The latest global reanalysis, ERA5, from the European Centre for Medium Range Weather Forecasts ECMWF; , is used in this study. The model configuration corresponds to IFS Cy41r2 and data is available at 0.25° horizontal grid spacing. The data are provided hourly on 137 vertical model levels extending up to 1 Pa . Consequently, the vertical spacing is approximately 20 m near the surface and around 300 m at 500 hPa. In this work, ERA5 single-level and model-level fields on the lowest 74 model levels (from the surface up to roughly 120 hPa) are employed. The domain encompasses northern Africa and Europe, specifically from 30° W to 60° E and 15 to 73° N, to calculate the trajectories, while the analysis is restricted to north of 37° N. For climatological reference, we use the 30-year period prior to the study period, hence January 1992–December 2021.

A lightning measurement dataset is used as a proxy for thunderstorm location. We use data from the lightning location network “Blitzortung” . A large number of volunteers around the world have contributed to this network by setting up very low-frequency sensors. The network allows to reliably locate widespread lightning activity, although it cannot detect weak strokes at this frequency range, and isolated single-stroke detections are more prone to false positives (e.g., from noise or misclassification). Physically, genuine convective lightning activity is expected to produce spatially clustered strokes rather than a single isolated detection. We therefore exclude grid cells where only a single flash is recorded with no other flashes in the adjacent ERA5 grid-cells in the same hour. This filtering is conservative and consistent with our focus on widespread lightning activity associated with ADs. Data are aggregated to the ERA5 grid and timestamps are floored to the previous full hour to match the hourly resolution. This results in a gridded dataset recording the presence or absence of lightning for each ERA5 grid cell and hour. In this work, “lightning occurrence” or “lightning probability” will refer to these binary, cell-aggregated lightning data, not individual strokes.

The fourth generation ECMWF global reanalysis of atmospheric composition, EAC4 ECMWF Atmospheric Composition Reanalysis 4;, is used as a dust reanalysis product. It provides dust aerosol optical depth at 550 nm (AOD_550 nm) every 3 h and at 0.75° grid spacing. For comparability, we bi-linearly remap (in space) and linearly interpolate (in time) the EAC4 data to match the spatio-temporal resolution of the ERA5 data 0.25°, 1 h; using cdo,. Dust aerosol optical depth (AOD_550 nm) is a single level variable which we use to determine unusually dusty periods during the study time period. Since the EAC4 data is only available from 2003 onwards, the years 2003–2021 are used for climatological reference in this case.

The calculation of the trajectories and detection of the AD – the air mass originating in the BL of desert, (semi-) arid and/or elevated source regions – follows : trajectories are calculated forward in time with the Lagrangian Trajectory Analysis Tool LAGRANTO;. They are initiated hourly along a “curtain” marking the northern boundary of the source region in North Africa (see Fig. ). The grid spacing of initialisation locations is 5 km in the horizontal and 10 hPa in the vertical between 1100 and 400 hPa. Only those trajectories are calculated forward that have a northward (Europe-ward) wind component and start below the interpolated boundary layer height BLH_i (linearly interpolated between daily maxima of the BLH, as a way to take into account former BLH air that resides above the night-time BLH as residual layer). Trajectories are integrated for 120 h. This results in approximately 108 million trajectories, of which 61 million pass 37° N and are therefore taken into account in this analysis. Trajectories are aggregated to grid boxes of 0.25° × 0.25° × 500 m. A grid box containing at least one trajectory is defined as an AD-cell, and the AD air mass consists of all AD-cells combined. If there is any AD-cell in a column, this is defined as an AD-column. For the statistical analysis in this study, “AD presence” refers to the presence of an AD-column, unless noted otherwise. For more details on the detection method refer to .

In order to analyse effects (especially thunderstorm occurrence) that are connected to the edge of the AD, the air mass edge has to be detected from the binary AD-cell data in a respective layer, L. To obtain a smoother and more continuous boundary, small isolated gaps within detected AD regions and isolated noisy pixels or pixel clusters outside the main regions were removed prior to edge detection. This is done using standard mathematical morphology operations used in image processing. The edge is then detected from this smoothed AD region, again using a morphology operation. A more detailed description and schematic figure of the edge detection algorithm can be found in Appendix A (Sect. ).

