Trends in compound extremes of air temperature and precipitation in Eastern Europe


 The spatial distribution of compound extremes of air temperature and precipitation was studied over the territory of Eastern Europe for the period 1950–2018 during winter and spring. Using daily data on air temperature and precipitation, we calculated the frequency and trends of the four indices – cold/dry, cold/wet, warm/dry and warm/wet. Also, we studying the connection between these indices and large-scale processes in the ocean-atmosphere system such as North Atlantic Oscillation, East Atlantic Oscillation and Scandinavian Oscillation. The results have shown that positive trends in the region are typical of the combinations with the temperatures above the 75th percentile, i.e., the warm extremes in winter and spring. Negative trends were obtained for the cold extremes. Statistically significant increase in the number of days with warm extremes was observed in the northern parts of the region in winter and spring. The analysis of the impacts of the large-scale processes in oceans-atmosphere system showed that the North Atlantic Oscillation index has a strong positive and statistically significant correlation with the warm indices of compound extremes in the northern part of Eastern Europe in winter, while the Scandinavian Oscillation shows the opposite picture.


Introduction
Simultaneous or consecutive occurrence of several extreme phenomena (events) in climatology is referred to as complex extreme phenomena (events). Over the last decade, these events have been attracting the attention of the academic community due to their increased impacts on nature and society (Zscheischler et al. 2018;Seneviratne et al. 2012;Trenberth et al. 2014;Beniston et al. 2007;AghaKouchak et al. 2020, etc). Extreme precipitation and temperature values, which are two of the key variables in climatology and hydrology, are multidimensional phenomena, and they can occur at different periods (e.g. blocking anticyclones with droughts and heatwaves) (Röthlisberger 2019;Zscheischler 2020). It is crucial to understand various types of compound precipitation types and extreme temperatures to develop proper strategies for reducing the potential impacts on society and ecosystems. Changes in temperature and precipitation are often physically linked. Droughts and heatwaves 2003in Europe, in 2010in Russia, and 2012-2014 in California featured extreme events in terms of temperature and precipitation (the lack of thereof) that resulted in signi cant casualties and economic effects (Fink et al. 2004;Barriopedro 2011;Trenberth and Fasullo 2012;Horton et al. 2016;Diffenbaugh et al. 2015). Extreme precipitation and temperature values are considered independently using monodimensional statistical methods (Cooley et al. 2007;Katz 2010;AghaKouchak and Nasrollahi 2010;Zhang et al 2011;Alexander 2016). There are several approaches to the analysis of compound extremes . The statistical methods include the following: empirical, multivariate distribution (Estrella and Menzel 2013;Schöelzel and Friederichs 2008, for instance), indicator approach (Gallant et al. 2014), quantile regression (Quesada 2012), and Markov chain model (Shaby et al. 2016) . The empirical approach to the analysis of compound extremes is manifested in the calculation of the number of simultaneous or consecutive occurrences of several extremes. Beniston (2009) suggested using the combination of air temperature and precipitation values exceeding the set thresholds (the 25th and 75th percentiles) in the empirical analysis of compound extremes. The joint distribution of the two weather variables like the temperature and the precipitation is a rational indicator of weather conditions and their stability (Beniston and Goyette 2007;Beniston et al. 2011). Joint distributions re ect weather conditions better than the statistics for the temperature or precipitation alone (Beniston et al. 2011;Zscheischler et al. 2018). Trenberth and Shea (2005) discovered a strong negative correlation between the monthly average temperature and the precipitation rates over continents in the summer in both of the hemispheres. This correlation changes to the opposite inland at high latitudes in winter. Long-term trends for joint quantiles of air temperature and precipitation rates for European cities with different climates (Mediterranean, coastal, and continental) since 1901, as well as their possible changes by the end of the 21st century, were analyzed in the research work by Beniston (2009). Gallant and Karoly (2010) studied the changes in air temperatures and extreme precipitations over Australia using two combined indices and discovered the increase in extreme heat and humidity and the reduction of extreme cold and droughts in all of the seasons throughout the 20th century. Similar research was carried out for other regions, such as North America (Tencer et al. 2014;Martin and Germain 2017;, China (Wu et al. 2019), India (Dash and Maity 2021), Europe (Morán-Tejeda et al. 2013;Arsenovic et al. 2015, Malinovic-Miliceviс et al. 2016Sedlmeier et al. 2018), and on the global scale (Hao et al. 2013).
The purpose of this research work is to analyze compound extremes of air temperature and precipitation based on the reanalysis of E-obs data for 1950-2018 in Eastern Europe, as well as studying the connection between these indices and large-scale processes in the ocean-atmosphere system.

