Causes and Course of Climate Change and Its Hydrological Consequences in the Greater Poland Region in 1951–2020

The long-term average (1951–2020) annual temperature in Poznań is 8.7°C, and shows a relatively significant inter-year variability; the minimum annual temperature recorded in this period was 6.6°C (in 1956), while the maximum was 11.8°C (in 2019). Spectral analysis of the data series shows the presence of a relatively strong periodicity of about 7.7 years. This periodicity (around 7–8 years) is typical for the annual air temperature throughout Poland and has been described many times by Polish researchers, including Boryczka (1998), Fortuniak (2000), and Fortuniak et al. (2001). It can be associated with a very similar periodicity occurring in the winter changes of the NAO (Boryczka et al. 1999), which, by regulating the temperature of the winter months, exerts a strong impact on the annual temperature in the areas around the Baltic Sea, and more generally, in Central Europe.

The course of the annual air temperature in Poznań corresponding to the period 1951–2020 is shown in Figure 2A. In that period, there is a positive trend in annual temperature in the series, equal to +0.035 (± 0.005)°C · year⁻¹ with high statistical significance (p <0.001). The temperature increases in Poznań estimated from the value of the linear trend for the analysed period of 70 years (1951–2020) is 2.4°C. Both the trend value and the resulting increase in annual temperature are greater than the global temperature and the temperature increase in the Northern Hemisphere estimated by the GISTEMP Team (Lenssen et al. 2019, NASA 2022) for this period. On the other hand, the value of the trend in Poznań is slightly lower than the value of the Northern Hemisphere trend reported by GISTEMP, which is +0.037 (±0.004)°C · year⁻¹.

Fig. 2

A detailed analysis of the annual temperature series, together with the analysis of the course of the envelope of the band of its inter-annual variability, shows that this series is unstable. The temperature course consists of two clearly different parts, with different ranges of variability and behaviour (Fig. 2A). The boundary between these two parts (discontinuity) is between 1987 and 1989. Next, it is arbitrarily assumed that the moment separating the two sub-periods occurs in 1988, with 1988 taken as the last year of the first sub-period and the first year of the second sub-period.

In the first sub-period (1951–1988), the inter-annual variability of temperature is significant, and there is no trend in the series – its value (+0.003 (±0.011)°C · year⁻¹) is statistically insignificant (p = 0.827). In the second sub-period, the inter-annual variability clearly decreases (Fig. 2A, Table 1) and a statistically significant positive trend appears in the course of the annual temperature (+0.057 (±0.014)°C · year⁻¹, p = 0.003). The increase in the value of the standard deviation (σ) in the second sub-period compared with the first one (Table 1) is a consequence of the occurrence of a trend in the temperature course, and not of an increase in the amplitude of inter-annual changes.

In statistical terms, the series of annual air temperature in Poznań is made up of two completely separate populations of variables, differing significantly both in terms of mean values and the distribution of values in both sub-periods. The scale of these differences is presented in Figure 2B, which shows that the lower limit of the second quartile in the second sub-period is above the upper limit of the third quartile in the first sub-period.

The temperature distribution chart shows that between 1987 and 1989, there was a noticeable change in its regime – there was a sudden, abrupt shift in the annual air temperature by about +1 degree, and then a further, still ongoing, increase began, interrupted only by two deeper chills in 1996 (7.0°C) and in 2010 (7.8°C) (see also Figure 2A).

Such an abrupt change in the structure of the temperature variability allows formulating a thesis that between 1987 and 1989, there was a change in the climate of Greater Poland. According to the definition of climate proposed by Monin (1982), climate is a certain set of multi-dimensional statistical characteristics describing the long-term state of the atmosphere over a given area. Going beyond the limits of long-term norms of even one climate element is tantamount to climate change.

The results of this analysis show that presentation of the air temperature increase in Poznań by means of a uniform trend covering the entire period in question is not correct, and such an operation does not represent the actual changes taking place in the function of time. In fact, in 1951–1988, despite the strong inter-annual variability of air temperature, there was no temperature increase, and the warming did not start until 1988. Research conducted by Kolendowicz et al. (2019) based on the changes of temperature throughout the whole period of the measurements (i.e. from 1848) carried out by the Institute of Meteorology and Water Management – National Research Institute (Warsaw) in relation to Poznań showed that despite the strong inter-annual variability, at least from 1902 to 1987, there was no statistically significant trend in the annual temperature

Kolendowicz et al. (2019; their Fig. 5) calculated the trend value of +0.002°C · year⁻¹ for the period 1902–1988, and its statistical significance (p) as 0.446.

