Trends in intraseasonal temperature variability in Europe, 1961–2018

1 INTRODUCTION

The current climate change affects all aspects of temperature distributions. The world faces long-term changes not only in mean values, which has been among essential research topics for a long time (Cohen et al., 2012; Van der Schrier et al., 2013; Van den Besselaar et al., 2015; Hong et al., 2017; Rahmstorf et al., 2017; Gonzales-Hidalgo et al., 2018; Marshall et al., 2018), but likewise in temperature variability and symmetry of its distribution (Matiu et al., 2016).

Changes in variability are often described as crucial for a changing frequency of temperature extremes and increase in the occurrence of heat waves (Katz and Brown, 1992; Fischer et al., 2012; Matiu et al., 2016). There are studies illustrating how the change in variability could contribute to extreme temperatures in both tails of temperature distributions (Schär et al., 2004; Beniston and Goyette, 2007; Field et al., 2012). In other papers (Klein Tank and Konnen, 2003; Moberg and Jones, 2005; Seneviratne et al., 2014; Christidis and Stott, 2016) trends in indices of temperature extremes are investigated. Such studies often indicate that warmer climate becomes also more variable and that recent heat waves cannot be explained only by the simple shift in the mean but are contributed also by the extension of temperature distributions.

However, trends in individual measures of variability are not discussed in such a detail, their studies having produced ambiguous or even contradicting results (Matiu et al., 2016). Therefore, the goal to conclude whether the temperature variability is stable or has changed together with the ongoing change in mean temperature is far from being simple. Various papers analyse trends in temperature variability on different time scales, that is, within a season (intraseasonal) or year-to-year (interannual); they focus typically on one specific variability measure, notwithstanding it is implied in Astatkie et al. (2003) that the simultaneous use of several measures can provide more comprehensive results.

Regarding the interannual scale, which has been investigated more frequently, Huntingford et al. (2013) conclude that time-evolving standard deviation of globally averaged temperature has been stable with substantial geographical variation over the past few decades. Scherrer et al. (2005) reveal a significant increase in year-to-year temperature variability in Europe in summer, decrease in spring and winter, and no change in autumn. Summer increase in interannual variability is detected also in Della-Marta et al. (2007) in western Europe and in Hansen et al. (2012) worldwide, which was later denied by Rhines and Huybers (2013). Interannual variability was also studied in the Tibetan Plateau (Song et al., 2014), indicating a significant overall increase.

On the intraseasonal scale, the majority of studies focus on standard deviation (SD) of temperature. Matiu et al. (2016) reveal significant changes in SD in both directions at 10 stations across Europe, negative trend in autumn between 1933 and 2012 and a positive trend in winter and spring between 1973 and 2012. In contrast, Rebetez (2001) discloses reduced intramonthly SD at both the mountain and low elevation sites in Switzerland, which is particularly apparent in winter. In the Southern Hemisphere, Rusticucci and Barrucand (2004) observe no change of SD of temperature in Argentina in winter but its significant decrease in summer.

Trends in day-to-day temperature change (DTD), defined as a temperature difference between two consecutive days (Piskala and Huth, 2020), are, to our knowledge, only investigated by Piotrowitz et al. (2017), concluding DTD has decreased in Krakow in last two centuries for both maximum and minimum temperature. Long-term change in interquantile ranges is seldom examined as well. Matiu et al. (2016) reveal, besides disparate trends (between seasons and between periods of time) in SD and various interquantile ranges, different trends in variability in the colder and warmer part of temperature distributions, pointing out to trends in the symmetry of temperature distributions. Temporal autocorrelation, which is another plausible measure of variability, has, to our knowledge, only been studied for monthly means (Lenton et al., 2017; Leasor et al., 2019), not daily values.

A specific group of studies are those investigating the evolution of entire temperature distributions where the change in variability is manifested as one of its components. Donat and Alexander (2012) found no significant change in the distribution of global temperature anomalies between two consecutive periods (1951–1980 and 1981–2010), referring to its noticeable spatial heterogeneity. Similarly, McKinnon et al. (2016) revealed an increase in summer variability (between 1980–1989 and 2006–2015) in eastern Europe while the opposite is true for western United States.

