## 1. Introduction

This paper focuses on the variations in time and space of turbulence observations in large cities with high building densities and many tall skyscrapers. Emphasis is on the Midtown 2005 field experiment (MID05) in Manhattan, New York (Allwine and Flaherty 2007). The observations are made using sonic anemometers at heights of a few meters above street level and at a few rooftop locations. Hanna et al. (2007) presented the results of analysis of similar street-level and rooftop turbulence observations obtained in short-term intensive urban field studies in Oklahoma City, Oklahoma (OKC), known as the Joint Urban 2003 experiment (JU2003; Allwine et al. 2004; Dugway Proving Ground 2005), and in Manhattan, known as the Madison Square Garden 2005 experiment (MSG05; Allwine and Flaherty 2006; Dugway Proving Ground 2008). The newer MID05 turbulence observations (Allwine and Flaherty 2007; Reynolds et al. 2007) tend to agree fairly well with those from JU2003 and MSG05, on average. The data from these three experiments are unique in that this is the first time that extensive turbulence observations have been made near street level among the skyscrapers in large cities. Because of the large amounts of data, Hanna et al. (2007) presented the 30-min averaged values of turbulence as averages over several time periods and sonic anemometers. We have received some comments that the averaging methodology may be inappropriate because wind tunnel experiments and computational fluid dynamics (CFD) models suggest that there is great variability. However, as we will demonstrate in this paper, the variability in the real city is not as great as some expect. We feel that there are two major reasons for the tendency toward uniformity—(i) there are always mesoscale meandering motions present that cause 20°–40° swings in wind direction, preventing a recirculating wake from setting up in one location for the entire period, and causing the actual wakes to “flop” back and forth; and (ii) there is always vigorous vertical mixing in the area of the tall buildings.

In MID05, observations are available from 12 sonic anemometers near street level (at height of 3 m) and from 5 sonic anemometers on the rooftops of tall buildings in an approximate 2 km by 2 km area centered on midtown Manhattan. The focus here is on use of data from this network of sonic anemometers to demonstrate that the space and time variability of the turbulence observations is less than the average magnitudes of the observations themselves.

Conceptual models of urban boundary layers have been developed over the past 10 or 20 yr based on use of the mean building height *H* as a scaling length, and defining terms such as the urban canopy layer (Oke 1987). The urban canopy layer encompasses heights ranging from street level to about *H*. The urban canopy observations taken during special research programs (e.g., see Roth 2000; Grimmond et al. 2004; Kastner-Klein and Rotach 2004) generally use towers in street canyons or on adjacent buildings, where the buildings are a few stories high and there are no tall skyscrapers nearby. However, in the Manhattan borough of New York City, where *H* is about 50–100 m and there are many buildings over 200 m tall, it is impractical to attempt to install towers extending from the street level to the building tops to generate vertical profiles. The MSG05 and MID05 planners (Allwine and Flaherty 2007; Reynolds et al. 2007) considered using remote sounders such as sodars in the deep street canyons but that idea was not pursued because of potential adverse noise effects for the public. Consequently, sonic anemometer observations are available only near street level and on building roofs.

As Grimmond et al. (2004) and Britter and Hanna (2003) point out, a key set of scaling parameters in urban areas is related to building morphology. Besides *H*, other key parameters are *λ _{f}* , which is the ratio of the building frontal area to the plot area, and

*λ*, which is the ratio of building plan area to the plot area. These can be calculated precisely using three-dimensional building data, which are available for many large cities. For the MID05 domain, the parameters have been approximately estimated using two-dimensional maps showing individual building footprints and heights to be

_{p}*H*= 60 m and

*λ*= 1.0. In a city such as Manhattan, with many tall skyscrapers that extend up to 4

_{f}*H*, and the Empire State Building at 7

*H*, the concept of

*H*has less use. Because the tall buildings extend upward so far, those buildings will significantly disrupt the flow far above

*H*[see the CFD simulations reported in Hanna et al. (2006)]. Also, because of the lack of a uniform rooftop height, some of the usual urban wind profile formulations with relatively high wind shears at

*H*have less applicability in Manhattan.

## 2. MID05 description

The MID05 (Allwine and Flaherty 2007; Reynolds et al. 2007; Dugway Proving Ground 2008) was similar to the MSG05 experiment but included a larger area (about a 2-km square vs a 1-km square) and more intensive observing period (IOP) days (6 versus 2). The Midtown domain has the largest concentration of tall buildings in New York City, New York. The objectives and general experiment design were about the same as for MSG05, except that during MID05, there were inside-building and inside-subway tracer releases and sampling. The present paper does not analyze the tracer data.

