A statistical linear relationship between NO2 surface concentration and its integrated content in the atmospheric boundary layer (ABL) is established in urban conditions, using ABL depth as an ancillary parameter. This relationship relies on a unique data set including 20 months of observations from a ground-based UV-visible light spectrometer and from an aerosol lidar, both located in Paris inner city center. Measurements show that in all seasons, large vertical gradients of NO2 concentration exist in Paris developed ABL, explaining why the average concentration retrieved is only about 25% of NO2 surface concentration. This result shows that the commonly used hypothesis of constant mixing ratio in the ABL is not valid over urban areas, where large NOx emissions occur. Moreover, the relationship obtained is robust, and the studied area lacks of any particular orographic features, so that our results should be more widely applicable to pollution survey from space-borne observations.
 Nitrogen dioxide (NO2) surface concentrations have become necessary measurements of air quality in cities due to road traffic and industrial activities. However, in situ measurements are affected by dilution and reactivity in the atmospheric boundary layer (ABL), and a large number of observations is required to derive a representative emission budget over extended urban areas. This makes NO2 surface concentration measurements difficult to use to monitor nitrogen oxides (NOx ≡ NO+ NO2) emissions. Moreover, not all cities are well equipped, particularly in developing countries, though they represent a growing part of NOx emissions.
 Satellite observations provide information on NO2 vertically integrated content in the troposphere. Over polluted areas, this quantity is mostly related to the ABL, and better suited than surface measurements to account for NOx emissions. But the use space-borne observations to monitor air quality presently suffers from a limited horizontal resolution and temporal coverage (clouds, overpass time). The main problem is that no relationship has been proven to be reliably usable to deduce the surface concentration from the measured integrated content. Indeed, to our knowledge, no NO2 concentration profile has ever been measured over urban areas, though they are new developments, for example, using Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) [Irie et al., 2011] or radiosondes [Sluis et al., 2010]. As a consequence, linking NO2 surface concentration to the integrated content in the ABL requires an hypothesis on NO2 vertical distribution in the ABL.
 To bridge this gap, some authors have supposed a homogeneous distribution in the ABL [e.g. Boersma et al., 2008], while others make use of NO2 profiles from chemistry-transport models [e.g. Lamsal et al., 2008]. This makes it possible to relate the year-to-year and seasonal variability of NO2 observed at ground level and from space, from which monthly NOx emissions can be estimated. However, neither of these solutions enables to monitor emissions at a shorter time scale, as point to point comparison between surface and space-borne observations show very large dispersion over cities. Yet, estimating daily NOx emissions is mandatory to monitor the impact of cities on regional air quality.
 In order to understand why previous studies experienced difficulties over urban areas, we have compared NO2 surface concentrations with ground-based NO2 integrated content and ABL depth measurements over the well-documented area of Paris. Surface NO2 observations are provided by the air quality network AIRPARIF (http://www.airparif.asso.fr/) that include surface stations and altitude measurements (300 m elevation). The NO2 integrated content is obtained by a zenith-sky UV-visible (UV-vis) light spectrometer located in Paris city center at the University Pierre et Marie Curie (UPMC) Qualair facility, along with an aerosol lidar giving ABL height information. This experimental setup provided us with a unique dataset over several years to analyze NO2 behavior in urban conditions.
 NO2 observations from the air quality network and from the UV-vis spectrometer will be presented in Section 2, and NO2 variability will be analyzed to underline vertical gradients in the urban ABL. Adding ABL depth measurements from the aerosol lidar, a statistical relationship between NO2 surface concentration and integrated content in the ABL will be derived in Section 3. The unexpected form of this relationship and its consequences in terms of NO2 vertical mixing and satellite validation will be discussed in Section 4.
2 NO2 Variability Over Paris
2.1 NO2 Surface Concentrations
 Hourly measurements of NO2 surface concentrations provided by Paris air quality network (AIRPARIF) are using the standard in situ NOx analyzers prescribed by air quality regulations. NO2 is measured after reduction to NO on a heated Molybdenum converter, which is known to convert efficiently other oxidized nitrogen species (NOz) like HNO3 and peroxyacetyl nitrate. NO2 concentrations can thus be overestimated by as much as 50%, depending on photochemical activity, as confirmed during urban campaigns [Dunlea et al., 2007] or in rural stations [Ordóñez et al., 2006]. The impact of this bias will be discussed in Section 4.