To assess effects caused by proximity to the edge or the air mass centre, we classify grid cells by their distance to the AD edge. Let L be the layer for which the edge is detected, d the shortest distance from a cell to the detected edge (Euclidean distance in number of cells), and D1 < D2 two distance criteria. Then cells are classified as follows: “near-edge”d<D1“AD centre”AD inLandd≥D2excludedAD inLbutD1≤d<D2 The cells with AD in L but D1 ≤ d < D2 are excluded to allow for a clear separation between “near-edge” and “centre” cells. Cells that do not have AD in L and satisfy d ≥ D2 are not considered, as they are neither close to the edge at the level of interest nor within the AD centre, even if they might have AD air present at other levels.

The edge detection can be applied for different layers L, which can be individual levels, or vertically aggregated layers. We applied the edge detection algorithm to individual levels (1500, 2000, 2500 m) and to 1.5 km thick layers (AD-cell centre in 1–2, 1.5–2.5, 2–4 km). The results showed little sensitivity to the exact altitude or layer thickness (Figs. , ), but using a layer of 1.5 km (3 levels thick) instead of only one level makes the edge less noisy. We therefore define the AD edge from a layer extending from 1250 to 2750 m (AD-cell centres at 1.5, 2.0, and 2.5 km), approximately corresponding to the region at and above the local BL and including the 800 hPa AD edge where lightning occurred in the study by .

A sensitivity analysis showed that the results are largely insensitive to whether D1 is chosen as 5 or 10 grid cells (approx. 150 or 300 km, Fig. ). We therefore adopt D1 = 5 (≈ 150 km) cells for the near-edge definition. Increasing D2 from 10 to 15 or 20 cells substantially reduces the number of AD-centre cells, hence the number of observations to interpret (Fig. ). We use D2 = 10 cells (≈ 300 km) for the AD centre definition, to retain as many observations as possible. We consider 10 cells sufficiently far from the edge to avoid edge-related influences. With these thresholds, 64.4 million grid cells were classified as near-edge and 9.2 million as AD-centre, while 12.2 million cells were excluded from either category to maintain a clear distinction between the two regions.

We identify hours with strong positive temperature anomaly and anomalously high amounts of dust, respectively, using standardised anomalies of T2m and AOD_550 m. For T2m we use 1992–2021 as the reference period, to follow the standard 30-year climatological window, which yields more robust estimates than a shorter period (especially in the presence of a climate trend). Because a climate-change signal can be expected in T2m, the full T2m time-series (January 1992–April 2024) is linearly detrended prior to anomaly calculation for each cell using cdo,. The dust reanalysis data is only available from 2003 onward, so we use 2003–2021 as reference period. As no significant long-term trend is present in the dust time series (January 2003–April 2024, area-weighted, annually averaged domain means; Theil–Sen trend: -1.32 × 10⁻⁵ yr⁻¹, p = 0.96), we do not detrend it and consider the shorter 2003–2021 reference period sufficient.

For each hour of the year, we define the climatological background as the median over the respective reference period, denoted medianclim(x), and the corresponding climatological standard deviation σclim(x). To smooth out synoptic scale variations, a 4th-order Butterworth low-pass filter is applied using a 30 d cutoff period (fc = 1/30 d⁻¹). To preserve the diurnal cycle, the filtering is performed separately for each hour of the day for T2m. Standardised anomalies are then calculated as: 1x′=x-lowpassmedianclim(x),fc=1/30d-1lowpassσclim(x),fc=1/30d-1 where x is the respective variable (AOD_550 m or detrended T2m) and x′ is its standardised anomaly (dimensionless). Strong events are defined by a threshold of 2 as in. This results in the following event definitions: T2m′>2strong positive temperature anomalyevent(PTA)AOD550m′>2dust event “Event” refers to individual hours in this study, i.e. it is not an analysis of heat waves but of individual hours (events) with strong positive temperature (or dust) anomalies. For thunderstorms, we use lightning as a proxy, so that an event is defined as any hour with a lightning flash.

