Wind tunnel experiment on the footprint of a block-arrayed urban model in a neutrally stratified boundary layer

doi:10.21203/rs.3.rs-3942292/v1

Download PDF

Research Article

Wind tunnel experiment on the footprint of a block-arrayed urban model in a neutrally stratified boundary layer

https://doi.org/10.21203/rs.3.rs-3942292/v1

This work is licensed under a CC BY 4.0 License

Journal Publication

published 17 Oct, 2024

Read the published version in Boundary-Layer Meteorology →

You are reading this latest preprint version

This study addresses the need to investigate footprint function features in urban areas and establish a validation database for numerical methods. Concentration and its flux footprints of a block-arrayed urban model were measured in a wind tunnel with a neutrally stratified boundary layer. The velocity and concentration were simultaneously measured by an X-probe hot wire anemometer and a fast-response flame ionization detector to evaluate the vertical flux. Experimental results highlighted the influence of the measurement heights on footprint distributions. Because the sensors were immersed in the roughness sublayer, their footprints showed strong heterogeneity across horizontal positions caused by building configurations. It was found that turbulent flux contributes up to 70% of total flux footprints, emphasizing the importance of accurate turbulent dispersion estimation in numerical methods. Furthermore, measured footprints were compared to those modeled by a widely used analytical method (Kormann and Meixner in Boundary-Layer Meteorol 99:207–224, 2001, https://doi.org/10.1023/A:1018991015119). The measured footprints extended further along the streamwise direction and their spanwise dispersions were constrained by the rows of blocks, which failed to be reproduced in the analytical method. This indicates the significant effects of building configurations on footprint functions in urban areas.

Footprint function

Wind tunnel experiment

Concentration flux measurement

Urban canopy model

Pollutant dispersion

Serving as the bedrock of data acquisition in atmosphere environment monitoring, sensors have been widely deployed worldwide to measure the concentration and flux of pollutants. Because the collected data is an integrated product of all potential upwind sources, it is necessary to elucidate the spatial coverage of the sensor device and scrutinize the predominant source areas during the measurement. To address this need, the concept of a footprint was introduced, offering a framework to articulate the response function between sensors and sources (Schuepp et al. 1990).

Although footprint is a frequently underestimated factor in the realm of sensing technology, understanding a sensor’s footprint is imperative for several applications. Firstly, a precise comprehension of the footprint function is essential to analyze the representativeness of the measurement data. Sugawara et al. (2021) observed changes in anthropogenic CO₂ concentration data at a measurement station in the residential area of Tokyo during the State of Emergency due to COVID-19. With the help of the sensor footprint, they demonstrated that the change was attributed to residents’ stay-at-home activities during the emergency. Secondly, the footprint function is a fundamental element in source term estimation. The unknown source’s information can be inferred by combining the footprint with inference methods. For instance, Lauvaux et al. (2016) estimated the distribution of CO₂ emission strength in Indianapolis based on a sensor network, footprint modeling, and the Bayesian inversion method. Serving as the source-sensor relationship, the concentration footprint is extensively employed to identify unknown single sources in urban environments (Jia and Kikumoto 2021a, b; Wang et al. 2022). Thirdly, the footprint function reflects the measurement effectiveness of sensor network systems, enabling the designing and evaluation of the monitoring strategy and systems. Utilizing the footprints of each sensor, Levin et al. (2020) designed a dedicated flask-sampling strategy for the Integrated Carbon Observation System across Europe. Jia and Kikumoto (2022) proposed a method to design the sensor network for source term estimation based on the information entropy of the concentration footprint.

Due to the benefits brought by the footprint function, several numerical methods have been proposed to model it in the literature. In the early phases, analytical solutions were formulated by introducing assumptions and approximations to the advection-diffusion equation (Schuepp et al. 1990; Horst and Weil 1992; Hsieh et al. 2000; Kormann and Meixner 2001).

Afterward, Kljun et al. (2002, 2004) proposed to model the footprint function based on the Lagrangian tracer method. This methodology involves the emission of numerous scalar particles either from the source area (forward mode) or the sensor volume (inverse mode) into the turbulent flow field, which is characterized by a one-point probability distribution. Subsequent research drove the scalar particles by advanced computational fluid dynamics (CFD) models like large-eddy simulations (LES). The refined footprint function was modeled by this enhanced method for the ABL (Glazunov et al. 2016), urban canopy model (Hellsten et al. 2015), and actual urban areas (Auvinen et al. 2017).

