To generate a high-resolution, gridded dataset of meteorological variables that can be used to drive a Lagrangian dispersion model, we used the Advanced Research WRF model version 4.0.3 . WRF is a state-of-the-art, non-hydrostatic, regional numerical weather prediction model that is used operationally and for research. Here we perform one 6-month-long continuous simulation starting on 6 December 2017 and ending on 31 May 2018. As the simulation and subsequent analysis is only 6 months long, this study provides detailed air mass information for the duration of the intensive period rather than a climatological description which would require a multiple-year study. Four nested domains are used (D01–D04), and their locations are shown in Fig. a and c. The outermost and largest domain (D01) has a grid spacing of 38 km, whereas the innermost and smallest domain (D04) has a grid spacing of 1 km. Full details of the domains are given in Table S1 in the Supplement. One-way nesting is used: the outer domain provides boundary data for the inner nest, but the inner nest does not provide any feedback to the outer domain. To ensure that the long simulation remains close to reality throughout the 6-month period, the outer domain is nudged (i.e. analysis nudging) to the boundary conditions every 6 h.

The initial and boundary conditions were taken from the National Centers for Environmental Prediction (NCEP) Climate Forecast System Version 2  with a temporal resolution of 6 h, a horizontal resolution of 0.5∘ and 64 sigma-pressure hybrid layers. The model topography was obtained from the global multi-resolution terrain elevation data model  with a resolution of ∼1 km. We use the following parameterizations: microphysics is parameterized by the Goddard scheme, cumulus convection is parameterized by the Grell–Freitas ensemble scheme in D01 and D02, no cumulus parameterization is used for D03 and D04, the short- and long-wave radiation is parameterized by the new Goddard short-wave and long-wave schemes, the planetary boundary layer (PBL) physics are represented by the Mellor–Yamada–Janjić (MYJ) scheme, and the land surface model is the Unified Noah Land Surface Model.

The surface temperature of Lake Titicaca was manually prescribed to monthly means obtained from  since values prescribed by WRF were unrealistically low. This is most likely due to the height of the lake (around 3.8 km a.s.l.) and the assumptions made by WRF when interpolating surface temperature of lakes from adjacent sea surface temperature (a similar lake temperature issue is reported by ).

There are some limitations to the WRF simulation, primarily related to the complexity of the terrain. The 1 km resolution inevitably smooths the topography in comparison to reality, which can affect the slope angles and furthermore affect the simulated thermally driven winds. However, temperature and precipitation comparisons with in situ observations at CHC show reasonable agreement. Figure S1 in the Supplement shows the 6-month time series of the modelled and observed hourly temperature, daily mean temperature and daily accumulated precipitation. Using these data, basic error metrics were computed. For the hourly temperature data, the mean bias, mean absolute error and root mean square error are -0.42, 1.35 and 1.73 ∘C, respectively. For the daily accumulated precipitation, we compiled contingency tables with different precipitation thresholds and computed the accuracy (see the Supplement for details of these calculations). For a threshold of 1 mm, the accuracy (i.e. fraction of correct forecasts) is 0.65. Additional evaluation using 0 and 5 mm thresholds, along with the number of hits, misses, false alarms and correct negatives, is shown in Table S2. Furthermore, an evaluation of the WRF-simulated monthly accumulated precipitation for December and May at a number of stations near CHC is presented by .

The FLEXible PARTicle dispersion model (FLEXPART) is a Lagrangian transport and dispersion model which can be used for both forward and backward simulations. We used version FLEXPART-WRF_v3.3.2  to perform backward simulations and thus to determine the source regions of air masses arriving at CHC. The FLEXPART simulations were driven using the meteorological output from the 6-month WRF simulation. Output from all four of the WRF output domains was used, and this was available at a temporal resolution of 15 min. This high temporal resolution is a clear advantage over using reanalysis data, which at best are only available once per hour.

In the FLEXPART simulations, we continuously release 20 000 particles per hour from CHC from 6 December 2017 until 31 May 2018 and compute their back trajectories for 4 d. The particles, passive air tracers, are released in a 10 m deep layer which extends from 0 to 10 m a.g.l. and over a 2×2 km square centred around CHC. With the choice of 4 d as the (backwards) simulation time, the average median particle spends 94 % of its residence time within the domain D01.

