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Article

Evaluation of the Spatio-Temporal Variation of Extreme Cold Events in Southeastern Europe Using an Intensity–Duration Model and Excess Cold Factor Severity Index

by
Krastina Malcheva
*,
Neyko Neykov
,
Lilia Bocheva
,
Anastasiya Stoycheva
and
Nadya Neykova
National Institute of Meteorology and Hydrology, 1784 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
Atmosphere 2025, 16(3), 313; https://doi.org/10.3390/atmos16030313
Submission received: 30 January 2025 / Revised: 22 February 2025 / Accepted: 6 March 2025 / Published: 9 March 2025
(This article belongs to the Special Issue Weather and Climate Extremes: Observations, Modeling, and Impacts (2nd Edition))
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Abstract

Recent studies have revealed a rise in extreme heat events worldwide, while extreme cold has reduced. It is highly likely that human-induced climate forcing will double the risk of exceptionally severe heat waves by the end of the century. Although extreme heat is expected to have more significant socioeconomic impacts than cold extremes, the latter contributes to a wide range of adverse effects on the environment, various economic sectors and human health. The present research aims to evaluate the contemporary spatio-temporal variations of extreme cold events in Southeastern Europe through the intensity–duration cold spell model developed for quantitative assessment of cold weather in Bulgaria. We defined and analyzed the suitability of three indicators, based on minimum temperature thresholds, for evaluating the severity of extreme cold in the period 1961–2020 across the Köppen–Geiger climate zones, using daily temperature data from 70 selected meteorological stations. All indicators show a statistically significant decreasing trend for the Cfb and Dfb climate zones. The proposed intensity–duration model demonstrated good spatio-temporal conformity with the Excess Cold Factor (ECF) severity index in classifying and estimating the severity of extreme cold events on a yearly basis.

1. Introduction

Over millions of years, the climate system behavior has been dominated by natural fluctuations at different time scales, but during the last 150 years, anthropogenic forcing has substantially influenced natural variability [1,2]. In the context of climate change scenarios, an increase in global temperature of 2 °C compared to the pre-industrial period is considered an upper limit above which the risk of dangerous and irreversible climate shifts increases sharply [3,4,5]. Given that the rise in global temperature has already exceeded half of this limit, it can be crossed in the next 20–30 years [1,6,7]. Heat and cold waves are among the most impactful large-scale natural phenomena strongly related to climate change. Prolonged periods of extreme temperatures cause thermal stress and may have adverse or fatal effects on human health [8,9,10]. They directly and indirectly influence labor productivity and well-being [11,12]. Extreme temperatures considerably increase the risk of energy supply outages and damage to the infrastructure [13,14]. They can even represent a limiting factor for agriculture in the changing climate due to the amplified likelihood of frosts and prolonged hot spells during the vegetation period [15,16,17].
Against the background of the expected rise in global temperatures, a decrease in cold extremes seems intuitively sound [1,18,19]. The impact of heat waves will significantly exceed those of cold waves till the end of the century. Across all studies, the authors point out the multifold increase in the duration, frequency and intensity of future extreme heat events as highly likely [1,20,21]. In Europe, since the beginning of the century, heat waves have caused more deaths than all other natural disasters [22]. Schär et al. [23] revealed that the record summer of 2003 cannot be explained by solely shifting the mean of the temperature distribution to higher temperatures but with an additional increase in variability. The changed shape of the temperature distribution contributes to the occurrence of more hot extremes but also suggests that future cold extremes cannot be inferred from changes in mean and variance alone [24,25]. In this sense, recent severe cold events in Europe, such as in 2010, 2012 and 2017, have received particular attention [26,27,28,29]. Cold extremes would still be possible in the current climate [30,31] and will continue to impact various socioeconomic sectors, particularly healthcare, due to the complex relationship between human thermal adaptation capability and warming rates. Recent studies indicate increased tolerance to hot weather and significant differences among age groups in response to cold events [10,32,33,34,35].
After the deadly European heatwave of 2003, heat extremes have become a priority topic in climate change research [36]. Despite remarkable progress in recent years and the apparent upward trend in heat wave intensity, duration, frequency and spatial extent, there is still no universally agreed definition for this phenomenon [37,38,39]. Therefore, criteria and procedures for identifying extreme heat at a national level are very diverse [40,41]. This lack of consensus also extends to cold wave definitions and warnings.
An extreme event occurs when a climate variable is above or below a defined threshold at the upper or lower end of the range of its observed values. This threshold can be calculated as an absolute (fixed) or relative (percentile-based) value [1]. Since around 60% of the national weather services that have criteria for heat/cold waves use absolute thresholds when considering heat and cold events, the World Meteorological Organization (WMO) Task Team for the Definition of Extreme Weather and Climate Events (TT-DEWCE) specified the term heatwave as unusually hot weather relative to the local climate lasting at least two consecutive days in the warmest months of the year. Similarly, cold waves denote unusually cold weather during the cold season, lasting at least two days and often preceded by a rapid and marked drop in air temperature caused by the advection of cold air [37]. These definitions allow flexibility in reporting heat/cold events when different criteria and approaches are used (from a simple descriptive approach to classification schemes based on local climatology, human perception of heat/cold stress or increased mortality risk [41]).
Extreme heat events can be quantitatively assessed by indices describing their particular characteristics [42,43,44], and similar indices can be defined analogously for extreme cold events (ECEs). Some basic requirements should be satisfied when developing indices of heat and cold extremes [45]. Generally, they should be suitable for various economic and social sectors or climates, but they should also allow comparative analysis. Indices should be easy to understand, calculate, represent and forecast. They should give the public and decision-makers direct, meaningful information on the expected severity of the heat and cold waves. The advantage of percentile-based indices is their global applicability, but fixed-threshold indices are indispensable when monitoring high or low temperatures, which negatively impact health or the economy, which is important [39]. Thresholds can be combined to define cascading schemes accounting for the spatio-temporal evolution of extreme events [46]. The rarity of heat and cold extremes should be determined relative to a standard climate period, so a balance must also be found between the threshold levels and the number of events identified as extreme [37,43].
The most popular and widely used set of climate indices consists of 27 core climate change indices (17 temperature-based) developed by the WMO Expert Team on Climate Change Detection and Indices (ETCCDI), initially designed for scientific purposes (http://etccdi.pacificclimate.org/list_27_indices.shtml) (accessed on 28 January 2025). Subsequently, the WMO Expert Team on Sector-specific Climate Indices (ET-SCI) expanded this list to include custom-defined threshold indices and new heat/cold wave indices based on definitions accounting for excessive heat/cold accumulation and short-term thermal acclimatization (https://climpact-sci.org/indices) (accessed on 28 January 2025). In recent years, there has been growing attention to indices based on health-related definitions, particularly for early warning purposes in large cities [41,47,48].
The region around the Mediterranean basin, including Southeastern Europe, is among the most vulnerable to climate change, experiencing more frequent and intense severe weather events and heat extremes [1,49,50,51]. Besides heat waves, cold events have also been the subject of various regional studies in recent decades. Tringa et al. [52] conducted an extensive climatological and synoptic analysis of winter cold spells in the Balkan Peninsula from 1961 to 2019. They found a decreasing trend in the frequency of cold spells toward the end of that period. Planchon et al. [27] performed a multi-scale agroclimatic analysis for Romanian vineyards in the meteorological context of the early 2012 European cold wave. Demirtaş [28] analyzed the anomalously cold January 2017 in Southeastern Europe through the connection between cold spells and atmospheric blocking using an objective cold wave indicator and a two-dimensional blocking indicator. Kostopoulou [53] investigated the potential effects of the January 2017 cold spell on mortality attributed to cardiovascular disease. Faranda et al. [54] conducted an attribution study on the winter storm Filomena in 2021, marked by historic snowfalls in the inland regions of the Iberian Peninsula and a prolonged 14-day cold spell. Kysely et al. [55] demonstrated that cold stress significantly impacts mortality in Central Europe, representing a public health threat comparable to that posed by heat waves. Díaz-Poso et al. [56] analyzed climate change scenarios using simulations from the EURO-CORDEX project, applying the ECF index for the Iberian Peninsula and the Balearic Islands. Their results indicated that despite the expected decrease in cold waves, they would continue to pose a serious local threat due to the population’s acclimatization to higher temperatures. Piticar et al. [57] found substantial changes in the indices of excess heat/cold factor and concluded that heat waves have become more frequent, longer and more intense, while cold waves have become less frequent but more intense in Romania.
Although the cold spells are typical for the cold season in Southeastern Europe, the research on their spatio-temporal changes has been somewhat neglected compared to the extreme heat. The main objective of our study is to evaluate the contemporary spatio-temporal variations of extreme cold events through the intensity–duration model of cold spells, developed for quantitative assessment of cold weather in Bulgaria. The study can be viewed as continuing the previous research on spatio-temporal variations of hot spells in Southeastern Europe [58]. We use the same methodology and datasets to investigate the changes in the prolonged retention of cold weather in the period 1961–2020. Three threshold indicators based on daily minimum temperature, presenting the unfavorable thermal conditions during the year, the cold weather persistence and the cold spell intensity duration combined characteristics in seven categories are analyzed and summarized by zones of the Köppen–Geiger climate classification. Given the increased mortality risk, agricultural losses and disruptions in the energy supply associated with prolonged cold weather and extremely low temperatures, we examined the effectiveness of the proposed intensity–duration model in classifying extreme cold events by comparing the cold spell categories with the levels of the ECF severity index on a yearly basis. To our knowledge, such a survey using solely threshold indicators to quantitatively evaluate various aspects of extreme cold events in the region has not been conducted till now. The proposed indicators could also be helpful in sector-specific climate assessments.
The rest of the paper is organized as follows: Section 2 describes the data sources and presents a detailed methodology, Section 3 presents and discusses the results, and Section 4 provides concluding remarks.

