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**Research article**
02 Oct 2018

**Research article** | 02 Oct 2018

Uncertainty of urban eddy covariance flux measurements

^{1}Institute for Atmospheric and Earth System Research (INAR)/Physics, Faculty of Science, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland^{2}Helsinki Institute of Sustainability Science, Faculty of Science, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland^{3}Finnish Meteorological Institute, P.O. Box 503, 00101 Helsinki, Finland^{4}A. M. Obukhov Institute of Atmospheric Physics, 119017 Moscow, Russia^{5}INAR/Forest Sciences, Faculty of Agriculture and Forestry, P.O. Box 27, 00014 University of Helsinki, Finland

Abstract

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The eddy covariance (EC) technique is the most direct method for measuring the exchange between the surface and the atmosphere in different ecosystems. Thus, it is commonly used to get information on air pollutant and greenhouse gas emissions, and on turbulent heat transfer. Typically an ecosystem is monitored by only one single EC measurement station at a time, making the ecosystem-level flux values subject to random and systematic uncertainties. Furthermore, in urban ecosystems we often have no choice but to conduct the single-point measurements in non-ideal locations such as close to buildings and/or in the roughness sublayer, bringing further complications to data analysis and flux estimations. In order to tackle the question of how representative a single EC measurement point in an urban area can be, two identical EC systems – measuring momentum, sensible and latent heat, and carbon dioxide fluxes – were installed on each side of the same building structure in central Helsinki, Finland, during July 2013–September 2015. The main interests were to understand the sensitivity of the vertical fluxes on the single measurement point and to estimate the systematic uncertainty in annual cumulative values due to missing data if certain, relatively wide, flow-distorted wind sectors are disregarded.

The momentum and measured scalar fluxes respond very differently to the
distortion caused by the building structure. The momentum flux is the most
sensitive to the measurement location, whereas scalar fluxes are less
impacted. The flow distortion areas of the two EC systems (40–150 and
230–340^{∘}) are best detected from the mean-wind-normalised turbulent
kinetic energy, and outside these areas the median relative random uncertainties of
the studied fluxes measured by one system are between 12 % and 28 %. Different
gap-filling methods with which to yield annual cumulative fluxes show how using data
from a single EC measurement point can cause up to a 12 %
(480 g C m^{−2}) underestimation in the cumulative carbon fluxes as
compared to combined data from the two systems. Combining the data from two
EC systems also increases the fraction of usable half-hourly carbon fluxes
from 45 % to 69 % at the annual level. For sensible and latent heat,
the respective underestimations are up to 5 % and 8 % (0.094 and
0.069 TJ m^{−2}). The obtained random and systematic uncertainties are in
the same range as observed in vegetated ecosystems. We also show how the
commonly used data flagging criteria in natural ecosystems, kurtosis and
skewness, are not necessarily suitable for filtering out data in a densely built
urban environment. The results show how the single measurement system can be
used to derive representative flux values for central Helsinki, but the
addition of second system to other side of the building structure decreases
the systematic uncertainties. Comparable results can be expected in similarly
dense city locations where no large directional deviations in the source area
are seen. In general, the obtained results will aid the scientific community
by providing information about the sensitivity of EC measurements and their
quality flagging in urban areas.

How to cite

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How to cite.

Järvi, L., Rannik, Ü., Kokkonen, T. V., Kurppa, M., Karppinen, A., Kouznetsov, R. D., Rantala, P., Vesala, T., and Wood, C. R.: Uncertainty of eddy covariance flux measurements over an urban area based on two towers, Atmos. Meas. Tech., 11, 5421-5438, https://doi.org/10.5194/amt-11-5421-2018, 2018.

1 Introduction

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It is recommended that surface fluxes measured using the eddy covariance (EC) technique are done in the inertial sublayer and free from obstructions (Roth, 2000). These assumptions are often easy to meet over natural surfaces but can be challenging for EC systems above cities. Often the EC measurements are made within or in the vicinity of the roughness sublayer, the adjacent layer to the surface with height of 2–5 times the mean building height (Raupach et al., 1991). In this layer, turbulence is not homogeneous but rather varies greatly in space, and the Monin–Obukhov similarity theory (MOST) is no longer strictly valid. Despite the non-ideal conditions, EC measurements from urban areas are needed for the purposes of wind engineering, understanding the urban surface–atmosphere interactions, in the estimation of urban carbon budgets (Christen et al., 2011; Nordbo et al., 2012a), and in order to improve the description of urban areas in numerical weather and air quality predictions via the measured turbulent fluxes of heat (Demuzere et al., 2017; Grimmond et al., 2010; Karsisto et al., 2015). In order for the urban EC systems to meet the requirements of the technique, we are often forced to conduct the measurements on top of buildings or other platforms such as telecommunication towers (Ao et al., 2016; Brümmer et al., 2013; Keogh et al., 2012; Liu et al., 2012; Nordbo et al., 2013; Wood et al., 2010) instead of narrow lattice masts, which would minimise the effect of the structure itself on the EC measurements. Thus strictly speaking, the measurements are not necessarily made completely free of the impact of roughness elements even if the measurement height is sufficiently above the surrounding roughness elements. The interaction between the EC measurements and the measurement platform itself causes challenges for obtaining high-quality EC data sets, and special attention should be paid to the effect of the so-called flow distortion area on the measurements (Barlow et al., 2011). Urban EC measurements have furthermore raised the need for local scaling of mean turbulent properties with minor deviations from inertial-sublayer scaling (Rotach, 1993; Roth, 2000; Vesala et al., 2008; Wood et al., 2010) and corrections for local-scale anthropogenic sources (Kotthaus and Grimmond, 2012).

