The air temperature in the Baltic Sea Basin and Central Europe, including Poland, has been growing rapidly and strongly over the last half century (Brázdil et al. 1996, Fortuniak et al. 2001, Kożuchowski, Żmudzka 2001, BACC 2008, Philipona et al. 2009, Wójcik, Miętus 2014). The warmest region of Poland is Lower Silesia. This area is the south-western part of Poland and borders the Federal Republic of Germany to the west and the Czech Republic to the south, from which it is separated by Sudetes – the mountain range with the elevation of about 1000–1600 m a.s.l. (Fig. 1). Relatively high air temperature over the Lower Silesia area is conditioned by an unrestricted inflow of air masses from the west and the occurrence of foehn effects on the leeward slopes of Sudetes with air inflows from the southwest (Kwiatkowski 1975, Dubicka 1994, Dubicki et al. 2002, Ustrnul 2006, Ojrzyńska 2015).

The capital of Lower Silesia is Wrocław, where a very rapid increase in air temperature is observed. The increase in annual air temperature in Wrocław (TWr) in the years 1951–2018, expressed in degrees, calculated as the difference between the arithmetic means of the first five data (the years 1951–1955) and the last five data (2014–2018) of this series, is 2.42°C. The difference between these averages is highly significant (^{−1} and is highly statistically significant (^{−1}) or the northern hemisphere temperature trend (+0.022°C · year^{−1}) between 1951 and 2017 as estimated by GISTEMP

Data source: ZonAnn.Ts.txt,

A strong rise in air temperature observed since the end of the 1980s is commonly explained by the effects of the so-called Anthropogenic Global Warming (AGW), which is, in turn, caused by an increase in the concentration of greenhouse gases in the atmosphere. CO_{2} concentration in the troposphere is particularly heavy and is undoubtedly an effect of human activity: the burning of fossil fuels, both hard coal and brown coal, as well as hydrocarbons. The remaining causes of this increase, such as deforestation, are also a result of human activity, although their role in shaping the increase in greenhouse gas concentration in the atmosphere is less significant.

Meanwhile, the analysis of the temperature course in Wrocław indicates that changes in CO_{2} concentration in the atmosphere do not explain a number of aspects of its variability – both short- and long-term, including discontinuity of this course and temperature increase much stronger than global or hemispheric one.

The latest IPCC (2014) account in the Synthesis Report in Figure 1.9 (p. 48) shows the contribution of individual components to the rise in air temperature in the years 1951–2010. The total contribution of anthropogenic factors is estimated at +0.7(±0.1)°C, while the contribution of natural factors at ±0.1°C and natural internal climate variability also at ±0.1°C. While the term

Therefore, the combined effect of

Paleoclimatic and palaeoceanographic studies reveal that in the relatively recent past, around the last 2000 years, both global Earth's climate and the climate over particular areas have shown long-term variability similar to that observed today in terms of its scale. These changes occurred synchronously on the scale of the northern hemisphere, and not only in Europe and the North Atlantic environment, as previously assumed (Mann 2002, Oreopoulos et al. 2012). Quite frequently, in dozens of paleoclimatic studies, there are successive periods of varied thermal conditions in the northern hemisphere in the last 2000 years: _{2}O, in the atmosphere (with ca. 280 ppm for CO_{2}) was lesser than that present currently (with ca. 410 ppm for CO_{2}). Therefore, there are no compelling reasons to believe that the above-mentioned variability merely stopped in the second half of the 20th and early 21st century, and all or almost all the observed changes in air temperature are linked to increased concentration of greenhouse gases in the atmosphere, which, in turn, leads to AGW.

Thereby, the shown premises direct an attempt to explain grounds of the air temperature increase in Wrocław to study the role of internal dynamics of the climatic system as a reason of the observed air temperature changes.

This study aims to assess the role of internal variability of the climate system in shaping the variability of TWr, a city with long-term meteorological observations. Several weather stations, not too distant from one another, operating at the same time in an area of little hypsometric differentiation (Dubicka, Pyka 2001) have enabled continuous record of changes in climatic elements after 1950. If we compare data from weather stations in Wrocław, we can see that they are very strongly correlated. Accordingly, regardless of inevitable minor differences resulting from the impact of the closest surroundings of these stations, they provide a highly reliable record of changes in the climate of Wrocław occurring from 1951 to the present day. Due to a strong increase in air temperature in recent years, it was decided to go beyond the analysed years 1951–2010 in the IPCC (2014) and cover the years 1951–2018 by the research in order to include the processes taking place presently in this research.

