Following the verification, the results are presented and discussed in this section.
4.1 Velocity results
The velocity results are analyzed to assess the stability of the measurements and understand the flow characteristics at different measurement positions.
Figure 7(a) presents the mean streamwise velocity of all measurement data at each position. The error bar means the STD of \(u\) measured across all dispersion cases. With the increase of \({z}_{m}\), \(\stackrel{}{u}\) gradually becomes larger, consistent with the expected tendency in the ABL profile. At the same height, deviations in mean values and STDs between different horizontal positions are limited. Compared to the inflow properties shown in Fig. 1, it is evident that the mean value decreases because of the effects of blocks, while the STDs approximately coincide with 0.15.
Figure 7(b) summarizes the mean and STDs of \(w\) measurements at each position. At all positions, the features of \(w\) barely change with the height. All mean values are positive and close to 0. Notice that \(\stackrel{}{w}\) in the profile in Fig. 1 is negative because the boundary layer starts to decay over the empty turntable, while \(\stackrel{}{w}\) here is positive, indicating a growing fetch. Part of the streamwise momentum has been transferred to the vertical and horizontal momentums by cubes. The STDs are consistent with the value in the inflow in Fig. 1 at different locations.
Figure 7(c) shows the mean values of the correlation coefficients \({R}_{uw}\) between \(u\) and \(w\) measured at each position. The error bar shows the STDs of \({R}_{uw}\) between different dispersion cases. \({R}_{uw}\) is nearly constant at each measurement position across all dispersion cases. The values of position (a) are smaller than others and below 0.35, which is a wellaccepted constant for a rough wall boundary layer (Cheng and Castro 2002). Because it is immersed in the separation flow of the roof, the turbulent characteristics of the boundary layer are highly destroyed. For the same reason, position (b) is in the row of blocks and is also affected. In these two positions, the momentum is mainly transferred by the bluff body separation flow and canyon vortex rather than the boundary layer. In contrast, in the row of the open street, positions (c) & (d) own the coefficients over 0.35, especially since the coefficients obtained the largest value at \({z}_{m} =0.75H\). This may result from a synergy of boundary layer effects and separation vortex caused by the side corners of blocks.
In general, the statistical results of velocity measurements are reasonable and steady through the dispersion cases for all sources.

Figure 7 Statistical results of measured velocities at each position for all dispersion cases. (a) streamwise velocity; (b) vertical velocity; (c) Correlation coefficients of streamwise and vertical velocities. 
4.2 Evaluation method of flux
The vertical flux is calculated based on the simultaneous samplings of velocities and concentrations. However, due to the inevitable distance between the tube header of FFID and Xprobe, their time series signals are not perfectly synchronized. Besides, it is also necessary to take the suction and burning process of the FFID system into consideration, which means that the concentration signals should lag the velocities. It is critical to correct this time lag \(\tau\) to accurately evaluate the turbulent flux by the following equation.
$$\stackrel{}{w{\prime }c{\prime }} = \frac{1}{T\tau }\underset{0}{\overset{T\tau }{\int }}w{\prime }\left(t\right)c{\prime }\left(t+\tau \right)dt$$
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Here, \(T=90 \text{s}\) is the length of the time series.
This study identifies \(\tau\) as the value corresponding to the peak in the correlation coefficient curve between \(w\) and \(c\), which is found to be effective by Marro et al. (2020). To promise that the measurements of velocities and concentrations represent the same fluid element, \(\tau\) is determined in the range of 0.2 s to 0.2 s. The identified \(\tau\) for each measurement is presented in Fig. 8. Most of values distribute between 0.04 s to 0.06 s, except for several sources (No. 1, 16, 17, 18, 30, 31, 33) located at the edge in the spanwise direction or just below the measurement position (Fig. 2). Concentration measurement for these sources is challenging, and intrinsic time lag information is mixed with other noises, causing the peak not to appear in the correlation function. While time lags for other sources vary, fluctuations are minimal. As a result, the time lag is fixed as the averaged value \(\tau =0.05s\) after removing abnormal sources’ values.