The basic-quality screening of a single sensor in measuring vertical fluxes
can be performed based on the vertical deflection angles and expected
turbulence, and sometimes even by simply disregarding whole (flow-distorted)
wind sectors (Barlow et al., 2011). It is not however ideal if we have to reject
a relatively large fraction of the data. For cumulative emission estimates,
the flux data need to be gap-filled – but in urban areas this is more
complex than in vegetated environments due to the large amount of explanatory
variables and the high spatial variability of the sources and sinks
(Menzer et al., 2015). The gap-filling methods used in urban EC flux data sets
vary from simple look-up tables to artificial neural networks
(Christen et al., 2011; Järvi et al., 2012; Kordowski and Kuttler, 2010; Schmidt et al., 2008), but the more
complex and time-demanding solutions might not always be considerably better
than the more simple ones. Järvi et al. (2012) found only a 4 % difference in
cumulative carbon dioxide (CO_{2}) fluxes when utilising median diurnal
cycles and neural networks in filling data gaps at a semi-urban site in
Helsinki. On top of that, any statistical gap-filling techniques can be
biased if certain wind directions are compromised above heterogeneous
surfaces, and therefore single-point EC measurements might not give realistic
cumulative flux values. The same applies to the representativeness of a
single measurement point for a studied ecosystem in general. Already at
forested sites, which are generally considered to be easier for EC
measurements than urban areas, the uncertainties in CO_{2} flux originating
from a single measurement point have been reported to be 6 %
(Hollinger et al., 2012). In the past, simultaneous observations from more than
one EC station have been used to estimate uncertainties in EC-measured fluxes
above vegetated surfaces (Hollinger and Richardson, 2005; Kessomkiat et al., 2010; Peltola et al., 2015; Post et al., 2015), but in urban areas no estimations have been derived from direct EC
measurements with more than one measurement system at the same level.

The aim of this work is twofold. Firstly, we want to examine the sensitivity of a single-point EC system in measuring the vertical fluxes of momentum, sensible and latent heat, and carbon dioxide in a highly dense urban area. Secondly, we want to understand what the implication is of the non-ideal measurement location and resulting data removal on the calculation of cumulative fluxes, which are important for emission-inventory comparison and planning of neighbourhoods. These two aims will be examined with the aid of two identical EC measurement systems located on the opposite sides of a bluff-body tower in the centre of Helsinki.

2 Methods

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The measurements were conducted in central Helsinki (Fig. 1), where
two identical EC setups were installed on top of a hotel building (Fig. 2)
at a height (*z*) of 60 m above the ground during July 2013 until
September 2015. Within a 1 km radius of the measurement location, 37 % of the
surface is covered with buildings and 41 % with paved surfaces, leaving only
22 % of the surface covered with vegetation (Nordbo et al., 2015). The
surrounding buildings are fairly uniform with a mean height of 24 m,
displacement height of 15 m and aerodynamic roughness length of 1.4 m
(Nordbo et al., 2013). However one notable exception is the Hotel Torni building
itself: its main building is up to 15 m above the ground level, the tower up
to 58 m and upper masonry extending up to 66 m. The two EC systems (EC1 and
EC2) were mounted on the opposite sides of an upper masonry on 2.3 m high
measurement masts (Fig. 2). The systems are located at 60 m,
which is 2.5 times the mean building height, and therefore they should be
above the roughness sublayer and blending height where local-scale surface
sources and sinks have aggregated together (Raupach et al., 1991). The centre of
Helsinki is located on a peninsula, but previous analyses on the source area
of the EC1 system have shown the flux footprint to lie above the city and not the
sea (Auvinen et al., 2017; Kurppa et al., 2015). The two systems have a separation
distance of 10 m and thus measure virtually the same source area. The
downside of the measurement location is that the upper masonry disturbs the
flow, and we choose to neglect data for certain wind directions based on
quality considerations. Based on the mean-wind-normalised turbulent kinetic
energy (TKE), the areas are approximated to be 40–150 and
230–340^{∘} for EC1 and EC2, respectively (Fig. 3).