In the analyses carried out, time series of values of meteorological elements with monthly resolution, characterising climatic conditions of Wrocław, were used. The annual values are calculated as simple arithmetic averages in a calendar year (January–December). The values of monthly air temperature, monthly sums of precipitation, number of days with precipitation, atmospheric pressure, relative humidity and general cloud cover come from official data collected by the state observation network of the Institute of Meteorology and Water Management (IMGW) at the meteorological station Wrocław (Czernecki et al. 2020). These series were taken from the database

The long (the years 1791–2007) annual temperature series used comes from Bryś and Bryś (2010). It was supplemented by official data from the IMGW observation network until 2018. The monthly sunshine values for the years 1951–1960 come from the Meteorological Observatory of the Wrocław University located in Wrocław-Biskupin (east district of the city: ϕ = 51°06′ N, λ = 17°05′ E, h = 116 m a.s.l.), for 1961–2018 from the Meteorological Observatory of the Wrocław University of Life Sciences located in Wrocław-Swojec (east district of the city: ϕ = 51°07′ N, λ = 17°10′ E, h = 121 m a.s.l.) (Bryś et al. 2019). The two stations are separated in a straight line by a distance of about 5 km. The series used in this work is a sequence connected from both these stations. Before the combination, these values were examined in detail for their homogeneity, and the result was positive.

An increase of the CO_{2} concentration in the atmosphere gives an additional flux of energy directed to the Earth's surface, which causes a rise in temperature. The IPCC (2001, 2007, 2014) refers to this stream as radiative forcing. The radiative forcing values (hereinafter referred to as variable DF; W · m^{−2}) were calculated from the series of annual concentrations of CO_{2} in the atmosphere using the formula (after IPCC (2001), chapter 6, Tab. 6.2).

ΔF – radiative forcing (W · m^{−2}),

C – current concentration of CO_{2} in the atmosphere (ppm),

C_{0} – concentration of CO_{2} in the pre-industrial era (280 ppm),

ln – natural logarithm.

The series values of the average annual CO_{2} concentration from which DF was calculated for the years 1951–1958 are taken from the Global Mean Mixing Ratios: NASA GISS (Goddard Institute for Space Studies) Data

_{2}annual mean data: NOAA Earth System Research Laboratory, Global Monitoring Division

The calendar of frequency of the middle-tropospheric circulation types (500 hPa) according to the Wangengeim-Girs classification (Girs 1971, Girs, Kondratovich 1978) comes for the years 1951–2018 from Arctic and Antarctic Research Institute, Russian Federation, St. Petersburg. These data for 1951–2005 were taken from Annex 1 of the work of Dimitrieev and Belyazo (2006), whereas the unpublished data for the remaining years were obtained directly from AARI. Illustrations showing patterns of long-wave distribution in the W, E and C circulation types are not presented in this work; they are among others published in Barry and Carleton (2013) as Fig. 7.9 (p. 569). A series of the NAO (Hurrell 1995) winter (DJFM) station indicators (collection: DJFM North Atlantic Oscillation Index Station-Based) was downloaded from the NCAR UCAR (National Center for Atmospheric Research, University Corporation for Atmospheric Research) Climate Data Guide

The analysis methods used are standard statistical methods – correlation analysis, regression analysis and variance analysis. Statistical significance of correlation coefficients and estimated regression coefficients were determined by the Student's

Wrocław has a relatively long series of instrumental measurements of air temperature compared to other places in Europe. Temperature recording started in 1791 and has continued at several points within the city area. Individual sections of the measurement series were checked and homogenised (Bryś and Bryś 2010), creating a uniform sequence covering the years 1791–2007. This allows us to compare the course of the temperature curve in the years 1951–2018 (processed period) to the changes occurring in a much longer period. The analysis is based on the annual average air temperature – a comprehensive measure of thermal changes occurring in Wrocław.

