The 43 high altitude stations (Table 1 and Fig. 1) were selected based on various criteria, such as the presence of aerosol or gaseous measurements, their representativeness of the mountainous massif and/or the possibility of comparing several stations from the same mountainous massif. The sites are representative of five continents and their altitudes range between 1074 (SHN) and 5352 m a.s.l (CHC). Note that when not specified, altitudes given in the text correspond to altitude above sea level (a.s.l.). Even if clearly situated within the ABL, some stations like HPB, MSY or ZEP were added to this analysis to verify the results of the ABL-TopoIndex at lower altitude sites. Several mountainous massifs such as the Alps, the Himalayas, the Rocky Mountains and the Andes Cordillera are well represented with three to five stations. Some other stations such as BEO in the Balkan Peninsula, HAC on the Peloponnese, WLG in China, PDI in Vietnam, MKN in Kenya and the high plains of ASK in the Hoggar Mountains of southern Algeria are the only representative of their massif. The volcanic islands form a category in themselves, despite being located in different oceans and at various latitudes.

The topography data were taken from the global digital elevation model GTopo30 (https://lta.cr.usgs.gov/GTOPO30, last access: 20 August 2018). GTopo30 has a horizontal grid spacing of 30 arcsec corresponding to a spatial resolution between 928 m in the East/West direction at the equator, 598 m at WHI (50∘ N) and 373 m at the SUM polar station (72.6∘ N). In the North/South direction, 30 arcsec are almost constant with latitude and correspond to 921 m at the equator and 931 m at the poles. The geographical coordinate system WGS84 (World Geodetic System revised in 1984) from GTopo30 was projected in the Universal Transverse Mercator (UTM) conformal projection to ensure homogeneity in vertical and horizontal coordinates. Due to the altitude averaging over each grid cell, there is typically an altitude difference between the true station altitude and its corresponding grid location. The mean and median of the differences between the station altitude and its representative grid point are 190 m (8.6 %) and 140 m (5.8 %). For stations situated near the summit, the difference can be significant: five stations have an underestimation of their altitude larger than 500 m corresponding to 15 %–32 % (see the Supplement and particularly Table S1 for further details), despite, according to the manual, the high reported GTOPO30 accuracy (minimum accuracy of 250 m at 90 % confidence level with a RMSE of 152 m).

The TopoToolbox-master version of the free shareware TopoToolbox (https://topotoolbox.wordpress.com/, last access: 20 August 2018), which is a set of matlab functions offering analytical GIS utilities in a non-GIS environment (Schwanghart and Scherler, 2014), was used as a principal tool for the topographic relief and flow pathways analysis in the Digital Elevation Model (DEM) analysis. The DEM were preprocessed by filling holes with a carving process prior to calculating the flow directions and the water flow paths were calculated with single flow direction representation.

To construct the ABL-TopoIndex, we rely on the following four criteria to indicate that the ABL influence will be low if the following criteria are met:

the station is one of the highest points in the mountainous massif,

Parameter 1 – hypso%. A hypsometric curve is the cumulative distribution function of elevation on the considered domain. The frequency percentage of the hypsometric curve at the station altitude (hypso%) provides a representation of criterion 1 for a large spatial scale (500 km × 500 km). Figure 3a presents several normalized hypsometric curves with dots indicating the station hypsometric value. While most of the high altitude stations (65 %) have hypso% values less than 10 %, some stations are situated on wide inflection points of the hypsometric curve (see, e.g., PYR and NCOS in Fig. 3a). Six stations (see Table S1) have hypso% values larger than 50 %. BEO and FWS are found at less than 0.1 % of the curve indicating they are located at one of the highest points of their respective mountainous massifs. The ABL influence should increase with increasing value of hypso%.

To summarize, the ABL influence should increase with decreasing values of hypsoD50, LocSlope and G8 and with increasing values of hypso% and DBinv. Thus, to determine the ABL-TopoIndex, the geometric mean is calculated on the inverse of hypsoD50, LocSlope and G8 along with the values of hypso% and DBinv. To avoid any particularities of the station site and due to the fact that the ABL influence is a regional factor, the mean of the values at the grid cell containing the station and at the eight neighboring grid cells (recall that grid spacing is 30 arcsec) are used to calculate the ABL-TopoIndex. The ABL-TopoIndex is then taken as the geometric mean of the five parameters: ABL-TopoIndex=hypso%×1hypsoD50×1LocSlope×1G8×DBinv5. The geometric mean is used here on strictly positive parameters that have widely different numeric ranges (e.g., Table 2). The geometric mean is used instead of the arithmetic mean because it effectively “normalizes” the various parameter ranges, so that no parameter dominates the weighting. Further, a given percentage change in any of the parameters will yield an identical change in the calculated geometric mean value. In that sense, the variability of each parameter is also normalized, leading to similar modifications of the ABL-TopoIndex for similar parameter's variations. Because of these properties, the geometric mean is the recommended method to determine meaningful indices from multiple parameters (Ebert and Welsch, 2004). The extrema, median and mean of the parameters constituting the ABL-TopoIndex are reported in Table 2. The value of the ABL-TopoIndex has no significance in itself, so that the units are not important, but it allows ranking of the stations as a function of the ABL influence due to convection.

Aerosol datasets from 25 high altitude and 3 mid-altitude stations (Table 1) were available for this study, 21 of them coming from GAW (Global Atmospheric Watch) stations. The datasets comprise absorption coefficient, scattering coefficient and/or number concentration and cover time periods ranging from at least a year up to more than a decade of measurement (see Table S3 in the Supplement). Stations with time series shorter than one year were not used, as their data are not representative of a complete seasonal cycle. Due to the non-normal distribution of the aerosol parameters, the 5th, 50th and 95th percentiles were taken as representative of the minimum, central position and maximum concentrations.

