Spatio-temporal variability of lightning activity in Europe and the relation to the North Atlantic Oscillation teleconnection pattern

Comprehensive lightning statistics are presented for a large, contiguous domain covering several European countries such as France, Germany, Austria, or Switzerland. Spatio-temporal variability of convective activity is investigated based on a 14-year time series (2001–2014) of lightning data. Based on the binary variable thunderstorm day, the mean spatial patterns of lightning activity and regional peculiarities regarding seasonality are discussed. Diurnal cycles are compared among several regions and evaluated with respect to major seasonal changes. Further analyzes are performed regarding interannual variability 5 and the impact of teleconnection patterns on convection. Mean convective activity across central Europe is characterized by a strong northwest-to-southeast gradient with pronounced secondary features superimposed. The zone of maximum values of thunderstorm days propagates southwestward along the southern Alpine range from April to July. Diurnal cycles vary substantially both between different months and regions, particularly regarding the incidence of nighttime lightning. The North Atlantic Oscillation (NAO) is shown to have a significant 10 impact on convective activity in several regions, which is primarily caused by variations of the large-scale lifting pattern in both NAO phases. This dynamical effect is partly compensated for by thermodynamical modifications of the pre-convective environment. The results point to a crucial role of large-scale flow in steering the spatio-temporal patterns of convective activity.

Oscillation (NAO) index. Those data were provided by the U.S. National Oceanic and Atmospheric Administration (NOAA).
The calculation of the index values is based on rotated S-mode principle component analysis (PCA; Richman, 1986) applied to monthly mean standardized 500 hPa height anomalies (Barnston and Livezey, 1987;Hurrell and Deser, 2010) obtained from the National Centers for Environmental Prediction -National Center for Atmospheric Research reanalysis (NCEP/NCAR1; Kalnay et al., 1996). The index time series is available from 1950 onwards. However, the relation between thunderstorm activity 5 and the NAO is studied based on a subsample of this time series, which is given by the period from 2001 to 2014 (SHY).

Reanalysis data
The output of the global reanalysis model NCEP/NCAR1 is used to examine the dynamical and thermodynamical effects of the NAO phases on convective activity. The NCEP/NCAR1 reanalysis is available for 17 pressure levels and exhibits a spatial resolution of 2.5 • × 2.5 • . For the analyzes performed in this paper, model fields of the wind vector and the equivalent potential 10 temperature at the 300 hPa and 850 hPa pressure levels, respectively, are evaluated. Only data sets at 1200 UTC are considered since they best mirror the prevailing convective conditions. NCEP/NCAR1 data are available from 1948 onwards. However, the analyzes are limited to the time period from 2001 to 2014 (SHY), for which lightning data are available.

Statistical methods
2.2.1 Binary measure of convective activity: Thunderstorm day 15 Lightning density usually is defined as the mean daily flash total within a certain grid box. This quantity has been used by several studies to estimate thunderstorm activity (e.g., Schulz et al., 2005;Manoochehrnia et al., 2007;Antonescu and Burcea, 2010;Santos et al., 2012). However, the explanatory value of lightning density suffers from sometimes being dominated by single severe convective storms producing several 10,000 flashes. Sporadic severe storm days may result in potentially misleading conclusions about the spatial patterns of convective activity. 20 This problem can be circumvented by defining a dichotomous variable thunderstorm day (TD hereafter), which takes the value one, if the number of daily flashes within a grid box exceeds a given threshold. Filtering those days with a low number of flashes enables us to focus on days with more intense thunderstorms and neglecting weak convective events such as, for example, embedded convection (Fuhrer and Schär, 2005). The optimum threshold in our TD definition is determined by an objective method. For this, the domain is subdivided into a grid consisting of 10 × 10 km 2 equidistant cells. Excluding all days 25 without any flash in a respective grid cell, the empirical probability density distribution is computed for each cell separately.
Averaging over the entire domain yields the distribution shown in Fig. 2. The threshold is determined by choosing the integer value just above the interval of strongest curvature, yielding a lower threshold of 5 flashes per day within a grid cell. This threshold excludes the large number of weak events, but simultaneously yields sufficiently large sample sizes. Therefore, for all subsequent investigations a day (from 00 to 00 on the next day) is classified as TD if at least 5 flashes were registered within 30 a 10 × 10 km 2 grid cell.