2. Data and Methods

We consider the same domain over Southeastern Europe (SEE), with coordinates 35° N–50° N and 15° E–30° E (the red frame in Figure 1), as in the previous study [58]. This area almost entirely falls within the Mediterranean region, as defined by the Mediterranean Experts on Climate and Environmental Change (MedECC) [59]. The European part of the Mediterranean region primarily belongs to the temperate climate zone. According to the Köppen–Geiger classification [60], the region includes an extensive area of temperate climates with no dry hot/warm summers (Cfa/Cfb), as well as areas of Mediterranean climates with dry hot/warm summers (Csa/Csb) in the south and continental climates with hot/warm/cold summers (Dfa/Dfb/Dfc) in the north [61].
The same dataset, developed for evaluating the spatio-temporal variations of extreme heat events in the period 1961–2020 in SEE [58], is used here to investigate extreme cold events. This dataset comprises daily maximum and minimum air temperature data from 70 selected meteorological stations, covering the domain relatively evenly (Figure 1).
Data from 12 stations of the national meteorological network of Bulgaria are provided by the National Institute of Meteorology and Hydrology (NIMH). Data from stations outside Bulgaria were downloaded from three freely available sources: the European Climate Assessment and Dataset (ECA&D) project [62], the U.S. National Climatic Data Center (NCDC) Global Historical Climatology Network daily dataset (GHCNd) [63] and the U.S. National Centers for Environmental Information (NCEI) Global Surface Summary of the Day (GSOD) dataset [64]. Most stations have altitudes below 500 m and are distributed across four Köppen–Geiger climate zones [60]—Cfa (25%), Cfb (34%), Csa (21%) and Dfb (20%). The stations’ metadata are presented in Appendix A, Table A1.
We have demonstrated in the previous study the suitability of climatologically justified for Bulgaria thresholds of daily maximum temperature (32, 34, 36, 38 and 40 °C) and corresponding duration thresholds (6, 5, 4, 3 and 2 consecutive days) to classify extreme heat events in SEE. Given that the prevailing in Bulgaria Köppen’s climate subtypes (Cfa and Cfb) are almost 60% of the whole domain, we expect to obtain a sufficiently accurate picture of changes in cold extremes in the period 1961–2020 by combining thresholds for daily minimum temperature and cold spell duration, using the same dataset and methodology as in the estimation of extreme hot spells.
The threshold indicators defined in [58] were developed using statistical modeling of daily maximum air temperature data from 36 stations, including the 12 stations shown in Figure 1, representative of the non-mountainous regions in Bulgaria with at least 80 years of observations in the period 1931–2020, referred to as BG36 hereafter (stations’ metadata are presented in Appendix A, Table A2). In the present study, we strictly followed this approach and used the same meteorological stations to ensure the methodologically consistent analysis of minimum temperatures and extreme cold events. Data on daily minimum air temperature from the BG36 dataset were processed to obtain the distribution of minimum temperatures and corresponding quantiles characteristic of the climate in the country.
Data processing has been performed in several steps, graphically summarized in Figure 2: (1) construction of empirical distributions of annual minimum temperatures for 1931–1980 (the period is regarded as being less impacted by global warming [2,65,66]); (2) calculation of quantiles corresponding to return periods 2, 5, 10, 20 and 50 years by fitting the Generalized Extreme Value (GEV) distribution to data, accounting for nonstationarity of time series [67]; (3) determination of appropriate thresholds for daily minimum temperature (tn); (4) determination of cold spells duration thresholds for the period 1961–2020 at the different tn-thresholds.
Until 1980, daily minimum temperatures in the coldest months in Bulgaria (January and February) fall mainly into the range from −27.4 °C to 11 °C across the selected stations, and the absolute minima are typically between −30.8 °C and −22.5 °C. We determined the set of thresholds (−10, −12, −14, −16 and −18 °C) using the estimated 2-, 5-, 10-, 20- and 50-year return levels by the GEV model (Figure 2, middle panel). These thresholds are achievable for more than 80% of the stations. In the period 1981–2020, tn-distributions substantially shift toward higher temperatures (Figure 2, left panel). Therefore, the cold spell duration thresholds were defined for the period 1961–2020 to provide a reliable analysis of ECEs in the current climate. Cold spells typically last 2–3 days, while the 90th percentile ranges between 3 and 5 days.
Since the research considers applying threshold indicators to analyze extreme cold in a climatically diverse region like Southeastern Europe, we examined the minimum temperature characteristics across the Köppen–Geiger climate zones. First, we calculated empirical quantiles, corresponding to the return periods used here, from the time series of annual minimum temperatures (1961–2020) for all 70 stations. As seen in the left panel of Figure 3, the median values remain well below the chosen tn-thresholds (blue dots in the chart). This suggests that more frequent and longer cold spells will be detected in at least 50% of the stations, determining the proposed cold spell duration indicator as an indicator of moderate extremes [42]. The chosen thresholds are well suited for more than 70% of stations in the domain but not for stations in the Csa climate zone. The thorough analysis showed that for 2-year return periods, −5 °C is achievable in 35% of the Csa stations and 85% of all stations, while −20 °C is achievable in around 10% of stations. The right panel of Figure 3 shows the calculated percentiles of the lower tail of distributions of daily minimum temperatures by stations in the four climate zones as box-plot diagrams. It is obvious that only percentiles below the 10th one, usually used in ECE definitions, fall within the range from −20 °C to −5 °C.

