The NO2 slant columns used in this work are retrieved by the UV–vis spectrometer OMI (Ozone Monitoring Instrument; Levelt et al., 2006) according to KNMI DOMINO version 2.0 (Boersma et al., 2007, 2011). The data files, which include total and stratospheric slant columns, averaging kernel information, cloud fraction, cloud pressure and assimilated trace gas profiles from the TM4 model, are available at http://www.temis.nl/airpollution/no2.html.

Of particular importance to this study are the cloud pressures and fractions retrieved by the OMI O2–O2 cloud algorithm (Acarreta et al., 2004). The OMI O2–O2 cloud algorithm uses an optically thick Lambertian cloud model with a fixed albedo of 0.8; the fraction of this Lambertian cloud model covering the pixel is called effective cloud fraction (ceff=(Robs-Rclear)/(Rcloudy-Rclear), where Rcloudy and Rclear are modeled clear- and cloudy-sky reflectances, and Robs is the observed continuum reflectance – i.e., the reflectance with the O2–O2 absorption line removed), which is not the same as the geometric cloud fraction but an equivalent amount that yields the same top-of-atmosphere (TOA) reflectance as observations; the altitude level of the Lambertian cloud model is then adjusted so that it results in the same amount of O2–O2 absorption as in observations (Stammes et al., 2008). The OMI O2–O2 cloud pressure refers to the optical radiative cloud pressure near the mid-level of the cloud and below the MODIS infrared-based cloud top, which is about 250 hPa higher than OMI for deep convective clouds or about 50–70 hPa higher for extratropical mid-level clouds. The OMI O2–O2 cloud pressure has been validated against PARASOL with a mean difference below 50 hPa and a SD below 100 hPa (Stammes et al., 2008). The OMI O2–O2 cloud fraction has been validated against MODIS with a mean difference of 0.01 and SD of 0.12 over cloudy scenes (effective cloud fractions larger than 50 % without surface snow or ice) (Sneep et al., 2008). In this paper, we use the cloud radiance fraction defined as CRF =ceffRcloudy/Robs – which represents the weight of the air mass factor of the cloudy part.

The TM4 chemistry transport model has a spatial resolution of 2∘×3∘ with 35 sigma pressure levels up to 0.38 hPa (and approximately 15 levels in the troposphere) driven by temperature and winds from ECMWF reanalyses and assimilated OMI stratospheric NO2 information from previous orbits. The tropospheric chemistry scheme is based on Houweling et al. (1998) using the POET emissions (Olivier et al., 2003) database based on the EDGAR inventory for anthropogenic sources, which are typical of years 1990–1995, with biomass emissions of NOx based on ATSR fire counts over 1997–2003 and released in the lowest model layers. The photolysis rates are calculated as in Landgraf and Crutzen (1998) and modified as in Krol and van Weele  (1997). In the TM4 model, the physical parameterization for convective tracer transport is calculated with a mass flux scheme that accounts for shallow, mid-level and deep convection (Tiedtke, 1989). Large-scale advection of tracers is performed by using the slopes scheme of Russell and Lerner (1981). The lightning NOx production is parameterized according to Meijer et al. (2001) using a linear relationship between lightning intensity and convective precipitation, with marine lightning 10 times less active than continental lightning and scaled to a total annual of 5 TgNyr-1 (Boersma et al., 2005). The vertical lightning NOx profile for injection into the model is an approximation of the outflow profile suggested by Pickering et al. (1998). Including free-tropospheric emissions from air traffic and lightning, the total NOx emissions for 1997 amount to 46 TgNyr-1. More about this model may be found in Boersma et al. (2011) and references therein.

A technique initially developed for estimating upper tropospheric ozone using nadir sounders (Ziemke et al., 2001), cloud slicing consists in arranging collections of trace gas VCDs measured above clouds against cloud pressure over a certain area and time period in order to estimate a gas VMR via the pressure derivative as VMR=0.1gMairNA⋅∂VCD∂p, where g=9.8 ms-2, Mair=28.97 gmol-1 and NA=6.022×1023 molecmol-1 with VCD expressed in moleccm-2 and cloud pressure expressed in hPa. The method determines an average trace gas volume mixing ratio over a certain area, time period and cloud pressure interval (Choi et al., 2014). In this paper, annual average tropospheric NO2 VCD lat–long grids from OMI and TM4 are produced for six tropospheric layers with bottom cloud pressures located within pressure intervals centered at about 330, 450, 570, 670, 770 and 870 hPa. The cloud pressure intervals used for cloud slicing were chosen after several trial runs and are laid out in Table 1 and Fig. 1. An annual climatology of NO2 VMR profiles is then estimated after differencing the annual tropospheric VCD arrays above cloud with respect to pressure.