Probability density function
To provide a rough overview of the diurnal lightning incidence in different subregions, 24 h flash totals are fitted to a theoretical probability density function. For this purpose, it is reasonable to consider all days with lightning events instead of setting a certain threshold. Due to high skewness expected in connection with a large number of days with only a small number of flashes, the two-parameter gamma distribution is an appropriate choice: where Γ is the gamma function and α and k are shape and scale parameter, respectively (Wilks, 1995). The fitting procedure is performed using the method of L-moments, which is a more robust alternative to the conventional method of moments (Hosking, 1990). Goodness of fit is assessed by analyzing a quantile-quantile-plot (Wilks, 1995).

Dispersion and correlation of annual TD numbers
To determine the sample dispersion of the annual TD time series within a specific grid cell, we considered the coefficient of 10 variationv, which is defined by the sample standard deviationσ normalized by the sample meanμ, thus independent of the latter quantity (Kohn, 2006): Apparently,v exhibits a singularity forμ → 0, which must be kept in mind when analyzing the dispersion in areas with weak convective activity.

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To identify and further examine related patterns of specific convective activity, monthly TD time series at selected locations were correlated with those of all grid points in the investigation area. We used the Spearman rank correlation coefficient r s since it is independent of the underlying pdf and more robust against outliers compared to the widely used Pearson productmoment coefficient (Wilks, 1995). In this way, correlation maps with respect to selected reference grid cells were obtained. For the sake of better comparability, the underlying time series were smoothed by a moving-window before. We tested the results 20 for statistical significance by applying the univariate bootstrap method, which should be preferred to bivariate bootstrapping especially for small sample sizes (Lee and Rodgers, 1998). If n represents the length of the sample time series, the univariate algorithm implies randomly drawing n times with replacement from each of the two samples separately. This procedure is repeated 1,000 times, leading to the null distribution of the correlation coefficient. In the sense of a two-sided test, the null hypothesis H 0 is rejected if the observed r s is greater than the 97.5%-quantile or less than the 2.5%-quantile of the null 25 distribution (α = 0.05).

NAO and convective activity
We investigated the influence of the NAO on the mean spatial distribution of convective activity in Europe by assessing the deviations of TD frequency from climatology during strongly positive (NAO > 1) and negative (NAO < -1) phases, respectively.
For this purpose, the variable D measuring the influence of the NAO index on convective activity was defined as with rf {a|b} denoting the mean relative frequency of event a given event b. Thus, mean relative frequencies obtained by averaging over the monthly TD frequency values were compared between the respective NAO phases and the climatology.
Since the NAO anomaly patterns do not exhibit strong spatial shifts during the summer half-year, we decided not to differentiate between the individual months. The variable D was calculated for each grid cell separately. A value of D = 1 means that 5 thunderstorm days are twice as frequent during the respective NAO phases (positive or negative) as compared to the total sample. We assessed significance by means of a two-sided bootstrap test (α ∈ {0.05, 0.10}) regarding the test statistic D ± .
Here, the null hypothesis H 0 states that an observed relation between NAO and lightning activity within a grid box is simply due to chance.

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In the following, spatial and temporal patterns of TD numbers across the investigation area are discussed. More detailed analyses are presented for four example sub-regions representative of specific characteristics of convective activity: the Ticino (m in Fig. 1), Côte d'Azur (y), Maritime Alps (l), and Bavarian Prealps (t).

