A Review of Extreme Air Temperature Analysis in Croatia

Abstract

A historical review of extreme air temperature analysis in Croatia is presented. Two capital works on the subject were published in the 1970s by the Croatian Meteorological and Hydrological Service (DHMZ) and Faculty of Science University of Zagreb (PMF-Zagreb), respectively. The first is a monography on extreme value theory or extreme value analysis (EVA) with an application on more than a century-long time series of annual minima air temperature for Zagreb Grič weather station (Croatia) for the period 1862–1969. It is just a case study, with a lot of instructions regarding how to estimate the generalized extreme value (GEV) distribution parameters. The second is a master’s thesis with an application of the EVA on maxima air temperature time series for 41 weather stations from Croatia for the period 1950–1969. The shortness of the time series of the presented data caused instability in the estimation of GEV distribution parameters in transition areas from continental to maritime climate, but in general, the results are acceptable after a reduction of the 1950–1969 time series data on a ‘normal climate period’ 1910–1969. Both works were pioneering for that time in the South-Eastern Europe scale. A routine application of GEV distribution on the extreme air temperature (both minimum and maximum) for ten representative weather stations from Croatia is represented in Climate atlas of Croatia for the period 1961–1990, published by DHMZ in 2008. Theoretically estimated results fit well with empirical data. A review of long-term “warm” and “cold” indices of extreme air temperature for 41 weather stations from Croatia for the period 1951–2010 is represented in the Sixth National Communication Report of Croatia under the UNFCCC published by the Ministry for Environment and Nature Protection of Croatia (MZOIP) in 2014, showing a positive trend of “warm” and a negative trend of “cold” indices during the period 1951–2010 which tackled the non-stationarity of extreme air temperature time series. That topic of non-stationarity is more extensively considered using the results of a series of scientific papers published in the international journals which conducted a study of extreme air temperature of the wider Western Europe territory, including Croatia and other countries close to Croatia. Some authors of these papers stated that the GEV distribution parameters have to be considered as a function of time rather than fixed in time using covariates like North Atlantic Oscillation (NAO), coherent atmospheric blocking regions, linear trends in data caused by global warming and others covariates. The EVA results, connected with the global climate warming, could contribute to the national Natural Disaster Risk Reduction (NDRR) efforts.

1. Introduction

This review is in line with the recommendations from [1] to mitigate the risks of the recent global climate warming and related summer heat waves, droughts, forest fires and other climate hazards by adaptation measures. Some extreme events, such as summer heat waves, are more and more frequent, with a higher magnitude (intensity) and longer duration. A consequence of that is the non-stationarity of extreme air temperature time series and an adopted statistical modeling approach is required instead of traditional modeling of stationary time series. The review is focused on territory of Croatia but within the context of neighboring countries and the wider area of the Western Europe. The results presented could be consider as an example of “good practice” on the topic for average developed countries with a rather long tradition and well-organized education system and reasonably well-organized meteorological and hydrological services, at least since the beginning of the 20th century (e.g., the establishment of Geophysical Institute in Zagreb in 1911). An important role in that was influence of Austro-Hungarian Monarchy as the most developed part of the world since beginning of 19th century [2].

For extreme air temperature time series or other similar atmospheric processes using statistical modeling, the extreme value theory or the extreme value analysis (EVA) is the preferable tool. The objective of the EVA is to quantify the stochastic behavior of a process at unusually large or small levels, e.g., minimum or maximum air temperature below or above certain thresholds, respectively. In particular, the EVA usually requires the estimation of the probability of events that are more extreme than any that have already been observed [3,4].

A precondition for climate studies in general, and thus for the EVA application, is the availability of extreme air temperature data, optimally for a 30-year-period. On the territory of today Croatia extreme air temperature historical data started to be collected since the middle of 19th century (Figure 1a) until today in a respectable number of weather stations (Figure 1b). Thus, using climate data for 250 weather stations, most of which for the period 1901–1910, and 37 for longer time series, university prof. Stjepan Škreb and his associates wrote a book on the climate [5] for the territory of today, namely Croatia, Bosnia and Herzegovina and a small part of Northern Serbia. All basic climate elements are described including extreme air temperature using simple statistical tools. It was found that the absolute air temperature maxima reached values up to 46.2 °C in Mostar located in the Neretva River valley (about 50 km north-easterly from Ploče weather station, located near of the estuary of the Neretva River) and minima down to −33.6 °C at Bjelašnica mountain weather station, just about 100 km north-easterly from Mostar. Thus, a difference between absolute maxima and minima is close to 80 °C; findings published by prof. Škreb with his associates.

