Tracing air mass transport through a turbulent atmosphere is (still) a complex problem, especially since the transport of aerosols and, consequently, the interactions with clouds, precipitation and radiation are required to capture the 4D history of an air parcel. When it comes to practical application, such as the analysis of aerosol observations or aerosol–cloud interaction studies, the ease of interpretation is often hindered by the amount of data that needs to be considered.

The European Research Infrastructure on Aerosol, Clouds and Trace Gases (ACTRIS) aims at investigating short-lived components in the atmosphere, among them aerosols and clouds. As part of ACTRIS, the European Research Lidar Network, EARLINET , operates lidar systems at more than 25 stations to observe atmospheric states and compositions up to 30 km height. The complementary network of Cloudnet utilizes continuous synergistic observations of ground based instruments such as ceilometers, cloud radars, microwave radiometers and Doppler wind lidars to provide comprehensive cloud observations within Europe and at key regions in the climate system. Both networks, as part of ACTRIS, need additional, continuous information about air mass sources to interpret the observations. Identifying the air mass source region supports the characterization of new particles, e.g., during volcanic eruptions or strong wildfires injecting aerosol into the stratosphere . Also, for aerosol typing e.g.,, air mass sources can provide an important constraint. Furthermore, operational height-resolved air mass source information could improve warning applications for hazardous events, as demonstrated for EARLINET in the frame of the European EUNADICS-AV exercise European Natural Disaster Coordination and Information System for Aviation;.

Models that simulate air mass transport can be broadly grouped into trajectory models and particle dispersion models overview provided by. Trajectory models calculate the transport of a single air parcel imposed by the mean meteorological fields. The model simulations can be run either forward or backward in time, providing information about the source and the destination of the air mass, respectively, after a given transport time. Turbulence and vertical motion during the transport are usually parameterized on the grid scale. Commonly used models are HYSPLIT Hybrid Single-Particle Lagrangian Integrated Trajectory model;, FLEXTRA flexible trajectories; and LAGRANTO Lagrangian analysis tool;. Due to the rather simple approach, the results are quite uncertain , but computational requirements are comparably low. A straightforward approach for representing some of the variability is calculating spatial or temporal ensembles of the trajectories . Lagrangian particle dispersion models (LPDM), with a large number of particles, are set up to cover turbulent and diffusive transport even more realistically . The fate of each particle is tracked individually, allowing more variability to be included into the transport simulation. A frequently used LPDM is FLEXPART FLEXible PARTicle dispersion model;.

Generally, the representation of chaotic motion in the atmosphere improves with larger ensembles of trajectories or increasing numbers of particles. But, with dozens to hundreds of air parcel locations available, interpretation rapidly becomes cumbersome. A number of infinitesimally small air parcels grouped together gives an air mass, which is a larger volume of air with similar properties. Residence times are a well-established technique for attributing regional information to air mass properties, such as being laden with aerosols, moisture or trace gases .

Using backward simulations of air parcel positions, analysis of the residence time yields useful information about the potential source region of an observed air mass. The basic assumption is that the longer an air parcel was present in a certain region, the more likely it will be influenced by the surface characteristics. Hence, the dimensionality of an air parcel's 4D location can be reduced to the residence time. Approaches for clustering backward trajectories by direction, source regions or latitude are widely used. The majority focus on the interpretation of time series observations at single heights – mostly close to ground e.g.,, for aircraft intersects e.g.,, or over a whole region . More sophisticated approaches blend the residence time with actual concentration measurements . However, these approaches require continuous concentration time series, which are generally not available for remote sensing observations. Furthermore, any profile information above the measurement site is neglected.

