The spatial and temporal variability of convective activity is examined using data from the ground-based LF lightning detection system BLIDS (BLitz-Informations-Dienst Siemens), which is part of the EUCLID (EUropean Cooperation for LIghtning Detection) network. The detection efficiency has been shown to be 96 % for flashes exhibiting a peak current of at least 2 kA, while the location accuracy is ∼ 100 m . Information about both polarity and current strength is neglected, and flashes rather than strokes are studied with the grouping procedure performed internally by EUCLID. Since the LF operational range implies a significantly lower detection efficiency of cloud-to-cloud (IC) lightning , only cloud-to-ground (CG) flashes are taken into account.

Convective conditions and related thunderstorm activity across Europe tend to form larger-scale patterns that exhibit a large annual and interannual variability e.g.,. To examine whether this variability may be partly controlled by major large-scale teleconnection patterns, we considered monthly values of the NAO index. Those data were provided by the US National Oceanic and Atmospheric Administration (NOAA). The calculation of the index values is based on rotated S-mode principal component analysis PCA; applied to monthly mean standardized 500 hPa height anomalies obtained from the National Centers for Environmental Prediction – National Center for Atmospheric Research reanalysis NCEP/NCAR1;. The index time series is available from 1950 onwards. However, the relation between thunderstorm activity and the NAO is studied based on a subsample of this time series, which is given by the period from 2001 to 2014 (SHY).

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 analyses performed in this paper, model fields of the wind vector and the equivalent potential temperature at the 300 and 850 hPa pressure levels, respectively, are evaluated. Only data sets at 12:00 UTC are considered since they best mirror the prevailing convective conditions. NCEP/NCAR1 data are available from 1948 onwards. However, the analyses are limited to the time period from 2001 to 2014 (SHY), for which lightning data are available.

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.,. However, the explanatory value of lightning density suffers from sometimes being dominated by single severe convective storms producing several tens of thousands of flashes. Sporadic severe storm days may result in potentially misleading conclusions about the spatial patterns of convective activity.

This problem can be circumvented by defining a dichotomous variable TD, which takes the value of 1, 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 embedded convection . 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 km2 equidistant cells. Excluding all days 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. . The threshold is determined by choosing the integer value just above the interval of strongest curvature, yielding a lower threshold of five 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 00:00 to 00:00 LT on the next day) is classified as TD if at least five flashes were registered within a 10 × 10 km2 grid cell.

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: f(x)=xkα-1exp⁡-xkkΓ(α), where Γ is the gamma function and α and k are shape and scale parameter, respectively . The fitting procedure is performed using the method of L moments, which is a more robust alternative to the conventional method of moments . Goodness of fit is assessed by analyzing a quantile–quantile plot .

To determine the sample dispersion of the annual TD time series within a specific grid cell, we considered the coefficient of variation v^, which is defined by the sample standard deviation σ^ normalized by the sample mean μ^, and thus independent of the latter quantity : v^=σ^μ^. Apparently, v^ exhibits a singularity for μ^ → 0, which must be kept in mind when analyzing the dispersion in areas with weak convective activity.

To identify and further examine related patterns of specific convective activity, annual 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 rs since it is independent of the underlying probability density function and more robust against outliers compared to the widely used Pearson product-moment coefficient . 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 for statistical significance by applying the univariate bootstrap method, which should be preferred to bivariate bootstrapping especially for small sample sizes . 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 1000 times, leading to the null distribution of the correlation coefficient. In the sense of a two-sided test, the null hypothesis H0 is rejected if the observed rs is greater than the 97.5 % quantile or less than the 2.5 % quantile of the null distribution (α = 0.05).

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. For this purpose, the variable D measuring the influence of the NAO index on convective activity was defined as D±=rf{TD=1|NAO≷±1}-rf{TD=1}rf{TD=1}, 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 SHY, 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 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 H0 states that an observed relation between NAO and lightning activity within a grid box is simply due to chance.

In addition to the large spatial variability in TDs as discussed in the previous section, the diurnal cycle of lightning frequency 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. ). While the maximum in the former region is registered around 14:00 LT, it occurs 4 h later at 18:00 LT in Ticino and at 20:00 LT in the Bavarian Prealps. Furthermore, while in Ticino lightning has an elevated frequency during nighttime, it is substantially reduced over the Maritime Alps, especially between 22:00 and 10:00 LT. Contrarily, high levels of lightning persist also throughout the night over the Côte d'Azur, yielding two broad peaks between 00:00 and 06:00 LT and between 13:00 and 20:00 LT.