Prof. Berislav Makjanić’s lectures, delivered in the 1969/70 academic year at Zagreb University, have been published as a monography in 1977 [6]. Development of the EVA theory is represented in [6] in a systematic way and it chose to use Jenkinson’s frequency distribution which later has been recognized as generalized extreme value (GEV) distribution, which is still in use. In addition, a very detailed procedure for the calculation of the GEV distribution parameters was presented. The GEV was applied for minima air temperature for Zagreb Grič weather station and the period 1862–1969. Additionally, “minima minimorum” for the return period of 100 years has been estimated to be −26.2 °C. Monography [6] is presented in more details in Section 2.1. The same theory has been applied by Dr. Nada Pleško in her master’s thesis [7] but focused on maxima air temperature for those weather stations which had maxima air temperature data for the period 1950–1969, in total 41 weather stations in Croatia. Dr. Pleško emphasized that the GEV theory application gave a more detailed insight on maxima air temperature by additional values obtained by that theory and she showed that the stability of the GEV theory parameters are dependent on the time series length and geographical position of the weather stations. More details of [7] are presented in Section 2.2. The general statistical theory and its application, including the EVA, are described in university textbook [8] by prof. Branka Penzar and prof. Berislav Makjanić.

A detailed climate atlas for the World Meteorological Organization (WMO) standard period 1931–1960 for territory of the Former Yugoslavia (SFRJ) was published by Federal Hydrometeorological Service (SHMZ—Savezni hidrometeorološki zavod) of Former Yugoslavia, [9,10]. A summary of the routine application of generalized extreme value (GEV) distribution on the extreme (maxima and minima) air temperature is represented in climate atlas of Croatia [11], described in more details in Section 2.3. A series of extreme air temperature indices was represented in the Sixth National Communication Report of the Republic of Croatia under the United Nations Framework Convention on Climate Change (UNFCCC) [12]. The non-stationarity in those indices are clearly noted which were estimated for future climate too by the downscaling of regional climate models. This national communication report could be a good base for national action planning in the area of climate monitoring, adaptation and mitigation. More details of [12] are represented in Section 2.4. A couple of references from Croatia [13,14], represented in Section 2.5 include the EVA application on extreme air temperature for Croatia. In [13], air temperature time series refers to the Eastern Adriatic coastal region showing the advantages of the GEV (Jenkinson’s distribution) in comparison to the Gumbel distribution. In [14], air temperature time series refers to urban, suburban, near airport and mountainous areas of Zagreb. Changes in extreme air temperature are the smallest for mountainous station, while the non-stationarity has been tried to be removed by analyzing 30-year overlapping periods instead of whole available time series.

Prof. Nadežda Šinik had her doctoral thesis “Variations of Zagreb Climate” published at Zagreb University in 1979 [15]. She cited Croatian authors [16,17,18] who tried to explain secular variations in air temperature for almost one century, the longest from 1862 to 1974 for Zagreb Grič. They recognized more prevailing meridional circulation during warmer and drier periods at Zagreb Grič and zonal during colder and wetter periods. In [19], cited also by prof. Šinik, an explanation of hemispheric air temperature variation via direct solar radiation was made and higher air temperature variations were observed at higher latitudes than lower latitudes. Optical transparency variations had shown to be important for surface air temperature variations. The author of [19] also discussed contribution of CO₂ concentration rising in atmosphere, produced by human activity in the 19th and 20th century, to the mean temperature rising close to the Earth’s surface, today called as global warming. He also discussed feedback mechanisms’ contribution to air temperature changes. Prof. Šinik made a physical interpretation of her statistical results, obtained for secular air temperature for Zagreb Grič, by means of energy balance equation representing the heat equivalent of temperature as a function of global radiation and cloudiness radiation as well as heat and humidity transport. Additional details on Zagreb Grič air temperature variations are represented in [20,21,22] and Section 2.6.

Finally, non-stationarity within long-term time series of extreme air temperature in the wider area of the Western Europe, covering also parts of Croatia, is represented in Section 2.7. A connection between summer heat waves in wider areas of Western Europe (including data for Zagreb Grič from Croatia) and large-scale atmospheric forcing, e.g., sea-level pressure—SLP, sea surface temperature—SST, blocking of atmospheric systems, etc., is described using data from 1880 to 2003 [23]. Linear trends of sets of air temperature indices in the wider area of the Western Europe for the period 1991 to 2000 are considered in [24]; because of the non-stationarity of maximum air temperature, the length of heat events in the wider area of Western Europe have doubled and the frequency tripled from 1880 to 2005 [25]. An improvement in identifying and predicting the changing frequency of extremely high temperatures in the Europe was attempted to be improved in [26]. In [27] the application of the GEV distribution to the weather station extreme temperature data for Belgrade (Serbia) was considered. Use of the EVA study in the mitigation of the impact of climate global warming is usually considered by sectors of the economy such as: agriculture, water management, health, transportation, etc., but here, it is just touched upon and recommended in further literature [28,29,30,31,32,33,34].