Figure 2 shows the course of annual temperature changes in Wrocław in the years 1791–2018, presenting the values of annual temperature as deviations from the long-term average. The average annual temperature in this period is 8.68°C, its SD being 1.05°C.

The course of annual TWr reveals the occurrence of long-term, multi-decadal variability of considerable amplitude (min 5.5°C in 1829, max 11.2°C in 2018), which manifests itself as successive periods of cooling and warming. The changes take place against the background of a long-term (in fact on a centennial timescale) positive trend in a series of annual temperatures. The rate of temperature rise varies and is a function of time, and thus the actual trend is non-linear in its nature. The highest rate of temperature increase occurs at the end of the course, approximately since the turn of the 1980s and 1990s (Fig. 2). The linear trend, calculated for the years 1791–2018, has a value equal to +0.0093(±0.0009)°C · year^{−1} and explains for (adj. ^{2}) around 34% of variance in the annual temperature in these 228 years. As a result of the positive trend in the series of annual temperatures in Wrocław in the 1890s, the annual temperature relatively permanently assumed higher values than the long-term average (Fig. 2), and since the beginning of the 1990s, on average, it has remained at the level higher by +1SD than the multi-annual average.

The period of 1951–2018, for which the analysis of the role of variability within the system in the shaping of temperature changes is made, is in the final part of the 228-year series and constitutes its warmest fragment. There is a strong (+0.034(±0.005)°C) and highly significant (

The review of TWr supported by an analysis of the envelope of its variability band indicates that it is divided into two parts (Fig. 3). The boundary between two different periods in the course of temperature curve occurs between 1987 and 1989, when there is a rapid increase in annual temperature and a remarkable shift in the nature of its course. The year 1988 is taken as the boundary year between the two periods.

In the first period (1951–1988), differences between particular years are significant, the average temperature is lower than the multi-annual average of 1791–2018 (+8.26°C), and the trend in the series is zero. In the second period (1988–2018), a strong (+0.052(±0.015)°C · year^{−1}) and statistically significant (

Such course of the TWr values explains that a rapid temperature increase began after 1988, and the whole temperature increase in the considered period 1951–2018 occurred in its second part, that is, between 1988 and 2018. This course differs considerably from the monotonically increasing course of CO_{2} concentration in the atmosphere (Fig. 5).

This course of the TWr value explains that the rapid increase in temperature began after 1988, and the entire increase in temperature in the considered period of 1951–2018 occurred only in its second part, in 1988–2018, while the uniform linear trend TWr calculated for the period 1951–2018 does not reflect the actual course of changes TWr.

The trends in the course of TWr and CO_{2} concentration coincide only after 1988; earlier on, increasing CO_{2} concentration is not reflected in the long-term (38 years) course of temperature. Moreover, the short-term variability of both courses (Fig. 5) shows that the monotonous increase in CO_{2} concentration does not seem to be connected with the strong variability of TWr over the years. It follows that the reasons for the sudden change in the TWr regime after 1988 are also to be sought in the processes related to the internal dynamics of the climate system rather than in the processes associated with AGW.

If we consider possible reasons for the increase in the annual TWr after 1988 from a purely thermodynamic point of view, a sensible conclusion is that the amount of heat must have increased in the atmosphere during the period in question. In addition, the increase in the amount of heat in the atmosphere must have occurred rapidly, in a relatively short time, within 2–3 years; and then it has been increasing progressively.

In general, an increase in the amount of heat over a research area can occur due to two factors:

by a more frequent advection of air masses with increasing enthalpy as a consequence of atmospheric circulation influence (advection factor) or/and

by changes in the net radiation of this area towards its growth (radiation factor).

In the last case, an increase in the heat resources may occur when the amount of solar energy reaching the ground increases or when heat loss from the atmosphere is reduced. The growth of radiation inflow to the ground may occur due to the limitation of the cloudiness and an increase of the sunshine duration (Sh), as well as an increase of the atmospheric transparency and/or an increase of the solar constant.