No correction for standard pressure and temperature was applied in order to use the measured aerosol properties and concentration at high altitude. For consistency, the measured hourly absorption and scattering coefficients were adjusted to a wavelength of 550 nm if reported at a different wavelength using an assumed scattering or absorption Ångström exponent of 1. Additionally, the scattering coefficients were corrected for angular truncation error. Due to the measurement technique and the low aerosol concentrations at many high altitudes, filter-based photometers regularly measure negative absorption coefficients at some of these sites. Some datasets contain up to 20 %–30 % of negative absorption values. Depending on the data owner's policy, these negative values were either left in the dataset, set to zero (or to a minimum value) or considered as missing values. To ensure a similar treatment for all datasets, negatives values, zeros and minimum values attributed to negatives were thus set to missing values.

The diurnal and seasonal cycles were only analyzed on datasets longer than 2 years. To be able to statistically calculate the diurnal and seasonal cycles, the autocorrelations at 1 h (first lag) were first removed from the dataset by a whitening procedure (Wang and Swail, 2001). The autocorrelations at each lag time were then calculated on the whitened dataset taking into account missing data (see Supplement for further explanations). Only autocorrelation values statistically significant at 95 % confidence level were kept. As the diurnal (24 h) and annual cycles (365 days) were not well defined due to variable meteorological conditions and some shorter datasets, the autocorrelation at lags of 22 to 26 h and at lags of 350 to 380 days were summed to obtain the strength (i.e., the cycle amplitude) of the diurnal and seasonal cycles, respectively. Noise in the aerosol measurements makes the strength of the cycle a somewhat qualitative value. The diurnal cycles were calculated for each month of the year in order to observe the seasonal change of the diurnal cycles.

Mount Moussala (BEO) is the highest summit not only in Bulgaria but of the whole Balkan massif. The regional GAW station is located at the summit (2925 m). The topographic dominance of BEO can be visualized on the topography map (Fig. 4a). Figure 4a also shows the main hydrological flow paths which follow the Iskar, Martisa and Metsa rivers. Figure 4b shows the water flow accumulations, which are the accumulated flows of all cells flowing into each downslope cell in the output raster, allowing visualization of the largest features of the Bulgaria hydrographic network. BEO is at the junction of four drainage basins corresponding to the four main rivers (Fig. 4c). Figure 4d shows that when the inverse drainage basin is calculated with the inverse topography, BEO is in the center of a large inverse drainage basin that covers most of the plotted domain. Even though BEO's altitude is under 3000 m, BEO's ABL-TopoIndex of 0.52 is one of the lowest, due to an almost zero hypso% (0.034 %), a high hypsoD50 of 2136 m and a relatively small DBinv of 1.15×105 (Tables 2 and S2). HAC is a very similar case to BEO as the site is situated near the top of Mount Helmos, the third highest mountain of the Peloponnese massif in Greece.

PYR (5079 m) is the second highest station of all stations considered in this study, but the station is located at the foot of Mount Everest (8848 m) at a confluence point of several valleys (Fig. 5a and b). Figure 5c shows that PYR is situated in the middle of a very large hydrological drainage basin highlighting the fact that the PYR station is not located at a dominant position in the Himalayas. The PYR ABL-TopoIndex is consequently quite high (3.43) and supports the observation of a large ABL influence in the Himalayan region (Bonasoni et al., 2008). The daily arrival of polluted air masses from the Indo-Gangetic plain is frequently reported in PYR data analyses (Bonasoni et al., 2010, 2012; Marinoni et al., 2010).

As the ABL-TopoIndex depends on the size of the chosen domain (Fig. 6a), we have conducted an evaluation of the sensitivity of the various algorithms to the domain size using a range from 50 to 1000 km2. The gradient criterion G8 and the local slope criterion LocSlope are calculated on small fixed horizontal scales (0.5–1 and 10 km, respectively) and are consequently constant with domain size (Fig. 6e, f), although there are small fluctuations due to some distortions occurring during the projection of GTOPO30 in the UTM WGS84 coordinate system, primarily when the analyzed domain extends beyond two UTM zones (see for example BEO). The other three parameters do change with domain size which is the reason that the ABL-TopoIndex also is a function of the domain area. DBinv tends to increase with the domain size for all stations (Fig. 6b), as the size of the low altitude area potentially contributing to thermally lifted pollutants increases with domain size. The hypso% decreases continuously with domain size for stations situated in a dominant position in their mountainous massif such as JFJ, SBO or BEO (Fig. 6c). For stations located at a lower position in their massif (see for example HPB), the hypso% first increases before decreasing once the domain contains all the highest peaks of the massif. Finally, stations situated atop a high local mountain but surrounded by higher mountains such as MUK (not shown in Fig. 6) have a continuously increasing hypso% up to very large domain sizes (106 km2 for MUK). HypsoD50, the difference between the station elevation and the minimum of elevation in the domain, always increases (or at least stays constant) with an increase in domain size but changes more or less rapidly depending on the domain topography (Fig. 6d). In general, the ABL-TopoIndex usually increases with an increase in domain size (i.e., more ABL influence). The largest increases are usually found for the stations with the highest ABL-TopoIndex at small domain sizes and are due to an increase in DBinv overcoming the decrease in hypso% and the increase in hypsoD50.