Spatial distribution of convective activity
The mean annual number of TDs presented in Fig. 3 shows a very large spatial variability. On the large scale, the distribution 15 is dominated by a distinct northwest-to-southeast gradient, which is mainly caused by the distance to the Atlantic substantially affecting the general climate. While less than two TDs occur on average over Brittany (indicated by b in Fig. 1) and Cornwall (a), more than 20 days are found in the vicinity of the Alps. Superimposed on this overall trend are several sub-structures on the regional scale such as the local maximum downstream of the Black Forest (s) or the minimum in the upper Rhône valley (i).
These sub-structures are mainly related to flow deviations, thermally-driven wind systems, and the local potential for moisture 20 flux convergence in the presence of orography.
The three primary maxima all extend along the southern Alpine range. One of them stretches across the region between the Ticino has already been identified in previous studies as one of Europe's core areas regarding thunderstorm activity (Van Delden, 2001;Schulz and Diendorfer, 2002;Nisi et al., 2016). The distinct maximum can be linked to increased instability due to the abundance of low-level moisture. Instability is even further increased when cold air masses advected from the northwest and 30 blocked by the Alps at lower levels reach Ticino aloft only (Costa et al., 2001). Convection triggering mechanisms are provided by orographically induced flow deviations, outflows from mature convective cells and catabatic-anabatic wind systems leading to low-level convergence zones (Gladich et al., 2011;Nisi et al., 2016). Over southern Austria, the high number of TDs already found by other authors (e.g., Wakonigg, 1978;Schulz et al., 2005;Punge and Kunz, 2016) can be plausibly explained by advection of unstable air from the southeast and subsequent lifting at the nearby foothills. Regarding the Maritime Alps (l), their close proximity to the Mediterranean allows for very moist and warm maritime air getting lifted over the complex topography.

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Besides the TD maxima connected to the Alps, elevated values are also found in the vicinity of low mountain ranges or hilly terrain. In Germany, the most prominent maxima are located over the Bavarian Prealps (t; ∼15 TDs) and between Black Forest and Swabian Jura (s; ∼12 TDs). Secondary maxima can be observed over the Ore mountains (x), the Bavarian-Bohemian Forest (u) and, unlike previously stated (Finke and Hauf, 1996), only over some parts of the hill terrain to the west, for example the Sauerland (w; 9-11 TDs). A further remarkable feature is the meridional streak of increased values along the German-

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Polish border (∼9 TDs). In France, the strongest extra-Alpine lightning activity is observed over the Pyrenees with highest values registered on Spanish territory in the south (c, ∼14 TDs). Other maxima are located over Massif Central (e) and the Jura Mountains (g). Remarkably, a broad streak of higher frequencies also ranges from the Bay of Biscay to the northeast.
Regarding ambient conditions, the increased TD values in Southern Germany can be attributed to a pronounced north-tosouth gradient in thermal stability or convective energy (Brooks et al., 2003;Mohr and Kunz, 2013). Specifically, the maximum Convective activity does not reach its minimum over glaciated mountain ranges as proposed by earlier studies (e.g. Manoochehrnia et al., 2007), but along the neighboring deep valleys. Due to shadowing effects, the evolution of moisture flux convergences 30 is strongly impeded there. In contrast, the presence of snow and ice cover in summit regions reduces thunderstorm frequency to a much lesser extent, as can be seen for example by the comparatively high number of TDs in the partially-glaciated Upper Tauern in Austria (q). Low TD numbers over the Brittany, and, likewise, along the Baltic Sea coast, can be explained by the stabilizing effect of the cool sea water during summer months. Note that the extension of the Breton landmass seemingly is not sufficiently large in order to allow for a local increase of convective activity due to solar heating. In spite of higher temperatures, the Mediterranean also stabilizes the maritime boundary layer leading to a reduction in thunderstorm activity along the Côte d'Azur (Anderson and Klugmann, 2014). It must be stressed that the Mediterranean simultaneously serves as an important source of moisture for convective cell formation over the neighboring Maritime Alps as aforementioned.
Considering lightning density instead of TDs, spatial variability is characterized by a largely similar large-scale pattern of minima and maxima (not shown). Moreover, it can be shown that the annual TD number at a specific grid cell is highly 5 correlated with the annual lightning density at this grid cell. Pronounced differences between TD number and lightning density on the local scale, however, occur where TDs go along with lower or higher flash numbers compared to the mean. This effect can be studied comparing gamma distributions fitted to diurnal flash numbers among six exemplary subregions (Table 1). Recall that increasing shape and scale parameters, α and k, result in less skewness and stretching towards higher values, respectively (see Eq. 1). Therefore, large values of both α and k imply a relatively high probability of those TDs exhibiting a high number 10 of lightning flashes. k generally has the same dimension as the quantity studied, and can therefore be looked upon as some sort of characteristic daily flash number describing the respective distribution. Conversely, α is dimensionless and a value of α < 1 implies that the distribution approaches infinity in the limit of zero. As expected, high flash numbers are emphasized in the distributions belonging to several hot spots of TD occurrence, such as Ticino (k = 33.0), Maritime Alps (k = 25.6) and southern Bavaria (k = 23.5). Conversely, the Pyrenees, albeit representing a prominent maximum with respect to TDs as well,