2. A Review of Extreme Theory Application on Air Temperature Analysis in Croatia

2.1. A Monography on the EVA Application in Geophysics

Eminent university professor at Zagreb University on dynamic meteorology, prof. Berislav Makjanić, delivered lectures on the EVA or extreme value theory (or just extreme theory) application in geophysics during the academic year 1969/70. His lectures have been published by the Croatian Meteorological and Hydrological Service (DHMZ) in 1977 as a monography [6]. Makjanić’s lectures have soon been cited in [7,8], respectively.

In the first, i.e., introductory chapter of the monography, Makjanić cited: “Statistical theory of extreme values is more and more applied in various researches. In order that our meteorologists and geophysicists be introduced by this very important tool for natural event studies, I have been delivered a basis of the extreme theory to students of postgraduate study of meteorology of the Faculty of Science of the Zagreb University during 1969/70 academic year. In this monography a much wider part on extreme amounts is represented while non-parametric methods, as less important, are omitted. A goal was to be given practical instructions for the theory application. It is presumed that readers are familiar with basic terminology and laws of mathematical statistics while the extreme value theory is deeply represented as necessary for understanding of described procedures”. According to Makjanić, the theory of extrema describes not only frequencies but also extreme values and so it can be used in a wider range of applications including meteorology and geophysics. “The theory is not widely known so it was not widely applied in scientific papers”, Makjanić cited in his monography, 45 years ago.

Very briefly, Makjanić described a history of extreme value theory: “A significant step forward was done when Frechet (1927) was published a stability principle. Fisher and Tippett, who independently from Frechet, published their paper in Reports of Cambridge Philosophical Society in 1928 and found that there are three types of functions which satisfy the functional equation of stability principle. These three functions are known as Fisher-Tippet (F-T) I, II, and III types of the functions. Gumbel, because of his contribution to the extreme theory, become famous scientist who published a scientific book on the extreme theory in 1958…

Jenkinson has made the extreme theory much simpler and its application much easier. He gave a new original solution of the functional equation which contains all three F-T types of functions and gave methods for easier estimation of the function parameters. His contributions are contained in two papers from 1955 and 1969, respectively.” According to recent scientific literature on the extreme value theory, e.g., in [3,4], Jenkinson’s model is called the generalized extreme value (GEV) model combined with the block extrema model for the creation of extreme value samples (one extreme value from each year).

Prof. Makjanić, in addition to others, applied described extrema theory on time series of annual minima air temperature for Zagreb Grič weather station for the period 1862–1969 (108 years). On the basis of data samples, it was possible to estimate the lowest minimum air temperature as well as the highest minimum air temperature using probability density function cited in Section 7.2.2 of the monography [6]. Makjanić stated, for example, that at Zagreb Grič weather station, the minimum air temperature of −18.8 °C can be expected for an average return period of 10 years, −22.5 °C for return period of 100 years and “an ever expected minimum” (Makjanić cited as “minimum minimorum”) air temperature of −26.2 °C (Section 7.2.2.1 of [6]).

In the ninth, literature chapter, Makjanić cited only publications which have been used for writing his monography. For other publications, until about 1957, according to him, the best source of the literature for the extreme theory is Gumbel’s book which is shown as original citation represented in Figure 2 of the present review paper “while”, he cited, “for the publications after that year we do not know for any their group bibliography”.

2.2. A Master’s Thesis Review on Distribution of Maximum Air Temperature on the Territory of Croatia

Dr. Nada Pleško was one of the most enthusiastic women from meteorological and hydrological research group at Croatian Meteorological and Hydrological Service (DHMZ) of that period, attended prof. Makjanić lectures on extreme values theory delivered at postdoctoral studies at Zagereb University in the academic year 1969/70. Her master’s thesis deals with probability distributions of maximum air temperature on territory of Croatia and was led by prof. Makjanić [7]. As authors of the present review know it is still unique master’s thesis on maximum air temperature made in Croatia since then. It is an indicator of the complexity of the topic.

In introductory chapter of the thesis Dr. Pleško, beside to other, cited:

“Humanity wish to make planning and make safer future as possible putting some requests to various branches of science including meteorology. Thus living in ground layer of the atmosphere, humanity tends to better recognize characteristics of the atmosphere to know what good or bad atmosphere brings not only tomorrow, for one week or a month, what is given by so called ‘short-range’ weather forecasts than what has to be expected at a particular location during a long-term period, perhaps during 50 or 100 years and longer, especially as extreme events. Such ‘long-range’ forecasts are produced by various statistical methods by which, using existing data, extrapolate expected values: their quantity (power), frequency and average period after which they could occur again.”