Differences between several intraseasonal measures of variability are examined by Moberg et al. (2000), who declare the standard deviation to be a good measure, while the absolute change in temperature anomaly from 1 day to the next is claimed to be sensitive to changes in observational procedures.

The main objective of this paper is to provide an overview of trends in temperature variability across Europe from the 1960s to the present. For Europe, this is the most extensive study on trends in temperature variability so far as 168 stations from the ECA&D database are included. We focus on short-term (intraseasonal) variability, which, rather than variability on the interannual scale, is essential for the formation of extreme temperature events, such as heat waves. We utilize four types of variability measures, which we have selected subjectively as the most representative for intraseasonal variability This is standard deviation (SD) of temperature, interquantile range between the 90th and 10th percentile (IQR), day-to-day temperature change (DTD) and temporal autocorrelation (LAG); see more details in the next section. While SD and IQR are standard measures of short-term variability, which characterize the width of a temperature distribution, DTD and LAG describe manifestations of weather (non)stationarity. Moreover, since sudden rises and falls in temperature are an important aspect of how the public perceives climate, and have a negative impact on human health and on various sectors of economy (e.g., agriculture and human health; Piotrowitz et al., 2017; Plavcová and Kyselý, 2010; 2014), we include DTD and LAG into our analysis in order to provide a more comprehensive view of a long-term development of short-term temperature variability in Europe.

2 DATA AND METHODS

Our analysis requires homogeneous temperature daily series with sufficient spatial coverage across Europe. Daily series of daily mean temperature were taken from the EUSTACE dataset (Squintu et al., 2019), which consists of homogenized blended series of European Climate Assessment and Dataset. The version of the dataset employed in this study was created in March 2019 and is publicly available at www.ecad.eu.

We analyse the period from March 1, 1961 to February 28, 2018, in which the sufficient number of temperature series overlap. Each conventional climatological season is examined separately; winter is defined as December in the previous year and January and February in the given year. It means that we analyse 1962–2018 period for winter and 1961–2017 period for spring, summer, and autumn.

Rather strict rules are applied on the completeness of temperature series, both within seasons and for time series of seasons. A season is considered missing if it contains more than seven missing daily values. We include into analysis only the series with maximum of four missing seasons in the series but not more than two missing seasons in both the beginning (nine seasons) and ending (nine seasons) parts of the series. These parts are considered more rigorously as trend estimates are highly sensitive to data near both ends of the time series (Liebmann et al., 2010).

Based on these criteria we utilize the set of 168 stations (Figure 1, colours). Criteria are not met at Edinburgh, Armagh, Sheffield and Vârful Omu in winter, which means that the winter analysis consists of only 164 stations.

We analyse four variability measures: (a) standard deviation (SD) of mean daily temperature, (b) mean absolute value of day-to-day temperature change (DTD), (c) the interquantile (between the 90th and 10th percentiles) range of mean daily temperature (IQR) and (d) 1-day lagged temporal autocorrelation of temperature (LAG). We also calculate trends of mean temperature (MEAN).

The four measures are complementary since each of them represents a different aspect of variability. While SD and IQR describe the width of temperature distribution, DTD and LAG represent the weather (non)stationarity. For example, temperatures can change very slowly (low variability according to DTD and LAG; high stationarity) during a season, but persistently in one direction, resulting in a high variability according to SD and IQR (wide temperature distribution) (Figure 2a). Conversely, temperatures may change abruptly from 1 day to the next (high variability as described by DTD and LAG), but in the same interval during the entire season, resulting in a relatively narrow temperature distribution and low SD and IQR (Figure 2b). The occasionally different behaviour of SD and IQR indicates a different shape of temperature distribution at its tails (Figure 2c) or of its higher moments (skewness, kurtosis) (Figure 2d). Unlike DTD, LAG is dimensionless, that is, does not take into account the amplitude of temperature variations, and thus is insensitive to the width of temperature distribution (Figure 2e). DTD does not attain high values where SD is low, although the variability according to LAG may be high there.

For analyses of variability measures (their climatology and linear trends), we use daily temperature anomalies from the long-term mean for that day. For MEAN and DTD, daily values are averaged into seasonal means. SD, IQR and LAG are calculated from all daily values in the season. The values of LAG (autocorrelation coefficients) are multiplied by (−1) in trend analysis so that their sign is consistent with other measures: positive/negative trends indicate increases/decreases in variability.