Plotting mean annual cycles of TD frequency for the four example subregions (Fig. ) 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 the normalized lightning frequency as a function of the two temporal modes (Fig. ). To better highlight the most important temporal patterns, two-dimensional smoothing of the data was performed by employing 10-day and 100 min 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. a) exhibits a symmetric diurnal cycle with almost vanishing nighttime activity and a maximum around 15:00 LT remaining approximately constant from the middle of June until the beginning of August. In Ticino, contrarily, nighttime and morning thunderstorms are quite common (Fig. b), but not before the end of June. The afternoon maximum is shifted into the early evening (18:00 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. c). Both in Ticino and the Bavarian Prealps, the late summer drop in evening lightning frequencies (see Fig. ) does not imply cessation of nighttime activity. In contrast, lightning frequencies behave completely differently 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. d).

Several other studies e.g., that focused on parts of our investigation area have already identified the afternoon peaks in lightning frequency as a prominent feature. Our results, however, suggest that lightning regimes behave more diversely in regard to the time of the maxima and, in particular, the seasonal variation of diurnal cycles. The large discrepancies between the Maritime Alps and Ticino lightning regimes, despite both being particularly steered by orographic lifting of Mediterranean air masses, can be plausibly explained by a differing level of convective organization. In the former domain, thunderstorms preferably are initiated as single cells at the mountain slopes, which dissipate quickly in the evening hours, when radiative cooling sets in. In contrast, nighttime thunderstorms in the latter region can be attributed to convergence zones due to complex orographic features and outflows from mature cells frequently leading to long-lived mesoscale convective systems . Organized convection has been shown to be also important in the Bavarian Prealps by . This type of convection causes the time shift of maximum lightning frequency relative to the Maritime Alps. The seasonally dependent influence of the Mediterranean on stability accounts for further noticeable features described above, such as the jump of Ticino lightning frequency at all times of the day found for the end of June and the distinct change in the Côte d'Azur diurnal cycle taking place in early autumn (see Sect. ). Frequent nighttime lightning in September over the western Mediterranean has also been found by . In the coastal zone, land breezes might additionally favor thunderstorm activity during night.

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. ). 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 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 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 (see Fig. ). 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 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 , which particularly affects the summit regions. Both factors lead to the southwestward shift of lightning activity in Austria culminating in very high TD numbers at the western edge of the High 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 (see Sect. ) 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 . In September, lightning events have become rather scarce because 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. showed that this effect even strengthens in October, for which we have no data.

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 (Fig. ).

Both patterns of first and last TD occurrence are connected to the mean spatial distribution of TDs (Fig. ) 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 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 regarding 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 to 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.

Three steering factors already mentioned in Sect.  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 (see Fig. a and b), convective season is delayed in those regions compared to their forelands, leading to the strong gradients observed in the first TD distribution (Fig. , left panel). The role of SST, already identified as one of the main drivers of annual TD cycle (see Figs.  and ), 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 prevailing orographic structures.

Annual lightning totals vary substantially during the time period considered. In the year 2006, for example, a total of 3.6 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. a and b), frequencies usually do not behave spatially consistently. One example is the pattern observed for the year 2001, when the Ticino–Turin maximum already discussed above has developed well in contrast to low values in southern Austria and over the Pyrenees. Other distinct local maxima such as those of the Paris Basin (d in Fig. ) or around Hamburg (v) are not present in the 14-year mean (see Fig. ). In 2013, contrariwise, the Pyrenees and Maritime Alps exhibit increased convective activity in contrast to Ticino and southern Austria.

The large annual and interannual variability of lightning frequency can be attributed – at least partly – to prevailing upper-tropospheric flow patterns favoring or preventing thunderstorm development. In addition, as shown by , days 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 of a longer-lasting convective situation. This persistent behaviour 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; Sect. ). Notably, large parts of the investigation area exhibit a fairly homogeneous CV pattern with values around 0.4 (Fig. ), taking into account a considerable background noise of ±0.1. Thus, no significant spatial fluctuations of dispersion are visible here in spite of the spatial peculiarities regarding year-to-year variability discussed above. Nonetheless, CV values are higher in areas where mean TD numbers are particularly low, and vice versa. For example, higher values at several grid points are obtained for regions with infrequent lightning such as northern Germany. Note, however, that higher values and larger gradients of CV may be caused by small integer numbers, where an increase in TD frequency by only 1 day in a specific year yields a stronger increase when the number of TDs is low. This effect culminates over the Atlantic with values up to 3.3, where CV approaches its singularity.

According to 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. ) 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. a) exhibits significant correlations with a vast region extending from the French Alsace to the easternmost parts of 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. b). 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. c), 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 location within the Ticino–Turin lightning maximum (Fig. d) 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.

