The Role of Increased Sunshine in Shaping Air Temperature Rise in Kraków (1951–2020)

The increase in air temperature can result from two processes: the increased influx of solar electromagnetic radiation (sunlight) to the surface and the increased horizontal heat flux brought into the area by atmospheric circulation. In both cases, these energy fluxes must exceed the sum of the losses. Sunshine, or the duration of sunlight exposure, is a direct measure of the amount of solar energy received at a given point. The course of the annual air temperature and the annual sums of sunshine in Kraków are shown in Figure 1. It can be observed that both trends are highly similar to each other, and the linear correlation coefficient between them is strong and highly statistically significant (r = 0.76, p < 0.000).

Fig. 1.

Course of average annual air temperature (°C) and annual totals of sunshine duration (SD in hours) in Kraków (1951–2020).

From the perspective of elementary physics, sunshine, as a simplified measure of the influx of solar electromagnetic radiation to the surface, is absorbed and converted into heat. This heat is then transported from the surface to the atmosphere through turbulent exchange processes, causing the air temperature to rise. On the other hand, the temperature in the near-surface air layer has minimal or no effect on sunshine. Therefore, it can be argued that the variability in annual sunshine is one of the (radiative) causes of changes in air temperature, which explains 58% of the annual variance in air temperature in Kraków from 1951 to 2020 (r² · 100%).

The temperature and sunshine patterns (Fig. 1) are very similar to the average area-wide sunshine and air temperature patterns over Poland (Matuszko et al. 2020, 2022a, Marsz, Styszyńska 2021, 2022). Both patterns show a weak, insignificant negative trend between 1951 and 1988, with a sharp increase in temperature and sunshine between 1987 and 1989, followed by a statistically significant positive trend in the subsequent period (1988–2020). This explains the fact that the increase in temperature in Poland only occurred after 1988. This abrupt shift in temperature and sunshine trends coincided with a phase change in the North Atlantic thermohaline circulation from negative to positive (1987–1989; Marsz, Styszyńska 2022) and a change in the mid-tropospheric circulation epoch in the Atlantic-European circulation sector, according to Wangengejm-Girs classification (Wangengejm 1952, Girs 1964), from the meridional E epoch to the zonal W epoch. This suggests that, despite certain local peculiarities, the temperature and sunshine duration trends in Kraków generally reflect large-scale changes. Therefore, the variability of temperature, cloud cover, cloud type structure, and sunshine duration in Kraków will be analysed in these two time periods: 1951–1988 and 1988–2020.

In the first period (1951–1988), the trend in annual air temperature in Kraków was not significant (p = 0.287) and equalled -0.011 (±0.010)°C per year. The trend in annual sunshine in Kraków was negative, statistically significant (p = 0.002), and equalled -6.28 (±1.89) hr per year. In the second period (1988–2020), the trend in annual air temperature was positive and highly statistically significant (p < 0.000), equal to 0.052 (±0.012)°C per year. The trend in annual sunshine was also positive and highly statistically significant (p < 0.000), equal to 11.5(±1.97) hr per year. The ranges of variability in air temperature and sunshine in Kraków during both periods are shown in Figure 2.

Fig. 2.

Ranges of variability of annual air temperature (°C) and annual sums of sunshine duration (SD in hours) in Kraków in the years 1951–1988 and 1988–2020.

The multi-year average values, when a trend is present, do not adequately describe the scale of changes taking place. A comparison of the average air temperature over the last 3 years of the second period (2018–2020), which was 10.7°C, with the average temperature of the 1951–1988 period (8.3°C), showed that the temperature in Kraków at the end of the 2020s had increased by 2.3–2.4°C compared to the 1951–1988 period. The same applies to sunshine. The average annual sunshine over the last 3 years (2018–2020) was 1927.4 hr, whereas the average from 1951 to 1988 was 504 hr lower (1423.2 hr). The increase in sunshine in recent years constitutes about 1/3 of the average sunshine value from the previous period (1951–1988).