2.1. Climatologically Justified Threshold Indicators

Given the obtained estimates about low temperatures in the studied domain, the cold spell duration indicator was developed based on samples from the BG36 dataset and the extended set of tn-thresholds (−5, −10, −12, −14, −16, −18 and −20 °C). The right panel in Figure 2 shows the distribution of cold spell durations at different tn-thresholds for the period 1961–2020. Duration thresholds were selected as the 90th percentile of the respective distributions: 7 days for tn ≤ −5 °C, 5 days for tn ≤ −10 °C, 4 days for thresholds of −12 °C and −14 °C and 3 days for thresholds of −16 °C and −18 °C. For cold spells with tn ≤ −20 °C, we selected a minimum duration of 2 days [37]. A recent study on cold waves in the non-mountainous regions of Bulgaria in the period 1952–2011 found that cold events, assessed using the ETCCDI Cold Spell Duration Index (CSDI), mostly last between 6 and 11 days, reaching minimum temperatures between −5 °C and −20 °C [68]. These results confirm that the proposed range of tn-thresholds and the 7-day duration threshold for lowest intensity cold spells are relevant to capturing the evolution of cold spells in the current climate.
Analogously to the hot weather indicators in [58], three climate indicators of cold weather have been defined:
  • Annual number of cold days (ncd-5)—i.e., the annual count of days when tn < −5 °C;
  • Maximum number of consecutive cold days (ccd-5)—i.e., the longest continuous calendar period when tn < −5 °C;
  • Cold spells duration at different tn-thresholds (csd-5/-10/-12/-14/-16/-18/-20)—i.e., the annual count of days when tn ≤ −5, −10, −12, −14, −16, −18 and −20 °C for at least 7, 5, 4, 4, 3, 3 and 2 consecutive days, respectively.
The first indicator represents a common measure of unfavorable cold-related conditions during the year. The second indicator delineates the upper bound of the cold weather persistence. The third indicator allows combined (intensity–duration) evaluation of ECEs in seven severity categories (very low/low/moderate/elevated/high/very high/extreme). The technology for the calculation of the csd indicator allows the separation of events and the analysis of their temporal evolution.
The results are summarized for the SEE domain by the Köppen–Geiger climate zones. The non-parametric Mann–Kendall test [69] and Sen’s method [70] were applied to estimate the significance and magnitude of trends in proposed indicators using the R-package ‘trend’ [71].

2.2. Excess Cold Factor (ECF)

Several studies have recently analyzed extreme heat events in Europe and worldwide using the excess heat factor (EHF) that accounts for short-term acclimatization (e.g., [72,73,74,75]). This approach can be analogously applied to extreme cold events by using the excess cold factor [56,76,77,78,79]. ECF measures cold wave intensity at each location with an additional component to account for adaptation [45]. The units of excess cold are °C2 as the ECF is a factorization of two cold indices representing the degree of acclimatization to cold and the climatological significance:
ECIaccl = (Ti + Ti−1 + Ti−2)/3 − (Ti−3 + … + Ti−32)/30
ECIsig = (Ti + Ti−1 + Ti−2)/3 − T05
Ti = (Tmaxi + Tmini)/2
ECF = −ECIsig × min(−1,ECIaccl)
where Ti represents the average daily temperature for day i and T05 is the 5th percentile, calculated within the given base period (1961–1990 in this study); Tmaxi and Tmini are the maximum and minimum temperatures for day i.
ECF is negative (i.e., cold wave is in progress) when ECIsig is negative (because the three-day period is cold in an absolute sense, being below the 5th percentile for daily mean temperature), but additionally, the three-day period is substantially cooler than the preceding 30 days (ECIaccl < −1 °C). Positive values of ECF mean a cold wave are not in progress [45].
The ECF severity (ECFsev) metric permits the comparison of cold wave events and their impacts across the world and can be readily implemented within early warning systems [80]. For given day i, ECF severity is defined as follows:
ECFsevi = ECFi /ECFp15, if ECFi < 0
ECFsevi = 0, if ECFi ≥ 0
where ECFp15 denotes the 15th percentile of all negative ECF values calculated for the base period.
Nairn et al. [80] defined three levels of ECE severity:
-
L1 (low intensity), when 0 < ECFsev < 1;
-
L2 (severe),       when 1 ≤ ECFsev < 3;
-
L3 (extreme),    when 3 ≤ ECFsev.
The annual summaries of ECFsev characteristics, such as mean and maximum magnitude and maximum number of consecutive days of excess cold, were calculated by stations and presented by the Köppen–Geiger climate zones.

