Table  catalogs eight confirmed summertime derecho cases and two derecho-type events in Finland. The confirmed derecho cases were identified using criteria similar to those of in the United States and in Europe. According to the criteria, measured wind gusts had to exceed 25 m s⁻¹ (slightly lower than 26 m s⁻¹ defined by ) and/or damage of tornado scale F1 had to occur along a major axis length of at least 400 km. In addition, the time between successive wind damage reports had to be no longer than 2 h along the axis, and the damage had to be attributed to the same convective system. From the confirmed events, a few have already been studied in literature: Unto , Asta , Sylvi and Paula . It is also worth noting that two separate derechos affected Finland on 8 August 2010. However, for the purposes of this study, it is sufficient to treat the date as a day when a derecho occurred.

In addition to the confirmed derechos, the table includes two events (storms Ahti and Aatu) which had characteristics typical for derechos by causing widespread damage and were also investigated by . Nevertheless, they did not fulfill all of the formal derecho criteria. For storm Ahti, the major axis of the wind gust and/or damage reports did not reach the required length of 400 km, and some of the damages were caused by isolated convective cells rather than a single system. Storm Aatu similarly fell slightly short of the path-length threshold for wind gusts and damage, which prevented it from being classified as a derecho.

Several potential derecho events cross national borders, which means their damage paths may be too short over Finland to meet the derecho criteria. For example, storm Aatu already affected Estonia (based on radar images), but it did not last long enough over Finland to classify as a derecho. Since storms Ahti and Aatu did not quite meet the requirements to be classified as derechos, they are classified as derecho-type events in this study. Importantly, the addition of these two events did not affect the criteria for derecho-favoring environments that are defined in Sect. .

The trajectories of all ten events are drawn in Fig. , which also shows the grid domain (21.5–34° E, 58.5–65.5° N) that was selected to study the atmospheric conditions favoring derecho formation in Finland. The trajectories were determined visually from radar images provided by Eerik Saarikalle at the Finnish Meteorological Institute (FMI). At least two of the derecho-producing systems (Asta 29 July 2010; ; and Sylvi 8 August 2010; ) clearly developed outside of our grid and radar image area but propagated far enough across Finland to be classified as derechos.

Environments of derechos have been analyzed in many studies using atmospheric soundings e.g.,. However, the sounding network in Finland is too sparse to comprehensively study the atmospheric conditions favoring derecho formation. Therefore, ERA5 reanalysis data were used instead. ERA5 has several atmospheric, oceanic and land variables available for download on 37 pressure levels, extending from 1000 hPa (surface) up to 1 hPa (approximately 80 km altitude). The dataset has a horizontal resolution of 0.25° and a temporal resolution of 1 h.

To study synoptic patterns during derecho events in Finland in Sect. , ERA5 hourly pressure-level data were downloaded for all dates of the events, and every 6 h for 5 d preceding and one day following each event. The grid selected for the synoptic-scale analysis covered most of Europe and eastern parts of the Atlantic (30° W–50° E, 35–75° N). Horizontal wind components (u, v), temperature (T), specific humidity (q) and geopotential (Z) were downloaded from pressure levels 1000, 850, 700, 500 and 250 hPa. Additionally, single-level parameters were acquired: mean sea level pressure (MSLP), 100 m horizontal wind components, convective available potential energy (CAPE), and 2 m air temperature. In this study, no attention is paid to the ERA5 surface winds and precipitation during derechos in Finland, but some details on how they compare to observations are mentioned in pp. 27–28.

In Sects. –, the focus will be on mesoscale environments favoring derecho formation. To analyze these conditions, the smaller grid area (21.5–34° E, 58.5–65.5° N) illustrated in Fig.  was utilized. For this grid, u, v, T, q and Z were downloaded from 21 pressure levels between 1000 and 250 hPa for all events. In addition, CAPE and 100 m horizontal wind components were acquired. CAPE in ERA5 is calculated by evaluating air parcels originating from model levels below the 350 hPa level, with the maximum value retained (i.e. the most unstable CAPE).