Evaluating the scale of climatic changes that occurred in Kraków between the two periods, it can be concluded that there has been a radical shift, encompassing not only air temperature but also sunshine.

The problem arises regarding which factors influence the variability of sunshine duration and, consequently, air temperature in Kraków. Clearly, the main factor influencing the variability of sunshine is the changes occurring in cloud cover during the daytime. The amount of cloudiness (N) defines the degree of sky coverage by clouds of all types and heights. It does not consider the differentiation of cloud types. For example, a total cloud cover of N = 8 can occur with the complete sky cover by Cirrostratus (Cs) clouds or Altostratus opacus (As op). These two clouds, due to their extremely different optical densities, give completely different responses on a sunshine measuring instrument. During Cs, sunshine will be registered by the instrument, while during As op, the instrument will not register sunshine. Even more complications arise when clouds of small horizontal size (such as Cu) are present in the sky. Many of these clouds (N = 5–6) may be present in the sky, but the measured sunshine will be high, only interrupted when a cloud is between the sun’s disc and the measuring instrument. These complexities are more broadly described by Matuszko (2012a, b, 2015). For these reasons, the relationships between cloud cover (N), sunshine (SD), and air temperature (T), although statistically significant, are relatively weak. In the case of the relationship between T and N, the correlation coefficient is –0.45 (p < 0.000), and in the case of the relationship between SD and N, the coefficient is –0.43 (p < 0.000). It is noteworthy that the values of both correlation coefficients are quite similar (with a difference of 0.02, which is not meaningful). This means that the variability in N explains the variance of SD and T to a similar extent (18–20%). The amount of cloudiness in both periods shows slight differentiation. The average annual cloudiness from 1951 to 1988 was 5.5(±0.06) oktas, and in the subsequent period (1988–2020), it slightly decreased to 5.2(±0.04) oktas. This small difference of about 0.3 oktas is statistically significant. The ranges of variability of total cloudiness in Kraków are shown in Figure 3.

Fig. 3.

Course of annual cloudiness values (oktas) in Kraków in the period 1951–2020, and ranges of its variability in periods 1951–1988 and 1988–2020.

The relationships between the cloud genera structure and sunshine duration and air temperature differ significantly. These relationships were detected and described earlier by Matuszko and Węglarczyk (2015, 2018). Generally, only three cloud genera (As, Ns, and St) show a negative correlation with sunshine and temperature. The remaining cloud genera are positively correlated with temperature. In the period from 1951 to 2020, the distribution of correlation coefficients is presented in Table 1.

Due to the different periods of the analyses, the strength of these relationships (Table 1) differs from those presented in the works of Matuszko and Węglarczyk (2015, 2018), but they are generally similar. It is noteworthy that only the occurrence of stratiform clouds is negatively correlated with both sunshine and air temperature. Additionally, changes in the frequency of these clouds (As, Ns, St) have a relatively strong impact on the variability of cloud cover (N), although not as strong as might be expected (positive correlations). The sum of occurrences of clouds As, Ns, and St is negatively correlated with changes in sunshine duration (r = –0.46, p < 0.000), also negatively, but more strongly, with air temperature (r = –0.58, p < 0.000), and most strongly, but positively, with cloud cover (r = 0.68, p < 0.000).

In both periods, 1951–1988 and 1988–2020, specific changes in the cloud type structure occurred (Fig. 4). In the second period, compared to the first, there was a significant decrease in the total number of observations with frontal clouds (As, Ns, St), while the number of observations of clouds associated with unstable weather conditions (Sc, Cu, Cb) significantly increased. This mutual ‘replacement’ of the two groups of cloud genera resulted in a relatively small decrease in the value of N in the second period compared to the first.

Fig. 4.

Ranges of variability in the number of days with observations of frontal clouds (As, Ns, St) and clouds occurring in unstable weather conditions in Kraków during the periods 1951–1988 and 1988–2020.

The data presented in Table 1 clearly indicate that the decrease in the frequency of stratiform clouds (As, Ns, St) in Kraków, as shown by Matuszko and Węglarczyk (2018) and Matuszko et al. (2020), must be the cause of the reduction in cloud cover (N) and the increase in sunshine (SD), and thus, indirectly, the rise in air temperature in Kraków.