Table 1 lists the general weather conditions for the six MID05 IOP days in August 2005. Each IOP lasted for about 7.5 h, from 0500 through 1230 LST. Figure 1 shows the domain and the locations of the 12 street-level (surface) sonic anemometers and the 5 rooftop sonic anemometers. All 12 street-level sonic anemometers were placed at a height of 3 m. The five rooftop sonic anemometers were mounted on 6-m masts. Taller masts were not used primarily because of safety concerns. The figure has four of the five rooftop sonic anemometers used in our analysis marked by shorthand symbols—General Motors anemometer at 225 m (GM1), McGraw Hill anemometer at 214 m (MGH1), Park Plaza anemometer at 183 m (PPZ), and One Penn Plaza anemometer at 230 m (OPP). The fifth rooftop sonic anemometer was on the Met Life building (METL; at 253 m), which is the dot seen in the lower middle right.

As Oke (2004) points out, the siting of anemometers in urban areas presents many challenges. Because of the presence of nearby tall buildings and recirculating vortices on all sides of the buildings and on their roofs, the anemometers are never completely free of interference. For all of the MID05 rooftop anemometers, which were placed on flat roofs because of safety issues, there are vents, HVAC systems, and fences and railings on the edge of the roof. At street level, where there are adjacent tall buildings, planters, parked cars, and pedestrians, the anemometers were placed about 1 m from the street curb of the sidewalk and about 4 or 5 m from the buildings. The Brookhaven National Laboratory (BNL) team of meteorologists who set up and operated the anemometers placed them as far away as possible from obstructions (Reynolds et al. 2007). Because the five rooftop anemometers could be operated without fear of vandalism, they were set out and produced data for the entire month of August 2005. But because the 12 street-level anemometers were within reaching distance, a technician had to be present at all times of operation of the sidewalk sites. Thus they were set out each morning and removed each afternoon during the IOP days. During the first three IOP days, some problems occurred (such as overheating of some of the laptop computers) that were resolved before the last three IOP days. Thus there were some missing data.

The sonic anemometers were R.M. Young Co. Model 81000. Standard quality assurance/quality control (QA/QC) procedures were followed as recommended by the manufacturer. After the last IOP, the BNL meteorologists carried out a detailed side-by-side comparison of all anemometers at BNL showing that RMSE differences in wind speed were less than 0.1 m s^{−1} most of the time. More details are given by Reynolds et al. (2007) and Allwine and Flaherty (2007).

The turbulent velocity components were aligned into E–W, N–S, and up–down directions. The actual mean wind directions at a given sonic anemometer might be along the direction of a street, but these rough rules did not always work. For *σ _{u}* and

*σ*, the coordinate alignment does not matter much, since they are always observed to be nearly equal in JU2003, MSG05, and MID05. We hypothesize that this near-equality occurs because of the large turbulence intensities that appear to be always present.

_{υ}As expected in urban areas with local influences of buildings, the mean vertical velocities *w**w*^{−1} at rooftop and 0.13 at street level. Since the overall mean *w**w*^{−1} at rooftop and from −0.13 to +0.13 m s^{−1} at street level. Partly because the street-level sonic anemometers were placed at least 4 or 5 m from the buildings, there were no observations of very large (i.e., 1 or 2 m s^{−1}) mean vertical velocities that might be caused by strong up- or downdrafts on the building side. Also, no systematic variations were clearly evident, such as shifts in mean vertical velocity magnitude depending on wind direction. At rooftop, there were no obvious variations of mean vertical velocity with wind direction, despite the fact that the sonic anemometers (on 6-m towers) were likely located in or near rooftop displacement zones.

For the analysis in this paper, all turbulence variables are “local” in the sense that they represent what was measured by a sonic anemometer at a specific location. This includes the friction velocity, *u*_{*}, which is calculated in the usual way using local observations of

## 3. Results

The 10-Hz records from the 17 MID05 sonic anemometers have been used to calculate several turbulence variables over 30-min averaging times. These same variables were previously calculated for JU2003 and MSG05 by Hanna et al. (2007), who showed that there was good agreement (within about ±20%) in the averages from one city to another. Because of the large numbers of anemometers, days, and 30-min time periods, considerable averaging was done to produce those turbulence variables, however. This has led to questions concerning whether there might be large magnitudes of the variations in the turbulence variables from one site to another and from one 30-min time period to another. Consequently, the current paper focuses on the variability. The following two subsections include 1) a brief overview of the averaged results for MID05, for comparison with the MSG05 and JU2003 results, and 2) a detailed analysis of the variability at MID05. Also, we present some comparisons of JU2003 and MID05 spatial variabilities.