Figure 8 Identified time lag between the vertical velocity and concentration signals at each measurement position during the dispersion of each source. 
4.3 Concentration footprint
Figure 9 shows the measured concentration footprint distributions for different measurement positions, revealing pronounced heterogeneity induced by varying measurement positions. Two distinct patterns emerge in the footprints.
In the first pattern, because positions (a) & (b) lie in the row of blocks, several secondary peaks are produced in the wakes upstream. Most of the footprint concentrates along with the central row of blocks. For “a_1.25H”, the peak appears at the wake just in front of the sensor with the distance of H. For “b_1.25H”, the peak moves to 2H upstream because there is a block in front of it. When \({z}_{m}\) increases to 1.5H, the distribution becomes flatter to distinguish the peak. Notice that the peak regions for positions (a) & (b) are shorter than those of (c) & (d), especially when \({z}_{m}=1.25H\). It indicates that (a) & (b) are more sensitive to the sources nearby. Due to the existence of the canopy vortex, the pollutants emitted in the wakes far upstream are quickly elevated and disperse above the sensors, diminishing their impact on the concentrations of position (a) & (b).
The second pattern occurs in positions (c) & (d), which are located above the open street between cubes. No matter what \({z}_{m}\) is, there is only one dominant peak and the extension along the open street is long due to the absence of roughness in front of the sensor. The pollutant can easily pass through the open street even if it is emitted far away. The footprint functions for these positions share similarities in terms of peak position, value, and spanwise width.

Figure 9 The concentration footprint of each measurement position. The red circle is the sensor location. 
A common feature across all horizontal positions is that with the increasing of \({z}_{m}\), the footprint function becomes flatter with smaller peak values and wider extension. The distance between the sensor and the peak value also expands.
4.4 Turbulent flux footprint
Figure 10 illustrates the footprint distributions of turbulent flux \(\stackrel{}{w{\prime }c{\prime }}\) for all measurement positions. The source area of the turbulent flux is much smaller than that of the concentration. Owing to the gradual homogenization of the concentration field during dispersion, when the source is far away from the sensor, the spatial gradient is diminished such that the turbulent fluctuations cannot result in extra mass flux at the sensor.
The two distinct patterns recognized in the concentration footprint persist. It is interesting to notice that positions (a) & (b) are so strongly affected by the emission from the first wake region upstream that the peak location even does not change with \({z}_{m}\). The main source areas are constrained within 8H along the streamwise direction. However, the source areas for (c) & (d) are much larger. When \({z}_{m}=0.75H\), the streamwise extension is over 10H, which surpasses those at (a) & (b) when \({z}_{m}=1.25H\). Besides, the peak properties of (c) & (d) exhibit similar trends of change in response to \({z}_{m}\) as the concentration footprint. The reason for this phenomenon is that the mean velocities and concentrations along the open street are not significantly mixed by cubes as the wake regions and keep vertical stratification. Turbulent fluctuations can promote the mixture of concentration fields even if the source is far away.

Figure 10 The turbulent flux footprint of each measurement position. The red circle is the sensor location. 
4.4 Total flux footprint
Because \(\stackrel{}{w}\) is almost unchanged across dispersion cases according to Fig. 7, the mean flux footprint \(\stackrel{}{w}\stackrel{}{c}\) almost has the same distribution as the concentration footprint. Therefore, its result is not presented here. Instead, the total flux footprints \((\stackrel{}{w}\stackrel{}{c}+\stackrel{}{{w}^{{\prime }}{c}^{{\prime }}})\) are summarized in Fig. 11.
Analogous characteristics as the concentration footprint can still be found in the total flux footprint. As \({z}_{m}\) increments, the footprint function has a broader range with modest values. The peak becomes flatter and further away from the sensor. Furthermore, the footprints for all positions mainly gather around the central row where the sensor is located. The streamwise length of the total flux footprints extends beyond that of the turbulent flux footprints due to the added mean flux \(\stackrel{}{w}\stackrel{}{c}\). The streamwise length is limited by the cubes at positions (a) & (b) while they reach longer along the open street at (c) & (d). However, the spanwise margins of total flux and turbulent flux footprints are similar, which are about H. This may indicate that the primary influence of sources situated at a certain distance along the yaxis is predominantly exerted by turbulent flux.

