This study focuses on the northern mid-latitudes (25–60∘ N) in order to avoid ill-defined PBL in the tropics due to deep convection and sparse data in boreal and polar regions. In this region, IAGOS profiles are available at 135 airports and ozonesonde profiles at 20 stations, as shown in Fig. 1. The number of profiles available over the period 1994–2016 is 20 762 for the ozonesondes and 72 382 for IAGOS, which represents a total of 93 144 profiles. For both IAGOS and ozonesondes, most profiles are sampled in Europe and North America (especially in the north-eastern United States), with a few in East Asia and the Middle East. It is worth noting at this stage that as O3 and CO mixing ratios can strongly vary from one location to the other, the PBL-referenced profiles that will be obtained from all profiles available at northern mid-latitudes are not expected to be representative of any location in this large latitudinal band. As profiles often show a very complex structure, aggregating such a large number of profiles allows for the smoothing of the vertical distribution and subsequently highlighting specific features. The idea of this study is to focus on the vertical stratification (i.e. the relative changes in mixing ratios with altitude) of O3 and CO rather than their mixing ratios themselves.

All profiles are expressed in metres above ground level (a.g.l.). Note that the altitude available in the IAGOS database corresponds to the barometric altitude above sea level (a.s.l.) estimated from the temperature and pressure measured by the aircraft, assuming standard conditions at the surface (temperature of 288.15 K, pressure of 1013.25 hPa). This leads to an uncertainty on the actual altitude of the aircraft. Under some atmospheric conditions (cyclonic conditions, for instance), the barometric altitude of the aircraft may be below the airport elevation. Without any information on the temperature and pressure at the surface close to the airport, it is not possible to get a more accurate estimation of the altitude. In this study, the altitude a.g.l. is deduced from the barometric altitude a.s.l. available in the IAGOS database by subtracting its first value measured by the aircraft, assuming that this first measurement of the profile is performed close to the surface. The IAGOS measurements are indeed programmed to start when the aircraft wheels leave (or touch) the ground. Some technical issues delaying the beginning of the measurements may occur, but this is expected to concern only a minor proportion of the profiles. Note that the GPS altitude has been available in the IAGOS database only since 2014.

For convenience, all profiles are linearly interpolated at a vertical resolution of 50 m from the surface (thus, this value of 50 m is to be considered as the truncation error in our study). This value was chosen following the sensitivity analysis on the vertical resolution (from 1 to 10 hPa, i.e. about 10 to 100 m) recently performed by Liu and Liang (2010), who concluded that it represents a good compromise between accuracy and uncertainty related to data noise. A sensitivity test with a vertical resolution of 100 m (not shown) confirmed the low sensitivity of the results to this parameter. Additionally, at any given (50 m deep) level, no interpolation is performed when the vertical distance between the two neighbouring points of the raw vertical profile used for the interpolation exceeds 100 m. In this case, the data are considered missing.

As the PBL characteristics exhibit strong diurnal variations, profiles used in this study are separated into different time slots: night (sunset to sunrise), morning (sunrise to solar noon), midday (solar noon to 3 h past solar noon), afternoon (3 h past solar noon to sunset), daytime (sunrise to sunset) and the whole day (denoted “all” in the figures). All time zones and daylight saving hours are properly taken into account.

