Introduction

The Earth radiation budget is a subject of many previous and recent discussions (Marti, et al. 2022; Loeb et al. 2021; Stephens et al. 2012; Kiehl and Trenberth 1997). The global radiation budget is the most important factor controlling climate change (IPCC 2021). Not only satellite observations, but also numerical models show that the radiation budget at the top of the atmosphere (TOA), known as the Earth’s Energy Imbalance (EEI), is slightly positive (Stephens et al. 2022). Although the EEI value is small (probably below 1 W/m2), satellite observations must be supported by numerical simulations and in situ ocean observations with estimation of the Earth’s imbalance. The typical uncertainty of the satellite detectors is a few W/m2; therefore, the calculation of the EEI is not straightforward. The EEI is a consequence of two factors radiative forcing (RF) and climate system response connected by the following formula

$${\text{EEI}} = {\text{RF}} - \lambda \Delta T$$
(1)

where λ is a feedback parameter, and ΔT is the temperature anomaly. Due to the inertia of the Earth’s climate system, the EEI is only partly responsible for the positive RF. The climate system is driven primarily by an increase in greenhouse gases (GHGs) concentrations and atmospheric aerosol (IPCC 2021). The total anthropogenic RF estimated in the last IPCC report (2021) in 2019 with respect to the year 1750 is 2.7 (2.0–3.5) W/m2. The previous RF (estimated for 2011) was 2.3 (1.1–3.3) W/m2 (Myhre et al. 2013). Thus, the fast positive trend of RF is responsible for the increase of the EEI in the last few decades.

Past research has shown that the EEI is close to zero. Based on the Earth Radiation Budget Experiment, Kiehl and Trenberth (1997) estimated values for the period from 1985 to 1989, that the radiation budget at the TOA is in balance. Later data from the Clouds and the Earth’s Radiant Energy System (CERES) measurements, taken between 2000 and 2004, indicated a radiation imbalance of 0.9 W/m2 (Trenberth et al. 2009). More recent studies show that the EEI trend per decade for 2001–2020 was 0.38 W/m2 (Raghuraman et al. 2021). Such an estimation is based on the CERES data, but also on simulations of the Coupled Model Intercomparison Project Phase 6 (CMIP6). The authors also estimated that due to natural climate variability, the EEI is twice smaller (0.19 W/m2 per 10 year) than the observed value. Stephens et al. (2022) discussed the positive trends of the EEI in terms of CERES and climate model results, which can be explained as a negative trend in the reflected by Earth to space shortwave (SW) flux. The positive trend of the outgoing longwave (LW) radiation (OLR) at the TOA, forced by the increase of the surface temperature, cannot balance the SW flux changes. Stephens et al. (2022) suggested that the reduction of the amount of sunlight reflected by Earth is equally caused by cloudy and clear regions of the atmosphere. However, climate models that match the global SW change very well show incorrectly that the reduction of solar flux is only due to clouds. Using independent satellite and in situ observations, Loeb et al. (2021) show EEI increases from mid-2005 to mid-2019 at a rate of 0.50 ± 0.47 W/m2/10 year. Since about 90% of the energy associated with EEI is stored in the ocean (von Schuckmann et al. 2016), estimation of the EEI can be done based on the ocean’s heating rate. Johnson et al. (2016) calculated the EEI to be 0.71 ± 0.10 W/m2, which corresponds to a net heat uptake of 0.61 ± 0.09 W/m2 by the ocean depth from 0 to 1800 m, 0.07 ± 0.04 W/m2 by the deeper ocean, and 0.03 ± 0.01 W/m2 by ice melting. Another estimation of the EEI based on ocean and satellite topography and gravity observation by Marti et al. (2022) indicates an EEI value of 0.74 W/m2 for 2002–2016. Dübal and Vahrenholt (2021), based on CERES observation between 2001 and 2020, estimated the EEI as 0.8 W/m2. Different methodology has been used by Goode et al. (2021) to determine the change of the global albedo. It was estimated at Big Bear Solar Observatory between 1998 and 2017 by observing the earthshine using photometric methodologies. Over the course of two decades, they observed a reduction of SW reflected flux by about 0.5 W/m2, which agrees with CERES (since 2001) data.

The motivation for this study is the rapid climate warming and the change in atmospheric transmittance in the SW range observed at ground stations in central Europe (Uscka-Kowalkowska 2013). The reduction of turbidity parameters is due to the decline of aerosol optical depth (AOD) (Markowicz et al. 2019) with respect to anthropogenic and volcanic emissions. As a consequence, aerosol radiative forcing (ARF) shows a significant positive trend (Markowicz et al. 2022), which emphasizes positive anthropogenic RF. However, there is a lack of information on the temporal variability of the SW and LW radiative budget. In this paper, the authors describe a temporal variability of radiative budget and its components from the perspective of atmospheric conditions (clouds, aerosol, GHG) and surface reflectance.

The methods and the datasets used for the study are described in Sect. "Methods." Sect. "Mean radiation budget" describes the mean long-term radiative budget. In Sect. "Variability of atmospheric physical properties," the variability of physical properties of the atmosphere is discussed, while in the following section, the variability of budget and RF is presented. Conclusions are drawn in the last section.

Methods

This study is based on The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2) for the years 1980–2021. The research domain is defined as an area between 48.5°N and 55°N and from 13.5°E to 24.5°E. MERRA-2 data are available at 0.5 × 0.625° resolution.