Each system comprised a 3-D ultrasonic anemometer measuring the sonic
temperature and 3-D orthogonal wind speeds (USA-1, Metek GmbH, Germany), and
an infrared gas analyser (LI-7200, LI-COR Biosciences, Lincoln, NE, USA)
giving concentrations of water vapour and CO_{2}. The air inlets were
positioned 0.15 m below the anemometer centre, and air was drawn through a 1 m
long stainless-steel tube (with inner diameter of 0.04 m) to the gas
analyser. The flow rates were 10 L min^{−1}. Tubes were heated with a
power of 9 W m^{−1} to avoid condensation of water vapour on their walls.
The raw EC data were sampled with a frequency of 10 Hz, from which the 30 min
flux values were calculated using commonly accepted procedures
(Nordbo et al., 2012b). The fluxes were determined using the maximum-covariance
technique where the window mean and width for the lag time were identical for
the two systems (0–1.2 s for CO_{2} and 0–7 s for H_{2}O). Before the
calculation of the fluxes, data were despiked and linearly detrended. The
high-response losses resulting from the tube attenuation were corrected with
the aid of measured temperature cospectra, yielding a CO_{2} response time of
0.11 s for EC1 and 0.14 s for EC2. Wind coming from the flow
distortion areas removed 27 % of the EC1 data and 38 % of the EC2 data. The
larger fraction with EC2 is due to the prevailing wind direction from
south to west.

In order to understand possible differences between the two measurement
setups, several variables and statistics describing turbulence
characteristics will be evaluated. Stationarity (FS), skewness (SK) and
kurtosis (*K*) are common variables used to examine the quality of EC data,
with the first providing information about the stationarity of the flux
measurements and the latter two providing information about the form of the probability function of
the measured concentration, temperature or wind speed (Vickers and Mahrt, 1997).
Stationarity is calculated by dividing each 30 min flux period into six
subsets for which the flux values are separately calculated and their mean
furthermore compared with the 30 min flux values. Typically, with differences
below 30 %, data are considered to be high quality and differences below
60 % still suitable for general data analysis. In this study, the strict
limit of 30 % will be used. SK describes the asymmetry of the probability
function of a variable and is calculated from

$$\begin{array}{}\text{(1)}& \mathrm{SK}={\displaystyle \frac{\stackrel{\mathrm{\u203e}}{\left({{x}^{\prime}}^{\mathrm{3}}\right)}}{{\mathit{\sigma}}_{x}^{\mathrm{3}}}},\end{array}$$

where *x* is a velocity or scalar variable, the overbar indicates the 30 min time
average, the prime indicates the deviation from the mean of the variable and *σ*_{x} is
its standard deviation. SK between −2 and +2 is considered to be
good-quality EC data. *K* is a measure of sharpness of the probability
function; i.e. its high values indicate peaks in the data. It is calculated from

$$\begin{array}{}\text{(2)}& K={\displaystyle \frac{\stackrel{\mathrm{\u203e}}{\left({{x}^{\prime}}^{\mathrm{4}}\right)}}{{\mathit{\sigma}}_{x}^{\mathrm{4}}}}.\end{array}$$

*K* between 1 and 8 is considered as reasonable-quality data.

The relative random error (RRE) of the vertical flux of scalar *x*
($F=\stackrel{\mathrm{\u203e}}{{w}^{\prime}{x}^{\prime}}$, where *w* is the vertical wind speed) is calculated as
the square root of the random error variance (${\mathit{\sigma}}_{F}^{\mathrm{2}}$) normalised with
the absolute value of the flux according to Lenschow et al. (1994):

$$\begin{array}{}\text{(3)}& \mathrm{RRE}={\displaystyle \frac{{\mathit{\sigma}}_{F}\left(\mathrm{\Gamma}\right)}{\left|F\right|}}=(\mathrm{2}{\mathit{\mu}}_{\mathit{\rho}}{\displaystyle \frac{{\mathrm{\Gamma}}_{\mathit{\rho}}}{\mathrm{\Gamma}}}{)}^{\mathrm{1}/\mathrm{2}},\end{array}$$

where *ρ* refers to the instantaneous flux (${w}^{\prime}{s}^{\prime}$). *μ*_{ρ} is the
flux variance:

$$\begin{array}{}\text{(4)}& {\mathit{\mu}}_{\mathit{\rho}}={\mathit{\mu}}_{w}{\mathit{\mu}}_{x}+{F}^{\mathrm{2}},\end{array}$$

where *μ*_{w} and *μ*_{x} are the variances of *w* and *x*, Γ is
the averaging period (30 min), and Γ_{ρ} is the integral timescale
defined as the integral over the autocovariance function (*R*_{ρ};
Rannik et al., 2016) and in practice is estimated as the lag when *R*_{ρ}
drops to *e*^{−1}.

