On 20 and 22 August 2019, a small tripod was outfitted with a sonic anemometer and placed in a highway shoulder to compare with measurements made on an instrumented car as it traveled past the tripod. The rural measurement site in this investigation was selected so that the instrumented car traveled past many upwind surface obstructions and experienced the occasional passing vehicle. To obtain an accurate mean wind speed and mean wind direction on a moving car, it is necessary to correct for flow distortion and remove the vehicle speed from the measured velocity component parallel to vehicle motion (for straight-line motion). In this study, the velocity variances and turbulent fluxes measured by the car are calculated using two approaches: (1) eddy covariance and (2) wavelet analysis. The results show that wavelet analysis can better resolve low frequency contributions, and this leads to a reduction in the horizontal velocity variances measured on the car, giving a better estimate for some measurement averages when compared to the tripod. A wavelet-based approach to remove the effects of sporadic passing traffic is developed and applied to a measurement period during which a heavy-duty truck passes in the opposite highway lane; removing the times with traffic in this measurement period gives a reduction of approximately 10 % in the turbulent kinetic energy. The vertical velocity variance and vertical turbulent heat flux measured on the car are biased low compared to the tripod. This low bias may be related to a mismatch in the flux footprint of the car versus the tripod or perhaps to rapid flow distortion at the measurement location on the car. When random measurement uncertainty is considered, the vertical momentum flux is found to be consistent with the tripod in the 95 % confidence interval and statistically different than 0 for most measurement periods.

Measurements of atmospheric means, variances, and covariances obtained from an instrumented mobile car can provide low-cost, in situ observations close to the ground and over a large measurement domain. Hereafter, “instrumented mobile car” refers to all potential on-road vehicles that could serve as a measurement platform, including cars, sport utility vehicles, pickup trucks, minivans, or larger mobile laboratories that use a heavy-duty truck. Previous investigations have largely used instrumented mobile cars for the measurement of near-surface atmospheric means, but minimal attention has been given to their use for the measurement of turbulence (i.e., variances and covariances). In the nocturnal boundary layer characterized by stable conditions and weak flow, turbulence near the surface mainly originates from poorly understood non-stationary mechanical shear and submesoscale motions (Mahrt et al., 2012; Van De Wiel et al., 2012), such as low-level jets, thermotopographic wind systems (i.e., katabatic flow), and breaking gravity waves (Salmond and McKendry, 2005). In the very-stable boundary layer, the generated turbulence is often intermittent and results in the vertical transport of scalars (i.e., heat, pollutants), but stationary towers may be too isolated and “site-specific” to adequately sample the temporally and spatially localized turbulence (Salmond and McKendry, 2005). The mobile car, however, can measure along a driven path, which may provide a more representative sample of turbulence near the surface compared to a stationary tower. In addition, the mobile car may also be used to obtain in situ wind and turbulence measurements near the surface within the urban boundary layer, measurements that may help validate high-resolution, street-level models. In the near-surface urban boundary layer, the strength of the wind and the intensity of turbulence are influenced by the composition of buildings and trees (Mochida et al., 2008; Gromke and Blocken, 2015; Hertwig et al., 2019; Krayenhoof et al., 2020) and can have a significant impact on pedestrian comfort (Hunt et al., 1976; Yu et al., 2020), and neighborhood-level pollutant dispersion (Aristodemou et al., 2018; Su et al., 2019). The mobile car involves fewer logistical limitations (i.e., permits, vandalism) and potentially affords a greater spatial coverage when compared to the installation of a stationary tower in a high-density urban area. Furthermore, as the resolution of numerical weather prediction models continues to improve, the measurement of localized variations in near-surface heat, momentum, and moisture fluxes may improve the prediction of convective storms (Markowski et al., 2019).

The instrumented mobile car has been used in various investigations to measure atmospheric means near the surface (Bogren and Gustavsson, 1991; Straka et al., 1996; Achberger and Bärring, 1999; Armi and Mayr, 2007; Mayr and Armi, 2008; Taylor et al., 2011; Smith et al., 2010; White, 2014; Curry et al., 2017; de Boer et al., 2021). Gordon et al. (2012) and Miller et al. (2019) used the instrumented car for the measurement of velocity variances on highways to quantify vehicle-induced turbulence. Despite the increasing number of investigations using instrumented mobile car systems for atmospheric measurements, there are limited studies that examine their performance and accuracy for the measurement of the mean flow, velocity variances, and covariances.