Meanwhile, the footprint function can also be modeled in the Eulerian framework. Sogachev et al. (2002) and Sogachev and Lloyd (2004) pioneered the Eulerian simulation method for footprint, where the dispersion field of each surface cell needs to be calculated. Jia and Kikumoto (2023) proposed to simulate the footprint function in the backward mode based on the adjoint equation, which only needs to resolve the concentration distribution of hypothetical tracer scalars emitted from the sensor.

Despite the proliferation of these numerical methods, it is crucial to acknowledge that their comprehensive validation remains a challenge due to the lack of database from experiments or field tests. According to the authors’ knowledge, previous research that measured the footprint distribution is quite sparse. Heidbach et al. (2017) conducted tracer experiments at a grassland site in Germany to assess the flux contributions from sources. They evaluated the analytical models and Lagrangian models with their dataset and revealed that these methods tend to underestimate the footprint maximum and overestimate the distance. Similarly, Kumari et al. (2020) conducted an artificial tracer experiment with CO₂ gas in an open land in India. It was claimed that although the Kormann-Meixner (K-M) model (Kormann and Meixner 2001) agrees well with the measurements, the model-to-measurements discrepancies were still high under heterogeneous conditions. Both of these experiments were conducted in outdoor open areas, potentially limiting their generality in validations for numerical methods. Unsteady and uncontrollable meteorological conditions (ABL stabilities, wind speed, wind direction, etc.) in outdoor settings introduce significant measurement noise into the final results. Moreover, databases based on open lands are more suitable for the footprint evaluation in agricultural applications within rural areas. It is necessary to build up a footprint database corresponding to urban areas for the comprehensive validation of numerical models under complex dispersion scenarios. However, conducting dispersion field tests in busy metropolitan districts poses significantly greater challenges compared to open land experiments.

Another widely adopted experimental technique for studying atmospheric dispersion is the wind tunnel, where the wind conditions are controlled, and intricate target models are tractable by proper scaling based on Reynolds independence (Snyder 1981; Fedorovich 2004; Ahmad et al. 2005). These advantages have made wind tunnel experiments (WTE) a valuable tool for exploring the dispersion mechanisms of pollutants in urban environments, leading to the development of benchmark databases. Most of classical WTE databases measured the velocity and concentration separately, but vertical flux measurement is indispensable to the flux footprint. In recent years, researchers have increasingly reported experimental methods for flux measurements.

Di Bernardino et al. (2018) explored the pollutant flux inside a two-dimensional street canyon caused by a line source by particle image velocimetry (PIV). They also applied the same technique to measure the flux above the three-dimensional cubic blocks to estimate the turbulent Schimdt number. Nosek et al. (2018) measured pollutant fluxes at the top and lateral opening of the street canyons by a laser Doppler anemometry (LDA) and a fast-response flame ionization detector (FFID). They used the experimental data to validate a LES simulation and further analyze the ventilation mechanism of the street canyon based on simulations. Marucci and Carpentieri (2019) analyzed the effects of stably stratified ABL and wall heating on the flow and dispersion in a two-dimensional street canyon by measuring the velocities, concentrations, temperatures, and fluxes with LDA and FFID. Iacobello et al. (2019) investigated the dynamics of passive scalar dispersion in a turbulent boundary layer by a X-probe hot-wire anemometer (HWA) and FFID. Marro et al. (2020) testified the reliability of flux measurements based on systems coupling LDA or a X-probe HWA with FFID. Their results confirmed that these two systems can yield good agreement provided the distance between two instruments and time lags are well configured. This evidence supports the feasibility of concentration and flux measurements for an urban model through WTE. However, the majority of these studies have primarily focused on single-source measurements. The exploration of source-receptor relationships with different source locations, or the footprint characteristics in the urban ABL, remains largely uncharted territory.

To fill this gap, we conducted a wind tunnel experiment on the footprints of a block-arrayed urban model within a neutrally stratified ABL. The velocity, concentration, and flux were simultaneously measured by a X-probe HWA and FFID. Our objective is to establish a comprehensive validation database for the numerical modeling of footprints in urban areas. Moreover, the experimental results can also deepen the insights into the footprint characteristics and dispersion mechanisms of sources immersed in the urban ABL.