Three types of PBL can be distinguished: the convective boundary layer (CBL) often occurring during daytime and characterized by strong turbulent mixing under the effect of convective thermals, the stable boundary layer (SBL) occurring mainly during night-time and characterized by the absence of turbulence mixing, and the residual layer (RL) occurring mostly during the night and morning and corresponding to the former CBL, usually delimitated by the SBL top and the capping inversion (Stull, 1988). In our study, for all individual profiles, we first look for any surface-based inversion (SBI) of temperature defined as a monotonic increase in (absolute) temperature from the surface up to a certain altitude (corresponding to the top of the SBI). When no SBI is found, numerous methods have been proposed over the past decades for estimating the PBL height (see Seibert et al., 2000, for a review), including the following: (i) the elevated inversion (EI) method in which the PBL top is located at the bottom of an elevated (absolute) temperature inversion; (ii) methods based on the search for an extremum of vertical gradient in the vertical profile of a relevant thermodynamic parameter (e.g. RH, potential temperature, refractivity); and (iii) methods in which the profile is scanned upward in order to identify at which altitude a certain thermodynamic parameter (e.g. virtual potential temperature, bulk Richardson number) equalizes or exceeds by a certain amount its surface value. Strong systematic differences in PBL height are found among these methods, both in terms of magnitude and seasonal–diurnal variability (e.g. Seidel et al., 2010; Wang and Wang, 2014). The reasons for the discrepancies between the methods are complex (and not clearly understood yet), but may comprise a poor vertical mixing of the PBL, the strong influence of the surface measurement (specifically for the last class of methods), the existence of clouds and/or the uncertainties on the RH measurements under cloudy conditions (Wang and Wang, 2014). As no consensus currently exists, we decided to retain the EI approach in which the PBL top is estimated as the first altitude above which the (absolute) temperature monotonically increases with altitude. The vertical gradient of temperature between the top and the bottom of the EI corresponds to the intensity of the inversion. We require that the difference of temperature between the EI base and the altitude level right above exceeds the value of 0.3 K in order to avoid erroneous identification of the EI base due to uncertainties on the temperature measurements estimated at ±0.25 K in IAGOS (Berkes et al., 2017). All profiles with no or too-weak (below 0.3 K) temperature inversion are discarded. Two examples of profiles are presented in Fig. 2. Note that as it relies only on temperature and not on RH measurements (that are not always fully available over the profiles since all RH data flagged as “doubtful” in IAGOS are rejected), the EI method allows us to maximize the number of profiles taken into account for deriving the climatological vertical distribution of O3 and CO.

Although the EI represents a real geophysical interface between two layers, it is important to note at this stage that this height does not necessarily always correspond to the height of the mixing layer as it may, for instance, correspond to the capping inversion aloft of the residual layer (rather than e.g. the top of an instable nocturnal boundary layer or a growing CBL in the morning). For convenience, we will hereafter refer to the PBL height but the reader should keep in mind that this term may sometimes be ambiguous.

Following previous studies (e.g. Seidel et al., 2010; Wang and Wang, 2014), a maximum PBL height of 4000 m a.g.l. is fixed. In order to further avoid erroneous PBL height estimations due to too-large data gaps in the profile, we require at least 75 % of available data between 0 and 4000 m a.g.l. In addition, for all PBL calculations, we require a maximum of 200 m (i.e. four 50 m deep levels) with missing data between the surface and the estimated PBL height. Among the 93 144 profiles available, SBI and EIs are found in 16 and 63 % of the profiles, respectively. The remaining profiles (21 %) either do not fulfil the previous criteria (due to data gaps) and/or show no significant temperature inversion in the first 4000 m a.g.l. and are thus discarded.

SBIs are important features for air pollution as they inhibit the vertical mixing of pollutants released at the surface. Concerning ozone, they can induce a strong depletion either by dry deposition or titration by the nitrogen oxide (NO) accumulated at the surface (Colbeck and Harrison, 1985). The distribution of the local time (LT) at which (IAGOS and ozonesondes) profiles are measured is shown in Fig. 3 with the proportion of SBI occurrences. Most of the available profiles are measured between 05:00 and 19:00 LT. Results highlight a strong diurnal variability in these SBIs and their characteristics. As expected, they are the most frequent during the night when their proportion continuously increases up to a maximum of 60 % at 03:00 LT (red curve in Fig. 3). Thus, although SBIs are more frequent during the night, many night-time profiles still show unstable conditions. At the locations close to large agglomerations (e.g. airports), the absence of SBIs during the night may be partly due to the urban heat island phenomenon that can turn a stable PBL into a near-neutral PBL (Dupont et al., 1999). The proportion of SBIs then progressively decreases to a broad minimum of 5–10 % between 10:00 and 17:00 LT. Very similar diurnal variations in the proportion of SBIs are observed during all four seasons (not shown).