Achberger and Bärring (1999) investigated the accuracy of mean
temperature measurements made on a minibus in low-speed driving conditions
(8 to 11 m s

Belušic et al. (2014) is the first known study to evaluate a three-dimensional sonic anemometer (model CSAT3, sampling frequency of 20 Hz) affixed to a passenger vehicle for its accuracy at measuring atmospheric variances and covariances in addition to atmospheric means. In their setup, the sonic anemometer was supported by a sophisticated arm and lattice aluminum frame; the arm held the sonic above the vehicle's top at a height of 3 m from the ground, positioned slightly ahead of the vehicle's front end. Recently, Hanlon and Risk (2020) investigated how the placement of a sonic anemometer on the vehicle affects the accuracy of velocity measurements by applying computational fluid dynamics modeling in combination with mobile car measurements. The anemometers were placed vertically upward on top of the vehicle's roof.

If 1 min averages are assumed, then measurements (i.e., wind velocity, gas
concentration) obtained from an instrumented car traveling at near-highway
speeds (i.e., 15 to 25 m s

The present work investigates an instrumented mobile car setup (shown in Fig. 1) by comparing car-based measurements with measurements made by a small roadside tripod. Our setup differs from Belušic et al. (2014) in two main ways, which are necessary to make the vehicle safe for on-road driving with other vehicles: (1) our sonic anemometer is held closer to the vehicle and situated over the vehicle's front end, and (2) the sonic anemometer is held closer to the ground at a height of 1.7 m, which is near the height of the vehicle's top. We selected this design to investigate whether the sonic anemometer can be held closer to the vehicle and still provide measurements that are representative of the mean flow and turbulence near the surface, allowing road-safe vehicle operation without compromising the measured data. While farmland is common in our measurement domain, the car also traveled past many large trees and houses and experienced the occasional passing vehicle traveling in the opposite direction. Therefore, we investigate if the mobile car measurements are still representative of the turbulence statistics near the surface in a less idealized case, where the upwind surface and terrain are not homogenous and where the measured flow is affected by many surface obstacles, including other traffic. Thus, this work aims to help design a low-cost experiment to measure and analyze on-road velocity variances and covariances using an instrumented car, in the presence of sporadic passing traffic and upwind surface inhomogeneities. This study investigates how these inhomogeneities affect the calculated statistics. Wavelet analysis is considered as an alternative technique to eddy covariance for the estimation of velocity variances and covariances measured on the car and is applied to quantify and remove the effects of sporadic passing traffic. The potential sources of measurement uncertainty on the car are quantified and discussed.

A front view of instrumented car (also referred to as a mobile car platform or mobile car laboratory) used in this investigation.

A sport utility vehicle (SUV) was outfitted with instrumentation fastened to
the vehicle using a roof rack, as shown in Fig. 1. A 40 Hz,
three-dimensional sonic anemometer (Applied Technologies, Inc., model type
“A” or “Vx”) was installed on a support arm located at the front end of
the vehicle at a height of

The coordinate system of the sonic anemometer on the car is defined
(assuming an observer is sitting inside of the vehicle facing toward the
front hood) so that measured velocity parallel to vehicle motion (

On 20 and 22 August 2019, a small tripod was assembled and placed at the
roadside (i.e., in the highway shoulder) to compare with measurements made
by the instrumented car as it traveled past the stationary tripod. The
tripod was equipped with a three-dimensional sonic anemometer (Applied
Technologies, Inc., model type “V”) that recorded at a frequency of either
10 Hz (20 August) or 20 Hz (22 August). Each day, the sonic was installed at a measurement height of

The measurement site was agricultural fields located on either side of a
two-lane highway. The traffic on 22 August passing our measurement site was
more significant than on 20 August; the traffic composition on 22 August included
occasional large trucks, and we did not observe any large trucks passing our
measurement site on 20 August. Both days featured fair weather, with sky
conditions ranging from mainly sunny on 20 August to partly cloudy on 22 August.
The wind direction measured at nearby Egbert weather station (maintained by
Environment and Climate Change Canada, with measurements obtained at a height
of 10 m) ranged between 160 and 200

The road is relatively flat near the tripod location, but in general, the
terrain is not flat and homogenous in this area. The study area (which spans
about 10 km) has several hills, with slopes up to 10

In this work, a

The measurement site on 20 August (top) and 22 August (bottom), with the 1000 m tracks driven by the car superimposed. Track #1 is shown as a yellow line, and Track #2 is shown as a blue line. Track #1 is centered on the location of the tripod; therefore, 500 m of highway are included in Track #1 on either side of the tripod location. Track #2 begins 120 m away from the tripod; therefore, it does not include any measurements made on the highway directly in front of the tripod. © Google Earth Images.