Dr. Pleško continued in introduction of her master’s thesis:

“One of the most frequent recent questions related to applied meteorology is: ‘what maximum values have to be expected of certain meteorological element in a particular region and what return period?’ These values are usually used as design parameters in the economy, giving certain security what was built using appropriate design will not be destroyed in short time by extreme weather conditions. Particularly, in questions are extreme values of air temperature, wind speed, precipitation amount, river water level, etc. Recently adopted codex for design practice in the Great Britain, for example for bridges construction design which are sensitive on extreme air temperature, specifies that for static accounting of bridge main construction elements has to be used maximum air temperature which occurs ones per 120 years while for non-constructive elements maximum air temperature which occurs ones in 20 years. In ‘our country’ that kind of regulation does not exist but designers more and more frequently asking such questions.”

Please note that term ‘our country’ refers to Former Yugoslavia whose part was today Croatia. Nowadays, about 45 years later, in Croatia there is a codex in question as part of a more general regulation called ‘civil engineering technical norms’.

The main task of this master’s thesis was to examine, in more details, one of the meteorological elements, i.e., the maximum air temperature for different regions of Croatia, using the application of the extreme value theory. In addition, to determine the maximum air temperature for which can be expected, in ‘a normal climate’, an overrun of return periods of 20, 50, 100 or 1000 years, as well as air temperature frontier values which can ever occur in our climate conditions. In that way, a more complete picture on air temperature regime in Croatia has been obtained by additional values about which it would be impossible to say anything using only available short time series of air temperature data. For that study, Jenkinson’s, i.e., GEV model, combined with the block maxima model for the creation of extreme value samples (one maximum value from each year) was applied. The GEV model has been applied on time series of those weather stations for which maximum air temperature data have been available for the period 1950–1969, in total for 41 weather stations in Croatia. Dr. Pleško noted that main obstacle for comparable expected maximum air temperature for different return periods over Croatia was different length of available maximum air temperature time series. Dr. Pleško cited:

“An experience obtained making this master’s thesis shown that estimations made by series different length, and additionally not long enough, can give a biased picture of spatial distribution of extrema, stronger biased when return period is longer for which are extrema of our interest. Thus a shorter series exhibits only characteristics of some short lasting climate conditions, which can, due to influence of various physical factors during that time, significantly deviate from normal climate for that region. Then, estimated extrema based on such ‘abnormal’ data, give underestimated or overestimated values of expected extrema.

As ‘normal’ climate is defined as a climate in which extrema probability distribution is stabilized up to a high level that an extreme value theory application on a longer time series of data can not practically change extrema probability distribution. It means that is a such climate, which can not be disrupted by short lasting effects aroused from combination of various physical factors. On that way defined climate does not require that a data period necessary for representation of normal climate has to be the same length for all regions. Those regions which have more variable weather conditions, thus less stable climate, need a longer period of data for representation of climate. These are especially those areas where an influence of continental and maritime climate is mixing. For representation of exclusively continental or maritime climate shorter time series of data are satisfying. Necessary lengths of the time series for representation of normal climate are represented in the second part of the master’s thesis. All estimated air temperature maxima obtained by short periods of weather observations are reduced on ‘a normal’ climate, by described method, and represented on the maps.”

Please note that statements regarding stationarity of time series data could be questionable nowadays because of the global climate warming caused by the human influence, which will be considered in Section 2.4, Section 2.5, Section 2.6 and Section 2.7 of the present review.

Dr Pleško cited in the master’s thesis summary:

“Temperature maxima (in the range from 30.6 °C to 44.1 °C) expected to be exceeded once in 20, 50, 100 and 1000 years as well as the absolute maxima (in the range from 38.3 °C to 53.8 °C) at 41 weather stations in Croatia have been evaluated by means of Jenkinson’s method of extrema estimation. For these meteorological stations mostly 20-year time series of data were available, and it has appeared that they are too short for the real and physically valid estimation of air temperature maxima values. Therefore an reduction method, of these extrema to those which are expected in a normal climate, has been applied.

It was postulated that the maximum temperatures reach their normal climate at the point when further increase of the period for several decades can not any longer causes a considerable change of extrema distribution. Although there are some regions in Croatia with more stable regimes of maxima temperature and where the shorter series are suffice (in more emphasized continental or maritime regions, respectively), for the whole territory of Croatia the use of the series 1910–1969 turned out to be the most convenient for description of the normal climate. Expected air temperature maxima in Croatia in a normal climate are represented on charts (without a reduction to the sea level).

A comparison with the observations indicates the reality of theoretical values, which differ only 1–2 °C of the highest observed maxima at each weather station for the return period of 1000 years. The theoretical maxima value of 44 °C in our warmest regions approximate closely to the maxima limits, which are physically possible in Croatia.