The radiation budget both on TOA and the Earth’s surface is defined as:

$$B = \left( {F^{ \downarrow } - F^{ \uparrow } } \right),$$

where \(F^{ \downarrow }\) and \(F^{ \uparrow }\) are a net (SW + LW) downward and upward flux. The radiation budget in the atmosphere is a difference between the budget at the TOA and at the surface. Instantaneous cloud radiative forcing (CFR) is defined as the difference between net (down–up) radiation flux under all-sky and clear-sky conditions:

$${\text{CRF}} = \left( {F^{ \downarrow } - F^{ \uparrow } } \right)_{{\text{all - sky}}} - \left( {F^{ \downarrow } - F^{ \uparrow } } \right)_{{\text{clear - sky}}}.$$
(2)

CRF is given for the pristine (without aerosol) and for polluted (with aerosol) cases separately. In addition, CRF is computed for the SW, LW, and total (SW + LW) cases. The ARF is defined as following:

$${\text{ARF}} = \left( {F^{ \downarrow } - F^{ \uparrow } } \right)_{{{\text{polluted}}}} - \left( {F^{ \downarrow } - F^{ \uparrow } } \right)_{{{\text{pristine}}}},$$
(3)

under clear-sky (no clouds) and all-sky (real clouds). CRF and ARF are computed at the TOA, the Earth’s surface, and the atmosphere. From Eqs. (2) and (3), the difference between CRF polluted and pristine conditions can be expressed by ARF as following:

$${\text{CRF}}_{{{\text{polluted}}}} - {\text{CRF}}_{{{\text{pristine}}}} = {\text{ARF}}_{{\text{all - sky}}} - {\text{ARF}}_{{\text{clear - sky}}}.$$
(4)

MERRA-2 reanalysis

MERRA-2 is a complex long-term reanalysis which assimilates space-based observations of aerosols and incorporates their interactions with other physical processes in the climate system (Molod et al. 2015; Reichle, et al. 2017). For the assimilation of the satellite radiance observations, MERRA-2 uses an automated bias correction scheme (Gelaro et al. 2017). The residual bias calculated for satellite detectors is defined by a small number of parameters (predictors) that depend on the atmospheric state, the radiative transfer model, as well as the sensor characteristics. Radiative transfer simulations are performed using version 2.1.3 of the Community Radiative Transfer Model (CRTM, Han et al. 2006; Chen et al. 2008).

Aerosol properties in MERRA-2 are based on the Goddard Chemistry, Aerosol, Radiation, and Transport model (GOCART; Chin et al. 2002; Colarco et al. 2010). The GOCART model describes the physical and chemical processes of the following particles: mineral dust, sulfate (SU), sea salt, black (BC) and organic carbon (OC). The optical properties of the aerosol mixture are calculated assuming an external mixed mixture, including hydrophobic and hydrophilic modes, for each particle type, excluding mineral dust.

Additional data

The concentration of CO2, CH4 is taken from the NOAA Earth System Research Laboratory database (Dlugokencky et al. 2018a; b). For this purpose, monthly mean data from the Baltic Sea (55.43°N, 16.95°E) available between September 1992 and June 2011 were used. Outside these dates, the monthly mean values were derived from the observations performed at the Barrow station (Alaska) after linear regression to the Baltic Sea observation.

Air temperature variability (averaged monthly) is obtained from the gridded anomalies for the area of Poland at 4 km resolution (version 1.08H) (https://meteomodel.pl/klimat/poltemp/1.0H8/poltemp-1.0H8.txt). The reference period for the calculation of temperature anomaly is defined between 1991 and 2020.

MERRA-2 solar flux was validated based on radiometer surface observation. For this purpose, the Kipp and Zonen (www.kippzonen.com) pyranometer CMP22 (Warsaw), CMP21 (Strzyżów, Belsk) and CMP11 (Sopot) were used (Fig. 1). LW surface flux was measured at two stations using the CGR3 pyrgeometer in Warsaw and the PIR precision infrared radiometer (http://www.eppleylab.com/) in Strzyżów (Table 1).

Fig. 1
figure 1

Localization of research stations in Poland used for MERRA-2 validation

Full size image
Table 1 List of stations and instrumentations used for validation of MERRA-2 radiation fluxes
Full size table

Additionally, the transport of air masses was estimated with the NOAA Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model (Stein et al. 2015). Calculations were based on the NCEP/NCAR meteorological data, with 2.5° × 2.5° spatial resolution. HYSPLIT was used to estimate the 3-day back-trajectories ending in Warsaw (central Poland) at 12:00 UTC, for each day between 1980 and 2021. The trajectories were obtained for three levels of air arrival: 0.5 km, 1.5 km, and 3.0 km a.g.l.

Estimation of aerosol contribution to climate warming

According to Glantz et al. (2022) methodology, the change in air temperature is estimated as a response to the variation in the surface radiation budget. For this purpose, the change in the radiation solar budget between 2021 and 1980 is estimated from linear regression. Since only part of this energy is used to heat the surface, the additional energy must be adjusted (Fadj) to transport the energy to the atmosphere by sensible (H) and latent (E) heat flux as follows:

$$F_{{{\text{adj}}}} = \left[ {\left( {F_{{{\text{SW}}}}^{ \downarrow } - F_{{{\text{SW}}}}^{ \uparrow } } \right)_{2021} - \left( {F_{{{\text{SW}}}}^{ \downarrow } - F_{{{\text{SW}}}}^{ \uparrow } } \right)_{1980} } \right]\left[ {1 - \overline{{\left( {\frac{H + E}{{F_{{{\text{SW}}}}^{ \downarrow } - F_{{{\text{SW}}}}^{ \uparrow } }}} \right)}} } \right],$$
(5)

where the first bracket describes the change in the surface SW budget during the study period and the second bracket describes the mean part of this change that is not transported from the surface. We assume that molecular heat transport at the ground can be neglected. To calculate increases in near-surface temperature, the Stefan–Boltzmann law has been applied to the adjusted surface SW flux and LW upward flux estimated from the surface skin temperature and averaged according to the 1980s:

$$\Delta T = \sqrt[4]{{\frac{{F_{{{\text{adj}}}} }}{\sigma \varepsilon } + T_{{{\text{skin}}}}^{4} }} - T_{{{\text{skin}}}} \approx \frac{{F_{{{\text{adj}}}} }}{{4\sigma \varepsilon T_{{{\text{skin}}}}^{3} }},$$
(6)

where σ is the Stefan–Boltzmann constant, ε is surface emissivity, while Tskin is the surface skin temperature in the 1980s.

