitted and people live. Moreover, shadowing and radiation trapping effects in urban canyons (usually neglected) play an important role in the surface energy budget. Several efforts to improve the representation of cities in mesoscale models have been made recently. Modelers have focused on either the thermal part (surface energy budget) or the mechanical part (wind field and turbulence). For the thermal part, particular attention has been directed to heat storage (the amount of heat stored in buildings and urban soil during daytime and released during nighttime). Taha (1999) incorporated the Objective Hysteresis Model (OHM) [an empirical relation between net radiation and storage; Arnfield and Grimmond (1998)] in the surface energy budget. Masson (2000) adopted a different approach, taking into account shadowing and radiation trapping in urban canyons. For the mechanical part, several studies have focused on the determination of roughness lengths and displacement heights as a function of different geometrical urban parameters (Bottema 1997; Grimmond and Oke 1999). Uno et al. (1989) and Brown and Williams (1998) adopted an alternative, porous approach in analogy with vegetation-canopy-flow techniques. In this case the lowest model level is at the street level. Moreover, Bornstein et al. (1993) represented New York City by an increase in the topography to reproduce the urban topographic barrier effect. The parameterization described in this paper includes urban thermal and mechanical effects both. For the thermal part, heat fluxes from roofs, streets, and walls are considered, as well as the reflections and trapping of radiation in street canyons (the effect of radiation trapping in a street canyon is considered only at the surface and not in the atmosphere); for the mechanical part, a porous approach is adopted. This approach makes it a FIG. 1. Schematic representation of the city in the model. Buildings are in gray. Horizontal dashed lines represent numerical levels (see appendix B for the meaning of the symbols). good tool to investigate the interactions between thermal and mechanical factors responsible of the modifications in UBL structure. A complete description of the urban module can be found in Martilli et al. (2002). Here only the basic principle and the equations are presented. In the module, the city is characterized by an array of buildings of the same size B located at the same distance from each other (canyon width W) but with different heights h [with a certain probability (h) to have a building with height h; see Fig. 1]. Street-canyon length is equal to horizontal grid size to simplify the formulation. 1) MECHANICAL FACTORS The lowest model level is at the physical ground. The momentum sink from friction on horizontal surfaces (roof and canyon floor) is, therefore, vertically distributed in all the model levels within the urban canopy as follows (symbols are in appendix B): 2 k z I/2 H hor hor H I 2 m B I I I z /2 z oi I [ ] Fu f,ri U U S, ln z oi (1) where Ri B is the bulk Richardson number of vertical level I (computed with wind and temperature of this level) and f m are the formulas used in Louis (1979). The drag force induced by the buildings is V ort ort V FuI C drag U I UI S I. (2) This method (porous approach) is usually adopted in vegetation canopy models. The use of horizontal wind speed orthogonal to street direction (maximum force for wind orthogonal to street direction) should be noted. Following Raupach (1992), C drag is 0.4. In this work a turbulent kinetic energy dissipation (k l) closure model is used [Bougeault and Lacarrère (1989); the parameterization can be easily generalized to other types of k l models]. In analogy with what is done in many vegetation canopy models, a source of turbulent kinetic energy (TKE) is introduced to repre-

3 DECEMBER 2002 MARTILLI 1249 sent the increase in the conversion of mean kinetic energy to TKE because of buildings: V ort 3 V FeI C drag U I S I. (3) Moreover, a new length scale is added to the traditional length scale to take into account building-induced eddies in the urban canopy layer (UCL) which are assumed to be of the same size as the buildings (building height is chosen to represent building dimensions): nu 1 1 (z iu). (4) l z b I iuibu In Bougeault and Lacarrère (1989), as in many other k l closure models, mixing length is a function of the height above ground. This height is modified to account for roofs at different heights: 1 l ground I. (5) ibu W 1 B 1 (z iu) B Wz B W Z z 2) THERMAL FACTORS I iu1 I iu For the temperature equation, the fluxes from the horizontal surfaces are computed as follows: 2 k z I/2 H hor H I 2 I h B I z /2 z oi I [ ] F U f,ri S. ln iu z oi (6) As previously described, f h refers to formulas used in Louis (1979). Temperature fluxes from walls are computed with Clarke s formulation (1985). For a north south-oriented street canyon, V wallwest walleast H I I I I I I C p F [( ) ( )]S, (7) and [ ] U hor I d c c a b. (8) c c c To compute surface temperatures of roofs, walls, and canyon floor, a heat diffusion equation is solved in several layers in the material (concrete or asphalt). The deepest-level temperature (room temperature for roof and walls) is constant for the entire simulation (e.g., by fixing this temperature, it is possible to take into account, at least partially, the anthropogenic heat). At the surface atmosphere interfaces, an energy budget is computed for each surface, considering sensible heat flux, incoming solar radiation, and