When FLEXPART is run in backward mode, it calculates the emission sensitivity response function, also referred to as the source–receptor relationship (SRR), on a user-specified three-dimensional longitude–latitude–height grid. The output of FLEXPART can be in different units, and here we configure the model so that the source (IND_SOURCE=2) and the receptor (IND_RECEPTOR=2) are in mass mixing ratio mode, and therefore the output (SRR) is in units of seconds (see Table 1 in ). We choose mass mixing ratios so that the SRR matrix is not affected by pressure variations in the 3D domain.

FLEXPART also permits two user-specified nested output domains with the inner domain closest to the release site (i.e. the receptor), having a higher resolution than the outer domain. We make use of this functionality and specify the first FLEXPART output domain to have the same geographic extent as D03 in the WRF simulation but with the same spatial resolution (1 km) as D04 in the WRF simulation. Our second, outer FLEXPART output domain covers the same region as D01 in the WRF simulation and has the same resolution (9.5 km) as D02 in WRF. In the vertical direction, we specify the FLEXPART output grid to have 30 uniform levels, each 500 m deep, extending from the surface to 15 km a.g.l. The rationale for using uniform level spacing is explained in Appendix .

FLEXPART also contains options for how turbulence and convection are included in the simulations. We take the values of the PBL height, surface sensible heat flux and the friction velocity directly from the WRF simulation (SCF_OPTION=1). Turbulence is parameterized using the Hanna scheme  as used in FLEXPART-ECMWF/GFS (TURB_OPTION=1), and we assume skewed rather than Gaussian turbulence in the convective boundary layer (CBL=1). Deep convection is also parameterized (LCONVECTION=1).

The output from FLEXPART is the source–receptor relationship (SRR), which is related to the particles' residence time in the output 3D grid cells. These cells are defined by a regular longitude (x), latitude (y) and height (z) grid. In addition to the three spatial dimensions, the SRR has two time dimensions: the release-time (t; the time when the particles arrive at the release location) and the backwards-time (τ; the amount of time before the release time, which varies from 0 to 96 h in our case). Thus, the SRR can be written as the five-dimensional matrix SRRxyztτ. The SRR is processed to remove the τ time dimension. This is achieved by summing over τ: 1SRRxyzt=∑τ=096hSRRxyztτ, where the outcome of this step, SRRxyzt, is a four-dimensional array. The τ dimension is removed as we primarily want to determine where the particles spent time 4 d prior to arriving at CHC and not when (during the past 4 d) they spent it in each location.

Furthermore, the output SRR is on two nested grids (Fig. a), which means we obtain high-resolution information for regions that are near the receptor and lower-resolution information for more distant locations. The rationale is that, on one hand, near the receptor, the higher resolution provides better detail on potential high-influence sources, for example, in our case, the nearby metropolitan area of La Paz–El Alto 20 km away. On the other hand, far away, a low-resolution grid cell suffices since localized potential source influences are diffused. However, specifying two output grids with different resolution introduces challenges such as the step change in resolution in SRRxyzt (Fig. a): as the SRR is related to the residence time and the number of each particle in a grid cell, smaller cells have fewer particles than larger cells, and typically particles move faster through smaller grid cells than larger grid cells, resulting in a smaller residence time and SRR, and thus a sharp boundary in the SRR field exists.

To overcome these limitations and more importantly to dramatically reduce the number of grid cells and thus the data volume, we propose the use of a log-polar transform  of the coordinate system (Fig. , step 3). The new log-polar grid has grid cells which gradually increase in size as the distance from the receptor increases with no sudden step changes to the resolution. This is also why in Fig. b, the SRR does not decrease significantly as the distance from the station is increased (as it does in Fig. c). Furthermore, this also implies that the underlying transport patterns are more readily distinguished using the SRR on the log-polar grid than on the equirectangular grid. The regridding process is complex as we had to devise a method that was both computationally efficient and accurate. A detailed explanation of this regridding procedure is given in Sect.  of the Appendix and visually illustrated in Fig. . The results of the regridding process are shown in Fig. b, which shows a smooth evolution of the SRR with no boundaries evident at the intersection between the two original nested grids. As a result of the grid transformation, we are left with 33 480 log-polar grid cells defined by 36 θ wedges, 31 r cylinders and 30 z levels: SRRθrzt. This is 328 times smaller than the original number of grid cells. In terms of data volume, this dramatically reduces the data volume from 186.6 GB (SRRxyzt) to 0.6 GB (SRRθrzt; see Table S3).