 The six urban background stations in Paris are averaged to estimate the mean hourly NO2 surface concentration in the city (CgM). Figure 1(a) presents the median diurnal and seasonal cycle of CgM, calculated over 6 years (2005–2010). The daily cycle of NO2 surface concentration is dominated by NOx emissions variability, that is, by traffic, which represents half of NOx emissions in Paris region. During traffic peak periods (07–10 and 17–20 LT), NO2 concentrations are mainly driven by emission level and by vertical dilution, that is, by ABL depth (this is why the evening peak on Figure 1(a) is much less visible in summer). Outside those peak periods, an off-peak regime exists around noon, where the seasonal cycle of NOx chemical lifetime and ABL depth are the dominant parameters.
2.2 NO2 Vertical Gradient
 AIRPARIF runs a station at Eiffel Tower top (300 m above ground level) that allows to monitor the vertical gradient in the lower ABL. The diurnal and seasonal variability of the relative difference (CgM − CET) ∕ CgM, where CET is the concentration at tower top, are presented on Figure 1(b). The difference is always positive, meaning there is less NO2 in altitude. Yet, concentrations could be expected to grow with altitude as NO emissions are converted to NO2 by reaction with ozone. This means that most of NO is converted below the tower top, which is confirmed by looking at NO gradient values (not shown here). Then, NO2 concentrations decrease with altitude due to dilution and chemical conversion to NOz.
 During the night, except in summer, the vertical gradient is very large as the tower top is often out of the nocturnal ABL. The large nighttime variations from one month to the next are due to ground-level variability as they do not appear on the absolute difference (not shown here). During daytime, the vertical gradient quickly decreases by a factor of two about 2–3 h after sunrise, when the convective ABL starts rising and reaches the tower top. However, even during the morning ABL growth, when the vertical mixing is most efficient, there is still at least 25% less NO2 at the tower top than at ground level. For comparisons with integrated content measurements, this means that the homogeneous ABL hypothesis will lead to a large overestimation of the columns.
2.3 NO2 Integrated Content
 The Système d'analyse par Observation au Zénith (SAOZ), a zenith-sky UV-visible spectrometer [Pommereau and Goutail, 1988], has been monitoring NO2 in Paris from January 2005 as part of the observation platform Qualair (http://qualair.aero.jussieu.fr/) on the UPMC Jussieu campus. Every 15 minutes, a spectrum of the sunlight diffused in the zenith direction is measured and NO2 total slant column density (SCD) is retrieved using Differential Optical Absorption Spectroscopy (DOAS) in NO2 absorption bands at 410–427 and 433–530 nm.
 The SCD stratospheric part is estimated using measurements at dawn (Solar Zenith Angle > 90°) when the light path is much longer in the stratosphere and absorption by tropospheric NO2 can be neglected. This hypothesis is not entirely true during a pollution episode so the median of the last 3 days is used instead of the current day measurement. The dawn column is corrected for NO2 daily cycle in the stratosphere using a stratospheric chemistry model. From a 1-year run of the Single Layer Isentropic Model of Chemistry and Transport (SLIMCAT), monthly averaged coefficients of the ratio between stratospheric SCD at various time of the day and at dawn were derived. After subtracting the stratospheric SCD, the remaining tropospheric SCD is converted to a vertical column density (VCD noted Ω) by division with an air mass factor (AMF).
 The SAOZ AMF is the average of the daily AMF calculated during the Cabauw Intercomparison campaign for Nitrogen Dioxide measuring Instruments (CINDI) in Netherlands, using NO2 and aerosol extinction profiles performed by a Multi-Axis UV-vis spectrometer (MAX-DOAS) Clémer et al., 2010 personal communication) [Piters et al.., 2012]. To limit the possible AMF underestimation due to multiple scattering in the larger aerosol optical depths (AOD) observed in Paris, the 550–600 nm sky color ratio is used to discard cloudy and high-AOD spectra. The threshold value was tuned using coincident measurements of the collocated Aerosol Robotic Network sunphotometer so as to reject AOD values greater than 0.35 at 440 nm [Dieudonné, 2012].
 The main sources of error are the possible overestimation of the stratospheric SCD and AMF underestimation, but they have opposite effects on the tropospheric VCD and will partly cancel each other. For another zenith-sky DOAS in Shanghai, Chen et al.  estimated that the total uncertainty on tropospheric VCD can reach 50% for small VCD ( < 10.1015 cm − 2). However, most observations over Paris are above this value, and the total uncertainty estimated by Chen et al.  is around 30–40%.
 The median diurnal and seasonal cycle of NO2 tropospheric VCD retrieved over Paris are presented on Figure 1(c). Over a polluted area like Paris, the tropospheric VCD (latter on just called column) is expected to be dominated by the ABL contribution. However, columns and surface concentrations are expected to show a very different behavior: in a growing ABL, vertical dilution will reduce surface concentrations, while columns can still increase as NO2 keeps accumulating in the ABL. Indeed, the column daily maximum in Paris occurs in late morning instead of during the morning traffic peak.