The aforementioned statements raise a number of further questions, some of which, considered to be the most important, need to be solved. These are:

Could it be that the discontinuity detected in the course of the trend in air temperature change in Poznań is not a case of a local peculiarity occurring only in Greater Poland, but possibly an observation resulting from a simple breach of the homogeneity of the dataset sequence?

The analysis of the annual temperature series at weather stations in Poland shows that this discontinuity is detected at almost all stations and occurs at the same time, and also shows similar features. It is clearly visible in the changes of the annual mean area temperature, which is the average temperature from a dozen or so stations evenly distributed throughout Poland (Marsz, Styszyńska 2019). This means that the described discontinuity in the temperature changes is not a case of breaking the homogeneity of the measurement data in Poznań, nor is it a local phenomenon, limited by its occurrence to the Greater Poland region.

The so-far unpublished studies of the authors on the variability of the annual air temperature in Europe allow the conclusion that the described jump in temperature and the change in the regime of its course occur, although with some differences in the size of the jump and the value of the positive trend after 1988, over almost the entire area of Europe – from the shores of the Bay of Biscay (Merignac, France; see Fig. 3A) to the interior of European Russia (Nizhny Novgorod; see Fig. 3B), and from the shores of the Mediterranean Sea (Larissa, Greece) to the shores of the White Sea (Arkhangelsk, Russia).

Fig. 3

At the majority of European stations from 1950 to 1988, the annual air temperature trend was nearly zero, and at a large number of European stations this trend has been zero since 1930. This means that also in vast areas of Europe, despite the large inter-annual temperature variability in 1930–1989, warming did not begin until 1988.

This indicates that the described change of the annual air temperature, with its discontinuity in 1987–1989, records the operation of a process of a large, macro-regional scale, covering the entire land part of the Atlantic-European circulation sector, which inevitably also appears in Greater Poland.

If in 1987–1989 there was an abrupt change in the temperature regime in Greater Poland, it is important to explain how the behaviour of climatic elements other than temperature in the same period was shaped and how their relationship with temperature (T) was formed. The following were selected for the analysis: annual cloud cover (hereinafter referred to as N), annual precipitation (P), annual relative humidity (f), annual SD and the warm half-year SD_Apr–Sep, as well as annual wind velocity (Vw).

The values of the correlation coefficients between these elements in the square matrix system are summarised in Table 2. Since the measurement series of SD cover only 62 years, each time the number of correlated pairs of variables, for which the correlation coefficient was calculated, is given in the table. The p-values were estimated according to the number of correlated pairs of values.

When analysing the distribution of the obtained correlation coefficients, it can be seen that they represent to a greater extent dependencies found in the analysis of weather conditions occurring under typical synoptic conditions than purely physical relationships between them.

In Table 2, there are two groups of the most closely related climatic elements, namely the group associated with cloudiness and precipitation, and the group associated with sunshine and temperature. Both these groups of elements behave autonomously, and the element constituting the resultant of their opposing action is the course of air humidity.

In the course of the annual precipitation totals in the entire multi-year period under consideration (1951–2020), no trend is detectable, and its characteristic feature is the occurrence of significant inter-annual variability. With the average annual precipitation of 521.2 mm, the minimum recorded value is 275.0 mm (in 1982), and the maximum is 772.1 mm (in 1967), while the standard deviation (σ) is 108.9 mm.

Total cloudiness and relative humidity are strongly positively correlated with the changes of precipitation (Table 2). The positive correlation of total cloudiness and precipitation totals is obvious, since precipitation cannot occur without cloud cover. Relative humidity is strongly positively related to the occurrence of precipitation and the process of subsequent evaporation of rainwater from the ground surface. Total cloudiness is negatively related to SD, which is also understandable, since the presence of a cloud cover limits the access of direct radiation to the Earth's surface. Precipitation and cloud cover do not show statistically significant relations with air temperature.

Temperature shows strong negative correlation with relative humidity and very weak (r = −0.12), insignificant correlation with total cloudiness. In this case, such weak relationships of the annual air temperature with cloudiness are confusing, as they can only be partially explained by the seasonal difference in the influence of cloud cover on temperature.

