a. Site and instrument descriptions

Tower locations 1, 3, and 4 are categorized as suburban (Table 1). The tower-1 location is the transit parking lot about 5 km southwest of the central business district (CBD) and is surrounded by fields to the south, east, and north and by a few one- to two-story buildings, 3.5–6 m tall, to the west and residential areas farther to the west (Fig. 1). There is also a mobile trailer office, 3 m tall, about 30 m to the south-southwest. The tower-3 location is a field about 5 km southeast of the CBD. A golf course is located to the south and southeast, stands of trees are to the east and west about 60 m from the tower, and a one-story building is in the trees to the east and another is to the north over 100 m from the tower. The tower-4 location is about 5 km north of the CBD in a grassy field near a school. The surroundings are mostly open except for a wooded area to the east and northeast and the school, 4 m tall, to the west-southwest. The field is elevated by about 2 m with respect to the base of the school.

Tower locations 2 and 5 are categorized as urban. The tower-2 location is about 1.0 km east of the CBD located in an open area surrounded by industrial buildings on all sides. The buildings nearest to the tower are to the north and west about 15 m from the tower. The buildings range in height from 9 to 10 m. The longest clear fetch is to the east. The tower-5 location is about 1.5 km west of the CBD, and is located near low industrial buildings to the east, south, and west. The buildings range in height from 5 to 7.5 m. To the southwest is a tall tree, about 12 m in height, very close to the tower, about 15 m away. Another tall tree (10–12 m) is located between buildings to the southeast over 50 m from the tower. To the north and northeast is an open area with several widely spaced tall trees 20 m or more from the tower. The trees at all of the locations are deciduous and in full leaf except for the trees to the west of tower 3, which are conifers.

Each tower was equipped with two R. M. Young Company 81000 ultrasonic anemometers. Wind vector and sonic temperature data were recorded at 10 Hz. The anemometer at 10 m was mounted above the tower and therefore the data are free from tower influences. The anemometer at 5 m was mounted on a boom extending more than 1 m south of the tower. Data from the 5-m instruments for northerly wind directions are subject to tower influence. Data subject to tower influence are included in the plots for completeness and comparison with other wind directions. All instruments were aligned to geographic cardinal directions, and their orientation was fixed throughout the duration of the experiment.

b. Basics of the data analysis

Because turbulence scales are smaller in the shallower nocturnal boundary layers than in larger convective layers, nighttime turbulence statistics are analyzed separately from daytime statistics. Based on multiresolution analyses of the data (Vickers and Mahrt 2003), daytime statistics are computed using deviations from the 10-min means, and nighttime turbulence statistics are computed using deviations from the 5-min means. The nonoverlapping half-hour mean values are then computed as the average of three contiguous daytime 10-min turbulent flux estimates or six contiguous nighttime 5-min flux estimates. For this paper, daytime is defined as 1400–2259 UTC and nighttime as 0300–1059 UTC. These times avoid the transition period right after sunrise, which ranges from 1118 to 1138 UTC over the month, and the transition at sunset, from 0149 to 0135 UTC. Solar noon was at about 1835 UTC throughout the month.

To eliminate mixed fetch conditions from the analysis, a 10-min (5 min) flux estimate is not used if its wind direction is highly variable as measured by the standard deviation of the wind direction in degrees. If the standard deviation of wind direction exceeded 60° during a segment, that 10-min (5 min) segment was not used. In addition, if the wind direction is too variable within a half hour, that half-hour average is not used, where the variability is measured using the standard deviation of the three (six) average wind directions associated with the 10-min (5 min) flux estimates. If the standard deviation exceeds 30° for any half hour, the averages for that half hour are not used in the analysis.

In addition to removing fixed fetch conditions, the wind direction variability criterion also removes much of the low–wind speed data, because high values of wind direction standard deviation correlate with low wind speeds. In addition, nearby obstacles tend to reduce wind speeds as well as increase wind direction standard deviation. The threshold of 60° was chosen to be high enough to retain most of the data with an upwind obstacle. Although there is a tendency for this criterion to reject low–wind speed data, it does not reject all low–wind speed data, especially at night. As an example, Table 2 gives the rejection statistics for low–wind speed data at tower 2. Turbulence parameters calculated from the rejected data are scattered over a wide range of values and seem to be randomly distributed relative to the retained data. The wind directions associated with the rejected data are fairly uniformly distributed, unlike the bulk of the data, which have predominantly south and southwest wind directions. The low–wind speed data (U ≤ 2 m s⁻¹) that are retained are indistinguishable from the rest of the retained data.