The TKE is obtained from

$$\begin{array}{}\text{(5)}& \mathrm{TKE}=\mathrm{0.5}(\stackrel{\mathrm{\u203e}}{{{u}^{\prime}}^{\mathrm{2}}}+\stackrel{\mathrm{\u203e}}{{v}^{\mathrm{2}}}+\stackrel{\mathrm{\u203e}}{{{w}^{\prime}}^{\mathrm{2}}}).\end{array}$$

The turbulent transfer efficiencies for momentum and heat fluxes are calculated from

$$\begin{array}{}\text{(6)}& \left|{r}_{uw}\right|={\displaystyle \frac{\stackrel{\mathrm{\u203e}}{{u}^{\prime}{w}^{\prime}}}{{\mathit{\sigma}}_{u}{\mathit{\sigma}}_{w}}},\end{array}$$

$$\begin{array}{}\text{(7)}& \left|{r}_{wT}\right|={\displaystyle \frac{\stackrel{\mathrm{\u203e}}{{w}^{\prime}{T}^{\prime}}}{{\mathit{\sigma}}_{w}{\mathit{\sigma}}_{T}}}.\end{array}$$

The power and cospectra of momentum (*τ*), sensible heat (*H*) and carbon
dioxide (*F*_{C}) fluxes are calculated using fast Fourier transforms for
60 min periods (2^{15} points) using widely used procedures
(Stull, 1998). Spectra are divided into 76 logarithmic, evenly spaced
bins for which the mean values are calculated. The normalised forms for power
spectra of the variable *x* (*S*_{x}(*f*)) and cospectra between *w* and *x*
(*S*_{xw}(*f*)) are used, where they are multiplied by the measurement
frequency (*f*) and divided by variance (var(*x*)=*μ*_{x}) and covariance
(cov(*x*,*w*)), according to

$$\begin{array}{}\text{(8)}& {\displaystyle \frac{f{S}_{x}\left(f\right)}{\mathrm{var}\left(x\right)}},\end{array}$$

$$\begin{array}{}\text{(9)}& {\displaystyle \frac{f{S}_{xw}\left(f\right)}{\mathrm{cov}(x,w)}}.\end{array}$$

The normalised spectra and cospectra are plotted against the normalised
frequency *n*:

$$\begin{array}{}\text{(10)}& n={\displaystyle \frac{f(z-d)}{U}},\end{array}$$

where *U* is the mean wind speed.

3 Results

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The flow distortion areas of both EC systems (no filtering based on FS,
SK and *K*) due to the upper masonry are clearly distinguishable from the
vertical deflection angle (*θ*), normalised TKE and turbulent transfer
coefficients (Fig. 3). Even though the two EC systems were, to the
best of our ability, designed to be identical and symmetrically located on the
opposite side of the masonry, we observe quantitative asymmetry in the first-
and second-moment statistics. The vertical deflection angle, which sets
*w*=0 in the two-dimensional coordinate rotation
(tan${}^{-\mathrm{1}}(\stackrel{\mathrm{\u203e}}{w}/U)$) and describes the distortion of the measurement
structure on the measurements, experiences fluctuating behaviour in these
areas, indicating modified flow structure due to the building masonry
(Fig. 3a). Some of the deviation can be explained by variation in the
surrounding topographies in the direction of flow distortion areas.

Outside the flow distortion areas, the vertical deflection angles vary
between 5 and 18^{∘} with EC1 and between 2 and 15^{∘} with EC2, which
are in the same range as observed at BT Tower in London (Barlow et al., 2011).
The normalised TKE at the flow distortion area measured with EC1 reaches 2.5,
while that measured with EC2 reaches 1.7, showing clearly the asymmetry in the areas. Both EC systems
give a mean value of 0.34 for the normalised TKE outside the flow distortion
areas, indicating that they measure similar turbulence (Fig. 3b).
Furthermore, TKE is fairly uniform with wind direction despite the
measurement location being considered to be complex from the point of view of
micrometeorological measurements. Also the transfer efficiencies for heat are
similar between the two systems with the values of 0.32 for EC1 and 0.29 for
EC2 outside the flow distortion areas (Fig. 3c). The transfer
efficiencies of momentum are clearly different from those of heat and have
the largest deviations between the two systems (Fig. 3d). The transfer
coefficient for heat has a clear dip when the flow is disturbed, whereas the
momentum transfer coefficients follow a more complex pattern. This indicates
the different effect of the measurement platform on the transport of momentum
and heat, with a stronger effect on the former.