Temporal variability on diurnal and seasonal scales
Besides the spatial variability discussed in the previous paragraph, convective activity exhibits a strong temporal variability on diurnal, seasonal, and interannual time scales. The following section investigates the two former modes of variation.

Joint annual-diurnal cycles of lightning frequency
In addition to the large spatial variability in TDs as discussed in the previous section, also the diurnal cycle of lightning fre-25 quency differs considerably across the investigation area. In the example regions, the global maxima occurring in the afternoon or evening over the Maritime Alps, Ticino, and Bavarian Prealps are distinctly shifted against each other by several hours (Fig. 4). While the maximum in the former region is registered around 14 LT, it occurs 4 hours later at 18 LT in Ticino and at 20 LT in the latter region. Furthermore, while in Ticino lightning has an elevated frequency during nighttime, it is substantially reduced over the Maritime Alps, especially between 22 and 10 LT. Contrarily, high levels of lightning persist also throughout 30 the night at the Côte d'Azur, yielding two broad peaks between 00 and 06 LT and between 13 and 20 LT.
Plotting mean annual cycles of TD frequency for the four example subregions (Fig. 5) likewise reveals distinct spatial features. Predominantly, convective activity exhibits a broad summer maximum accompanied by a strong increase and decrease in spring and autumn, respectively, whereas it is characterized by a sharp autumn maximum at Côte d'Azur. However, even those regimes with frequent summer lightning differ significantly from one another, for example TD frequency increases much later in Ticino than in Southern Bavaria or the Maritime Alps, where autumn decrease in turn is delayed.
To consider both, daily and annual cycle, jointly, we used a kind of Hovmöller diagram for the four example regions showing 5 the normalized lightning frequency as a function of the two temporal modes (Fig. 6). To better highlight the most important temporal patterns, two-dimensional smoothing of the data was performed by employing 10-day and 100-minute running means, respectively. As can be seen, most diurnal cycles vary substantially throughout the year with large differences found also among neighboring regions such as Maritime Alps and Ticino. The former distribution (Fig. 6a) exhibits a symmetric diurnal cycle with almost vanishing nighttime activity and a maximum around 15 LT remaining approximately constant from the middle of 10 June until the beginning of August. In Ticino, contrarily, nighttime and morning thunderstorms are quite common (Fig. 6b), but not before the end of June. The afternoon maximum is shifted into the early evening (18 LT) with the season of highest values distinctly shortened compared to the Maritime Alps. Along the Bavarian Prealps, the diurnal cycle has some similarities with that of the Maritime Alps, but it is clearly displaced towards later hours and consequently extends until after midnight (Fig. 6c).
Both in Ticino and the Bavarian Prealps, the late summer drop in evening lightning frequencies (see Fig. 5) does not imply 15 cessation also of nighttime activity. By contrast, lightning frequencies behave completely different at Côte d'Azur, where a weak afternoon maximum is visible during summer months in addition to sporadic nighttime activity, before the diurnal cycle changes entirely in September with a pronounced maximum extending from the afternoon all over the night (Fig. 6d).
Several other studies (e.g. Schulz et al., 2005;Novák and Kyznarová, 2011;Wapler, 2013)  2). Frequent nighttime lightning in September over the Western Mediterranean has also been found by Santos et al. (2013). In the coastal zone, land breezes might additionally favor thunderstorm activity during night.