The prevailing wind direction for OKC in July is south to southwest. For the time period of JU2003, 80% of the data have wind directions between 150° and 240°. Some sectors have very little data, and, after eliminating variable wind direction conditions from the analysis, very few data points remain for some wind directions. Some towers have large gaps of missing data because of these factors.

Because of the complex nature of the urban environment, a planar tilt correction method is not applicable except at the relatively open tower-1 location (Klipp et al. 2004). For all of the analyses in this paper, tilt correction is done by setting V = W = 0 for each 10-min (5 min) segment. Before this rotation, u is the east–west component of the wind vector, υ is the north–south component, and w is the vertical component. After the rotation, u is the along-wind component, υ is the crosswind component, and w is the vertical component of the wind vector. All turbulent fluxes were computed using the rotated data. For the data from tower 1, a separate analysis was undertaken after using the planar tilt correction method outlined by Wilczak et al. (2001). The analyses for tower 1 using the planar tilt correction were nearly identical to those using the more traditional rotation.

Most 5-m turbulent flux values are not within 10% of the 10-m value at the same tower, even at the open tower-1 location (Table 3). This indicates that the 5-m instruments are not always in a constant flux layer. Some of the 10-m instruments may be in a constant-flux layer, but with no other measurement elevations with which to compare, identifying the location of a constant-flux layer is not possible. Surface-layer similarity is not expected to apply outside of the constant-flux layer.

a. Coefficient of drag

The coefficient of drag C_D (Figs. 2, 3), increases dramatically where a nearby obstruction is immediately upwind of an instrument. The coefficient of drag is defined as C_D = u²_*/U², where U is the vector mean wind and the full Reynolds stress vector is used for u_* = (² + ²)^1/4 because the vertical flux of lateral momentum usually does not vanish for these data (Weber 1999; Rotach 1993). Of all of the suburban towers, tower 1 is in a relatively open setting and shows relatively low values of C_D for all directions. Tower 3 shows increased C_D values due to the trees to the east and west, but there are insufficient data from the north to know whether the building there produces any significant change in measured drag values. Tower 4 also shows larger C_D values due to a small forested area to the northeast and a more subtle increase due to the school to the west-southwest.

The C_D values at the urban towers are larger than the suburban values. The tower-2 data show elevated C_D values except for the clear fetch region to the east. The nighttime values appear to be detailed enough to distinguish between individual buildings, with nearer buildings having larger C_D values than buildings farther away from the tower. Because of insufficient data, it cannot be determined whether the building to the west increases measured C_D values in a way that is comparable to the similar building to the north. At tower 5, the largest C_D values correspond to locations of the trees to the north and the tree to the southwest. The nighttime tower-5 data also show elevated C_D values to the southeast. The buildings to the south are all 5–6 m tall and either adjacent to each other or closely spaced. The elevated C_D values near 150° correspond to the location of a tree 10–12 m tall.

The buildings at tower 5, which are not as tall as the trees, correspond to C_D values that are smaller than those for the trees at that location but are larger than the C_D values measured at the open locations. The buildings at tower 2 have C_D values comparable to those corresponding to the trees at tower 5. Both the tower-2 buildings and the tower-5 trees are of similar height. From this, it is concluded that the height of an obstacle is very important whether the obstacle is a building or a tree. This result seems to be in conflict with the impression that buildings should be the primary source of roughness in an urban area (Oke 1995). Trees are a surprisingly large fraction of most urban areas, especially outside the immediate central high-rise district (Nowak et al. 1996). Although some studies have included trees in their analyses of urban morphology (Burian et al. 2005), little has been done to measure the effects of different urban forest types on the turbulence measured in cities. This could be one source of the differences found from one experiment to another. If the effect of the trees is comparable to the effect of buildings, then knowing more about these effects and their regional and seasonal differences could be very important to the characterization of urban turbulence.

The fact that comparable-height trees and buildings produce comparable measurements of C_D values also seems to be in conflict with the expectation that the nature of the turbulence created by these obstacles should be very different. An elevated value of C_D can be due to an elevated u_*, reduced U, or both. Because of the spread in measured values for both u_* and U that is typical in any field experiment, which of these is responsible for changes in C_D measurements can be difficult to discern. Because of the large sampling of surface types in this experiment, some broad qualitative conclusions are made possible by comparing the relative spread of the u_* and U measurements at the open tower-1 location to the corresponding spread in those values at the other locations. In general, u_* values downwind from buildings are either comparable to or slightly larger than open-fetch values and U values are reduced from open-fetch values. Downwind from trees, u_* values are comparable to or slightly smaller than open-fetch values while U values are greatly reduced relative to open-fetch values. Although trees and buildings result in similar increases in measured C_D values, the nature of the underlying turbulence is slightly different.