Changes in overall cloud cover and the cloud genera present in the sky are the result of atmospheric dynamics (atmospheric circulation), which determines the course of synoptic situations. Thus, the influence of atmospheric circulation manifests in short-term synoptic processes (weather changes), while long-term climatic effects are only the outcome of the interactions of synoptic-scale processes. The clouds As, Ns, and St, which have the greatest impact on changes in sunshine, are frontal clouds. Meteorological fronts occur exclusively in low-pressure systems. Frontal stratiform clouds typically have large horizontal extensions and relatively slow movement, which results in a long duration of sky coverage. It is evident that the reflection of incoming solar radiation from the upper surface of these clouds (albedo), followed by strong scattering and absorption of radiation within the cloud mass, significantly reduces the radiation reaching the Earth’s surface (amount of energy). As a result, there is a decrease in surface temperature, weakening of turbulent exchange, and, consequently, a reduction in air temperature.

The changes in cloud genera for Kraków described by Matuszko and Węglarczyk (2015, 2018), as well as Wibig (2008) for Łódź, Filipiak (2021), and Matuszko et al. (2022b) for Poland, involving a decrease in the frequency of frontal clouds, can therefore be clearly interpreted as a reduction in the number of low-pressure systems passing over Central Europe, accompanied by an increase in anticyclonic synoptic situations. It can thus be argued that the underlying cause of the observed changes in solar radiation and air temperature in Kraków is the change in the nature of large-scale atmospheric circulation, leading to alterations in the structure of synoptic situations. These changes in large-scale atmospheric circulation, in turn, are influenced by the variability of the thermal state of the North Atlantic, regulated by changes in thermohaline circulation in the ocean. These processes are explained in detail in the works of Marsz et al. (2024) and Marsz and Styszyńska (2024a, b). It is also worth noting that a decrease in cloud cover and changes in cloud genera across the Northern Hemisphere or Europe in the past 20–30 years have been highlighted by other researchers (e.g., Veretenenko, Ogurtsov 2016, Pfeifroth et al. 2018, Dübal, Vahrenholt 2021, Sfîcă et al. 2021, Post, Aun 2024).

The relationship between annual air temperature in Kraków and annual sunshine duration in the city is strong, highly significant (r = 0.76, p < 0.001), and explains 58% of the variance in annual air temperature over the entire period from 1951 to 2020. The relationships between monthly mean air temperature in Kraków and the annual total solar radiation are statistically significant in all months of the year except for February and October (Table 2), with the strongest correlations in the warm half of the year (April–September, r ranging from 0.29 in May to 0.68 in August). This indicates a relatively strong and consistent influence of sunshine duration (SD) on the course of annual air temperature (T) in Kraków. Regression analysis (T = a + b × SD) shows that this relationship is linear. Estimated annual air temperature values in Kraków based on annual sunshine duration reproduce the interannual variability quite well, and a discontinuity in the estimated temperature trend is evident in the second half of the 1980s (Fig. 5). The estimated values show a positive trend of 0.018(±0.004)°C · year⁻¹, which is lower than the observed trend in Kraków for the same period (0.027(±0.005)°C · year⁻¹). The difference between the two trend values is statistically significant.

Fig. 5.

The course of the observed mean annual air temperature (°C) in Kraków (Obs) and the estimated air temperature based on sunshine duration (est) from 1951 to 2020. The trend values are marked in boxes (with the standard error of estimation values in parentheses).

The relationship between the annual air temperature in Kraków and the annual sunshine duration (SD) in the city during the years 1951–2020 takes the form of: 2 T=2.8457(±0.6277)+0.0040(±0.0004)×SD (values provided with increased precision). This means that an increase in the annual sunshine duration (SD) in Kraków by 1 hr led to an increase in the annual air temperature by ~0.004°C. Considering that between the periods 1951–1988 and 2018–2020 there was an increase in SD by approximately 500 hr, the increase in sunshine duration during this period, without the influence of other factors, resulted in an air temperature rise of about 2.0°C in Kraków.