Linear trends of seasonal values are calculated for each measure, season and station by ordinary linear regression. Trends in variability are normalized by dividing by the station average of the measure in the whole period and expressed in percents per decade. The normalization allows trends to be compared between different measures and between different climate conditions.

In order to evaluate whether the locally detected trend could or could not occur due to mere chance (e.g., Wilks, 2016), the global (field) significance is assessed by Monte Carlo approach. To this end, maps of each variability measure for 57 years were shuffled 1,000 times. The number of stations with statistically significant trends is calculated then for each shuffled series of maps. These numbers are ordered into a series; the percentile of the real number of stations with statistically significant trends in that series, p, indicates the level of global significance, 1 − p. For example, if the number of locally significant trends corresponds to the 95th percentile of the ordered series, the trend map is considered significant at the 5% level.

For regional and correlation analyses, stations are subjectively divided into six geographical domains (Figure 1, symbols): (a) western Europe (WE), (b) northern Europe (NE), (c) central Europe (CE), (d) Baltic (BA), (e) southern Europe (SE) and (f) eastern Europe (EE).

3 TRENDS IN MEAN TEMPERATURE

We first briefly assess trends in mean temperature. In period 1961–2018, temperature trends are positive at all stations in all seasons. This attests global significance regardless of the amplitude of trends at individual stations in line with the sign test for global significance introduced by Huth and Dubrovský (2021). By simply averaging the temperature trend over all stations, Europe is warming up by 0.39, 0.36, 0.23 and 0.44°C·decade⁻¹ in spring, summer, autumn and winter, respectively. Compared to our previous study (Krauskopf and Huth, 2020) where a less recent period (1957–2002) is examined and seasonal warming of 0.27, 0.24, 0.03 and 0.34°C·decade⁻¹ is detected, this indicates an acceleration of warming in all seasons.

Spatial distribution of mean temperature trends in all seasons is displayed in Figure 3. The strongest warming is observed in northern and northeastern Europe in winter. Trends do not get below 0.5°C·decade⁻¹ at most stations there. The highest trends are located in the Arctic Ocean (1.7°C·decade⁻¹ at Hopen). Vardø exhibits the highest trend in continental Europe (0.8°C·decade⁻¹). In spring, almost entire Europe warms up by 0.3–0.5°C·decade⁻¹; trends are higher at several stations in the north only. In contrast, weaker trends are found in the British Isles and in the southeast. Summer shows different distribution of trends than winter and spring with the fastest warming in the Mediterranean (0.56°C·decade⁻¹ in Zagreb-Grič) and slowest warming in the north. In autumn, the strongest trends are observed in western Mediterranean (0.38°C·decade⁻¹ in Malaga) and in the Arctic Ocean (0.86°C·decade⁻¹ at Hopen). The rest of Europe exhibits slight trends, but the warming is much more distinct than when a less recent period is considered (1961–2000 in Pokorná et al., 2018). Trends are statistically significant at all stations except Vârful Omu in spring, at 97% of stations in winter, 96% in summer, and 77% in autumn.

4 SHORT-TERM VARIABILITY

4.2 Overall trends in temperature variability in Europe

Trends in variability are not as unilateral as trends in mean. Their sign and magnitude vary seasonally and regionally and differ among variability measures. Figure 4 shows the percentage of positive, negative and statistically significant trends as well as the mean linear trend and the range of trends across Europe in both normalized (%) and absolute values for all measures in all seasons. All trends are per decade, which is omitted in the description for brevity.

The standard deviation of temperature is predominantly decreasing in Europe in all seasons except summer. The most notable is winter when the decline of SD is observed at almost 80% of stations exceeds 1% on average and locally is as high as over 12% at Bjørnøya. The situation is opposite in summer when an increase in SD is detected at 70% of stations. The largest increases are not as large as the largest decreases in other seasons; nevertheless, they exceed 3%·decade⁻¹.

The IQR shows behaviour fairly similar to SD in all seasons, both in percentages and normalized trend values. The only difference occurs in summer when IQR shows a somewhat higher percentage of positive (statistically significant as well) trends. Similarly, the mean trend is higher (0.8% compared to 0.5% in SD) in summer as well as the highest positive trends. This may indicate a more pronounced increase of variability in the tails of temperature distribution, and therefore in extreme values, which is reflected in IQR rather than in SD.