2.3. Software Products Used in the Research

All calculations were made using the free software environment R, version 4.4.2 [81] and RStudio 2024.09.1 [82]. The map shown in Figure 1 was prepared using QGIS Desktop 3.28.5 [83].

3. Results and Discussion

In recent years, many studies have focused on the rising temperatures in Europe since the last decades of the 20th century. Twardosz et al. [84] found that the rate of increase is almost twice as rapid from 1985 to 2020 as in the whole period after 1951 (0.027 and 0.051 °C/year, respectively). This aligns with results, stated in [58], concerning trends in annual mean temperatures in the SEE domain: 0.032 °C/year for 1961–2020 and 0.055 °C/year for 1985–2020. However, the authors conclude that the rise in temperature during the winter should be considered much less steady than in the summer. Sippel et al. [65] found that the observed rapid increase in cold-season temperatures in the late 1980s was followed by relatively modest temperature trends thereafter, which can be interpreted as a manifestation of internal variability superimposed upon the long-term warming component.
Table 1 shows the trends’ magnitude in annual mean (Ta), annual mean minimum (Tmn) and annual minimum temperatures (Tn) from 1961 to 2020, summarized by climate zones. The most significant trends were observed for Tn in the Cfb and Dfb climate zones. The larger trend magnitudes occurred mainly in the central and northern parts of the SEE domain. In contrast to Ta, showing statistically significant trends for all stations, the proportion of stations with significant trends in Tmn and Tn varies between 82% (Cfa) and 100% (Cfb) for Tmn and between 6 and7% (Cfa and Csa) and 50% (Cfb) for Tn.
Figure 4 shows a clear downward tendency in ncd-5 and ccd-5 (calculated individually by stations and averaged by climate zones) over the period 1961–2020 across all climate zones except for Csa. The trend in ncd-5 is statistically significant for 18% of Cfa stations, 88% of Cfb stations and 86% of Dfb stations; correspondingly, the changes in ccd-5 are significant for 18% of Cfa stations, 67% of Cfb stations and 43% of Dfb stations (Table 2). The average magnitude of the ncd-5 trends ranges from −3.1 days/10 years in the Dfb and Cfb climate zones to −1.5 days/10 years in the Cfa climate zone, with the most significant decline occurring in the Cfb zone (−4.5 days/10 years). The ncd-5 maxima vary between 0 and 118 days across stations, with lower values typically observed in the coastal Csa stations. Around 50% of maxima were recorded in 1963, 10% in 1985 and 6% in 1987 and 1993.
The average trend magnitudes of ccd-5 vary from −1.0 days/10 years (Cfb) to −0.4 days/10 years (Cfa). The maximum trend magnitude reaches −1.3 days/10 years in the Cfb climate zone. The maxima of ccd-5 range from 0 to 50 days at different stations, and the lowest values are registered again at the Csa stations. The distribution of maxima over the years differs from that of ncd-5. Most maxima occur in 1963 (41%) and 1985 (13%), followed by 2012 (10%), 1964 (7%) and 1996 (6%).
Figure 5 compares the multiyear means of ncd-5 and ccd-5 for 1961–1990 and 1991–2020. The number of cold days decreased during the second period by 14% and 21% in the Dfb and Cfb climate zones, respectively, but there was no substantial change in the Cfa and Csa zones. The most significant change in ccd-5, both in absolute terms (−2.4 days) and as a percentage change (−24%), was registered in the Cfb climate zone.
Figure 6 presents the evolution of the cold spell duration indicator (csd) by categories, averaged by climate zones. The highest values for csd-5 were reached in 1963 (Dfb and Cfb) and 1985 (Cfa and Csa). The csd indicator distinguished the severity of extreme cold weather well in most of the SEE domain and marked some extremely severe cold events in the Csa climate zone, such as in 1968, 1985 and 2001 [85,86]. The calculated average trend magnitudes decreased with the csd category increasing, varying from −2.7 to −0.2 days/10 years in Dfb and from −1.7 to −0.3 days/10 years in Cfb climate zone (Table 2).
Our results regarding the relatively weakly expressed trends in cold weather indicators can be viewed in the context of the less steady rise in winter temperatures compared to the rapid increase in summer temperatures in Europe [84]. Moreover, a recent study shows that little has changed with cold extremes since 1990, despite the intuitive suggestion that Northern Hemisphere cold extremes would become less intense and frequent not only with global warming but as the Arctic warms at an accelerated pace [87]. Concerning SEE, these findings align with the research of Buric and Doderovic [88], which reported a decrease in the number of cold nights (defined as days when tn < 10th percentile) during winter in Montenegro. This reduction varies from 0 to −2.5 days/10 years for stations with altitudes below 800 m, but it is statistically insignificant at nine out of eleven stations.
Temperature thresholds underlying the proposed method for detecting and classifying ECEs through an intensity–duration model include some physiological and technological limits, which crossing could have significant adverse health and economic consequences, such as increasing morbidity and mortality rates in cardiovascular, respiratory and some other illnesses [10,89]; agricultural damage [15,17,90] and disruptions in energy production and supply [13,91]. On the other hand, ECF severity is helpful as an exposure index that scales well against a human health impact [80] and an extreme cold indicator in climate studies [45]. Therefore, we choose the ECFsev index to assess the suitability of the proposed threshold indicators. First, we examine the consistency between the most extended periods of consecutive cold days on a yearly basis, calculated as ccd-5 and ccd-ECF (where the latter is defined as the longest period of excess cold, ECFsev > 0) using the SEE dataset. Long-term variations of ccd-5 and ccd-ECF, averaged by climate zones, are shown in Figure 7. It is evident that the −5 °C threshold is rather strict for Csa but quite soft for Dfb climates when assessing the excess cold that populations may experience. However, the correlation between ccd-5 and ccd-ECF remains high enough, even for the Csa zone.
During the studied period, each station reached a daily value of ECFsev ≥ 3 at least once. The absolute maxima of ECFsev range from 3 to 11.3, with the highest value recorded in December 2001 in Larissa, Greece. The number of days with excess cold varies slightly by station (12 to 17 days per year). Approximately 81% of the calculated daily values of ECFsev are below 1.0 (severity level L1). Excess-cold days mainly occurred in January (45%) and February (25%). The estimated statistically significant trend magnitudes for ccd-ECF vary between −0.4 and −1.0 days/10 years, affecting 6–7% of stations in Cfa and Csa climates, 21% in Dfb and 75% in Cfb climates.
The indices averaged over the domain (ccd-5d and ccd-ECFd) indicate a strong linear relationship (r = 0.958). According to the definition of ccd-5, the longest cold period of the year typically falls into the coldest winter months, January and February. Thus, an interesting classification of winter severity can be derived by the scatter plot of ccd-ECFd vs. ccd-5d, accounting for the average yearly maxima of ECFsev (Figure 8). Most years with mild winters (severity level L1) in SEE are associated with ccd-5d below 7 days. For years with severe winters (L2), ccd-5d is usually between 7 and 10. A few winters have prolonged cold periods exceeding 13 days, with ECFsev above 2.5, categorizing them as significantly more severe. The only winter with the highest severity level (L3) is that in 1963, also characterized by the most prolonged cold period (ccd-5d = 18 days). Generally, this categorization of winters is confirmed by various regional analyses and studies (e.g., [85,86,92,93]).
Figure 9 shows the changes in extreme cold weather in SEE by comparing the 1961–1990 and 1991–2020 periods based on the mean ECFsev, calculated on a yearly basis, over all periods of at least 7 days with tn ≤ −5 °C (thus synchronizing with the lowest severity category of the cold spell duration indicator, csd-5).
The results show that despite the decreasing number of ECEs in recent decades, the severity of cold weather in SEE has changed little regarding the excess cold that populations may experience. Percentage changes indicate that the Cfb climate zone is the most affected by regional warming.
The detailed comparison between yearly maxima of csd categories (denoted by C1 to C7) and ECFsev levels demonstrated good spatio-temporal conformity, as seen in the left panel of Figure 10. The relationship between the categories and severity levels is complex, but the data indicate that categories C4 to C6 are more closely associated with L2. In contrast, the other categories are fuzzified between neighbor ECFsev levels: the C1 category mainly corresponds to L1, and over 30% of cases in the C7 category align with L3 (Figure 10, right panel).