As mentioned in Sect. , found parameters that distinguished summertime derecho-producing systems from other MCSs in the US. The most discriminating parameters were the 0–10 and 0–6 km vertical wind shear, and the 6–10 km layer mean wind speed (in addition to system propagation speed, which is not analyzed here). To calculate these parameters, ERA5 data was first interpolated to levels of constant altitudes (above ground level) at 500 m intervals from 500 m to 10 km using geopotential data from the pressure levels.

Shear parameters were computed as the magnitude of the vector difference between the wind at 100 m above the surface and the wind at either 6 or 10 km altitude. Hereafter, references to 0–6 or 0–10 km shear denote these two wind vector differences. The wind vector at 100 m was preferred over the 10 m wind to mitigate the effects of surface roughness. Nevertheless, the wind vector difference between 10 and 100 m was small.

The 6–10 km layer mean wind speed (hereafter 6–10 km U) was also calculated in the same manner as in . The corresponding formula is given in Eq. (), where u and v are the wind vector components at all the interpolated altitude levels within the 6–10 km layer. 16–10 km U=u2‾+v2‾

In many studies the 850 hPa equivalent potential temperature (θE) has been observed to be particularly high during European derechos (discussed further in Sect. ). Therefore, θE was also calculated at the 850 hPa level using the “equivalent_potential_temperature” function from Python's MetPy library .

To find out whether the frequency of derecho-favoring atmospheric conditions has changed during recent decades, ERA5 data were downloaded for the period 1940–2022. Since we were interested in the warm-season derechos in Finland, only data for June, July and August were analyzed. Additionally, based on our small sample of derecho cases in Finland, European derecho studies e.g.,, and intense MCSs observed in Finland , derechos and intense MCSs usually occur during the afternoon and evening hours. Consequently, ERA5 data were only acquired for 12:00, 15:00 and 18:00 UTC each day, which correspond to Finnish summer times 03:00, 06:00 and 09:00 p.m. These selected times provide sufficient sampling for the convectively relevant hours.

The trend analysis was carried out using several approaches. The three sets of criteria – the 10 km shear criteria, 6 km shear criteria and Derecho-favoring environments in Finland criteria that are presented in Sect.  – were applied separately in all trend analyses. For each summer, we calculated the number of favorable days (N) on which a given criteria set was satisfied at least once per day (1pd), twice per day (2pd, not necessarily consecutive), or at all three times (3pd) during 12:00, 15:00, and 18:00 UTC. The trends were then determined separately for the 1pd, 2pd and 3pd cases.

The warming of the global climate has become much more pronounced after ca. 1980 . Furthermore, assimilation of satellite data into ERA5 began after 1979, producing more reliable data . Therefore, we analyzed the trends within the 1980–2022 period, in addition to the full 1940–2022 time range.

After separately computing N for conditions satisfied once, twice, and three times per day using each criteria set in each summer, we calculated the Pearson and Spearman correlation coefficients between N and time (year number) for both time periods. The p-values of these correlations were then used to evaluate the statistical significance of the trends. We used p-value of 0.05 as the threshold for statistical significance.

In Sect.  we analyze the effects large-scale atmospheric teleconnections on N, using monthly teleconnection indeces from . The data extend from 1950 to present and include North Atlantic Oscillation (NAO), Scandinavian (SCAND), Eastern Atlantic (EA), and Eastern Atlantic/Western Russia (EAWR) indices. Additionally, we acquired monthly Atlantic Multi-decadal Oscillation (AMO) index timeseries that extends from 1948 to 2023 .

Figure  illustrates the large-scale weather pattern during three derecho events that occurred in Finland during 2010 and 2021 (storms Asta, Veera and Paula). Similar figures for the other seven cases are presented in the Supplement (Figs. S1–S3).