Monthly patterns of thunderstorm days
The findings obtained in the previous subsection suggest analyzing the regional peculiarities of seasonality more in detail.
For this purpose, we calculated the mean spatial distribution of TD numbers for each month separately (Fig. 7). Generally, these maps confirm the dominance of a single summertime maximum in most areas caused by the seasonality of insolation and low-level temperature. However, several pronounced local differences are visible as well. In April, convective activity is already slightly increased in those regions, where the overall primary maxima occur. Over the High Alps, TDs do not occur 5 at all. In May and June, maximum values are observed in southern Austria (3.5 and 5 TDs, respectively) with the area of peak activity shifted southwestward. At this time, TD frequency in Ticino yet is markedly lower than in Austria, before the Ticino maximum becomes dominant from July onwards (up to 7 TDs). Note the clear delay of springtime increase in the latter area compared to the Bavarian Prealps (cf. Fig. 5). In August, lightning activity decreases nearly everywhere except for the Côte d'Azur area. There and in the adjacent lower Rhône valley, convection even becomes more frequent in September (up to 10 1.8 TDs). Although TDs have turned quite rare in most regions by then, the Ticino and Pyrenees maxima are still present (2 and 2.5 TDs, respectively).
In Graz Basin, low level moisture is able to accumulate much earlier than in the Alpine areas located farther to the west.
There, later snow melt additionally prevents the slopes from being heated by the sun in spring (Wakonigg, 1978;Bertram, 2000), which particularly affects the summit regions. Both factors lead to the southwestward shift of lightning activity in Austria 15 culminating in very high TD numbers at the western edge of the Upper Tauern in July, which might be caused by moisture flux convergence at the junction of the two major Drau and Puster valleys. Whereas stabilization by the cool Mediterranean damps the Ticino maximum until June, the favorable local orographic features (cf. Sec. 3.1) lead to the extremely intense activity observed in July. This southwestward relocation of the peak convective region agrees with the results of an earlier study concerning MCS frequency (Morel and Senesi, 2002). In September, lightning events have become rather scarce because 20 of a decrease of mean potential instability in connection with solar insolation weakening. Simultaneously, the Mediterranean meanwhile has warmed considerably relative to the air, favoring thunderstorm formation in the adjacent areas and leading to the striking rearrangement of the spatial pattern of convective activity observed. Anderson and Klugmann (2014) showed that this effect even strengthens in October, where we have got no data.

Duration of annual lightning period 25
The large differences in seasonality suggest investigating the duration of annual lightning period separately for each grid cell.
For this, we determined the average values of those days-of-year when the first and last TD occur, respectively (Fig. 8).
Both patterns of first and last TD occurrence are connected to the mean spatial distribution of TDs (Fig. 3) in the sense that a high/low local TD number usually implies a longer/shorter lightning period. Examples for this relation include the pronounced northwest-to-southeast gradient, and the discrepancy between the Ticino-Turin region (end of April until beginning 30 of September) and the nearby upper Rhône valley (end of June until first half of August). Apparently, locations favoring the development of convective cells are in many cases characterized by a long persistency of these conditions as well. However, lightning regimes behave in a more complex way in several regions. For instance, orographic features are attenuated considering the distribution of the last TD recording (e.g. Maritime Alps, upper Rhône valley and northern Alpine range), which, in addition, bears much less resemblance with the mean pattern of convective activity than the distribution of the first TD. Instead, that pattern is characterized by a broad area in Southern France, where TDs occur widely spread late in the year, particularly in the surroundings of the lower Rhône valley near to the Mediterranean coast (middle of September). Furthermore, the convective period over the Mediterranean itself starts late, but lasts quite long with the last TD observed in the first half of September.

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Three steering factors already mentioned in Sec. 3.2.2 trigger these pronounced differences: persistent snow cover, lack of low-level moisture and the annual cycle of sea surface temperature (SST) of the Mediterranean. Since the two former conditions strongly impede thunderstorm formation in the High Alps and the adjacent deep valleys until late spring (cf. Fig. 7 a,b), convective season is delayed in those regions compared to their forelands, leading to the strong gradients observed in the first TD distribution (Fig. 8, left). The role of SST, already identified as one of the main drivers of annual TD cycle (see Fig. 5 and 10   7), is reflected by the very late cessation dates occurring north of the French coast. Note in particular that the reduced thermal stability connected to high SST allows for late last TDs everywhere in that region, independent of orographic structures prevailing.