Validation of the MERRA-2 surface radiation fluxes

Validation of the SW downward flux at the surface has been done in the frame of the Poland-AOD network (Markowicz et al. 2021). Figure 2 shows a comparison of MERRA-2 and ground-based observations at four stations. MERRA-2 overestimated the surface incoming flux at all-sky conditions by 19.2, 20.0, 23.9, and 16.5 W/m2, respectively, in Warsaw, Strzyżów, Sopot, and Belsk sites. The root mean square difference error (RMSE) varies from 22.2 W/m2 to 30.9 W/m2. Both mean bias and RMSE are larger in Sopot, probably due to coastal location. Significantly better agreement is for clear-sky fluxes. The mean bias in this case is 7.5, 8.6, 11.5, and 4.1 W/m2, respectively, for Warsaw, Strzyżów, Sopot, and Belsk. The RMSE is about two times smaller than for all-sky conditions. A possible explanation for nonzero bias in solar flux is a poor spatial resolution of MERRA-2 data (0.5 × 0.625°), representativeness of ground-based observation, but also inaccurate MERRA-2 properties of the atmosphere. For example, Strzyżów site is localized at the top of the mountain, so the mean altitude in the MERRA-2 pixel is lower than the research station. In the case of the Warsaw site, the multi-scattering process between the atmosphere and human-modified land surface can impact the observed surface solar flux. Previous results for Poland reported by Markowicz et al. (2022) show that the off-line model based on the Fu-Liou radiation transfer code shows significantly better agreement with observation than MERRA-2, especially for cloudy conditions. Stamatis et al. (2022) provided global validation of MERRA-2 radiation products versus data from the Global Energy Balance Archive (GEBA) and Baseline Surface Radiation Network (BSRN). However, a high correlation coefficient 0.95 for GABA and 0.97 for BSRN, and a significant positive bias is reported. For example, MERRA surface fluxes are overestimated by 24.4 W/m2 (15.3%) against GEBA and 10.3 W/m2 (5.9%) against BSRN. In the case of the individual stations, MERRA-2 underestimates surface SW flux at low latitudes and polar regions and overestimates in middle latitudes. In addition, Stamatis et al. (2022) showed an agreement in the long-term trend sign of incoming surface SW flux: 63.4% in the case of GEBA and 50% of BSRN stations.

Fig. 2
figure 2

Comparison of monthly mean surface downward all-sky (a, c, e, g) and clear-sky (b, d, f, h) SW fluxes in Warsaw (a, b), Strzyżów (c, d), Sopot (e, f), and Belsk (g, h) obtained from MERRA-2 and ground-based observations. The dotted line corresponds to perfect agreement

Full size image

Draper et al. (2018) reported a positive bias of MERRA-2 global downwelling SW by 14 W/m2 while negative bias for the downwelling and upwelling LW flux by 10–15 W/m2. In addition, the sensible and latent heat flux are also overestimated globally, respectively, by 6 and 5 W/m2.

Yunfei et al. (2022) also reported that MERRA-2 overestimates the surface incoming daily solar flux by 27.5 W/m2 in China (based on 37 ground stations). However, the RMSE for all-sky conditions is almost twice that of the clear-sky value. Comparison of AOD and cloud fraction in MERRA-2 and from Moderate-resolution Imaging Spectroradiometer (MODIS) retrievals indicate that the overestimation of the MERRA-2 surface flux in most areas is induced by the underestimation of its cloud cover. While AOD in MERRA-2 is underestimated in North China, it is overestimated in the Sichuan Basin and Southeastern China.

Figure 3 shows a comparison of the surface LW flux at the Warsaw and Strzyżów sites. For both stations, the MERRA-2 LW fluxes are significantly underestimated (by 21.1 W/m2 in Warsaw and 17.2 W/m2 in Strzyżów). This fact can be explained by the too transparent atmosphere in MERRA-2 due to cloud properties. Such results are consistent with overestimated SW all-sky flux.

Fig. 3
figure 3

Comparison of monthly mean surface downward all-sky LW fluxes in Warsaw (a) and in Strzyżów (b) obtained from MERRA-2 and ground-based observations. The dotted line corresponds to perfect agreement

Full size image

Markowicz et al. (2022) show that the AOD from MERRA-2 in Poland is in agreement with surface observation (bias almost zero). The MERRA-2 AOD is significantly overestimated due to poor representation of the orography in the MERRA-2 reanalysis only in mountain stations. In the case of the absorbing aerosol optical depth (AAOD) and single-scattering albedo (SSA) the agreement with AERONET retrieval is much worse. The positive bias for AAOD and negative for SSA can indicate an overestimation of the absorbing particle in the MERRA-2. However, the AERONET data for AAOD and SSA are highly uncertain (Chiliński et al. 2019) and limited to high AOD values (AERONET Level 2.0 product is available when AOD at 440 nm is greater than 0.4), so the conclusion about MERRA-2 validation must be balanced. For example, Buchard et al. (2017) report that AAOD from MERRA-2 compares well with the Ozone Monitoring Instrument (OMI) observations.

Mean radiation budget

The mean total (SW + LW) radiation budget under all-sky conditions at TOA is negative (− 44.3 W/m2), indicating a deficit of energy in the total column of the atmosphere over Poland (Table 2). On the contrary, the total radiation budget at the Earth’s surface is positive (63.1 W/m2) and strongly negative in the atmosphere (− 107.4 W/m2). In the case of TOA and atmosphere, SW absorption cannot balance the LW emission (Fig. 4). Therefore, energy from the surface must be transmitted to the atmosphere as sensible and latent heat flux and by thermal conduction to the ground. The negative radiation budget in the atmosphere can be partly compensated by air mass subsidence and the advection of warmer air masses.