The remainder of the paper is as follows. Section 2 introduces the definition of the footprint function, the measurement techniques, and the arrangements of the WTE. Then, we validate the measurement technique by replicating two existing experimental databases in Section 3. Section 4 demonstrates the results of the concentration and flux footprints of the urban model. Additionally, we analyze the turbulent contribution to the overall flux transportation at each measurement position. The obtained footprint distributions are compared to the K-M analytical model. Section 5 is the concluding remarks.

2.1 Definition of the Footprint Function

First of all, we introduce the definition of the footprint function (Schmid 2002).

$$\eta \left({\varvec{x}}_{\text{m}}\right) = \underset{\mathcal{S}}{\overset{}{\int }}f\left({\varvec{\chi }}_{\text{m}}|\varvec{x}\right){q}_{s}\left(\varvec{x}\right)d\varvec{x}$$

Here, $\mathcal{S}$ is the target surface where potential sources may appear. $\varvec{x}$ is a two-dimensional coordinate system for $\mathcal{S}$. ${\varvec{\chi }}_{\text{m}}$ is the coordinate of the sensor in a three-dimensional domain. ${q}_{s}\left(\varvec{x}\right)$ ($\text{g}\bullet {\text{m}}^{-2}\bullet {\text{s}}^{-1}$) is the strength of the source or sink at each location. $\eta \left({\varvec{\chi }}_{\text{m}}\right)$ is the measured quantity at the sensor, which can be either concentration ($\text{g}\bullet {\text{m}}^{-3}$) or flux ($\text{g}\bullet {\text{m}}^{-2}\bullet {\text{s}}^{-1}$). $f\left({\varvec{\chi }}_{\text{m}}|\varvec{x}\right)$ represents the footprint function (concentration or vertical concentration flux) of the sensor at ${\varvec{\chi }}_{\text{m}}$. In terms of mass concentration units set, the concentration footprint and flux footprint have units of ($\text{s}\bullet {\text{m}}^{-3}$) and (${\text{m}}^{-2}$) respectively.

In the WTE, if the jet size of a single point source is infinitely small compared to the size of the target surface, the strength distribution function at each dispersion case can be approximated as a spike function.

$${q}_{s}\left(\varvec{x}\right)={Q}_{0}\delta \left(\varvec{x}-{\varvec{x}}_{s}\right)$$

${Q}_{0}$ ($\text{g}\bullet {\text{s}}^{-1}$) is the emission strength of the source. $\delta$(${\text{m}}^{-2}$) is the Dirac delta function. ${\varvec{x}}_{s}$ is the coordinate of the source for each dispersion case. In this case, Eq. (1) can be written as:

$$\eta \left({\varvec{\chi }}_{m}\right)= \underset{\mathcal{S}}{\overset{}{\int }}f\left({\varvec{\chi }}_{m}\left|\varvec{x}\right.\right){Q}_{0}\delta \left(\varvec{x}-{\varvec{x}}_{s}\right)d\varvec{x}={Q}_{0}f\left({\varvec{\chi }}_{m}\left|{\varvec{x}}_{s}\right.\right)$$

$$f\left({\varvec{\chi }}_{\text{m}}\left|{\varvec{x}}_{\text{s}}\right.\right)=\frac{\eta \left({\varvec{\chi }}_{\text{m}}\right)}{{Q}_{0}}$$

According to Eq. (4), the footprint function can be obtained by normalizing the measurements based on ${Q}_{0}$. This relationship was used in this study to measure both concentration and flux footprints.

2.2 Description of the Wind Tunnel Experiment

The wind tunnel experiment was operated in the boundary layer wind tunnel at the Institute of Industrial Science, the University of Tokyo. The test section of the wind tunnel is $1.8m\left(\text{h}\text{e}\text{i}\text{g}\text{h}\text{t}\right)\times 2.2m\left(\text{w}\text{i}\text{d}\text{t}\text{h}\right)\times 16.47m\left(\text{l}\text{e}\text{n}\text{g}\text{t}\text{h}\right)$. To generate the ABL with neutral stratification, spires and roughness cubes were placed in the upstream. Figure 1 shows the incident flow profiles of mean streamwise ($\stackrel{-}{u}$) and vertical ($\stackrel{-}{w}$) velocities measured in the middle of the empty turntable where the urban model is arranged afterward. $\stackrel{-}{u}$ followed the power law with an index of 0.22. The averaged streamwise velocity at the reference height ${Z}_{ref}=0.2 m$ was defined as the reference speed ${U}_{ref}=1.79 m/s$.