Figure 1 shows the latitude–height section of annual zonal mean OMI cloud frequency for the year 2006, showing that cloud slicing does not provide uniform global sampling. Most high clouds (mainly deep cumulus, since cirrus clouds pass generally undetected by OMI) occur along the Intertropical Convergence Zone (ITCZ) near the Equator and over tropical continents, but can also be seen in the mid-latitude storm track regions and over mid-latitude continents in the summer; mid-level clouds are prominent in the mid-latitude storm tracks, usually guided by the tropospheric westerly jets, and some occur in the ITCZ; and low clouds, including shallow cumulus and stratiform clouds, occur essentially over the oceans but are most prevalent over cooler subtropical oceans and in polar regions (Boucher et al., 2013). In summary, cloud sampling proves best at low to mid-altitudes in the extratropics and mid- to high altitudes in the deep tropics. However, cloud sampling is typically poor off the west coasts of subtropical (Pacific, Atlantic and Indian) landmasses at high altitudes – which are areas of large-scale subsidence with persistent low stratocumulus, and at low altitudes over the tropical landmasses, particularly the Amazon Basin and central Africa.

Figure 3a shows the annual mean tropospheric NO2 VCD aggregates on 1∘×1∘ grids observed by OMI for the year 2006 above clouds with mean pressures centered at around 330, 450, 570, 670, 770 and 870 hPa – see Fig. 1 and Table 1. A similar set of annual mean NO2 VCDs above cloud has been extracted from the TM4 model using identical cloud sampling (i.e., using the cloud fraction and cloud pressure from OMI) for comparison (see Fig. 3b).

Most of the lightning NO2 emissions are expected above clouds higher than 450 hPa (i.e., the upper two levels in Fig. 3a), although some deep convection may also be present over strong industrial sources (like the northeastern USA, Europe, China, and the Johannesburg, South Africa, area) or biomass burning sources in central Africa, the Amazon Basin or northeastern India, complicating the problem of process attribution.

The two middle levels in Fig. 3a are expected to carry, along with the NO2 burden inherited from the upper levels, additional signatures from frontal uplifting into the mid-troposphere by conveyor belts over major industrial sources in the northeastern USA, central Europe and China, as well as convective transport of biomass burning sources over central Africa, South America, Indonesia and northern Australia. The strong convective signatures of surface industrial and biomass burning sources, along with their low tropospheric outflows, dominate the two lowest levels in Fig. 3a. Note the extensive lack of data over the tropical continents at low altitudes, a region where persistent high cloud precludes penetration into the lowest levels, and over the subtropical subsidence areas.

By differencing the annual average VCD arrays with respect to pressure, we expect to separate the contributions from different altitudes to the total tropospheric column. But before that, let us take a look at the scattering sensitivities above cloud and the effects of correcting for below-cloud leakage in these results. Figure 4 shows the annual mean tropospheric scattering sensitivity above cloud level (AMFabove in Eq. ) applied to generate the OMI NO2 VCDs shown in Fig. 3a. Globally, the tropospheric scattering sensitivity above the cloud does not deviate by more than 10 % from the geometric air mass factor at most cloud altitudes, except at the lowest levels, where it suffers reductions of up to 30 %. This reduction in scattering sensitivity at the lowest cloud levels may come as a surprise, particularly when clouds are known to boost the scattering sensitivity just above the cloud top. However, the pronounced decrease in scattering sensitivity at the lowest cloud levels is related to penetration of substantial amounts of NO2 (from strong or elevated surface sources) into the cloud mid-level, where extinction acts to reduce the scattering sensitivity. Other than the extinction effect, the variability in scattering sensitivity is governed by changes in the observation geometry (AMFabove decreases as the sun angle increases) and the temperature correction introduced in Eq. (), which is responsible for the subtropical bands and the variability at high southern latitudes.

The corrections for the surface leaked component introduced in Eq. () are largest (see Supplement) over polluted regions for the highest clouds (up to 50–66 %) and smallest over clean areas like the oceans. In order to verify that the model-based below-cloud leak corrections do not appreciably change the OMI NO2 VCDs arrays, we have performed a separate trial run where the CRF threshold (at grid level) is increased from 50 to 80 % (see Supplement) to conclude that none of the prominent VCD signatures seen in Fig. 3a (or none of the VMR features that we will see later) changes appreciably in the restricted CRF >80 % case. Results from the CRF >80 % trial run include notably diminished cloud frequencies and spatial coverage, seriously thinning the population that produces the annual averages and generally damaging their representativity. This effect is particularly notable in the upper two levels (280 and 380 hPa) and to lesser extent over the large-scale subsidence area in the lowest level, since deep convective and low marine stratocumulus clouds are not particularly extensive but have a preference for low effective cloud fractions. Excluding the contributions from these cloud types in the CRF >80 % case does not change the mid-tropospheric NO2 patterns relative to the CRF >50 % case, but it biases the OMI aggregates in the upper troposphere low relative to the modeled average, which is not particularly sensitive to this change. In summary, the CRF >80 % trial run does not show any clear signs of a priori information constraining the results, but it provides hints of results being influenced detrimentally by the lower sampling densities afforded by a higher CRF threshold.