Table 2 Mean long-term (1980–2021) radiation budget defined for polluted all-sky, polluted clear-sky, and pristine clear sky conditions averaged over Poland at the TOA, the Earth’s surface (SURF) and in the atmosphere (ATM)
Full size table
Fig. 4
figure 4

Long-term (1980–2021) mean annual radiation budget at the TOA, the Earth’s surface, and in the atmosphere in [W/m2]. Yellow, red, and black values show SW, LW, and total (SW + LW) all-sky polluted budget (left columns), respectively. In the case of clear-sky polluted (middle column), the values indicate the difference between all-sky polluted and clear-sky budget (cloud effect). For clear-sky pristine (right column), the values show the difference between clear-sky polluted and pristine budget change (aerosol effect)

Full size image

For the clear-sky polluted condition, the TOA SW + LW net flux is less negative (− 31.1 W/m2) than for all-sky polluted conditions. Thus, clouds cool the whole system by about 13.2 W/m2 (Fig. 4) due to stronger SW reflection (− 40.1 W/m2) than the reduction of the LW emission to space (26.9 W/m2). The total radiation flux at the Earth’s surface under clear-sky conditions is shifted by 12.8 W/m2 toward a positive value compared to the all-sky case. Hence, the clouds have a stronger effect on SW than on LW surface flux. Since both TOA and surface values are similar, the change of radiation budget in the atmosphere by clouds is very small (− 0.4 W/m2). It can be explained by the nearly complete compensation of the SW absorption and LW emission effects. The radiation budget at the pristine clear-sky condition is less negative at the TOA and more positive at the Earth’s surface. Thus, aerosol at the TOA increases SW reflection by 5.4 W/m2 and reduces the net surface flux by 8.4 W/m2. The budget in the atmosphere for polluted conditions is less negative by 3.0 W/m2 than for pristine conditions due to the absorption of SW radiation. Note that the radiation budget under clear-sky polluted and pristine conditions was estimated based on the radiative transfer model assuming the same thermodynamic properties as in the real (all-sky) case. Therefore, some climate effects of removing clouds and aerosol on surface and atmospheric temperatures are not taken into account.

The radiation budget varies significantly between seasons (Table 2). At the TOA total (SW + LW) net downward flux for all-sky conditions is strongly negative in winter and autumn and positive in spring and summer. On the Earth’s surface, negative flux is observed only during winter. In the case of the atmosphere, the strongest negative flux in winter and autumn is a consequence of low SW absorption due to the small incoming solar flux.

Variability of atmospheric physical properties

The radiation budget is determined by external properties (such as extraterrestrial solar flux) and physical properties of the atmosphere and the Earth’s surface. Therefore, selected parameters that mostly impact the transfer of radiation and radiation budget such as aerosol, cloud, surface albedo, and GHG are discussed.

Aerosol optical properties

Table 3 shows linear trends of cloud and aerosol properties over the last 4 decades. Significant negative trends of total AOD at 550 nm (− 0.05 per 10 year) indicate a reduction of pollution emission over central Europe. The rapid decline of AOD was observed after the Mount Pinatubo eruption in the early 1990s due to aerosol deposition and reduction of volcanic emission after this event but also due to the transformation of the economy into a free market (Markowicz et al. 2022). This conclusion can be supported by higher AOD changes observed at low than high mountain stations in Central Europe (Markowicz et al. 2019; Ruckstuhl et al. 2008). The most important contribution to the reduction of total AOD is from the sulfate particles (the same value of negative trends). In the case of the mineral dust particle, the trend is slightly positive (statistically significant only during winter and summer). The sea salt AOD has small negative trends in winter and positive trends in summer, both significant. For the OC AOD, slightly negative trends are observed in winter and spring and positive in summer and autumn. BC AOD trends are also small and negative and nearly zero in summer. The negative AE trends are statistically significant for all seasons. The high trend for the annual mean (− 0.06) is a consequence of the reduction of small sulfate particles. This also leads to negative trends of SSA due to the fact that sulfates are non-absorbing particles. Thus, data show an increase in the relative contribution of absorbing particles to the total AOD. The AAOD trends are positive only during the summer. In summer, all absorbing aerosol types show small but positive trends, which can probably be explained by the increased frequency or intensity of the biomass burning events. During winter, spring, and autumn, the trends of AAOD are negative due to the significant reduction of AOD and the absorbing particles.

Table 3 Long-term mean (1980–2021) trends (per 10 year) of aerosol, cloud, GHG, surface properties, and air temperature at 2 m height averaged over Poland
Full size table

Cloud properties

Physical properties of the clouds (Table 3) are discussed in terms of cloud optical depth (COD) cloud cover for the total, high, middle, and lower categories. Total COD shows small trends, which are not statistically significant (for the 95% confidence level). For high and middle clouds, the trends in COD are positive, especially in summer. The reduction of COD is visible for lower clouds. Negative, significant trends are observed in summer (− 8.2%). Temporal variability of cloud cover shows a reduction for all cloud levels. Statistically significant negative trends of total cloud cover are obtained for spring (− 3.5%) and summer (− 3.1%). In winter, cloud cover is slightly increased, and in autumn slightly decreased, but the values are not significant at the 95% confidence level. In the case of annual mean, the reduction of high, middle and low-level cloud cover is, respectively, − 2.2%, − 2.7%, and − 1.6%. Matuszko et al. (2022a, b) report, based on 34 weather stations in Poland, that there are no statistically significant trends in the total cloud cover between 1971 and 2020. Only during winter, the trend is significant and positive (1.2%/10 years). Statistically significant trends were reported for different cloud types. For example, decreasing trends of low-level and mid-level clouds in winter and spring while increasing trends of high-level clouds. Filipiak and Miętus (2009) show that a statistically significant change in cloud cover in 1971–2000 was observed at about 25% of Polish stations. However, their distribution over the country is quite chaotic, and for some stations (lakeland), trends are positive, and for some (coastal regions) are negative.