The last chapter of the master’s thesis discusses the correlation of air maxima temperature and energy balance in the near-ground atmosphere with the suggestion of a certain possibility of the air temperature maxima forecast.”

2.3. An Overview of Climate Atlas of Former Yugoslavia for the Period 1931–1960 and the Routine Application of GEV Distribution on the Extreme Air Temperature Representation in the Climate Atlas of Croatia for the Periods 1961–1990 and 1971–2000

Long-lasting efforts were made to be published a detailed climate atlas for the World Meteorological Organization (WMO) standard period 1931–1960 for territory of the Former Yugoslavia (SFRJ). The atlas was published by Federal Hydrometeorological Service (SHMZ—Savezni hidrometeorološki zavod) of Former Yugoslavia during the period 1969–1985. It includes territory of Croatia and extreme air temperature as well [9]. Eminent professors at Zagreb University (Croatia) prof. Ivan Penzar, prof. Branka Penzar and prof. Božena Volarić participated in preparation of that atlas. A part their contribution has been published in the article: “On the methodology on making the climatic maps related to the occurrence of cold days” [10], i.e., a calculation of three parameters: P—means the beginning of the period in a year in which cold days occur; S—means the end of the period in a year in which cold periods occur; D—means the duration of the period in a year in which there are not cold days. For that purpose, extreme air temperature data for 288 weather stations for the period 1931–1960 were used. Then, climate regions with constant vertical gradients of P, S, and D on the mountain slopes were performed [Figure 3]. Although growing season, in average, is recently rising, it seems (via present review authors’ personal observation) spring frost-related damages in agriculture are becoming higher. The reason is the higher sensitivity of the vegetation on the frost at higher phenological phases of vegetation growing. Thus, this type of data can also be applied in national climate adaptation strategy.

On the margins of a traditional air temperature presentation for the WMO standard period 1961–1990 in the recent climate atlas of Croatia, eminent DHMZ climatologist Dr. Marjana Gajić-Čapka prepared a qualitative comparison of observed minimum and maximum air temperatures with their estimated values according to distributions of the GEV for ten weather stations from the northern Croatia [11]. The parameters of distributions were estimated by extreme air temperature samples for the period 1961–1990. In Figure 4, the corresponding cited results are represented for four weather stations from the northern Croatia only. There is a very good agreement between empirical and the GEV distribution estimated extreme air temperature values. According to these results, “the strongest continentality” is present for Osijek weather station located in the north-eastern Croatia, while “the weakest continentality” for Parg mountain station is located in the north-western part of Croatia.

2.4. A Review of Long-Term Extreme Air Temperature Trend Analysis Represented in the Sixth Communication Report of the Republic of Croatia under the UNFCCC

In the previous sections, maximum air temperature time series have been considered as stationary. Recently, because of the global warming, the maximum air temperature becomes more and more non-stationary. This was shown in the Sixth National Communication Report of the Republic of Croatia under the UNFCCC [12]. Thus, from Figure 5, it is obvious that there is a significant positive trend, for almost all of 41 weather stations in Croatia, of annual average, average minimum and average maximum air temperature, in degrees Celsius per 10 years, for the period 1951–2010, notably stronger in the northern than in the southern Croatia. The highest contribution to the total (annual) positive air temperature trends are contributed by summer trends, while the contribution to the average maximum air temperature is equally contributed by summer, winter and spring. The smallest, still mostly positive but mostly not significant trends, are reported for autumn (details are in [12]).

More comprehensive air temperature trend indicators, for 41 weather stations from Croatia for the period 1951–2010, are “warm” and “cold” indices of minimum and maximum air temperature expressed as trends of number of days per 10 years represented in

Table 1. Relative frequency (in percentages from the second to the last column) of trends of the number of days per 10 years (the first column), for “warm” and “cold” air temperature indices defined below this table (according to [12]).

Trend	SU	Tx90	Tn90	WSDI	FD	Tx10	Tn10	CSDI
≤−6.0	0.0	0.0	0.0	0.0	2.4	0.0	2.4	0.0
−5.9–4.0	0.0	0.0	0.0	0.0	7.3	7.3	17.1	0.0
−3.9–2.0	0.0	0.0	0.0	0.0	36.6	63.4	39.0	2.4
−1.9–0.0	0.0	0.0	0.0	0.0	43.9	29.3	31.7	92.7
0.1–2.0	4.9	0.0	2.4	0.0	7.3	0.0	7.3	4.9
2.1–4.0	29.3	0.0	2.4	29.3	2.4	0.0	2.4	0.0
4.1–6.0	36.6	2.4	12.2	46.3	0.0	0.0	0.0	0.0
6.1–8.0	29.3	29.3	12.2	14.6	0.0	0.0	0.0	0.0
8.1–10.0	0.0	26.8	22.0	9.8	0.0	0.0	0.0	0.0
10.1–12.0	0.0	17.1	24.4	0.0	0.0	0.0	0.0	0.0
12.1–14.0	0.0	19.5	14.6	0.0	0.0	0.0	0.0	0.0
14.1–16.0	0.0	4.9	4.9	0.0	0.0	0.0	0.0	0.0
16.1–18.0	0.0	0.0	2.4	0.0	0.0	0.0	0.0	0.0
18.1–20.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
>20.0	0.0	0.0	2.4	0.0	0.0	0.0	0.0	0.0