incoming and outgoing longwave radiation. These radiative quantities result from shadowing, reflection, and trapping in the street canyon [Appendix A; for more details, see Martilli et al. (2002)]. The urban latent heat fluxes are neglected in the current formulation. b. Mesoscale model The parameterization described above is implemented in a mesoscale model. The model is nonhydrostatic, Boussinesq, and anelastic. It solves the following conservation equations [in (9) (12), repeated indices are summed]: U i 0, (9) x i Ui P UiUj uiw g t x x z i3 i j o G Dui 2ijk j(uk U k), (10) Ui w D t xi z R/C p 1 Po Rlwave, and (11) C P z p Q QUi qw Dq. (12) t xi z In the last equation, no condensation or cloud formation is considered. The D terms in (10) (12) represent others terms, such as interactions between the buildings or the ground surface and the atmosphere. At the ground surface in rural areas, turbulent fluxes are computed using MOST with the formulation of Louis (1979). The Tremback and Kessler (1985) module gives rural temperature and moisture. Solar radiation is computed using the method of Schayes (1982), and longwave radiation is computed with that of Sasamori (1968). The spatial discretization is based on the finite-volume method. More details about the model formulation can be found in Clappier et al. (1996) and Martilli et al. (2002). In urban areas, the extra terms D A in (10) and (11) and in the TKE equation (for a variable A that is wind speed, temperature, or TKE) are equal to the fluxes owing to the presence of buildings divided by the volume of air present in the grid cell. In other words, in a numerical way, V Fa FaI D, (13) A I H I V A I A where V I is the volume of air in the grid cell I (grid cell volume minus volume of buildings in the cell), and V H FaI and FaI are the terms computed previously. Model results have been compared with sets of experimental data from different cities (Martilli et al. 2002). The new approach is able to reproduce the increase with height (in magnitude) of Reynolds stress in the URS as observed in several cities and wind-tunnel studies (Ro-

4 1250 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 TABLE 1. Parameters used in the urban module; K s is the substrate thermal conductivity of the material, C s is the specific heat of the material, T(int) is the initial temperature of the material and also temperature of the deepest layer, is the emissivity of the surface, is the albedo of the surface, and z o is the roughness length of the surface. Surface K s (m 2 s 1 ) C s (J m 3 K 1 ) T(int) (C) z o (m) Wall Roof Floor tach 2001), which cannot be reproduced by the traditional approach consisting of an increase in the roughness length. Moreover, model results agree well with the OHM of Arnfield and Grimmond (1998), giving us confidence that the model is able to reproduce correctly the urban energy balance. As a consequence, a nocturnal UHI can be modeled, whereas with the traditional methodology it is not possible. Further comparisons with field observations are in sections 3 and 4. c. Model setup The modeling domain is flat and 2D. In the horizontal plane, there are 100 numerical grid points with a spacing of 1 km. Vertical spacing is 10 m for the first 50 m near the ground, and then it is stretched (with a ratio 1.1) up to 6000 m (the top of the domain). The city is located at the center of the domain and is 10 km wide (10 grid points). Urban characteristics are the same for all the points. As a first test, the following morphology is considered: 5% of the buildings are 5 m high, 25% are 10 m, 40% are 40 m, 25% are 20 m, and 5% are 25 m, resulting in an average building height of 15 m with a standard deviation of 5 m, which are, for example, typical values for European cities (Ratti et al. 2001). The street canyon width is 15 m, and so is the building horizontal size, with a mean height-to-width (H/W) ratio of 1. The street canyons are north south oriented (orthogonal to the plane of the simulation). The rural area around the city has a sandy clay loam soil type (Tremback and Kessler 1985) and an initial soil moisture content of 0.25 (volume of water per volume of soil). The roughness length is 0.1 m. The simulation day is 10 June; the latitude is 45N. Simulations start at 2000 LST and last for 36 h. This combination gives a maximum sensible heat flux during the day of 210 W m 2 and a Bowen ratio of 0.5, which are realistic values (Stull 1988). The initial atmospheric stability is 3.5 K km 1, and the wind speed (constant with height) is 3 m s 1 (simulation used as base case, called w3) from the west (from the left in the plane of the simulation). The geostrophic wind is equal to the initial wind. Other simulation parameters are given in Table 1. Starting from this base case, sensitivity tests are made by modifying only one variable at a time. 1) Wind speed. Two additional cases are run with 1 (w1) and 5 (w5) m s 1 initial wind speed, respectively. 2) Urban morphology. A case with low buildings (50% 5 m high and 50% 10 m), called h7, (average building height is 7.5 m with a standard deviation of 2.5 m, H/W 0.5) and a case with high buildings (3% 10 m high, 7% 15 m, 12% 20 m, 18% 25 m, 20% 30 m, 18% 35 m, 12% 40 m, 7% 45 m, and 3% 50 m), called h30, (average building height is 30 m with a standard deviation of 10 m, H/W 2) are run. 3) Rural soil moisture. A case is run with rural soil moisture content equal to 0.21 (maximum sensible heat flux of about 400 W m 2 ). For all of the simulations, a passive tracer is emitted at a constant rate in the entire urban area at ground level. The tracer dispersion is computed on the same grid and with the same numerical schemes used to solve the other equations. 