When interpreting ground-based remote sensing observations, as obtained from aerosol lidars or cloud radars, the air mass sources have usually been assigned by manually selected periods (time and height above ground) that seem interesting for further investigation and calculation of backward transport for those specific cases e.g.,. If air mass source estimates are required for longer time periods or multiple heights, calculating, visualizing and interpreting the results become tedious. Hence, a continuous, computationally efficient, easy to interpret and automated air mass source estimate is required. To be broadly and easily applicable, such a source estimate should not require extensive a priori information, such as clusters of trajectories or potential source contribution functions. The required approach is intended to also be simpler than using a coupled aerosol model, such as CAMS Copernicus Atmosphere Monitoring Service;, COSMO-MUSCAT COnsortium for Small-scale MOdeling MUltiScale Chemistry Aerosol Transport Model; or ICON-ART ICOsahedral Nonhydrostatic Aerosols and Reactive Trace gases;. Although these models can provide profiles of atmospheric composition, they usually do not provide information on the source.

Herein, we propose a combination of automated backward trajectory calculations and geographical information for the setup of a simple, spatiotemporally resolved air mass source attribution scheme. As a proxy for geographical information, two products are used, namely a land cover classification mask and manually defined geographical areas. The methodology is described in Sect. 2. A comprehensive, easy-to-use software package is also provided. Earlier versions were already used in , and . Afterwards, two applications illustrate the potential use cases. In the first example, the temporal and vertical evolution of the air mass source is analyzed for three lidar observations of different aerosol conditions from Limassol (Cyprus), Punta Arenas (Chile) and on board R/V Polarstern off Cabo Verde. In the second example, vertically resolved air mass source statistics are used to assess potential observation biases of long-term lidar-based aerosol statistics. Two multi-week campaigns of the PollyNET , as a part of EARLINET, are presented, namely Finokalia (Greece) and Krauthausen (Germany).

In a conceptualized view, properties of an air parcel arriving over a location of interest are characterized by a certain surface type if the air was close to the surface during its traveled path. The proximity to the surface can be parameterized as a reception height, which depends on the mixing state of the atmosphere at this location and on the type of aerosol particles that could potentially be emitted (i.e., mineral dust or sea salt). Conceivable choices for the reception height are the model-derived depth of the atmospheric boundary layer or fixed thresholds. As a first estimate for the identification of possible surface effects on an air parcel, 2 km is widely used . It is assumed that the longer an air parcel resides close to the surface, the more likely it will acquire the aerosol footprint of the surface. The residence time – the total time an air parcel spent over a certain surface and below the reception height – is a first hint of the aerosol characteristics of the air parcel.

The transport pathway of an air mass arriving over the site can be computed using either mean-wind trajectories or a particle dispersion model. Both approaches can be used with the method proposed in this study. Mean wind trajectories for the past 10 d are calculated using HYSPLIT . To account for variability, ensemble trajectories consisting of 27 members, spaced 0.3∘ horizontally and 220 m vertically around the end point, are used (Fig. a). Meteorological input data for HYSPLIT are obtained from the Global Data Assimilation System data set at 1∘ horizontal resolution (GDAS1) and are provided by the Air Resources Laboratory (ARL) of the U.S. National Weather Service's National Centers for Environmental Prediction NCEP;. The location of the air parcel is stored in 1 h steps. A more realistic representation of turbulence and mixing can be achieved using a LPDM, which simulates the pathway of hundreds to thousands of particles. Here, the most recent version of FLEXPART is used. Meteorological data are obtained from the GFS (Global Forecast System) analysis at a horizontal resolution of 1∘ . For each height, 500 particles are used, with the particle positions being stored every 3 h. These simulations are run every 3 h, with height steps of 500 m for the whole period of interest.

In this work, the surface is classified by two methods. The first method is based on a simplified version of the MODIS land cover classification . The 17 categories of the original data set are grouped into seven categories according to Table  in order to allow for robust statistics in the output (Fig. ). Additionally, the horizontal resolution is reduced to 0.1∘. The categories do not resolve the annual cycles, for example, due to growing seasons. The second method involves custom defined areas as polygons, named according to their geographical context (Fig. ). These areas can be tailored to the measurement location and/or scientific interest.