The annual mean tropospheric NO2 VMR pseudoprofiles observed by OMI for the year 2006 are compared against their TM4 model counterparts in Fig. 5a–c. Note that pseudoprofile errors do not affect this comparison, since both observed and modeled pseudoprofiles are observing identical (if somewhat unphysical, because of sampling and representation issues) atmospheric states. After the pressure difference, there remain some instances where negative VMRs are found, but these are mainly associated with poorly populated cells (such as at high latitudes, near the tropics at low altitudes, or around subsidence regions). These instances are identified and dealt with by recourse to information from nearby cells, when available, or otherwise ignored.

Many of the cloud-slicing features observed at the upper two levels (280 and 380 hPa) in Fig. 5a can be attributed to actual biomass burning, lightning and deep convection. It may be difficult to separate these components clearly without a proper seasonal analysis (deferred to Sect. 3.6), although one can identify areas of predominant lightning production as those regions that do not seem connected via convection to surface sources underneath and use the LIS-OTD flash rate climatology and the ATSR fire counts (see Fig. 6 below) as interpretation aids for attribution. Positive anomalies (observations larger than modeled amounts) are detected in Fig. 5a over all major industrial areas (eastern USA, central Europe and eastern China) both at 280 and 380 hPa levels, suggesting that deep transport of boundary layer NO2 may be too weak in the model. However, there are extensive negative anomalies (meaning observations lower than modeled amounts) in background upper tropospheric NO2 both at 280 and 380 hPa, which is consistent with reports of model overestimation of the amount of NO2 attributed to lightning over the tropical oceans in Boersma (2005).

Negative anomalies in Fig. 5a are particularly large over Siberia, Amazonia and the Bay of Bengal. The negative anomaly over eastern Siberia, an area of predominant biomass burning, could be related to excessive fire-induced NO2 emission over boreal forests in the model (Huijnen et al., 2012). In South America, lightning NO2 contributions seen by OMI appear confined mostly to the western equatorial coast (Peru, Ecuador and Colombia) on the one hand, and southern Brazil and off the east coast of Uruguay on the other hand (more in line with the LIS-OTD flash climatology shown in Fig. 6) – in stark contrast with model amounts, which locate the lightning maximum further to the north over the Brazilian Matto Grosso, where the maxima in precipitation related to the South American monsoon system usually takes place. It is worth noting that the lightning intensity in the TM4 model is solely driven by convective precipitation, although Albrecht et al. (2011) report that convective precipitation is not always well correlated with lightning in this area, showing that the most efficient storms in producing lightning per rainfall are located in the south regions of Brazil. The negative anomaly over Amazonia is therefore very likely related to problems with the TM4 lightning scheme. The negative anomaly over the Bay of Bengal, an area of maxima in precipitation related to the Indian monsoon, could also be a reflection of excess model lightning linked to convection.

Other notable discrepancies in Fig. 5a include positive anomalies over central Africa and northeastern India at 280 hPa. Over central Africa, the pattern of positive anomalies bears only partial resemblance to the pattern of biomass burning emission underneath (see mid-level OMI VMRs in Fig. 5b) – suggesting that upper level positive anomalies in central Africa may be related more to deficiencies in the lightning scheme than to convective transport. Actually, Barret et al. (2010) report that lightning flash frequencies simulated by TM4 are lower than measured by the LIS climatology over the southern Sahel, which is consistent with our observations. On the other hand, the large positive anomaly observed over the Tibetan Plateau at 280 hPa, which significantly deviates from the LIS-OTD flash rate climatology in the area (confined to the Himalayan foothills only), is very likely an effect of deep transport associated with the Asian monsoon. The model does show an enhancement in upper tropospheric NO2 over India, but not moving far enough north into the Tibetan Plateau and failing to reproduce the strong enhancements in upper tropospheric NO2 over northeastern India and southern China related to the Asian summer monsoon plume – which Kar et al. (2004) also detected in the MOPITT CO profiles.

The cloud-slicing features observed at the mid-tropospheric levels (500 and 620 hPa) in Fig. 5b may be mostly attributed to mid-tropospheric convection of strong surface sources and their associated outflows. We observe a remarkable agreement between model and observations on the localization and intensity of major convective signals over industrial sources (eastern USA, central Europe, China and India) as well as over typical biomass burning sources in central Africa, Indonesia and South America. Contrary to what is observed in the upper levels (see prevalent negative anomalies in Fig. 5a), there are extensive positive anomalies (meaning observations larger than modeled amounts) in background middle tropospheric NO2 both at 500 and 620 hPa in Fig. 5b, particularly over the tropics and subtropics – which is indicative of deficient model mid-tropospheric outflows at these levels. Positive anomalies over the continents are particularly large over China (with an outflow-related positive anomaly downwind over the Pacific), the central USA, and the biomass burning regions in central Africa and South America. While it may be more or less clear that enhanced mid-tropospheric NO2 concentrations observed over the oceans are related to enhanced convective inflows into this level (without definitely discarding a problem with NO2 lifetime), the origin of the convective anomalies remains ambiguous. A cursory look at the NO2 concentrations observed at lower levels might help determine whether flux anomalies into the mid-troposphere are related to deficiencies in model-prescribed surface emissions or problems with the convective transport scheme, or both.