Figure 1 Inflow profiles used in the wind tunnel experiment.

The urban canopy model was formed by uniformly distributed cubes, which is a common setting in previous research on urban wind environments (Cheng and Castro 2002; Coceal et al. 2007; Wang and Okaze 2022). The model consists of 11 rows $\times$ 9 columns cubes with an edge length of $H=0.06m$ as shown in Figs. 2 & 3(a). The Reynolds number based on ${U}_{ref}$ and $H$ is approximately $7.2\times {10}^{3}$.


Figure 2 The configurations of blocks, sources, and measurement positions in the wind tunnel experiment

The concentration and vertical flux footprints are measured at 10 positions in total comprising 4 different horizontal positions and 3 different heights. Given the features of the current urban model, 4 horizontal positions are: above the roof (a), wake region (b), the cross-section (c), and the road between the buildings (d) as depicted in Fig. 2. Because the measurement height is a key factor to the footprint distribution, three heights are selected: ${z}_{m} =0.75H, 1.25H, 1.5H$. It should be noted that there is no ${z}_{m} =0.75H$ at position (a), and the vertical velocity fluctuations below the block ($z<H$) in the wake region cannot be accurately recorded by X-probe (standard $\pm 45^\circ$ wires). Thereby, ${z}_{m} =0.75H$ for positions (a) & (b) are not measured. Meanwhile, all three heights are still in the roughness sublayer of the block, where the flow is highly influenced by the block element and exhibits spatial inhomogeneity. The reason that no higher positions were measured is that the tracer gas disperses quickly in the upper stream, making meaningful concentration data difficult to capture.

Because the footprint function describes the relationship between a fixed sensor and different sources, the source is designed to be a mobile bronze tube with an upward circular opening having a diameter $d=1 mm$ as shown in Fig. 3(b). In contrast to conventional dispersion experiments, the source is tightly taped on the floor at an emission position during one dispersion case and then relocated to another. The distribution of all 36 emission positions is shown in Fig. 2. The pure ethylene (C₂H₄) is used as the tracer gas with the volume rate of ${Q}_{s}=6.4\times {10}^{-7}{m}^{3}/s$.


Figure 3 Image of the wind tunnel experiment. (a) the block-arrayed urban model; (b) the moveable source tube; (c) the settings of the X-probe and FID tube

During the experiment, the velocities (u, w) and the concentration (c) were measured simultaneously by a X-probe HWA (55P61, Dantec) and a FFID system. $9\times {10}^{4}$ sampling data (90 s) was recorded with 1000 Hz for each measurement point. The voltage data from three channels were logged as 16-bits signals by a NI-9215 connector (National Instruments) and processed with LabVIEW. To estimate the vertical flux, the probe and tube header of FFID were placed close to each other as shown in Fig. 3(c). Care was taken to ensure that the suction behavior of the FFID tube did not contaminate the velocity signals. The detailed estimation method for vertical flux is introduced in Section 4.

Because the flux measurement is one of the most challenging techniques in the wind tunnel, we first verify our measurement system’s reliability by reproducing two WTEs with open database.

3.1 Comparison with AIJ database

The first database is a point-source dispersion in a cube arrays model, provided by the Architectural Institute of Japan (AIJ). The size and configuration of cube elements are the same as the one in Section 2.2. However, the incident flow profile of the database has a larger power law index (about 0.31) than our wind tunnel. One point source of tracer gas is set on the bottom surface behind a block, marked as a red star in Fig. 4. Further details about the database can be found in Case K with the link: https://www.aij.or.jp/jpn/publish/cfdguide/.


Figure 4 Distribution of the pollutant source and measurement positions. Only 3 rows of blocks are shown here.

In the verification, we reproduced the measurements at 15 positions as shown in Fig. 4. All points are in the horizontal plane at a height of $7H/6$. Because the velocities and concentrations were separately measured in the AIJ database, we can only compare the mean values and standard deviations (STDs). The velocities results are nondimensionalized by ${U}_{ref}$, and the concentration results are nondimensionalized by ${C}_{gas}{Q}_{s}/\left({U}_{ref}{{Z}_{ref}}^{2}\right)$. Here, ${C}_{gas}$ is the concentration of the jet flow emitted from the source.