4. Conclusions

The aim of the study is to evaluate the contemporary spatio-temporal variations of extreme cold events in Southeastern Europe through the intensity–duration model of cold spells, developed for quantitative assessment of cold weather in Bulgaria. The study can be viewed as a natural continuation of the previous research on spatio-temporal variations of hot spells in Southeastern Europe [58]. We use the same methodology and datasets to investigate the changes in the prolonged retention of cold weather in the period 1961–2020, thus ensuring the methodologically consistent analysis for both cold and hot extreme events. For deriving the tn-distributions and corresponding quantiles characteristic of the climate in the country, data from the dataset BG36 was processed in several steps: (1) constructing empirical distributions of annual minimum temperatures for a period considered as less affected by the regional warming; (2) calculating quantiles corresponding to different return periods by fitting the GEV distribution to the data, accounting for nonstationarity of time series; (3) determining appropriate thresholds for tn; and (4) establishing cold spells duration thresholds for the studied period 1961–2020. We defined three threshold indicators to assess unfavorable cold weather conditions: the number of cold days (ncd-5), the longest period of consecutive cold days (ccd-5) and a combined intensity–duration characteristic for cold spells in seven categories (csd-5/-10/-12/-14/-16/-18/-20). These indicators were analyzed and summarized by the Köppen–Geiger climate zones.
All indicators indicate a statistically significant decreasing trend (p < 0.05, Mann–Kendall method) during the period 1961–2020 for Dfb and Cfb climate zones, mainly in the northern and central parts of the studied domain. The comparison of multiyear means of ncd-5 and ccd-5 for 1961–1990 and 1991–2020 shows that cold days decreased in the Dfb and Cfb climate zones, but there was no substantial change in the Cfa and Csa zones. The csd indicator distinguishes the severity of extreme cold weather well in most parts of the domain and catches some extremely severe cold events in the Csa climate zone. The average trend magnitudes decreased with the csd category increasing, varying from −2.7 to −0.2 days/10 years in Dfb and from −1.7 to −0.3 days/10 years in the Cfb climate zone. Generally, our results show relatively weakly expressed trends in both annual minimum temperatures and cold weather indicators across the domain. This aligns with some recent studies [65,84,87], which have found a less steady rise in cold-season temperatures and cold extremes in Europe since the second half of the 20th century. At a regional scale, our findings correlate with [88] regarding the weak decrease in cold nights during winters in Montenegro.
We chose the ECFsev index to evaluate the suitability of the proposed threshold indicators because it can serve as both the exposure index and the extreme cold indicator. The results show that despite the decreasing number of ECEs in recent decades, the severity of cold weather in SEE has changed little regarding the excess cold that populations may experience. We also examined the effectiveness of the proposed intensity–duration model in classifying extreme cold events. The detailed comparison between csd categories and the ECFsev levels demonstrated good spatio-temporal conformity on a yearly basis.
Additionally, we presented a classification of winter severity in the SEE domain based on the average yearly maxima of ccd-5 and ECFsev. Most years with mild winters (ECFsev is below 1.0) are associated with a short retention of cold weather (under 7 days), while in more severe winters, ECFsev is above 2.5, and cold periods exceed 13 days.
As far as we know, no survey has been conducted on the different aspects of using threshold indicators for assessing quantitatively the extreme cold events in the region. This research also outlines the goal of our future work to integrate independently defined metrics, such as the threshold indicators and ECF-based indices presented here, in the development of early warning systems.