Greenhouse gases

Temporal variability of the total water vapor content (precipitable water, PW) shows small positive (1.3%) but not significant trends during the last decades (Table 3). Significant trends were obtained for spring (10.7%) and autumn (− 6.9%) and negligible for winter (1.4%) and summer (1.0%). Significant changes are observed for the total ozone column, which is reduced at a rate of − 1.0% per decade. The surface concentration of the CO2 and CH4 gases shows significant positive annual trends, respectively, 4.9% and 3.0%. The increase in the concentration is almost the same in all seasons and as a result of anthropogenic emission.

Surface albedo

Surface albedo during the last four decades shows relatively small variability. Only during the summer are the trends positive and statistically significant. Especially during the first two decades, the trend is more significant (about 1%), while during the last two decades, the trend is almost zero. During winter, the surface albedo decreases at a rate of about − 0.01 (± 0.008) per decade, but due to the large variability from year to year, this value is not significant (at 95% confidence interval). The annual trend is negative (− 0.004 ± 0.002) but not statistically significant due to the high variability of snow cover during the winter season.

Temporal variability of radiation budget

TOA

During the last four decades, the radiation budget changed significantly (up to almost 10%, see Table 4). At TOA the positive trend is observed in the SW range, while negative in the LW range. The total (SW + LW) radiation trend was positive, so the deficit of the energy over Poland (Fig. 5) was reduced during the 1980–2021 period. Changes in SW fluxes are more substantial than in the LW due to two opposite effects in the LW range. The first corresponds to an increase in surface temperature, which leads to the enhancement of the LW upward flux. The second one is a reduction in atmospheric LW transmission, which corresponds to an increase in atmospheric emissivity. LW radiation transmittance is mostly controlled by GHG concentration (e.g., water vapor, CO2, CH4), atmospheric temperature, and cloud properties, while aerosols have a small impact on LW transfer in the atmosphere. The nonzero trend of the LW atmospheric transmittance is statistically significant only for clear-sky conditions. The annual mean trend for clear-sky is − 0.3% per decade, with a maximum reduction in summer (− 0.5%/10 year). However, for both clear-sky and all-sky cases, the trends are negative due to the increase of the GHG columnar amount and reduction of the stratosphere temperature. Reduction of LW transmittance cannot balance the increase in upward LW flux due to surface warming. Therefore, the outgoing LW flux at the TOA shows a positive trend. In contrast, SW atmospheric transmittance (clear-sky pristine) is also negative but very small (− 0.06%/10 year) and not statistically significant. In this case, the reduction of SW flux transmittance is due to the enhancement of absorption by an increase in water vapor and slightly by an increase of CO2. Note that the reduction of the ozone column (Table 3) leads to an increase in transmittance mostly in the UV but also slightly in the visible spectrum. The reduction of LW transmittance can also be partially explained by stratospheric cooling, which has been observed during recent decades (Maycock et al. 2018). The impact of aerosol on OLR at the TOA is negligible as a consequence of a small concentration of coarse particles, which can affect the LW fluxes (by absorption and scattering LW radiation). The reduction of cloud fraction and COD (Table 3) leads to increased LW TOA upward flux.

Table 4 Change of the radiation budget [W/m2] at TOA, at surface and in the atmosphere between 1980 and 2021 for SW, LW and total (SW + LW) radiation, as well as for all-sky polluted, clear sky polluted, and clear-sky pristine cases over Poland
Full size table
Fig. 5
figure 5

Annual mean total (SW + LW) radiation budget at the TOA under all-sky polluted (blue), clear-sky polluted (red), and clear-sky pristine (orange) conditions obtained for Poland. Black lines show linear fit

Full size image

In the SW spectrum, the positive change in the radiation budget at the TOA has a few reasons. One of them is the variability of clouds and aerosol physical properties. Both climate forcing drivers have the same physical aspect (reduction of cooling effect). However, the reduction of aerosol is responsible for 4.7 W/m2, while the reduction of the cloud for 2.3 W/m2 of SW budget changes. Other quantities (e.g., gases and surface reflectance) produce 1.7 W/m2 change of SW TOA fluxes (Table 4; Fig. S1).

Both SW plus LW budget changes are positive and equal 2.7 W/m2 for all-sky polluted and 2.8 W/m2 for clear-sky polluted cases. Thus, the effect of clouds is almost canceled at TOA. For the clear-sky pristine case, the budget change is negative (− 1.7 W/m2); therefore, the aerosol has had the most important impact on the budget variability during the last decades. The reduction of aerosol and the change in its properties have led to a positive change in the net SW + LW flux at the TOA by 4.5 W/m2 during the last 41 years. On the other hand, absorption by atmospheric gases (CO2, CH4, H2O) as well as surface reflectance and temperature changes reduces TOA net flux.

Surface

The radiation budget at the Earth’s surface also shows a positive and statistically significant trend (Fig. 6). In the SW budget, the change is 7.9 W/m2 for all-sky polluted, 5.3 W/m2 for clear-sky polluted, and 0.9 W/m2 for clear-sky pristine case (Table 4). Positive SW net flux (downward minus upward) under pristine cloudless conditions is due to the small negative trend of surface albedo and the reduction of the total ozone column. The increase in water vapor content and CO2 concentration, which enhance SW absorption in the atmosphere has a smaller effect on surface net SW flux than ozone and albedo. The reduction of aerosol and clouds leads to 4.2 W/m2 and 2.6 W/m2 reduction of the SW surface budget.

Fig. 6
figure 6

Annual mean SW + LW radiation budget at the Earth’s surface under all-sky polluted (blue), clear-sky polluted (red), and clear-sky pristine (orange) conditions obtained for Poland. Black lines show linear fit

Full size image

In the LW range, the surface budget change is negative (− 1.7 W/m2) for the polluted all-sky and small positive (0.4 and 0.9 W/m2) for the clear-sky polluted and pristine case. The positive trend for clean, cloudless conditions indicated that the increase in downward flux by increasing GHG concentration is larger than the increase in surface upward flux as a result of increased surface temperature. The effect of aerosol in LW is very small, while the reduction of low-level cloud cover is responsible for negative LW radiation budget changes under all-sky conditions.