3. Nocturnal urban boundary layer a. Elevated inversion layer Field experiments have shown an elevated inversion layer above a city [Bornstein (1968), over New York, New York; Clarke (1969) over Cincinnati, Ohio, Godowitch et al. (1985), over St. Louis, Missouri; Uno et al. (1988), over Sapporo, Japan; and Sang et al. (2000) over Shenyang, China]. Following Godowitch s definition of the inversion base altitude Z h (the height at which the vertical temperature gradient become positive), values range between m for Sapporo and 150 m for St. Louis. In Fig. 2a, modeled vertical temperature profiles (base case w3) are compared with those obtained with a traditional approach [roughness length equal to 1.5 m, in agreement with the rule of thumb mentioned by Grimmond and Oke (1999) and soil thermal characteristics of concrete] at the center of the city at 0300 LST. Results obtained with the new approach show an inversion layer, with Z h of about 80 m (above ground level; note that all the heights in the following are above ground level), in the range of the observations mentioned above, whereas the traditional approach fails to reproduce this layer. Godowitch et al. (1985) and Uno et al. (1992, 1988) give information, also, about the top of the inversion layer Z t (the height above Z h at which the vertical gradient of potential temperature becomes negative). For St. Louis, mean Z t was 325 m with a standard deviation of 103 m; it was much lower for Sapporo ( m). The potential temperature jump (difference between the potential temperature at Z t and at Z h )

5 DECEMBER 2002 MARTILLI 1251 FIG. 2. Comparison between new (solid line) and traditional (dashed line) approaches for vertical profiles of (a) temperature and (b) vertical turbulent heat fluxes at the center of the urban area at 0300 LST. Simulations use 3 m s 1 wind speed. was K in Sapporo (resulting in a potential temperature gradient of K m 1 ); in St. Louis it was between 0.2 and 4.4 K (with a potential temperature gradient of K m 1 ). As can be seen in Table 2, model results are in between these two sets of data. Moreover, modeled vertical profiles of turbulent heat fluxes are compared with those measured by Uno et al. (1992) over Sapporo. Even if there is substantial scatter in the data, those profiles show a maximum of K m s 1 in the UCL and a minimum of 0.01 K m s 1 close to Z h. Again, the new approach gives very good agreement with those profiles, in shape and magnitude, and the traditional approach fails to do so (Fig. 2b). These comparisons give us confidence that the model is able to capture the most important features of the nocturnal UBL. TABLE 2. Values of the height of the inversion base Z h, inversion top Z t, inversion depth Z t Z h, difference in potential temperature between the inversion top and inversion base, and inversion strength. Values are computed in the center of the city at 0300 LST. Case w3 w1 w5 wd wb wc 1) SENSITIVITY TO WIND SPEED By using the model, it is possible to investigate the sensitivity of nocturnal UBL structure to wind speed and possibly to advance a hypothesis to explain the differences among the data measured in various locations. A variation in wind speed is expected to influence directly the drag and TKE production induced by buildings (mechanical factors defined above) as well as advection. Z t (m) Z h (m) Z t Z h (m) (Z t ) (Z h ) (K) d/dz (K m 1 ) The three simulations with different wind speeds (w1 with wind speed of 1 m s 1,w3with3ms 1, and w5 with 5 m s 1 ) and the same urban morphology reproduce an elevated inversion layer (Fig. 3a). As the wind speed increases, the values of Z h increase from 50 m for w1 up to 154 m for w5 (Table 2). A stronger vertical mixing of potential temperature is responsible for this behavior. As represented in Fig. 3b, vertical turbulent fluxes are slightly positive in the UCL and are strongly negative aloft up to Z t. However, below Z h the vertical gradient of turbulent heat flux is negative, and between Z h and Z t the gradient is positive. The net result of the vertical turbulent transport is to heat the layer below Z h and to cool the inversion layer. These effects are counterbalanced by the horizontal advection of temperature, negative below Z h and positive in the inversion layer. Because, as expected (Fig. 3c), simulations with stronger synoptic wind have stronger winds above the urban areas, they also have colder advection below Z h and warmer advection in the inversion layer. The shapes of the three profiles of TKE are similar (Fig. 3d), with a maximum near the average building height. However, higher values are computed for stronger winds (higher mechanical TKE production induced by buildings and by stronger vertical shear). This also explains why the simulations with stronger winds have higher (in magnitude) turbulent heat fluxes (and gradients) below Z h. The PBL height (defined as the lowest model level at which TKE is less than 0.01 m 2 s 2 )is higher for stronger winds. The effect of this boundary layer structure on the passive tracer dispersion is represented in Fig. 3e. In w1 the pollutants are vertically diffused in a layer only 50 m deep, that is, shallower than in w3 (120 m) and w5 (200 m). The highest ground level concentrations in the city are consequently computed for w1.