### a. Brief overview of averaged results

Some of the MID05 averaged results are listed in Table 2, where the average values of scalar wind speed (WS), *σ _{u}*,

*σ*,

_{w}*σ*,

_{T}*u*

_{*}, and

*σ*/

_{w}*u*

_{*}for the 5 individual rooftop sites and the 12 individual street-level sites are given. The averages for the rooftop sites combined and the street-level sites combined are listed at the bottom of each section of the table. As found for MSG05, the average scalar wind speed at street level (at

*z*= 3 m) during MID05 is about 0.4 times that at the rooftops. Also in agreement with the results from MSG05, the magnitudes of the turbulent speed standard deviations (e.g.,

*σ*,

_{u}*σ*) and

_{w}*u*

_{*}at the street-level average about one-half of their magnitudes at rooftop. At street level versus rooftop,

*σ*and

_{T}*σ*/

_{w}*u*

_{*}are slightly larger (by about 20%). The average ratio

*u*

_{*}/WS is about 0.20 for the street-level measurements and about 0.16 for the rooftop measurements at MID05. These averaged turbulence variables from MID05 are within ±20% of those from MSG05 and JU2003 most of the time.

Of course, the above results for the overall averages have less meaning if there is a great deal of variability in time and space. For example, if the *u*_{*} average at location S1 is 0.24 m s^{−1}, is it possible for the spread of the sixteen 30-min averages during one IOP to be as high as two orders of magnitude or more? The next subsection addresses this type of question.

### b. Results of analysis of variation of turbulence in time and space

The urban domain, more so than any other domain, is likely to show variations in time and in space due to the influence of the buildings combined with other land use heterogeneities such as parks. The observed variability is investigated in this subsection.

To illustrate the variations in time of the 30-min averages for specific anemometers, we have picked one IOP (day 6), one rooftop anemometer (METL), and one street-level anemometer (S9). These are picked just as representative examples, and we tried not to pick the time or the site with the smallest or largest variability. Figures 2 and 3 are photographs of these two sonic anemometers, their masts, and their surroundings. In Table 3, for the rooftop METL site, the variables *σ _{υ}*,

*σ*,

_{w}*σ*,

_{T}*u*

_{*}are listed for each 30-min period from 0500 to 1230 LST during IOP 6. The overall average, minimum, maximum, and ±% range are also listed. The variables involving velocity fluctuations (

*σ*,

_{υ}*σ*, and

_{w}*u*

_{*}) have ranges from about ±27% to 50%. The variables involving temperature fluctuations (

*σ*and

_{T}*σ*range is also less (±27%). Given the obstructions visible in the photograph, it is surprising that the turbulence variables are so relatively steady, but this is again evidence of large amounts of mixing.

_{T}Table 5 slices the data differently from Tables 3 and 4. In Table 5, the 30-min averaged observed turbulence variables are listed for the ten operating street-level anemometers for a specific 30-min period (0930–1000 LST during IOP 6). Note that the spatial ±% ranges here are similar to those for the time variations in Tables 3 and 4.

The three final Tables 6, 7, and 8 focus on the standard deviations (STD) of the variations in 30-min averaged turbulence over all locations and times. The spread here is represented by STD. The ±% ranges (of the maximum and minimum about the mean) used in Tables 3 –5 are no longer included. For a normal distribution the range encompassed by ±STD would include 68% of the data. For example, Table 6 contains values of the overall mean (also listed in Table 2) and the standard deviation of the set of 30-min averaged values of the turbulence variables measured at street level (*z* = 3 m) during MID05. The ratios of STD to the overall mean are also listed. The averaged STDs can be calculated in different ways (e.g., directly calculate the STDs over all the 30-min observations or calculate the averages over the STDs of certain groups of observations). We used the following three methodologies:

- The STD of the space
*s*and time*t*variations [STD(*s*and*t*)] is based on the fifteen 30-min averages during an IOP at the 12 sites at street level. Thus there is a maximum of 15 × 12 = 180 numbers at street level for calculating STD(*s*and*t*) for an IOP. Then the six STD(*s*and*t*) values for the six IOPs are averaged to give the numbers in Table 6. Note that the actual number of data points used in the calculation is often less than the maximum because of missing data or data that did not pass QA/QC. - The STD of the space variations [STD(
*s*)] is based on the 30-min averages at the 12 surface sites during each 30-min period. Thus there is a maximum of 12 numbers for calculating each STD(*s*) for an IOP. The STD(*s*) values in Table 6 represent an average over all 30-min time periods and all IOPs. - The STD of the time variations [STD(
*t*)] is based on the 30-min averages at each site over the fifteen 30-min periods during each IOP. The resulting STD(*t*) is then averaged over the 12 sites at the surface for each IOP and further averaged over the six IOPs.