The residence times at each time and height step are summed for each land cover class or polygon, where the air parcel was below the reception height. Within this study, the widely applicable reception height threshold of 2 km is used . Different settings can be easily applied to study events which are entrained at greater heights, such as wildfire smoke emission or volcanic eruptions. The vertical air mass transport during such events is usually not accurately covered by atmospheric models. Setting the reception height to the maximum emission height of such events (as can be estimated, e.g., from satellite observations) can bypass the uncertainties in the modeled vertical motion. The residence times for each category and each height can then be visualized as a profile (Fig. b). Where the residence time is 0, no air parcels were observed below the reception height during the duration of the backward simulation. In the example shown in Fig. b, above 5 km height, no air masses resided at heights below 2 km above the ground in the previous 10 d. The theoretical maximum residence time (in hours) depends on the number of trajectories or particles n, the duration of backward calculation d in days and the interval of output Δo in hours as follows: 1tmax=nd24Δo.

To illustrate the temporal evolution, successive air mass source profiles can be shown one after another. This visualization condenses the 4D history of a multitude of trajectories (or thousands of particle positions) to a quickly understandable summary, which structures information on air mass source into a time–height cross section. Such a format is usually obtained from vertically or nadir-pointed active ground-based remote sensing observations (e.g., Fig. ).

The air mass source estimate is used to interpret observations conducted with the PollyXT lidar . PollyXT is equipped with backscatter channels at 1064, 532 and 355 nm and Raman and depolarization channels at the shorter two wavelengths. The optical properties are derived using the automated PollyNET retrieval and manual analysis of single profiles. One product of the PollyNET retrieval is the quasi backscatter coefficient, where the attenuated backscatter is corrected for molecular extinction. For this approach, the background, range and dead-time-corrected lidar profiles are normalized by the so-called lidar calibration parameter (also sometimes called the lidar constant even though it is not constant) which is derived from Raman or Klett retrievals see. This normalization gives the attenuated backscatter coefficient from ground (note that, for the same atmospheric scene, the attenuated backscatter measured from ground is different to the one measured from space as it is not corrected for attenuation by molecules and particles). The molecular contribution to the atmospheric backscattering and extinction can be calculated from pressure and temperature profiles; the attenuated backscatter coefficient is corrected for the molecular scattering. Furthermore, an assumption of a fixed lidar ratio is applied on the attenuated backscatter corrected for molecular contribution to account for a first guess of the particulate attenuation. This procedure gives the quasi particle backscatter coefficient, which is a good proxy for the real particle backscatter coefficient that cannot yet be obtained at a high temporal resolution for all atmospheric scenes. More details are covered in .

PollyXT was deployed to various field campaigns and longer-term measurements during the last 15 years . A broad variety of meteorological conditions and aerosol regimes was covered. The multi-wavelength observations of PollyXT contain unique fingerprints of the observed aerosol types from different source regions .

In Sects. 4 and 5, the air mass source attribution will be applied to selected case studies and measurement campaigns in order to demonstrate its applicability for determinating the air mass source regions and for the estimate of potential observation biases. The case studies are chosen from deployments of PollyXT to Limassol (Cyprus; 34.7∘ N, 33.0∘ E; 12 m above sea level (a.s.l.); October 2016 to March 2018), Punta Arenas (Chile; 53.1∘ S, 70.9∘ W; 10 m a.s.l.; November 2018 and ongoing) and the Atlantic transit of R/V Polarstern in 2018 when passing Cabo Verde (18.1∘ N, 21.3∘ W to 21.3∘ N, 20.8∘ W). The estimate of potential observation biases is done for two multi-week campaigns. One at Krauthausen (Germany; 50.9∘ N, 6.4∘ E; 99 m a.s.l.) took place for 8 weeks in April–May 2013 and the second one was at Finokalia (Greece; 35.3∘ N 25.7∘ E; 250 m a.s.l.) for 6.5 weeks in June–July 2014.