6 1252 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 FIG. 3. Vertical profiles of (a) temperature, (b) vertical turbulent heat fluxes, (c) horizontal wind speed, (d) TKE, and (e) passive tracer at the center of the urban area at 0300 LST. Simulations use 1, 3, and 5ms 1 wind speed (w1, w3, and w5, respectively), as denoted in (a).

7 DECEMBER 2002 MARTILLI 1253 FIG. 4. Same as Fig. 3 but for simulations with 7.5-, 15-, and 30-m mean building height (h7, h15, and h30, respectively). 2) SENSITIVITY TO URBAN MORPHOLOGY A variation of the mean building height is expected to have a direct effect on the vertical distribution on both the drag force and TKE production caused by buildings (mechanical factors described above). On the other hand, different H/W ratios induce different view factors and, as a consequence, different cooling rates (effect on the thermal factors). Again, the three simulations with different urban morphology (h7; h15, which is equivalent to w3 of the previous section; and h30; see section 2c), but with the same

8 1254 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 synoptic wind speed have an elevated inversion layer. The values of Z h increase with the mean building height (Fig. 4a) (from 40 m for h7 to 155 m for h30; see Table 2). The highest surface temperature (e.g., the strongest nocturnal UHI) is observed in the simulation with the highest H/W ratio (which reduces nocturnal cooling) and the highest buildings (which reduces the advection of cold air from the rural area). The vertical profiles of turbulent heat fluxes (Fig. 4b) have the same structure described previously, with the negative peak located close to Z h for the three simulations. The intensity of the peak increases slightly with building height. As expected, the strongest reduction in wind speed is computed for h30 (Fig. 4c) and the lowest for h7. The wind speed reduction is greater below Z t. This situation is in agreement with TKE profiles (Fig. 4d) because TKE intensity increases and boundary layer height increases with building height. For the three profiles, the maximum of TKE is near the average building height. The presence of a strong, deep turbulent layer in h30 has an influence on the passive tracer dispersion. As shown in Fig. 4e, the passive tracer emitted at ground is dispersed up to nearly 200 m in h30 but only up to 70 m in h7. 3) SENSITIVITY TO RURAL SOIL MOISTURE In Fig. 5, results of the simulations with rural soil moisture content of 0.21 and 0.25 (base case) are compared. Lower rural soil moisture content increases temperatures during daytime (because of stronger sensible heat fluxes), but also increases the strength of the nocturnal stability close to the ground (faster cooling because of a lower heat capacity of drier soil). The differences observed in the vertical structure of the nocturnal UBL are then mainly due to a different stability of the approaching flow. As a consequence, the inversion layer height and the peak of negative turbulent heat flux are reduced in the simulation with lower soil moisture content (Figs. 5a,b and Table 2). Wind speeds are similar in the UCL (or slightly above), where the dominant mechanism is building drag, whereas above the UCL the simulation with lower soil moisture content yields a stronger increase with height of wind speed (Fig. 5c). In fact, this is due to the stronger stability of the approaching flow, which destroys TKE above the urban canopy (see Fig. 5d) and reduces the turbulent vertical transport of momentum. Vertical profiles of passive tracers are coherent with this picture, showing higher ground concentrations, in the urban areas, for the simulation with drier soil (Fig. 5e). Results of these tests on the inversion parameters are summarized in Table 2. Values of Z t, Z h, and, to a lesser extent, Z t Z h, increase with wind speed. On the other hand Z t and Z h increase with building height (and H/W ratio), but inversion layer depth (Z t Z h ) decreases when building heights increase. So, Z t is more influenced by wind speed, whereas Z h is more sensitive to the mean building heights and H/W ratio. A rural soil moisture reduction, having an effect on approaching flow stability, decreases Z h. A wind speed increase induces an increase of inversion strength (d/dz in the inversion layer), and an increase of the building heights reduces inversion strength. b. Urban heat island Another phenomenon observed during nighttime in urban areas and connected with the elevated inversion layer is the UHI. In Fig. 6a, vertical profiles of the differences between the urban and rural temperature are plotted for all of the simulations presented above. Maximum UHI intensity is at ground level and ranges between 4.5C for the drier rural soil case and 2C for the lower buildings and lower H/W ratio case. At a certain height above the city, air becomes colder than above the rural area. This cooling effect increases with wind speed and thermal stability of the rural profile, but it is insensitive to building height. Figure 6b (horizontal spatial distribution of the lowest-level temperature) shows that the higher UHI of the dry rural soil simulation is due both to a stronger rural cooling and to the downward turbulent mixing of heat. Because during daytime the rural area heats more than in the simulations with moister soil, and because the nocturnal vertical stability is stronger, rural temperature above the surface layer is higher in the simulation with drier soil. Once this heat is advected above the city, it is mixed down to ground