We quantify the association between AD occurrence and extreme weather events using conditional probabilities and log-odds ratios lnOR; similar approaches used in. The conditional probability P(Event∣AD) can help answer what percentage of AD occurrences comes with an event, or how likely an event is to occur, given the presence of AD air. The odds ratio (OR) compares the odds of an event in the presence of AD to those of an event in the absence of AD. The standardised log-odds ratio, ln⁡ORstd, is based on the full 2 × 2 contingency table of joint occurrences and accounts for all combinations of event and AD presence. It is defined as the logarithm of the odds ratio divided by its standard error: 2ln⁡ORstd=ln⁡ORSE(ln⁡(OR))=ln⁡P(Event∣AD)/P(no Event∣AD)P(Event∣no AD)/P(no Event∣no AD)SE(ln⁡(OR)) Here, OR is the odds ratio and SE is the standard error (derivation provided in Appendix A, Sect. ). ln⁡ORstd is centred around zero with positive values indicating increased odds of the event in the presence of AD or decreased odds in the absence of ADs. Negative values indicate decreased odds in the presence of AD or increased odds in its absence. Larger magnitudes indicate stronger evidence relative to sampling variability. Increased odds can indicate that the event may be a consequence of an AD, or that they have a common driver.

This analysis is applied to strong positive temperature anomaly events and dust events. For lightning, the same framework is additionally applied using “near AD edge” or “AD centre” as conditioning states. The shown quantities are the same, but the colour scales may vary to ensure visibility for different magnitudes.

The co-occurrence of strong positive temperature anomalies and ADs is investigated using the conditional probability and the standardised ln⁡OR for a strong positive temperature anomaly event given the presence of AD air. Figure a shows the total, unconditional probability of a strong positive temperature anomaly event P(PTA Event). In some regions, particularly in western Europe and over the sea, strong positive temperature anomaly events occur in more than 9 % of the time during the study period. Figure b shows the probability of a strong positive temperature anomaly event, given the presence of an AD (P(PTA Event ∣ AD), shading), and the conditioning probability (P(AD), contours). Conditional probabilities are highest in an arc from southwestern to northern Europe, where temperatures are unusually high during more than 10 % of the time that AD air is present (orange colours in Fig. b). Figure c shows the standardised ln⁡OR. Positive values (green colours) in Fig. c indicate that strong positive temperature anomaly events are more likely to occur in the presence of AD than during its absence. It is obvious that this is the case in most of the domain, and the large values indicate strong evidence with respect to the variability. The strongest effect is visible over the Bay of Biscay and the British Isles, as well as over the Mediterranean Sea and regions neighbouring the Baltic Sea, while in the Alps and over the Anatolian peninsula the effect is much smaller or non-existent. This pattern is also reflected in the mean and median of the standardised anomalies T2m′ during AD and non-AD periods: the mean and median T2m′ are higher during AD than during non-AD periods in the entire domain (median is shown in Fig.  in Appendix B). The difference is largest in the region of the Bay of Biscay and over the British Isles, where the difference between AD and non-AD median standardised temperature anomalies reaches 1.

A striking feature in Fig. a is the increased probability of positive temperature anomalies in the western Mediterranean Sea and the Atlantic, especially close to the Iberian and French coasts. This pattern is likely linked to marine heat waves that occurred in the North Atlantic and Mediterranean during the study period e.g., as unusually high sea surface temperatures in these regions could explain unusually high near-surface air temperatures. To test this, we repeated the analysis excluding the periods of the two major marine heat waves (summer 2022 and summer 2023) as a diagnostic check. This reduced the probability of strong positive anomalies around the British Isles and in the western Mediterranean, supporting the interpretation that these heat waves substantially contribute to the observed pattern. We emphasize that this exclusion was used only for diagnostic purposes and is not applied in the final analysis presented here. Removing these two summers would substantially shrink our already limited two-year dataset and would eliminate summer data entirely. Extending the time series to dilute the influence of these events is not feasible given data storage constraints.