One location at which an upwind obstacle does not result in elevated C_D values is the 5-m level at tower 5. There is no difference in C_D values in that direction relative to nearby directions. The branches and leaves of the tree to the southwest of tower 5 extend to within 2 m of the ground, well below the 5-m instrument height. At both the 10- and 5-m levels, U is comparably reduced downwind of the tree while u_* values are greatly reduced at 5 m relative to 10-m u_* values. It is possible that the proximity of the vertical surfaces of the tree creates a situation in which the effective surface normal is not vertical, making the chosen coordinate system inadequate to calculate u_*.

b. Stability effects

The nighttime values for C_D are in general slightly lower than the corresponding daytime values except near some of the larger obstacles, where the nighttime values are slightly larger than the corresponding daytime values. No other effect due to stability is seen in the C_D analysis. This is because the stability was primarily near neutral throughout most of the field campaign. Ninety-five percent of daytime values for z/L = −(kzg/T)(/u³_*) were within the range −0.35 < z/L < 0, except for the 10-m instrument at tower 1 where 95% of the daytime values fell in the range −0.70 < z/L < 0. Nighttime stability at towers 1, 3, and 4 (suburban) were in the range 0 < z/L < 0.35. Nighttime heat fluxes at the urban towers were often upward throughout much of the night. The range of stabilities at tower 2 was −0.08 < z/L < 0.05, and at tower 5 the range was −0.07 < z/L < 0.07. No wind direction is associated with large or small values of z/L. Within the range of −0.5 < z/L < 0.1, differences in C_D are expected to be primarily from differences in surface roughness (Stull 1997). A lack of temperature profile data makes evaluation of the gradient Richardson number impossible.

c. Turbulence intensity

The turbulence intensity TKE/U², where TKE = ( + + )/2, shows directional variation similar to C_D (Fig. 4) with upwind obstacles resulting in elevated measured TKE/U² values. Because of the spread in measured values for TKE, it is not possible to discern, even qualitatively, whether there are differences between the TKE values downwind of trees and buildings. The mean wind is reduced downwind of both types of obstacles.

The 5-m TKE/U² data follow the 10-m data closely and so are not reproduced here. This includes the tower-5 data, where the tree to the southwest does produce elevated TKE/U² values at 5 m. This is consistent with the possibility that a change in coordinate system is adversely affecting the u_* calculation, because TKE values remain constant with a rotation in coordinates.

d. Scaled turbulence

By scaling the turbulent kinetic energy with u²_* instead of U², it can be seen that the ratio of TKE and u²_* is nearly constant as indicated in the plots in Figs. 5 and 6. One exception is in the vicinity of the large tree to the SW of tower 5. This discrepancy can be explained by the coordinate system problems for u_* calculations as noted above. The scatter in daytime TKE/u²_* values is attributable to the presence of additional TKE production by buoyancy. The scatter is larger for the suburban areas than for the urban areas probably because a larger proportion of the turbulence in the urban area is due to shear production. Nighttime scatter is similar for both types of locations and is less than daytime scatter. Most reported results give a value of about 5 for TKE/u²_* for stable and near-neutral conditions (Sorbjan 1989). This is a typical value for the nighttime JU2003 results. Average daytime values are larger because of the scatter, with 4.5–5.0 as the lower limit.

For convective conditions, Roth (2000) reports that the scaled standard deviations (σ_u/u_*, σ_υ/u_*, and σ_w/u_*) are proportional to (−z/L)^1/3 for −z/L > 0.1. A similar stability dependence is also found with the JU2003 data, but these results are suspect. In addition to the JU2003 data having very little data with −z/L > 0.1, self-correlation is a possibility because both the scaled variances and −z/L contain u_* in the denominator (Klipp and Mahrt 2004). Because the largest values of −z/L in this study correspond to very small values of u_* in the JU2003 data, it is highly probable that the computed values of the scaled variances and −z/L are being dominated by the common u_* term.

e. Proportion of TKE in the vertical and crosswind components

The ratios / and / (Figs. 7, 8) are measures of the isotropy of the turbulence. In purely isotropic turbulence, both of these ratios would be unity because all three components would contain an equal amount of energy (Choi and Lumley 2001). Near a surface, this does not hold, because the component normal to the surface becomes suppressed. This is seen in the / values of less than 0.5. The proportion of TKE in the vertical component is only slightly influenced by local obstructions, if at all. The measured values for / and / will change whenever there is a change in coordinate system.