The comparison results are summarized in Fig. 5. The error bar means the standard deviation. It can be confirmed that the $\stackrel{-}{u}$ in this paper is slightly higher than AIJ because our power law index is smaller. $\stackrel{-}{w}$ agrees well with AIJ, with all values near 0, and the limited deviation may result from measurement noise. Additionally, the STDs of the two velocity components are almost the same, which is reasonable because the dominant fluctuations are caused by the roughness elements at this measurement height. Regarding concentration, the averaged values of all points agree well with each other. Although the STDs in this study are higher than those of AIJ, they are still in the same order of magnitude. One possible reason is that our FID equipment is newer with higher sampling frequency. In general, it can be concluded that our measurement system, which measures velocities and concentrations simultaneously, achieves a similar level of accuracy as a system that measures them separately.


Figure 5 Comparisons of measurements between AIJ and this study. (a) the streamwise velocity; (b) the vertical velocity; (c) the concentration. The error bar is the standard deviation.

3.2 Flux measurements for a passive scalar dispersion in a boundary layer

Because there is no flux measurement in the AIJ database in Section 3.1, we referred to another paper (Iacobello et al. 2019) to verify the reliability of our system’s flux measurement. This literature discussed the meandering behavior during the turbulent transport of a passive scalar emitted from an elevated source in a boundary layer. Because the length scales of eddies are larger than the plume size in the early stage of dispersion, the dynamics of the plume are governed not only by the spreading but also by the meandering, where the vertical turbulent flux is positive above the central axis of the plume and negative below the axis. We testified whether our system with HWA and FFID can capture this trend.

The boundary layer was generated in the same wind tunnel introduced in Section 2. with roughness cubes of 0.03 m height uniformly placed on the floor. The resultant turbulent boundary layer had a thickness $\delta \approx 1 m$ and a free stream velocity ${U}_{\infty }=2.4 m/s$. The tracer gas C₂H₄ was emitted in the streamwise direction from a metal L-shape tube with a diameter of 6 mm. The jet opening was elevated to the height of $0.24\delta$. The vertical profile for the turbulent vertical flux of the tracer was measured at $x=0.15\delta$. Note that scales of the ABL and measurement position here are different from those in the literature because the size of our wind tunnel is much larger than theirs (the size of cross-section is about 5.6 times larger). It is difficult to sample the concentration data if we completely reproduced their experimental settings. However, because the existence of meandering is independent of the ABL size, the objective of the verification is to measure the meandering behaviors rather than completely replicating their results.

The vertical profiles of the turbulent flux are compared in Fig. 6. The velocities results are nondimensionalized by ${U}_{\infty }$, and the concentration results are nondimensionalized by ${C}_{gas}{Q}_{s}/\left({U}_{\infty }{\delta }^{2}\right)$. The meandering behavior of the plume was successfully measured by the system, with the vertical fluxes showing antisymmetry along the central axis. The curve shape of the profile agrees well with that of the literature. Although the magnitudes are also close, it should be mentioned that this is coincidental due to different ABL settings. Because the measurement position is closer to the source in our experiment, it is reasonable to notice that the vertical length scale of the plume (about $0.1\delta$) is smaller than that of the literature (about $0.16\delta$). Despite these differences, the system effectively captured the representative flux of the meandering, establishing the reliability of the measurement system used in this paper.


Figure 6 Vertical profiles of turbulent flux in the vertical direction measured in this study (at $x=0.15\delta$) and the literature (at $x=0.325\delta$).

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 well-accepted 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 X-probe, 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.

$$\stackrel{-}{w{\prime }c{\prime }} = \frac{1}{T-\tau }\underset{0}{\overset{T-\tau }{\int }}w{\prime }\left(t\right)c{\prime }\left(t+\tau \right)dt$$

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 y-axis 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.

$$r = \frac{\stackrel{-}{{w}^{{\prime }}{c}^{{\prime }}}}{\stackrel{-}{w}\stackrel{-}{c}+\stackrel{-}{{w}^{{\prime }}{c}^{{\prime }}}}$$

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 well-developed 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 well-developed 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 K-M plume model

Until now, the K-M 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 K-M modeling results to reveal its limitations in urban application.