Material And Methods
In this work, the authors used the data on daily average air temperature and precipitation amounts over the period of 1950-2018 in Eastern Europe (Central and North-Eastern Europe). The data were retrieved from the reanalysis of E-obs 20.0 (with a spatial resolution of 0.25*0.25°) (Haylock et al. 2008). The study region is located within the following coordinates: 25-45° east longitude, 42-61° north latitude. The quality control of the initial data was done. The data availability maps for the region were constructed.
There is enough data on the air temperature and precipitation rates in the region, the amount of data in Eobs reanalysis mesh points over 1950-2018 is over 80% for the study region.
To characterize compound extremes, combined air temperature and precipitation indices were used (Beniston 2009). The cold/wet (CW) index was calculated as a combination of the number of days with the average temperature below the 25th percentile (T25) and the daily precipitation amount higher than the 75th percentile (R75) at the same time. The same procedures were applied to calculate other indices combining the cold/wet parameters, such as the cold/dry days (CD -Т25/R25), warm/dry days (WD -Т75/R25), and warm/wet days (WW -Т75/R75). This research work does not use so-called extreme percentiles (25th and 75th ) to identify a large number of compound extreme events for air temperature and precipitation (Beniston 2009).
The threshold values for air temperature and precipitation were calculated for each of the seasons over the basic climate period of 1961-1990. The compound temperature and precipitation extreme was identi ed if the speci c extremes occurred on the same day in 1950-2018. After that, the total number of such coincidences per month/season/year was counted. It should be noted that the precipitation percentiles were calculated for the series of days in question if the precipitation exceeded 1 mm. Calculations were performed for winter and spring. Summer and autumn seasons did not consider due to the low precipitation during these seasons. Spring corresponds to March, April, and May (MAM) of the current year, while winter stands for January and February of the current year, and December of the previous year.
To analyze the correlations between the compound extreme indices and circulation modes, the North Atlantic Oscillation (NAO), East Atlantic Oscillation (EA), and Scandinavian Oscillation (SKA) over the period of 1950-2018 were used. The indices were taken from the Climate Explorer website (https://climexp.knmi.nl).
The values of linear trend coe cients were determined using the least-squares method. The nonparametric test of Mann-Kendall was used to obtain the statistical signi cance of trends (with a signi cance level of 95%). To identify the correlations between air temperature and precipitation, compound extreme indices, and circulation modes, the Pearson's correlation coe cient was calculated and obtained its statistical signi cance using Student's criterion (95% signi cance).

The occurrence rates of temperature and precipitation combinations
The average number of CD (cold/dry) days in winter for the study region is 1-3 days a year ( Fig. 1, left). The number increases to 4 days on the eastern coast of the Black Sea (the Black Sea coast of the Caucasus). The CW (cold/wet) combination occurred up to 1-2 days a year in the entire region, except the Caucasus (up to 5 days a year). The WD (warm/dry) combination amounts to 2-3 days a year up to the 52nd parallel, while northwards it increases to 3-4 days a year. The WW (warm/wet) days are the most numerous in the region during winter. For the south of European Russia, eastern and Northern Ukraine, and Belarus, the number increases to 5 days a year, and in the north of the study region, this number of days with this index is 7-8 per year.
The number of days per year with the compound air temperature and precipitation extremes in spring is lower than in winter (Fig. 1, right). All of the indices occur 1-3 days a year. The CD index occurs more frequently in the Caucasus (up to 5 days a year), the CW index is often observed on the eastern coast of the Black Sea (up to 5 days a year), and the WW index occurs in the northern parts of the region. Fig. 1 The spatial distribution of average days with compound air temperature and precipitation extremes over the period of 1950-2018 in winter (left) and spring (right) The repeatability of compound extremes can be partially attributed to the correlations between precipitation and temperatures. The spatial distribution of correlation coe cients for the air temperature and precipitation over the period of 1950-2018 is shown in Fig. 2. In winter, the positive (statistically signi cant) correlation is typical of the Crimean Peninsula, the south of European Russia (excluding the North Caucasus), the southeast regions of Ukraine, and all of the region to the north of the 54th parallel (Fig. 2a). A negative statistically signi cant correlation between the air temperature and precipitation rates can be observed on the western coast of the Black Sea (in Romania, Ukraine, and Moldova).
In spring, the study region shows a negative correlation between air temperatures and precipitation.
Statistically signi cant negative coe cients are observed in the southeast of the Crimean Peninsula (the Crimean Mountains), Bulgaria, and the northeast of the region. The positive statistically signi cant correlation (p<0.05) was observed on the eastern coast of the Black Sea, in the south of Belarus, and the parts of Russia bordering the Baltic states (Fig. 2b).
The frequency distribution of the WW combination corresponds to the distribution of correlation coe cients of the air temperature and precipitation rates during winter.