level. In the other simulations, higher UHIs are computed for lower wind speeds and for higher building heights and H/W ratios. Differences of about 1C between (average) H/W ratio equal to 1 and 2 and between H/W of 2 and 3 are consistent with the results obtained by Oke (1981) with a physical model. c. Factor separation analysis Godowitch et al. (1985) observed that the nocturnal UBL vertical temperature structure is determined by an input of heat from building surfaces and anthropogenic sources and also by downward transport of warmer air from the elevated inversion, as well as by mechanically generated turbulence. However, they did not quantify the relative importance of these processes. Uno et al. (1988), using field measurements, and Uno et al. (1989), using numerical models, outlined the importance of TKE generation from urban canopy elements in the formation of the nocturnal UBL structure. In their speculation, they used TKE budget terms and concluded that turbulence in the nocturnal UBL is mechanically produced (in contrast to the daytime situation when the thermal production terms are dominant). A different method is adopted here. The factor separation technique of Stein and Alpert (1993) is used to investigate the relative importance of the mechanical and thermal factors in the formation of the nocturnal UBL. For the base case w3 (wind speed of 3 m s 1 and mean building height of 15 m) analyzed before,

9 DECEMBER 2002 MARTILLI 1255 FIG. 5. Same as Fig. 3 but for simulations with soil moisture content equal to 0.25 and 0.21 (sm25 and sm21, respectively). three other simulations are carried out to evaluate the relative effects of the thermal and mechanical factors. The evaluation of the simultaneous impact of two factors is complicated though the nonlinearity of the processes involved. Stein and Alpert (1993) proposed a simple method to compute the interactions among various factors influencing the atmospheric circulation, and they applied their method to study the relative effect of surface fluxes and topography on rainfall distribution during a typical cyclone evolution in the Mediterranean area. In summary, this method requires four simulations to

10 1256 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 FIG. 6. Vertical profiles of (a) differences between urban and rural temperatures and (b) horizontal profiles (lowest model level) of temperatures at 0300 LST, for all the simulations: 15-m mean building height and 3 m s 1 wind speed (h15w3); 30-m mean building height and3ms 1 wind speed (h30w3); 7.5-m mean building height and 3 m s 1 wind speed (h7w3); 15-m mean building height and 1ms 1 wind speed (h15w1); 15-m mean building height and 5 m s 1 wind speed (h30w5); and 15-m mean building height, 3 m s 1 wind speed, and soil moisture content equal to 0.21 (dry). evaluate the impact of two factors. In this case, the simulations needed are as follows. 1) The simulation described above (synoptic wind speed of 3 m s 1 and mean building height of 15 m), in which the thermal and mechanical factors are both present (simulation wtm). 2) A simulation (wm) with only the mechanical terms in the equations [terms in section 2a (1) of the model description]. This means that only the momentum and the TKE equations see the buildings. For the thermal part, heat fluxes are computed as in the rural areas using the Louis (1979) formulation and the Tremback and Kessler (1985) soil module (soil type sandy clay loam with initial moisture content equal to 0.25). 3) A simulation (wt) with only the thermal part [the terms in section 2a (2)]. Only the temperature equation sees the buildings. For the momentum and TKE equations the technique used in the rural areas is adopted (roughness length equal to 0.1 m, etc.). 4) A reference simulation (wr) without the city. All points are treated as rural. By using the results of these four simulations, it is possible to identify the effect of all of the factors on the results. For a certain variable A(wtm) (obtained in the simulation wtm in which both factors are computed), the following relation is valid: A(wtm) Sr St Sm Stm, where Sr represents the effects of all of the factors that are neither mechanical nor thermal (in this case, it represents a kind of rural situation without any city), St represents the influence of thermal factors, Sm represents the effects of mechanical factors, and Stm represents the mutual interactions between thermal and mechanical factors. The effect Sr is easy to determine. Its value is that of the variable obtained in the simulation without city wr: Sr A(wr). The effect St is defined as the value obtained in the simulation with the thermal factors only (wt) minus the value obtained in the simulation without city. In other words, this is the modification induced by the thermal factors as compared with the rural situation: St A(wt) A(wr). In a similar way the effect of the mechanical factor is defined as Sm A(wm) A(wr). Last, the mutual interactions between the mechanical and thermal factors Stm can be computed straightforwardly from the previous relations: Stm A(wtm) Sr St Sm A(wtm) A(wm) A(wt) A(wr). For the potential temperature, the value considered is the difference between the value computed by the model and the initial value (to have values for Sr of the same order as the others terms). The temperature profile (Fig. 7a) shows an important negative (cooling) contribution of Sr (which includes radiative cooling). In a layer near the ground (below 40 m, roughly 2 times the UCL depth), positive effects (higher temperature as compared with the rural case) are computed for mechanical (Sm) and thermal (St) factors and a negative effect is computed for the interactions (Stm). In this layer, and in particular at ground level, St is greater than Sm, meaning that thermal factors are more important than mechanical ones in the UHI formation in the lower UBL. Above that height, there is a second layer (about 50 m deep) in which Sm and, to a lesser extent, St are negative and Stm is positive. Mechanical factors, then, are more important than thermal ones in cooling (because of vertical mixing) the upper UBL. Both layers are below Z h. Aloft, in the inversion layer, St, Sm, and Stm are negative, all acting to increase the inversion strength, but again thermal factors are less important, mechanical factors are dom-