The standardised ln⁡OR is largest in the Bay of Biscay and over the British Isles, as well as over the western Mediterranean Sea, indicating that the effect of the presence of AD air on positive temperature anomalies is strongest there (Fig. c). Interestingly, the British Isles experience AD air less than 10 % of the time, but more than 20 % of those cases co-occur with positive temperature anomalies (Fig. b). Several studies report positive temperature anomalies over the UK during Spanish plume events . The Spanish plume is an EML originating over the Iberian Peninsula, although the term has frequently been misused . Some studies suggest that during Spanish plume events air also originates in northern Africa , so that some Spanish plume air streams can be seen as a subset of ADs. Given that Spanish plumes are reported to produce strong warming over the UK, it may seem surprising that only around 20 % of AD events co-occur with a strong positive temperature anomaly there, even though the British Isles are among the regions where this co-occurrence is most likely. This has an important implication: even in the region where the standardised log-odds ratio suggests the strongest relationship between strong positive temperature anomaly events and the presence of ADs, AD occurrence alone is not a sufficient indicator. Therefore, additional conditions like the presence of subsidence, near-surface advection, or the stability of the AD layer, may determine whether such events occur. This emphasises the need to extend the EML (and Spanish plume) concept to the more general case of ADs, and to investigate systematically which of these conditions determine whether high temperatures accompany a given AD event.

In Fig. c the Alps and the Anatolian peninsula stand out as the only land regions that do not have a strongly positive standardised log-odds ratio. In these regions, also the probability of intrusion of AD air into the local BL is increased their Fig. 7. Additionally, these regions have the lowest number of joint occurrences of AD air and strong positive temperature anomaly events (fewer than 100 occurrences, see Fig. ). This indicates that, although the BL in these regions frequently reaches potential temperatures similar to those in the AD and thus allows penetration, other processes play a larger role in producing strong positive temperature anomalies. This is not the case for all regions with elevated terrain; the most prominent counterexample is the Iberian Peninsula, another region of elevated topography. There, the probability of AD air intruding into the local BL is likewise increased their Fig. 7, yet ADs also co-occur with strong positive temperature anomaly events more frequently, and the odds of strong temperature anomaly events are increased in the presence of AD (Fig. c). One possible explanation is the near-surface intrusion of warm air into the Western Mediterranean region in combination with the AD, as described by .

In , 66 dates with extensive AD coverage were identified. On 19 of those dates at least 10 % of the area covered by AD (north of 37° N) also experienced strong positive temperature anomalies. Often, the area with strong positive temperature anomaly events is on the upstream side of the ridge axis, sometimes coinciding with areas without or with only high clouds (not shown). We do not have further explanation for this behaviour and further investigations are beyond the scope of this study or the available data. As ERA5 is not informed of the aerosol optical depth, its radiation variables are of limited use in investigating the reasons behind the patterns in strong positive temperature anomalies.

The proposed mechanism for enhanced near-surface temperatures during an EML (and thus during an AD) is that a cap of stable stratification limits the vertical growth of the CBL. Convective turbulence distributes the surface sensible heat input through the mixed layer. When that layer remains shallow, the same heat input produces larger temperature increase . According to one day of insolation in the presence of a capping EML can be enough to increase the wet-bulb temperature in the underlying BL significantly. However, the joint occurrence of a strong positive temperature event with an AD-imposed cap (defined as the lowest AD trajectory residing within 500 m above the BLH and the stratification in that 500 m-layer being nearly isothermal) is too rare to permit meaningful analysis. This suggests that the increased odds of strong positive temperature anomalies in the presence of AD air seen in Fig. c are unlikely to be primarily due to situations in which a cap of stable stratification limits BL growth leading to larger temperature increase in a shallower layer. While investigating the direct co-occurrence of ADs with strong positive temperature anomaly events already yields insightful results, potential time-lagged responses may not be captured by our co-occurrence analysis.

Moreover, strong positive temperature anomaly events frequently co-occur with ADs, but this does not necessarily imply a causal relationship. showed that the average duration of AD streaks is below one day across most of the domain (their Fig. 4) and that the lowest AD-cell resides close to the BLH is uncommon (their Fig. 6). High near-surface temperatures during ADs could be due to short-lived AD-related capping stable layers and reduced cloudiness, or unrelated diabatic heating, subsidence-driven adiabatic warming, and/or warm-air advection . Disentangling these contributions and whether or how they are related to ADs or confounding factors is beyond the scope of this study.