Figure 11 The total flux footprint of each measurement position. The red circle is the sensor location. 
Because the total flux is a combination of turbulent contributions and mean flow contributions, to discern the respective influences on the total flux measurements, the turbulent ratio \(r\) for each source’s dispersion was calculated at all measurement positions.
$$r = \frac{\stackrel{}{{w}^{{\prime }}{c}^{{\prime }}}}{\stackrel{}{w}\stackrel{}{c}+\stackrel{}{{w}^{{\prime }}{c}^{{\prime }}}}$$
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The results are demonstrated in Fig. 12. A shared feature emerges wherein the turbulent ratios of far sources exhibit smaller scales compared to those near the sensor, which is consistent with the limited source areas of turbulent footprint functions in Fig. 10. It can be noticed that the largest value of each sensor mainly occurs at the place where the flux footprint’s peak is located at. Almost 70% flux is contributed by the turbulence, so accurate modeling of turbulent dispersion is significant to the numerical methods for footprint functions. Besides, with the increase in measurement height, the turbulent contributions of most sources also amplify. A sensor situated at a high place is insensitive to the mean flux of ground emissions. The pollution it measured is transported by the boundary layer turbulence.
Among all results, “a_1.25H” owns the smallest turbulent ratios because it is in the separation layer above the cube. The mean flow has dominant effects on scalar transportation. As a result, when the sensor is deployed on the roof, the effects of the surrounding flow of the building on the flux footprint are unignorable.
Nevertheless, it should be admitted that the turbulent ratio inside the total flux is possibly underestimated in this study. Our experimental subject is an idealized neighborhood encountering a designed incident flow rather than a scenario with a welldeveloped boundary layer featuring infinitely arranged cubes. Although the measured \(\stackrel{}{w}\) is in proximity to 0 as shown in Fig. 7, residual positive values still exist while \(\stackrel{}{w}\) in a welldeveloped boundary layer should be completely 0. This occurrence arises from the finite size of the urban canopy model in our experiment, leading to the ongoing growth of fetch at the measurement positions. Consequently, the mean flux still contributes approximately 50% to the total value according to Fig. 12. In the real application, especially in cases where the boundary layer is spatially steady, the flux footprint can be estimated only by measuring the turbulent flux.

Figure 12 The contribution ratio of turbulent flux to total flux for each source at each measurement position. (The red circle is the sensor location) 
4.5 Comparison to KM plume model
Until now, the KM plume model (Kormann and Meixner 2001) remains widely used to calculate the footprint function for the sensors deployed in urban areas because of its computational cheapness. However, the estimation accuracy is skeptical because it ignores the horizontal turbulent diffusion. In light of this, we compared our measured flux footprint to KM modeling results to reveal its limitations in urban application.
To calculate the KM flux footprints under neutral stability, the Obuklov length was set as \({10}^{5} m\). All three measurement heights \({z}_{m} =0.75H, 1.25H, 1.5H\) were considered. Because we did not measure the friction stress on the bottom surface, the friction speed \({u}^{*}\) and the roughness length \({z}_{0}\) were determined by the empirical equation provided by Cheng and Castro (2002) as follows.
$${u}^{*}=0.07{U}_{\infty }$$
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Here, \({U}_{\infty }\) is the free stream velocity above the boundary layer. The von Kármán constant is 0.41. The \(\stackrel{}{u}\) and the STDs of \(v\) at each \({z}_{m}\) were imposed as the average values of measurements across all measurement positions at that height.
The comparisons between KM models and measurements at different \({z}_{m}\) are shown in Figs. 13 ~ 15. The solid line denotes the 10% contour of the flux footprint, which well represents the peak region. The dotted line signifies the 50% contour of the flux footprint, which is the main body of the function in this paper because our measurements only cover about 70% at \({z}_{m} =1.25H, 1.5H\). Notice that the percentage contour evaluation is based on the integration of the interpolated results of discrete measurements, and the footprint values inside cubes are regarded as 0 in the plots. In each figure, the coordinate is adjusted to place the sensor at the axis origin.
When \({z}_{m}=0.75H\), only positions (c) & (d) were measured. The comparison reveals that the measured footprint extends as long as the KM model in the streamwise direction including the peak region. However, the measured footprints become irregular due to the existence of cubes. They also distribute along the central open street with a smaller spanwise length than the KM model because the spanwise dispersion is hindered by the separation flow of the building’s side.
When \({z}_{m}=1.25H\), it can be observed that the peak locations of (a) & (b) are about 2H closer to the sensor than the KM model. Normally, the tracer emitted from the source just in front of the sensor cannot be transported to the measurement height so quickly in the open land. However, the canyon vortex and separation flow elevate the tracer gas in the wake region, resulting in this deviation. Concerning the main body with 50% contour, footprints of (a) & (b) are limited within about 4H in the spanwise direction, merely half of what the KM model predicts. The footprints of (c) & (d) even gather around the central open street only. Across all measurement positions, the spanwise dispersion is considerably blocked by the row of cubes. Meanwhile, the wind pass between rows of cubes advances the transportation of pollutants, so the measured footprints tend to develop along the streamwise direction. The difference between measurement positions and the KM model underscores the inherent heterogeneity of the footprint functions in the urban area.