As mentioned earlier, the variability in air temperature in Kraków is a function of several variables, not just changes in solar radiation. In addition to solar radiation, at least two other factors should be considered: large-scale atmospheric circulation, which transfers heat along with air mass transport, and radiative forcing (△F).

The relationships between atmospheric circulation and cloudiness (N), SD, and air temperature (T) in Kraków have typically been considered as connections between local atmospheric circulation indices (Niedźwiedź 1981) and the previously mentioned elements (Matuszko, Węglarczyk 2018). Generally, large-scale circulation, which operates across the entire Atlantic-European circulation sector, was not taken into account, with some exceptions (Matuszko 2007). The shaping of air temperature variability in Kraków demonstrates the separate influence of two factors. During the warm season, the primary role is played by the changes in solar energy influx regulated by the variability in SD. This is understandable, given the influence of the astronomical factor (day length, Sun’s altitude). In the cold season, the role of radiative influx takes a back seat to the horizontal heat transport. The form of atmospheric circulation that most strongly influences the shaping of air temperature in the cold season, particularly during the ‘extended winter’ period (December–March; DJFM), is the North Atlantic Oscillation (NAO). The NAO index (Hurrell et al. 2003) is significantly correlated with temperature trends from January to April (Table 2). The correlation between the NAO index and the annual air temperature in Kraków is 0.54, which is highly significant (p < 0.001), meaning that the variability of the winter NAO index explains 29% of the variance in the annual air temperature. In the period 1951–2020, a statistically significant positive trend of 0.020(±0.006) (p = 0.002) can be observed in the NAO. The variability of the NAO index also shows significant differences between the periods 1951–1988 and 1988–2020 (Fig. 6). This indicates that the increase in the intensity of westerly (zonal) circulation in the winter period after 1988 is one of the reasons for the observed rise in annual temperature in Kraków.

Fig. 6.

The course of the North Atlantic Oscillation principal components (NAO PC) DJFM Hurrell index from 1951 to 2020 and the ranges of its variability in the periods 1951–1988 and 1988–2020.

The estimated annual temperature (T) in Kraków, based on the NAO index values (T = a + b × NAO), shows a discontinuity at the end of the 1980s and a positive trend of 0.009°C · year⁻¹. This trend is significantly smaller than the trend observed in the actual air temperature data (0.027°C · year⁻¹). Additionally, the interannual variability of the temperature in the estimated course is clearly underestimated, and the standard error of estimation (SEE) is substantial (±0.80°C).

The combined effect of changes in annual sunshine (SD) in Kraków and the winter (DJFM) NAO index (NAO) is expressed by the equation: 3 T= 3.730(±0.620)+0.003(±0.000)×SD+0.250(±0.066)×NAO statistical characteristics of which are as follows: R = 0.807, adj. R² = 0.641, SEE = 0.563, p < 0.001. This equation is highly significant (F(2, 67) = 62.6; p << 0.001). The distribution of residuals from the estimated values is normal, indicating a very good fit of the estimated temperature values to the observed ones. The combined effect of both variables explains 64% of the variance in the observed air temperature. Variance analysis shows that the variability of sunshine (SD) in this equation explains 57.7%, while the variability of the NAO index explains 7.4% of the variance in the observed annual temperature in Kraków. The trend of the estimated annual temperature from eq. (3) is 0.020(±0.004)°C · year⁻¹. This trend value is higher than the trend estimated from sunshine alone but lower than the trend in the analysed air temperature series (0.027(±0.005)°C · year⁻¹).

The comparison of the estimated values from Eq. (3) and the observed temperature values indicates a good fit of the estimated values to the observed ones (Fig. 7), as well as the presence of a discontinuity in the series at the end of the 1980s.

Fig. 7.

Course of the observed mean annual air temperature (°C) in Kraków (Obs) and the estimated (est) from the course of two variables: sunshine duration (SD) and North Atlantic Oscillation (NAO) in the years 1951–2020. The trend values are marked in the boxes (with standard error of estimation values in parentheses).

