The measurements were conducted in central Helsinki (Fig. ), where two identical EC setups were installed on top of a hotel building (Fig. ) 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 . 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 . 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. ). 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 . 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 . 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. ).

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 CO2. 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 . 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 CO2 and 0–7 s for H2O). 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 CO2 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 . 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 SK=(x′3)‾σx3, 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 σx 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 K=(x′4)‾σx4. K between 1 and 8 is considered as reasonable-quality data.

The relative random error (RRE) of the vertical flux of scalar x (F=w′x′‾, where w is the vertical wind speed) is calculated as the square root of the random error variance (σF2) normalised with the absolute value of the flux according to : RRE=σF(Γ)|F|=(2μρΓρΓ)1/2, where ρ refers to the instantaneous flux (w′s′). μρ is the flux variance: μρ=μwμx+F2, where μw and μx are the variances of w and x, Γ is the averaging period (30 min), and Γρ is the integral timescale defined as the integral over the autocovariance function (Rρ; ) and in practice is estimated as the lag when Rρ drops to e-1.

The TKE is obtained from TKE=0.5(u′2‾+v2‾+w′2‾). The turbulent transfer efficiencies for momentum and heat fluxes are calculated from |ruw|=u′w′‾σuσw, |rwT|=w′T′‾σwσT.

The power and cospectra of momentum (τ), sensible heat (H) and carbon dioxide (FC) fluxes are calculated using fast Fourier transforms for 60 min periods (215 points) using widely used procedures . 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 (Sx(f)) and cospectra between w and x (Sxw(f)) are used, where they are multiplied by the measurement frequency (f) and divided by variance (var(x)=μx) and covariance (cov(x,w)), according to fSx(f)var(x), fSxw(f)cov(x,w). The normalised spectra and cospectra are plotted against the normalised frequency n: n=f(z-d)U, where U is the mean wind speed.

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. ). 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-1(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. a). 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 . 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. b). 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. c). The transfer efficiencies of momentum are clearly different from those of heat and have the largest deviations between the two systems (Fig. d). 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 CO2 (FC) (Fig. ). 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 (R2 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. ). The maximum difference in the absolute values is 20 W m-2 (Fig. b) 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. a, b). Furthermore, the median R2 between the two measurement systems is 0.85 (Fig. c). The directional dependencies and correlations between the two systems in measuring LE and FC follow a similar pattern, indicating similarity between the two variables (Figs. c, d and ). For LE, the correlation statistics are however somewhat lower than for FC. 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 FC 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 , where R2 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 . 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. ). 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 , which is because of the complex measurement location and source–sink distribution at our site.

Both statistical variables RRE and R2 should theoretically be a measure of random uncertainty. When RREs measured with the two systems are larger, R2 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 R2 the fluxes can be ranked in increasing order LE, FC, 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 R2 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 (-2<SK<2) for all studied variables, excluding CO2 (Fig. , Table ). Particularly elevated values in the skewness of CO2 (SKC) are seen during the daytime in directions 150–200∘, with the median SKC 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 . A similar elevated pattern can also be seen in the kurtosis of CO2 (KC) with the median values reaching 25, indicating spiky behaviour in CO2 (Fig. ). These elevated values are only seen during the daytime, so these must relate to the daily activities emitting CO2 and/or prevailing meteorological conditions. The same can clearly be seen from the diurnal variability of both SKC and KC shown in Fig.  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 SKC and KC is relatively flat, with the 90th percentiles remaining mostly below 2 and 6, respectively.

In the direction of elevated SKC and KC, 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 . Two clear peaks in SKC and KC 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 . 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 . This could also be a potential explanation for the high SKC and KC 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 , which is in accord with our results related to the timing of the maximum SKC and KC. But the effect of meteorological background conditions cannot be ruled out since the directions with elevated SKC and KC correspond with flow coming from the sea, which can further modify the flow and skewed distribution of CO2 concentration. High skewness values of CO2 data have previously been connected to local-scale anthropogenic sources . 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 SKC and KC. Furthermore, these local-scale sources have been connected to increased fluxes FC and H as well as decreased LE, whereas in our case slightly higher flux values are only seen in FC in unstable conditions in directions 150–200∘ (Fig. ). Notwithstanding the reason for the elevated SKC and KC, filtering FC data based on these variables would remove realistic flux values, and therefore they should be used with caution in post-processing of CO2 fluxes.

At the same time, with increased SKC and KC in the southern direction, the flux stationarity of FC remains below 0.2, which is considered to constitute high-quality flux data (Fig. ). 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. FSh 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. ). The largest differences outside the flow distortion areas can be seen in the cospectrum of momentum flux with similar contribution only at n=0.02-0.1 between the two systems (Fig. a). With EC1, more contribution is seen at larger eddies, and in the inertial subrange (n=0.1-0.4) 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 FC 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. c). Thus, the flux differences seen in τ and FC 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. e), 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. b, d, f). This indicates different transport mechanisms for temperature and CO2, which has also been found when comparing the transfer efficiencies of the different scalars in this study and in 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 FC having mean data coverages of 44 % and 45 % as compared to LE of 31 % (Table ). The inclusion of the second EC system increases the data coverage substantially, with H having mean coverage of 65 %, LE of 45 % and FC 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 CO2 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. . 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 FC, 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 ). 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 FC 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 .

If, in addition to the flux stationarity, we had used the common limits of K<1 and K>8 and |SK|>2 to filter out data, the data coverages of the single EC systems would have decreased by 11 % for FC and 3 % and 1 % for H and LE, respectively (Table ). This would have given a mean cumulative FC 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-2=4284 g C m-2). Thus, using FS, SK and K to filter our flux data will cause 4.5 % lower cumulative FC 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.