Nitrogen oxides play an important role in tropospheric chemistry as they control O3 photochemical catalytic production (Crutzen, 1979), the abundance of hydroxyl radicals, and they contribute to the formation of nitrate aerosols. In a background unpolluted atmosphere where NOx concentrations are low, net ozone loss occurs during photochemically active periods (Liu et al., 1983; Isaksen et al., 2005). NOx abundance is highly variable since it is influenced by non-steady natural and anthropogenic emissions and its global distribution is still uncertain. Free troposphere (FT) source inventories indicate that major production comes from lightning (2–16 Tg N yr-1), followed by NH3 oxidation (0.3–3 Tg N yr-1), stratospheric intrusion (0.08–1 Tg N yr-1) and aircraft (0.6-0.7 Tg N yr-1). Contribution from the boundary layer in remote regions is rare (Bradshaw et al., 2000).

Information about surface NOx in polluted areas is available due to extended governmental air-quality networks. During the last decade, satellite instruments have demonstrated a capability for successful retrieval of tropospheric NO2, identifying enhanced concentrations over urban and industrial areas in the boundary layer (Richter et al., 2005; Irie et al., 2005) and tracking the temporal trends (Hilboll et al., 2013; Cuevas et al., 2014). However, direct NO2 measurements in the background FT are scarce due to the requirement of observational platforms above, typically, 2000 m a.s.l., but also due to the low concentrations present at those levels.

Airborne NO2 measurements have been performed for decades (Ridley et al., 1988; Carroll et al., 1990); however the need for very short response times at concentrations close to the instrumental detection limit make the FT observations a challenging task. Even though well-characterized aircraft instruments reach detection limits as low as 10 pptv (Heland et al., 2002), few studies are reported in the literature. Measurements are generally collected during individual field campaigns associated to specific targets such as chemistry missions or satellite validations (Jacob et al., 2003; Bucsela et al., 2008; Boersma et al., 2008; Baidar et al., 2013; Flynn et al., 2014). These time and space sparse data limit the study of seasonalities or trends in the FT. Only recently, attempts to obtain global FT NO2 abundances from a satellite OMI instrument has been performed for the first time (Choi et al., 2014) by using the cloud-slicing technique (Ziemke et al., 2001). The method is based on the comparison of cloud and cloudless scenes to derive the FT mean concentrations. Results show that valuable information on NO2 large-scale phenomena can be derived from areas where cloud presence is frequent, but does not provide results in places such as at east Atlantic subtropical latitudes, where high pressure is a dominant feature.

Instruments operating in the few high mountain stations existent around the world are the only alternative to monitor NO2 in the background FT. However, the in situ measurements are often affected by the “upslope breeze effect” (Kleissl et al., 2007; Val-Martin et al., 2008; Rodríguez et al., 2009; Reidmiller et al., 2010; Cuevas et al., 2013). Radiative heating in the mountain slopes results in air upwelling from the boundary layer, contaminating the daytime measurements by generally larger values over the polluted lower layers.

Recently, Gomez et al. (2014) presented a simple method based on a modified geometrical approximation (MGA) to estimate concentrations of trace gases at the level of the Izaña observatory from multi-axis differential optical absorption spectroscopy (MAXDOAS) measurements. The horizontal path length is obtained from the oxygen collisional complex (O4, hereafter) simultaneously measured with the tracer under consideration (NO2 and O3). Gomez et al. (2014) examined a short summer period to demonstrate the validity of the method. Here we apply the same technique to data covering 3 full years (2011–2013) to analyze the seasonal evolution of the NO2 concentrations in volume mixing ratio (vmr). MAXDOAS present two main advantages with respect to the in situ instrument at this location, both related to the very long optical path of the measurements of over 60 km. Firstly, it minimizes the potential contribution of NO2 that may be upwelled from the marine boundary layer (MBL). The breeze layer has a limited vertical extension and its relative contribution to the MAXDOAS long path is small. On the contrary, Izaña in situ data around noon are strongly influenced by the underlying polluted MBL (Puentedura et al., 2012; Gomez et al., 2014). Secondly, due to the long light paths achieved by MAXDOAS in the FT, very low concentrations, of a few parts per trillion, can be measured.