The asymmetry of the flow distortion areas is furthermore reflected in the
vertical fluxes of momentum (*τ*), sensible (*H*) and latent heat (LE),
and CO_{2} (*F*_{C}) (Fig. 4). The strength of
asymmetry varies with atmospheric stability and between variables, indicating
that purely prevailing meteorology cannot be responsible for the observed
differences but rather that the morphological effects play a role. Outside the
flow distortion areas, differences between the two systems are small and
depend on the studied flux. The best correlation between the two EC systems
is seen in *H*, with the median of coefficient of determination (*R*^{2}
calculated as the square of the Pearson correlation coefficient) being 0.95,
the slope of the linear least square regression
(EC2 = slope ⋅ EC1 + intercept) being close to 1 and the
intercept being within ±5 W m^{−2} (Fig. 5). The maximum
difference in the absolute values is 20 W m^{−2} (Fig. 4b) in
unstable conditions. In the correlation of *τ*, the largest differences of all
fluxes with a sinusoidal pattern as a function of wind direction are seen.
The slope varies between 0.5 and 1.8, and the intercept is systematically below
0, indicating lower momentum flux measured by the EC2 than EC1
(Fig. 5a, b). Furthermore, the median *R*^{2} between the two
measurement systems is 0.85 (Fig. 5c). The directional
dependencies and correlations between the two systems in measuring LE and
*F*_{C} follow a similar pattern, indicating similarity between the two
variables (Figs. 4c, d and 5). For LE, the correlation
statistics are however somewhat lower than for *F*_{C}. LE has a
coefficient of determination in the range of 0.6–0.9, a slope in the range
of 0.7–1.0 and an intercept of the order of 10 W m^{−2}, with a greater
flux measured with EC2 than EC1. For *F*_{C} the respective values are
0.8–0.9, 0.7–1.1 and 0–5 µmol m^{−2} s^{−1}. The absolute
differences yield −1.9 W m^{−2} and
−0.3 µmol m^{−2} s^{−1}, respectively. The correlation
statistics in our case are slightly poorer than observed over a a grassland
in the UK (Mccalmont et al., 2017), where *R*^{2} scatter suggested sampling
uncertainty between 5 % and 7 % as compared to our 10 %–20 %.

The separation distance between the two EC systems is less than 10 m, and thus
they are expected to measure the same source area outside the flow distortion
areas. At the same time the observed differences cannot arise from the
post-processing as fluxes were calculated and processed in a similar manner.
Some of the difference can still originate from instrument drifting, but this
would indicate non-directional dependence. As a result, the differences in
the fluxes measured by the two systems very probably relate to the variation
of the flux field caused by complex terrain. In past studies above vegetated
ecosystems, the random uncertainty of flux measurements resulting from
instrumental errors, heterogeneity of the surface and turbulence has been
determined using the so-called two-tower approach (Hollinger and Richardson, 2005; Kessomkiat et al., 2010). Its assumption is that the two time series should be
independent from each other and thus cannot be used in our case when the two
systems are measuring the same footprint. We can however still calculate the
RRE in order to get an understanding about the random
uncertainties of our EC measurements. Of all studied vertical fluxes, the
largest random uncertainties relate to *τ* (medians between 23 % and 28 %) and
the lowest to daytime *H* (medians 12 % and 13 %) (Fig. 6). For
*τ* no systematic pattern between daytime and night-time is seen, whereas for
the other fluxes nocturnal uncertainties tend to be larger when the
scalar fluxes are small. For fluxes other than momentum, RREs from EC2 are slightly larger than
those from EC1, whereas for *τ* it is vice versa. The RREs are of the same
order of magnitude as observed at the semi-urban site in Kumpula and above
vegetated ecosystems. In these, however, the RRE associated with *τ* tends
to be the lowest contrary to our study (Billesbach, 2011; Finkelstein and Sims, 2001; Nordbo et al., 2012b), which is because of the complex measurement
location and source–sink distribution at our site.

Both statistical variables RRE and *R*^{2} should theoretically be a measure of
random uncertainty. When RREs measured with the two systems are larger, *R*^{2}
between the systems is expected to be smaller. Furthermore, we expected the
two resulting uncertainty rankings (according to RRE and R2) across the
different fluxes to be consistent. However, this is not observed, and based on
R^{2} the fluxes can be ranked in increasing order LE, *F*_{C}, *τ* and
*H* both in day- and night-time (0.79, 0.82, 0.86, 0.92 and 0.66, 0.85, 0.88,
0.94). A possible explanation for this is that *R*^{2} is calculated between
the two EC systems and is impacted by systematic disturbances and the
building masonry. Thus, RRE is considered to be more representative for flux
random uncertainties.