3 Concentration/Column Relationship
3.1 Boundary Layer Depth Observations
 In order to derive a relationship between NO2 surface concentration and integrated content, we used measurements of ABL depth provided by the Qualair 532 nm aerosol lidar [Dieudonné, 2012]. ABL top can be determined above a 180 m height using a gradient detection method as in Menut et al. . To match the time resolution of in situ observations, this method is applied on the hourly averaged signal. The dataset used in this paper spans over 20 months, from July 2009 to February 2011, and covers around 50% of the days, generally from 9 to 18 LT. Observations occurring less than 3 h after sunrise are discarded so as to limit to the NO2 off-peak conditions. This leaves 821 coincident measurements of NO2 surface concentration, NO2 column, and ABL depth. As afternoons are generally more cloudy, limiting SAOZ observations, only 21% of points occur after 15 UTC—10% after 16 UTC—so that this data set mostly corresponds to the developing ABL.
3.2 Statistical Treatment
 The scatter plot of NO2 column as a function of the surface concentration is presented on Figure 2, with a color code for ABL depth. When the ABL is deeper, the NO2 column Ω grows faster along with the surface concentration CgM. To investigate this dependency, observations are split into eight classes following ABL depth values (Table 1a). The eight correlation coefficients between CgM and Ω lie between 0.69 and 0.77, indicating a rather homogeneous behavior for similar values of ABL depth. In each class, a linear fit of Ω versus CgM is performed. The resulting fit lines are plotted on Figure 2, while Table 1(a) gives the slope (p) and intercept (q) values. As expected from previous observations, p increases with growing ABL depth.
Table 1. (a) Classes of ABL Depth With Number of Points N, Correlation Coefficient r and Results of the Linear Fit Ω ∕ K = p × CgM + q Between NO2 Tropospheric VCD Ω and Surface Concentration CgM for Each Classa. (b) Correlation Coefficient and Results of the Linear Fit p or q = a × h + b Between the Slopes p or Intercepts q and the Median ABL Depth h in Each Classb
(a) Linear fit Ω ∕ K = p × CgM + q
(cm − 2 ∕ μg.m − 3)
(cm − 2)
aK = 1.31.1015 is a constant factor coming from unit conversion between h in km, CgM in μg.m − 3 and Ω in cm − 2.
bThe first step fits are least-square (Y|X) without error. The second step fits are least-square (Y|X) using uncertainties on p and q as Y-error.
0.260 ± 0.044
− 2.107 ± 2.295
0.289 ± 0.028
− 1.718 ± 1.244
0.388 ± 0.035
− 4.721 ± 1.286
0.448 ± 0.071
− 4.232 ± 2.106
0.443 ± 0.058
− 3.050 ± 1.550
0.503 ± 0.053
− 1.857 ± 1.200
0.616 ± 0.078
− 4.732 ± 1.542
0.692 ± 0.101
− 5.314 ± 1.753
(b) Linear fit p or q = a × h + b
0.244 ± 0.038
0.184 ± 0.034
− 0.337 ± 0.323
− 0.512 ± 0.297
 These slopes and intercepts values are then plotted as a function of the median ABL depth h in each class (Figure 3) and a linear fit of p and q versus h is performed (results in Table 1b). The slopes p increase in a remarkably linear way with ABL depth, leading to a correlation coefficient of 0.98. This means that ABL depth is a main parameter to account for slope variability. However, the linear fit has a nonzero intercept, which means that the integrated content is not directly proportional to the product hCgM (homogeneous column) but includes a term independent of ABL depth as will be further discussed in the next section.
 The intercepts q tend to decrease while ABL depths increase, but their behavior appears slightly different in the 0.6–1.6 km height range. Observations in these classes often correspond to the late morning period when the ABL grows rapidly. At this time, the entrainment of large amounts of clean air in the ABL could explain the different behavior. Anyway, the correlation coefficient being only − 0.55, ABL depth is not the only parameter influencing the intercepts.
 To discuss the dependency of NO2 column against ABL depth and NO2 surface concentration, results of the slopes and intercepts fits are combined to create a bilinear model as follows:
where K is a unit conversion factor (see note (a) in Table 1).