Definitions of air temperature indices: SU—warm days (absolute threshold); Tn90%—warm nights (threshold by percentiles); Tx90%—warm days (threshold by percentiles); WDSI—duration of warm periods; FD—cold days (absolute threshold); Tx10%—cold days (threshold by percentiles); Tn10%—cold nights (threshold by percentiles); CSDI—duration of cold periods.

. It is obvious from Table 1 that “warm” indices have a positive trend while “cold” indices have a negative trend [12].

Two-meter air temperature (T2m) has been performed for Croatia by DHMZ downscaling simulations for the period 1961–1990 which represent present climate (P0) and for the period 2011–2040 which represent future climate (P1). A statistic of cold and warm days is presented in Figure 6: (a) average number of cold days in winter for present climate (P0) and (b) difference in number of cold days in winter for present climate (P0) and future climate (P1); (c) average number of warm days in summer for present climate (P0) and (d) difference in number of warm days in summer for present climate (P0) and future climate (P1). Obviously, a smaller number of cold days in winter and higher number of warm days in summer can be expected in the future climate compared to the present climate.

2.5. Other Publications on the EVA for Croatia

In the Summary of [13] is cited: “The air temperature maxima are estimated by Gumbel and Jenkinson methods on 9 locations along the Adriatic on the basis of 30 years long periods of the observed annual air temperature maxima (1950–1979). It was shown that a use of Gumbel method for the estimation of the air temperature maxima is justified for return periods not longer than 30 years. The estimation of air temperature maxima by Jenkinson method shows that on the Adriatic we can expect the absolute air temperature maxima between 37.9 and 46.4 °C.”

In [14], its authors in its abstract cited: “Characteristics and changes in minimum and maximum air temperature and associated climate indices are analyzed for Zagreb city (Croatia). Daily data from the period 1960–2019 for four meteorological stations (located in urban, suburban, airport and mountainous area of Zagreb) are used. Generally, changes in extreme air temperature showed to be the least expressed for the mountainous site comparing to other city stations. An increase (decrease) in the frequencies of warm (cold) extremes is obtained using both stationary (applied on non-overlapping 30-year periods and non-stationary (applied to the whole period of the analysis) GEV distribution.”

2.6. Large-Scale Spatial Climate Variation and Change Impact on Air Temperature in Croatia

Although climate variations and changes, including their impacts, are the most visible on the local and regional scale, the main drivers of such variations and changes are larger-scale processes: synoptic, hemispheric or even global. Examples of such drivers are: the prevailing type of large-scale circulation (meridional or zonal frequently joined with long-lasting blocking), NAO (North Atlantic Oscillation) ENSO (El Nino Southern Oscillation), global greenhouse gases concentration rising, etc. In recent EVA terminology, these drivers referred to “covariates” which can be included in the EVA model introducing time dependence of the EVA model parameters [3]. This Section 2.6 has a slightly different approach to air temperature analysis then the rest of the sections in this Chapter (2). Part of the analysis was made before the EVA had more wider been applied, and instead, “absolute” extreme air temperature time series in monthly, seasonal, annual or decadal averages of their deviations from multiannual averages of air temperature are analyzed. However, this review could be a useful introduction into the following Section 2.7 in terms of its interpretation of secular time series variations and changes by large-scale atmospheric circulation variables (referred to as covariates).

A compilation of existing interpretations of Zagreb Grič (Croatia) air temperature secular time series variations for the period around one hundred years (since 1862 to the 1960s or 1970s) were presented in introduction of prof. Nadežda Šinik doctoral thesis: “Variations of Zagreb Climate”, published at Zagreb University in 1979 [15]. Croatian authors, cited in the doctoral thesis [16,17,18], tried to explain secular variations in air temperature for almost one century, starting in 1862 for Zagreb Grič. They recognized more prevailing meridional circulation during warmer and drier periods at Zagreb Grič and zonal during colder and wetter periods. Prof. Šinik cited available literature on the topic of climate variations on the northern hemisphere, which are comprehensively presented in [19]. It was shown that the amplitude of air temperature variations are higher at higher latitudes than lower latitudes which thus confirmed the fact that meridional air temperature gradients are lower during warmer periods than colder periods.This means that the prevailing meridional circulation and drier climate is due to less humid air coming into the Euro-Asian continent from the oceans. In addition to others, in [19] is cited; “It is assumed that during ‘the last century’, CO2 concentration in the atmosphere increased by 10–15% and by the end of the twentieth century this rise will reach 30–35%. Using the semi-empirical model of the atmospheric thermal regime permits the revelation that a rise in CO2 concentration by 10% raises the mean temperature near the earth’s surface by 0.3 °C.” Please note that here cited ‘the last century’ refers to the 19th century.