11 DECEMBER 2002 MARTILLI 1257 FIG. 7. Vertical profiles of thermal (St), mechanical (Sm), interactions between thermal and mechanical (Stm), and rural (Sr) factors for (a) difference between temperature and initial temperature, (b) horizontal wind speed, (c) TKE, and (d) passive tracer. Values are at 0300 LST at the center of the city for simulation with 3 m s 1 wind speed and 15-m mean building height. inant in the lower part of the layer, and interactions are dominant in the central part of the inversion layer. The vertical profiles of the factors for horizontal wind speed (Fig. 7b) show a negative Sm (it slows the wind), as expected, roughly up to the inversion base. Above, it becomes slightly positive. On the other hand, St is positive (the wind speed is stronger as compared with the reference case wr) in a shallow layer close to the ground (20 30 m, around UCL depth) and is negative aloft. The Stm has the opposite sign as compared with St up to about 70 m and is negative above. The TKE profiles (Fig. 7c) show positive contributions for all the factors (except for Sm very close to the ground). In particular, Sm and St have similar magnitudes in the lowest 100 m. Mechanical and thermal factors are both important in TKE production in the UBL. The vertical extension of Stm is higher than all of the other effects, meaning that the highest boundary layer is obtained when both effects are taken into account. The physical interpretation of these results is the following: the mechanical factors generate TKE, which acts to increase vertical mixing of potential temperature (Sm for potential temperature is positive near the ground and negative aloft) against the strong stability induced by the surface cooling. Moreover, the trapping of radiation in street canyons reduces the cooling in the UCL (positive effect of St on temperature) and generates TKE that increases the vertical mixing (negative St aloft for temperature). The interactions between the two factors cause an increase of TKE (Stm is positive, meaning that the TKE for the wtm simulation is greater than the sum of that produced in wm and wt minus wr), mainly because the thermal effects reduce the destruction of the mechanically produced TKE by buoyancy. The greater

12 1258 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 amount of TKE available results in a higher UBL depth. This means that the vertical mixing (linked to TKE intensity) of potential temperature, but also momentum, is stronger in wtm than in wm and wt. As a consequence, in wtm, part of the variation in potential temperature produced by the mechanical and thermal factors is mixed vertically. This explains why the Stm term has, in general, the opposite sign as compared with St and Sm for potential temperature below 90 m. The situation is slightly different for the horizontal wind speed in a layer near the ground, where St and Sm have opposite signs. There, thermal factors (St) increase wind speed because of the temperature gradient between the colder rural area and the hotter city, and the mechanical factors (Sm) act to reduce the speed because of the buildings drag. Here, the interactions (Stm) act to reduce the wind speed. The effect on the passive tracer dispersion is presented in Fig. 7d. As expected, Sm and St act to increase the vertical mixing and are negative near the ground (where the emissions are) and are positive aloft. For the reasons explained above, the interaction term Stm has the opposite sign as compared with St and Sm and is positive in the upper layer, showing that in the wtm simulation the tracer is diffused in a deeper layer than in the other simulations. In conclusion, all the factors are important in determining the nocturnal UBL structure. In particular, thermal factors are more important in the lower part of the UBL where they strongly contribute to the UHI intensity. Mechanical factors are more important in the upper part of the UBL and, in particular, in the inversion layer. These results can be used for interpretation of the results presented in the previous sections. Because an increase of wind speed has an effect mainly on mechanical factors, the most sensitive parameters are those of the upper UBL (Z t, Z t Z h, and the strength of the inversion). On the other hand, an increase of the H/W ratio reduces the cooling effect, and it has a greater effect on the thermal factors. As a consequence, the most sensitive parameters are those of the lower UBL (Z h, and a reduction of the inversion strength). 