 Results from Section 2 underline the existence of strong vertical gradients of NO2 concentration in Paris urban ABL. Moreover, the large diurnal and seasonal variability results in very different behaviors for NO2 surface concentrations and columns. As a consequence, the homogeneous ABL hypothesis often used to calculate DOAS AMF and for satellite validation appears unrealistic over high-emission areas. Yet, we showed in Section 3 that in spite of large uncertainties on NO2 observations, a robust relationship between NO2 surface concentration and column can be established, using only ABL depth as an ancillary parameter. This relationship covers all seasons and describes NO2 vertical mixing over Paris in the daytime developing ABL.
 Equation (1b) shows that NO2 column depends on an effective surface concentration lower than the measured concentration by 1.38 ± 1.32 μg.m − 3 in the first term and 2.83 ± 1.61 μg.m − 3 in the second one. Given the uncertainties, both values are compatible with a mean value around 2 ± 1 μg.m − 3. This could be interpreted as a bias in NO2 measurements due to NOz interferences in standard NOx analyzers. The large uncertainties would then result from interference variability, following local photochemical activity and nonlocal production (import from Benelux and Ruhr regions). Another explanation could be that ground-level stations do not represent the true urban background because horizontal dilution is not complete.
 The second term of equation (1b) is a product between the effective concentration and a fixed height h0 = 184 ± 34 m. h0 is too large to be the actual depth of the surface layer but can be interpreted as an effective mixing height, describing turbulent transfer processes from the surface layer to the mixed part of the ABL. The first term of equation (1b) corresponds to the homogeneous ABL column but with a 24.4 ± 3.8% factor, which means that the average ABL concentration is only one fourth of the ground-level effective concentration. According to Stull , the entrainment zone occupies in average 40% of the convective ABL, with concentrations being in average half of their mixed layer value, so that entrainment could explain only a 0.8 factor. Correcting for NOz interferences would lead to concentrations smaller by a 0.5 to 1.0 factor, depending on the hour and season [Dunlea et al., 2007; Ordóñez et al., 2006]. The slopes p would then increase by an average 1 ∕ 0.75 = 1.3 factor, resulting in an ABL average to surface concentration ratio around 33%. The effect of SAOZ errors is probably much smaller due to the partly canceling errors.
 To account for a 0.33 factor, NO2 has to be efficiently removed before it can reach the ABL upper levels. Photochemical losses (conversion to NOz) are unlikely to be responsible. Indeed, NOx lifetime estimations available in the literature are all above 1 h (Kondo et al.  and references therein), while the vertical mixing time is 10 to 20 min [Stull, 1988]. However, this time is long enough to allow part of the NO2 to be pushed away from the city center by the wind. Turbulent dispersion modeling studies like Vinuesa and Galmarini  confirm that horizontal export could create such a vertical gradient, even at moderate wind speeds.
 Simple models with linear or exponential concentration profiles in the ABL were also tested but both lead to large overestimations of the columns and neither can reproduce their seasonal variability [Dieudonné, 2012]. Adding a surface layer with higher concentrations, as suggested by the second term of equation (1b), may help solving the problem, but then, we lack information to conclude on the exact profile shape. Further analysis of our data will thus investigate the influence of wind speed, try to quantify the relative contribution of the dynamical and chemical processes and refine the error budget. However, urban profile measurements are urgently needed to bring more information on the profile shape and support future modeling studies.
 In this paper, we showed that strong vertical gradients of NO2 concentration exist in Paris daytime urban ABL. This makes the uniform profile hypothesis often used in satellite retrieval process and validation irrelevant over high-emission areas. As an alternative, we used multiseasonal observations from Paris air quality network, a ground-based UV-visible spectrometer and an aerosol lidar to develop an empirical relationship between NO2 surface concentration, NO2 integrated content, and ABL depth.
 This relationship enables the use of satellite observations to derive surface concentrations over Paris and is very likely exportable to other cities. Indeed, Paris is 150 km away from the sea and has a low orography (below 200 m above sea level) so that no sea or mountain-breeze effects would affect the mixing processes taking place in the urban ABL. The values of the relationship parameters might have to be adjusted over other cities, but this will give insight into the relative contributions of the different processes involved.
 Application to satellite observations will be the object of future work, particularly for morning satellite instruments like SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography), and GOME-2 (Global Ozone Monitoring Experiment-2). Indeed, we showed in Section 2 that their overpass time coincides with NO2 maximum accumulation in the ABL, making them best suited to monitor NOx emissions when their resolution will be improved. Alternatively, to avoid a heavy network setting, measurements of the integrated column may be implemented in city centers. Our results also show that future observation campaigns dedicated to urban pollution should put a priority on measuring urban concentrations profiles in addition to horizontal transects, as both vertical and horizontal gradients matter for satellite validation.
 The authors would like to thank AIRPARIF for the in situ observations as well as IPSL and UPMC for supporting the Qualair station.