The changes in the solar constant which is a conventional measure of mean Total Solar Irradiance (TSI), i.e. solar energy reaching the upper boundary of the atmosphere, as a basic reason for air temperature increase after 1988 can be ignored. Differences in the amount of the solar constant, being a result of the variable solar activity are virtually insignificant, because it reaches only 1.7 W · m^{−2} (in the year 1680, when the Maunder Minimum was – 1360.0 W · m^{−2} and maximum in the year 2002 – 1361.7 W · m^{−2}, at the mean value – 1360.45 W · m^{−2}; Kopp et al. 2016). In the examined period 1951–2018, they are on average lesser from 1 W · m^{−2}; moreover, the course of TSI variability doesn’t appear to be a reliable basis of their connections with the observed rapid increase of TWr after 1988. The changes in the stratospheric aerosol concentration (GISS stratospheric aerosol optical depth at 550 nm) also do not show any significant connections with the course of TWr (

Limitation of heat loss may take place as a result of chemical changes in the atmosphere: an increase in the content of greenhouse gases in the atmosphere (mostly CO_{2}) or an increase in cloud cover during the cold season of the year. In both cases, return radiation increases. Reduction of heat loss by increasing greenhouse gas concentration, mostly CO_{2}, and hence a rise in annual temperature is nothing other than AGW. In this case, human activity is the cause of the change in the heat balance; this change is not brought about by any processes of changeability within the system. This indicates that despite the unsatisfactory explanation of the changes in TWr by the changes in CO_{2} concentration, the radiative forcing (DF) cannot be ignored in further considerations and estimates.

Studies into the factors resulting from the internal variability of the climate system in shaping variability of the annual air temperature require identification and selection of variables most strongly influencing the deviation in the annual temperature value from its idealised annual cycle resulting from the inflow of solar energy and heat brought in by advection.

At a point with given geographical coordinates, potential solar energy inflow is the same on successive days in the year. A potential source of solar energy is defined as the amount of solar energy penetrating the atmosphere at its upper boundary on a given day. It is a function of the astronomical factors (length of a day, the Sun's height, which, in turn, are function of the Sun's declination and the latitude) and TSI values. Thus, both monthly and annual values of the potential solar radiation inflow, being daily totals in a given month or year, cannot differ from each other in successive years. Therefore, if the annual average temperature involves variation within the year, this variation, if caused by changes in the amount of solar energy supplied, with a relatively constant TSI value, must be brought about primarily by factors that interfere with the flow of solar energy to the Earth's surface at given geographical coordinates.

The basic factor regulating the flow of solar energy to the Earth's surface is cloudiness. Clouds are shaped by changing weather conditions or, alternatively, by the variability of synoptic situations. Internal processes of the climate system are manifested through this type of variability. Cloudiness is observed as general cloud cover (N), both during the day and night, and then averaged to daily, monthly and eventually to annual values. Solar energy flows to the Earth's surface only during the day. For this reason, data on cloud cover do not provide fully reliable information about the amount of solar energy flowing to the Earth's surface. Correlation of monthly and annual values of general cloudiness in Wrocław with the same series of air temperature shows that such relation changes the sign into negative or positive during the year, and statistically significant correlations occur only in some months of the warm season (Table 1). Statistically significant relationships between annual cloudiness and annual temperature are missing.

Values of correlation coefficients (r) between monthly and annual cloudiness in Wrocław and air temperature in Wrocław (TWr) and their statistical significance (p). Analysis period: 1951–2018.

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year | Jan |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r | 0.100 | 0.210 | −0.180 | − | − | − | − | −0.24 | − | 0.010 | 0.090 | 0.130 | 0.120 |

0.401 | 0.092 | 0.152 | −0.004 | 0.001 | 0.006 | 0.000 | 0.053 | 0.000 | 0.929 | 0.477 | 0.280 | 0.344 |

Significant correlations (

Sunshine duration is a climatic element that informs us about the time of solar operation during a day, month or year. It considers the

Values of correlation coefficients (r) between monthly and annual sunshine, and monthly and annual air temperature in Wrocław (1951–2018) along with their statistical significance (

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year | Jan |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r | 0.070 | −0.110 | 0.270 | 0.640 | 0.620 | 0.140 | 0.020 | 0.140 | |||||

0.583 | 0.381 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.847 | 0.239 | 0.000 |

Symbols as in Table 1.

The distribution of the values of correlation coefficients indicates that in the period from March to September inclusive, sunshine and air temperature correlations in Wrocław are significant, while the correlations in the period from April to September are highly significant. Accordingly, the annual air temperature is also quite strongly and significantly associated with annual ShWr and its variability is explained by approximately 37% of TWr variance.