Air temperature is strongly related to SD – the strongest temperature correlation occurs with the warm half-year SD (T&SD_Apr–Sep; r = 0.73). The overview of the changes of the annual SD in Poznań (Fig. 4A) reveals the presence of discontinuities in it in the same period as the temperature discontinuity. Both the range of variability in SD and the value of the trend show changes, and in 1987–1989 there is a sharp shift in SD to a higher level (Fig. 4B). This indicates that patterns of both SD and temperature change under the same factors or have the same cause.

Fig. 4

In the first sub-period (1959–1988; 30 years) the SD_y trend is 4.90 (±3.47) h · year⁻¹ and is insignificant (p = 0.169), while in the second sub-period (1988–2020; 33 years) the trend is 7.14 (±2.25) h · year⁻¹ and is statistically significant (p = 0.003). The average annual SD in the two sub-periods is 1524.7 and 1856.1 h, respectively, and the difference between these averages is highly significant. The SD values in both sub-periods also represent separate populations (Fig. 4B), as is the case with air temperature (Fig. 2B).

Changes in SD are controlled by changes in cloud cover. The correlation coefficient between SD and cloud cover is highly significant, but of moderate strength (−0.42; Table 2). The analysis of the changes of total cloud cover in Poznań and its comparison with these of SD (Fig. 5) produces counter-intuitive results.

Fig. 5

Throughout their courses the values of cloud cover (N) and SD change – in accordance with the nature of the relationship between these elements – in the counter-phase (see Table 2). In the first sub-period, the trends in both series are close to zero and statistically insignificant. In the second sub-period the cloud cover trend becomes positive (+0.012 (±0.004) N · year⁻¹) and significant (p = 0.011), similar to the SD trend. This is a logical contradiction, since with changes in N and SD in the counter-phase (anti-correlation), the occurrence of a positive N trend should be accompanied by a negative SD trend.

However, the presented state of dependence of both climatic elements is not an observational error – analysis of the relationship between SD and N at other weather stations in Poland confirms the common occurrence of simultaneous increases in total cloudiness and SD. This statistical paradox is relatively simple to explain. The climatic element of total cloud cover records the degree of coverage of the sky by clouds of all levels and types. Such a state is possible only when the percentage of high optical density, layered clouds gradually decreases, and the degree of sky coverage by high-level clouds with low and minimum optical density increases faster than the decrease in sky coverage. In other words, the cloud structure changes during this period, which is to a small extent related to the degree of sky coverage by clouds

It is extremely difficult to correctly determine the actual cloud structure from ground-based observations. In the case of greater coverage of the sky by low-layered clouds, it is not possible to correctly determine the cloud structure in the middle and high layers. Similarly, in the presence of a middle-layered cloud (As) with a larger horizontal extent, it is not possible to determine the types of clouds and the degree of coverage of the sky by high-layered clouds.

The occurrence of changes in the cloud structure over Poland in the second half of the multi-year period 1951–2000 and the beginning of the 21^st century was concluded in a number of papers, as for example those published by Żmudzka (2007), Wibig (2008), Filipiak and Miętus (2009), and Matuszko and Węglarczyk (2018). In that period, the general tendency was a progressive decrease in the share of clouds with high optical density, especially Ns, St and As, and an increase in the frequency of Ac clouds and cirrus clouds (Ci, Cc), with a variable share of Cu clouds. Thus, one of the manifestations of the climate change that took place in Poland in 1987–1989 is also the change in the cloud structure.

Table 2 also reveals highly significant negative relationships between SD and wind speed. These relationships indicate that a decrease in wind speed in Greater Poland is accompanied by an increase in SD. This can be interpreted as an indicator of SD increases in weak-gradient and non-gradient situations. Such situations occur most often when Greater Poland is within the range of the axial parts of high-pressure wedges or within the range of an anticyclone.

Sunshine duration also shows very strong negative relationships with relative humidity. These relationships are stronger than those between temperature and humidity (see Table 2), which may indicate that an increase in SD is the most important reason for an increase in temperature and a decrease in relative humidity. The occurrence of negative trends appears in the relative humidity data series. In the first sub-period (1951–1988), this trend is close to zero (0.0033% · year⁻¹, p = 0.240) and statistically insignificant; in the second sub-period (1988–2020) it is also negative (−0.1262% · year⁻¹), but statistically significant (p = 0.004). Thus, in the second sub-period, relative humidity also decreases along with increasing SD and air temperature.