Prof. Šinik made a physical interpretation of her statistical results by means of an energy balance equation representing the heat equivalent of temperature as a function of global radiation and cloudiness radiation as well as heat and humidity transport. By a model, the estimated air temperatures for Zagreb Grid are the best for annual or higher time-scales. The aforementioned estimations are also appropriate for the monthly scale for November only.

In [20], a relationship between monthly air temperature anomalies and large-scale atmospheric circulation has been established for the period 1961–1980. Within six types of anomalies, two of them are with extreme composite monthly anomalies in Croatia. Cold anomalies are followed by prevailing north-eastern wind direction over Croatia, while warm anomalies are followed with prevailing south-western wind direction. In both cases, meridional atmospheric circulation prevails, but north-westerly from Croatia are high pressure systems during cold air temperature anomalies in Croatia, but during warm anomalies, low pressure systems prevail over approximately the same area. In [21], in addition to the others, time series of air temperature for Zagreb Grič are analyzed for the period 1862–2000 using 25-year moving averages and principal component analysis. It was concluded that air temperature variations are probably a consequence of the global warming trends, shorter periods atmospheric processes’ variations and longer periods oceanic processes. Those variations in air temperature had a significant influence on water balance components such as evapotranspiration, soil water content as well as on the discharge of the Sava River Basin. In [22], a comprehensive statistical analysis has been done for Zagreb Grič air temperature time series including: minimum, mean and maximum air temperature for daily, monthly and annual time scales. In [22] is cited: “The analysis in this paper showed that the warming trend in minimum air temperature started in 1970, of the mean air temperature in 1988, and of maximum air temperature in 1998. Before these landmark years there were no statistically significant increasing trends in all characteristic air temperature to be observed. It seems that global warming made effect on Zagreb Grič air temperature during the 20th century, till the 1970, was not very strong. The statistically significant increasing trend of minimum temperature started in 1970.”

2.7. On Doubled Length of Western European Summer “Heat Waves since 1880

As the authors of the present review know, there are no additional significant analysis of extreme air temperature for Croatia except described in previous sections. However, there are such analysis for wider territory of Europe which includes at least the time series of extreme air temperature data for Zagreb Grič weather station for which good quality extreme air temperature data exists from 1881 to the present day [23]. Some of the analyses will be briefly described in this section, mostly in a chronological order of their publishing. Please note that terminology in the field of the ERA applications still is not unified, for example, different wording for periods of extremely high air temperature is frequently called as: “heat waves”, “heat event” or “heat wave events” etc.

An analysis of extreme air temperature indices has been conducted in [24] for the Western Europe using time series of daily minimum and maximum air temperature data for one century period, 1901–2000, using daily extreme air temperature percentile-based indices such as in [12], but the authors of [24] cited: “Our choice of temperature indices makes comparison of trends in the cold and warm tails with the trends more easily interpreted than the day-count indices, as the unit in all our indices is °C”. For temperature thresholds of, e.g., 2%, 5% and 10% corresponding abbreviations, TX2P, TX5P, TX10P, etc., for daily maximum air temperatures are used and TN2P, TN5P, TN10, etc.; for the minimum daily air temperature, indices are used.

Authors in [24] summarized their results: “Linear trends in these indices are assessed over the period 1901–2000. Average trends, for 75 stations mostly representing Europe west of 60 °E, show a warming for all temperature indices. Winter has, on average, warmed more (~1.0 °C/100 yr) than summer (~0.8 °C), both for daily maximum (TX) and minimum (TN) temperatures. Overall, the warming of TX in winter was stronger in the warm tail than in cold tail (1.6 and 1.5 °C for 98th and 95th, but ~1.0 °C for 2nd, 5th and 10th percentiles). There are, however, large regional differences in temperature trend patterns. For summer, there is a tendency for stronger warming, both TX and TN, in the warm than the cold tail only in parts of central Europe. Data inhomogeneity and relatively insufficient spatial coverage of weather stations in many parts of Europe preclude more robust conclusions. It is important that new methods are developed for homogenizing daily values of meteorological data.”