As stated in the introduction, the development of the ABL-TopoIndex relies on the assumption that the station position in the mountain massif is a better criterion for determining the ABL influence than the station altitude alone. To compare these two parameters, we show in Fig. 7 the ABL-TopoIndex as a function of the altitude for all grid cells in a 5 km × 5 km domain for a subset of stations. For the grid cells at the highest altitudes, there is a clear relationship between the ABL-TopoIndex and the altitude. The ABL-TopoIndex decreases (less ABL influence) as altitude increases. Figure 7 shows that the OMP and PYR regions have a very large ABL-TopoIndex decrease with altitude while ASK exhibits a very small ABL-TopoIndex decrease with altitude. At lower altitudes for each massif, the valleys, high plains and various mountainous slopes lead to a wide range of the altitudes corresponding to the same ABL-TopoIndex value. For example, the altitude range corresponding to an ABL-TopoIndex of 3 varies between 3000 and 6000 m at PYR, while at OMP an ABL-TopoIndex of 2 is achieved at an altitude range between 250–350 m. At PYR and CHC, there are discrete groupings of points likely corresponding to the basins of different valleys around the site. The ABL-TopoIndex values of the stations are indicated by the square markers, allowing visualization of their relative situation in their respective mountain massifs: OMP, HAC and CHC and to some extent SBO were located at places with the lowest ABL-TopoIndex of their regions thus minimizing potential ABL influence. In contrast the region around PYR (and to a lesser extent ASK) shows locations with much lower ABL-TopoIndex (less ABL influence) at similar altitudes to the stations.

The ABL-TopoIndex values for the forty-six stations are grouped as shown in Fig. 8 by continents and mountainous massifs or regions (see Table 1 and Fig. 1) that can correspond to various geomorphologies. The first obvious observation is that all islands have very low ABL-TopoIndex (note the logarithmic scale for the ABL-TopoIndex), whereas the stations in the Himalayan massif have the highest ABL-TopoIndex. The values of the ABL-TopoIndex and of all its constituting parameters are given in Table S1. From this, the following conclusions can be drawn.

Islands. The islands with sites included in this study have a small area, are delimited by the large flat ocean (though most of them are grouped in archipelagos) and their summits were formed by volcanic activity leading to steep slopes. All these factors lead to very low ABL-TopoIndex values. The Teide Observatory on Izaña, an island of the Canary Islands archipelago (TDE) and Pico Mountain Observatory (OMP) in the Portuguese Azores archipelago rank as the monitoring stations with the lowest ABL influence. The low ABL-TopoIndex of both stations is caused by the following reasons: (1) both mountains are the only summit of the island and the highest mountain of their archipelago (3715 and 2350 m, respectively), (2) both islands have small surface area (2034 and 447 km2) and (3) both research stations are just below the mountain summits (177 and 126 m from the summit). The effect of the proximity to the summit can be clearly seen by the difference between TDE (ABL-TopoIndex of 0.22) and IZO (ABL-TopoIndex of 0.57). These two sites, both located on the island of Tenerife, are separated by only 15 km in horizontal distance but a vertical distance of 1165 m, with TDE being the higher station. Taiwan, where LLN is located, has the largest surface area (36 193 km2) of the islands considered here and, additionally, is in close proximity to a continent (China is 130 km to the west). Both of these factors explain LLN's high ABL-TopoIndex in the island category. MLO in Hawaii is at high altitude (3397 m), but the island of Hawaii has a second summit, Mauna Kea (4205 m). Further, the MLO research station is 870 m beneath the volcano top and has a relatively low G8, explaining why it has a higher ABL-TopoIndex than most of the islands. This difference in ABL-TopoIndex between OMP and MLO is confirmed by an almost daily occurrence of buoyant upslope flow at MLO while such flow patterns are much less frequent (<20 % of the time) at OMP (Kleissl et al., 2007).

Alps. The European Alps consist of a broad mountainous massif with the highest summits between 4500 and 4800 m. The four high research stations (JFJ, SBO and ZUG/ZSF) are located between 2900 and 3600 m (ZSF being only some 300 m below ZUG). HPB (985 m) was added to this study as a low elevation station in the Alps. All three high elevation stations have low ABL-TopoIndex: JFJ (0.64), SBO (1.24) and ZUG (1.35). Their ABL-TopoIndex values are generally a little higher than those determined for the islands. As expected, the ABL influence at HPB is much stronger (ABL-TopoIndex is 5.38) due to both its lower altitude and position near the bottom of the Zugspitze massif.

Pyrenees. The Pyrenees are a natural border between France and Spain and peak at 3400 m. PDM is a high altitude station (2877 m) with an ABL-TopoIndex similar to the European alpine high altitude stations. MSA is located at a mid-altitude range of the massif and has a median ABL-TopoIndex, while the low altitude MSY station, added for comparison purposes, has a high ABL-TopoIndex.

Other European stations. BEO and HAC are situated at the highest points of their massifs and thus have very low ABL-TopoIndex values, comparable to those of the island high elevation sites. The lower altitudes of CMN and PUY, their middle position in mountainous massifs containing several higher summits and, to a lesser extent, their proximity to other massifs such as the Alps and the Pyrenees result in higher ABL-TopoIndex values for these two sites.