Interannual variability
Even though a period of 14 years, where lightning observations are available, is far below a climatological time span (e.g., 30 15 years), it is sufficient to study interannual variability in addition to the diurnal and seasonal cycles discussed above. However, owing to the relatively short time series, the main focus is put on the spatial scales of convective activity and the potential relation to teleconnections.

Variability of annual TD numbers
Annual lightning totals vary substantially during the time period considered. In the year of 2006, for example, a total of 3.6 20 million lightning flashes were recorded, whereas convective activity was rather low with approximately 2.1 million flashes in 2010 and 2012. Simultaneously, complex spatial differences regarding interannual variability are present. Although there are some years with increased or reduced TDs nearly everywhere, such as in 2006 or 2010, respectively (Fig. 9 a,b), frequencies usually do not behave spatially consistently. One example is the pattern observed for the year of 2001, when the Ticino-Turin maximum already discussed above has developed well in contrast to low values in southern Austria and over the Pyrenees.

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Other distinct local maxima such as those of the Paris basin (d in Fig. 1) or around Hamburg (v) are not present in the 14-year mean (cf. Fig. 3). In 2013, contrariwise, the Pyrenees and Maritime Alps exhibit increased convective activity as opposed to Ticino and southern Austria.
The large annual and interannual variability of lightning frequency can be attributed -at least partly -to prevailing upper troposphere flow patterns favoring or preventing thunderstorm development. In addition, as shown by Piper et al. (2016), days 30 with large-scale weather types favorable for convection frequently form clusters of several days, i.e. the incidence of such weather types implies a considerable probability for a convective situation lasting for a longer time period. This persistence effect amplifies the number of the corresponding favorable flow patterns in those years, when they frequently set in, and hence, the interannual variability of convective activity.
Another aspect of interannual convective variability is the dispersion of TD numbers, which can be assessed for each grid cell using the coefficient of variation (CV; Sec. 2.2.3). Notably, large parts of the investigation area exhibit a fairly homogeneous CV pattern with values around 0.4 (Fig. 10), taking into account a considerable background noise of ±0.

Spatial correlations
According of the findings described in the previous subsection, interannual variability is only partially coupled among different regions. Comparing correlation maps for four different reference points (Fig. 11) shows that the peripheries, inside of which the time series tend to cohere, largely vary in terms of area and shape. The grid cell located between the Black Forest and Swabian Jura (Fig. 11a) exhibits significant correlations with a vast region extending from the French Alsace to the easternmost parts of 15 Austria. Conversely, the area of correlated grid cells strongly decreases when the reference cell is set to a location northeast of the Ore Mountains (Fig. 11b). Here, significant correlations lie inside of a narrow band ranging from the western edge of the Ore Mountains along the Czech and Polish border all the way northward to the Baltic Sea coast. When looking at correlations with respect to the southern Pyrenees (Fig. 11c), we find high values not only along the main axis of the Pyrenees, but also inside of a detached area basically comprising the Maritime Alps. By contrast, the correlation pattern obtained with respect to a 20 location within the Ticino-Turin lightning maximum (Fig. 11d) features significant values only inside a closely confined region.
In particular, there is no correlation even with large parts of the Ticino itself. Negative values are visible within a remote region, comprising for example grid points in northwestern Spain. The relatively large area in the Netherlands exhibiting significant positive values might be explained either by a complex spurious correlation or, more realistically, by random effects despite the high significance level employed.