In general, clustering algorithms benefit from pre-processing of the input dataset, which here is the SRRθrzt matrix. This pre-processing modifies the dataset for the sake of grouping the grid cells into clusters – that is assigning each grid cell to a group. In our case, we apply three pre-processing procedures (Fig. , step 4): Gaussian filter smoothing, quantile transform and filtering out non-relevant elements. In this pre-processing the four-dimensional SRRθrzt matrix is also stacked into a two-dimensional SRRρt′ matrix. Specific details about and additional justification for using the Gaussian filter smoothing, quantile transform and filtering are presented in the Appendix, Sect. . As a side note, it is important to highlight that the processed SRR values (SRRρt′) are only used to group the grid cells and not to determine the statistics of each resulting cluster. Instead we combined the cluster numbers with original, non-processed data (SRRθrzt) to obtain the results that we present in Sect. .

The next step (Fig. , step 5) consists of clustering the SRRρt′; i.e. the goal is to divide the SRRρt′ matrix into k number of groups (clusters), whose individual grid cell SRR values have a similar evolution in the t dimension. To be clear, the overall objective is to cluster 3D grid cells in the domain based on the SRR contribution that they have over time (t) as opposed to clustering the spatial patterns (snapshots), which is the approach taken by .

In order to perform a cluster analysis on this dataset, we need to define the elements that will be clustered or grouped, the number of clusters, and the features of each element used to determine the group identification. The 33 480 log-polar grid cells are taken to be the elements to be clustered. The element's features are the SRR intensities at each release time (although called the release time, it is indeed the arrival time at the destination, i.e. the receptor). There are 4248 features for each element, one for each of the hourly releases from 6 December 2017 to 31 May 2018.

We use the k-means  clustering algorithm due to its generalized use, speed and adequate performance with a large number of elements and medium-sized number of clusters. Additional details on how the k-means algorithm is applied are presented in Appendix . The result of the k-means clustering is that each grid cell in the 3D log-polar grid is allocated a cluster number.

However, the k-means algorithm does not automatically select the number of clusters k, and there is not a right answer for the number of clusters. Too few clusters (e.g. 2) means that no meaningful information is obtained, whereas too many clusters (e.g. 100) is impractical and risks overfitting. The optimal number of clusters is usually determined by trying a variety of options and calculating quantitative measures of how similar an element is to its own cluster compared to other clusters.

Here we try 2 to 24 clusters and use the silhouette score , which ranges from -1 to +1, to determine the optimal number (Fig.  step 6). Large positive values of the silhouette score indicate that the element is well matched within its clusters and poorly matched to other clusters, while a low or negative value implies possible misclassification. The overall silhouette score is obtained by averaging over the scores for each individual element, and in our case we do a weighted average based on the total SRR of each element so that cells with a high density have a bigger influence on the overall score. The resulting silhouette scores for 2 to 24 clusters are shown in Fig. . We select the number of clusters based on three considerations: firstly and primarily by identifying localized maximums in the silhouette score, secondly by considering the applicability to our scientific question, and lastly by accounting for practical aspects (e.g. very large number of clusters are not easy to analyse and visualize).

Based on the silhouette score (Fig. ), we first select six clusters as this is a clear local maximum and a suitable number to identify the direction from which air masses approach CHC. In addition it is easy to analyse and interpret. However, this likely lacks details, and in our case, we are interested in the air mass footprint in terms of not only their direction from CHC but also the distance from the station and the vertical heights. Therefore we are also interested in a solution with more descriptive clusters. Therefore, in addition to k=6, we also chose the next local maximum in the silhouette score, which is k=18 clusters. The 18-cluster solution adequately describes the data while maintaining a straightforward interpretation. Localized maximums in the silhouette score also exist for k=21 and k=23 clusters. However, we perform our detailed analysis using 18 clusters rather than 21 or 23 clusters as it is more practical to work with a smaller number of clusters. To ensure the 6 clusters can be directly related to the set of 18 clusters (i.e. share the same boundaries), we first create the 18 clusters and then perform a second round of clustering (starting from the 18 clusters) to obtain the 6 clusters. The 6 clusters are subsequently referred to as the 6 main pathways following the terminology used by .