Figure a–c show that storms Veera and Paula feature a southerly to southwesterly flow into Finland, whereas the flow is southeasterly during storm Asta. In all three cases, the flow extends from southern Europe into Finland, and is driven by a quasi-stationary high over Russia and a trough digging into central or western Europe. In storm Paula, the trough had developed into a cut-off low prior to derecho formation, whereas in storm Asta it had developed into a mature low. Jet streaks are observed over or just north of Finland, with all three events moving quasi-parallel and on the right-hand side of the jet streak. Moreover, storms Veera and Paula, in particular, are located near the right jet entrance region, which is known to favor ascent.

Figure d–f present 500 hPa winds that exceed 20 m s⁻¹ in all three cases. Storms Asta and Veera move under a 500 hPa jet (≥ 20 m s⁻¹), whereas storm Paula is located in the vicinity of a particularly strong midtropospheric jet streak, with the maximum exceeding 35 m s⁻¹.

At the surface, the three events feature a strong high over Russia (Fig. j–l). Furthermore, a local surface low is observed, with the low center located over southern Sweden (Asta) or the Baltic Sea in between Finland and Sweden (Veera and Paula). The strongest low-pressure system among all 10 cases is observed during the only nighttime event, storm Asta, which is located near the cold front of the low. For the other two cases, the lows are significantly shallower, with the low associated with storm Veera being deeper than that associated with storm Paula. The air mass over Finland is also very warm and humid in the three cases as the 850 hPa specific humidity (q) exceeds 9 g kg⁻¹ in large areas over Finland (Fig. g–i), while the 850 hPa temperature (T) surpasses 285 K in southern and central Finland (Fig. j–l). This observation is explained by the quasi-southerly flow, advecting warm and humid air to southern Finland. Finally, Fig. j–l indicate that the systems move perpendicular to an 850 hPa horizontal temperature gradient, with colder air to the left of the movement. For storm Paula, this temperature gradient is particularly strong (approximately 15 K (300 km)⁻¹).

Overall, many European warm-season derechos have been associated with an upper-level trough pattern e.g., and thus commonly have a meridional component of forward motion, which is also observed in our cases. In fact, the flow into Finland throughout the free troposphere has a southerly component during all 10 events, generally driven by a quasi-stationary high over Russia and a trough digging into central or western Europe. This type of pattern has been observed to increase lightning activity over southern Finland (e.g., clusters 13 and 14 in ). In at least 6 of the 10 cases, the trough has already developed into a cut-off low before the formation of the event (see Table  in Appendix for the corresponding events and figure numbers). This flow pattern advects warm and moist air from southern Europe, resulting in 850 hPa temperature and specific humidity exceeding 285 K and 9 g kg⁻¹, respectively, along the trajectories of all 10 cases. Furthermore, all 10 events seemed to move approximately perpendicular to the 850 hPa horizontal temperature gradient vector and are located either within the region of strongest local gradient or slightly on its warmer side. A similar characteristic has been commonly observed also for the US bow echoes and derechos , as well as in European derecho events e.g..

At the surface, all ten cases feature a strong high over Russia (as in Fig. j–l). Furthermore, a weak local low is typically observed, with the low center located over the Nordic countries. Overall, a low centered over the Nordics is found in 9 of the 10 cases (Table ), excluding only storm Lahja (Fig. S1l).

The 500 hPa wind speed exceeds 20 m s⁻¹ over some parts of Finland in all cases, which is consistent with the strong mid- to upper-level winds identified by e.g. as a characteristic of derecho environments. In total, 6 of the 10 cases are located under the 500 hPa jet (Table ), while the rest of the cases occur in close proximity. These observed 500 hPa wind speed values seem to fall within the range reported in Europe; for example, the 500 hPa flow in a derecho in Poland was found to have been only 10–15 m s⁻¹ , whereas warm season derechos have also been observed to occur under midtropospheric jet streams reaching 40 m s⁻¹ . It has also been reported that wind speeds throughout the troposphere tend to be stronger in the environments of the quasi-linear convective systems producing warm-season derechos than in non-derecho-producing systems in Europe, with the largest median difference reported in the midtroposphere . This agrees with our result of derechos in Finland tending to occur under a midtropospheric jet streak. Interestingly, in 6 out of the 10 events (Table ), the maximum of this jet streak is located directly behind the system (as in storm Veera in Fig. e).