Both the height and the temperature lapse rate (vertical gradient of temperature between the surface and the SBI top) of these SBIs are shown with their diurnal and seasonal variations in Fig. 4 (considering both IAGOS and ozonesonde profiles). SBIs occur all year with almost no seasonal variations in their frequency. This type of inversion leads to very shallow stable layers with a mean depth of 110 m. A moderate seasonal variability of 23 % is highlighted (as calculated as the difference between the maximum and the minimum SBI height normalized by the annual SBI height), with mean SBI heights ranging from 97 m in summer to 123 m in winter. However, the diurnal variability of the SBI height is strong (71 %), with the largest SBIs being observed during night-time (131 m on annual average) and the smallest during midday (53 m on annual average). The 95th percentile reaches about 300 m. This is substantially lower than the SBIs reported by Seidel et al. (2010), whose median heights ranged around 200–500 m. Differences may be (at least partly) due to the fact that our results are based on profiles measured at northern mid-latitude stations (most of them being located in the latitudinal band 35–55∘ N) essentially during daytime, while the dataset analysed by Seidel et al. (2010) extends to stations located further north up to polar regions and includes a predominant proportion of night-time–morning radiosonde profiles. On average, the temperature lapse rate is about 13 K km-1, with moderate seasonal differences (12 %). Some diurnal variations are also observed during most seasons, with usually decreasing temperature lapse rates from night-time to the afternoon.

We investigated some characteristics of the EIs, namely the temperature difference, width and temperature vertical gradient (see Fig. S1 in the Supplement). The difference in temperature between the base and the top of the EIs is 1.5 K on annual average, with strong seasonal variations from 1.1 K in summer to 2.1 K in winter. The 95th percentile also exhibits high seasonality with values ranging from 3.3 K in summer to 7.2 K in winter. The mean width of these EIs increases from 76 m in summer to 103 m in winter, in reasonable agreement with EI thicknesses estimated by other authors (e.g. Cohn and Angevine, 2000). This leads to mean temperature vertical gradients of 1.4 and 1.9 K hm-1 (where hm stands for hectometre, i.e. 100 m) during these two seasons, respectively. Interestingly, none of these characteristics exhibits diurnal variation (whatever the statistical metric).

The seasonal and diurnal variations in the PBL height estimated with the EI method are shown in Fig. 5 for all seasons and time slots. Averaged over all profiles, the mean PBL height is 1253 m, with values ranging from 1132 m during the night to 1483 m in the afternoon. This corresponds to diurnal variability of 28 %, the diurnal variability here being calculated as the maximum minus minimum PBL height normalized by the mean PBL height based on the values available during the different time slots shown in Fig. 5 (for this example (1483-1132) × 100/1253 = 28 %). Such high night-time values and moderate diurnal variability indicate that the EI height often corresponds to the top of the nocturnal RL (as previously mentioned in Sect. 2.3). As expected, the diurnal variability is much lower in winter (17 %) than in the other seasons (30–38 %). The highest PBL heights are observed during summertime afternoon with 1707 m on average. Similarly, the seasonal variability strongly varies with the time of day, with values of 22, 23, 32 and 35 % during the night, morning, midday and afternoon, respectively.

The PBL-referenced profiles of potential temperature in the absence of SBI (and in the presence of an EI) are shown in Fig. 7. On average, the potential temperature is found to be slightly superadiabatic in the surface layer (i.e. θ decreases with altitude) during both morning (-0.08 ∘C hm-1) and midday (-0.13 ∘C hm-1). The width of this superadiabatic layer never exceeds 5–10 % of the PBL height.