For example, the pattern of anomalies over China at lowest levels (see Fig. 5c) is prominently positive, but it carries a dipolar positive–negative (China–Japan) pattern that is no longer observed at higher levels. Thus, while it is possible that some of the mid-tropospheric convective anomalies are a response to flux anomalies carried from underneath (i.e., a deficiency in the originally prescribed surface emission), as happens over the eastern USA and Europe, where negative anomalies are carried upwards (see Fig. 5b), the overall effect does not exclude net deficiencies in model convective transport. As far as biomass burning is concerned, the pattern of anomalies over central Africa and South America in the lowest tropospheric levels (see Fig. 5c) is unfortunately not as evident (given the lack of low-cloud detections) as over China but mostly neutral or slightly negative, indicating that mid-tropospheric positive anomalies in this area respond to either a convective transport scheme that is too weak or a model injection height that is too low.

The lower tropospheric levels (720 and 820 hPa) in NO2 sampled by the cloud-slicing technique are shown in Fig. 5c. These levels sustain the highest NO2 concentrations in the vicinity of major industrial hubs (eastern USA, central Europe and China) and the strongest anomalies as well, which in this case can be linked directly to deficiencies in prescribed surface emissions. All major features in the anomaly patterns at these levels can be matched unambiguously to the pattern of OMI to TM4 total tropospheric NO2 column differences for clear-sky conditions shown later in Fig. 12, characterized by positive anomalies over the northeastern USA, central Europe and Japan, and negative anomalies over China. These low-level signatures are consistent with NO2 increases over China, India and the Middle East, and NO2 decreases over the eastern USA and central Europe, which are not reflected in the model emission inventory. Other salient features at these levels include an interesting band of negative anomalies along the ITCZ (perhaps related to rapid convective mixing of relative “clean” air from the boundary layer) and extensive positive anomalies over the oceans (more so at 720 than at 820 hPa) – revealing deficient model outflows at high latitudes and suggesting that poleward transport of NO2 in the model may not be vigorous enough (a problem likely related to horizontal diffusion in the model).

In summary, there is remarkable agreement between observed and modeled upper/middle/lower tropospheric NO2 amounts, their main distributions resembling each other at continental scale, with localized differences suggesting that the cloud-slicing technique holds promise for testing model features related to anthropogenic emission, convection and uplift, horizontal advection and lightning NOx production.

In the previous section, we studied the geographical distribution of observed and modeled NO2 amounts on different pressure layers. In this section, we focus on the vertical dimension by looking at NO2 VMR amounts across pressure layers. In order to simplify the analysis, we have defined a set of geographical classes based on the amount of variance contained in the TM4 model NO2 profiles. These classes characterize how much of the NO2 content in the profile can be apportioned to surface sources and how much to outflows – further subdivided into outflows with low-, mid- or high-altitude components. Annual mean NO2 VMR profiles are plotted for each class, along with reference to pseudoprofile error. A standard empirical orthogonal function (EOF) decomposition of the reference TM4 profiles (VMRref in Eq. ) is employed to characterize the geographical variance of NO2 vertical profiles under cloudy conditions and identify major spatial patterns. The first four EOF eigenvectors (out of a total of six) are shown in Fig. 7a. The first EOF represents profiles with higher concentrations near the surface – a profile over a surface source. The second EOF represents profiles with concentrations uniformly distributed across the column – a profile for a generic outflow type. The third and fourth EOF eigenvectors divide the generic outflow type into subtypes with stronger high-altitude (EOF3 >0), low-altitude (EOF3 <0) or mid-tropospheric (EOF4 >0) components. The classes that result from applying masks based on the conditions defined in Table 2 are shown in Fig. 7b. According to the TM4 model, the classes containing all primary and secondary industrial sources (i.e., strong projections on EOF1) are mainly confined to the USA, Europe and China. Other secondary industrial sources relate to India, the Middle East and the Baykal Highway (a major road connecting Moscow to Irkutsk, passing through Chelyabinsk, Omsk and Novosibirsk). Major biomass burning sources include large sectors in Africa and South America, Indonesia, New Guinea, and northern Australia. NO2 outflows over the tropics (i.e., strong projections on EOF2) are subdivided into generic tropical outflows (with strong upper and mid-tropospheric components, or larger projections on EOF3 and EOF4) and outflows over large-scale subsidence areas (with stronger lower tropospheric components, or negative projections on EOF3). The extratropical outflows differ from the tropical outflows in that the sign of the mid-tropospheric projection is reversed, so that extratropical profiles are more C-shaped (according to the model). The boreal outflow differs from the extratropical outflow in that it has an extremely large upper tropospheric component (i.e., a very large projection on EOF3). Finally, we have defined a separate class, labeled clean background, including all those areas without significant projections on either source or outflow eigenvectors.