Vertically resolved aerosol statistics are prone to observation biases, as they usually depend on cloud-free conditions. When clouds or precipitation are present, no aerosol properties can be obtained from optical techniques. However, respective statistics, for example, obtained from lidar observations, provide key quantities for the determination of the environmental conditions at a certain site . It is therefore an open question whether the data from suitable (cloud-free) measurement periods are representative for the full observational period. Chances are that cloudy conditions are related to certain air masses which would stay unidentified in the lidar-based statistics of aerosol optical properties. One way to assess this bias is to compare the air mass residence time statistics of the full observational period with the one subsampled to the times when aerosol information is available.

When applied to lidar data, the automatically analyzed profiles of particle backscatter at 532 nm from are used. In their work, the raw profiles are grouped into 30 min chunks, cloud screened, averaged and analyzed by either the Klett or the Raman method to see if signal-to-noise ratio is high enough for a reference height to be set. All profiles that pass a basic quality control are then included in the backscatter statistics. Obviously, this statistic will only be intermittent, due to overcast cloud conditions or interruptions in the measurement. Subsampling the air mass source statistics is done by selecting only the air mass source profiles that are temporally close to a valid lidar profile. A time threshold of 1.5 h is used for the following statistics. However, covering representative air mass conditions is only a necessary condition and not a sufficient for obtaining representative aerosol statistics.

PollyXT observations at Krauthausen (Germany; April–May 2013) and Finokalia (Greece; June–July 2014) are used here. At Finokalia, 940 profiles could be analyzed with the Klett method. Hence, the particle backscatter statistic covers 457.7 h, which is 42 % of the campaign duration. The statistics of particle backscatter are shown in Fig. a. For the Krauthausen deployment, 315 profiles could be analyzed with the Klett method, covering 154.2 h or 11 % of the campaign. Figure a shows the particle backscatter statistics.

Profiles of air mass source for the Finokalia deployment are shown in Fig. b and c, again with a reception height threshold of 2 km. The summed residence time of the subsampled profiles is divided by the fraction of time covered to make them comparable to the full residence time. Most dominant land surface categories are water, barren ground and grass-/cropland. The residence time of air masses from barren ground shows a pronounced maximum between 2 and 6 km height. The residence time of all other categories decreases monotonically. Air masses from urban and snow- or ice-covered areas are 10–100 times less frequent than the other categories.

In terms of geographical areas (Fig. c), Europe is the most dominant source up to 3 km and again above 9 km height. Between 3 and 6 km height, the Sahara is the most dominant air mass source. During the campaign period, no air masses from the Arabian Peninsula, that fulfilled the <2 km criterion were transported to Finokalia.

The dominant sources are well covered by the lidar profiles in terms of land surface; only the barren class is subsampled by a factor of 10 above 6.5 km height (Fig. b). This agrees with the Sahara also being subsampled above that height. Air masses originating over Europe were also subsampled at heights above 5 km. An undersampling of potentially aerosol-laden air masses by the lidar statistics will cause the backscatter statistics to be biased as low values.

During the Krauthausen campaign, air masses originating over water were the most frequent ones, followed by grass-/cropland, forest, shrubland and barren ground (Fig. b). Again, the residence times of the barren class show a distinct peak between 6 and 8 km height. Air masses from the Sahara area agree with the barren class (Fig. c). As expected, Europe is the dominant air mass source in the lowest 6 km height, but due to increasing residence times with height for the Sahara source, both appear with equal frequency in the upper troposphere. In the lidar observations, Europe is potentially undersampled by 70 % between 1 and 10 km height, which is consistent with the grass/cropland and forest class also being undersampled. Barren land surfaces and the Sahara are oversampled by approximately 20 % up to 7 km height. In the lowermost 2 km height, the land surface classes urban and snow/ice also contribute to the air mass mixture and are slightly oversampled.