To summarise, it can be stated that the conducted analyses show that in 1951–1988 the state of the climate over the Greater Poland region was stable, and its parameters remained within the long-term standard corresponding to the average 30-year period 1951–1980, and perhaps also the norms from the period 1931–1980. In 1987–1989, there was an abrupt change in the state of the climate, in which the values of a number of elements exceeded the ranges of the previous norms. The course of SD and air temperature changed abruptly, and there was a relatively systematic increase in the value of these two elements – the period of rapid warming began. At the same time, a slow decrease in relative humidity began and the cloud structure changed. Within the limits of the climate norm from 1951–1980, the amount of precipitation remained unchanged, whereas total cloud cover, after a temporary decrease in 1989–1992 (Fig. 5), was increasing slowly and irregularly.

The presented picture poses a question about the mechanisms leading to the occurrence of climate change, which is most clearly demonstrated by an increase in air temperature. For air temperature to rise, the amount of heat in the atmosphere must increase. This may occur as a result of an increase in the amount of radiation flowing into the ground, a decrease in the size of radiation losses (radiation) and/or an increase in the horizontal heat inflow over a given area along with the advection of air masses.

The analysis of the relationship between temperature in Poznań and TSI showed that the influence of changes in the solar constant on changes in air temperature can be neglected. The relationships are weak (r = 0.21) and statistically insignificant (p = 0.082; 1951–2018), and the TSI changes are nothing like the temperature changes.

It is commonly recognised (Mann et al. 1998, IPCC 2001, 2007a, b, 2014, Hansen et al. 2007, Lacis et al. 2010, Kundzewicz 2011) that the cause of the observed global temperature increase is an increase in concentration of CO₂ and other greenhouse gases in the atmosphere, changing the radiation balance of the Earth. As a result of changes in the atmosphere chemistry, there is an additional stream of energy (long-wave radiation, reverse radiation) directed to the surface, referred to as radiative forcing (IPCC 2001), increasing non-linearly with an increasing CO₂ concentration (see Eq. [1]). As the concentration of greenhouse gases in the atmosphere increases mainly as a result of human activity, this process is referred to as AGW. As an additional factor influencing global temperature changes, besides an increase in CO₂ concentration, numerous authors point to the action of natural factors. Among them, the most frequently considered is the varying impact of heat fluxes transferred from the ocean to the atmosphere by various types of oscillations of the thermal state of the ocean surface (El Niño-Southern Oscillation [ENSO], Atlantic Multi-decadal Oscillation [AMO], Atlantic Multi-decadal Overturning Circulation [AMOC], North Atlantic thermohaline circulation [NA THC), Pacific Decadal Oscillation [PDO]; e.g. Kushnir 1994, Lean, Rind 2008, Compo, Sardeshmukh 2009, Foster, Rahmstorf 2011, Zhou, Tung 2013, Chylek et al. 2014, van der Werf, Dolman 2014, Willis et al. 2018, Kundzewicz et al. 2020).

In the case of the analysis of the relationship between the temperature changes in Greater Poland and the value of radiative forcing (variable ΔF), there is no other common variability than the trend occurring in both series. The variability of the monotonically increasing value of ΔF, without sharp twists and discontinuities in the course, explains a very high percentage of temperature variation (as much as 46%) in 1951–2020. The correlation coefficient between temperature (T) and radiative forcing (ΔF) in 1951–2020 is very high (r = 0.69). However, in each sub-period of the temperature course, the values of the correlation coefficients and the levels of their significance are different – in the first sub-period (1951–1988) the correlation coefficient between T and ΔF is equal to 0.03 and is insignificant (p = 0.861), while in the second sub-period (1988–2020) r reaches the value of 0.62 and becomes highly significant (p << 0.001), being, however, lower than the value of r in the entire period 1951–2020. Since the temperature increase caused by radiative forcing (T = f(ΔF)) is a physical and therefore deterministic process, it is not possible for a monotonically increasing value of ΔF in one sub-period (1988–2020) to be the cause of the temperature increase, while in another (1951–1988) it was not.