Himalayas and Tibetan Plateau. The Himalayas are the highest mountainous massif on Earth with 14 summits peaking at more than 8000 m. The altitudes of the research stations fall between 2200 and 5100 m but are at relatively low elevation in comparison to the summits. This is clearly reflected in their high ABL-TopoIndex values (between 3 and 30). MUK and SZZ are both situated in the foothills of the Himalayas in India (Uttarakhand region) and in south China (Yunnan region), respectively, and both have an ABL-TopoIndex value in the 3–10 range. Although MUK is at a lower altitude than SZZ, it is located at a higher position than SZZ relative to the mean altitude of its meso-scale environment. The high ABL-TopoIndex values for HLE and NCOS are due to their positions in a large valley and on the edge of a vast lake, respectively. Such positioning largely decreases all the parameters related to criteria 1, 2 and 3 (see Sect. 2.3). WLG is constructed within a few meters of Mount Waliguan's summit on the northeastern part of the Tibetan plateau; its dominant position in its meso-scale domain leads to a middle range ABL-TopoIndex value.

Japan. Mount Fuji is the highest peak of Japan and the research station is located at the top of the symmetric volcano located near the coast. The second highest peak in Japan is some 500 m lower than Mount Fuji. This particular topography leads to an ABL-TopoIndex similar to the volcanic islands. The two other Japanese stations are at much lower altitudes and have mid-range ABL-TopoIndex values.

North America. Mount Washington Observatory is located in the Presidential Range of the White Mountains. It is the highest peak in the northeastern United States and the most prominent mountain east of the Mississippi River. MWO is consequently the North American station with the lowest ABL-TopoIndex due to very low hypso% and relatively high G8, LocSlope and hypsoD50. Four stations (MZW, NWR, SPL and YEL) are situated in the Rocky Mountains, whose summits peak at 4400 m. The three stations higher than 3000 m have lower ABL-TopoIndex values similar to some of the European mountain sites, whereas YEL is situated on the wide Yellowstone high plains with an average elevation of 2400 m. Thus, YEL has a high ABL-TopoIndex (7.2) that is similar to the values for NCOS and HLE. Mount Bachelor (MBO) is located near the top of an isolated volcano from the Cascade volcanic arc that dominates the plains surrounding it, explaining its low ABL-TopoIndex. WHI is located in the Pacific Coast Range, the mountain range referring to the vicinity between the high altitude massif and the ocean coast. The highest peaks in the Pacific Coast Range have summits between 3000 and 4000 m (WHI is at 2182 m). WHI has a middle range ABL-TopoIndex (1.4) despite its low altitude due to the proximity of the ocean and to the rather narrow width of the massif (300 km). APP and SHN are both situated at the same altitude in the Blue Ridge Mountains of the Appalachian range. At the latitude of SHN, the width of the Blue Ridge mountain range is much narrower than at APP's latitude. Moreover SHN is almost on the top of the ridge whereas APP is on a high plain. Therefore, SHN has higher G8 and LocSlope and lower hyps% and DBinv, leading to much lower ABL-TopoIndex than is found for APP.

Andes. CHC (5320 m), the highest station in this study, is located in the Cordillera Oriental, itself a sub-range of the Bolivian Andes massif, and is part of the mountain bell surrounding the Altiplano (literal translation high plain) with an average height of 3750 m. This position explains its mid-range ABL-TopoIndex of about 1.3 due to relatively high hypso% (1.03 %) and low hypsoD50 (1311 m). PEV (4765 m), the South America station with the lowest ABL-TopoIndex, is located at the extreme northeastern extension of the South America's Andes mountain range that peaks at about 5000 m. Its high position in its mountain range is characterized by a very low hypso% (0.28 %) and the highest hypsoD50 of 4019 m. TLL is situated in the foothills of the Andes in Chile near to the Pacific ocean and has a similar ABL-TopoIndex to SZZ due similarities in topography. LQO is at higher altitude than TLL but located in the middle of the Altiplano leading to an ABL-TopoIndex larger than 20.

Africa. Mount Kenya (5199 m), the second highest peak in Africa and the highest in Kenya, is an isolated volcanic massif with several peaks. MKN observatory is located some 1500 m under Mount Kenya's summit resulting in a mid-range ABL-TopoIndex of about 1. Assekrem (ASK, 2710 m) is located on a small (about 2.5 km2) high plain in the Hoggar Mountains located in central Sahara. The highest summit in the Hoggar range peaks at 2908 m. Despite being situated in a relatively flat area, ASK has quite low ABL-TopoIndex value because of its relatively high elevation in the Hoggar Mountains.

Arctic. SUM is located high atop the Greenland ice sheet in the central Arctic. The ice sheet has a very smooth topography due to its build up by glaciation and precipitation. While SUM has a high hypso%, its hypsoD50, G8 and LocSLope are very low and its DBinv is large, leading to high ABL-TopoIndex. The Zeppelin Observatory (475 m) in Svalbard is located near the top of Zeppelinfjellet (556 m), above Ny-Ålesund, but cannot be considered as a high altitude site and was added to the study for comparison purposes. Its ABL-TopoIndex is consequently very high as the highest summit on Spitzbergen Island is at 1717 m.