Note that none of these STD definitions includes the variability from one day to another for the six IOP days of MID05. This is because the different IOPs had different wind speeds and directions and cloudiness (see Table 1), which would produce an obvious difference that would have dominated the variability in some cases. If a given IOP day has a complete dataset for all 12 sites and all 15 time periods, then, for that IOP day, [STD(*s* and *t*)]^{2} would be expected to equal [STD(*s*)]^{2} + [STD(*t*)]^{2}. This does not occur for the data in Table 6 though, because those data are averaged over all IOP days.

Table 6, for the street-level anemometers, first lists the group of STD values and then lists the group of STD/mean values. Typically, for the street-level anemometers, the magnitude of STD(*s*) is about 90% of the magnitude of STD(*s* and *t*), and the magnitude of STD(*t*) is about 70% of the magnitude of STD(*s* and *t*). The relative variation, STD(*s* and *t*)/mean, is in the range from 0.21 to 0.33 for WS and for *σ _{u}*,

*σ*, and

_{υ}*σ*. STD(

_{w}*s*and

*t*)/mean is in the range from 0.40 to 0.43 for

*u*

_{*}and

*σ*, and for the ratios of

_{T}*σ*,

_{u}*σ*, and

_{υ}*σ*to

_{w}*u*

_{*}. We also calculated the ratios of the STD of the mean WS or the mean vertical velocity

*w*to the mean 30-min average turbulent standard deviation of that variable. For example, it is seen that [STD(

*s*and

*t*) of WS]/(

*σ*

_{u}^{2}+

*σ*

_{υ}^{2})

^{1/2}is 0.42 and [STD(

*s*and

*t*) of

*w*]/

*σ*is 0.35 for the street-level observations.

_{w}To show that these variability results are not unique to just the MID05 observations, we also calculated the variabilities in space for the 20 street-level sonic anemometers used in the JU2003 field experiment. Table 7 lists the JU2003 and MID05 values of STD(*s*)/mean for the six variables. It is seen that the JU2003 and MID05 ratios are quite close—within about 20% for five of the six and within about a factor of 2 for *σ _{u}*.

Table 8 contains the same information as Table 6 but for the rooftop anemometers. Because there are five sites, there is a maximum of 16 × 5 = 80 numbers at the rooftops for calculating STD. As in Table 6, the STD values for the six IOPs are averaged to give the numbers in the table. No space variations are listed because of the small number of sites; during most IOPs, fewer than five rooftop sites were operating. As found for the street-level sites, the magnitude of STD(*t*) is about 70% of the magnitude of STD(*s* and *t*). The relative value of STD(*s* and *t*)/mean ranges from 0.27 to 0.34 for WS and for *σ _{u}*,

*σ*, and

_{υ}*σ*. Thus STD(

_{w}*s*and

*t*)/mean is about 20%–30% larger than the value for the street-level anemometers. STD(

*s*and

*t*)/mean ranges from 0.39 to 0.46 for

*u*

_{*}and

*σ*, and for the ratios of

_{T}*σ*,

_{u}*σ*, and

_{υ}*σ*to

_{w}*u*

_{*}. These magnitudes are only about 10% larger than those at street level. [STD(

*s*and

*t*) of WS]/(

*σ*

_{u}^{2}+

*σ*

_{υ}^{2})

^{1/2}is 0.56 and [STD(

*s*and

*t*) of

*w*]/

*σ*is 0.45, which are about 30% higher than those for the street-level anemometers.

_{w}In general it is found that the contribution of the time and space variations to the total standard deviation during MID05 is usually less than 50% of the standard deviation for the 30-min sampling times quoted in section 3a. This is encouraging, since it verifies that the averaged results are not overwhelmed by site-to-site variations or time variations from one 30-min average to the next.