To calculate the K-M 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.

$${u}^{*}=0.07{U}_{\infty }$$

$${z}_{0}=0.053H$$

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 K-M 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 K-M 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 K-M 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 K-M 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 K-M 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 K-M 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 K-M 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 K-M 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 K-M 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 real-world 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 long-term 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 K-M 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.

In this study, the WTE measurements of footprints in a uniform block-arrayed urban model immersed in a neutrally stratified ABL were reported. The footprints for 10 measurement positions in total, encompassing 4 horizontal positions at 3 vertical heights, were investigated. Velocities and concentrations were simultaneously measured by a X-probe HWA and FFID. Vertical flux was estimated by the simultaneous recordings considering the time lag between two signals. The reliability of the experiment was verified by reproducing two available dispersion WTE benchmarks. The main conclusions are as follows.

The footprint function exhibits characteristics influenced by measurement height and position. As the measurement height increases, the footprint becomes larger and flatter, with a smaller peak value and a shifted peak location. Heterogeneous features are observed across measurement positions, with sensors located near roughness cubes experiencing considerable blocking effects, while those in open streets have footprints extending along the streamwise direction. Notably, a rooftop sensor's footprint is dominated by the surrounding wakes due to the canyon vortex and separation flow.
The turbulent contribution to the flux measurement is critical and increases with the measurement height. The turbulent ratios of the total flux for each measurement position can reach up to 70% near the footprint peak. It is important to accurately estimate the turbulent dispersion in the numerical simulation of footprint.
The footprint function in the urban area is significantly affected by the building configuration, which means that the analytical solution of the widely used K-M model fails to reproduce it. The measured footprints are hindered by the row of cubes in the spanwise direction and consequently, they extend along the streamwise direction.

This paper provides a comprehensive validation database for the numerical simulation methods for footprint modeling in urban areas. It also enhances the understanding of essential features of footprints for urban atmospheric monitoring. However, several limitations should be clarified. The effects of boundary layer stability on the dispersion and footprint are not considered in the experiment, which may underestimate the complexity of reality. The experiment used an idealized urban model with regularly arranged cubes under a single wind direction. However, real urban areas contain diverse types and distributions of buildings. The incoming wind is also unsteady and multiple-directional. More cases should be measured to reveal the influence of these factors on the footprint functions. Besides, because the X-probe cannot measure the reverse flow, the footprint of the sensor in the wake region was not investigated. The distance between the probe and the FID tube may result in extra errors in the evaluation of flux. To deal with these problems, a well-calibrated PIV system may serve as an applicable option in the following research.

Author Contribution

Hongyuan Jia: Writing – original draft, Visualization, Validation, Methodology, Experiment, Conceptualization. Chao Lin: Writing – review & editing, Validation, MethodologyXiang Wang: Writing – review & editing, ExperimentHideki Kikumoto: Writing – review & editing, Supervision, Funding acquisition, Conceptualization.

Acknowledgments

This work was partly supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI, Grant Number 23H01563 and Grant Number 23KF0202. The first author also wants to express gratitude to Dr. Hong Hu, Dr. Rongmao Li, and Mr. Yichen Wang for their help and experience in the experiment.