Nonetheless, several processes discussed in the heat-wave literature share features with ADs and may help contextualise our findings. For example, describe low-level warm air intrusions from the Sahara into the Mediterranean, although find horizontal advection to play a minor role in European high temperatures. When air ascends in a warm conveyor belt, it releases latent heat and brings low potential vorticity air to higher levels, which can lead to an intensification of the ridge or even atmospheric blocking;. Since one air stream identified within the AD is similar to a warm conveyor belt (although from a drier source region), and ADs often occur within amplified ridges , ADs may also intensify these ridges. High temperatures can be observed in ridge situations, and especially in summer they are caused by diabatic heating due to increased insolation, and to a lesser degree due to adiabatic heating from subsidence, or even advection .

Lightning throughout the year is a rare event locally. The unconditional probability of lightning is generally below 2 % (Fig. a). Higher probabilities coincide with land areas, especially mountainous regions (see white contours, Fig. a), where orographic lifting of the larger scale flow and orographically induced circulations provide additional mechanisms for releasing CAPE in agreement with. As lightning is already a rare event, conditioning it on the presence of ADs, their edges, or their centres results in relatively small datasets (tens to hundreds of occurrences per grid cell). We therefore interpret the following analysis as an exploratory assessment which is still useful as it establishes a foundational understanding of AD behaviour in relation to lightning.

Figure b shows that lightning probability approximately doubles when AD air is present in the levels 1.5, 2, and 2.5 km, which is the case in up to 40 % over the Mediterranean (white contours, Fig. b). Also the standardised log-odds ratio confirms that lightning is more likely in the presence of AD air at those levels by being strongly positive (green, Fig. c) in large parts of the study region.

ERA5 grid cells can be within a swath of about 1.25° (5 cells) on either side of the AD edge in an astonishing 30 % of the time in the Mediterranean (Fig. d, white contours). This probability gradually decreases northwards to 5 % in northern Europe. In a large part of the domain, the probability of lightning is strongly increased, given an AD edge is close (Fig. d, shading), which is also supported by strongly positive values in the standardised log-odds ratio (green, Fig. e). In fact, almost 27 % of all lightning occurs within the 5 cell margin around the AD edge (not shown).

The probability of an ERA5 cell being in the centre of an AD (at least 10 cells ≈ 2.5° interior of the edge) is lower than for the edge, with 10 % in the Mediterranean, decreasing northwards and being negligible in northern Europe (Fig. f, white contours). The probability of lightning conditional on the presence of the AD centre is increased (yellow colours in Fig. f) and the standardised log-odds ratio is positive (Fig. ), indicating that lightning is more likely in the presence of the AD centre.

Several past studies have investigated the initiation of particularly violent thunderstorms near the edges of EMLs, and the processes discussed therein provide a framework for understanding convective initiation at AD edges. It is described that near the edge, a convergence zone forms, possibly ahead of a cold front or dryline . In this region, a strong stability gradient is present and it is characterised by a baroclinic zone. describe how due to confluence and anticyclonic shear in this baroclinic zone, a thermally direct ageostrophic circulation forms at the midlevel air mass boundary, while a thermally indirect cell forms higher up. This leads to ascent near the EML edge, which is likely too weak to initiate convection, but can diminish the strength of the cap and, together with other lifting mechanisms, lead to the initiation of thunderstorms along EML edges. Another mechanism fostering convective outbreaks near EML edges is “underrunning” , where the moist and heated air in the local BL moves horizontally, until it reaches the lateral edges of the EML, where inhibition is weaker, so that convection can occur.

The results presented above also show increased odds for lightning near the AD edge across large parts of continental Europe, which indicates that the processes described for EMLs also occur along AD edges and foster thunderstorm formation. The increased odds of lightning in western and central Europe near the AD edges are also supported by who find that western and central Europe are regions with “temperature-limited severe convective outbreak types”. In temperature-limited regions, the advection of warm and moist air leads to instability. They also appreciate that EMLs support this instability for these types. Convective outbreaks happen on the western flank of a ridge, ahead of a trough, and strong positive temperature anomalies are found within the ridge – hence, a synoptic set-up that is similar to those leading to ADs, and convective outbreaks in regions where their edges can be expected. Only in the Slavic and Balkan regions the standardised log-odds ratio of lightning occurrence near the edge is small, or even negative (Fig. e). This likely reflects the low joint occurrence of lightning and AD-edge conditions in these areas, which results in large uncertainty and therefore low values of the standardised log-odds ratio.