Section 2 presents the method, its limits and its associated errors. In Sect. 3 the station and data sets are depicted. Section 4 describes the method used for the retrieval of profiles. The description of the chemical and back trajectories models is done in Sect. 5. Finally, Sects. 6 and 7 present the results and discussion, and summary, respectively.

In the year 2010, the DOAS (differential optical absorption spectroscopy) spectrometer, operating in zenith mode at that time, was upgraded for MAXDOAS measurements. The spectrometer records the sky spectrum in the visible range at a spectral resolution of 0.55 nm in 10 elevation angles from -1 to 90∘, and 1∘ field of view, covering a full cycle in 20 min. The number of cycles per day ranges from 26 at winter solstice to 38 in summer. NO2 is evaluated in the 425–520 nm range in order to simultaneously retrieve the O4 from the 477 nm absorbing band. The scanning plane is at 0∘ azimuth (north) to minimize the dependence of the path with the azimuth (Wittrock et al., 2004). The instrument is part of the Network for the Detection of the Atmospheric Composition Change (NDACC) and other settings are those recommended for DOAS-type spectrometers. NO2 at 294 K temperature from Vandaele et al. (1998) and O4 from Hermans (2011) cross sections have been used. Details of the instrument, settings and operational mode can be found in Puentedura et al. (2012) and Gomez et al. (2014).

The modified geometrical approximation (MGA) described in Gomez et at. (2014) has been used for the data analysis. NO2 vmr at the level of the station is obtained by dividing the differential slant column density (DSCD) measured in the horizontal geometry by the horizontal optical path. The DSCD is obtained by subtracting the measurement obtained at the zenith (SZA = 90∘) from the measurement in the horizontal path. In a first approximation, the slant paths' contributions of 0 and 90∘ geometries are cancelled out, and only the signal of the tracers present in the horizontal path remains (see Gomez et al., 2014 for details). The method assumes a quasi-Rayleigh atmosphere, i.e., very low aerosol optical depth (AOD), and a single scattering before the photon reaches the detector. The path is obtained from the O4 horizontal column since the amount of O2 is known from the independent air pressure measurements. The path length is then corrected to account for the differences in wavelengths between the O4 and NO2 analysis ranges. In practice, the scattering of the zenith path does not take place near the instrument but at a few kilometers above the level of the station. The actual concentration of a measured species X at the station level is given by Xvmr=XDSCDO4DSCD[O4]surface⋅f+c, where XDSCD and O4DSCD are the slant measured columns of the species X and O4, respectively. [O4]surface is the O4 at the level of the station, f is the correction factor due to differences in wavelength absorption ranges of the species under study, with respect to O4 that can be computed from a radiative transfer model (RTM), and c is the error of the approach. The latter is a factor accounting for the dependence with the different vertical distributions of both species and air mass factors (AMF): c=h(Rg-R′g′), where h is the effective scattering height of the vertical ray. R and R′ are the ratio of the mean concentration of the layer divided by the concentration at the level of the station of tracer X and O4, respectively, and g and g′ account for their AMF in the zenith geometry (g = AMF(SZA) - 1), where SZA stands for solar zenith angle.

The effective scattering height is defined as h(z)=∑surfacetopI(z)∫surfacetopI(z)dzz, where I(z)∫surfacetopI(z)dz represents the normalized contribution of the ray scattered at each atmospheric layer to the total flux at surface. From radiative transfer calculations it can be shown that the effective scattering height ranges between 6.5 and 7.5 km above the station for a solar zenith angle (SZA) below 70∘, which we estimate as the validity limit of the method.

Since both NO2 and O4 are analyzed in the same spectral range, the difference between the weighted center of the range for NO2, i.e., the effective wavelength, and that of O4, is small. The value of f is 0.9 for a near-Rayleigh atmosphere.

By using Eq. (2), the error introduced in NO2 vmr due to the geometrical approximation, if assuming a constant mixing ratio of both O4 and NO2 with height, is 9.0 % at 70∘ SZA and 2.3 % at 50∘. Since the scattering heights and the AMF are well known, the data can be corrected. The only uncertainty is due to the R value related to the vertical distribution of NO2 within the FT. However, aircraft measurements over the ocean far from large industrial areas show that the tropospheric vertical distribution is nearly constant above the MBL (Bucsela et al., 2008).