Figure 13 The percentage contours of the flux footprints at \({z}_{m} =0.75H\). The solid line is 10% contour, and the dotted line is 50% contour. 

Figure 14 The percentage contours of the flux footprints at \({z}_{m} =1.25H\). The solid line is 10% contour, and the dotted line is 50% contour. 
When \({z}_{m}=1.5H\), the 50% contour of the KM model keeps the same shape as observed at \({z}_{m}=1.25H\) but the peak region becomes notably larger. In our measurements, the appearance of several secondary peaks in positions (a) & (b) show higher complexity than the numerical results. This may result from the existence of cubes, measurement noise, and numerical errors introduced by the interpolation process. Despite that, it is apparent that the peak regions of measured footprints have much more irregular patterns than those predicted by the KM model. The distance between the peak and the sensor remains short at positions (a) & (b) as discussed above. Because the measurement position becomes higher, the blocking effects of cubes on the dispersion can be overcome with sufficient turbulent transportation. Thereby, the most recognizable transitions at positions (c) & (d) is that the spanwise width increased to 4H, which aligns closely with those of (a) & (b) and half of the KM model. However, the spanwise expansion at positions (a) & (b) remains limited when compared to \({z}_{m}=1.25H\). This suggests that the effects of building configurations on the monitoring of sensors located in the roughness sublayer cannot be ignored.

Figure 15 The percentage contours of the flux footprints at \({z}_{m} =1.5H\). The solid line is 10% contour, and the dotted line is 50% contour. 
4.6 Discussions
Based on the results above, implications for realworld applications are discussed here. When sensors are employed to monitor the vertical transportation of anthropogenic emissions into the atmosphere, the deployment positions need careful consideration. The inhomogeneous footprints as shown above emphasize that the measurement positions may significantly affect the source area and, consequently, the measurement efficiency of the sensor. Practically, monitoring stations are usually located on the rooftops of tall buildings for convenience. However, as indicated by the experimental results for position (a), it is crucial to make sure that the sensor is free from the influence of separation flows induced by the building’s roof. Otherwise, the measurable domain may be limited to the adjacent areas.
The largest measurement height in this study is limited to 1.5H due to the experimental constraints. The footprint function still remarkably relies on the building configurations of the urban model according to the results. The expected homogenous footprint has failed to be found at least at this height. In common, the sensor footprint is desired to be independent of the surrounding buildings for easier control of the monitoring domain and more straightforward modeling of complex turbulent dispersion in numerical simulations. For this aim, it is suggested that the measurement height exceeds at least twice the nominal height of the monitoring area, corresponding to the depth of the roughness sublayer as proposed in the literature (Cheng and Castro 2002). Notice that this threshold is derived from the experimental results for an ideal urban boundary layer, and the actual safe value for real neighborhoods may be higher and more diverse.
Unfortunately, achieving longterm monitoring over the roughness sublayer of the urban areas may be challenging. The tower structures are beneficial, but the cost and land use problems remain unresolved. In other words, it is inevitable to deploy sensors immersed into the sublayer, where the footprints are dependent on the building configurations. In such cases, the analytical plume model like the KM method may fail to properly estimate the footprint functions. The application of numerical methods, capable of reproducing complex turbulent diffusion through CFD models, becomes necessary.