The fact that lightning is more likely in the presence of the AD centre is surprising, as in the centres of EMLs, thunderstorms are thought to be suppressed as a capping stable layer confines convection to the layer below . While strong convective inhibition (CIN) hinders convection, medium values of CIN (50–200 J kg⁻¹) can actually be favourable. Thunderstorm initiation is delayed, which allows for further surface heating and destabilisation until strong enough triggers overcome the inhibition . Air that originates within a deep, warm CBL in the source region is typically well-mixed with a near-dry-adiabatic lapse rate. If this air is advected downstream with modest modification, it causes steep lapse rates and conditionally unstable stratification over a moister local BL. Once an air parcel is lifted beyond its level of free convection and CIN is overcome, e.g. by surface heating, low-level convergence, or synoptic ascent, deep moist convection can initiate – even in the centre of the AD, if it causes low values of CIN.

A layer is conditionally unstable when the saturation equivalent potential temperature decreases with height ∂θEs/∂z = θEs,BLH+2km-θEs,BLH/2 km < 0 K km⁻¹. The top row of Fig.  (panels a–d) shows daytime conditions for the edge of the AD, the bottom row (panels e–h) for its centre. On average, the layer above the BL is not, or only weakly, conditionally unstable everywhere along the AD edge (grey and light yellow colours in Fig. b). For the AD centre, ∂θEs/∂z is strongly negative (orange colours in Fig. ) in regions, where AD centre occurrence is non-negligible (≥ 1 %, white contours in Fig. f). Figure c and g show the minimum ∂θEs/∂z on days on which lightning occurs near the AD edge or in the AD centre, respectively (daily minimum is computed from only those sub-daily samples when the cell is classified as near-edge or centre, respectively). The time of maximal instability (minimal gradient of θEs) is used here, because the profile at the time of the lightning may no longer be representative for the (pre-) convective environment. Figure , panels (c) and (g) show that on days, when lightning occurred near the AD edge or in its centre, the most unstable profile was strongly conditionally unstable (orange colours). CIN at the times of the greatest instability on days when lightning occurred near the AD edge or in its centre, is, on average, in the favourable range of less than 200 J kg⁻¹ (Fig. d and h, CIN at the same times as used in panels c and g). Moderate, non-zero values of CIN can delay thunderstorm initiation which allows for further surface heating and destabilisation. A parcel that overcomes the CIN and is lifted beyond its lifting condensation level, will freely rise in the conditionally unstable layer aloft. The combination of a conditionally unstable layer provided by the AD and modest CIN values therefore creates conditions favourable for thunderstorm development even in the centre of ADs, which can explain why the standardised log-odds ratio for lightning is positive both near the AD edges and in the AD centre (Fig. a, e, green colours).

The fact that the combination of conditionally unstable air aloft and modest CIN is favourable for thunderstorms along the edges of ADs has been extensively documented for the special case of EMLs, e.g.. The favourable vertical profiles also help explain how lightning can occur at AD centres, contrary to the expectation that ADs, like EMLs, inhibit convection .

Since the patterns of standardised log-odds ratios for daytime hours (Fig. a, e) are very similar to those for the entire day (Fig. e, g), we expect the explanation to also approximately hold for the whole day. Considering that the joint occurrence of lightning and AD centre is very rare (only on the order of tens of events, Fig. c), the values of individual cells of Fig. g and the bottom row of Fig.  have to be interpreted carefully, because they might be driven by single long-loved or highly organised systems such as mesoscale convective systems. An example is the isolated extremum over southern France in Fig. f, g. Despite this limitation, these results are interpretable: first, the log-odds ratios are suitably standardised to reduce the influence of rare events with large variances. Second, the band of elevated log-odds ratios extending across the Iberian Peninsula and along the northern flank of the Alps (Fig. g) is coherent over several hundred kilometres and hundreds of independent grid cells. Thus, this cannot be driven a single convective system. The same arguments hold for the analysis of lightning in the presence of AD and near the AD edge, for which the joint occurrences are also rare but less so than for the AD centre (Fig. ).