The total (SW + LW) radiation budget changes at the surface are positive in all cases (6.2, 5.8, 1.3 W/m2, for, respectively, all-sky polluted, clear-sky polluted, and clear-sky pristine). The most important impact on such changes is aerosol reduction and increased GHG concentration. The small difference between all-sky polluted and clear-sky polluted case indicates that clouds have a relatively small effect on the total radiation budget at the surface.

Atmosphere

The radiation budget in the atmosphere shows a negative and statistically significant trend (Fig. 7). For the all-sky, clear-sky polluted, and clear-sky pristine cases, the trends are − 0.8 ± 0.2, − 0.7 ± 0.1, − 0.9 ± 0.1 W/m2/10 year. Changes in the radiation budget in the atmosphere are positive (close to 1 W/m2) in the SW spectrum and negative for LW and the total (SW + LW) spectrum (Table 4). The increase in absorption in the atmosphere is relatively small in all cloudy and aerosol and pristine conditions. The most important contribution comes from the change in GHG concentration. In the LW range, a strong negative change (close to − 4 W/m2) is the consequence of enhanced emission by GHG concentration. (Changes in aerosol and cloud cover are negligible.) Therefore, SW + LW radiation budget variability is mostly due to LW flux changes.

Fig. 7
figure 7

Annual mean SW + LW radiation budget in the atmosphere under all-sky polluted (blue), clear-sky polluted (red), and clear-sky pristine (orange) conditions obtained for Poland. Black lines show linear fit

Full size image

Aerosol radiative forcing temporal variability

A significant reduction of aerosol amount in the atmosphere leads to a change in ARF. Figure 8 shows the temporal variability of ARF defined at the TOA, surface, and in the atmosphere for both clear- and all-sky conditions. In all cases, the trends are positive, indicating a reduction of aerosol cooling. Both TOA and surface trends are the same and statistically significant (0.6 ± 0.1 W/m2/10 year for all-sky and 1.1 W/m2/10 year for clear-sky conditions). However, trends in the atmosphere are negligible and not statistically significant (0.1 ± 0.1 W/m2/10 year). This is a consequence of the reduction of AOD and the increase of the relative contribution of absorbing particles.

Fig. 8
figure 8

Annual mean aerosol radiative forcing a at the TOA, b the atmosphere, c at the surface for all-sky (blue) and clear-sky (red) conditions obtained for Poland. Black lines show linear fit

Full size image

During the last 41 years, two periods with stronger negative ARF in 1983 and 1992 are visible. Both cases correspond to volcanic activity, respectively, to Mount St. Helens and to Mount Pinatubo. Reduction of the ARF in the atmosphere shows that aerosol emitted during volcanic eruption is less absorbing than non-volcanic particles. In 2002, ARF showed an opposite relationship, which means that stronger negative ARF at the TOA and surface corresponds to higher ARF in the atmosphere. This can be explained by the high biomass burning activity during the 2002 summer (Zielinski et al. 2016), visible by an increase in organic carbon and black carbon AOD.

Cloud radiative forcing temporal variability

Table 5 shows the long-term mean CRF and CRF trend for the SW, LW, and SW + LW spectral ranges. SW CRF at the TOA and Earth’s surface under aerosol conditions is the same (− 40.1 W/m2). Therefore, clouds over Poland have a negligible effect on radiation heating in the atmosphere. Some SW absorption by water droplets and ice crystals in the near-infrared can produce additional SW heating; however, it is not detectable in the MERRA-2 data. The statistically significant trend of SW CRF at the TOA is positive 1.1 and 0.6 W/m2/10 year (Fig. 9a), respectively, for pristine and polluted atmospheres. The reduction of cloud cover leads to a decline of the TOA reflected radiation. On the Earth’s surface, both trends are similar (1.2 and 0.5 W/m2/10 year) due to an increase in downward SW flux under cloudy conditions. In the atmosphere, the trend in SW CRF is slightly negative − 0.1 W/m2/10 year and not statistically significant (Fig. 9b).

Table 5 Long-term mean (1980–2021) of cloud radiative forcing and its trend per decade with uncertainty averaged over Poland for SW, LW and SW + LW radiation
Full size table
Fig. 9
figure 9

Annual mean cloud radiative forcing a at the TOA, b in the atmosphere, and c at the surface under polluted (blue) and pristine (red) conditions obtained for Poland. Black lines show linear fit

Full size image

In the case of LW, there is a slight difference between positive CRF at the TOA (26.9 W/m2) and at the Earth’s surface (27.3 W/m2) for real (polluted) aerosol conditions. Thus, the atmospheric CRF is slightly negative (− 0.4 W/m2). A similar value of the LW CRF at the TOA and surface can be explained by the specific vertical distribution of clouds. In the case of high-level clouds, the LW CRF is strongly positive (at the TOA and in the atmosphere) in contrast to low-level clouds, which leads to strongly negative forcing at the surface and in the atmosphere. The temporal variability of the LW CRF is negative and statistically significant − 0.6 and − 0.5 W/m2/10 year at TOA and surface, respectively. Similarly to SW, in the LW, the CRF trend in the atmosphere is negative but negligible (not statistically significant).

The total (SW + LW) CRF is − 13.4 W/m2 at the TOA, − 12.8 W/m2 at the surface, and − 0.4 W/m2 in the atmosphere; thus, the cooling effect in SW is not fully compensated by LW heating. Trends for TOA (0.0 W/m2/10 year), surface (0.1 W/m2/10 year) and atmosphere (− 0.1 W/m2/10 year) CRF are negligible for polluted case, but statistically significant if they are obtained for the pristine case (Table 4). Although the CRF trend is similar to ARF in SW, the total (SW + LW) effect for clouds is almost zero due to significant LW CRF.