The largest amount of solar energy is supplied during the _{Apr–Aug}) in Wrocław is clearly more strongly correlated with the annual temperature (r = 0.70) than with the annual ShWr (Table 2).

A review of scatterplots and courses (Fig. 7) of the annual TWr as a linear function of ShWr_{Apr–Aug} reveals that the most important features of temperature changes, such as a rapid change of the temperature from one variability regime to another and a positive trend after 1988, are quite well represented. This proves that ShWr_{Apr–Aug} variability is one of the causes of TWr variability. At the same time, it can be observed that in some years, there are significant differences between the observed TWr values and the TWr values estimated from the dependencies, indicating that other factors than ShWr_{Apr–Aug} need to be considered, which shape the variability of TWr.

Residual analysis revealed that the differences between the observed values of TWr and those estimated from ShWr_{Apr–Aug} are particularly large when the average temperature of the first quarter in Wrocław is either significantly lower than the average (e.g. 1956, 1963, 1969, 1996) or much higher than the average (e.g. 1974, 1975, 1989, 1990). This indicates that possibly the most important yet ignored factor is one that regulates thermal relations in the cold season of the year.

The above statement moves our search for the next variable to advection processes, which are controlled by atmospheric circulation. This sought for variable is atmospheric circulation in the cold period, in which sunshine duration does not significantly affect the variability of TWr. The NAO essentially regulates winter temperature over large areas of Europe and Poland (van Loon, Rogers 1978, Hurrell 1995, Hurrell et al. 2003, Marsz, Styszyńska 2010).

NAO is the result of climate variability within the system and results from the interaction of the ocean and atmosphere over the North Atlantic (Curry, McCartney 2001, Frankignoul et al. 2001, Czaja, Frankignoul 2002, Czaja et al. 2003). A number of studies (e.g. Cohen, Barlow 2005, Semenov et al. 2008) have shown that there are no causal relationships between increasing CO_{2} concentration in the atmosphere or AGW in general and NAO variability.

In winter periods (December–March), when NAO reaches the highest intensity, in the positive phase of oscillation, maritime Polar air mass

In the negative phase of NAO, southern circulation dominates and the relations of air temperature with the NAO index value become non-stationary, due to the possibility of advection from both the northern and eastern sector as well as the southern sector. However,

The station-based winter (DJFM) NAO Hurrell index was used for the analysis of NAO relations with monthly TWr. The results of the analysis are presented in Table 3.

Values of correlation coefficients (r) and their statistical significance (

Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r | 0.610 | 0.190 | 0.190 | 0.020 | 0.210 | 0.230 | 0.140 | −0.160 | 0.240 | ||||

0.000 | 0.000 | 0.000 | 0.114 | 0.125 | 0.895 | 0.080 | 0.008 | 0.058 | 0.258 | 0.198 | 0.052 | 0.000 |

Symbols as in Table 1.

The variability of the winter NAO Hurrell index shows, except for November, a positive correlation with the monthly temperature in Wrocław. Highly significant correlations with monthly temperature occur in the period from January to March. Additionally, there is a significant asynchronous correlation in August, which is delayed in relation to NAO. In the remaining months, the values of correlation coefficients of the NAO index with TWr are insignificant. Such correlation of the winter NAO index with monthly temperature, distributed over time, including asynchronous August correlation, is typical for the whole of Poland (Marsz, Styszyńska 2010).

The range of seasonal variations in air temperature is the largest during winter. For this reason, the variability of air temperature of the first quarter (January–March) explains (adj. R^{2} 100%) 57.5% the variance of annual TWr in the years 1951–2018. The reliable explanation of monthly temperature variability in Wrocław in the first quarter by the winter NAO index (about 50%) is the most important reason for the strong and highly significant correlation of the winter NAO Hurrell index also with TWr.

Thus, the two variables can be used to determine the role of factors operating within the system in shaping the variability of annual TWr: sunshine duration in the _{Apr–Aug} and the winter NAO Hurrell index (1995) – NAO_{H} variable. These are not all possible variables; however, these are possibly the most important ones.