Compound extreme indices trends
The CD index mainly features negative trends across the region during winters (Fig. 3, left). Positive trends are observed on the western coast of the Black Sea, yet they are not statistically signi cant.
Compound extremes combining cold and wet conditions (СW) show a statistically signi cant increase in the number of days in central Ukraine, as well as negative trends on the eastern coast of the Black Sea near the Caucasus featuring the greatest negatives of up between -0.7 and -0.8 days /10 years. The linear trends for the wet/dry extreme combination are inhomogeneous. In the north of the region, there is a positive trend with statistically signi cant values observed in Belarus, Estonia, and some parts of Russia.
The statistically signi cant increase in the WW index is observed throughout the entire region north of the 50th parallel (up to +1 days in 10 years). Negative trends were found near the Caucasus.
The distribution of trends for this index during spring is similar to the winter one, yet the trend values are smaller (Fig. 3, right). The CD index mainly features negative trends across the entire region. The statistically signi cant reduction of compound extremes is observed in the North Caucasus, eastern Ukraine, and some parts of Russia. A statistically signi cant reduction of CW extremes is observed near the Caucasus (up to -0.9 days/10 years). The WD demonstrates a mixed structure in the distribution of linear trend coe cients. The trends for the extremes combining high temperatures and heavy precipitation are positive in the center of the region (they are also statistically signi cant).

Correlation of compound indices and large-scale processes
The European climate is in uenced by large-scale processes in the oceans and atmosphere, such as the North Atlantic Oscillation, East Atlantic Oscillation, etc. The impacts of these signals were covered by many researchers from different regions of the world (Hurrell 1995;Nesterov 2009 For each of the seasons, we took the season average value of the large-scale signals (NAO, EA, and SKA) and calculated the winter and spring indices. After that, we calculated Pearson's correlation coe cient for the compound extreme indices and the winter and spring signal indices.
The correlation analysis of the compound extreme indices and the NAO index in winter produced the following results (Fig. 4, left). Negative correlations were found between the NAO index and the "cold" CD and CW indices across the region and the 95% statistically signi cant indices in Belarus, Eastern Ukraine, and the Black Earth Regions. The warm indices (WD and WW) showed a statistically signi cant positive correlation (up to 0.8) with the winter NAO index above the 50th parallel. A negative correlation was observed between the WW and the NAO indices in the North Caucasus and the Caucasus ridge (up to -0.8).
The correlation between the CD index and the winter EA index is negative throughout the region with little statistically signi cant areas (Fig. 4, center). The CW index features a mainly positive correlation with the EA index above the 50th parallel, while on the Black Sea coast of the Caucasus the correlation is negative (and statistically signi cant). The warm compound extreme indices (WD and WW) have a positive correlation with the winter EA index throughout almost the entire region. The WW index features a statistically signi cant correlation in Belarus, the Baltic, and the northern part of European Russia.
The correlation between the cold indices of CD and CW and the winter SKA index is quite heterogeneous (Fig. 4, right). There are areas with a positive statistically signi cant correlation on the western coast of the Black Sea (Bulgaria, Romania, Moldova, and a part of Ukraine), as well as in the north of the region.
The warm indices (WD and WW) feature a largely negative correlation with the winter SKA index with statistically signi cant values in the north of the region. The spring is characterized by the following results (Fig. 5). Cold indices demonstrate a negative correlation with the spring NAO index throughout almost the entire region. For the CD index, positive correlation coe cients were observed near the Caucasus, and in eastern Ukraine for the CW index. The compound extreme WW index and the NAO index have a statistically signi cant correlation in Belarus, Bulgaria, and some parts of Russia.
The correlation between the CD index and the spring EA index is negative throughout the region with statistically signi cant values west of the 36th degree. The CW index has a positive correlation with the EA index in the left-bank region of Ukraine and the northeast of the region. Negative correlation coe cients were found in Romania and Moldova. The WW index is characterized by the positive values of the correlation coe cient across the region with large areas of statistically signi cant values.
Ukraine, Belarus, as well as the western and eastern coasts of the Black Sea, are characterized by positive correlation coe cients for the spring CD and the spring SKA indices. A negative (statistically signi cant) correlation between the CW index and the spring SKA index was observed in the southeast of Ukraine, and a positive correlation was observed in central Ukraine. The WW index features a largely negative correlation across the entire region with the areas of statistically signi cant correlation coe cients in the center and the east of the region.
The distribution of the correlation coe cient between the WD index and the spring indices of large-scale circulation is characterized by great spatial heterogeneity.