Discussion of the temperature temporal variability in light of radiation budget change

The mean air temperature measured at 2 m a.g.l. has increased rapidly during the last four decades. The annual trend for Poland is 0.48 ± 0.09 °C/10 year (Table 2). The fastest warming is observed in summer (0.65 ± 0.09 °C/10 year), while the slowest is in spring (0.36 ± 0.14 °C/10 year). Warming during winter is also high (0.49 ± 0.24 °C/10 year) but not statistically significant due to high year-to-year temperature variability triggered mainly by the North Atlantic Oscillation (NAO; Tomczyk et al. 2021; Ye and Lau 2017). The mean amplitude of air temperature anomaly is 2.3 °C in winter, 1.3 °C in spring, 1.2 °C in summer, 1.3 °C in autumn. However, this quantity shows a negative but statistically not significant trend of − 0.1 °C/10 year, respectively, in winter, spring and summer, and zero in autumn.

The Pearson correlation coefficient between temperature anomaly and different parameters of the radiation budget is shown in Table 6. The surface radiation budget is statistically correlated with the temperature anomaly (r = 0.71). Higher correlation coefficients were obtained for summer than for autumn and winter. Since the temperature anomaly as well as other quantities shows significant trends, the correlation coefficient after detrending was calculated (see values in parentheses). In this case, the correlation coefficient is lower but significant. In the case of the SW surface incoming flux, the correlation coefficient is positive 0.63 and 0.43 for annual original and detrended data, respectively. However, the value is negative in winter and positive in summer. Cold conditions during higher solar surface flux can be explained by cloud reduction and increased LW upward flux. Typically, high-pressure system conditions in winter correspond to continental and cold air masses. Similar synoptic conditions in summer are responsible for heat waves.

Table 6 Pearson correlation coefficient between air temperature anomaly and different parameters for all seasons and annual mean
Full size table

The largest correlation coefficient was found for incoming surface LW flux. This flux corresponds to the mean atmosphere temperature. In this case, higher values of the Pearson correlation coefficient are observed in winter and autumn than in the warm season. A possible explanation for that is low level cloud cover. In the cold period, the increase in cloud cover increases downward LW flux, which corresponds to positive temperature anomaly, while during summer to negative anomaly. The correlation between air temperature and AOD is negative, but after removing the linear trend, the correlation is very low and not significant. It may result from the correlation between air mass transport and temperature. For example, the Arctic clean air mass brings very low AOD, while polluted mineral dust from the Sahara is usually transported in the tropical air mass. Therefore, the statistical analysis between long-term variability in air temperature and AOD is not unambiguous. For the cloud fraction, the correlation coefficient is negative (mostly in summer). After removing the linear trends, the correlation coefficient is significant (negative) in summer, indicating a warmer climate in the case of cloud reduction.

To verify the influence of air mass transport on air temperature, the correlation coefficient between temperature anomaly and monthly mean position (longitude and latitude) of 3 days back-trajectories (ended in Warsaw at 500 m a.g.l.) was calculated. In the case of latitude, the negative correlation (r = − 0.81) in winter and the positive correlation (0.46) in summer indicate western advection, which in summer brings a lower air temperature and in winter a higher one. Both results are similar after removing the liner trend. For the meridional circulation (latitude), the correlation is very low. Only in autumn the correlation coefficient is singly higher in absolute value (− 0.37). Figure 10 shows the position of the 3 days back-trajectories ending at Warsaw as a function (color) of the mean air temperature anomaly averaged in Poland. During winter (Fig. 10a), the separation of points is visible due to air temperature anomalies. Mostly westerly flows (Atlantic air mass) bring positive temperature anomalies. Points located over Poland (with a few exceptions) show negative anomalies, which can be explained by continental air mass. Therefore, Pearson’s correlation coefficient between air temperature anomaly and longitude of the ending point of back-trajectories is negative and significant (− 0.81). The temperature in winter is mainly controlled by advection and horizontal transport of heat rather than by the local energy budget. During the rest of the seasons, the separation of back-trajectory ending points is relatively low. However, in spring, transport (Fig. 10b) from the north shows a slightly negative anomaly, and in summer (Fig. 10c), colder air masses are observed during western circulation. During autumn, transport from the south-west direction is responsible for positive anomalies.

Fig. 10
figure 10

Monthly mean position of the start points of 72 h back-trajectories ending in Warsaw (black square) at 500 m a.g.l. in seasons: winter (a), spring (b), summer (c), and autumn (d). The color corresponds to the mean air temperature anomaly over Poland

Full size image

MERRA-2 reanalysis shows changes in wind patterns during the last 4 decades. The mean annual zonal (west) wind speed at 10 m is reduced with trends of − 0.25 ± 0.11 m/s/10 year. In winter, the trend is − 0.48 ± 0.22 m/s/10 year (statistically significant), while in summer only − 0.05 ± 0.16 m/s/10 year (not statistically significant). A reduction in zonal transport is observed in middle latitudes as a result of accelerating Arctic warming and a weakened equator-to-pole thermal gradient (Coumou et al. 2018). In Central Europe, the reduction of western circulation in the winter and autumn reduces the warm Atlantic air mass transport. Meridian components of the wind change sign throughout the year. The positive value (southern wind) is observed in the cold season, and the negative (northern wind) in the warm season. In the colder seasons, the meridional wind trend is 0 and 0.3 m/s/10 year (stronger wind from the southern direction), respectively, for winter and autumn. In spring and summer, the trends are − 0.4 and − 0.1 m/s/10 year, indicating stronger wind from the north. Note that only the trend in autumn is statistically significant. Due to the change in wind speed, the distance of back-trajectories is reduced (mostly in autumn) with the exception of the spring season. From a radiation budget point of view, reducing the negative budget in winter may reduce the advection of heat transport and enhance the positive budget, and in summer may increase the heat transport (colder air mass).