Radiative forcing (ΔF) shows an even stronger relationship with SD than with temperature – for 1959–2020 the correlation coefficient between ΔF and SD is 0.76, which means that with an increase of radiative forcing, SD also increases. While, despite the above-mentioned objections, it is possible to physically justify the effect of radiative forcing on the temperature, the processes in which changes in ΔF could result in changes in SD are not known so far, and their relatively simple physical justification does not seem possible. This prompts us to consider also reasons for the increase in temperature and, more generally, climate change in Greater Poland, other than the impact of AGW.

The high compliance between the changes of SD and air temperature suggests that both have, or may have, a common cause. While temperature changes cannot be the cause of changes in SD, changes in SD, determining changes in the amount of solar energy reaching the ground (see the Black formula in Black 1954), are the obvious cause of the air temperature changes (apart from the influence of other factors). This explains that the discontinuity of the course followed by a positive trend should be a feature of the course of SD, and the discontinuities in the course of temperature, followed by a positive trend, is a reaction of air temperature to a change in the amount of energy reaching the ground, which leads to the replication of the course of SD by the course of temperature (T).

The regression analysis shows that the change in the annual SD_y by 1 h ∙ year⁻¹ in 1959–2020 entails a change in the average annual temperature in Poznań by 0.0034 (±0.0004) C (p << 0.001), consistent with the change in SD. The variability of SD_y in 1959–2020 explains (adj. R² 100%) half (50.2%) of the T_y variance at the same time. To a slightly greater extent (52%), the variability of the annual temperature is explained by the changes in SD that take place in the warm half-year (April-September; variable SD_Apr–Sep), which may be defined as the period in which the day (i.e. the theoretical time of solar operation) is on average greater than 12 h ∙ day⁻¹. This is obviously a more reasonable explanation of the annual temperature variation than the explanation that involves radiative forcing (46%). The standard error of the estimate (SEE) is relatively small and equals ±0.74 deg.

The estimated variability of air temperature in Poznań as a function of the warm half-year SD (variable SD_Apr–Sep; Fig. 6) proves that the temperature variability quite well reproduces the SD variability, including the discontinuity in its course and the change of the trend after 1988.

Fig. 6

Analysis of the residuals shows that in the estimation of temperature, the amplitude of its variation is lower, which indicates that the variability of air temperature is influenced by factors other than SD. More often, large residual values occur in situations with low annual temperature values.

The variable SD_Apr–Sep may affect the annual temperature only during its operation, i.e. in the warm half-year. The equation linking the SD of the warm half-year (Fig. 6) with T_y explains only the influence of temperature of that half-year on the annual temperature (T_y). The temperature of the winter period, when – due to the long duration of the night – SD is regulated in a non-uniform manner and only to a small extent

In the winter period, as in other seasons of the year, high daily amounts of sunshine are recorded with a cloudless sky or with strongly reduced cloudiness. However, in view of the low altitude of the sun in winter, the amount of incoming solar energy per unit surface area of the ground is small. Due to the long duration of night in winter, night radiation (long-wave radiation) in the absence or reduction of cloud cover significantly exceeds the energy supply of short-wave radiation, which in such conditions is the cause of deep temperature drops.

Fig. 7

Analysis of the residuals of the temperature course calculated with the help of the two variables (Fig. 7) shows that the residual distribution is normal, the residuals and deleted residuals are closely related linearly, and there is a very weak and statistically insignificant positive trend in the residual's series. The analysis of the dispersion of the observed values and the squares of the residuals indicates the presence of three strong outliers in the set, exceeding the limits of 1.5 standard deviation of the observed temperature (1966, 1976 and 2019) and significantly reducing the precision of estimating the parameters of the equation. It was not possible to determine whether the error was caused by the temperature data (T_y) or by the independent variables (SD_Apr–Sep, NAO_DJFM). There is presumably another factor or other factors that are not taken into account.

The reduced value of the temperature trend estimated based on the SD value of the warm and winter half-year NAO index, as compared to the observed values, and a weak positive trend detected in a number of residuals, indicate the need to check whether the omission of the radiative forcing (ΔF) in the estimates is not the cause of the trend underestimation.