In the presence of moderate or high aerosol loading at the level of the observational point, multiple scattering takes place and the method is no longer valid. Assuming that the aerosol layer is a well-mixed layer, we estimate an AOD of 0.1 at 500 nm as a safe limit (Gomez et al., 2014).

Since the path length is obtained from O4 measurements, uncertainty in the magnitude of its absolute cross section is an additional source of error. It has been reported that paths obtained from O4 are even larger than that RT computed for a Rayleigh atmosphere (Wagner et al., 2002) when using the generally accepted cross sections reported in the literature (Greenblatt, 1990; Hermans, 2011), suggesting that cross sections are underestimated. There is, however, no agreement in the magnitude of the correct values. We performed direct Sun measurements on a very clear morning (aerosol optical density at 500 nm over the observatory was 0.007 ± 0.00077) at an O4 effective temperature of 250 K, and compared the retrieved slant columns with the ones calculated from the local radio sounding of the day (7 October 2014) up to 30 km and the tropical standard atmosphere from 30 km upwards. Results show an excellent agreement with no difference at the error level when the retrieval includes O4 cross sections at two temperatures (Fig. 1). In this exercise, the Thalman and Volkamer (2013) cross sections at 203 and 293 K were used. When including only the room temperature cross section in the retrieval, the obtained O4 is 3–5 % too large.

Our results agree with the very recent report by Spinei et al. (2015) who found a temperature dependence of 9 % for a variation of 44 K and no pressure dependence based on direct Sun and aircraft MAXDOAS measurements. The conclusion of their work is that no corrections need to be made for effective temperatures near 275 K. Since the present method uses only the horizontal path, the temperature along the path is nearly constant and the seasonal variability in the subtropical FT is small. Air temperature at the level of Izaña ranges from 277 K in January–February to 287 K in July–August. Consequently, no more than 2 % of error is expected due to this effect.

Typical NO2 slant column density (SCD) root-mean-square error of the fit for horizontal geometry is of 3×1014 molec. cm-2. These errors represent 15–20 % of the typical differential SCD. A summary of the analysis errors is shown in Table 1.

Izaña (28.3∘ N, 16.5∘ W) is a well-known GAW-NDACC station located at the top of the Izaña Mountain, one of the peaks of the great crater of the Teide volcano, at 2370 m a.s.l., on Tenerife Island. The observatory and related meteorology has been extensively described in previous publications (i.e., Rodríguez et al., 2009; Cuevas et al., 2013). It is representative of the FT at night. During daytime it is frequently affected by anabatic winds resulting from heating of the ground. This upslope breeze carries boundary layer air masses to the FT. The intensity of the wind peaks near local noon and can extend well into the afternoon. It can be indirectly quantified using the measurements of water vapor on the station since air masses from below carry high humidity to the height of the observatory. The measurements of in situ NO2 are also useful for this purpose, since the boundary layer (BL) NO2 concentrations in populated areas near the coast are typically more than 1 order of magnitude larger than the background FT.

For the present work, only the horizontal spectra are analyzed. If the SZA was lower than 10∘, then the 70∘ elevation spectrum was used as reference to avoid spectral distortions due to integration times that are too short. In all other cases, the reference was the zenith spectrum of the same cycle.

Data from 3 complete years (2011–2013) have been used after screening for (a) NO2 RMSE: fit error is limited to 2×1015 molec. cm-2 and a signal to noise ratio of 0.5, which is approximately the detection limit of the instrument. (b) High SZA: only data corresponding to data below SZA 70∘ are used in the present analysis to limit the error in the path calculations. (c) Aerosol loading: measurements on days with aerosol optical depth (AOD) at 500 nm over 0.1 were rejected. (d) Length of the path: individual measurements with paths shorter than 30 km were also rejected (broken clouds or narrow dust layers might cause this effect). (e) Unrealistic negative values appeared occasionally. Over 15 000 data passed all filters for the 3-year period (40 % of all possible data).