The air temperature change due to the increase of the surface SW net downward flux is estimated, based on the methodology described in Sect. "Estimation of aerosol contribution to climate warming," is presented in Table 6. An increase of the surface SW net flux leads to 0.8 °C warming, while the total annual warming in this period is 2.0 °C. The increase of the surface SW flux due to the reduction of aerosol leads to the increase of the near surface temperature by 0.4 °C, while the reduction of clouds adds the next 0.2 °C. In summer and spring, aerosol reduction leads to an increase in surface temperature by 0.7 °C and 0.5 °C, respectively. The observed increase in summer temperature is extremely high (2.7 °C), and a significant contribution to this is due to the decline of aerosol (0.5 °C) and cloud cover (0.6 °C) (Table 7).

Table 7 Air temperature change [°C] between 1980 and 2021 obtained from observation and from a simple model applied to change of SW surface flux
Full size table

Summary

Climate change observed in Central Europe has accelerated in recent decades. On the global scale, the main driver of global warming is an increase in GHG concentration. However, at the local scale, other factors can play a significant role in the climate system. In Central Europe, the rapid change in the economy after the early 1990s and the subsequent transition to green energy in the last two decades has contributed to the reduction of the aerosols in the atmosphere. Based on MERRA-2 reanalysis, the changes of the radiation budget in view of temperature trends are discussed (Fig. 11). The most important findings of this study about the radiation budget over Poland have been:

  • The negative radiation budget at the TOA is reducing (an increase in absolute value) at a statistically significant (95% confidence level) rate of 0.7 ± 0.2 W/m2 per decade, while the positive budget at the surface is increasing at a rate of 1.5 ± 0.2 W/m2 per decade.

  • The most crucial changes in the radiation budget components are:

    1. A.

      An increase of incoming to the surface and decrease of reflected to the space SW fluxes.

      • The increase in SW fluxes can be explained mostly by the reduction of aerosol load and cloud cover.

      • The increase in SW absorption by GHG (mostly by water vapor, ozone and CO2) in the atmosphere leads to a reduction in the incoming surface flux and reflected TOA flux. Therefore, changes in GHG enhance the SW flux changes at the TOA and reduce the flux changes at the surface associated with aerosols and cloud variability.

    2. B.

      An increase in OLR at the TOA.

      • The positive trend of OLR at the TOA is due to an increase in surface temperature. An increase in GHG concentration cannot completely balance the TOA OLR changes by reduction of LW transmittance. The LW transmittance is reduced only by 0.3%/10 year (statistically significant) under clear-sky conditions and 0.03%/10 year (not statistically significant) for all-sky conditions.

    3. C.

      An increase in downward and upward LW fluxes at the surface, however, both fluxes balance each other.

    4. D.

      In contrast to TOA and surface, the radiation budget in the atmosphere became more negative due to the increase in GHG LW emission slightly balanced by the increase in SW flux absorption.

  • During the last 4 decades, rapid climate warming has been observed in Poland with a rate of 0.48 ± 0.09 °C/10 year (about twice the global rate). This can be explained by the positive trend in the radiation budget. Especially during the warm season, the radiation budget is positively correlated with the temperature anomaly.

  • An enhancement of the sensible (4.7%./10 year, statistically significant) and latent (1.7%/10 year, not statistically significant) heat flux is the consequence of strong radiative surface heating and atmosphere cooling, which can partly be related to the growth in intensity of extreme weather deep convection phenomena during the warm season.

  • During the cold season, the main factor responsible for temperature anomaly is air mass advection, while radiation budget, especially in the SW range, has a rather negligible effect on climate warming.

  • The estimated climate warming due to an increase in surface SW net flux is 0.8 °C (for 1980–2021). The temperature increase by 0.4 °C and 0.2 °C corresponds to the reduction of aerosol and cloud, respectively.

Fig. 11
figure 11

Change of the radiation budget components between 1980 and 2021 for real (all-sky and polluted) conditions over Poland

Full size image

Previous research by Hinkelman (2019) shows that MERRA-2 better represents the variability and trends of radiative fluxes over time compared to the mean energy budget. The atmosphere in MERRA-2 is too transparent, which leads to an overestimation of downward SW surface flux and an underestimation of LW flux. Consequently, systematic uncertainty is nearly canceled out, and the total (SW + LW) flux has a small bias compared to observations. Validation of the radiation flux in Poland shows similar discrepancies in MERRA-2, both for all-sky and clear-sky conditions. According to ground-based observation, the mean SW flux at the surface is positively biased by 13%, while LW is negatively biased by − 6%. The difference between total (SW + LW) surface flux in MERRA-2 and observation is slightly negative in Warsaw (− 2.0 W/m2) and positive in Strzyżów 2.7 W/m2). Verification of AOD in the last years by Markowicz et al. in 2022 provides nearly zero bias. Therefore, the overly transparent atmosphere under clear-sky conditions cannot be explained by inaccurate properties of atmospheric aerosols. In addition, the relatively short database (10–20 years) of AOD and radiation flux observations does not allow for the verification of time trends.

Our research is consistent with Glantz et al. (2022), who reported (based on ERA5 reanalysis) a significant increase in surface SW flux in Europe during the last 4 decades. Increases in near-surface temperature, for both clear-sky and all-sky conditions, are slightly greater in our study (up to about 1 °C for Central and Eastern Europe). Thus, the change in aerosol plays a significant role in the amplification of climate warming over Poland. Another study by Matuszko et al. (2022a, b) showed that air temperature in the warm part of the year (from April to September) is highly correlated with sunshine duration. The increase in sunshine was explained by the reduction in aerosol and, in part, by the variability in the cloudiness (caused by a change in atmospheric circulation and changes in the content of water vapor content). In addition, their work showed that climate warming in the cold season (October–March) is not related to sunshine duration trends.