## 4. Further discussion and caveats

It is hoped that these extensive JU2003, MSG05, and MID05 turbulence observations can be analyzed by other researchers from several viewpoints. The meteorological data can be downloaded from the Dugway Proving Ground (2008) Internet site (once a username and password are acquired). These three urban field experiments are unique because they mark the first time that extensive turbulence observations have been made near street level in the built-up downtown area in the midst of tall skyscrapers. We have tried to demonstrate that observed 30-min averages of *σ _{υ}*,

*σ*,

_{w}*u*

_{*},

*σ*, and

_{T}Our explanation for the unexpected uniformity of the turbulence observations in such a complex environment is that there is extensive mixing horizontally and vertically that has a tendency to homogenize the turbulence. Note that we are not saying that the mean wind speeds and directions are homogenized, because there are obviously effects of buildings and street canyons on the mean flow. A main contributor to the horizontal mixing is the usual ambient mesoscale meandering that always takes place. But in an area of large buildings, this meandering with periods of a few minutes causes the wakes of buildings and other vortices to shift or flop back and forth, so that the vortices are often shifting and never get “fixed” or “set up” in one position. Similarly, as shown by the CFD calculations of the MSG05 domain discussed in Hanna et al. (2006), there is extensive vertical mixing around the tall buildings, with aloft air brought to the surface on the windward side of tall buildings and street-level air brought aloft on the leeward side. Besides the homogenizing effect of this mixing on the turbulence, the large amount of mechanical mixing also causes the stability in the urban canopy to be forced toward neutrality (see Hanna et al. 2007; Roth 2000).

As for caveats, it is clear that this analysis is based on only a few days of observations, during good weather, and usually with steady winds. The Manhattan MSG05 and MID05 data are all taken at the same time of day—from about 0500 to 1200 LST. All Manhattan sonic anemometers were located in the built-up downtown area and none were in the areas with lower buildings or in the suburbs. Some JU2003 sonic anemometers were set up in areas with smaller buildings, but we have not yet analyzed these data.

The Manhattan sonic anemometers were located so that they had as good exposure as possible, considering the surroundings. However, as mentioned earlier, the skyscraper rooftop masts were only 6 m tall and were on flat roofs. These restrictions were imposed by safety concerns. Clearly it would be better to use taller masts on the very tips of the building tops, but that would require the safety concerns to be thoroughly addressed.

This research has been sponsored by the National Science Foundation, the Urban Dispersion Program (UDP) of the Department of Homeland Security, and the Defense Threat Reduction Agency (DTRA). The UDP project manager was Dr. Jerry Allwine of Pacific Northwest National Laboratory (PNNL), and the DTRA project manager is Rick Fry. The authors appreciate the assistance provided by Michael Reynolds and Victor Cassella of BNL who operated the sonic anemometers at MID05 and produced the raw 10-Hz data files. Mena Bassily of HSPH carried out the variability analyses for the JU2003 observations. The authors thank Jerry Allwine and Julia Flaherty, of PNNL, who have put together the final MSG05 and MID05 data archives and summary reports and who have provided us with much advice on the characteristics of the observing networks, as well as supplying high-resolution figures.

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Dates and weather conditions for the six MID05 IOPs, based on observations at the METL rooftop (253 m) sonic anemometer (except the MGH1 sonic anemometer is used for IOP 5). All IOPs began at about 0500 and lasted until about 1230 LST (from Allwine and Flaherty 2006).

Summary results of average turbulence over all IOPs and times (with 30-min averaging time) for 17 MID05 sonic anemometers. See subsequent tables for variability.

Example of variation in time (from 0500 to 1230 LST on IOP 6) of 30-min average turbulence observations from the METL rooftop sonic anemometer.

Example of variation in time (from 0500 to 1130 LST on IOP 6) of 30-min average turbulence observations from the near-surface (street level) sonic anemometer number S9.

Variation of observed turbulence in space over 10 near-surface (street level) sonic anemometers for the 30-min averaging period from 0930 to 1000 LST on IOP 6. Data from sonic anemometers S2 and S6 were missing during this period.

Variability in time and space over all days and times for *N* = 12 MID05 surface anemometers. The “mean” in row 2 is the 30-min average value consistent with Table 2. STD is of a set of *N* 30-min averages of the variable listed, over space and time (*s* and *t*) for a given IOP and then averaged over all IOPs, over space *s* for a given 30-min time period and then averaged over all time periods and IOPs, and over time *t* for a given anemometer location and IOP and then averaged over all locations and IOPs.

Comparison of variability in space for *N* = 12 MID05 and *N* = 20 JU2003 surface anemometers. STD(*s*) is the std dev of a set of *N* 30-min averages of the variable listed, over space for a given IOP and time period, and then averaged over all time periods and IOPs.

Variability in time and space for five MID05 rooftop anemometers. The mean is consistent with the 30-min average value from Table 2. STD is the std dev of a set of *N* 30-min averages of the variable listed, for space and time (*s* and *t*) for a given IOP and then averaged over all IOPs, and over time *t* for a given anemometer location and IOP, and then averaged over all locations and IOPs. The STD over space is not listed because the number of sites is at most five and is often less than five.