The average tropospheric NO2 profiles estimated using the cloud-slicing method on OMI and TM4 data sets for all the 11 classes (15 classes when primary and secondary industrial regions are subdivided geographically into China, USA and Europe subclasses) defined in Table 2 and Fig. 7b are shown next in Figs. 8 and 9. These plots compare the OMI and TM4 VMR pseudoprofile estimates calculated in a cloud-slicing fashion as in Eq. (), along with the reference TM4 VMRref profile calculated as in Eq. () for an average cloudy atmosphere. Recall that the difference between the TM4 VMR and VMRref profiles gives an indication of pseudoprofile error – or the representativity of the cloud-slicing estimate relative to a general cloudy situation. The OMI VMR cloud-slicing estimate is bounded by error bars calculated from standard error propagation as in Eq. (), and scaling by the square root of the number of profiles collected per grid cell – also shown in right subpanels in Figs. 8 and 9.

The cloud-slicing estimates for the annual tropospheric NO2 profiles over primary industrial centers in the eastern USA, Europe and China are shown in the first row in Fig. 8. There is a remarkably good correspondence between observed and modeled tropospheric NO2 profiles over these strongly emitting areas, particularly over central Europe, attesting to the accuracy and representativity of the cloud-slicing estimates for yearly means. Pseudoprofile errors are small in these areas, so that cloud-slicing estimates remain a good representation of average cloudy conditions. The OMI to TM4 VMR differences at the lowest levels are consistent with known deficiencies in model-prescribed surface emissions (OMI smaller than TM4 over the eastern USA and central Europe, but larger over China). These low-level anomalies are carried upwards to a level of 500–600 hPa, above which the effects of enhanced convective mid-tropospheric and deep transport start to dominate regardless of the signature of the surface difference. The second row in Fig. 8 shows the annual tropospheric NO2 profiles over secondary industrial centers around eastern USA, Europe and China. The low-level features related to surface emission are identical to those of the primary centers, but the signature of enhanced mid-tropospheric convection is clearer – indicating that vertical transport in the model is too weak or lifetime too short, regardless of the sign of the surface anomaly. The sign of the OMI to TM4 difference is reversed in the upper two levels, in line with the generalized model overestimation of NO2 in the upper troposphere. The third row in Fig. 8 shows the cloud-slicing estimate for the annual tropospheric NO2 profiles over secondary industrial pollution centers in India, the Middle East and the Baykal Highway – note that pseudoprofile errors are larger in this case. For India, the differences between OMI and TM4 profiles at low levels point to a large underestimation of model surface emissions, and model overestimation of upper tropospheric NO2 amounts – this upper level anomaly related to the misplaced Asian summer monsoon signal, which in observations appears located over the Tibetan Plateau. For the Middle East, the difference between OMI and TM4 profiles points to large differences at mid-tropospheric level (OMI larger than TM4). The agreement between OMI and TM4 profiles for the Baykal Highway class is reasonably good – allowing for a small underestimation of model surface emissions. After deep transport in China, this is the class with higher upper level NO2 amounts, most likely related to fire-induced convection from boreal fires. The left panel in the fourth row in Fig. 8 shows the cloud-slicing estimate for the annual tropospheric NO2 profile over tropical biomass burning regions, featuring positive anomalies at middle levels and negative anomalies at lower and upper levels, again pointing at defective model convective transport into the mid-troposphere (or issues with the pyro-convection height). The cloud-slicing estimates for annual tropospheric NO2 profiles over typical outflow regions are shown in the middle and right panels in the fourth row (tropical and tropical subsidence outflows) and left and middle panels in the fifth row (extratropical and boreal outflows) in Fig. 8. As a salient feature, all of the outflow profiles share a prominent mid-tropospheric plume centered at around 620 hPa in the tropics and a little lower in the extratropics, around 720 hPa, with NO2 amounts much smaller than the model in the upper troposphere and general agreement at the lowest level, producing profiles which are generally S-shaped (instead of C-shaped as in the model). The mid-tropospheric plume is likely related to enhanced convective fluxes of NO2 over industrial and biomass burning areas (but definitely not discarding issues with NO2 lifetime or substantial chemical NOx recycling from HNO3 and PAN sources at this level). Note also the generalized model overestimation of NO2 in the upper levels (tropical and extratropical), which is consistent with reports of excess lightning NOx production over the tropical oceans in Boersma et al. (2005). The upper level overestimation is particularly large for the boreal outflow class, which we also mentioned could be related to the excess fire-induced convection over Siberia or too large NOx emission factors. Finally, the cloud-slicing estimate for the annual tropospheric NO2 profile over the clean Southern Ocean is shown in the right panel of the last row in Fig. 8, with good agreement at the top levels and gradually increasing model underestimation towards the surface, suggesting enhanced lateral contributions at high latitudes from horizontal eddy diffusion.