4. Daytime urban boundary layer As observed in several field studies, urban areas are, in general, warmer and drier (in summer) than adjacent rural areas, mainly because urban surfaces absorb less water (smaller latent heat fluxes) and have different thermal characteristics, as compared with rural surfaces. In addition, urban areas can produce significant mesoscale wind perturbations in which the urban heating and roughness induce surface convergence, upward flow over the city, and divergence aloft. However, large differences exist among different locations and meteorological situations. Hildebrand and Ackerman (1984), in their measurements over St. Louis, found urban sensible heat fluxes to be 2 3 times as high as TABLE 3. Boundary layer height (fixed at the lowest level where TKE is less than 0.01 m 2 s 2 ) at the city center at 1500 LST (Zi u ), and the difference between the urban and rural values (Zi t Zi u )at the same hour. Case w3 w1 w5 wd wb wc Zi u (m) Zi r Zi u (m) rural sensible heat fluxes; urban temperatures were about 1C higher, and PBL height was increased by m. On the other hand, Spanton and Williams (1988) observed a PBL height increase over London of about m. Even lower differences were found over Paris (Dupont et al. 1999), but much greater increases ( m) were found over Nashville (White et al. 1999). The intensity of the differences between urban and rural areas is mainly a function of wind speed and of rural soil moisture. Drier rural soil can strongly reduce the differences between the urban and rural boundary layer heights. As shown in Table 3, model results are in the range of the measurements mentioned above. The model can overestimate the differences between urban and rural areas, because urban areas are considered to be dry (no latent heat fluxes), which is equivalent to assuming that there are no parks or gardens in the city. However, the differences observed are not only due to the differences in the soil moisture between the city and the rural areas, because the model also takes into account the higher capability of the urban surfaces to store energy during daytime and reduces the amount of sensible heat flux released to the atmosphere. For the same reason, the traditional approach (modification of roughness length and soil thermal properties), because it stores less energy, has a higher sensible heat flux and, as a consequence, a higher PBL height. In the following, attention is paid to the case of moist rural soil, because it is the case in which the strongest differences are simulated. a. Sensitivity to wind speed For w1 (low synoptic wind speed; see section 2c), the vertical section of potential temperature and boundary layer height (Fig. 8a) shows a column of hot, unstable air above the city and a PBL height of about 1500 m. The horizontal gradient of temperature between air above the city and air above the rural area generates a thermal circulation, as clearly shown in Fig. 8b. When the wind speed increases (simulation w3) the column of hot air (Fig. 8c) is still present, but it is advected downwind. Moreover, PBL height is lower (around 1300 m) than in w1, but the region in which PBL height is influenced by the presence of the city is horizontally

13 DECEMBER 2002 MARTILLI 1259 FIG. 8. (a), (c), (e) Vertical section of potential temperature (K) and (b), (d), (f) horizontal wind speed (m s 1 ) for simulation with (a), (b) 1; (c), (d) 3; and (e), (f) 5 m s 1 at 1200 LST. On the potential temperature sections, PBL height (fixed at the lowest level where TKE is less than 0.01 m 2 s 2 ) is represented.

14 1260 JOURNAL OF APPLIED METEOROLOGY VOLUME 41 FIG. 9. (a) Time evolution of PBL height at the center of the urban area for simulations with 1, 3, and 5 m s 1 wind speed (w1, w3, and w5, respectively). (b) Time evolution of thermal (St), mechanical (Sm), interactions between thermal and mechanical (Stm), and rural (Sr) factors for PBL height evolution at the center of the city for w3. larger. Wind speed (Fig. 8d) increases above the city and is reduced downwind, again because of the temperature gradient. A further increase of wind speed (simulation w5, Fig. 8e) reduces the differences in temperature between the city and the rural area. The urban rural PBL height difference is also reduced to a few hundred meters. A reduction in wind speed is present in the UCL (Fig. 8f), but a small increase in wind speed is present aloft because of the temperature gradient. Bornstein and Johnson (1977) measured a similar transition value (3.6 m s 1 ) over New York City. Above the city, wind speed increases for weaker wind and decreases for stronger winds. In the w1 simulation, PBL height in the center of the city (Fig. 9a) increases quickly in the morning and reaches a maximum at around 1500 LST. After, PBL height remains constant until 1900 LST, when it decreases. For stronger winds (w3 and w5), the PBL height increase in the morning is slower. In both simulations, maximum PBL height is reached at around LST (slightly higher in w3 than in w5), and it decreases at around LST. The reason for this different behavior is the stronger advection of cold and stable rural air in w3 and w5 as compared with w1. This is opposite to what is observed during nighttime, when higher PBL heights are computed for stronger wind speeds. The delay in PBL height decrease, on the other hand, is due to a stronger mechanically induced TKE FIG. 10. Horizontal distribution of passive tracer concentration (a) at the lowest model level (5 m above ground) at 0900 LST for simulations with 7.5-, 15-, and 30-m mean building height (h7, h15, and h30, respectively) and (b) at the same level for thermal (St), mechanical (Sm), interactions between thermal and mechanical (Stm), and rural (Sr) factors at the same hour for h15.