Radiative forcing (△F), a function of CO₂ concentration in the atmosphere, is widely considered (IPCC Reports 2007, 2013, 2023) as the most important factor causing anthropogenic global warming. In the period 1951–2020, △F systematically increased from 0.592 in 1951 to 2.224 W · m⁻² in 2020. This increase is monotonic, and the course is weakly exponential. The correlation coefficient between △F and the annual air temperature (T) in Kraków is 0.64, highly significant (p < 0.001), and explains 40% of the variance in the observed air temperature. This is a high explanation. Regression analysis (T = a + b × △F) shows (Fig. 8) that the estimated air temperature course based on △F variability does not reveal any interannual variability or a change in temperature regime in the 1980s. In the first period (1951– 1988), when the temperature trend in Kraków is zero, the estimated temperature trend is positive. The regression merely ‘rescaled’ the △F values to match the air temperature values. This pattern suggests that the main cause of the strong correlation between these values is the common trend observed in both series. Interpreting this relationship, it can be considered either a statistical artefact or that △F only contributes to the positive trend observed in the temperature course.

Fig. 8.

Course of the observed mean annual air temperature (°C) in Kraków (Obs) and the estimated (Est) from the course of radiative forcing in the years 1951–2020.

A more detailed analysis of the relationships between △F and the monthly air temperature course in Kraków reveals significant statistical relationships between these variables only from January to August (inclusive) (Table 2). The strongest correlations are observed during the summer months (June, July, August), when the highest air temperatures (as well as the highest solar radiation) are recorded.

The estimation of the annual air temperature (T) course in Kraków using the three explanatory variables – solar radiation (SD), the winter NAO Hurrell PC index (NAO), and radiative forcing (△F) – resulted in a statistically highly significant equation (F(3.66) = 48.3; p << 0.001) in the form of: 4 T=4.145(±0.610)+0.003(±0.000)× SD+0.218(±0.064)×NAO+0.454(±0.165)×ΔF with the following characteristics: R = 0.829, adj. R² = 0.673, SEE = 0.538. The estimation of the intercept and all regression coefficients is statistically significant. The residual analysis shows that they follow an almost perfect normal distribution, and there is no trend in the series. Variance analysis shows that in Eq. (4), the variability of SD explains 57.7%, NAO explains 7.7%, and △F explains 3.6% of the observed annual temperature variance in Kraków (T). A remaining 32.7% of the variance remains unexplained. Such an explanation of the variability in annual air temperature in Kraków through the combined action of the three variables should be considered high (Fig. 9). The smaller explanation of temperature variance by NAO and △F in the multiple regression Eq. (4), compared to each variable individually in the single-variable regression equations, results from the covariance (redundancy) between the independent variables.

Fig. 9.

The course of the observed annual average air temperature (°C) in Kraków (Obs) and the estimated (est) temperature based on the course of three variables: sunshine duration (SD), North Atlantic Oscillation (NAO), and △F from 1951 to 2020.

The estimated trend of air temperature based on Eq. (4) is 0.028(±0.003)°C · year⁻¹, which is not statistically different from the observed trend of annual air temperature in Kraków (0.027(±0.005)°C · year⁻¹). This stage of the analysis explains that the △F contributes only a sole, very weak positive trend (on the order of thousandths of a °C per year) to the variability of air temperature. The combined effect of solar radiation variability, the winter NAO index, and radiative forcing thus satisfactorily explains the increase in air temperature in Kraków, although it does not fully explain the entire pattern of this variability (Fig. 10).

Fig. 10.

Course of the observed average annual air temperature (°C) in Kraków (Obs) and the estimated temperature (Est) based on the course of two variables sunshine duration (SD) and North Atlantic Oscillation (NAO) and three variables (SD, NAO, and △F) in the years 1951–2020. Trend lines are marked. The differences between the observed temperature trend and the estimated temperature trend based on three variables are so small (0.001°C · year⁻¹) that they overlap in the graphical representation