Author Contributions

Conceptualization, K.M. and L.B.; methodology, K.M.; software, K.M., N.N. (Neyko Neykov) and N.N. (Nadya Neykova); validation, K.M. and N.N. (Neyko Neykov); formal analysis, A.S.; data curation, L.B.; writing—original draft preparation, K.M.; writing—review and editing, N.N. (Neyko Neykov) and L.B.; visualization, K.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The datasets presented in this article are not readily available because the data are part of an ongoing study. Requests to access the datasets should be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
tnDaily minimum temperature
Csa/Csb Köppen–Geiger classification: temperate climate with dry hot/warm summer
Cfa/CfbKöppen–Geiger classification: temperate climate with no dry hot/warm summer
Dfa/Dfb/DfcKöppen–Geiger classification: boreal climate with hot/warm/cold summer
ECA&DEuropean Climate Assessment and Dataset project
ECEExtreme cold event
ECFExcess cold factor
ECFsevECF severity index
EHFExcess heat factor
ETCCDIWMO Expert Team on Climate Change Detection and Indices
EURO-CORDEXCoordinated Downscaling Experiment—European Domain
GHCNdGlobal Historical Climatology Network daily dataset of the U.S. National Climatic Data Center (NCDC)
GSODGlobal Surface Summary of the Day (GSOD) dataset of the U.S. National Centers for Environmental Information (NCEI)
NIMH National Institute of Meteorology and Hydrology, Bulgaria
SEE Southeastern Europe
WMOWorld Meteorological Organization

Appendix A

Table A1. Key information for the selected 70 stations from the SEE domain, used for evaluating the spatio-temporal variations of extreme heat events in the period 1961–2020 [58]; KGC denotes the Köppen–Geiger climate classification.
Table A1. Key information for the selected 70 stations from the SEE domain, used for evaluating the spatio-temporal variations of extreme heat events in the period 1961–2020 [58]; KGC denotes the Köppen–Geiger climate classification.
Station ID Station NameCountry Code (ISO 3166-1) [94]Latitude (N)Longitude (E)Altitude (m)Data SourceKGCEnvironment
S1Belgrade (Obs.)RS44.800020.4667132ECA&D Cfaurban
S2TulceaRO45.183128.81674ECA&D Cfasuburban
S3SulinaRO45.166729.73313ECA&D Cfarural
S4Roșiorii de VedeRO44.100024.9831102ECA&D Cfarural
S5CraiovaRO44.230023.8700192ECA&D Cfarural
S6ConstanțaRO44.220028.630013ECA&D Cfasuburban
S7Thessaloniki AirportGR40.520022.97007GHCNdCfaairport
S8EdirneTR41.670026.570051GHCNdCfaurban
S9SadovoBG42.150024.9500155NIMHCfarural
S10SandanskiBG41.520023.2700206NIMHCfasuburban
S11Obraztsov ChiflikBG43.800026.0331156NIMHCfasuburban
S12Goren ChiflikBG43.009427.629729NIMHCfasuburban
S13BurgasBG42.497727.482722NIMHCfasuburban
S14KardzhaliBG41.650025.3700331NIMHCfasuburban
S15VidinBG43.994222.852531NIMHCfasuburban
S16KnezhaBG43.500024.0831116NIMHCfarural
S17SevlievoBG43.025625.1151197NIMHCfasuburban
S18IhtimanBG42.438123.8196637NIMHCfburban
S19ShumenBG43.279626.9440217NIMHCfbsuburban
S20SlivenBG42.677626.3398259NIMHCfburban
S21Zagreb- GričHR45.816715.9781156ECA&D Cfburban
S22BudapestHU47.510819.0206153ECA&D Cfburban
S23AradRO46.133121.3500116ECA&D Cfbsuburban
S24Drobeta-TurnuSeverinRO44.633122.633177ECA&D Cfbsuburban
S25HurbanovoSK47.866718.1831115ECA&D Cfbsuburban
S26Niš RS43.333121.9000201ECA&D Cfbsuburban
S27SarajevoBA43.867818.4228630ECA&D Cfburban
S28Pécs-PogányHU46.005618.2328202ECA&D Cfbairport
S29Szeged HU46.255820.090381ECA&D Cfbsuburban
S30Debrecen AirportHU47.490321.6106107ECA&D Cfbairport
S31GospićHR44.550015.3667564ECA&D Cfbsuburban
S32OsijekHR45.533118.633188ECA&D Cfbsuburban
S33Novi SadRS45.333119.850084ECA&D Cfbsuburban
S34Šmartno priSlovenj GradcuSI46.489415.1108444ECA&D Cfbrural
S35OgulinHR45.203915.2717326ECA&D Cfbrural
S36FürstenfeldAT47.030816.0806323ECA&D Cfbrural
S37Gross-EnzersdorfAT48.199416.5589154ECA&D Cfbsuburban
S38KisinevMD47.020028.8700173GHCNdCfburban
S39PřibyslavCZ49.582815.7625532GHCNdCfbrural
S40Brno–TuřanyCZ49.153116.6889241GHCNdCfbairport
S41Skopje International AirportMK41.961621.6214238GSODCfbairport
S42Heraklion GR35.333125.183139ECA&D Csaairport
S43MethoniGR36.833121.700051ECA&D Csarural
S44Brindisi IT40.633117.933110ECA&D Csaurban
S45IstanbulTR40.966729.083133ECA&D Csaurban
S46Split Marjan HR43.516716.4331122ECA&D Csaurban
S47Dubrovnik HR42.560018.270052ECA&D Csaurban
S48CorfuGR39.620019.920011GHCNdCsaurban
S49HellinikonGR37.900023.750010GHCNdCsaurban
S50Cape PalinuroIT40.025115.2805185GHCNdCsarural
S51TekirdagTR40.980027.55003GHCNdCsaurban
S52ÇanakkaleTR40.140026.43007GHCNdCsaairport
S53BalikesirTR39.620027.9300104GHCNdCsaairport
S54LarissaGR39.650022.450073GHCNdCsaairport
S55MuglaTR37.220028.3700646GHCNdCsaurban
S56TiranaAL41.333319.783338GHCNdCsaurban
S57BuzauRO45.133126.850097ECA&D Dfbsuburban
S58Poprad-TatrySK49.066720.2331694ECA&D Dfbairport
S59SibiuRO45.800024.1500444ECA&D Dfbairport
S60Bielsko-BiałaPL49.806919.0003396ECA&D Dfbsuburban
S61Nowy SączPL49.627220.6886292ECA&D Dfbsuburban
S62LeskoPL49.466422.3417420ECA&D Dfbsuburban
S63Miercurea CiucRO46.366725.7331661ECA&D Dfbrural
S64UzhhorodUA48.633122.2667124ECA&D Dfbsuburban
S65CaransebeșRO45.420022.2500241ECA&D Dfbairport
S66Râmnicu VâlceaRO45.100024.3700239ECA&D Dfburban
S67LvivUA49.816723.9500323ECA&D Dfburban
S68KošiceSK48.666721.2167230ECA&D Dfbairport
S69VinnytsiaUA49.230028.6000298GHCNdDfbairport
S70ChernivtsiUA48.366725.9000246GHCNdDfbrural
Table A2. Key information for the selected 36 stations from the NIMH network with at least 80 years of observations in the period 1931–2020, used in the BG36 dataset. The stations’ names included in Table A1 are highlighted in bold.
Table A2. Key information for the selected 36 stations from the NIMH network with at least 80 years of observations in the period 1931–2020, used in the BG36 dataset. The stations’ names included in Table A1 are highlighted in bold.
Station ID Station NameLatitude (N)Longitude (E)Altitude (m)KGCEnvironment
1Vidin43.994222.852531Cfasuburban
2Lom43.830723.222836Cfasuburban
3Varshets43.197223.2830412Cfbsuburban
4Vratsa43.231223.5292311Cfbsuburban
5Knezha43.500024.0831116Cfarural
6Pleven43.407324.6062160Cfasuburban
7Sevlievo43.025625.1151197Cfasuburban
8Pavlikeni43.234125.3252140Cfarural
9Ruse43.840125.945046Cfaurban
10Obraztsov Chiflik43.800026.0331156Cfasuburban
11Suvorovo43.316627.5833173Cfbrural
12Shumen43.279626.9440217Cfbsuburban
13Goren Chiflik43.009427.629729Cfasuburban
14Burgas42.497727.482722Cfasuburban
15Karnobat42.655826.9848190Cfbsuburban
16Yambol42.475126.5315132Cfasuburban
17Sliven42.677626.3398259Cfburban
18Chirpan42.214625.2824162Cfarural
19Kazanlak42.635825.3878397Cfbrural
20Hisarya42.485724.7179320Cfasuburban
21Velingrad42.012023.9888734Cfbsuburban
22Sadovo42.150024.9500155Cfarural
23Haskovo41.927925.5414237Cfaurban
24Kardzhali41.650025.3700331Cfasuburban
25Dzhebel41.497825.2958324Csbsuburban
26Ivaylovgrad41.528626.1211202Csasuburban
27Raykovo41.573924.7135906Cfburban
28Sandanski41.520023.2700206Cfasuburban
29Blagoevgrad42.001923.0981424Cfasuburban
30Kyustendil42.281922.7231520Cfbsuburban
31Rila42.125323.1308528Cfbsuburban
32Ihtiman42.438123.8196637Cfburban
33Tran42.833122.6578747Dfbsuburban
34Samokov42.339223.5653946Dfbsuburban
35Iskrets42.981723.2758565Cfbrural
36Bozhurishte42.761923.2069562Cfbsuburban