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From the examples shown in Fig. 11, it can be concluded that the large-scale flow configurations leading to convectionfavoring conditions and sufficient lifting substantially differ among the various regions. For example, the relation of the temporal variability in TD numbers between the Pyrenees and the Maritime Alps points to a large relevance of weather types causing Mediterranean air to impinge on the respective mountain slopes. Strikingly, the latter region is not correlated with the nearby Ticino-Turin lightning maximum at all, where strong meso-scale correlation coefficient gradients show that even neighbor-30 ing locations may behave inconsistently given a specific large-scale flow situation prevailing, presumably due to the complex orography. Large correlations along the German-Polish border similar to the area of the local lightning maximum (Fig. 3) point to the influence of potentially instable air originating from the southeast in connection with the southern Polish lightning maximum addressed in Sec. 3.1. Flow patterns advecting warm and moist subtropical air masses to Southern Germany, where they spread to the east and persist in a large region over a longer period of several days, might cause the interrelation of the time series in this area. However, low-level moisture and instability are also generated locally by means of evaporation and solar heating, yielding another contribution to the interannual variability observed. Note furthermore that convection may be triggered, in addition to large-scale lifting as discussed above, by processes taking place in the boundary layer and depending on local characteristics such as soil moisture and land use. For instance, Kotroni and Lagouvardos (2008) showed for the 5 Mediterranean region that lightning activity is favored over woodland areas compared to places with little vegetation due to an increased soil moisture. Differentiating the impact of large-scale processes on interannual variability from those local factors might yield further insights. However, this aspect is beyond the scope of this paper.

Relationship between convective activity and the NAO
The complex characteristics of interannual variability found in the time series of TDs suggest investigating whether a systematic 10 relation can be established between convective activity and atmospheric teleconnection patterns in terms of the NAO index, which is of relevance for European weather and climate (e.g. Della-Marta et al., 2007;Hurrell and Deser, 2010).
As can be clearly seen in Fig, 12, there is a distinct relation between NAO phases and lightning activity. Over most of the area, TD frequency is considerably increased during strongly negative NAO phases (N − ; Fig. 12  Positive NAO phases (N + ) predominantly go along with a decrease of TD frequency (Fig. 12 a,b). The most striking feature Since the NAO index considered in this paper has been defined by the leading mode of a PCA performed separately for each month (see Sec. 2.1.2), the centers of action change their position throughout the year. Thus, we cannot interpret the 30 positive NAO phase as a period of strong zonal flow in central Europe, as would be the case using the classical normalized pressure difference between two points. Instead, the southern center of action is given by a positive/negative anomaly band stretching from the United States to Europe when the NAO index is positive/negative, with its latitude oscillating between 30 glects small-scale weak thunderstorms. We studied the mean spatial distribution of annual TD numbers, compared diurnal and seasonal cycles of lightning incidence among several European sub-regions, and performed analyzes of interannual variability.
In particular, the impact of the NAO on convective activity was investigated, as it represents the dominant low-frequency mode of the large-scale flow configuration.
It was found that the mean spatial pattern of thunderstorm activity is characterized by a pronounced northwest-to-southeast gradient between very low values (∼2 TD pear year) observed in northwestern France and strong maxima (∼21 TD) in some 5 parts of the southern Alps, for instance in the Swiss Canton of Ticino. Superimposed on this large-scale trend are several distinct regional structures such as the pronounced lightning minima over the deepest Alpine valleys. Seasonality is characterized by a single maximum in July in most places. However, the area of maximum convective activity moves in a southwestward direction from southeastern Austria in April to the surroundings of Ticino in July. At the French Mediterranean coast, contrarily, thunderstorm activity does not reach its maximum until September. Regional diurnal cycles of flash frequency mostly exhibit 10 a single afternoon or evening maximum, with its exact time varying substantially. Distinct spatial differences are present regarding the occurrence of nighttime thunderstorms. Moreover, most diurnal cycles feature pronounced seasonal changes, such as along Côte d'Azur in September, when a transition takes places from a regime dominated by a weak afternoon maximum to frequent nighttime lightning.
Multi-annual TD time series are spatially interrelated to a limited extent only. Correlation maps show that the area exhibit-15 ing a high and significant degree of correlation varies strongly in size for different reference points, and can be extremely small in some cases. The NAO has a significant impact on lightning probability with its negative/positive phase generally favoring/reducing convective activity. In some areas, the strength of this effect depends on the orographic structures prevailing.
Three main factors governing the spatio-temporal variability as described above are given by the variable distance to marine areas, local orographic features leading to flow deviations and, consequently, convergence zones, and regional differences in 20 the abundance of low-level moisture. During summer half-year, the Atlantic, North Sea, and Baltic Sea represent sinks of lowlevel sensible heat stabilizing the atmospheric boundary layer. The Mediterranean, however, additionally provides a source of latent heat due to the higher temperatures prevailing. Therefore, thunderstorms are inhibited over the Mediterranean coastal zone during summer, while they are promoted farther inland, where the humid air impinges on the Alps. In September, the Mediterranean has become warm relative to the air leading to more unstable conditions over the water, also during nighttime.