While Fig. 8 shows that there are some clear patterns in the ABL-TopoIndex, it is also instructive to see how the ABL-TopoIndex relates to measurements at mountain sites. The NCOS and SUM stations have a very high ABL-TopoIndex due to their situation on a high altitude plain near a vast lake and on the smooth shape of the Greenland inland ice sheet, respectively. As they are not situated in a complex topography, they were excluded from this analysis due to their clear outlier status. ZEP, situated at very low altitude (475 m) and very high latitude (78.9∘), also has a very high ABL-TopoIndex value. It was also not included in the correlation analysis as its seasonal and diurnal cycles exhibit different features than the high altitude or middle latitude stations (see Sect. 4.1). In order to have a robust estimate of the correlation between the aerosol measurements (following a Johnson distribution) and the topographical parameters (following a normal or a log-normal distribution depending on the parameter) the Spearman's rank correlation was calculated. It should be noted that the Kendall's tau correlation analysis leads to the same conclusions (see Table S4). The Spearman's rank correlation measures the strength and direction between two ranked variables without the requirement that the variables are normally distributed. Here it is also used to verify that the assumed relationships between topographical and aerosol parameters correspond to those proposed in Sect. 2.3 (e.g., that a positive correlation with aerosol loading as a surrogate for ABL influence in the case of lifting processes without precipitation is found for the ABL-TopoIndex, hypso%, DBinv and station altitude and an anti-correlation with aerosol loading is found for hypsoD50, LocSlope and G8). The expected positive or negative correlations with aerosol parameters are found for ABL-TopoIndex and all five topographical parameters contributing to the ABL-TopoIndex. The Spearman's rank correlation coefficients of the 5th, 50th and 95th percentiles of the measured aerosol parameters with site altitude latitude, ABL-TopoIndex as well as all the individual parameters constituting the ABL-TopoIndex are presented in Fig. 9. (Similar to the ABL-TopoIndex calculation, the mean of the altitudes of the grid cell containing the station and its eight neighboring cells was used.)

The ABL-TopoIndex has statistically significant (SS) correlation for all of the percentiles of all aerosol parameters except for the 95th percentile of the scattering coefficient. The highest correlation and SS are found for the fifth percentile of the absorption and scattering coefficient, whereas for number concentration the ABL-TopoIndex is most highly correlated with the 50th percentile. The correlation coefficient of ABL-TopoIndex with the maximum of the aerosol parameters (95th percentile) is always lower than with the minimum (5th percentile) and is SS at 95 % of confidence level only for the absorption coefficient. The fifth percentiles of the aerosol parameters, particularly of the absorption coefficient, correspond to the measurement of air masses with the lowest aerosol concentration, namely FT air masses with the lowest ABL influence and no advection of polluted air masses. In contrast, the 95th percentiles correspond to the advection or convection of air masses with high aerosol loads and can, to some extent, be caused by special events such as dust or biomass burning events. In contrast to the absorption coefficient, the particle number concentration (and, to a far lower extent, the scattering coefficient) depend not only on the ABL influence but also on the new particle formation (NPF) that can be enhanced at high altitudes (Boulon et al., 2011; Rose et al., 2015). Thus, the high correlation of the ABL-TopoIndex with the fifth percentile of the aerosol absorption coefficient as well as lower correlation with the 95th percentile of absorption coefficient, the fifth percentile of number concentration and the 95th percentile of scattering coefficient suggest the ABL-TopoIndex is indeed a promising indicator for ABL influence based on station topography.

The hypso%, a large scale parameter, has SS correlations with all the percentages of all the aerosol optical properties, whereas LocSlope and G8, two small scale parameters, have SS anticorrelations except for the 95th percentile of the scattering coefficient where no SS correlations are observed. The hypsoD50 is SS for the 5th and 50th percentile of the absorption and scattering coefficients and for the 50th and 95th percentile of the number concentration. Only the DBinv exhibits no SS correlation with any of the aerosol parameters.

There are no SS correlations between the station altitude and the percentiles of any of the aerosol parameters. The station elevation alone is thus not a good predictor of the ABL influence (at least as it relates to particle concentration and aerosol optical properties). The latitude is SS anticorrelated with the 5th and 50th percentile of the scattering coefficient.

The correlations of the topographical parameters with the strength of the diurnal and seasonal cycles of the aerosol measurements exhibit a different pattern. Figure 10 shows the Spearman's rank correlation coefficients of the topographical parameters with the minimum (Dmin) and maximum (Dmax) strength of the monthly diurnal cycle as well as with the strength of the seasonal cycle (Season) of the aerosol parameters. The diurnal cycles were calculated for each of the 12 months, so that Dmin and Dmax correspond to the lowest and the highest monthly amplitudes, respectively. For many mountain sites, Dmin occurs when the station remains in the FT during the whole day resulting in no systematic diurnal cycle. In contrast Dmax occurs when the site is in the FT during the night (without any influence of the RL) and influenced by the ABL during the day. The diurnal and the seasonal cycles were both calculated as the strength of the autocorrelation function (see Sect. 2.4 and Supplement) so that the underlying parameters are de facto normalized and that the cycles of each station can be directly compared. The highest correlation (a negative correlation) is found between the amplitudes of the diurnal cycles and the latitude for all three aerosol parameters. This anticorrelation is particularly noticeable for the number concentration diurnal cycles. At low latitudes, the stronger insolation enhances the surface temperature and the thermal convection leading to stronger diurnal cycles, particularly in summer, while the convective flow is less likely to be inhibited during the winter due to longer daylight hours. Together these effects result in a larger ABL influence year round and explain the high correlations of latitude with the diurnal cycle amplitude. The high correlation between the maximal diurnal cycle and the number concentration can also be explained by the promotion of NPF due to the stronger insolation at low latitude.

The ABL-TopoIndex is SS correlated with the minimum and the maximum of the monthly diurnal cycles of the absorption coefficient. This correlation is, once again, primarily due to the hypso% and G8, and to a lesser extent, the LocSlope. The highest correlation is found for the absorption coefficient which directly depends on uplift of ABL air masses, in contrast to the number concentration and scattering coefficient cycles which are also influenced by gas-to-particle conversion processes such as NPF. As NPF can be enhanced at low temperature, (i.e., NPF seasonal cycle can be anticorrelated with the seasonality of the CBL height) the relationship between number concentration (and, to a lesser extent, scattering) with diurnal cycle strength may be obscured by seasonal changes in atmospheric dynamics.