We define a dust event to occur when the standardised dust aerosol optical depth at 550 nm anomaly (AOD550nm′, Eq. ) exceeds 2 at the given time (Sect. ). Figure a shows the total, unconditional probability of dust events, P(dust). The Mediterranean region experiences strong dust events more than 9 % of the time, and also regions around the Baltic Sea and north-east of the Black Sea have enhanced dust event probabilities. It becomes apparent that the pattern of the unconditional probability for dust (Fig. a, shading) is similar to the pattern of the probability of AD (Fig. b, contours), with higher values in the southern part of the domain, and a north-eastward extension of the region with enhanced values. Figure b shows the probability of a dust event, given the presence of an AD (P(Dust Event ∣ AD), shading), and the conditioning probability (P(AD), contours, same as in Fig. b). Conditional probabilities are enhanced compared to the unconditional probability throughout the domain, and they are highest north and northwest of the Iberian peninsula. In these regions, ADs occur less than 10 % of the time, yet several hundred co-occurrences of ADs with dust events are recorded, resulting in conditional probabilities of beyond 40 % (Fig. b). Figure c shows the standardised ln⁡OR. Positive values (green colours) in Fig. c highlight that dust events are more likely to occur in the presence of AD than during its absence. It is obvious that this is the case everywhere in the domain, and the very large values indicate strong evidence with respect to the variability. This is most pronounced from the Iberian Peninsula, across the English Channel and to southern Scandinavia, but less pronounced over the Mediterranean and the far east of the domain. However even in the Mediterranean log⁡ORstd exceeds 10, which is clearly robust with respect to the sample variability.

The conditional probability of dust events given that an AD is present in the column (P(Dust Event | AD); Fig. b, shading) also gives insight into what fraction of AD events are dusty. While the probability of AD (P(AD); Fig. b, contours) decreases towards the north and northwest, the probability of a dust event given the presence of AD (P(Dust Event ∣ AD), Fig. b, shading) increases towards the northwest. Especially in the western part of the domain (western Europe and southern British Isles), more than 40 % of AD occurrences also bring dust events (yellow colours in Fig. b).

The pattern of P(Dust Event) (Fig. a) is similar to P(AD), and logically so. The probability for a dust event is highest closest to the source region, while regions further away have a reduced probability – because the dust-carrying air does not reach as far as often, and because more dust can be deposited during the longer journey. The only region that draws attention is the very east of the domain. Here, the probability of a dust event is higher than in neighbouring regions, and the effect of the AD is less pronounced (light colours in Fig. c). Additionally, east of 30° E is the only region, where P(dust event ∣ AD‾) exceeds 5 %. This indicates that in the very east of the domain, the presence of ADs is not as important for the occurrence of a dust event as in the rest of the domain. Two reasons are possible: (1) The dust may originate from source regions not represented in our study, such as the Arabian peninsula or central Asian arid regions. (2) The air may take longer than 120 h to reach eastern Europe and thus is no longer tracked as AD air by our algorithm.

The frequent co-occurrence of dust events and ADs is in agreement with the results from and who find that dust over Europe typically occurs when a far-south-reaching trough over the Iberian peninsula transports dust towards Europe across the western Mediterranean. find that during more than half of the late winter/early spring dust events in the western Mediterranean region, a cut-off low was present west of the Iberian peninsula. They also find increased blocking over the Euro-Atlantic sector. identify dust transport pathways towards Europe across the Mediterranean and via recirculation from the Atlantic. These are all synoptic situations and trajectory pathways that resemble those typical for ADs, found by .

An interesting intersection with aerosol atmospheric rivers (AAR) and atmospheric rivers (ARs) emerges: ARs are narrow, elongated regions of enhanced water vapour transport . apply this concept to narrow, elongated regions of aerosol transport and define AARs. They attribute 40 % to > 100 % of the total integrated aerosol transport over many regions to these AARs. By definition, AARs originating in the boundary layers of desert regions will also be ADs. A combination of the concepts is presented by and , who describe that ARs can pick up dust, when travelling over desert areas, forming dusty atmospheric rivers. also describe how the phenomena are interlinked: ARs cause higher near-surface wind, which makes dust air-borne. They report that 78 % of ARs crossing Northwest Africa are linked to dust events in Europe. In this context, it could be interesting for future research to examine the extent and nature of the overlap among (dusty) atmospheric rivers (ARs), aerosol atmospheric rivers (AARs), and atmospheric deserts (ADs).