SK is within the limits of good data quality ($-\mathrm{2}<\mathrm{SK}<\mathrm{2}$) for all studied
variables, excluding CO_{2} (Fig. 7, Table 1). Particularly
elevated values in the skewness of CO_{2} (SK_{C}) are seen during the
daytime in directions 150–200^{∘}, with the median SK_{C} reaching
4, whereas in other directions the medians are around 1. The 90th
percentiles can reach as high as 5 in directions 150–200^{∘} as is
summarised in Table 1. A similar elevated pattern can also be seen
in the kurtosis of CO_{2} (*K*_{C}) with the median values reaching
25, indicating spiky behaviour in CO_{2} (Fig. A1). These elevated values
are only seen during the daytime, so these must relate to the daily activities
emitting CO_{2} and/or prevailing meteorological conditions. The same can
clearly be seen from the diurnal variability of both SK_{C} and *K*_{C} shown
in Fig. 8 for summer months from June till August. Same
behaviour is also seen in other months (not shown). While for directions
150–200^{∘} elevated values for both statistical variables are seen,
in other directions the diurnal variability of SK_{C} and *K*_{C} is relatively
flat, with the 90th percentiles remaining mostly below 2 and 6, respectively.

In the direction of elevated SK_{C} and *K*_{C}, both variables start to
increase in the morning at 06:00 (UTC + 2), corresponding with the increase in both road
traffic and atmospheric instability observed in Helsinki (Kurppa et al., 2015).
Two clear peaks in SK_{C} and *K*_{C} are seen around noon and afternoon
between 15:00 and 19:00. The first peak corresponds with maxima mixing conditions, and
the second peak with afternoon rush hour. Commonly, at the time of morning rush
hour (07:00–09:00) the atmospheric mixing is still relatively weak and
pollutants from the street level are not necessarily as easily transported to
the measurement level (Contini et al., 2012; Kurppa et al., 2015). Previously, a skewed
distribution of turbulent velocity components within and just above the
street canyon has been linked to street canyon vortexes causing sweeps and
ejections (Oikawa and Meng, 1995). This could also be a potential explanation for
the high SK_{C} and *K*_{C} values in directions 150–200^{∘} since these
directions correspond with wind blowing perpendicular to the streets in the grid
type street network in Helsinki. Previous studies utilising large-eddy
simulation have also shown how street canyon ventilation and sweeps increase in
more unstable conditions (Gronemeier et al., 2017; Raupach et al., 2015), which is in
accord with our results related to the timing of the maximum SK_{C} and *K*_{C}. But
the effect of meteorological background conditions cannot be ruled out since
the directions with elevated SK_{C} and *K*_{C} correspond with flow coming from the
sea, which can further modify the flow and skewed distribution of CO_{2}
concentration. High skewness values of CO_{2} data have previously been
connected to local-scale anthropogenic sources (Kotthaus and Grimmond, 2012). At the
hotel building, small ventilation units are located 9 m below the measurement
systems in the north-eastern, north-western and south-western corners, but, as
these do not match the directions 150–200^{∘} and systematic signals
are seen in both EC1 and EC2, these units cannot be responsible for the
increased SK_{C} and *K*_{C}. Furthermore, these local-scale sources have been
connected to increased fluxes *F*_{C} and *H* as well as decreased LE, whereas
in our case slightly higher flux values are only seen in *F*_{C} in unstable
conditions in directions 150–200^{∘} (Fig. B1). Notwithstanding
the reason for the elevated SK_{C} and *K*_{C}, filtering *F*_{C} data based on
these variables would remove realistic flux values, and therefore they should
be used with caution in post-processing of CO_{2} fluxes.

At the same time, with increased SK_{C} and *K*_{C} in the southern direction,
the flux stationarity of *F*_{C} remains below 0.2, which is considered to
constitute high-quality flux data (Fig. 9). Thus, applying only the
stationarity criteria with either a 30 % or a 60 % limit but no skewness
or kurtosis criteria would leave most of the data for further data analysis. The
most non-stationary variable is the latent heat flux, with 90th
percentiles systematically over 1 in all directions and hours as measured by
both setups. FS_{h} gets slightly greater values with EC1 than EC2, with the
former having median values of 0.24 (90th percentile: 1.24) in summer and
0.39 (1.56) in winter, and the latter 0.21 (1.08) and 0.39(1.53),
respectively. Interestingly, relatively large flux stationary values of
momentum flux are seen both by day and night. Usually, the momentum flux is
least filtered based on the stationarity criteria, but in our case, due to the
complex measurements location, relatively large data proportions would be
filtered away. The median values are 0.27 (0.69) in summer and 0.17 (0.51) in
winter for EC1, which is fairly similar to EC2, with median values of 0.28 (0.67)
and 0.19 (0.45). Despite the similar magnitude quartile values, EC1 gets
greater values in directions 190–360^{∘} and EC2 symmetrically in
directions 0–180^{∘}.