Before the clustering results are presented, we first give a brief overview of the 6-month average, vertically integrated SRR on the log-polar grid and its spatial distribution (Fig. ). The average SRR is not uniformly distributed, even when similar horizontal ranges are considered. Two distinct large-scale areas exist with high SRR values. The first of these is the lowlands of Bolivia to the south-east and east of CHC, and the second is the lowlands of Peru to the north-west as well as parts of the Pacific. These two distinct areas are divided by the Andes (see Fig. b), which run approximately north–south and act as a barrier. The presence of the steep topography is also why areas of low SRR are identified in northern Bolivia; the easterly winds in this region are blocked and deflected by the topographic barrier, preventing air masses from these regions from easily reaching CHC.

The inset in Fig. b also shows the average influence that La Paz–El Alto has on CHC. The average, vertically integrated SRR values in this area are surprisingly low and much lower than other areas at a similar radial distance from CHC (∼20 km). For example, the region 20 km north-east of CHC has average, vertically integrated SRR values that are more than double those found in the La Paz–El Alto area. Figure b only gives a very basic overview of where air masses that affect CHC originate from. At this point, before having clustered the SRR, the vertical distribution and temporal evolution of air masses influencing CHC cannot easily be determined or visualized.

As stated in the introduction, high-altitude mountaintop sites are often used in an attempt to sample free-tropospheric air. In this section, we use the SRR output from FLEXPART to determine the relative influence of the surface, PBL and FT air on the total sampled air mass at CHC over the 6-month period and the diurnal pattern of this influence. Our method is probabilistic and, for each observation time, determines the percentage of the sampled air mass influenced by the PBL or FT. Figure a shows frequency histograms of the percentage influence of the “surface” and of a pseudo-PBL (see Eqs.  and for definitions) for each hour. There is a strong linear correlation between the surface and PBL influence (slope = 2.38 and r2=0.9), which implies that the 1.5 km deep pseudo-boundary layer is in general within the well-mixed boundary layer.

The median influence of the surface is 9 %, meaning that on average 9 % of the air sampled at CHC has been in contact with the surface in the last 4 d. In terms of the pseudo-PBL, on average 24 % of the sampled air masses represent PBL air. Indirectly this means that approximately 76 % of the air sampled at CHC can be considered representative of the FT. Note that this does not mean 76 % of observation times are representative of the FT; it should be interpreted as, in an average simulation hour, 24 % of the measured air mass represent the PBL and the remainder the FT. This is a key strength of our method; it can determine at any given time what percentage of the sampled air mass arrives from different locations. An additional interpretation of the results shown in Fig. a is to consider the percentage of time when there is no influence (0 % on the x axis) from the surface or pseudo-BL, i.e. where there is purely free-tropospheric air masses. This situation is never detected, which indicates that CHC is rarely representative of purely FT air. However, this is partly an artefact of the method employed here as all particles are forced to arrive at the surface (10 m a.g.l.) at the station.

Figure b shows the diurnal cycle of the surface influence for each day of the 6-month study period, whereas Fig. c shows the average diurnal cycle. The largest positive values, indicative of a large surface influence, occur during daytime. The peak emerges at 10:00 local time (panel c) and happens almost every day (panel b). The duration of the high surface influence increases throughout the campaign, with higher values of surface influence extending later in the afternoon in April and May. This gradual increase in the surface influence during the campaign might be explained by the transition towards the dry season, when clear-sky conditions become more frequent, increasing insolation periods, which in turn favour deep well-mixed PBL structures.

In this section we describe the results from clustering the SRR log-polar cells into six groups. We call these six groups the main pathways (PWs) since they tend to start near the station and reach far away from it as opposed to the 18 clusters that occupy more localized regions. Also, the limits of many of these are delimited by the Andean plateau. Furthermore, we label each cluster based on their “clock direction” from CHC and append them with the abbreviation PW to distinguish them from the 18 clusters. For example, cluster label “03_PW” refers to the cluster whose centroid position is located east from the station.

In Fig. a and b we show the 6 main PWs along with the 18 cluster centroids. The pathways are the shaded coloured regions and contain 2 to 4 clusters from the 18-cluster grouping. The 03_PW is located geographically in the lowlands to the east of the station, occupying the biomes 1, 2, 6 and 9, which in general are tropical forests and grasslands (Fig. e and f).