15 DECEMBER 2002 MARTILLI 1261 production, which is an obstacle to the formation of a strong stable layer near the ground. With the same technique used previously (see section 3c), a factor separation analysis is done to determine the effect of mechanical and thermal factors and interactions (for simulation w3, the base case). At the city center, before 1400 LST (Fig. 9b), the most important terms are Sr and St, which are positive. Mechanical factors are close to zero. When both factors are taken into account, a lower PBL height is computed (negative Stm) than in the case for which only thermal factors are considered. In fact, this is due to the reduction in wind speed induced by mechanical factors, which reduces the heat exchange coefficients between surface and air [(6) (8)] and, as a consequence, the sensible heat fluxes. On the other hand, in the evening, St and, in particular, Sm have a strong positive peak, resulting in a delay of PBL height decrease. This means that the TKE mechanically induced by the presence of the buildings acts against the stability induced by the surface cooling and delays the PBL height decrease. b. Sensitivity to urban morphology The mesoscale circulations produced in h7 and h30 during daytime are similar to those of the base case w3 (Fig. 8). The increase of PBL height in the morning is also similar for the three simulations. Some differences can be observed in the horizontal distribution of groundlevel passive tracer concentrations during daytime. At 900 LST (Fig. 10a) in the city area, where emissions are located, the highest concentration is computed for h30 and the lowest is computed for h7 (opposite to the nocturnal situation). The main reason is that TKE is reduced in the UCL as compared with its value above, as has been observed in several field experiments (Rotach 1993b; Louka et al. 2000) and wind tunnel studies (Kastner-Klein et al. 2001). This reduction is stronger for higher buildings, and the modifications in the length scales reproduce this fact in the model. Moreover, streetlevel wind speeds are lower for higher buildings, reducing the dispersion caused by advection. On the other hand, about 20 km downwind of the city, there is a second peak of passive tracer concentration. Here, the highest peak is for h7 and the lowest is for h30. This second peak is the result of the advection of the tracer accumulated in the urban area during the night and early morning (when simulation h7 has higher concentrations; see Fig. 4e). When the boundary layer increases in the morning, it mixes down momentum and increases ground-level wind speed, and the tracer concentrated in the urban area is advected downwind at this time. This means that the nighttime pollutant distribution can have an effect on daytime values. Factor separation analysis is then used to study mechanisms governing the horizontal distribution of ground-level passive tracer concentration (simulation w3) in the morning. In the urban area, Sr and Sm are positive and St and Stm are negative (Fig. 10b). Mechanical factors reduce wind speed and TKE in the UCL, reducing the tracer dispersion. Thermal factors, on the other hand, increase TKE and wind speed (because of the horizontal temperature gradient between the rural and urban areas) and, as a consequence, tracer dispersion. Interactions are negative once again because, when both factors are considered, wind speed is reduced in the UCL, with a consequent reduction in sensible heat fluxes as compared with the case in which only thermal factors are taken into account. This reduces thermal generation of TKE and tracer dispersion. The second peak computed at 900 LST in the rural area, around km downwind of the city, is the result of the tracer accumulated in the city during night and early morning and then advected downwind. As a consequence, the relative importance of the different factors is similar to that computed during nighttime, with the negative effects of thermal and mechanical factors, and positive effects of the interactions (see Fig. 6d and description in section 3e). Last, it must be stressed that all these considerations are valid only for ground- (or street-) level emissions. 5. Conclusions In this paper, an urban surface exchange parameterization for mesoscale models is described. It takes into account both thermal and mechanical effects on the boundary layer structure induced by an urban area, and it has been implemented in a mesoscale model. Several 2D simulations are made to test the model and to analyze the sensitivity of UBL structure to wind speed, urban morphology, and rural soil moisture. Two distinct behaviors can be defined, one during nighttime and one during daytime. a. Night The parameterization described in the paper is able to reproduce an elevated inversion layer above the city, as has been observed in several field campaigns in different cities. Moreover, the vertical profiles of turbulent heat fluxes have the same structure as those observed in the city of Sapporo. A traditional approach, representing a city only by a modification of the roughness length and the soil thermal characteristics, is not able to reproduce the observed structure. An increase of wind speed induces an increase of Z t, Z h, Z t Z h, and the strength of the inversion. On the other hand, an increase of the mean building height and H/W ratio induces an increase of Z t and Z h but a reduction of Z t Z h and the inversion strength. This means that Z t is more influenced by wind speed and Z h is more influenced by mean building height and H/W ratio. A reduction of rural soil moisture, increasing the atmo-