From the examples shown in Fig. , it can be concluded that the large-scale flow configurations leading to convection-favoring 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 mesoscale correlation coefficient gradients show that even neighboring 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. ) point to the influence of potentially instable air originating from the southeast in connection with the southern Polish lightning maximum addressed in Sect. . 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, showed for the 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.

The complex characteristics of interannual variability found in the time series of TDs suggest investigating whether a systematic 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.,.

As can be clearly seen in Fig. , 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. c and d). A prominent feature, for example, is the absolute maximum in eastern Austria, where TD frequency doubles in places (D- = 1) compared to the entire sample. Statistically significant positive values of D- are reached in several other areas, for example in the southern half of Germany and along the German–Polish border. However, a sharply delineated zone of near-zero negative D- values is located inside the margins of the French Alps, comprising all the mountain ranges between the Maritime Alps and Lake Geneva. Within a marine area, which can be perceived as a southward extension of this region, even significant negative values are observed.

Positive NAO phases (N+) predominantly go along with a decrease of TD frequency (Fig. a and b). The most striking feature is a zone of strong reduction stretching from the Mediterranean coast in northwestern Italy along the French–Italian border northward to the upper Rhône Valley in Switzerland with an eastward extension to Grisons and Tyrol (see Fig. ). Note that the Ticino–Turin lightning maximum situated in between is characterized by a weaker decrease. Other regions where D+ exhibits significantly negative values are the lower Danube Valley in northeastern Austria, the northern foreland of the Pyrenees, and parts of the North German Plain. The almost contiguous zone of highly significant results extending from the western Bay of Biscay to Cornwall suggests that the area-wide suppression of convection (D+ = -1) is a reliable observation instead of a statistical artifact due to the small event sample sizes in that region. Comparing the locations of the D+ minima to the mean spatial pattern of TDs (Fig. ) leads to the observation that most of them are characterized by weak average convective activity.

Since the NAO index considered in this paper has been defined by the leading mode of a PCA performed separately for each month (see Sect. ), the centers of action change their position throughout the year. Thus, we cannot interpret the 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 and 35∘ N in winter between 40 and 50∘ N in summer . Consequently, during SHY, negative phases, N-, go along with high geopotential gradients over southern central Europe, as shown by the anomaly pattern of the 300 hPa wind field (Fig. a). Therefore, shortwave troughs frequently affect the investigation area and provide, primarily in the southern and eastern parts, quasi-geostrophic forcing, which is conducive to convection initiation. This mechanism might explain the increase in TD frequency connected to N-. The contrary decrease of TD frequency over the French Alps confirms the exceptional nature of this lightning regime (see Sect. ). In contrast, positive phases, N+, correspond to a jet stream shifted to northern Europe (Fig. c) and, hence, a positive geopotential anomaly located over central Europe. The lack of lifting associated with this anomaly pattern explains the reduction of convective activity observed during N+. Furthermore, strong capping inversions inside of deep high-pressure systems might additionally inhibit cell formation. Both factors seem to be detrimental especially in those areas where convective activity is low on average, such as over the marine areas around Brittany. Another example is the upper Rhône Valley, where ambient conditions have shaped up to be rarely conducive to convection due to shadowing effects (see Sect. ), and a favorable flow pattern therefore is indispensable for thunderstorm development. In contrast, complex lifting mechanisms in nearby Ticino allow for convection in spite of the absence of large-scale forcing.

Additional insights into the relationship between convective activity and NAO can be gained by studying anomaly patterns of the equivalent potential temperature θe at 850 hPa for both N+ and N-. Since high θe values in the lower troposphere often go along with strong vertical θe gradients equivalent to high levels of potential instability, θe represents a suitable parameter for assessing the pre-convective environment . During N-, the negative geopotential anomaly over large parts of Europe goes along with lower values of θe (Fig. b). Hence, conditions over most of the investigation area are governed by air masses rather detrimental to thunderstorm formation from a thermodynamical point of view. This effect partly compensates for the convection-favoring impact of the dynamical processes ahead of a trough (see Fig. a). During N+, conversely, the positive geopotential anomaly that is associated with the northward displacement of the jet stream (see Fig. c) implies a pronounced increase in θe over the entire investigation area (Fig. d). Consequently, N+ yields favorable thermodynamical conditions for thunderstorm formation, but the simultaneous lack of large-scale forcing mechanisms in combination with convection suppression due to large-scale subsidence leads to the decrease of TD numbers observed in many regions. However, convective activity may even be enhanced during N+, when local-scale lifting is present, such as convergence zones inside of the boundary layer. Indeed, some areas in western France exhibit positive values of D+ that might be related to this effect. Hence, the impact of the NAO on convective activity is governed by the modification of both thermodynamical and dynamical conditions relevant for the formation of thunderstorms.