Ahmad K, Khare M, Chaudhry KK (2005) Wind tunnel simulation studies on dispersion at urban street canyons and intersections—a review. Journal of Wind Engineering and Industrial Aerodynamics 93:697–717. https://doi.org/10.1016/j.jweia.2005.04.002
Auvinen M, Järvi L, Hellsten A, et al (2017) Numerical framework for the computation of urban flux footprints employing large-eddy simulation and Lagrangian stochastic modeling. Geoscientific Model Development 10:4187–4205. https://doi.org/10.5194/gmd-10-4187-2017
Cheng H, Castro IP (2002) Near wall flow over urban-like roughness. Boundary-Layer Meteorology 104:229–259. https://doi.org/10.1023/A:1016060103448
Coceal O, Dobre A, Thomas TG (2007) Unsteady dynamics and organized structures from DNS over an idealized building canopy. International Journal of Climatology 27:1943–1953. https://doi.org/10.1002/joc.1549
Di Bernardino A, Monti P, Leuzzi G, Querzoli G (2018) Pollutant fluxes in two-dimensional street canyons. Urban Climate 24:80–93. https://doi.org/10.1016/j.uclim.2018.02.002
Fedorovich E (2004) Dispersion of passive tracer in the atmospheric convective boundary layer with wind shears: a review of laboratory and numerical model studies. Meteorol Atmos Phys 87:. https://doi.org/10.1007/s00703-003-0058-3
Glazunov A, Rannik Ü, Stepanenko V, et al (2016) Large-eddy simulation and stochastic modeling of Lagrangian particles for footprint determination in the stable boundary layer. Geoscientific Model Development 9:2925–2949. https://doi.org/10.5194/gmd-9-2925-2016
Heidbach K, Schmid HP, Mauder M (2017) Experimental evaluation of flux footprint models. Agricultural and Forest Meteorology 246:142–153. https://doi.org/10.1016/j.agrformet.2017.06.008
Hellsten A, Luukkonen SM, Steinfeld G, et al (2015) Footprint Evaluation for Flux and Concentration Measurements for an Urban-Like Canopy with Coupled Lagrangian Stochastic and Large-Eddy Simulation Models. Boundary-Layer Meteorology 157:191–217. https://doi.org/10.1007/s10546-015-0062-4
Horst TW, Weil JC (1992) Footprint estimation for scalar flux measurements in the atmospheric surface layer. Boundary-Layer Meteorol 59:279–296. https://doi.org/10.1007/BF00119817
Hsieh C-I, Katul G, Chi T (2000) An approximate analytical model for footprint estimation of scalar fuxes in thermally stratified atmospheric flows. Advances in Water Resources 23:765–772. https://doi.org/10.1016/S0309-1708(99)00042-1
Iacobello G, Marro M, Ridolfi L, et al (2019) Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis. Phys Rev Fluids 4:104501. https://doi.org/10.1103/PhysRevFluids.4.104501
Jia H, Kikumoto H (2021a) Line source estimation of environmental pollutants using super-Gaussian geometry model and Bayesian inference. Environmental Research 194:110706–110706. https://doi.org/10.1016/j.envres.2020.110706
Jia H, Kikumoto H (2021b) Source term estimation in complex urban environments based on Bayesian inference and unsteady adjoint equations simulated via large eddy simulation. Building and Environment 193:107669–107669. https://doi.org/10.1016/j.buildenv.2021.107669
Jia H, Kikumoto H (2022) Sensor configuration optimization based on the entropy of adjoint concentration distribution for stochastic source term estimation in urban environment. Sustainable Cities and Society 103726. https://doi.org/10.1016/j.scs.2022.103726
Jia H, Kikumoto H (2023) Backward-Eulerian Footprint Modelling Based on the Adjoint Equation for Atmospheric and Urban-Terrain Dispersion. Boundary-Layer Meteorol 188:159–183. https://doi.org/10.1007/s10546-023-00807-z
Kljun N, Calanca P, Rotach MW, Schmid HP (2004) A Simple Parameterisation for Flux Footprint Predictions. Boundary-Layer Meteorology 112:503–523. https://doi.org/10.1023/B:BOUN.0000030653.71031.96
Kljun N, Rotach MW, Schmid HP (2002) A Three-Dimensional Backward Lagrangian Footprint Model For A Wide Range Of Boundary-Layer Stratifications. Boundary-Layer Meteorology 103:205–226. https://doi.org/10.1023/A:1014556300021
Kormann R, Meixner FX (2001) An Analytical Footprint Model For Non-Neutral Stratification. Boundary-Layer Meteorology 99:207–224. https://doi.org/10.1023/A:1018991015119
Kumari S, Kambhammettu BVNP, Niyogi D (2020) Sensitivity of Analytical Flux Footprint Models in Diverse Source‐Receptor Configurations: A Field Experimental Study. J Geophys Res Biogeosci 125:. https://doi.org/10.1029/2020JG005694
Lauvaux T, Miles NL, Deng A, et al (2016) High‐resolution atmospheric inversion of urban CO ₂ emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX). J Geophys Res Atmos 121:5213–5236. https://doi.org/10.1002/2015JD024473
Levin I, Karstens U, Eritt M, et al (2020) A dedicated flask sampling strategy developed for Integrated Carbon Observation System (ICOS) stations based on CO₂ and CO measurements and Stochastic Time-Inverted Lagrangian Transport (STILT) footprint modelling. Atmospheric Chemistry and Physics 20:11161–11180. https://doi.org/10.5194/acp-20-11161-2020
Marro M, Gamel H, Méjean P, et al (2020) High-frequency simultaneous measurements of velocity and concentration within turbulent flows in wind-tunnel experiments. Exp Fluids 61:245. https://doi.org/10.1007/s00348-020-03074-7
Marucci D, Carpentieri M (2019) Effect of local and upwind stratification on flow and dispersion inside and above a bi-dimensional street canyon. Building and Environment 156:74–88. https://doi.org/10.1016/j.buildenv.2019.04.013
Nosek Š, Fuka V, Kukačka L, et al (2018) Street-canyon pollution with respect to urban-array complexity: The role of lateral and mean pollution fluxes. Building and Environment 138:221–234. https://doi.org/10.1016/j.buildenv.2018.04.036
Schmid HP (2002) Footprint modeling for vegetation atmosphere exchange studies: A review and perspective. Agricultural and Forest Meteorology 113:159–183. https://doi.org/10.1016/S0168-1923(02)00107-7
Schuepp PH, Leclerc MY, MacPherson JI, Desjardins RL (1990) Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation. Boundary-Layer Meteorol 50:355–373. https://doi.org/10.1007/BF00120530
Snyder WH (1981) Guideline for Fluid Modeling of Atmospheric Diffusion. Environmental Sciences Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency
Sogachev A, Lloyd J (2004) Using a One-and-a-Half Order Closure Model of the Atmospheric Boundary Layer for Surface Flux Footprint Estimation. Boundary-Layer Meteorology 112:467–502. https://doi.org/10.1023/B:BOUN.0000030664.52282.ee
Sogachev A, Menzhulin GV, Heimann M, Lloyd J (2002) A simple three-dimensional canopy - planetary boundary layer simulation model for scalar concentrations and fluxes. Tellus B 54:784–819. https://doi.org/10.1034/j.1600-0889.2002.201353.x
Sugawara H, Ishidoya S, Terao Y, et al (2021) Anthropogenic CO2 Emissions Changes in an Urban Area of Tokyo, Japan, Due to the COVID-19 Pandemic: A Case Study During the State of Emergency in April–May 2020. Geophysical Research Letters 48:e2021GL092600. https://doi.org/10.1029/2021GL092600
Wang F, Zhou X, Huang J, et al (2022) Natural gas leakage estimation in underground utility tunnels using Bayesian inference based on flow fields with gas jet disturbance. Process Safety and Environmental Protection 165:532–544. https://doi.org/10.1016/j.psep.2022.07.041
Wang W, Okaze T (2022) Estimating low-occurrence wind speeds from mean velocity and turbulent kinetic energy: Development of statistical method and validation with idealized cases. Building and Environment 224:109499. https://doi.org/10.1016/j.buildenv.2022.109499