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Figure 1. Location of meteorological stations on the background of the map of Köppen–Geiger classification (1986–2010), http://koeppen-geiger.vu-wien.ac.at/present.htm (accessed on 28 January 2025); the selected stations are marked as follows: grey triangles—12 stations from NIMH; blue dots—16 stations from GHCNd dataset; red dot—one station from GSOD dataset; and asterisks—41 stations from ECA&D database.
Figure 1. Location of meteorological stations on the background of the map of Köppen–Geiger classification (1986–2010), http://koeppen-geiger.vu-wien.ac.at/present.htm (accessed on 28 January 2025); the selected stations are marked as follows: grey triangles—12 stations from NIMH; blue dots—16 stations from GHCNd dataset; red dot—one station from GSOD dataset; and asterisks—41 stations from ECA&D database.
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Figure 2. (Left panel): Medians of calculated percentiles of tn-distributions by stations for 1931–1980 and 1981–2020. (Middle panel): Median of calculated lower percentiles of tn-distributions and 2-, 5-, 10-, 20- and 50-year return levels (estimated by GEV model) by stations for yearly minima (1931–1980). (Right panel): Box plot of distributions of cold spells duration at the different tn-thresholds for 1961–2020. The BG36 dataset was used for all calculations.
Figure 2. (Left panel): Medians of calculated percentiles of tn-distributions by stations for 1931–1980 and 1981–2020. (Middle panel): Median of calculated lower percentiles of tn-distributions and 2-, 5-, 10-, 20- and 50-year return levels (estimated by GEV model) by stations for yearly minima (1931–1980). (Right panel): Box plot of distributions of cold spells duration at the different tn-thresholds for 1961–2020. The BG36 dataset was used for all calculations.
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Figure 3. (Left panel): Distribution of calculated empirical quantiles (q2 to q50) on time series of annual minimum temperatures (Tn) for 1961–2020 by stations across SEE; (Right panel): Medians (p50); 20th, 15th, 10th, 5th and 1st percentiles (p20, p15, p10, p05 and p01) and absolute minima (min) of daily minimum temperature (tn) for 1961–2020 by climate zones; the range of values used in threshold indicators is shown in bright blue.
Figure 3. (Left panel): Distribution of calculated empirical quantiles (q2 to q50) on time series of annual minimum temperatures (Tn) for 1961–2020 by stations across SEE; (Right panel): Medians (p50); 20th, 15th, 10th, 5th and 1st percentiles (p20, p15, p10, p05 and p01) and absolute minima (min) of daily minimum temperature (tn) for 1961–2020 by climate zones; the range of values used in threshold indicators is shown in bright blue.
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Figure 4. Long-term variations of ncd-5 and ccd-5 indicators averaged by Köppen–Geiger climate zones.
Figure 4. Long-term variations of ncd-5 and ccd-5 indicators averaged by Köppen–Geiger climate zones.
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Figure 5. Multiyear means of ncd-5 (right panel) and ccd-5 (left panel) for 1961–1990 and 1991–2020, summarized by the Köppen–Geiger climate zones.
Figure 5. Multiyear means of ncd-5 (right panel) and ccd-5 (left panel) for 1961–1990 and 1991–2020, summarized by the Köppen–Geiger climate zones.
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Figure 6. Long-term variations of csd-5/-10/-12/-14/-16/-18/-20 (unit: days) averaged by Köppen–Geiger climate zones.
Figure 6. Long-term variations of csd-5/-10/-12/-14/-16/-18/-20 (unit: days) averaged by Köppen–Geiger climate zones.
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Figure 7. Long-term variations of ccd-5 and ccd-ECF (unit: days) averaged by Köppen–Geiger climate zones; r denotes the Pearson’s correlation coefficient.
Figure 7. Long-term variations of ccd-5 and ccd-ECF (unit: days) averaged by Köppen–Geiger climate zones; r denotes the Pearson’s correlation coefficient.
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Figure 8. Scatter plot of ccd-ECFd vs. ccd-5d. The size of the bubbles is proportional to the yearly maxima of ECFsev calculated by stations and averaged over the SEE domain. Several years by each severity category are shown in different font colors: orange for mild, light blue for severe and dark blue for significantly more severe winters.
Figure 8. Scatter plot of ccd-ECFd vs. ccd-5d. The size of the bubbles is proportional to the yearly maxima of ECFsev calculated by stations and averaged over the SEE domain. Several years by each severity category are shown in different font colors: orange for mild, light blue for severe and dark blue for significantly more severe winters.
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Figure 9. (Left panel): Mean ECFsev across SEE by severity levels for 1961–1990 and 1991–2020 by climate zones; (Right panel): Percentage change in the mean ECFsev for 1991–2020L1–L3 denote severity levels, as defined in [80]; L0—no excess cold.