Finally, the 250 hPa jet streaks are also observed over or just north of Finland in all ten cases, with derechos moving quasi-parallel to them on their right-hand side. In fact, at least 4 out of 10 of the cases (Table ) are located in the right jet entrance region which has strong deep-layer vertical wind shear and is a dynamically favorable location for ascent. Additionally, this region lies on the warm side of the jet, with high 850 hPa temperature and humidity values observed in these cases. Of the remaining events, five (storms Unto, Asta, Lahja, Sylvi, and Verneri) are also located near the canonical entrance region but their location relative to the jet streak varies. Storm Saima was both near the left exit of a strong jet on its western side and in the right entrance of a secondary flow maximum on its northern side (Fig. S1b). Similar observations have been made in Europe where derechos have been connected to either the left jet exits e.g. or right jet entrances e.g.. Comparable findings have also been reported in the US e.g..

In this section, the mesoscale atmospheric environments of derechos in Finland are examined, focusing on conditions along their approximate trajectories. The main interest is in the environment throughout the lifetime of each event rather than in single-point extremes. Thus, noting that a variable exceeds a threshold along the full trajectory (recall Fig. ) means that even the lowest values along the trajectory exceed it (unless otherwise stated). Figure  presents mesoscale conditions for the same three example cases shown in Fig. . Storms Veera and Paula were selected as representative of an “average” derecho in Finland, as their mesoscale conditions were typical of the range observed in Finland, while storm Asta is an interesting case of being the only known nighttime derecho in Finland. Similar figures for other cases are again available in the Supplement (Figs. S4–S6).

The high air mass temperature and humidity noted in the synoptic-scale analysis in Sect.  is suggestive of convective instability in these three cases. Indeed, moderate convective available potential energy (CAPE) values are present during the three derechos (Fig. a–c). Throughout the lifetime of storm Veera, CAPE ranges from 500 to 1000 J kg⁻¹ in its near environment (region extending ca. 100 km ahead of the storm along its direction of propagation), which represents mid-range of all analyzed cases. In storm Paula, the CAPE values are among the highest as CAPE exceeds 2000 J kg⁻¹ in the vicinity of the derecho. During the nighttime event, Asta, the CAPE values are slightly higher compared to storm Veera but slightly lower compared to storm Paula. In total, CAPE values surpass 500 J kg⁻¹ along 9 of the 10 trajectories, with only storm Lahja remaining partly below this value (Fig. S4c). The maximum CAPE, exceeding 3000 J kg⁻¹, is observed on the trajectory of storm Sylvi (Fig. S5a), so the variability among the cases is large.

On average, the CAPE values are lower than those reported by in the United States (US), as expected given that CAPE tends to be lower in Europe than in the US . Furthermore, and also found that derechos typically exhibit lower CAPE than other severe convective storms in the US and Europe, respectively. The relatively frequently occurring elevated mixed layer in the US is likely one reason for higher CAPE values in the US derechos. Additionally, the equilibrium level is higher in the US than in Europe contributing to higher CAPE values .

Nonetheless, the CAPE values we observe are similar to or slightly lower than those reported in European derechos. An 18-year climatological study of derechos in Germany noted that a mixed-layer CAPE median for warm-season derechos occurring in Germany was 513 J kg⁻¹ based on proximity soundings , which is close to the ERA5 (most unstable) CAPE values observed in most derechos in Finland. Additionally, most unstable CAPE associated with the formation environment of a derecho in Poland ranged between 1000–2500 J kg⁻¹ , which is comparable to our high-end cases, whereas a derecho in Spain had (surface-based) CAPE exceeding 3000 J kg⁻¹ near the genesis region, with similarly high (most unstable) CAPE values being observed only for storm Sylvi in Finland. Importantly, the CAPE values we observe do not appear to be higher than those associated with intense MCSs reported by . This finding is inline with the results of who found that CAPE does not distinguish derecho-producing from non-derecho-producing systems.