The Optical Estimation Method (OEM) has been extensively used in the last years to obtain NO2 vertical profiles of moderate to high polluted environments. However, on free troposphere background conditions, the concentrations are near the instrumental detection limit (10–100 pptv), and in these conditions, the method provides unrealistic profiles. In this work we have used it only to characterize the vertical distribution of the plume in a particular case study in which a high NO2 air mass arrived at the station. The mean AOD at 500 nm on the studied day was only 0.02. Under these conditions the impact of the aerosol loading in the retrieval is very low. A test with and without aerosols yielded a mean difference of 1.6 % in the retrieval for heights between 1 and 5 km. Since uncertainties in the OEM method are larger than that value, aerosols have not been included in the analysis.

Given a set of measurements y with error covariance Sε, the OEM (Rodgers, 2000) provides the state vector x that maximizes the probability that x, containing the trace gas vertical distribution, belongs to the interval [x, x+dx]. Following the OEM approach, the maximum a posteriori solution is calculated as x^=xa+SaKT(KSaKT+Sϵ)-1(y-Kxa)=xa+Gy(y-Kxa), where the weighting functions matrix K expresses the sensitivity of the measurements to variations in the trace gas profile (NO2 in this case). In this work, K is obtained with the SPSDISORT pseudo-spherical radiative transfer solver of the libRadtran software package (Mayer and Kylling, 2005). The xa vector and Sa matrix correspond to an a priori NO2 profile and its corresponding error covariance matrix, respectively.

The gain matrix Gy, given by the following expression, quantifies the sensitivity of the retrieval to the measurements: Gy=SaKT(KSaKT+Sϵ)-1. The averaging kernel matrix A, is then obtained as follows: A=GyK. A expresses the sensitivity of the retrieval to the true state, and it has an important role in the characterization of the retrieval. The retrieval at a given altitude is an average of the total profile weighted by the corresponding row of A, also known as the averaging kernel function AK. In general, the AKs are functions with a single peak in the appropriate level, where the measurement provides additional information to add to the a priori profile. The trace of A provides the number of independent pieces that can be extracted from the retrieval, usually known as degrees of freedom (DFS). Typical values of the DFS in our retrievals are around 1.8.

Another parameter determining the quality of the retrievals is the total error of the state vector elements. This parameter is the addition of three contributions: (1) the smoothing of the true profiles given by Sa; (2) the systematic errors of the measurements, provided by Sε and (3) systematic errors of the forward model, mainly provided by the uncertainties in the parameters characterizing the atmosphere. Average total error (considering the three mentioned contributions) for all the considered profiles and altitudes ranging from 1 to 5 km is 0.01 ppb. The choice of the values corresponding to these three sources of error (Sa, Sε and the atmosphere parameters) in our study will be described in the following paragraphs.

The NO2 hourly profiles used as a priori profiles in our calculations were obtained using a photochemical box model (Denis et al., 2005) derived from the SLIMCAT 3-D chemical transport model (Chipperfield, 2006). Diagonal elements of Sa are usually chosen to be a percentage of xa. In this case, following the L-curve method described in Schofield et al. (2003), they have been set to 100 % of xa, and its non-diagonal elements are calculated as follows (Barret et al., 2002; Friess et al., 2006): Saij=SaiiSajjexp⁡(-ln⁡(2)((zi-zj)/y)2), where zi and zj are the altitudes of the altitude grid levels i and j respectively, and γ is a half of the correlation length. The functions represented in the last equation are Gaussian correlation functions which account for correlations between trace gas concentrations at different altitudes. After several tests on the retrieval, γ value has been chosen to be 300 m, corresponding to the value (between 0.1 and 1 km) that maximizes the DFS (trace of A), for the overall retrieval as well as for the altitudes closer to the station (2.3–2.6 km).

In this work, y represents the differential slant column densities (DSCD) of NO2 measured with the MAXDOAS spectrometer, and Sε is set to a diagonal matrix of which diagonal elements correspond to the molecular errors of the measurements.