Decreases in DTD prevail, in contrast to the previous measures, also in summer, although by a rather narrow margin. The share of stations with significant trends of both signs is largest for this measure in all seasons except for increases in winter. In winter, DTD decreases are strongest of all measures, with an average relative trend of more than −2% and a negative trend revealed at 82% of stations.

LAG is the variable with the most balanced ratios of positive/negative trends. This is particularly so in spring and summer, while negative trends prevail in autumn and winter. The number of statistically significant negative trends is higher than for SD and IQR, especially in winter.

Test of global statistical significance (Table 1) indicate that trends in DTD in all seasons and LAG in autumn and winter are significant at the 5% level. The global significance is below 20% for the majority of cases. We believe that this allows us to discuss spatial distribution of trends without being at risk of overinterpretation.

TABLE 1. Global significance

	Spring (%)	Summer (%)	Autumn (%)	Winter (%)
SD	16.3	18.8	24.6	12.8
IQR	17.6	12.6	39.9	10.5
DTD	0.0	2.4	0.2	0.0
LAG	47.7	15.0	3.9	0.3

• Note: Displayed is the probability of randomly exceeding the number of locally significant trends.

4.3 Regional analysis

In this section, trends (in absolute values per decade) in temperature variability are provided for the six European regions (Figures 5 and S3).

Northern Europe, facing the strongest warming of all domains in all seasons except summer, dominates also in trends of all variability measures except LAG. DTD decreases significantly in all seasons, with the highest trend occurring in winter when it decreased by more than 1°C during the entire analysis period. SD and IQR disclose the highest negative (statistically significant) trend in winter as well, which makes winter in northern Europe the most outstanding case of our results. SD and IQR decrease also in spring and autumn (SD in spring statistically significantly) while almost zero trends are observed in summer. Contrarily, LAG shows only a slight decrease in winter and almost no change in other seasons. It indicates that long term changes in DTD and LAG are likely to have a different origin and, therefore, a different direction of trends as was already suggested in section 2. However, these two measures do not differ as much in other domains.

The Baltic region manifests much stronger warming in spring and winter than in summer and autumn. Whereas a considerable decrease of SD and IQR (although not statistically significant) is detected in spring, DTD and LAG remain almost unchanged. Contrarily, DTD and LAG are significantly decreasing in winter, while the decrease in SD and IQR is weak. In summer, all variability measures increase, although DTD rises only very slightly.

Eastern Europe is the region with the most pronounced increase of variability in summer, although statistically significant for IQR only (0.14°C·decade⁻¹). The heat wave in summer 2010 (Barriopedro et al., 2011), which is likely to be related to increased temperature variability, and thus contribute to positive trends, is apparent in SD and IQR series as well as in the series of mean temperature anomalies. Otherwise, features similar to the Baltic are revealed, in particular the decrease of SD and IQR in spring and the statistically significant decrease in DTD and LAG in winter.

In western, central and southern Europe, trends in all variability measures are mostly close to zero, although mean temperature trends remain conspicuous (e.g., southern Europe exhibits strongest warming in summer of all domains; 0.50°C·decade⁻¹). The exceptions are autumn in central Europe with decreases of DTD and LAG (the latter being statistically significant), and summer in western Europe where a slight increase of SD and IQR (especially in the first half of the observed period) is revealed. The exceptionally warm summer of 2003 (Schär et al., 2004) is apparent in plots of mean temperature, but not in plots of SD and IQR.

To sum up, while mean temperature rises significantly in all domains in all seasons except eastern Europe in autumn, statistically significant increase in variability is detected only in one case: eastern Europe in summer for IQR. A statistically significant decrease in variability is most often observed for DTD, in all seasons in northern Europe, and in the Baltic and eastern Europe in winter. SD decreases significantly in northern Europe in spring and winter, IQR in the same region merely in winter and LAG in central Europe in autumn.

4.4 Geographical distribution

This part goes into more details and presents values of trends at individual stations. It reveals remarkable trends in regions where no areal mean trend is reported as well as noticeable outliers, which indicates that spatial differences in trends are present on smaller scales as well. The spatial distribution and values of trends in SD throughout Europe are demonstrated in Figure 6.