The left panel in Fig. 9 shows the annual tropospheric NO2 profile for all the primary surface sources together (eastern USA, central Europe and China), indicating that differences at surface level average out globally, leaving the effects of enhanced observed mid-tropospheric convection and deep transport to stand out. The signature of enhanced mid-tropospheric convection becomes even clearer in the middle panel in Fig. 9, which shows the annual tropospheric NO2 profile for all secondary surface sources together (around primary sources, plus India, the Middle East, the Baykal Highway and the biomass burning areas), where the signature of enhanced deep transport is in this case replaced by model overestimation of upper tropospheric NO2. The model overestimation of upper level NO2 appears clearly in the right panel in Fig. 9, which shows the annual tropospheric NO2 profile for all the outflow classes, along with a prominent model underestimation of mid-tropospheric NO2 levels. In summary, and consistent with our comments on Fig. 5a–c, the average profiles that result from applying the cloud-slicing technique on observed OMI and modeled TM4 data sets show striking overall similarities, which confer great confidence to the cloud-slicing approach, along with more localized differences that probe into particular model processes and parameterization schemes.

We would like to wrap up our results in the form of observed and modeled annual zonal mean and longitudinal NO2 cross sections along the tropics (Figs. 10a, b and 11). Note that in order to bypass pseudoprofile errors, the observed NO2 pseudoprofiles are scaled in this section by the model profile-to-pseudoprofile ratio as in Eq. () to form what is called the observation update.

For the annual zonal mean tropospheric NO2, the left-to-right panel comparison in Fig. 10a shows that, although the observation update does not change the strength of major industrial emission over the northern mid-latitudes at the lowest levels, the associated convective cloud is reaching higher in altitude. In the tropics and southern latitudes, vertical transport of the combination of biomass burning and industrial emissions is stronger and reaching higher – with a prominent high plume originating from the Johannesburg area. The observation update does bring notably stronger midtropospheric outflows distributed over a broader latitude band and weaker NO2 signatures at high altitude. The enhanced mid-tropospheric plume is best appreciated in Fig. 10b, which shows the annual zonal mean tropospheric NO2 averaged over the Pacific Ocean sector (180–135 W) – the dominant sources of NO2 over the oceans are thought to include the long-range transport from continental source regions, as well as chemical recycling of HNO3 and PAN sources (Staudt et al., 2003). Schultz et al. (1999) actually show that the decomposition of PAN originating from biomass burning actually accounts for most of the mid-tropospheric NOx in the remote southern Pacific, suggesting that enhanced convective flux from surface sources may not be the only agent responsible for the enhanced mid-tropospheric outflows observed by OMI.

Figure 11 shows a picture for the annual longitudinal NO2 cross section for tropical latitudes between 10∘ N and 20∘ S, where the observation update raises the convective plumes from major biomass burning areas in South America, central Africa and Indonesia/northern Australia to higher altitude, between 500 and 600 hPa, with a slight westward tilt and longer downstream transport of cloud outflow at upper levels caused by the tropical easterly jet, and generally weaker NO2 signatures at high altitude.

In summary, the OMI cloud-slicing NO2 profiles seem to suggest that raising the polluted plumes to higher altitudes allows for much longer residence and chemical lifetimes, and longer and more widely distributed horizontal transport of NO2 (following poleward advection and dispersion by the subtropical jet and by baroclinic waves at lower levels) in the mid-troposphere. These observations are in line with reports in Williams et al. (2010) showing that the underestimation of upper tropospheric O3 in TM4 relative to observations over Africa may be linked to a too weak convective uplift using the Tiedtke scheme. The studies of Tost et al. (2007), Barret et al. (2010) and Hoyle et al. (2011) corroborate this finding, indicating that the vertical extent of tropical convection and associated transport of CO and O3 in the middle and upper troposphere is underestimated in Tiedtke-based models. Accurately constraining the convective transport in CTMs should contribute to the determination of the vertical distribution of lightning NOx, since knowledge of the extent of mixing of air into the cloud as a function of altitude is required to separate the NOx produced by lightning from that produced by upward transport (Dickerson, 1984).

Because of the annual and global character of the OMI annual tropospheric NO2 profile climatology estimates, we do not have any direct means to validate them in the same way as has been done, for example, in Choi et al. (2014). But we can check their consistency by demanding that the total tropospheric NO2 column from the cloud-slicing technique does not deviate significantly from the total tropospheric NO2 column observed in clear-sky conditions (see Fig. 12). The total tropospheric NO2 column from the cloud-slicing technique, VCDslicing, is calculated as the sum of partial vertical column densities obtained from the annual mean pseudoprofile VMR as VCDslicing(lat,lon)=∑n=16VMRi(lat,lon)(〈pi+1〉-〈pi〉)/C, where C is the same constant defined in Eq. (). Note that absent VMR grid values (such as at high altitude over subsidence regions, or at low altitude over the tropical continents) are ignored without provision of a priori information.