The number of measurement passes performed on each measurement track on 20 and 22 August.

Measurements made on an instrumented car may be significantly impacted by
flow distortion. Flow distortion originates from vehicle movement (speed

Without flow distortion, the average measured vertical velocity (

The average velocity recorded over both travel directions (

The lateral velocity

Figure 3a shows

Corrections as shown in Fig. 3, except for 30 August. Black dashed
lines give a least-square fit:

Figure 3b shows

The continuous wavelet transform of a discrete time series

Using the real part of the wavelet coefficients, the original time series

To compare the measurements made on the tripod to those made on the car, the
coordinate systems must be consistent. The initial step is to rotate the
individual measurements made on the vehicle into a meteorological coordinate
system (i.e.,

After rotation into meteorological coordinates, each track (on the car and
tripod) is then rotated into a mean streamwise coordinate system following
Wilczak et al. (2001), where

For the calculation of turbulence statistics, the use of a finite record
length gives rise to a random measurement uncertainty, since the record will
not contain enough independent samples to accurately represent the ensemble
mean (Lenschow et al., 1994). Further random measurement uncertainty can be
introduced by non-stationarity in the record and white noise in the
measured signal (Rannik et al., 2016). In this work, the magnitude of the
random measurement uncertainty is estimated using two methodologies. All
uncertainty estimations are after correction for flow distortion and
rotation into a streamwise coordinate system. The first method, developed by
Mann and Lenschow (1994), can be defined as

The second methodology outlined in Finkelstein and Sims (2001) gives an
estimation of the variance of a covariance (

For wavelet analysis, Eq. (14) is applied to generate a wavelet
reconstructed time series (

The sonic anemometer's signal may be impacted by white noise, a form of
random measurement uncertainty. Lenschow et al. (2000) consider a stationary
time series with its mean removed (i.e.,

In this work, we follow the approach of Belušić et al. (2014) and select a
fixed ground path to investigate means, variances, and covariances on the
car. Two different fixed 1000 m ground paths (

The averaging period (

The averaging periods (

Figure 5 shows a scatter plot of (a) the 5 min mean wind direction on the
tripod compared to the mean wind direction measured on the mobile car, and
(b) the 5 min mean wind speed measured on the tripod compared to the mean
wind speed measured on the mobile car. The mean wind speed shown is after
rotation into streamwise coordinates. The gray lines in Fig. 5 denote a
specific percentage of the tripod measured value (i.e., 100 % gives a
one-to-one relationship), and this convention is used in the figures that
follow. The mean bias error,

A scatter plot showing the mean wind direction

Statistics calculated over all measurement passes (i.e., on both tracks on 20 and 22 August). Subscript EC denotes a statistical variance or a covariance calculated using eddy covariance. A subscript W denotes a variance or covariance calculated using wavelet analysis.

The mean wind speed shown in Fig. 5b shows relatively good agreement between the car and tripod, with no significant bias (

Statistics of the mean flow measured by the car on 20 and 22 August.
The averaging period is 10 s; therefore, the statistics are calculated from
a set of

To investigate how the car performs for shorter averaging periods,
non-overlapping intervals of 10 s duration are examined on 20 and 22 August. There are 263 and 250 such intervals on 20 and 22 August, respectively, and these
represent times that the vehicle is driving in the vicinity of the tripod
(i.e., within about 10 km) and not necessarily on a 1000 m track. The
results are shown in Table 4, which displays the average meteorological wind
components (

Figure 6 shows the velocity variances measured on the instrumented car
compared to the velocity variances measured on the tripod. The velocity
variances measured on the car are calculated using the typical statistical
approach, denoted as EC (i.e., for time series

The horizontal streamwise velocity variance,

Applying wavelet analysis to estimate the horizontal velocity variances
leads to a significant reduction in the magnitude compared to EC for some
passes, specifically for those passes reporting the largest horizontal
velocity variances, as shown in Fig. 6a and b. This reduction results in
an improved agreement between the two measurement systems; for

Despite the improved agreement when wavelet analysis is applied to estimate
the horizontal velocity variances, there are still instances where

Car-measured velocity variances on three different 1000 m tracks, calculated every second using wavelet analysis. The data shown are from 22 August. The black circled areas denote the passage of traffic in the lane adjacent to the instrumented car (i.e., traveling in the opposite direction), as determined from visual inspection of the dashboard camera video. The text located to the right of the circle gives the traffic composition. The data shown are measurements from the lane closet to the tripod. The velocity variances shown are in a meteorological coordinate system.