Concerning parameters that characterize the atmosphere in our calculations, vertical profiles of O3, O2, CO2 and H2O have been obtained from the standard atmosphere for tropical latitudes (Anderson, 1986). Radio-sounding data performed the same day of our calculations provided the pressure, temperature and air density vertical profiles used in our retrieval. We have considered layers of 100 m from 0 to 10 km, and with the same width of those corresponding to the standard atmosphere for tropical latitudes (Anderson, 1986) for altitudes over 10 km. In this work, AKs are near zero for altitudes lower than 0.5 km and higher than 5 km (see Fig. 2). The retrieved profiles have been obtained for altitudes up to 6 km.

CAM-Chem (Community Atmosphere Model with chemistry) is a global 3-D chemistry–climate model fully integrated into the CESM (Community Earth System Model) framework (Lamarque et al., 2012). In this work, CAM-Chem has been configured using a horizontal grid resolution of 1.91 latitude × 2.5∘ longitude and 26 hybrid vertical levels from the surface to approximately 38 km. All simulations have been performed in specified dynamics (SD), using offline meteorological fields to compute the atmospheric transport, considering the same high-frequency meteorological input from a previous CAM-Chem 15-year simulation. This implies that the model is forced to evolve as if it were a chemical transport model.

The model includes the tropospheric chemistry mechanism of MOZART-4, implementing also organic and inorganic halogen (chlorine, bromine and iodine) photochemistry mechanisms, taking into account natural and anthropogenic sources, heterogeneous recycling and dry and wet deposition (Saiz-Lopez et al., 2012; Ordoñez et al., 2012; Fernandez et al., 2014). Anthropogenic emissions due to fossil fuel and biofuel combustions come from the POET (precursors of ozone and their effects in the troposphere) database for 2000.

To investigate the air masses reaching the area of study, back trajectories were computed with the HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory) model, developed by NOAA Air Resources Laboratory (ARL) (Draxler et al., 2009). The ECMWF (European Centre for Medium-Range Weather Forecasts) meteorological fields were used with a spatial resolution of 0.25∘ × 0.25∘, 22 vertical levels from the surface to 250 mb and a time resolution of 6 h. Three-dimensional kinematic back trajectories were calculated. A daily back trajectory at 12:00 UTC, with a 168 h pathway (7 days) at 2370 m a.s.l., was computed. Following the HYSPLIT model tools, back trajectories have been grouped into clusters (Stunder, 1996), arriving at the Izaña observatory.

NO2 volume mixing ratio at the level of the high mountain observatory of Izaña (2370 m a.s.l.) has been obtained for 3 years of data using the MAXDOAS technique and the recently reported Modified Geometrical Approximation (MGA). The method uses the absorption of the O2–O2 collisional complex at 477 nm to obtain the horizontal path and is applicable in a near-Rayleigh atmosphere. Only data from air masses of aerosol optical depths below 0.1 were considered, thus removing African air masses loaded with Saharan dust. Results show that on most of the observation days, data are representative of the free troposphere. Exceptions are found when wind blows from the south. On these occasions, we find evidence that orographically forced surface air masses ascend upslope to the Izaña observatory, providing a channel for the irreversible transport of surface origin species to the free troposphere; this might provide an explanation for the concentrations of halogen oxides found in this region.

The NO2 seasonal evolution shows a well-defined annual cycle in phase with solar radiation. Mean mixing ratios range from 20 pptv in midwinter to 42 pptv in summer with a significant day to day variability. By contrast, we find a small interannual variability during the 3-year observation period. A number of possible causes to explain the observed seasonality have been discussed, including seasonal changes in transport and contamination due to seasonality in the upslope winds (anabatic winds) but individually, they could not provide an explanation of the observations. The CAM-Chem chemistry–climate model reproduces the monthly distribution with great accuracy. The results of the back trajectory cluster together with the model analysis show that the seasonality in NO2 vmr is related to a combined effect of long-range transport and subsidence in the free troposphere. Dust-free trajectories follow North American/North Atlantic pathways, with air masses coming from the mid-free troposphere between 4000 and 5500 m a.s.l. The model and previous satellite estimations show a seasonality in NOy and NO2 in the mid-free troposphere in phase with the MAXDOAS observations at Izaña. Larger summer values are probably due to a combination of seasonality in convection and lightning.