More information about the similarity/dissimilarity of the two EC systems can
be obtained via spectral analysis (Fig. 10). The largest
differences outside the flow distortion areas can be seen in the cospectrum
of momentum flux with similar contribution only at $n=\mathrm{0.02}-\mathrm{0.1}$ between the
two systems (Fig. 10a). With EC1, more contribution is seen
at larger eddies, and in the inertial subrange ($n=\mathrm{0.1}-\mathrm{0.4}$) the decay is
faster than with EC2. A possible explanation for the higher-energy, larger
eddies is the building wake effect. With both systems, negative contributions
to the total momentum flux are seen at normalised frequencies >0.5, which
are likely to be related to the measurement location being on top of a tower.
This supports the previous findings that velocity components are more
impacted by the measurement location than the scalars. Similarly to *τ*,
in the cospectra of *F*_{C} the larger eddies (below normalised frequency
0.03) contribute slightly more to the total flux measured by EC1 than
EC2 and the energy decaying in the inertial subrange (*n*>2) is faster than
in the case of EC2 (Fig. 10c). Thus, the flux differences
seen in *τ* and *F*_{C} between the two systems are to a large extent caused
by the larger eddies rather than small-scale variations. For the temperature
flux covariance (Fig. 10e), such differences are not seen,
but rather the contribution of different-sized eddies is very similar between
the two systems. Atmospheric spectra of all quantities measured by both
systems are similar (Fig. 10b, d, f). This indicates different
transport mechanisms for temperature and CO_{2}, which has also been found
when comparing the transfer efficiencies of the different scalars in this
study and in Nordbo et al. (2013) at the same site.

One of the key questions of this study is on how representative a single EC
measurement point, in measuring vertical fluxes, can be when the measurements
are forced to be conducted close to urban structures, potentially causing a
large removal of data due to flow distortion areas. After flow distortion and
stationarity filtering, the temporal annual coverages at the continuous
measurement site EC1 vary from 24 % to 50 %, with *H* and *F*_{C} having mean data
coverages of 44 % and 45 % as compared to LE of 31 % (Table 2).
The inclusion of the second EC system increases the data coverage
substantially, with *H* having mean coverage of 65 %, LE of 45 % and *F*_{C} of 69 %.
The next step is to examine the impact of the different data coverages on the
cumulative flux values.

The annual cumulative flux values of CO_{2} and sensible and latent heat
calculated for two annual periods (July 2013–June 2014 and July 2014–June 2015) using different gap-filling methods are shown in Fig. 11.
EC1 and EC2 are gap-filled with their own median cycles using a 3-month
period around the month being gap-filled with a separation into workdays and
weekends. EC1 + EC2 is a combination of EC1 and EC2 systems, with data from
the first taken in directions 230–340^{∘} and the latter in directions
40–130^{∘}, and in other directions the mean of the two systems is
calculated. Missing data were furthermore gap-filled in a similar fashion to
EC1 and EC2. In the case of *F*_{C}, EC1 + EC2 gives 3 %–12 % larger cumulative
flux values than using only EC1 or EC2, with an annual mean value of
0.375 kmol m^{−2}, corresponding to 4500 g C m^{−2} (Table 2).
This indicates that the resulting error in cumulative carbon fluxes due to
the single EC measurement point is up to 12 % when other error sources are
ignored. For *H* and LE, the differences between the combination data set
and EC1 and EC2 are up to 5.3 % and 8.1 %, respectively, with larger
cumulative values obtained with EC1 + EC2 than the separate instruments. The
difference in *F*_{C} is of the same order of magnitude as what has been
observed above a forest site within a separation of 30 m between two EC
systems (Rannik et al., 2006).

If, in addition to the flux stationarity, we had used the common limits
of *K*<1 and *K*>8 and $\left|\mathrm{SK}\right|>\mathrm{2}$ to filter out data, the data
coverages of the single EC systems would have decreased by 11 % for
*F*_{C} and 3 % and 1 % for *H* and LE, respectively (Table 2). This
would have given a mean cumulative *F*_{C} of 0.3445 kmol m^{−2}
(4134 g C m^{−2}), which is 3.5 % lower than what was obtained by using
a combination of EC1 + EC2 (0.357 kmol m${}^{-\mathrm{2}}=\mathrm{4284}$ g C m^{−2}).
Thus, using FS, SK and *K* to filter our flux data will cause 4.5 %
lower cumulative *F*_{C} than using only FS.