High values of equivalent potential temperature (θe) have been reported in several European derecho studies, especially at 850 hPa. For example, in a derecho in Germany , θe values as high as 340 K were advected to the area, and in a derecho in Belgium , the θe maximum at 850 hPa was ca. 341 K. Our findings (e.g. in Fig. d–f) are broadly consistent with these observations. θe (850 hPa) surpasses 325 K in all 10 cases on their trajectories throughout their lifetime, with the maximum value in Finland reaching over 340 K during storm Sylvi (Fig. S5c). Since the 850 hPa θe average over the grid area for the three summer months (considering times 12:00, 15:00 and 18:00 UTC) is 310 K during 2000–2022, the values observed along the derecho trajectories are anomalously large. High values of θe above the boundary layer diminish the adverse effects of entrainment , and thereby favor strong convection. Additionally, showed that dry mid-level (850–500 hPa) strongly suppresses convective storms even when conditions for convection are otherwise favorable, which could be the reason why derechos in Finland tend to occur only when 850 hPa θe is sufficiently large.

For the kinematic parameters, both the 0–10 km (Fig. g–i) and 0–6 km shear (Fig. j–l) are relatively strong over large areas during the three example derechos. Indeed, the 0–6 km shear is well above 15 m s⁻¹ along the trajectories of storms Veera and Paula. Nevertheless, the strongest deep-layer shear is noted during storm Asta, where the 0–6 and 0–10 km shears exceed 25 and 30 m s⁻¹, respectively. However, due to the locations of the jet streaks (recall Sect. 3.1), the highest 0–10 km shear values are generally located to the left of the derecho trajectories, whereas the highest 0–6 km shear values generally match better along the trajectories due to derechos being located under or in the vicinity of the 500 hPa jet. In two cases (storms Unto (Fig. S4g) and Verneri (Fig. S6f), the 0–10 km shear is even below 10 m s⁻¹ on the trajectories. Additionally, the 0–6 km shear is stronger than the 0–10 km shear during storms Unto (Fig. S4), Lahja (Fig. S4) and Verneri (Fig. S6) which is the opposite to the other events. Storm Verneri stands out as an outlier, with abnormally weak upper-level winds and relatively low instability compared to other events. Furthermore, the surface winds (as observed from the MSLP contours in Fig. S3h) were stronger during Verneri, partly explaining the weaker deep-layer shear.

While the variability in the 0–6 km shear is relatively small, with a majority of the values being above 15 m s⁻¹, the 0–10 km shear exhibits considerably larger variability between the events as the values vary approximately from 5 to 35 m s⁻¹ along the trajectories. found that 90 % of the US derechos experienced the 0–10 km shear stronger than about 19.5 m s⁻¹, which is higher than in most of our cases. Only during storm Asta the 0–10 km shear exceeds 19.5 m s⁻¹ along the trajectory throughout the lifetime of the system. Thus, the 0–10 km shear is relatively weak in derechos in Finland compared to the US. Additionally, the equilibrium level for lightning events is lower in Europe than in the US , implying that shear between the near-surface and 10 km wind may be less relevant for European convective environments. Therefore, it was considered whether the 8 km altitude should be used instead of the 10 km altitude. However, Pearson correlation between the 0–10 km shear and 0–8 km shear in convective situations (in grid points where CAPE ≥ 250 J kg⁻¹) is strong (0.89) during 1980–2022, suggesting that the use of 0–10 km shear is adequate. Additionally, the difference between our observations and US derechos regarding the 0–10 km shear is expected as found that the vertical wind shear in European convective environments is generally weaker than in the US. We also use the 100 m altitude as ground (0 km altitude) which might play a minor role in our shear value comparison.

On the other hand, found that the 0–6 km shear exceeded approximately 12 m s⁻¹ in 90 % of the US derechos, and this value is met during every derecho in Finland, with a small majority of the events surpassing 15 m s⁻¹ along the trajectories (as in Fig. j–l). While the 0–6 km shear values are known to be underestimated in ERA5 compared to soundings , the observed 0–6 km shear values in Finland are still clearly lower than, for example, in Germany where a median of 20.1 m s⁻¹ was reported based on proximity soundings for an 18-year warm-season derecho climatology .