Figure 7 displays the 1 s wavelet variance calculated using Eq. (11) for
three different measurement passes from Track #2 (on 22 August); Fig. 7a
had two simultaneously passing sport utility vehicles (SUV), and Fig. 7c had a
passing heavy-duty truck followed in quick succession by an SUV. Wavelet
analysis is performed on the measured velocities in a meteorological
coordinate system (i.e.,

For the measurement pass shown in Fig. 7b, there is a noticeable increase in the 1 s horizontal velocity variances about 450 m into the measurement track. A similar trend is also seen in Fig. 7c. Before 450 m, there are many large trees and houses upwind of the highway, but after 450 m, the upwind environment becomes open farmland (i.e., limited obstructions to the mean flow). The presence of many trees and houses in close proximity acts as a windbreak, forcing the flow to accelerate and rise over the surface obstructions. The flow is reduced downwind of the surface obstruction (Taylor and Salmon, 1993; Mochida et al., 2008), and close to the surface just after the obstruction (i.e., the near wake) is the “quiet zone”, where the horizontal velocity variances are reduced in comparison with the undisturbed upwind flow (Lee and Lee, 2012; Lyu et al., 2020). Therefore, the reduced horizontal velocity variances for the first few hundred meters of the track may be related to the quiet zone generated by the many trees and houses upwind of the road. After about 450 m, the upwind environment becomes relatively open, and the flow measured on the car increases, with this increase continuing over the remainder of the track. The changing wind speed along the track introduces a trend in the horizontal velocity record measured on the car.

The vertical momentum flux,

On the instrumented car,

The sonic temperature variance,

The discrepancy between the car and the tripod for

To investigate the flux footprint of the tripod versus the instrumented car,
the footprint model of Kljun et al. (2015) is applied with

Another factor that may influence the velocity measurements made by the
sonic anemometer is rapid distortion of the flow caused by the moving
vehicle. Wyngard (1988) shows that the variance of scalar quantities (such
as the sonic temperature or a gas concentration) remains unchanged during
rapid flow distortion. The velocity variances, however, may be altered
during stretching and compression of the flow, as it is forced to rise over
the front end of the vehicle, similar to isotropic turbulence and flow
over a symmetric hill (Britter et al., 1981; Gong and Ibbetson, 1989). If it
is assumed that the low bias in the measured

For EC, there is no significant bias for

Figure 10 displays the binned power spectral density (multiplied by
frequency) of the velocity components for measurement Pass 5 (Fig. 10a),
Pass 7 (Fig. 10b), and Pass 8 (Fig. 10c) from Track #1. These three
measurement passes have been chosen, since they demonstrate unique features
in the car spectra, which are representative of the spectra from the
remaining measurement passes not shown (see Fig. S6). The frequencies are
normalized to give a wavelength as

Binned power spectral density (multiplied by frequency) of the
velocity components

Despite the rather strong relationship between the measured vertical
velocity (

Statistics calculated over all measurement passes (i.e., Track #1 and Track #2), but with

A significant concern when obtaining atmospheric measurements from an instrumented mobile car is the impact of sampling errors. Sampling errors on the mobile car may result from (i) the use of a record length that is too short to be representative of an ensemble mean, (ii) non-stationarity of the flow introduced by microscale variations or inhomogeneities in the terrain and surrounding structures (i.e., trees, buildings), or (iii) white noise and persistent structured signals introduced by vehicle resonance and vibrations.

In this work, three methods to quantity the random measurement uncertainty
are investigated: (1) the method of Finkelstein and Sims (2001), referred to
as F&S (Eq. 17, denoted as

Random measurement uncertainty of the horizontal velocity
variance measured on the car, plotted as a function of

Random measurement uncertainty of the vertical velocity variance
measured

Measurement uncertainty of

The random uncertainty estimates calculated from M&L and F&S agree
well on the mobile car platform for velocity variances when

The random measurement uncertainty calculated from F&S and M&L scales
approximately linearly with increasing magnitude of the velocity variance or
covariance, as shown in Figs. 11 to 13. For Track #2, there are
several instances where

Reconstructing the time series using wavelet analysis produces a filtered
time series, where the resolved low frequency contributions are excluded.
Applying F&S to the reconstructed time series gives an estimate of

For the measurement tracks investigated here, the use of a linear fit to
estimate