Cluster 05_PW originates from the south of the station in the altiplanic (montane grass and shrubland, biome 4) and lowland (subtropical dry broadleaf, biome 6) regions. Horizontally, it follows the Altiplano plateau and its eastern slopes to the station. The cluster 07_PW comes from the south-west, and most of its area is located above the Pacific Ocean and coast (biomes 3, 5, 7 and 8). Cluster 09_PW comes from a relatively short distance, and it occupies the altiplanic biome 4, Lake Titicaca (13) and two Pacific biomes (5, 8). The cluster 11_PW comes from the north and north-west. It occupies the lowlands, Altiplano and the Pacific coast, i.e. biomes 1, 4 and 11. As it gets closer to CHC, cluster 11_PW is located higher than 12_PW and thus goes above 12_PW. Finally, 12_PW comes from the lowlands north of the station and is contained within biome 1 (tropical broadleaf forest). Additional information containing the pathway boundaries and their spatial SRR distribution at different z levels is shown in Fig. S9.

In Fig. a to d, we respectively describe the pathways' centroids in terms of their height above ground, height above sea level, surface influence (SSRR; Eq. ) and SRR percentage influence. In general, the farther the centroid is from CHC, the higher above ground level its centroid location is. The same pattern is observed for their height above sea level; however, if the location of the centroid is not too far away and above a location where the ground height is considerably lower than CHC, then the centroid location is located below the linear trend, e.g. 03_PW and 12_PW. In terms of their SSRR, a decreasing trend is observed; in other words, the farther the centroid, the lower the influence from the surface. Therefore, 12_PW is highly influenced by its contact with ground (62 %; Figs.  and S2), while 07_PW is almost unperturbed by the surface (8 %). Finally, the SRR influence of each pathway seems to be uncorrelated with the distance from CHC. Pathway 03_PW has the highest influence over CHC with a share of 29 %. This is in agreement with previous studies at CHC , where air masses from the Amazon were identified as the major contributors during the wet season (DJFM; our modelling period covers DJFMAM).

Finally, in Fig. , we show the temporal influence of each of the pathways. We quantify the influence in percentage of each pathway by dividing the pathway's SRR values by the theoretical total residence time of the simulation, 96 h × 3600 s. Note again that the sum of the influence for all six pathways shown in Fig.  does not always sum to exactly 100, which is due to particles leaving the domain. A clear change in the influence pattern at the beginning of May is seen: on one hand, the influence of pathways 03_PW and 05_PW and to a lesser extent 12_PW becomes almost negligible. On the other hand, pathways 07_PW and 08_PW increase their influence. This is consistent with , where it was shown that during the wet season (DJFMA) air masses from the lowlands and the east-south-east tend to have a bigger influence on CHC. In our case, 12_PW and 03_PW are clearly lowland pathways, while 05_PW has a mixture of Altiplano and lowland influence that, nonetheless, comes from the south-west and therefore is mostly favoured during the wet season. The pathway 11_PW does not present a clear change during the 6-month period. Finally, visual inspection shows that the influence of each pathway varies on a timescale of 1 to 2 weeks. We will further develop this point when focusing on the detailed 18 clusters (Sect. ).

In the previous section, we provided a general picture of the air masses that influence CHC by using the six pathways. However, for an in-depth description, we now focus on the more detailed 18 clusters. We have subdivided these 18 clusters into 4 subgroups based on their horizontal distance from CHC: short range (SR), short-medium range (SM), medium range (MR) and long range (LR) for distances ranging from 0 to 100, 100 to 300, 300 to 800 and >800 km, respectively. Furthermore, we have labelled each cluster based on their distance range along with their “clock direction” from CHC. For example, cluster label “09_MR” refers to the cluster whose centroid position is located west from the station at a distance between 300 and 800 km. As done before, we first describe the clusters in terms of their horizontal location, then their vertical centroid properties and finally their temporal evolution. In Fig. c and d, we show the clusters' geographical location along with a reference to the biomes that they occupy in space (Fig. e and f). Additional information containing the clusters' boundaries and their spatial SRR distribution at different z levels is shown in Fig. S1.