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Complex local flow patterns in combination with moist low-level air allow for distinct convective maxima along the Alps and some low mountain ranges, for example downstream of Black Forest. The local orographic structures also affect the degree of convective organization relevant in the context of diurnal cycles, as long-lived convective systems often are responsible for substantial nighttime activity. However, thunderstorm activity diminishes strongly, where orographic shadowing effects imply a reduction of moisture. Differing humidity levels along the southern Alpine range during early summer cause the shift of the 30 peak convective area observed in this region.
The analysis of interannual variability shows that the steering factors of convective activity described above are not sufficient in order to explain some of the aspects observed. Instead, time series of annual lightning incidence seem to depend on specific large-scale drivers prevailing frequently in some years and inducing the advection of unstable air and lifting at higher troposphere levels in those regions, where high TD numbers are observed. Our results suggest that different large-scale conditions might favor convection in the various sub-regions. The substantial impact of the NAO has to be dicussed by considering dynamical and thermodynamical aspects separately. On the one hand, negative NAO phases are connected to flow patterns that are associated with frequent short-wave troughs providing lifting over Central Europe, whereas during positive phases a high geopotential anomaly tends to suppress convection due to a lack of large-scale lifting. On the other hand, negative phases go along with a pronounced reduction of θ e at 850 hPa over most of the investigation area, which is detrimental to convective ac-5 tivity, while a positive θ e anomaly is present during positive phases. Hence, the thermodynamical effects of the NAO phases on convective activity partly compensate for the dynamical effects. Owing to pronounced seasonal variations of the NAO pattern, the features discussed above are characteristic for the summer half-year only.
A potential weakness of our research is that the 14-year time series of lightning data does not reach the climatological time range. However, this sample should be sufficient for reliable analyzes regarding spatio-temporal variability on diurnal and 10 seasonal time scales. As opposed to earlier studies, which all are based on shorter time spans, we were able to additionally investigate multi-annual modes of variability using well-suited significance tests in order to ensure that no misleading conclusions are drawn due to the limited sample size. Furthermore, the analyzes presented in this paper focus on CG lightning only.
In fact, present-day LF location systems are capable of detecting IC lightning as well. For instance, Marra et al. (2017) studied IC activity within a strong convective cell using LF data. However, multi-annual statistical analyzes regarding IC lightning 15 suffer from a significant reduction of both detection efficiency and location accuracy compared to CG lightning (Schulz et al., 2014). Although an IC climatology might potentially reflect further meteorological aspects, we therefore decided to neglect IC lightning. A further interesting issue is the spatio-temporal variability of winter lightning, particularly in view of the connections between thunderstorm genesis in marine regions and the seasonal variations of the temperature difference between water and air. However, much longer time series would be necessary for statistically reliable studies of winter lightning owing to the 20 small event samples.
The clear and significant impact of the NAO pattern on convective activity in Europe motivates us to scrutinize the crucial role of large-scale flow in future research. The objective is to gain further insight into the physics behind the complex spatiotemporal variability discussed in this paper. This involves evaluating additional teleconnection modes obtained by Barnston and Livezey (1987) such as the East Atlantic Pattern. To generate longer, multi-decadal time series allowing for further investi-25 gations such as trend and spectral analysis, we have additionally implemented objective weather types as indicators for a high convective predisposition (Piper et al., 2016).          the southern side of the Pyrenees (c), and southwest of Ticino (d). Values that are not statistically significant (Si = 95%) have been set to zero. Figure 12. Relative deviation (D) of the monthly number of thunderstorm days calculated with respect to months with an NAO index greater than +1 (N+) from that calculated with respect to all months (a). Results of a bootstrap significance test with green/yellow grid boxes corresponding to areas where the null hypothesis has been rejected with Si = 95% and Si = 90%, respectively, and red boxes denoting acceptance of null hypothesis (b). The same applies to (c)/(d), but D is evaluated with respect to an NAO index below -1 (N−).