In spring, SD is decreasing markedly not only in northern Europe (as revealed in the regional analysis), where the northernmost stations exhibit the negative trends even around −7%·decade⁻¹, but also at most stations in Estonia and eastern Europe. The rise of SD is noticed in the Mediterranean, Normandy and at several high-elevation sites (Säntis, Kredarica, Vârful Omu), nowhere statistically significant. Summer increase in SD is confined to the belt between 45° and 60°N, quite frequently exceeding 2%. To the north and south of this belt, SD is decreasing, but only seldom more than by 2%·decade⁻¹. In winter and autumn, most of Europe undergoes decrease of SD, the highest negative trends being detected again in northern Europe, with values rising from the Southern Scandinavia towards the Arctic Ocean where trends become −12%·decade⁻¹ in winter and −8%·decade⁻¹ in autumn. SD trends are slightly positive (not over 2%) on the southern Baltic coast in winter, on the eastern coast of Spain in autumn and in southeastern Europe in both winter and autumn.

Trends in IQR are similar to trends in SD: they differ from each other to some extent solely in summer (Figure 7). Several stations in Romania, northern Germany and southern Scandinavia exhibit increases in IQR by more than 2%, while SD trends do not reach this value there.

DTD is the variable with the highest spatial variability of trends (Figure 8). This does not stand for winter when almost entire Europe is experiencing a declining trend, the decline being faster than for the other measures. Nearly every station in northern and eastern Europe exhibits a decrease in DTD stronger than −2% and stations in Arctic Ocean and on the coast of Norway even stronger than −7%. In other seasons, predominantly negative trends are detected in northern Europe and Germany, while in the rest of Europe the number of positive trends is increasing towards the warmer part of the year without distinct geographical features.

For LAG, trends only seldom exceed 2%·decade⁻¹ (Figure 9). The trends are weakest in spring. Noticeable spatial features are difficult to reveal, similarly to DTD. The exceptions are the Iberian Peninsula where LAG decreases significantly in summer and increases in autumn, and Germany where statistically significant decline is detected in these seasons. LAG also decreases in southeastern Europe in autumn, the trends being statistically significant and below −2%. In winter, trends are below −2% most often, mainly in eastern Europe and around Baltic Sea. Interestingly, the northernmost stations do not show the highest negative trends, as was the case for all previous measures in winter, and trends are even close to zero there.

It is evident that long-term changes in LAG and to an even greater extent in DTD are much more spatially heterogeneous than trends in SD, IQR and MEAN. DTD and LAG often decrease or increase at small clusters of stations or at one single station while trends of the opposite sign are disclosed at nearby stations. This holds, for example, for German stations where the decrease of DTD and LAG in spring and summer exceeds that in neighbouring countries considerably. We examine these discrepancies by comparing the time series of anomalies of SD (Figure 10a), DTD (Figure 10b) and LAG (Figure 10c) for two groups of four stations, German (Regensburg, Bamberg, Frankfurt, Wuppertal) and in the neighbouring countries (Praha-Klementinum, Maastricht, Eelde, De Bilt). A noticeable drop in DTD and to some extent also in LAG appears to occur at German stations approximately in 2001. From this year on, the German stations exhibit about 0.2°C lower DTD, while they have almost the same values as the neighbouring stations before 2001. No drop is evident in 2001 in the SD series (Figure 10c). Taking into consideration that this effect happens in spring, summer, and autumn (not shown) and is limited to a single country, it is very unlikely that climatic factors would play a role here; it is rather a manifestation of a data problem (inhomogeneity) at German stations. The procedure for calculation of mean daily temperature was changed in Germany in March 2001 from the calculation from three observation times to the hourly observations. The claim by Kaspar et al. (2016) that this transition did not result in inhomogeneities appears to hold for mean values, but not for some measures of variability, the behaviour of which is more complex.

A similar feature is detected in Dublin where a discrepancy in DTD series against neighbouring stations (exemplified by Armagh) starts in 1995 in all seasons (see Figure S4). On the other hand, differences in trends between close stations are not always connected with jumps in the series of variability measures, which would suggest inhomogeneity; station pairs Granada–Malaga; Kredarica–Ljubljana; and Vârful Omu–Cluj may serve as illustrative examples (see Figure S6). Trends in DTD differ between the two stations in each pair, but there are no clear breaks in the time series of their differences. This indicates that local and regional climate-forming factors such as the elevation and orography may also play a role in the strength and even direction of trends of DTD and/or LAG.