Above that surface layer, the potential temperature increases with altitude. While neutral adiabatic profiles (i.e. no variations in θ with altitude) were expected within the convective PBL, at least during daytime (Stull, 1988), all climatological profiles appear subadiabatic (positive vertical gradient of θ). This subadiabatism varies with the season with strongest values in spring–winter (0.51 ∘C hm-1 on average over the PBL) and lowest values in summer (0.25 ∘C hm-1). As expected, a very sharp increase in the potential temperature is highlighted at the top of the PBL where vertical gradients reach +1.3 ∘C hm-1 on average. This maximum gradient is found to be much higher in winter (+1.6 ∘C hm-1) than in summer (+1.1 ∘C hm-1), as previously analysed (see Sect. 3.2). These seasonal variations are the strongest during the afternoon (+1.8 and +1.0 ∘C hm-1 in winter and summer, respectively). Above, in the lower FT, the increase in temperature with altitude is reduced but remains higher than in the PBL.

As mentioned in Sect. 2.1, several important differences of sampling exist between these two datasets, including the fact that (i) IAGOS aircraft fly at a 30 % higher descent–ascent rate and cover a horizontal distance 10 times larger in the lower troposphere, and (ii) IAGOS measurements are performed in the vicinity of international airports and large agglomerations, while ozonesonde stations are usually located in remote, rural or low-density urban areas (leading to a population density around IAGOS airports of about 2000 inhabitants km-2 on average within ±0.1∘ in longitude and latitude against about 1150 inhabitants km-2 for ozonesonde stations; see Sect. S1 in the Supplement for details). This raises the question of whether or not these sampling differences impact the PBL-referenced vertical distribution. Answering this question would require collocated (in time and space) IAGOS and ozonesonde profiles, but far too few profiles fulfil these conditions. However, in order to give some insights about this question, we calculated the climatological profiles from both datasets taken separately (Fig. 8). Only daytime profiles are shown as ozonesondes and are much sparser during the night. Again, these PBL-referenced profiles obtained with IAGOS and ozonesondes are not expected to be the same since they are sampled in different locations and times and thus correspond to different PBL heights; considering the profiles used in Fig. 8, the mean PBL height is 10–20 % higher in ozonesondes than in IAGOS profiles depending on the season.

Results obtained using both datasets are in reasonable agreement. The main difference is found near the surface where only ozonesondes highlight a small superadiabatism. This may be partly due to the fact that in contrast to ozonesondes, IAGOS measurements do not start at the surface but at a minimum height of a few metres a.g.l. (since instruments are located in the lower part of the fuselage). However, as individual IAGOS profiles sometimes do show a superadiabatism at the surface, the main reason is more likely related to the inherent uncertainties of the IAGOS barometric altitude, which is deduced from the pressure assuming standard atmospheric conditions at the surface (as explained in Sect. 2.2). This may partly smooth the superadiabatism at the surface (as the mean potential temperature in the first 0–50 m altitude level would include some points actually outside the 0–50 m layer and/or ignore some other points actually belonging to this layer). At the annual scale, considering all time slots and z/h levels, the mean bias (MB), root mean square error (RMSE) and correlation (R) between the PBL-referenced profiles of both datasets are 2 ∘C, 3 ∘C and 0.97, respectively (with ozonesondes here taken as the reference).

The PBL-referenced profiles of RH are shown in Fig. 9. At the surface, the mean RH ranges between 55 and 80 % with a well-known seasonal and diurnal pattern characterized by highest values during the wintertime nights and lowest values during the springtime–summertime afternoons. As one moves higher in altitude, RH increases quite regularly up to a maximum located around z/h= 0.8, which is thus just below the top of the PBL. At this level, RH values range between 70 and 85 %. The seasonal differences persist but the diurnal ones are greatly reduced (the absolute difference between the night-time maximum and the afternoon minimum remains below 10 %). A sharp decrease in RH is observed at the PBL–FT interface. The vertical gradient reaches its minimum right above the PBL top (at z/h= 1.05) with -12 % hm-1 on average. The diurnal and seasonal variability of these strongest RH gradients remains low (between -11 and -15 % hm-1). In the lower FT, RH decreases with altitude, usually with stronger (negative) gradients in winter than in summer.