To further quantify the superposition of clusters and biomes presented in Fig. e and f, in Fig.  we show a heat map of the percentage of area that each cluster and biome share. For example, the geographical area of cluster 02_MR is split between the tropical and subtropical moist broadleaf forests (biome 1, 56 %), the tropical and subtropical grasslands, savannas and shrublands (biome 2, 28 %), the tropical and subtropical dry broadleaf forests (biome 6, 10 %), and the flooded grasslands and savannas (biome 9, 6 %). In general, there is a clear split between clusters located north-east (i.e. clock direction of 11 to 05) and south-west (clock direction of 05 to 11) from the station. The first are located in the generally more tropical and humid lowland biomes (1, 2, 6, 9), while the latter are located in drier altiplanic biomes (4, 13) and pacific biomes (3, 5, 7, 8, 10, 11, 8).

In Fig. a to d, we respectively describe the clusters' centroids in terms of their height above ground, height above sea level, surface influence (SSRR; Eq. ) and SRR percentage influence. In general, they follow the same patterns that we described for the six pathways with the exception that there are more clusters below the CHC station's height a.s.l. (Fig. b). These clusters, namely 02_SR, 12_SM and 03_SM, are located close to CHC in the lowlands located north and north-east from the station.

Specifically, all of the short-range clusters' centroids are below 2 km a.g.l. and below 5.2 km a.s.l. (Fig. a and b), which is below the CHC station height (5.2 km a.s.l.). Furthermore, these clusters are in close contact with the surface since their SSRR (Eq. ) is greater than 50 % (Fig. c).

The short-medium-range clusters' centroids are between 2.4 and 2.6 km a.g.l. However, their height a.s.l. varies from 4.1 to 6.1 km. This is due to clusters coming from both the Altiplano to the south-west and the lowlands to the north-east of the station. In general, only one-third of these clusters' air masses are below 1.5 km (SSRR), and thus these clusters include notably more influence from the free troposphere than the SR clusters.

The medium-range centroids are between 3.2 and 6.8 km a.g.l. This variance is mostly proportional to the distance from CHC (Fig. a), with clusters 04_MR and 05_MR being slightly below the rest due to their location in the lowlands. Their height above sea level varies from 6.1 to 7.1 km (Fig. b). In terms of their SSRR, these clusters vary from 7 % to 20 %. These values are approximately inversely proportional to their centroid distance from the station (Fig. c).

Finally, for the long-range subgroup, the far distance of their clusters' centroid from CHC is reflected in their mean height a.g.l. of 8.0 km, mean height a.s.l. of 8.4 km and their low mean SSRR of 0.7 %. Furthermore, due to this high altitude and low influence from the surface, air masses arriving from these clusters are likely to present free-troposphere characteristics. These clusters are all located west of the station (clock direction 07–10).

The temporal evolution of the clusters is shown in Figs.  and . All clusters within the short-range subgroup show a high degree of temporal variability (Fig. a and b). Cluster 02_SR presents a high variability in frequency, which upon further analysis (via Fourier transform; Fig. S4) is shown to be a clear diurnal pattern. However, this pattern does not happen every day (Fig. S5) but in 81 out of the 176 modelled days (46 %). During these days, the peak happens in the early afternoon (13:00 local time).

The cluster 04_SR is highly variable as well; however it does not present a diurnal pattern (Fig. S4), and its variation is similar to that of 05_MR, probably due to the fact that both clusters belong to the same pathway. Cluster 07_SR does present a sharp diurnal pattern in 41 (23 %) out of 176 modelled days (Fig. S6), peaking at 11:00 local time. We conjecture that the peak time difference between 02_SR (13:00 local time) and 07_SR (11:00 local time) is due to the different land type; 02_SR originates from the high-humidity biome 1 (tropical and subtropical forest; Fig. f), whereas 07_SR originates from the less humid biome 4 (montane grasslands). This difference would entail different thermal inertia, different diurnal cycles, and partitioning of the sensible and latent heat fluxes and thus a different boundary layer evolution. Cluster 07_SR is of particular interest since intense anthropogenic emission sampled at CHC would most likely be generated in this highly populated area. Furthermore, the close contact of cluster 07_SR with the surface and its diurnal variability favour transport of emissions to the station during the day, when PBL air from La Paz and El Alto is advected upslope by thermally driven winds. The cluster 10_SR, which originates close to Lake Titicaca, presents a diurnal pattern in 63 (36 %) out of 176 d, peaking at 08:00 local time (Fig. S7). We conjecture that this early-morning peak is related to the lake breeze circulation that develops due to the temperature difference between land and the lake. The average surface temperature of the lake, obtained from , is 10 ∘C and does not have a diurnal cycle. At 08:00 local time, the lake's surface temperature is higher than the surroundings, favouring a land breeze (airflow from land to the lake) near the surface and ascent over the lake. The return flow, near the top of the BL, potentially advects air masses from the lake to CHC.