We do, however, know that there are some basic differences between NO2 profiles observed under clear and cloudy conditions. In the TM4 model, the differences between cloudy (CRF >50 %) and clear (CRF <25 %) profile climatologies (see left panel in Fig. 13 below) show strong negative anomalies over the biomass burning areas (central Africa, southern America, northern Australia, southern India, but also in the Persian Gulf and Turkestan) most likely related to fire suppression during the wet/cloudy season. Over industrial areas (USA, Europe and China) a more complex pattern of anomalies arises that likely results from the competing effects of suppressed photolysis under clouds (small positive anomaly), venting by passing fronts (large negative anomalies) and accumulation patterns dependent on a predominant synoptic weather type (cyclonic or anticyclonic, Pope et al., 2014). This pattern of differences between cloudy and clear annual NO2 profile climatologies is well reproduced by OMI observations (see right panel in Fig. 13 below). The sole difference is that OMI sees larger outflows at higher latitudes in the cloudy case – perhaps a deficiency of the model in redistributing its horizontal flows under frontal conditions.

Another more direct way to perform this consistency check is to look at the differences in total NO2 columns between model (TM4) and observations (OMI) for the clear and cloudy cases separately, as shown in Fig. 14. For the clear-sky case (see left panel in Fig. 14) the pattern of anomalies that arises is consistent with existing long-term satellite NO2 trend studies (van der A et al., 2008; Richter et al., 2005) that report significant reductions in NO2 in Europe and eastern parts of the United States as well as strong increases in China, along with evidence of decreasing NO2 in Japan and increasing NO2 in India, the Middle East, and central Russia – as well as over some spots in the central USA and South Africa. The differences between model and clear-sky OMI NO2 total columns are being used to update the surface emission inventories (Mijling and van der A, 2012; Ding et al., 2015). What is comforting is that a similar pattern of differences arises in the cloudy case (using the cloud-slicing TM4 and OMI profiles), and with a similar amplitude, verifying that the OMI cloud-slicing columns are internally consistent with the clear-sky OMI observations in detecting anomalies that can be ultimately related to outdated model emission inventories.

In Fig. 14, note that the model total tropospheric NO2 columns over clean remote areas (i.e., tropical and extratropical outflow regions over the oceans) in the cloudy case do not deviate in general by more than 0.1×10-15 moleccm-2 from observations. This is a good result, showing that the estimate of the stratospheric column (by data assimilation) does not produce significant cloud-cover dependent biases in the tropospheric column. If we recall that the observed cloud-slicing NO2 profile over clean remote areas is S-shaped, with a much stronger mid-tropospheric component and a much reduced upper tropospheric load than in the model, then we can infer that there has been as much gain in the mid-tropospheric component as there has been loss at high altitude, which is another form of closure.

The seasonal mean tropospheric NO2 VMR pseudoprofiles for the DJF, MAM, JJA and SON periods observed by OMI over the year 2006 compared against their TM4 model counterparts are shown next. These plots (Figs. 15–33) have been generated using the same cloud-slicing grid and CRF threshold configurations applied for the annual means, with a required minimum of 7 measurements collected per bin during each season (instead of 30 for the annual means). This section is not intended to provide a thorough analysis of seasonal variability in (observed or modeled) tropospheric NO2 profiles but rather to demonstrate the potential of the cloud-slicing technique to provide details that pertain to seasonal as well as to annual means.

The largest signatures of seasonal variability expected to appear in these figures are (a) a seasonal cycle in lightning activity in the upper levels (280–380 hPa) that shifts in latitude following the Sun's declination; (b) a seasonal cycle of biomass burning in the mid-levels (500–620 hPa) basically opposite to that of lightning in case of man-made fires during the dry season, otherwise in phase with lightning; and (c) a seasonal cycle over industrial areas at lower levels (720–820 hPa), featuring minimum NO2 levels in the summer months due to changes in the lifetime of NOx (van der A et al., 2008). The seasonal cycle in lightning NOx emissions may be verified against the climatology of lightning flashes observed by LIS-OTD (data set available online, ftp://ghrc.nsstc.nasa.gov/pub/lis/climatology; see Cecil et al., 2014). The seasonal cycle in biomass burning may be verified against the climatology of ATSR and AVHRR fire counts from Dwyer et al. (2000) and Schultz (2002).

Over Africa, persistent lightning activity at upper levels is expected to take place about the Equator (the Congo Basin) all year long, shifting southward towards South Africa in SON and DJF, and northward towards the Gulf of Guinea, the Sahel and Sudan in MAM and JJA, features which are all captured by OMI in Fig. 15 (in reasonable agreement with TM4, though some discrepancies are apparent too). These lightning signatures are not to be confused with traces of NO2 lifted from biomass burning underneath, which feature a precisely opposite phase. Remarkable biomass burning signatures can be appreciated throughout the entire tropospheric column in Figs. 15–18 as NO2 enhancements north of the Equator (Sahel) in DJF and south of the Equator (Angola and Zambia) in JJA, shifting eastward towards Mozambique and Madagascar in SON (best seen at 500 and 620 hPa in Figs. 17–18). We note that the penetration of seasonal biomass burning signatures into 280–500 hPa is stronger in OMI than in TM4. In addition, note the strong enhancement in lightning activity seen by OMI off the southeast coast of Africa in MAM and JJA at 380 hPa in Fig. 16, in connection with the confluence of the warm Agulhas and the cold Antarctic Circumpolar Current, which is virtually missed by TM4.