4.5 Correlations between trends in variability measures

The trends differ considerably between individual variability measures since they describe different aspects of variability, as discussed in section 2. To provide a deeper insight into this issue, we correlate trend values between variability measures and also of the variability measures with the mean.

We begin with correlation of DTD with SD (Figure 11). The correlations when taken over the whole of Europe are positive, ranging from 0.52 in autumn to 0.68 in winter. Positive are also correlations over all domains in all seasons (with two exceptions: central Europe in spring and autumn manifesting weak negative correlations), however, with large spatial and temporal variations. This suggests that trends in DTD are related to trends in SD (a decrease in day-to-day change contributes to a decrease in variability, and hence to a lower standard deviation), but to a different degree in different domains and different seasons. The strongest correlations are revealed in northern Europe in all seasons; decreases in DTD are accompanied by decreases in SD of similar relative magnitude there as is suggested by the slope of the regression lines, which is close to 1:1. In most other cases, correlations are lower and relative trends in SD are smaller than trends in DTD, which suggests that factors other than decreasing variance contribute to declining day-to-day variations (and analogously for increases). So, additional factors contributing to trends in DTD appear to play a role where correlations are low.

Figure 12 indicates that trends in temperature persistence, that is, LAG, is the other factor contributing to trends in DTD. Increasing SD and/or increasing LAG (we recall that LAG is defined as autocorrelation coefficient with reversed sign in order that high values of all measures indicate high variability) both result in increasing DTD, whereas opposing trends in SD and LAG would tend to cancel each other, resulting in only a small or no trend in DTD. Correlations of trends in SD and LAG are weak in all domains and seasons (Figure S6), indicating that they are almost independent of each other. Therefore, one can expect trends in DTD to be positively correlated with trends in LAG; Figure 12 confirms this is indeed the case. Trends in LAG and trends in SD appear to be complementary in their association to trends in DTD: where the correlations and regression slopes between DTD and SD are high, those between DTD and LAG are low (e.g., northern Europe), and vice versa (e.g., western, central and eastern Europe). That is, DTD decreases in northern Europe are largely due to decreases in overall temperature variability, whereas in the rest of Europe, changing temperature persistence is an important factor (or even the more important factor) of trends in DTD.

We are also interested in the relationship between trend in temperature variability and trend in mean temperature. In that case, correlations are rather negative (Figure 13). That is, the more the temperature rises the more its variability decreases (or the less it increases). This is particularly true for winter when this relationship is significantly negative in entire Europe and most domains. However, the correlations vary among variability measures. While in northern and eastern Europe, temperature rise correlates with trends in SD and DTD and not in LAG, in western and central Europe it correlates with trends in LAG and DTD but not in SD. This again demonstrates that SD and LAG have no relationship with each other and as a result, the temperature rise is most correlated with trend in DTD. In other seasons, statistically significant correlations can rarely be found, but in spring and autumn similar features appear in northern and eastern Europe as in winter.

Since both SD and IQR quantify spread of a distribution, their trends are highly similar (Figure 14): For entire Europe as well as for all domains, correlations are strong and exceed 0.8 (except for western and southern Europe in winter). Slight differences between SD and IQR may point to differences in higher-order moments (skewness, kurtosis) and to differences in distribution tails. Therefore, we focus on the direction of notional regression line and deviations from the diagonal in Figure 14. It is evident that increases of SD are often accompanied by even higher increases of IQR. This is most apparent in summer for stations in eastern and western Europe and in the Baltic. This indicates that increases in variance project more into the tails of a temperature distribution than into its centre. Decreases in SD and IQR are almost identical in spring and winter, particularly in northern Europe where the decreases are strongest. In contrast, decreases in SD are larger than decreases in IQR at stations with strong declines in variability in autumn. In summer, stations in northern Europe are located to the right from the diagonal, which points to a tendency for trends in IQR to be more positive than trends in SD. This effect is particularly strong in Hopen where IQR has risen by 4%·decade⁻¹, while SD only by 1%·decade⁻¹.