The cluster 11_SR does not present a diurnal variation (Fig. S4), and its influence seems to be mostly driven by the medium-range cluster 11_MR (Fig. ). Cluster 12_SR does present a diurnal pattern (Fig. S8) in 48 d out of the 176 modelled days (27 %), with a peak around 10:00 local time. This earlier peak, in comparison to 07_SR, is most likely due to its close location to CHC (the closest one, 14 km) so that early-morning irradiation would create favourable conditions for up-slope winds.

The SM, MR and LR clusters' temporal variability is shown in Figs. c and d and a to d. The power spectra of the SRR intensity for these clusters are shown in Fig. S4 and are between 1 and 2 weeks except for 08_SM and 12_SM, which, in addition, also show a small diurnal variability.

The prevalence of some short-medium-range clusters changes during the 6-month period. Clusters 03_SM, 12_SM, 02_MR, 04_MR and 05_MR occur regularly from December (wet season) to April (transition season) but cease influencing in May (dry season). In contrast, the influence of clusters 06_SM, 11_MR and 10_LR do not change substantially during the 6 months, whereas the influence of clusters 08_SM, 09_MR, 07_LR and 08_LR increases in May.

Finally, in Fig.  we present a quantitative summary of the 18 clusters' centroid properties along with their average SRR influence. Furthermore, we also link each of the 18 clusters to their main pathway. On average, there are three clusters per pathway and at least two distinct distance ranges. Furthermore, the clusters within each pathway are heterogeneous in position, surface influence and age, which supports the idea that further insight into the air mass transport patterns can be attained by further subdividing the pathways.

This section presents a proof of concept for our newly developed method to identify source regions of air sampled at CHC. We use in situ observations of particulate sulfate at CHC taken with a Q-ACSM instrument together with the results of our air mass history clustering analysis presented above to identify the source of the emissions. During March and April, satellite imagery showed that while the Ubinas volcano was not degassing, the Sabancaya volcano, located 400 km WNW from CHC, was emitting, and thus there was a clear, known, almost point source of particulate sulfate. As there are no other comparable strong point sources of particulate sulfate in the domain of interest, we assume that when high levels of particulate sulfate were measured at CHC, the air mass passed through the area near the volcano. Therefore, there should be a high correlation between the time series of sulfate and the SRR time series for clusters originating near the volcano.

To determine if this is the case, we calculated the “Pearson” correlation coefficients for all available measurements of sulfate from the Q-ACSM to the SRR time series of each of the 18 clusters and all of the 6 pathways which are shown in Fig. a.

The cluster and pathway with the highest coefficients are 09_MR (0.40) and 08_PW (0.42), and both correlations have a pvalue<0.001. The horizontal locations of this cluster and pathway are shown in Fig. b, and their corresponding time series are shown in Fig. d. The time series for the sulfate measurements is shown in Fig. c. The correlation in combination with either the simplified (6 pathways) or the specific (18 clusters) clustering scheme correctly assigns the source region to the location of the degassing Sabancaya volcano.

The coefficients from the pathways are quite clear; the highest value of 0.42 is at least twice as high as the next candidate, 07_PW. This clearly distinguishes 08_PW as the best candidate for the source of measured sulfate. The 18 clusters also assign the highest coefficient value correctly to 09_MR. However, 10_SR, 11_SR and 08_LR all have similarly high correlation coefficients. Therefore, while the results from 18 clusters are better at pinpointing the source region of sulfate, other regions also appear as plausible candidates, so there is a risk of overfitting when too many regions are considered. This may be a result of these source regions being entangled in terms of their temporal influence over the station. For example, in this particular case, the high correlation of 10_SR, 11_SR and 08_LR could be attributed to the fact that air masses that travel through the region of the volcano also have a time residence in the regions where 10_SR, 11_SR and 08_LR are located.

This example shows that the clustering scheme is successful in identifying regions in its simplified version (6 pathways) and also in its more detailed version (18 clusters), although care must be taken when drawing conclusions so that we do not overfit to the source regions. Finally, it should be noted that only one example is presented here. Future work will include the extension to additional case studies, for example, comparing the clusters to measurements of black carbon.