Finally, the 6–10 km U exceeds 20 m s⁻¹ along the trajectories of the three example derechos (Fig. m–o). Across all the events, the 6–10 km U surpasses 15 m s⁻¹ along the full trajectory, except for storm Aatu (Fig. S6i). The result is consistent with the US derechos since 90 % of them experienced upper-level winds stronger than approximately 16 m s⁻¹ . The strongest 6–10 km mean winds (> 25 m s⁻¹) are observed during storms Saima (Fig. S4n) and Asta (Fig. m), with the former being associated with a particularly strong upper-level jet, and the latter influenced by the moderately deep low-pressure system.

The 10th percentiles for the discriminating variables (recall Sect. ) found by were selected as baseline thresholds for the criteria sets. These thresholds correspond roughly to 19.5 m s⁻¹ for 0–10 km shear, 12 m s⁻¹ for 0–6 km shear and 16 m s⁻¹ for 6–10 km U. Even though CAPE was not found to be a discriminating variable, it was used as a proxy to distinguish derecho environments from non-convective windstorms. Since all ten cases exceeded a CAPE value of 250 J kg⁻¹ along their trajectories (Sect. ), it was selected as the minimum threshold for a derecho-favoring environment in Finland.

The first criteria set, hereafter the 10 km criteria set, required that the 0–10 km shear, 6–10 km U and CAPE meet their respective minimum thresholds of 19.5 m s⁻¹, 16 m s⁻¹ and 250 J kg⁻¹ at the same grid point. Since the formation of derechos requires favorable atmospheric conditions over a sufficiently large area, it was also required that at least 3.5 % of the selected grid area (Sect. ) satisfy these thresholds. The area fraction was chosen so that the Finnish derecho events would meet the criteria at least once per day (1pd), with the exception of the outlier storm Verneri. This area was not required to be contiguous since derechos do not necessarily decay when passing through small regions that are not favorable.

The second criteria set, hereafter the 6 km criteria set, was similar to the 10 km criteria set but it used 0–6 km shear and its respective threshold value of 12 m s⁻¹ instead of 0–10 km shear. Additionally, the required area fraction was increased to 5 %. The 6–10 km U and CAPE thresholds remained the same as in the 10 km criteria set. The overview of criteria sets and their respective thresholds is summarized in Table .

The 10 and 6 km criteria sets have limitations, which are discussed in Sect. . Thus, the third criteria set, hereafter the Derecho-favoring environments in Finland (DEF) criteria set, was developed to adapt the 10 and 6 km criteria set framework to the specific atmospheric conditions in Finland. It was tailor-made to be satisfied during the observed summertime derechos in Finland along their trajectories throughout their lifetime, including the outlier storm Verneri. The adaptation of parameter thresholds was done by selecting values that are marginally exceeded in the observed cases and that minimize the number of DEF-positive days otherwise.

The CAPE condition in the DEF criteria set was implemented in the same manner as in the 10 km and 6 km criteria sets, with the minimum threshold of 250 J kg⁻¹. Since the results of Sect.  showed that particularly high 850 hPa θe values were present along the derecho trajectories, the 6–10 km U criterion used in the 10 and 6 km criteria sets was replaced with an 850 hPa θe threshold of 325 K. Similar to the CAPE criterion, this threshold was marginally satisfied along the trajectory of every event. Conversely, the 6–10 km U criterion was found to provide negligible additional value to the DEF criteria set.

We also considered using the difference of θe at the surface and midtroposphere (Δθe) since it is considered as an indicator for damaging microbursts . However, the variability between the cases was too high (from approximately 5 to 25 K, not shown), and therefore Δθe was eventually not used. The variability in Δθe in European derechos has also been found to be high in other studies e.g.,.