Figure 9. (Left panel): Mean ECFsev across SEE by severity levels for 1961–1990 and 1991–2020 by climate zones; (Right panel): Percentage change in the mean ECFsev for 1991–2020L1–L3 denote severity levels, as defined in [80]; L0—no excess cold.
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Figure 10. (Left panel): Spatio-temporal variation of yearly maximum ECE intensity represented by categories of csd indicator (bottom) and ECFsev levels (top); (Right panel): Percentage of cold spell categories (C1–C7) associated with ECFsev levels (L0–L3). L0 denotes no excess cold.
Figure 10. (Left panel): Spatio-temporal variation of yearly maximum ECE intensity represented by categories of csd indicator (bottom) and ECFsev levels (top); (Right panel): Percentage of cold spell categories (C1–C7) associated with ECFsev levels (L0–L3). L0 denotes no excess cold.
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Table 1. Average and maximum values (slash separated) of Sen’s slope estimates (unit: °C/10 years) of statistically significant linear trends (p < 0.05, Mann–Kendall method) of the annual mean (Ta), annual mean minimum (Tmn) and annual minimum (Tn) temperatures in the period 1961–2020, summarized across the Köppen–Geiger climate zones; IDs of stations (see Appendix A, Table A1) in which maximum values reached are shown in brackets; the percentage of stations with statistically significant trends in each climate zone is also shown.
Table 1. Average and maximum values (slash separated) of Sen’s slope estimates (unit: °C/10 years) of statistically significant linear trends (p < 0.05, Mann–Kendall method) of the annual mean (Ta), annual mean minimum (Tmn) and annual minimum (Tn) temperatures in the period 1961–2020, summarized across the Köppen–Geiger climate zones; IDs of stations (see Appendix A, Table A1) in which maximum values reached are shown in brackets; the percentage of stations with statistically significant trends in each climate zone is also shown.
Cfa Cfb Csa Dfb
Ta+0.29/+0.43 (S1)100%+0.39/+0.55 (S18)100%+0.24/+0.37 (S45)100%+0.34/+0.44 (S60)100%
Tmn+0.26/+0.46 (S1)82%+0.34/+0.58 (S18)100%+0.23/+0.47 (S45)87%+0.32/+0.41 (S60)93%
Tn+0.54/+0.54 (S7)6%+0.76/+1.09 (S37)50%+0.28/+0.28 (S48)7%+0.79/+1.00 (S60)36%
Table 2. Average and maximum values (slash separated) of Sen’s slope estimates (unit: days/10 years) of statistically significant linear trends (p < 0.05, Mann–Kendall method) of threshold indicators in the period 1961–2020, summarized across the Köppen–Geiger climate zones; IDs of stations (see Appendix A, Table A1) in which maximum values reached are shown in brackets; the percentage of stations with statistically significant trends in each climate zone is also shown.
Table 2. Average and maximum values (slash separated) of Sen’s slope estimates (unit: days/10 years) of statistically significant linear trends (p < 0.05, Mann–Kendall method) of threshold indicators in the period 1961–2020, summarized across the Köppen–Geiger climate zones; IDs of stations (see Appendix A, Table A1) in which maximum values reached are shown in brackets; the percentage of stations with statistically significant trends in each climate zone is also shown.
Cfa Cfb CsaDfb
ncd-5−1.5/−2.3 (S5)18%−3.1/−4.5 (S34 and S36)88% −3.1/−4.1 (S60 and S70)86%
ccd-5−0.4/−0.7 (S1)18%−1.0/−1.3 (S34 and S40)67% −0.8/−0.9 (S67 and S68)43%
csd-5 −1.7/−3.6 (S31 and S39)71% −2.7/−4.0 (S67)79%
csd-10 −0.3/−0.7 (S34)21% −1.3/−1.8 (S67 and S69)43%
csd-12 −0.8/−1.6 (S69)36%
csd-14 −0.3/−0.8 (S69)21%
csd-16 −0.2/−0.3 (S69)14%
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Malcheva, K.; Neykov, N.; Bocheva, L.; Stoycheva, A.; Neykova, N. Evaluation of the Spatio-Temporal Variation of Extreme Cold Events in Southeastern Europe Using an Intensity–Duration Model and Excess Cold Factor Severity Index. Atmosphere 2025, 16, 313. https://doi.org/10.3390/atmos16030313

AMA Style

Malcheva K, Neykov N, Bocheva L, Stoycheva A, Neykova N. Evaluation of the Spatio-Temporal Variation of Extreme Cold Events in Southeastern Europe Using an Intensity–Duration Model and Excess Cold Factor Severity Index. Atmosphere. 2025; 16(3):313. https://doi.org/10.3390/atmos16030313

Chicago/Turabian Style

Malcheva, Krastina, Neyko Neykov, Lilia Bocheva, Anastasiya Stoycheva, and Nadya Neykova. 2025. "Evaluation of the Spatio-Temporal Variation of Extreme Cold Events in Southeastern Europe Using an Intensity–Duration Model and Excess Cold Factor Severity Index" Atmosphere 16, no. 3: 313. https://doi.org/10.3390/atmos16030313

APA Style

Malcheva, K., Neykov, N., Bocheva, L., Stoycheva, A., & Neykova, N. (2025). Evaluation of the Spatio-Temporal Variation of Extreme Cold Events in Southeastern Europe Using an Intensity–Duration Model and Excess Cold Factor Severity Index. Atmosphere, 16(3), 313. https://doi.org/10.3390/atmos16030313

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