The only SS correlation with station altitude is found for the scattering coefficient seasonal cycle. Similar to the anticorrelation of G8 with the aerosol parameter percentiles, there is also a high anticorrelation between the particle number concentration diurnal cycles and G8 suggesting that the local slope steepness inhibits both the transport of polluted air masses and NPF. Apart from a correlation at 90 % confidence level between DBinv and the absorption coefficient, the lack of further SS correlations for topographic parameters with the aerosol parameter seasonal cycles can be attributed to several factors: (i) the relatively small time period (2–5 years) covered by most of the datasets leading to difficulties in the statistical determination of a yearly periodicity due to inter-annual variability, (ii) the low aerosol concentration at high altitude sites often resulting in measurements near the detection limits of the instruments (see for example the problem with the absorption coefficient at Sect. 2.4), (iii) the seasonal long-range transport effects masking ABL transport and (iv) the necessary whitening procedure (see Supplement) increasing the dataset noise.

In order to test the relevance of the ABL-TopoIndex, it is first necessary to find a parameter commonly measured at high altitude stations that can be used as an ABL tracer. Pollutants emitted at the Earth's surface and having a (typically) minimal concentration in the FT could act as potential tracers of the ABL influence. Our results showed that of the three aerosol parameters tested in this study (number concentration, absorption coefficient and scattering coefficient), absorption coefficient has the highest correlation with the ABL-TopoIndex values. Other possible candidates for testing the ABL-TopoIndex include the aerosol mass concentration, size distribution and chemical composition, the water vapor and the trace gases concentrations (e.g., CO2, PAN, NOx, NOy, O3, SO2, isotopologue ratio of water vapor) and the radon222 concentration. These parameters have been used in different studies to provide information about the seasonal and diurnal cycles (e.g., Collaud Coen et al., 2011; Griffiths et al., 2014; Marinoni et al., 2010; McClure et al., 2016; Okamoto and Tanimoto, 2016; Pandolfi et al., 2014; Ripoll et al., 2015; Zellweger et al., 2009), the sources and transport of aerosol to the site (e.g., Cuevas et al., 2013; García et al., 2017; Pandey Deolal et al., 2014; Ripoll et al., 2014), the local orographic flows and the effect of the synoptic- and meso-scale weather types (e.g., Bonasoni et al., 2010; Gallagher et al., 2011; González et al., 2016; Henne et al., 2005; Kleissl et al., 2007; Tsamalis et al., 2014; Zellweger et al., 2003). All of the extensive aerosol parameters, the radon222, water vapor concentration, particulate nitrate (NO3-) and organics have been shown to be correlated with ABL transport whereas CO / NOy and NOx / NOy ratios are anticorrelated (Legreid et al., 2008; Zellweger et al., 2003). Zellweger et al. (2003) concluded that, in contrast to NOy, the major process for upward transport of aerosol is the thermally induced vertical transport, confirming that the aerosol parameters used in this study could, in most cases, be good tracers for ABL influence. However, one has to keep in mind that many lifting processes co-occur with precipitation and, hence, potential aerosol washout. The present validation of the ABL-TopoIndex by aerosol measurements at high altitude stations is consequently valid only for thermally induced processes without precipitation. ABL events involving air masses with low aerosol concentrations due to washout – for example synoptic lifting or foehn – were not directly analyzed.

Because there are variable pollution levels in the vicinity of the stations, a single absolute value of a pollutant cannot be used to evaluate the ABL-TopoIndex (or ABL influence in general) when considering multiple high altitude stations. An inventory of the proximate pollution sources constraining simulations with meteorological models able to explicitly resolve the role of fine resolution orography would be required before using absolute pollutant concentrations as indicators of ABL influence at high altitude sites. Another possibility would be to weight the pollution source inventories by factors depending on their vertical and horizontal distances to the high altitude stations, as well as on a seasonal parameter representing the potential ABL height. A further use of DBinv to restrict the area of potential pollution sources can also be envisaged, as this parameter describes the domain from which pollutants can reach the high altitude station by convection without crossing topographical barriers. The identification of pollution source areas potentially affecting the high altitude stations can be avoided by instead considering dynamic parameters such as the temporal cycles of various pollutants.

At most of the high altitude stations, a seasonal cycle in ABL-indicator species is frequently observed. The maximum values of the seasonal cycles are often correlated with ABL transport and typically occur in summer or in the pre-monsoon season, while the minimum of the seasonal cycle occurs in winter or monsoon seasons. Usually, at high altitude stations, the spring leads to higher aerosol loading than the autumn; this is probably related to higher ABL height in the spring. These seasonal cycles are explained by the stronger thermal heating of the soil, which induces convection and buoyancy in summer and by the atmospheric cleaning effect of precipitation during the monsoon. It would be expected that stations continuously situated in the ABL throughout the year could exhibit different seasonal cycles than high altitude sites due to the seasonal modification of the sources and/or of the synoptic and meso-scale meteorological conditions (see for example the difference between HPB and JFJ in Fig. S2). In contrast, a station located such that it is continuously impacted by FT air masses or with weak seasonal cycle of the ABL influence would have a seasonal cycle that depends mostly on long-range, high altitude transport climatology, e.g., long-range transport of Asian dust and pollution at MLO in spring (Collaud Coen et al., 2013), North-America ABL transport to IZO through westerlies in spring (García et al., 2017), and dust events in EU spring and autumn (Collaud Coen et al., 2004). As seasonally changing parameters (e.g., temperatures, cloud cover, solar radiation, wind speeds, surface albedo, precipitation) were not studied and as the length of most of the time series were too short to smooth these effects, the ABL-TopoIndex will probably not represent an overall picture of ABL influence except at seasonally invariant sites (e.g., very low latitude sites).