The outcome of our study is that a single EC measurement point can produce reasonable estimations for surface fluxes above relatively homogeneous urban surface, but the next question naturally is how applicable this result is for other urban EC sites. Each urban measurement location is unique; in order to get a final answer, each site should be separately evaluated with more than one measurement setup. Nevertheless, the obtained uncertainties from this study can be used as a first approximation for urban EC measurements in the same way as the few two- or multiple-tower studies made in vegetated ecosystems are used to give general guidelines for the uncertainties.

4 Conclusions

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In this study, simultaneous measurements from two EC systems were compared over the highly built-up Helsinki city centre. The identical systems were located symmetrically on either side atop a tower structure with building masonry located in between. Data were identically analysed. This allowed us to examine the sensitivity of a single-point EC system in measuring the vertical fluxes of momentum, sensible and latent heat, and carbon dioxide, and to understand what the implications are of the non-ideal measurement location and resulting data removal of the studied fluxes.

The flow distortion areas (40–150 and 230–340^{∘}) of the
two EC systems caused by the building masonry are most clearly
distinguishable from wind-normalised TKE. These areas together with a
stationarity limit of 30 % resulted in data coverage ranging 24 %–50 %
when measured with a single system. Outside the flow distortion areas, momentum flux is the
most sensitive of all fluxes for the measurement location and flow
modifications caused by the masonry, with random uncertainties being around
25 %. With scalar fluxes these remained between 18 % and 22 %. Most of the
differences in momentum fluxes are due to larger-scale eddies as revealed by
spectral analysis indicating larger-scale structures being responsible for
the observed differences between these two fluxes.

The two systems had a separation distance of 10 m, indicating that both systems
were measuring virtually the same source area, and therefore the differences are
considered to be caused by variations in flux fields due to the complex
surroundings and measurement platform. Despite the measurement location of
the EC systems being non-ideal from the point of view of flow distortion, the
possible bias caused by a single measurement point is less than 12 % for
CO_{2} flux and less than 5 % and 8 % for sensible and latent heat fluxes,
respectively. In general, the results show how a single-point EC measurement
can be representative for flux estimates in Helsinki city centre despite the
relatively large flow distortion area removing 27 % of the data. This result
is naturally location-specific for this highly built-up site with vegetation
cover comprising only 22 % and a relatively homogeneous roof level (Nordbo et al., 2013).
The same result could be considered to apply also in other dense city centres
with similar relatively homogeneous surface characteristics.

We furthermore show that kurtosis and skewness of concentration measurements,
common variables used to flag EC data over vegetated surroundings, are not
reasonable measures to filter CO_{2} flux data in dense urban environment due
to the combined effect of temporally varying traffic network, meteorological
conditions and characteristics of the upwind source area causing natural
spikiness in the CO_{2} data. Flux stationarity is not impacted in a similar
fashion and is therefore considered to be more suitable for filtering CO_{2}
flux data in urban areas. The usage of all three variables to filter out
CO_{2} flux data will cause an underestimation of 4.5 % in annual cumulative
carbon fluxes.

Our results are the first from urban areas to characterise the representativeness of single-point EC flux measurements in a densely built urban environment using a combination of two EC systems located close to each other. The related uncertainties are of the same order of magnitude as observed above vegetated ecosystems. The obtained values can be used as a rule of thumb when evaluating in general the representativeness of urban EC measurements used to estimate direct vehicular and building emissions of greenhouse gases and air pollutants. We point out how particular attention should be paid to the data quality control procedures commonly used above vegetated surfaces.

Data availability

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Data availability.

Data sets used in the data analysis will be saved to and can be freely downloaded from https://avaa.tdata.fi/web/smart/smear/ (last access: 1 October 2018).

Appendix A

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Appendix B

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Author contributions

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Author contributions.

LJ, AK, RDK, TV and CRW planned the measurements; TVK and PR were responsible for the eddy covariance measurements; MK calculated the eddy covariance data; and LJ and ÜR performed further data analysis. All authors participated in writing the manuscript.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The work was supported by the Academy of Finland project ICOS-Finland and
Centre of Excellence programme (grant no. 307331), and Atmospheric
Mathematics collaboration (AtMath) of the Faculty of Science, University of
Helsinki, and Maa- ja vesitekniikan tuki ry (grant no. 36663). We also thank
Sokos Hotel Torni for allowing us to use their building for our EC
measurements and Jaakko Kukkonen, Annika Nordbo and Risto Taipale for
additional help with the measurements and data analysis.

Edited by: Christian Brümmer

Reviewed by: Olaf Menzer and one anonymous referee

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