The differential behaviour of SD and IQR trends is examined in more detail in Figure 15 by the comparison of probability density functions of mean daily temperature anomalies (from the respective station average) between three consecutive periods (1961–1979, 1980–1998 and 1999–2017) at selected stations indicated in Figure 14. Relative frequencies are calculated based on counts of temperature anomalies, using a bin width of 1°C. We delimit the estimates of probability density functions at their tails by including only bins with at least 1% probability.

Hopen in summer (Figure 15, top) is an example of trends in IQR being more positive or less negative than in SD in northern Europe. The distribution became more asymmetric, with heavier left tail and median shifted to the right in the most recent period. Q10 is much more negative in the most recent period while Q90 did not change much, resulting in an increase in IQR but a little change in SD. Vestervig in summer (Figure 15, second from top) is one of the few cases where a large increase in IQR than SD is caused by the increase of probability at both tails of the distribution; the change occurred between the first and second period in the cold tail, while between the second and third period in the warm tail. București in summer (Figure 15, middle) is another example of faster increases in IQR than SD; a decrease in kurtosis appears to be the cause here. The distribution flattened in the most recent period, Q10 and Q90 having shifted towards extremes. The dramatic decrease of variability at the northernmost stations in winter is evident in the temperature distribution at Bjørnøya (Figure 15, second from bottom). The decrease is the same for SD and IQR (both around −12%·decade⁻¹) because the change in probability occurs proportionally in all parts of the distribution. The narrower upper part of the distribution in the most recent period is what causes a larger decrease of SD than IQR in Bjørnøya in autumn (Figure 15, bottom). The interesting feature of this case is the reversal of the skewness from negative to positive. This means that while the peak of the distribution remains almost the same (if the change in average temperature is considered, that is, when the dashed line for 1961–1979 is compared to the dotted line for 1999–2017), the mean has increased by 2°C. Our results point to the fact that the difference between trends in SD and IQR may result from different causes, which vary regionally and during year. Even a simultaneous use of several variability measures may not be sufficient to uncover these causes.

5 DISCUSSION

Our results show that Europe experienced a considerable decrease of intraseasonal variability in spring, autumn and winter and its slight increase in summer. While the summer increase of variability was previously revealed worldwide (Hansen et al., 2012) and in Europe on both the interannual (Scherrer et al., 2005; Della-Marta et al., 2007) and intraseasonal (Matiu et al., 2016; McKinnon et al., 2016) scales, we are not aware of any study that would detect such noticeable decreases (trends reaching far below −5%·decade⁻¹) in the rest of year, not even in northern Europe, where the declines are strongest. Matiu et al. (2016) reveal a decrease of SD in winter in 1933–2012 (but an increase in 1973–2012) and Rebetez (2001) detects a decrease of winter SD of 0.02°C·decade⁻¹ (which corresponds to about −0.4%·decade⁻¹) at the station of Neuchatel. Focusing on northern midlatitudes, Screen (2014) and Collow et al. (2019) explain the reduction in temperature variability by a weakened latitudinal temperature gradient caused by Arctic amplification, which results in reduced variability of meridional temperature advection. Furthermore, LaJoie and DelSole (2016) show that temperature variance decreases in regions with newly exposed water after sea ice melting because of its larger heat capacity. The connection of reduced variability with the intensification of North Atlantic Oscillation in the second half of the twentieth century (Delworth et al., 2016; Iles and Hegerl, 2017) is also presumable as its positive phase strengthens warm advection from the North Atlantic and reduces variability by making cold intrusions from north and east less frequent and weaker. All this is in good agreement with our finding that the largest decline in variability in all seasons except summer is detected in northern Europe, the Baltic, and eastern Europe. Moreover, similar spatial features were revealed in Rhines et al. (2017) for North America in winter.