The ratio of the cross-stream component of TKE to the streamwise component is larger in the daytime than at night. The daytime values of / exhibit large scatter at all of the tower sites, with most values falling in the range of 0.5–1.5 and occasionally surpassing 2.0. It is not clear what is responsible for the scatter in / values. Convection would be expected to affect the vertical component significantly but not the horizontal components. The tower-1 / values are randomly distributed with respect to wind direction. At the other towers, some wind directions show smaller average values for / as well as reduced scatter. Some of these directions correlate not with the nearby obstructions, but with directions to either side of obstructions. The reduced / values may also indicate regions in which persistent wind stream convergence alters the isotropy (Choi and Lumley 2001). The nighttime values of / show much less scatter and are usually less than 1.0. Smaller average values are also seen at towers 2, 3, 4, and 5 for some wind directions. These directions often coincide with the directions of reduced / during the day. The exceptions may be due to fine details being obscured by the larger daytime scatter. The relative amount of energy in each of the TKE components influences the dispersion of pollutants. These results hint at a more complex behavior in urban areas than many dispersion models currently incorporate.

f. Ejection–sweep relative fractions

Quadrant analysis has been used as a tool to characterize the large-scale structure of turbulence for several decades (Robinson 1991). The technique partitions the eddy correlation flux, in this case of momentum, into four quadrants based on the sign of the turbulent fluctuations. To calculate the ejection–sweep relative fraction, the contributions to the momentum flux () from updrafts of slower-moving surface fluid (quadrant 2; ejections) are subtracted from the contributions to the momentum flux due to downdrafts of faster fluid (quadrant 4; sweeps). The difference is then normalized by the total momentum flux to obtain the ejection–sweep relative fraction, ΔS. In most cases the contributions from quadrants 1 and 3 are small relative to the contributions from quadrants 2 and 4.

The wind-tunnel studies of Raupach (1981) and Krogstad et al. (1992) report ΔS to be a function of both the surface roughness and the measurement height scaled by the boundary layer depth. Near the surface, the contribution to the momentum flux due to sweeps is larger than the contribution due to ejections, making ΔS positive, except over smooth surfaces where the relative contributions are nearly equal or ejections contribute slightly more (ΔS slightly negative). Larger values of ΔS are reported over rougher surfaces at the same scaled height. This is consistent with quadrant analysis studies within forest canopies as well (Su et al. 1998). Because the boundary layers for OKC are usually very deep even at night relative to the 10- and 5-m instrument elevations, the scaled heights for this study are comparable to the lowest elevations reported in the wind-tunnel studies; thus, most of the differences in ΔS values are expected to be due to differences in the local roughness, with a small amount of scatter attributable to boundary layer depth differences. Although a function of surface roughness, measurements of ΔS may or may not be altered by local obstructions.

The plots of relative fraction ΔS versus wind direction (Figs. 9 –11) show little wind direction dependence overall. If the coherent structures studied by quadrant analysis are primarily driven by the large-scale eddies, then ΔS values might be driven more by large-scale roughness features than by the influence of single local obstructions. The CBD is 1.5 km to the east of tower 5, yet no significant difference in ΔS values is noted in that direction. The CBD is 1.0 km to the west of tower 2. Again, no significant difference is noted in ΔS values in that direction; however, the data are very sparse for winds from that direction.

The largest ΔS values occur in the direction of the nearby tree to the southwest of tower 5, especially at the 5-m level. The choice of coordinate directions for this wind direction at this instrument has already been questioned. Quadrant analysis of can be expected to be just as sensitive to the choice of coordinates as calculations of , if not more sensitive. The smallest ΔS values are seen to the southwest of tower 1 in the direction of the low trailer. This obstruction was not observed to alter the value of the other turbulence parameters, and it may be altering ΔS because quadrant analysis calculations are more sensitive to choice of coordinates than calculations. In this case, the mean streamwise direction may not be parallel to the surface, yet the choice of instrument tilt correction for this study forces the mean vertical wind always to be zero. The smaller ΔS values are also observed in the calculations using planar fit tilt-corrected data. The presence of the trailer violates the assumptions of the planar fit method, and it cannot be determined whether the trailer is altering the ΔS values or whether the coordinate directions have been poorly chosen. Other local obstruction effects on ΔS values are subtle in comparison with the scatter and may not be significant.

g. Displacement height and roughness length

The aerodynamic roughness length z₀ and the zero plane displacement D are defined by the logarithmic wind profile above the canopy. The presence of more, larger, or more densely spaced canopy elements will result in changes in the logarithmic wind profile and therefore different values of z₀ and D. Values for z₀ and D cannot be directly determined with this data because of insufficient wind profile information. Although values for z₀ and D can be calculated from building morphology, these values are a bulk description of the canopy for use above the canopy and are not adequate to describe the effect of single obstacles within the canopy.