Discussion And Conclusions
The overall increase in the frequency and intensity of extreme events associated with air temperature and precipitation requires that this problem should be studied in more detail . Extensive research on the extreme trends in air temperatures and precipitation rates in the study region has been conducted. They include the data on Russia (Vyshkvarkova 2021;Aleshina et al. 2018;Aleshina et al. 2021), Georgia (Keggenhoff et al. 2014), the western coast of the Black Sea (Croitoru et al. 2013;2016), Ukraine (Boychenko et al. 2016), etc. The research works differ in the methods used and the observation period. However, the key outcome of the majority of works is a statistically signi cant increase in the air temperature and its extreme values, as well as the heterogeneous precipitation values (Cardell et al. 2020).
We used the empirical approach to de ne the joint extremes of air temperature and precipitation and analyze their spatial and temporal distribution over 1950-2018 in Eastern Europe. We evaluated the occurrence frequency and trends typical of compound extremes in winter and spring. Positive trends in the region are typical of the combinations with the temperatures above the 75th percentile, i.e., the warm extremes in winter and spring. Negative trends were obtained for the CD and CW indices (cold extremes). Statistically signi cant increase in the number of days with warm extremes was observed in the northern parts of the region in winter and spring.
The results obtained correlate with those obtained previously by other researchers. The compound extremes in European countries and regions show that the warm combinations (warm/dry and warm/wet) are growing while the cold combinations are decreasing (Beniston 2009;Morán-Tejeda et al. 2013). Aleshina et al. (2021) used the data from observations and ERA5 reanalysis to demonstrate that the 95th percentile precipitation increases against the growth of temperatures in winter all over Russia.
Global research (Hao et al. 2013) based on the CRU data also showed the increase in WD and WW extremes in Russia in the second half of the 20th century. The comparison of compound extremes produced using the CRU data and CMIP5 project models showed correlation, which allows for the further use of the CMIP project results for global climate modeling to assess any possible changes in compound extremes in the future. According to IPCC experts, the occurrence rates and intensity of extremes associated with air temperature and precipitation will increase in the future (IPCC 2014). The analysis performed using various models and scenarios for the European regions con rms this claim (Khlebnikova et al. 2019;Kjellström et al. 2018). The growth of hydrological extremes is predicted in Great Britain by the end of the 21st century (Visser-Quinn et al. 2019), for instance.
The increase in the occurrence rates of the extremes combining high temperature and a lack of precipitation may result in droughts similar to the weather conditions observed in Russia and Central Europe in 2010, 2015, and 2021. Such conditions may provoke forest res (AghaKouchak et al. 2020) and aggravate their effects, e.g., the smog and air pollution. Positive trends for the WW combination can be attributed to the intensi cation of cyclonic activity and, as a result, they result in heavy rains and oods. These may include the ood in Krymsk (Krasnodar Territory) of 2015 when 2-5 monthly rainfall fell over a short period, the ooding of the cities on the Black Sea coast of the Caucasus and the east of Crimean Peninsula in 2021, and the 2021 oods in Germany. This kind of research remains vital and requires further efforts due to the ongoing climate change.
We used the NAO, EA, and SKA indices as circulation modes. According to various authors, they impact the air temperatures and precipitation rates in Eastern Europe (Zubiate et al. 2017;Tsanis and Tapoglou 2019;Cio et al. 2015;Mikhailova and Yurovsky 2016, etc). The analysis of the impacts of the largescale processes in oceans-atmosphere system showed that the NAO index has a strong positive and statistically signi cant correlation with the WD and WW indices of compound extremes in the northern part of Eastern Europe in winter. The correlation with the EA index is similar but its correlation coe cients are smaller. The Scandinavian oscillation features the opposite: there is a negative correlation in the north of the region. The results for spring are less straightforward. The circulation types change and cyclone paths shift during various signal phases, which impacts the occurrence and distribution of compound extremes of air temperatures and precipitation in the Eastern Europe region.
The changes observed in the occurrence and frequency of compound extremes are affecting and shall continue affecting various areas of life including healthcare, agriculture, transportation, infrastructure, power industry, etc. The results obtained can be used to develop adaptations to climate changes, compound extremes in particular.

Declarations Funding
The study was supported by state assignment of Institute of natural and technical systems (Project Reg. No. АААА-А19-119031490078-9).
Competing Interests Figure 1 The spatial distribution of average days with compound air temperature and precipitation extremes over the period of 1950-2018 in winter (left) and spring (right) Figure 2 The spatial distribution of Pearson's correlation coe cients for the air temperature and precipitation in winter (a) and spring (b) throughout 1950-2018. Statistically signi cant correlation coe cients (p<0.05) are shown as black dots The spatial distribution of correlation coe cients for compound extreme indices and atmospheric circulation signals in winter. Statistically signi cant correlation coe cients (p<0.05) are shown as black dots Figure 5 The spatial distribution of correlation coe cients for compound extreme indices and atmospheric circulation signals in spring. Statistically signi cant correlation coe cients (p<0.05) are shown as black dots