Although Moberg et al. (2000) conclude that SD is a good representative measure for intraseasonal variability, correlated well with all other measures, our results suggest that it is beneficial to use multiple variability measures as recommended by Astatkie et al. (2003) and not to confine oneself only to standard deviation. Different measures represent different aspects of variability, which is reflected in relatively different spatial distributions of trends. Our analysis reveals that the decrease in variability in eastern Europe is related to a change in persistence and not to a change in temperature distributions. This is in a good agreement with Zhang et al. (2012) who revealed an increase in persistence of anticyclonic activity over Eurasia. Our results further suggest that inconsistent trends between SD or IQR on one hand and DTD or LAG on the other hand across domains in central and western Europe are likely due to inhomogeneities that appear to only project into DTD and LAG series. This confirms the statement of Moberg et al. (2000) that the absolute change of daily temperature from 1 day to the next is particularly sensitive to changes in observational procedures and may serve as a diagnostic tool in searching for discontinuities in the series.

Although these are very similar measures, discrepancies were revealed between trends of SD and IQR as well, similarly to Matiu et al. (2016): IQR usually grows faster than SD, thus enhancing the probability of extremes. However, our investigations of probability density functions show that although there are many variations of how temperature distributions and thus IQR and SD change, the shift of distributions to the right in the direction of the trend in mean temperature is dramatically more conspicuous so that we cannot confirm claims of Katz and Brown (1992) and Fischer et al. (2012) that increasing variability contributes to the occurrence of extremes equally or even more than a change in mean temperature.

6 CONCLUSIONS

This study is, to our knowledge, the first to investigate trends in various types of variability measures (standard deviation of temperature, interquantile range, day-to-day temperature change, and temporal autocorrelation), on an intraseasonal time scale and on a continental (European) spatial scale. It helps us to better paint the entire picture of changing variability, reflecting not only the width of temperature distributions (i.e., variance-based changes), but also temporal variability (changes related to temperature non-stationarity). Furthermore, a relatively detailed scale of the study (168 climate stations) allows us to answer the question of how the variability measures have changed in various domains of Europe.

Trends in temperature variability, as well as trends in mean temperature, differ both spatially and between seasons. Substantial regional and seasonal differences suggest that the variability is changing in connection with synoptic to local conditions, making impossible to draw a general conclusion about the evolution of global and annual variability.

We have revealed a considerable decrease in variability in the northern part of Europe in winter, spring and autumn. Thus, one can certainly look for a connection with Arctic amplification, which has been discussed essentially in current literature (e.g., Walsh, 2014). This is indicated in our results by close link between the decrease in variability measures and the increase in mean temperature in northern Europe, eastern Europe and Baltic. More stable conditions coming to these parts of Europe in winter can thus be considered as one of the few positive consequences of climate change.

The correlation analysis between the variability measures allows us to deduce whether the trend in the day-to-day change is produced more by a trend in standard deviation (strong correlation between DTD and SD) or by a change in persistence (strong correlation between DTD and LAG), with both variants having opposite effect on occurrence of climate extremes. Decreasing DTD correlated more with LAG leads to an increase in the likelihood of extremes due to the increasing persistence (e.g., eastern Europe in winter) while decreasing DTD correlated more with SD leads to less extremes due to the decreasing variance (e.g., northern Europe in winter. A closer look at the winter trend in IQR (not shown in our results) disclosed that Q10 is usually growing faster than Q90, which was revealed in Rhines et al., 2017 as well, which further reduces the likelihood of cold extremes.

The only season when the rise of variability prevails in Europe is summer, and only for SD and IQR. Considerable increases were revealed particularly between 45 and 55 N. The widening of the temperature distribution and unchanged or increasing persistence may contribute to the increased frequency of extremes here.

Our study exposed not only the real trends in variability but also those resulting from data issues, such as inhomogeneities in temperature series. To separate them is a difficult task and requires additional analyses, such as comparison of individual time series. A simultaneous analysis of various types of data sources, including gridded data and reanalyses, may facilitate the identification of artificial trends: we plan such an extended analysis, similar to our previous study of temperature trends (Krauskopf and Huth, 2020) as the next step in our research. Some of the data issues, including inhomogeneities, may be caused by changes (both temporal and spatial) in the definition of daily mean temperature. This can be circumvented by the evaluation of trends in minimum and maximum temperature, which in addition would distinguish the evolution of variability between day and night. This is also planned for our future research.

AUTHOR CONTRIBUTIONS

Tomáš Krauskopf: Conceptualization; data curation; funding acquisition; methodology; project administration; resources; software; visualization; writing – original draft. Radan Huth: Conceptualization; formal analysis; funding acquisition; methodology; project administration; supervision; validation; writing – review and editing.