In the DEF criteria set, the two shear parameters from the 10 and 6 km criteria sets were combined into a single combined shear criterion. Based on the results of Sect.  and additional sensitivity testing, merging the areas satisfying the 0–10 and 0–6 km shear thresholds produced a larger favorable area that better aligned with the derecho trajectories without substantially increasing the number of favorable days on which no derechos were observed. First, the 0–6 km shear threshold was increased from 12 to 12.5 m s⁻¹ (compared to the 6 km criteria set) since this change did not significantly reduce the size of favorable area on derecho days, but it nevertheless reduced the number of favorable days on which derechos did not occur. Increasing the threshold further to 13 m s⁻¹, however, made the criteria too restrictive for some events. Secondly, reducing the 0–10 km shear threshold (compared to the 10 km criteria set) from 19.5 to 15 m s⁻¹ and requiring that at least one of the two modified shear criteria to be satisfied (0–10 km shear > 15 m s⁻¹ or 0–6 km shear > 12.5 m s⁻¹) provided the best trade-off between limiting the number of favorable non-derecho days and still capturing all derecho events.

The combined shear, 850 hPa θe and CAPE conditions were required to be satisfied simultaneously at the same grid point. As in the 10 km criteria set, these conditions also needed to be met over at least 3.5 % of the grid area. Compared to the 10 and 6 km criteria sets in which the area thresholds were selected so that the criteria sets were satisfied at least once on a derecho day, the DEF criteria set was required to be met at all three analyzed times. The area fraction for the DEF criteria set could have been set higher if storm Verneri had been excluded. However, given the small number of derechos observed in Finland, it was decided to not omit any event. The threshold values for the DEF criteria set are also summarized in Table .

Figure  shows the performance of all three criteria sets during storms Asta, Veera and Paula at the same analysis times as in Figs.  and (performance during the seven other events is shown in Figs. S7–S9). In both cases, all three criteria sets are satisfied in sufficiently large areas in the surroundings of the observed locations of the derechos. During storms Asta and Paula, in particular, the area where all three criteria sets are satisfied aligns well along the trajectory of the system (Fig. a, c).

In the case of storm Veera, a quite common problem for the 10 km shear criteria set arises: the satisfied area is more to the left of the derecho trajectory than along it (Fig. b). The problem is even worse for storm Unto (Fig. S7a) as the region satisfied by the 10 km criteria is ca. 150 km to the left of the trajectory due to weaker upper-level winds. Overall, the 10 km criteria set aligns moderately with the path of the derecho in roughly 6 out of 10 events. However, this set fails in Unto (as mentioned above) and Verneri (where the 10 km criteria were not fulfilled anywhere in the study area, Fig. S9b). Additionally, during storms Lahja (Fig. S7c) and Aatu (Fig. S9a) the regions where the 10 km criteria set is satisfied are too far to the north. Therefore, we can conclude that the 0–10 km shear threshold of 19.5 m s⁻¹ is too strict for some derechos, which relates to the jet stream at 250 hPa being more leftward relative to the derecho's trajectory. Hence, the area satisfied by the 10 km criteria is generally smaller than for the other two criteria sets during the derechos.

The 6 km shear criteria set works better than the 10 km criteria set since the satisfied regions match better with the paths of the derechos. Still, some limitations are obvious. Similarly as for the 10 km criteria, the regions satisfied by the 6 km criteria during storm Aatu (Fig. S9a) are too much to the north due to the weaker midtropospheric winds (Sect. ). Also, in the outlier storm Verneri, it was only satisfied once per day (Fig. S9b). Furthermore, even though the satisfied regions during storm Lahja were closer to the location of the system compared to the 10 km criteria (Fig. S7c), they were still slightly too far to the north because the regions fulfilled by the 6–10 km U and CAPE thresholds did not coincide. Nonetheless, the 6 km criteria set outperformed the 10 km criteria set as it was satisfied very well along the trajectories of the seven remaining cases.

The DEF criteria set was developed to avoid the aforementioned issues, and it matched quite well with all 10 cases. However, since the formation environments for derechos varied, it was not possible to achieve one perfect criteria set. For example, the outlier storm Verneri was a tricky one to include in any criteria set. Additionally, in the near surroundings of storm Saima (Fig. S7b), CAPE and 850 hPa θe (Fig. S4b, e) were untypically low, although they were rapidly increasing along the trajectory. Despite these minor problems, the DEF criteria set captured well the environments favoring derecho formation in Finland.