The equation with three independent variables (SD_Apr–Sep, NAO_DJFM and ΔF) is statistically significant and all its parameters (intercept, regression coefficients) are also statistically significant. The multiple correlation coefficient (R) of this equation is 0.81, the equation explains (adj. R²) 63.87% of the T_y variance and the standard error decreased by 0.02 deg. (SEE= 0.66). In this equation, the variability of SD_Apr–Sep is explained by 52.6%, the variability of NAO_DJFM by 8.6% and ΔF by 4.4% of the T_y variance. The value of the T_y trend across the 1959–2020 series increased by 0.0006 C · year⁻¹. The differences in the course of the T_y values reproduced using the three-variable equation compared to those using the two-variable equation are almost imperceptible.

Thus, the introduction of radiative forcing (ΔF) as the main factor representing AGW, together with two variables ‘representing’ the action of natural factors (SD in the warm half-year [SD_Apr–Sep] and the winter atmospheric circulation [NAO_DJFM]), increases the degree of explanation of the temperature variability by a negligible percentage (4.4%), indicating that the observed warming after 1988 is largely the result of processes related to the internal variability of the climate system.

Since an increase in SD is the cause of an increase in temperature, the question is what process led to the change in SD. Research by Marsz et al. (2022) showed that changes in the intensity of the North Atlantic thermohaline circulation (NA THC) controlled changes in solar radiation in Central Europe by regulating the course of the processes of the middle and lower circulation. The intensity of NA THC is characterised by the index defined by the acronym DG_3L. It shows to what extent the heat transport, together with the transport of water through NA THC from the Atlantic tropics to the north, is higher or lower than the 1901–2000 average.

In the changes of the DG_3L index, there are several decades of positive phases, in which the heat transport through NA THC is, on average, higher than the mean value, and negative phases, in which this transport is, on average, lower. The course of the DG_3L index value in 1951–2020 is presented in Figure 8. The limits of the NA THC phase change are the years 1963–1964, when NA THC changed from positive to negative, and 1988–1989, when NA THC changed from negative to positive.

Fig. 8

The boundaries of the NA THC phases correspond with a good approximation to the boundaries of the so-called circulation periods (epochs), determined based on changes in the frequency of macrotypes of the mid-tropospheric circulation, according to the Wangengejm-Girs classification (Wangengejm 1952, Girs 1964, 1971). The period names indicate the dominant or dominant and sub-dominant macrotype in a given period. In the multi-year period 1949–2014, Savichev et al. (2015) distinguished the following circulation periods: in 1949–1965 – period E + C, in 1966–1988 – period E, and in 1989–2014 – period W. While 2014 was the last year of their analysis, it was reported by Savichev et al. (2015) that, according to their calculations, period W would continue additionally at least until 2017

In order to determine the boundary of the circulation periods according to the Wangengejm-Girs classification, not less than 6–7 additional years of observation of the macrotype frequency are needed. At the moment (the last year with data is 2020) it is not yet possible to determine whether the circulation period W has ended and another circulation period has started.

The mechanism by which changes in the NA THC phases control the frequency changes of macrotypes of the mid-tropospheric circulation and, consequently, the boundaries of the circulation periods is explained in the papers of Wrzesiński et al. (2019) and Marsz et al. (2022).

In the periods when NA THC becomes positive, there is an increase in the frequency of the zonal macrotype W and a simultaneous decrease in the frequency of the meridional macrotype E, according to the Wangengejm-Girs classification

The value of the correlation coefficient between the DG_3L index and the annual frequency of macrotype W is +0.63, and the frequency of macrotype E is −0.61. The correlation coefficient between the annual frequency of these two macrotypes is −0.83 (all correlation coefficients are highly significant [p << 0.001]; correlation period: 1951–2015).

In the periods when NA THC becomes negative, the frequency of macrotype E increases, while the frequency of macrotype W decreases, leading to a decrease in sun exposure and the appearance of the global dimming periods. These processes, related to the change in the cloud structure presented in Section 3.3, occur with the changes of the circulation periods.

The relationship between changes in the annual frequency of macrotypes W and E and the annual SD in Poznań is presented in Figure 9. Due to the strong correlation of the annual frequency of macrotypes, this relationship cannot be presented in the form of linear relationships.

Fig. 9

The value of the DG_3L index, which characterises the NA THC intensity, shows a strong and highly significant correlation with the annual SD in Poznań (r = 0.63, p << 0.001, see Fig. 10). Almost the same value (r = 0.62, p << 0.001) has the correlation coefficient between the DG_3L index and SD of the warm half-year. These values do not differ from the correlation coefficient value between DG_3L and the average annual SD in Central Europe (r = 0.60, p << 0.001) in 1951–2015 (Marsz et al. 2022).