Three of four authors of [24] continued in [25] a complementary analysis of a set of 54 high-quality daily maximum air temperature time series from the Western Europe (including Zagreb Grič weather station from Croatia) for the period 1880–2005, which has been started in [23]. Authors considered three daily air temperature indices: daily summer maximum temperature (DSMT), hot days (HD) index expressed as a number of summer (JJA) daily maximum air temperature above the 95th percentile, and “heat wave” (HW), defined as the maximum number of the consecutive days where the DSMT exceeds the long-term daily 95th percentile of DSMT during summer season.

They showed that the length of summer season heat waves over the Western Europe has doubled during the period 1880–2005 and frequency of hot days has almost tripled. Additionally, it was indicated that the DSMT probability density function shows significant changes in the mean (about +1.6 °C) and variance (about +6%). These results indicated that Europe’s climate has become more extreme than previously thought.

An improvement of identifying and predicting the changing frequency of extremely high temperatures in Europe has tried to be improved in [26] “by combining statistical and physical approaches by including known atmospheric driving patterns in extreme value analysis (EVA)”. According to [26], very seldom has there been a quantification of any influence of atmospheric drivers on hot spells in Europe, such as atmospheric blocking, the North Atlantic Oscillation (NAO), the El Nino Southern-Oscillation (ENSO). In [26] is cited:

“We applied a novel combination of extreme value and geometric distribution to observed maxima from 74 stations across Europe, covering 1951–2010, to establish a stationary model of the expected magnitude, frequency and duration of hot spells that did not explicitly account for atmospheric drivers. Monthly time series of NAO, ENSO and 4 coherent atmospheric blocking regions were then incorporated as non-stationary covariates in the distribution parameter estimates to assess the dependence of hot spells on atmospheric covariates“. We concluded that ENSO does not have a significant influence on hot spell magnitude or frequency, the NAO is a significant driver of hot spell magnitude (maximum attained temperature), frequency (annual event count) and duration (length of event) in northern Europe and Atlantic bordering stations, and atmospheric blocking is a significant drivers of all aspects of hot spells in all parts of Europe. While NAO may increase peak temperatures by 2–4 °C only in the north, relatively strong atmospheric blocking could result in increased temperatures of at least 4 °C higher across Europe, with a commensurate increase in hot spell duration of 2–4 days.”

Among many references cited in [26], there is also [23], dealing with connection between heat waves in western Europe and large-scale forcing, and [27] deals with the application of the EVA “with inclusion of the trend and North Atlantic Oscillation index as covariates in the location parameter when applying the GEV fitting to the AMINW” (minimum winter air temperature) “resulted in a significant improvement over the model without covariates” to the weather station extreme temperature data for Belgrade (Serbia) located in the southern edge of Pannonian lowland.

The EVA results, connected with the global climate warming, could contribute to the Natural Disaster Risk Reduction (NDRR) national efforts, i.e., in protection of both human lives and their properties. The mitigation of global climate warming impact is usually considered by sectors of the economy such as agriculture, water management, health, transportation, etc. [28,29,30,31,32,33,34].

3. Conclusions

A detailed review of scientific literature on the EVA has been represented for Croatia and a less detailed review of the same topic for the Western Europe which includes some historical climate data for Croatia as well as for nearby countries. The review mostly gives a historical aspect of the EVA application in Croatia described in [6,7,11]. Although all three are important contributions, they are adapted for stationary extreme air temperature processes. In spite that, comparing the results for estimation “minima minimorum” values of minimum air temperature for Zagreb Grič weather station [6], e.g., for 100 and 200 years return periods, with minimum air temperature data for the period 1862–1969, are still approximately realistic [6]. Similar conclusion can be conducted for estimations in [7,11] including maxima for an “infinite” long-period, considered in [7]. However, a consideration of extreme air temperature non-stationarity was included in [12] by considering seasonal or annual averages of extreme air temperature trends and trends of “warm” and “cold” indices, defined as number of days with extreme air temperature above or below defined thresholds.), respectively. Trends of all of cited indices are significant for Croatia but positive for “warm” and negative for “cold” indices [12].

In [23,24,25,26,27], a more comprehensive approach for non-stationarity has been mostly applied for the Western Europe. For that purpose, good quality and homogenized secular time series of extreme air temperature data were used. The non-stationarity has been tried to be represented by covariates related to global climate warming, such as NAO, ENSO and atmospheric blocking incorporated as non-stationary covariates in the distribution parameter estimates, to assess the dependence of extreme air temperature indices on atmospheric covariates. The mitigation of the global climate variation and change impacts, usually considered by sectors of the economy as: protection of the environment, the construction industry, agriculture, water management, forestry, health, tourism, transportation and others, are among the highest national priorities. The results achieved could contribute to the NDRR on the local and national level [1,12,33,34]. The authors of present review recommend worldwide references for further reading [35,36,37,38,39].