Figure  demonstrates the performance of all three criteria sets during the summer of 2010 which was an exceptionally warm summer in Finland and resulted in four derecho days in a span of 1.5 weeks. The regions where the criteria sets are satisfied in comparison to the grid area are quite large during the derecho days, especially for the 6 km and DEF criteria sets, with relative area values exceeding 50 % during storms Veera and Sylvi (Fig. a). Overall, Fig. a shows that all criteria sets easily meet the requirements for classification of a favorable day for derecho (recall Sect. ), with conditions being satisfied at least once per day (1pd) of the three analyzed times (12:00, 15:00 and 18:00 UTC). All of the criteria sets also satisfy the conditions at least twice per day (2pd), but the 10 km criteria set is not satisfied at all three times (3pd) on the days of storms Asta and Lahja (Fig. b). Storm Asta is the only event that occurred mostly during the night, and therefore the favorable conditions (based on the 10 km criteria set) were present slightly later during the day compared to other events. For storm Lahja, the regions satisfying the 0–10 km shear and CAPE conditions did not coincide well.

From Fig. b, we can also determine how many favorable days each criteria set captures during the summer of 2010, with conditions satisfied 1pd, 2pd and 3pd. The number of favorable days (N) decreases when more times (pd's) are required, as expected. Nevertheless, N is much larger for all the criteria sets and pd’s than the number of derecho days (four). One reason for this may be that the criteria do not account for whether convection is actually initiated. Nonetheless, the summer of 2010 was indeed special due to its prolonged periods of warm and humid air mass being present in Finland. During the time periods when the conditions were satisfied (e.g. in early/mid July), severe thunderstorms occurred in Finland, but they were not classified as derechos.

During the other summers when derechos occurred (2002; Fig. S10, 2006; Fig. S11, 2021; Fig. S12, and 2022; Fig. S13), N is clearly smaller than in the summer of 2010. For example, the DEF criteria set finds only six favorable days for the 1pd condition and four for both 2pd and 3pd from the summer of 2006 (Fig. S11). Nevertheless, there were also more derechos in summer 2010 than in other summers, indicating that the prevalence of N is related to the frequency of derechos, including the 2010 indirect series of derechos (as defined by ).

Since the DEF criteria set is the best suited for derechos in Finland, the impacts of its individual criteria conditions to N are studied in more detail. Figure  illustrates how excluding one condition at a time from the criteria set affects the area of satisfied conditions (a) and N (b) during the summer of 2010. From both panels, it can be determined that each individual criterion has an effect on N. Despite the combined shear criterion (recall Sect. ) being satisfied during most of the summer, at least somewhere within the grid area (not shown), it still contributes to the DEF criteria set. In fact, the areas where the shear criterion is satisfied do not necessarily match with the areas where the other conditions (CAPE and 850 hPa θe) are fulfilled.

Importantly, during the summer of 2010, the combined shear and CAPE conditions (DEF-THE) were quite often satisfied at least once per day, but when they were demanded to be met at least twice per day, N clearly decreased. This observation repeats across all derecho summers (2002; Fig. S14, 2006; Fig. S15, 2021; Fig. S16, and 2022; Fig. S17). Furthermore, N obtained without the θe condition is much higher compared to that obtained with the full DEF criteria, particularly during derecho summers other than 2010 (Figs. S14–S17). Thus, it is not rare for shear and CAPE to meet their respective criteria conditions simultaneously, but it is much less common that high values of shear, CAPE and 850 hPa θe coexist for a prolonged time period (> 3 h). Thus, a key strength of the criteria set is its ability to discriminate derecho-producing atmospheric environments from those that do not produce derechos. In particular, the results in Fig.  highlight the importance of 850 hPa θe in the DEF criteria set and the presence of high 850 hPa θe during derechos in Finland.