The typical diurnal cycle of ABL pollutants at high altitude stations that are partially influenced by the ABL consists of a minimum in the early morning (04:00–06:00 LTC) followed by an increase of the compound with a maximum in the late afternoon (15:00–17:00 LTC) and a decrease during the night. If the ABL influence is mostly due to orographic winds, upslope or valley winds begin to flow some hours after sunrise and downslope or mountain winds initiate after the occurrence of negative vertical heat flux. Stations always situated in the FT should exhibit no systematic diurnal cycles, whereas the stations always situated in the ABL often show various diurnal cycles that can be explained by the behavior of local sources, the diurnal cycle of the ABL height and/or local meteorological conditions. At high elevation and high latitude stations the diurnal cycle typically vanishes during winter but is clearly present during summer, spring and, to a lesser extent, autumn. For stations at lower altitude that stay in the ABL (or CBL, SBL or RL) during the whole day in summer (e.g., MSA, Pandolfi et al., 2013; HPB and PUY, Hervo et al., 2014), the diurnal cycle may also vanish during that period.

Testing the ABL-TopoIndex using pollutant diurnal cycles is further complicated by the presence of the residual layer (RL) that keeps the pollutants brought to high altitudes during the previous days at those elevated levels during the nighttime. The climatology of the RL height usually exhibits a similar seasonality as the ABL height, with a maximum in summer (or pre-monsoon) season and a minimum in winter (Birmili et al., 2009, 2010; Collaud Coen et al., 2014; Wang et al., 2016). Further, the RL has a similar dependency as the ABL on latitude, i.e., the RL's maximum height also depends on the duration of the incoming radiation. The RL pollutant concentrations are much higher than nighttime FT concentrations, leading to less marked diurnal cycles in summer than in spring (Blay-Carreras et al., 2014; Collaud Coen et al., 2011; Hallar et al., 2016; Hervo et al., 2014). The impact of the RL on the aerosol concentration is probably one of the most important reasons for the low correlation between the topographical parameters and the aerosol temporal cycles. However, the statistical determination of the diurnal and seasonal cycle amplitudes suffer from several difficulties: (1) the low aerosol concentrations observed at high altitude often result in measurements near the detection limit leading to large uncertainties, (2) the high hourly autocorrelation of the data requires a pre-whitening procedure (see Supplement) in order to be able to detect the diurnal and seasonal cycle, (3) meteorological conditions (e.g., cloud coverage, precipitation, seasonal fluctuations, etc.) modify the clear-sky diurnal cycles. These factors constraining the observation of clear statistical temporal cycles in the measurement data also contribute to the observed low correlations between the diurnal and seasonal cycles of the aerosol parameters and the ABL-TopoIndex.

Recently, the influences of the local and of the more regional or meso-scale ABL at the JFJ were separated by differentiating the Local Convective Boundary Layer (LCBL) height from the high altitude aerosol layer (Poltera et al., 2017). The LCBL was found to rarely influence the JFJ research station (never in winter, 4 % of the time in summer corresponding to 22 % of the days with ABL influence), whereas the continuous aerosol layer has a large influence on the JFJ pollutant concentrations (21 % of the time in winter and 41 % of the time in summer corresponding to 77 % of the days with ABL influence). This suggests that the mechanisms explaining the heights of the LCBL and the more horizontally extended aerosol layer have different causes and do not follow the same diurnal pattern. This phenomenon will be more pronounced at continental high altitude stations than at marine isolated island stations since the marine ABL is less prone to strong diurnal cycles.

The correlations between topographical and aerosol parameters presented in Sect. 3.5 can now be further discussed in light of the pollutant temporal cycles. The absorption coefficient is primarily due to the presence of black carbon emitted from combustion processes occurring mostly in the ABL and rarely near the high altitude stations; additionally, BC aerosol is not produced by any secondary processes. Among the aerosol parameters studied here, the absorption coefficient is thus the best tracer for anthropogenic pollution and biomass burning and consequently for ABL influence. It is thus expected that a better correlation will be obtained between the topography parameters increasing the ABL influence and the absorption coefficient. The ABL-TopoIndex reflects this correspondence, particularly through the contribution of the hypso% parameter (recall that hypso% represents the relative altitude of a station in its mountain range), the LocSlope and G8. The best correlation for both ABL-TopoIndex, hypso%, Locslope and hypsoD50 are found for the fifth percentile of the absorption coefficient, since the minima of the aerosol loading is a better tracer of the lowest ABL influence, whereas the maxima is much more dependent on source intensity and special events. Similar to this result, a clear correlation was also found between the continuous aerosol layer maximum height and the absorption coefficient measured in situ at the JFJ (Fig. 8 in Poltera et al., 2017). The absorption coefficient amplitudes of the diurnal cycle are also the only aerosol cycles having a SS correlation with the ABL-TopoIndex.