Compared to

In addition to Track #1 and Track #2, the car was driven on a gravel
road at relatively high vehicle speeds (

Since the study was designed to investigate measurements in non-idealized conditions, the highway locations have public access; therefore, other vehicle traffic was present during the measurements. The traffic consisted largely of passenger vehicles (such as cars, pickup trucks, sport utility vehicles, and minivans), but the traffic on 22 August was more significant and was comprised of occasional large trucks (dump trucks and tractor-trailers). For measurement passes on 22 August (with video recordings available on the tripod), the dashboard camera recorded between 26 and 40 total passing vehicles, of which 0 to 4 were large trucks. The car takes about 45 s to complete a track, but on the tripod, the equivalent averaging period is between 6 to 8 min. For some measurement passes, the mobile car does not experience any traffic contamination, but this is not the case for the tripod. Therefore, the tripod will measure a different composition and amount of passing traffic than the car, potentially leading to differences in the measurements made by the two systems.

Large trucks produce a significant amount of vehicle-induced turbulence, but passenger cars and sport utility vehicles produce much less in comparison (Miller et al., 2019; Gordon et al., 2012). Furthermore, the wake has limited lateral spread relative to the vehicle travel direction (Kim et al., 2016), except perhaps for times with significant advection, so the most noticeable effect on the tripod will be from traffic in the adjacent highway lane (i.e., closet to the tripod). For measurements on the car, passing traffic (particularly large trucks) is found to enhance the measured velocity variances (i.e., Fig. 7c). Like the car, the main effect of passing traffic on the tripod measurements would also be an enhancement of the velocity variances. Thus, for times when there is no traffic contamination on the car, the differences shown in Fig. 6 between the car and tripod-measured velocity variances may be underestimated, since the tripod velocity variances are enhanced due to passing traffic but the car measurements are not. Therefore, the presence of traffic measured by the tripod and not the car introduces an additional uncertainty into the measurement comparisons shown in Sect. 3.

The results presented in Sect. 3 demonstrate that the instrumented car
design used in this study can successfully measure the mean atmospheric
boundary layer close to the surface, but the car measurements may vary
significantly based on the surrounding features such as trees, buildings,
and other traffic. Therefore, the interpretation of the car-based
measurements depends largely on the specific application, since the car may
measure turbulence that is localized and not represented in single-point
measurements made at a stationary tower. In the previous study of
Belušić et al. (2014), there was limited upwind surface obstructions and no other traffic during their measurements. Despite the more idealized
environment, their measurements revealed times when the horizontal velocity
variances (

Evidence from this investigation shows that passing traffic (especially large trucks) can also lead to an increase in the velocity variances measured on the car. However, if the passing traffic is sporadic, the resulting increase in the measured velocity variances from vehicle-induced turbulence can be identified and removed using wavelet analysis. In this study, for a measurement pass that experienced a passing heavy-duty truck and sport utility vehicle, removing the times when the traffic passes the mobile car (9 out of 46 s) decreases the turbulent kinetic energy by about 10 %. This highlights the importance of video recordings in conjunction with sonic anemometer measurements on a car, so that times with possible traffic contamination can be identified in applications where its measurement is not intended.

The sampling uncertainties in Sect. 3 suggest that it is possible to measure
a statistically significant vertical momentum flux on the mobile car at
vehicle speeds near 20 m s

The vertical velocity (

The mean wind speed and mean wind direction were found to be consistent with
measurements made on the tripod. For

The results presented in this investigation demonstrate that car-based measurements of turbulence require care when selecting the appropriate spatial and temporal averaging and when selecting the measurement location to ensure that the measurements obtained are representative of the specific application. This is demonstrated in our measurements, where the highway surface or flux footprint, upwind obstructions, and passing traffic are all found to have a significant effect on the measured values but are not necessarily errors, since they do represent real features that can generate atmospheric turbulence.

The data used to generate the figures and complete the analysis presented herein are available online at

The supplement related to this article is available online at:

SJM and MG designed and performed the experiment. SJM completed the analysis of the measured data and complied the results. SJM prepared the manuscript with contributions from Mark Gordon.

The contact author has declared that neither of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Peter Taylor for providing the SUV used in this study and for his assistance during the experimental data collection (as a driver in the experiment) on 30 August.

This research has been supported by the Natural Sciences and Engineering Research Council of Canada (grant no. RGPIN 2015–04292).

This paper was edited by Cléo Quaresma Dias-Junior and reviewed by Luca Mortarini and one anonymous referee.