Fig. 10

A change in the DG_3L index value by one unit results in an average change in the annual SD in Poznań by 105 (±16.5) h; the change is consistent with the direction of change of the DG_3L index (see framed equation in Fig. 10). Thus, with the variability of the DG_3L index in 1959–2020 in the range from about −2 to about +4, the range of changes in the annual SD in Poznań should be on average from about 1426 h to about 2026 h. These values are close to the observed values of SD_y – with the minimum of 1251 h (in 1966), and the maximum of 2224 h (in 2018).

There is a very strong positive trend in the course of the DG_3L index after 1988 (Fig. 8). Between 1987 and 1990, the value of that index increased from −1.58 to +1.08, and then it did not drop to negative values in the following years. This period corresponds to the period of the change of circulation periods from E to W and the occurrence of the ‘jump’ in the course of SD (and temperature). The positive trend after 1988 in the course of SD and temperature is consistent with the positive trend of the DG_3L index after 1988.

In such a situation, in the equation with two independent variables (framed in Fig. 7), it is possible to replace the variable characterising SD_Apr–Sep directly with the variable DG_3L. This will allow estimation of the direct impact of the change in the thermal state of the North Atlantic on the temperature in Greater Poland, excluding intermediate stages, in the entire period 1951–2020. Estimation of the parameters of the equation, in which the annual temperature variability (T_y) is a function of the DG_3L index and the winter NAO index, gives the result: (2) Ty=8.43(±0.09)+0.44(±0.07)⋅DG3L+0.40(±0.08)⋅NAODJFM, {{\rm{T}}_{\rm{y}}} = 8.43\left( { \pm 0.09} \right) + 0.44\left( { \pm 0.07} \right) \cdot {\rm{D}}{{\rm{G}}_{3{\rm{L}}}} + 0.40\left( { \pm 0.08} \right) \cdot {\rm{NA}}{{\rm{O}}_{{\rm{DJFM}}}}, in which the variability of both independent variables explains a total of 57.3%, the variability of DG_3L is explained by 42.6%, and the variability of NAO_DJFM by 15.8% of the variance of T_y. The equation is highly significant (F(2.67) = 47.4, p << 0.001), since all its parameters (intercept, regression coefficients) are estimated with high significance (p << 0.001). The multiple regression coefficient (R) is 0.765 and the standard error of T_y estimation (SEE) is 0.70 deg. The scatter plot of the T_y values estimated using this equation in relation to the observed values is presented in Figure 11A, while the course of the observed and estimated values of T_y in Figure 11B.

Fig. 11

Thus, Eq. (2), in which the independent variables are the DG_3L index and the winter NAO index, taking into account the standard error of the T_y value estimation, reproduces the course of the annual temperature in Poznań in the analysed period of 70 years, as correctly as the formula in which the independent variable (besides NAO) is represented by sunshine. The same two variables also allow estimation of the annual air temperature at other weather stations in Greater Poland. Thus, at the aforementioned weather stations in Kalisz, Koło and Gorzów, the same independent variables explain, respectively, 60.8%, 60.6% and 62.0% of the variance of their annual temperature in the period of 70 years (1951–2020) without the need to take into account radiative forcing.

It can therefore be concluded that one of the primary causes of changes in the annual air temperature, not only in Greater Poland but also over large parts of Europe, are changes in the thermal state of the North Atlantic, which, along with the change of the NA THC phase from negative to positive in 1987–1989, resulted in an abrupt change of the macro-circulation conditions in the Atlantic-Eurasian circulation sector. The change in macro-circulation conditions in the middle atmosphere led to the same change in the nature of the lower circulation (SLP), in which there was a change in the cloud structure and an increase in SD and temperature. At the same time, the structure of advection over Europe changed: along with the increase in the frequency of macrotype W and the decrease in the frequency of macrotype E in the last circulation period, the frequency and intensity of the positive NAO phases in winter increased

Between the value of the PC-based winter NAO Hurrell index and the frequency of macrotype W in the first quarter, the correlation coefficient is 0.63 (p < 0.001) and the frequency of macrotype E in the first quarter is −0.49 (p < 0.001). Throughout the winter period (DJFM), the correlation coefficient between the frequency of macrotype W and the NAO index is 0.69 (1951–2020).