In this study, we propose an easy-to-use method for a continuous, height-resolved automated air mass source estimate. With the combination of air mass transport modeling and geographical information, the dimensionality can be reduced, and straightforward visualizations accelerate the interpretation of air mass origin. The air mass source estimate can be used to assist (profiling) aerosol observations, as aerosol load and characteristics are strongly controlled by surface properties and atmospheric transport. Three case studies illustrated the applicability at different sites and under different large-scale flow conditions. In a second application, we showed how the source estimate supports the interpretation of lidar case studies and how potential observation biases can be investigated for longer-term campaigns.

The major constraints of the proposed method are discussed in the following. While the air mass transport itself is generally covered well by trajectory models or LPDMs, linking it to aerosol properties has to be done with care. First, the reception height is modeled by using the mixing depth of the input fields or fixed values for all surfaces and aerosol particles, where differences could be expected for dust, smoke or wildfire smoke. Nevertheless, the assumption for a general reception height might be valid and can be improved in future. The 2 km height used in this work was also reported by other studies e.g., for wildfires and seem to be applicable over wide ranges of climates and meteorological conditions. In summary, a high residence time over a certain class is only a necessary, not a sufficient, condition for the aerosol load of an air parcel.

Second, aerosol particles might be removed by (wet) deposition between the source and observation site. Currently, such processes are not sufficiently reproduced in trajectory models or LPDMs as they require detailed representation of aerosol microphysics and precipitation amount. Some improvements in this regard incorporated in the most recent version of FLEXPART . However, deposition changes only the aerosol load of an air parcel and not the air mass source itself. Judging from the air mass source residence times alone, this process cannot be distinguished from cases in which no emission happened in the first place. These questions could be addressed in future with a fully fledged aerosol transport model that also includes a tracer of the air mass origin, similar to the scheme shown here.

Some uncertainty is caused by the turbulent nature of the transport. For HYSPLIT, a first estimate for the uncertainty of a single parcel location is 20 % of the distance from the trajectory's origin . Hence, for HYSPLIT, a 27-member ensemble was used to attribute this uncertainty. Compared to HYSPLIT, the LPDM FLEXPART allows for a more realistic representation of turbulent transport and better sampling when using hundreds or thousands of particles. However, a qualitatively good agreement between both simulations suggests that the presented air mass source estimate is rather robust, considering uncertainty in the models.

In summary, the described compromises are necessary to obtain a continuous, height-resolved, automated air mass source estimate. The provided source code allows us to use FLEXPART particle positions and HYSPLIT trajectories as input. User-defined named geographical areas can be easily added. The runtime environment is provided as a docker container, including FLEXPART v10.4. With that setup, 1 d of air mass source estimate, with the resolution used in this study, can be processed in less than 1 h on a standard desktop computer (2.1 GHz processor; 4 GB RAM; single-threaded).

Such an automated air mass source estimate can provide valuable auxiliary information for the analysis of long-term data sets of profiling aerosol observations, such as those collected in the network of EARLINET . The methodology could also be adapted to existing and future space-borne lidar observations, e.g., CALIPSO Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation;, Aeolus or EarthCARE Earth Clouds, Aerosols and Radiation Explorer;. A first estimate of air mass source could be used to constrain retrievals of optical parameters by narrowing the assumed lidar ratio, as in the case of CALIPSO, or guide subsequent aerosol typing based on intensive aerosol optical properties, as in the case of Aeolus and EarthCARE. But, simulating enough air parcels with sufficient along-track resolution might require further development.

With respect to aerosol typing, downstream products, such as estimates of concentration of cloud condensation nuclei or ice nucleating particles , will benefit from the air mass source estimate. Having air mass source information available will advance the implementation of such retrievals into automatic processing, such as the single calculus chain for EARLINET from the ground or for EarthCARE from space. Also, further synergy between lidar target categorizations, such as and the source estimate, remain subject to further investigation.

Apart from the shown applications, the presented methodology can be utilized to assess profiles of air mass sources when planning field campaigns. Questions on where, when or how long to measure in order to capture a certain mix of aerosol scenarios can easily be answered. In future, the proposed method can be extended further by source maps, for example, by dust source maps derived by the approach of or temporally varying information on wildfires and snow and ice cover or biological productivity.