The PBL-referenced vertical profiles of RH obtained with IAGOS and ozonesondes taken separately are shown in Fig. 10. Although the shape of the profiles remains in reasonable agreement, some differences are highlighted. In particular, ozonesondes show a stronger RH vertical gradient within the PBL and a sharper decrease in the lowermost FT with much lower RH in the FT. This sharper decrease above the PBL top might be due to the fact that, as briefly mentioned in Sect. 2.1.2, RH measurements with radiosondes are generally affected by a radiation dry bias due to the heating of the sensors by solar radiation, which can lead to a negative bias on the RH measurements of the order of 5–10 % in the lower troposphere (e.g. Vömel et al., 2007; Bian et al., 2011; Wang et al., 2013). In our case, this bias could be further enhanced in the lower FT due to solar reflection by clouds at the top of the PBL. This is also supported by the fact that the differences between IAGOS and sondes are largely reduced when considering only night-time profiles, i.e. when radiosonde measurements are not affected by heating effects due to solar radiation (not shown). These sources of bias are also expected to vary from one season to the other following the seasonality of solar radiation that is strongest in spring–summer and lowest in winter–fall. This may (at least partly) explain the distortion of the seasonal variations of RH in ozonesondes compared to IAGOS in the lower free troposphere. At the annual scale, taking into account all time slots and z/h levels and considering ozonesondes as the reference, the comparison between IAGOS and ozonesonde datasets gives MB, RMSE and R of +0 %, 9 % and 0.67, respectively.

The PBL-referenced profiles of CO are shown in Fig. 11. The uncertainties of these mean profiles are substantially higher than for the previous meteorological parameters, notably due to a much lower number of measurements (as CO is only measured by IAGOS aircraft and starting from 2002). Considering all profiles, the mean CO mixing ratios at the surface increase from about 240 ppbv in summer to 340 ppbv in winter. The CO mixing ratios decrease with altitude at a varying rate depending on the altitude. The normalized profiles (Fig. 11b, e, h, k, n, r) show that the difference in CO between the surface and the PBL top reaches a factor of 1.3 on average. The first important result shown by these PBL-referenced profiles is therefore the substantial vertical stratification of CO mixing ratios within the PBL.

In order to investigate that stratification on a quantitative basis, we introduce a first factor of vertical stratification (γ) here defined as the standard deviation of the mixing ratio profile between the surface and the PBL top (i.e. over the 21 z/h levels comprised between 0 to 1) normalized by the mean. We also define a second factor of vertical stratification (δ) calculated by normalizing γ by the PBL height. The calculations are first done on each individual profile and then averaged over all profiles. The γ and δ factors will be expressed in % and % hm-1, respectively. Results are reported in Table 2 for the different seasons and time slots. On average, the γ factor of CO vertical stratification is 11 % and varies little with the season and time of day (from 8 to 12 %), the strongest values usually being found in winter–fall. The δ factor exhibits relatively stronger variations, with values ranging from ∼ 1 % hm-1 during summer midday to more than ∼ 2 % hm-1 during winter–fall night.

The strongest vertical gradients are observed at the PBL top and close to the surface. At the PBL top, the strong vertical gradients involve the presence of a clear inflexion point in the mean CO profile (as shown by gradient profiles in the right panels of Fig. 11). With a traditional vertical coordinate system (i.e. z rather than z/h), this feature would have been smoothed (see Fig. 6). The presence of this inflexion point on an independent variable (i.e. a variable not used in the estimation of the PBL height) gives confidence in our ability to capture reasonably well a real geophysical interface with the EI approach. It illustrates the fact that as expected, EIs act as an effective although porous geophysical barrier that limits the vertical exchanges between the PBL and FT, leading to a distinct chemical composition on each side. The sharp gradients at the PBL–FT interface are strongest in winter and lowest in summer. Such seasonal variations are consistent with the fact that EIs are deeper and characterized by a stronger temperature gradient in winter than in summer (as previously shown in Sect. 3.2), which greatly inhibits the ventilation of the polluted PBL and the exchanges with the cleaner FT. The strong gradients at the surface ensue from the presence of CO emissions and are usually maximum during night-time and morning. Substantially lower vertical gradients are found in the FT.