No competing interests reported.

Download PDF

Journal Publication

published 17 Oct, 2024

Read the published version in Boundary-Layer Meteorology →

Editorial decision: Revision requested
16 May, 2024
Reviews received at journal
12 Mar, 2024
Reviews received at journal
27 Feb, 2024
Reviewers agreed at journal
14 Feb, 2024
Reviewers agreed at journal
13 Feb, 2024
Reviewers agreed at journal
13 Feb, 2024
Reviewers invited by journal
13 Feb, 2024
Editor assigned by journal
12 Feb, 2024
Submission checks completed at journal
12 Feb, 2024
First submitted to journal
09 Feb, 2024

You are reading this latest preprint version

Wind tunnel experiment on the footprint of a block-arrayed urban model in a neutrally stratified boundary layer

Status:

Journal Publication

Version 1

Abstract

Figures

1 Introduction

2 Materials and methods

2.1 Definition of the Footprint Function

2.2 Description of the Wind Tunnel Experiment

3 Measurement verification

3.1 Comparison with AIJ database

3.2 Flux measurements for a passive scalar dispersion in a boundary layer

4 Results & Discussions

4.1 Velocity results

4.2 Evaluation method of flux

4.3 Concentration footprint

4.4 Turbulent flux footprint

4.4 Total flux footprint

4.5 Comparison to K-M plume model

4.6 Discussions

5 Conclusion

Declarations

Author Contribution

References

Additional Declarations

Status:

Journal Publication

Version 1