It is more difficult to directly tie scattering and number concentration to the ABL incursions. This is because the formation of new particles and their subsequent growth are well-known to be very efficient processes at high altitudes due to the high insolation and the low temperature. Moreover, the NPF is also enhanced by local thermal winds and forced convection due to favorable changes in thermodynamic conditions (Boulon et al., 2011; Rose et al., 2015). It was found at the JFJ and confirmed at other stations that new particle formation, and particularly strong nucleation events, occur mostly when the air masses were in contact with the ABL within 2 days before arriving at high altitudes (Bianchi et al., 2016). NPF and subsequent growth of the particles have a large impact on the number concentration and its temporal cycles and a smaller influence on the scattering coefficient. The parameters describing the local topography (G8 and LocSlope) have the highest correlation with the number concentration and are probably more relevant to the local CBL transport than to the longer range continuous aerosol layer as defined in Poltera et al. (2017). The number concentration and, to a lesser extent, the absorption coefficient percentiles and diurnal cycles are anti-correlated with the local (G8: 0.5–1 km) and regional (LocSlope and hypsD50: 10 km) slopes, suggesting there is an increase of particle number concentration when there are small altitude differences and gentle slopes around the station. This dependence on the ease of local transport can be explained by transport to the station not only of aerosol, but also of gaseous precursors for NPF and of newly formed particles at lower elevations. The higher correlation of local slope (G8 and LocSlope) with the 50th percentile of number concentration rather than with the absorption coefficient can be explained both by the sources of black carbon being very few in the vicinity of most of the high altitude stations and by the smooth pressure decrease experienced by the precursors during their upslope transport along gentle slopes leading to more condensation processes and nucleation.

The aerosol diurnal cycles are influenced by numerous phenomena (see Sect. 4.1) leading to a non-trivial relationship with the ABL influence. The study of the diurnal cycles can bring valuable results if specific cases are analyzed and compared. The statistical approach used here is confounded to the noise in the data (low aerosol concentration and whitening process), to the inter-annual variability of the meteorological processes and to cloud, precipitation and long-range advection involving a large day to day variability. There are consequently few statistical correlations between topography parameters and the diurnal cycles. The clearest correlation is the influence of the insolation on the aerosol diurnal cycles amplitudes. This dependence between the latitude and the aerosol concentration has been noted by Kleissl et al. (2007) and is easily understandable, as the convection and the new particle formation are directly dependent on the solar radiation intensity. However, the other correlations found between some topography parameters (ABL-TopoIndex, hypso%, G8 and LocSlope) and the absorption coefficient are directly tied to the ABL influence.

The choice of the five parameters included in the ABL-TopoIndex was initially based on several assumptions relating the topography to the ABL influence (see Sect. 2.3). Several other parameters taken from the topography, morphology or hydrology fields such as the topographical wetness index, the upstream catchment area, the Efremov–Krcho landform classification, the integral and index of the hypsometric curve and the topographic prominence were tested but eliminated as being not relevant for various reasons (Table S2). Indeed, most of the parameters comprising the ABL-TopoIndex exhibit some correlations with aerosol parameters. The hypso%, LocSlope and G8 are the parameters explaining the highest variance in the aerosol optical properties, with the hypsoD50 having a lower influence than the other three parameters. It also seems evident that the topographical parameters linked to the steepness and the altitude differences (G8 and LocSlope) are clear indicators for NPF. The DBinv seems to be the least explanatory parameter in terms of ABL influence and this large scale parameter should probably be combined with a source inventory to increase its relevance for identifying boundary layer influence (see Sect. 4.1). However, DBinv does have a clear influence on the statistical significance of the correlations between the ABL-TopoIndex and the aerosol cycles (not shown in the paper) and has the highest correlation with aerosol seasonal cycles. However, the aerosol parameters and, particularly, the absorption coefficient cannot be considered as unique tracers of the ABL, particularly in case of lifting processes with precipitation. Analysis of other ABL marker (gaseous species, radon, wind turbulence, etc.) can provide information on additional transport mechanisms, which would allow for refinement of this topographic analysis by adding further parameters. East-oriented slopes are heated early during the day and thus have a larger contribution to the thermal convection and the associated valley winds. A parameter weighting the east slope area could thus be added to the ABL-TopoIndex. The various geomorphologies of the mountainous ranges included in this study also raise the question of whether the stations should all be combined together for analysis as was done here, or if a morphological parameter should instead be found for each massif. The mountain steepness (at larger scales than LocSlope and G8) also determines the necessary velocity for the wind to cross the mountains and could be an additional parameter. Finally, future studies should attempt to build a direction dependent ABL-TopoIndex that also takes into account the topography of each valley up to the meso-scale range.

It is important to understand the FT vs. ABL influence on historical data sets from established high altitude observatories. The ABL-TopoIndex is one tool that can help elucidate the different influences. A further improvement could include an angular dependency of the ABL-TopoIndex allowing quantification of the potential direction of the maximum ABL influence and the pollutant sources with the largest influence. The ABL-TopoIndex may also be useful a priori in locating measurements for a field campaign or identifying potential sites for long-term observatories if FT measurements are the goal, particularly when no previous measurements exist. For example, in situ aerosol measurements are done at IZO at an altitude of 2373 m, whereas aerosol optical depth and water vapor isotopologues measurements are done at TDE at 3538 m on the same volcano. TDE has a much lower ABL-TopoIndex than IZO and consequently TDE's measurements are more likely to represent the FT. The topography around the PYR station suffers from several factors (see Fig. 7 and Sect. 3.1) leading to a high ABL influence. Even if the choice of the actual site is driven by compelling and practical logistical arguments, other positions at similar altitudes in the massif would have ensured lower pollution impact than is observed at PYR. Finally, some stations such as BEO (2925 m), HAC (2314 m) and MWO (1916 m) are not situated at very high altitudes but present excellent locations for FT sampling. Obviously there are other issues to consider when deploying instruments as well (e.g., ease of access, power availability, presence of local pollution sources, etc.), but the ABL-TopoIndex is one factor that could be considered to maximize the potential for FT sampling.