Multiple regression was used to analyse the relationships between the variables, in which the explained variable was the annual TWr and the explanatory variable (independent) was sunshine duration in the _{Apr–Aug}) and the station-based NAO Hurrell index (NAO_{H}). The estimation of the parameters of the multiple regression equation using the least squares method produced the following result:

There is the statistical characteristics of the equation: R (multiple regression correlation coefficient) = 0.80, adj. R^{2} (corrected for the number of degrees of freedom, the coefficient of determination) = 0.6290, F(2,65)) = 57.8 (Fisher-Snedecor test), p (significance of the equation) << 0.001, standard error of estimation (SEE) = 0.63. The estimation of intercept and regression coefficients is highly statistically significant (

In Eq. (2), the variability ShWr_{Apr–Aug} explains for 48.6% and the variability NAO_{H} for 15.4% of the annual variance of TWr in the years 1951–2018. The scatterplot of the values estimated using this Eq. (2) in relation to the observed values is presented in Figure 8, and the courses of the observed and calculated TWr values (using the Eq. (2)) is shown in Figure 9.

In the course of the TWr values, estimated with Eq. (2), a few cases of strong underestimation of annual temperature value (e.g. in 2013) can be noted. The residual analysis showed that these are the cases in which, with a negative NAO value in the cold period, advection of warm air from the south predominated.

A weak, statistically insignificant trend is observed in the remainder of Eq. (2), and the whole series of residuals is quite strongly (r = 0.53) correlated with the temperature of the fourth quarter (October–December) in Wrocław. This indicates that Eq. (2) does not include an increase in air temperature occurring in this part of the year. Considering the selection of explanatory variables, it is understandable. After introducing the NAO station-based index from December as the third variable in the equation, the equation remains highly significant, but the degree of explanation of the dependent variable increases so slightly (by 2%) that it does not justify its further complication.

The estimated TWr trend in the series of values calculated from Eq. (2) is equal to +0.025(±0.004)°C. It is a trend of 0.009°C · year^{−1}, and it is lower than the trend occurring in the observed series of annual TWr in the period in question (+0.034(±0.005)°C · year^{−1}). Considering the errors in estimating both trends, the difference is statistically insignificant. It can be assumed, however, that the reduced value of the annual temperature trend in Wrocław results from ignoring the influence of CO_{2} concentration increase in the atmosphere, giving an additional energy stream directed to the Earth's surface, which is the cause of temperature growth, that is radiative forcing (DF variable, see Eq. (1)).

The calculated values of radiative forcing according to the formula (1) for the years 1951–2018 were introduced as the third variable into Eq. (2) and the parameters of this equation (Eq. (3)) and its statistical characteristics were calculated. The obtained results are as follows:

Equation (3) is highly significant (F(3,64) = 49.5, ^{2} = 0.685). The SEE of the TWr value decreased slightly (SEE = 0.58).

From the analysis of variance, it follows that, in the Eq. (3), variability ShWr_{Apr–Aug} explains for 49%, variability NAO_{H} for 15% and variability DF for 5.9% of the variance of the annual TWr in the considered period. The trend of TWr values calculated from Eq. (3) increased and is practically the same (+0.035(±0.003)°C · year^{−1}) as in the series of observed values. This suggests that variable DF introduces only a better fit of the trend (in relation to the real TWr trend) into Eq. (3), as a manifestation of TWr variability.

A review of the graphs of series TWr, ShWr_{Apr–Aug}, NAO_{H} and DF, from which the trends were removed, and their comparison with the course of observed TWr values confirms the above-mentioned suggestion. Similarly, regression analysis, in which TWr devoid of the trend was the explained variable, and ShWr_{Apr–Aug}, NAO_{H} and DF were the explanatory variables from which the trend was removed, allowed us to create an equation with only two variables: The ShWr_{Apr–Aug} and NAO_{H} jointly explain ~46% of the variance of the explained variable. The calculation program (progressive stepwise regression) eliminated the variable DF without trend as statistically insignificant (p = 0.939).

The obtained results of the analysis show that variability of the three simple independent variables ShWr_{Apr–Aug}, NAO_{H} and DF explains together 68.5% of the annual variance of the TWr in the years 1951–2018. A proportion of the explained variance is high, because without explanation is only 31.5% of the TWr variability.