Over South America, a maximum in lightning activity is expected to occur over central Brazil in SON, as captured by OMI in Figs. 19–20 (in agreement with TM4, though some discrepancies persist relative to the location of the lightning maximum, as we mentioned when describing the annual means), migrating towards the southeast in DJF. Lightning and precipitation are persistent in the northwest (Colombia, Venezuela and Central America) all year round, intensifying in MAM and JJA, as reasonably captured by OMI in Fig. 19, along with some persistent NO2 enhancements over La Plata Basin and off into the Brazil–Malvinas Confluence Zone. The lightning signatures at upper levels may be partly overlapped by those from biomass burning lifted from underneath, but their separation is more difficult in this case. For instance, the NO2 enhancements detected by OMI at 500 hPa over Brazil in SON and DJF in Fig. 21 correlate well with the lightning signatures at 380 hPa, but they also correlate with the biomass burning signals at 620 hPa, indicating that both processes may be occurring at the same time in separate but nearby locations (e.g., combining the start of the wet season in the Amazon Basin in DJF, with the end of the burning season in eastern Brazil). The cycle of biomass burning in South America, which takes place over the dry season, starts in southern Brazil in JJA, finding a maximum in SON eastward towards the coastal states, as OMI captures in Figs. 21–23 (in reasonable agreement with TM4). In DJF, some activity may persist in eastern Brazil and new activity develops over the lower slopes of the Argentinian Andes during the austral summer, generally complicating attribution. Finally, it is interesting to note in Fig. 23 the remarkable decrease in NO2 levels at 720 hPa over the Amazon Basin during the rainy season in DJF and MAM, as if in connection with an efficient NO2 removal mechanism.

At upper levels, one should expect to see some persistent lightning activity over Indonesia all year round, as qualitatively observed by OMI in Fig. 24 (and in agreement with TM4), migrating northward towards South Asia in MAM and JJA, and southward towards Australia in SON and DJF. These lightning signatures may be mixed to greater or lesser degree with NO2 lifted from biomass burning and/or anthropogenic sources underneath. Over South Asia, biomass burning is expected to reach its maximum in MAM, as OMI captures in Figs. 26–28 particularly over northern India and Myanmar. These emissions are likely responsible for a large part of the NO2 enhancement observed around India at upper levels in MAM. The very strong NO2 enhancement observed over South Asia at upper levels in JJA (Figs. 24–25) is very likely related to deep transport of surface emissions (biomass and industrial) during the monsoon season, which TM4 locates over the Indo-Gangetic area and OMI locates further east over the Tibetan Plateau. Over Indonesia and northern Australia, a maximum in biomass burning activity is expected be reached in SON, as OMI captures reasonably well in Figs. 26–28, indicating that the strong NO2 enhancement seen by OMI over northern Australia at 280 hPa in SON may well be tainted by deep transport of biomass burning.

Over a major industrial hub like China, near-surface concentrations of NO2 around 720–820 hPa are expected to reach minimum/maximum levels in JJA/DJF, just on account of increased/reduced exposure to sunlight (i.e., reduced/increased NOx lifetime), as shown by both OMI and TM4 in Fig. 28. At mid-tropospheric levels though, other effects such as vertical transport intervene. Note in Figs. 26–27 that the TM4 model registers maximum mid-tropospheric NO2 levels over China in JJA, and minimum in DJF. However, OMI observes stronger mid-tropospheric NO2 levels in DJF than in JJA. According to OMI, surface emissions from China (and also from Europe and the USA, as we shall see next) are being transported in larger quantities and to higher altitudes than in the model, particularly during the winter months.

In connection with summer convection, lightning activity at northern mid-latitudes is expected to be strongest in JJA. Enhancements in upper tropospheric NO2 are observed by OMI (and TM4) in Fig. 29 over the eastern Mediterranean in JJA and SON. Enhanced NO2 levels over Siberia in JJA may also be related to summer convection and increased biomass burning. In the USA, lightning activity is expected to reach a maximum in JJA and shift southward towards the Gulf of Mexico in SON and DJF, features which are all registered by OMI in Fig. 29 (in reasonable agreement with TM4, though some discrepancies are apparent in DJF). Figures 30–31 reveal an interesting discrepancy between the OMI and TM4 pseudoprofiles regarding the intensity and reach of convective penetration at 500 hPa of anthropogenic NO2 above major industrial areas. As already noted for China, the TM4 model is placing enhancements of mid-tropospheric NO2 over central Europe and the eastern USA in MAM and JJA, whereas OMI registers a more uniform distribution of mid-tropospheric signatures across the year, showing maxima in DJF and SON. This disagreement is suggestive of problems with the model convective scheme, possibly related to frontal uplift by conveyor belts in the wintertime. At levels closest to the surface, the variation in NO2 concentration over major industrial areas (Europe and the USA, but also China, India and the Middle East) registered by OMI in Figs. 19–20 shows minima in JJA and maxima in DJF, just as expected and in agreement with TM4.