It is significant, that no discontinuity in the DF course for the years 1951–2018 does not occur. On the other hand, such discontinuity, less or more distinct, in the similar courses of the two variables ShWr_{Apr–Aug} and NAO_{H} occurs in the years 1987–1989. It explains, in the statistical sense, a radical change of the annual air temperature course in Wrocław. It is only from this time (1987–1989), we could say, that a progressive warming occurs. However, there is a question: what climatic process or a group of these processes are the reason for this warming and why since 1988?

The reason for the observed warming is a change in the macro-circulation conditions in the Atlantic-Eurasian circular sector, expressed as a change of the so-called

In the years 1951–2018, circulation epochs changed twice. Savichev et al. (2015) define the following circulation epochs: until 1965 (1949–1965) – The E+C Epoch, from 1966 to 1989 – The E Epoch and from 1990 to 2014 – The W Epoch (the quoted year 2014 does not indicate that circulation epoch has closed in that year. It indicates only that (Savichev et al., 2015) made of the series of macro-types frequency solely to the year 2014). Degirmendžić and Kożuchowski (2018) distinguish the same epochs in the years 1951–2018, and their limits show small shifts in relation to the limits set by Savichev et al. (2015). According to Degirmendžić and Kożuchowski (2018), the end of the E+C Epoch falls in 1969, the beginning and the end of the E Epoch, respectively, in 1970 and 1991, and the beginning of the W Epoch in 1992. In view of the different methods of defining the boundaries of macro-circulation epochs by the quoted authors and the different moments of the beginning of the analysis, these differences are of little significance.

The moment the annual air temperature regime in Wrocław changed and a strong upward trend appeared in a series happened in the years 1987–1989, which is very close to the change of the circulation epoch E to W according to Savichev et al. (2015) in 1989/1990 and according to the divisions by Degirmendžić and Kożuchowski (2018) in the years 1991/1992.

At the same time (1987–1989), a similar change in the annual air temperature regime has taken place at numerous European stations, from the French coast of the Bay of Biscay (Merignac Aeroport de Bordeaux: 44.8°N, 0.7°W) to the British Isles and the southern Scandinavian. It was also noted all over Germany, Switzerland and other countries of Central Europe as well as in vast areas of the Russia Lowland (Minsk, Moscow) up to Kazan (55.7°N, 49.2°E) and Arkhangelsk (64.3°N, 40.3°E). The change in temperature regime was also manifested at some European high mountain stations in the Alps (Saentis, Zugspitze) and in the Sudetes (Śnieżka) and the Carpathians (Kasprowy Wierch). This confirms that the revealed change in the annual temperature regime in Wrocław is a manifestation of macro-scale processes, not local processes.

The review of the annual anomaly of the attendance of W, E and C macro-types in the years 1951–2018 (Fig. 10) shows that in 1987, the frequency of all three macro-types of the middle-tropospheric circulation approached the values corresponding to the multi-annual average of the period 1951–2015. After 1988, the frequency of the macro-type W became higher than the long-term norm, the attendance of the macro-type E dropped below the long-term norm and the frequency of the macro-type C oscillates around the long-term average.

The frequency of macro-type W which is higher than normal of the last circulation epoch, after 1988, results in a change in weather structure in relation to the previous epoch. Each macro-type is associated with the occurrence of a specific synoptic situations in the lower troposphere (e.g.

Values of correlation coefficients (r) and their statistical significance (_{Apr–Aug}) and annual precipitation (PWr) in Wrocław (1951–2018). Markings as in Table 1.

Macro-types | TWr | ShWr | ShWr_{Apr–Aug} | PWr | |
---|---|---|---|---|---|

W | r | 0.470 | 0.620 | 0.630 | −0.310 |

E | r | −0.300 | −0.600 | −0.590 | 0.330 |

C | r | −0.240 | 0.090 | 0.040 | −0.100 |

Lower frequency of macro-type E and the simultaneous increase of macro-type W frequency led to an increase in the sunshine (see Fig. 6), also during the

The winter NAO index, which increased in the same period, also generously contributed to air temperature increase (Głogowski et al. 2020). The winter NAO index is highly significantly associated with the macro-type W frequency from January to March (r = 0.51,

Therefore, the mechanism of temperature increase in Wrocław is linked to the increase in winter temperature forced by the increased attendance of the positive phase of NAO and summer temperature caused, in turn, by the increase in sunshine duration, can be consistently explained by the change of macro-circulation conditions. Both result from processes functioning within the climate system and have rather little to do with AGW in terms of causes.

The regression analysis shows that the two independent variables together, being a manifestation of the internal dynamics of the climate system, explain about 63% of the annual variance of the TWr between 1951 and 2018. It means that all other factors that are not included in Eq. (2) but which influence the formation of the annual temperature variance over can explain at most ~40% of its variability. The inclusion of radiative forcing as the third independent variable (Eq. (3)) explains that the increase in CO_{2} concentration in the atmosphere, i.e. the process that leads to the AGW, accounts for only ~6% of the annual variance of air temperature. This last value constitutes only about 1/10 of the part of the TWr variance that is explained by the effects of intra-system climatic factors.

This indicates that the variability of the annual TWr is mostly shaped by the processes resulting from the internal dynamics of the climate system and these processes play an essential role in the increase in air temperature. Two simple factors – the sunshine duration of the

The increase in the heat resources in the atmosphere that causes the air temperature to rise during the warm season comes from the increased inflow of solar radiation (ShWr_{Apr–Aug}) to the ground. This is the simplest possible process leading to an increase in air temperature. The heat causing the temperature rise during the cold season comes from the surface of the North Atlantic from where it was transported to Poland together with air masses by atmospheric circulation (NAO), raising the temperature during the winter months. The heat taken from the surface of the North Atlantic is also solar heat – it comes from short-wave radiation, which was previously absorbed and accumulated in near-surface volumes of ocean waters.

In the light of the above, the hypothesis of the dominant role of increasing CO_{2} concentration in the atmosphere as the main, or the only, cause of the temperature increase observed at present should be carefully addressed. Its share in explaining the annual air temperature variation in Wrocław does not exceed 6%. The role of increasing CO_{2} concentration, and thus the role of human activity in shaping the currently observed increase in air temperature, seems to be definitely overestimated.

#### Values of correlation coefficients (r) and their statistical significance (p) between the annual frequency of W, E and C macro-types of the middle-tropospheric circulation and annual air temperature (TWr), annual sunshine duration (ShWr) and sunshine duration of the long-day months. (ShWrApr–Aug) and annual precipitation (PWr) in Wrocław (1951–2018). Markings as in Table 1.

Macro-types | TWr | ShWr | ShWr_{Apr–Aug} |
PWr | |
---|---|---|---|---|---|

W | r |
0.470 |
0.620 |
0.630 |
−0.310 |

E | r |
−0.300 |
−0.600 |
−0.590 |
0.330 |

C | r |
−0.240 |
0.090 |
0.040 |
−0.100 |

#### Values of correlation coefficients (r) and their statistical significance (p) between (DJFM) winter NAO Hurrell index and monthly and annual air temperature in Wrocław (1951–2018).

Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r | 0.610 | 0.190 | 0.190 | 0.020 | 0.210 | 0.230 | 0.140 | −0.160 | 0.240 | ||||

0.000 | 0.000 | 0.000 | 0.114 | 0.125 | 0.895 | 0.080 | 0.008 | 0.058 | 0.258 | 0.198 | 0.052 | 0.000 |

#### Values of correlation coefficients (r) between monthly and annual sunshine, and monthly and annual air temperature in Wrocław (1951–2018) along with their statistical significance (p).

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year | Jan |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r | 0.070 | −0.110 | 0.270 | 0.640 | 0.620 | 0.140 | 0.020 | 0.140 | |||||

0.583 | 0.381 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.847 | 0.239 | 0.000 |

#### Values of correlation coefficients (r) between monthly and annual cloudiness in Wrocław and air temperature in Wrocław (TWr) and their statistical significance (p). Analysis period: 1951–2018.

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year | Jan |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r | 0.100 | 0.210 | −0.180 | − |
− |
− |
− |
−0.24 | − |
0.010 | 0.090 | 0.130 | 0.120 |

0.401 | 0.092 | 0.152 | −0.004 | 0.001 | 0.006 | 0.000 | 0.053 | 0.000 | 0.929 | 0.477 | 0.280 | 0.344 |