There are 35 CMIP6 models (Eyring et al., 2016) used in this study, listed in Table B1. Since the study is focused on the spread between the models, we weigh each model the same even though some of the models are from the same modelling community or share the same physics and parameterizations. Historical forcings for the model simulations are based on observations of greenhouse gases, land use, solar forcing, volcanic emissions etc. and cover the period 1850–2014 (Eyring et al., 2016). For future projections (2015–2100) we use a high greenhouse gas scenario SSP5-5.8 and a medium forcing scenario SSP2-4.5 (O'Neill et al., 2016). To compare models over the historical period (1980–2023), we extend the historical simulations using SSP5-5.8 from 2015.

Reanalysis data from ERA5 (Hersbach et al., 2020) and MERRA-2 (Gelaro et al., 2017) are compared with the CMIP6 models. ERA5 has a resolution of 0.25° for latitude and longitude, while MERRA-2 has a coarser resolution of 0.5° in latitude and 0.625 in the longitude. MERRA-2 includes aerosol data assimilation, while ERA5 uses aerosol, greenhouse gases, ozone fields and total solar irradiance from CMIP5.

We also compare precipitation with gridded daily precipitation observations from E-OBS with 0.1° resolution (Cornes et al., 2018). While ERA5 does not assimilate gauge data, and is therefore independent of precipitation observations, MERRA-2 corrects the precipitation from observationally based precipitation products.

Globally, the atmospheric energy budget represents the balance between surface precipitation and the column integrated diabatic cooling Q (excluding latent heat). Q is expressed as net longwave (LW) and shortwave (SW) radiative losses of the atmospheric column minus the net upward sensible heat (SH) flux. The radiative cooling is found by the difference between upward radiation at the top of the atmosphere (TOA) and at the surface.

The atmospheric energy balance is true only in a global-mean sense, and to get the regional atmospheric energy budget, a column integrated dry static energy flux divergence (H) needs to be included (Muller and O'Gorman, 2011). The precipitation (P) response to a change in climate (δ) can therefore be expressed as: 1LcδP=δSW+δLW-δSH+δH Here, the latent heat of condensation Lc converts precipitation change so that all terms are expressed in W m⁻². An increase in temperature due to increased greenhouse gases will increase LW radiative cooling making a positive contribution to precipitation change (O'Gorman et al., 2012). Warming also causes an increase in water vapor concentration that in turn causes increased absorption of SW radiation and a heating of the atmosphere, which has a negative contribution to precipitation. In addition, aerosols can both scatter (e.g., sulphate) and absorb (e.g., black carbon) SW radiation depending on their composition and altitude (DeAngelis et al., 2015; Pendergrass, 2020; Wild, 2020). Clouds have a large impact on the atmospheric energy budget with direct radiative effects and feedback mechanisms, clouds absorb or scatter incoming SW radiation and outgoing LW radiation. The physical representation and geographical location of clouds is found to be critically important for whether they contribute to radiative cooling or heating found in both observations and models increasing the climate sensitivity (Zelinka et al., 2020; Gjermundsen et al., 2021; Loeb et al., 2024). SH depends on the difference between the surface and the overlying air, turbulence and convection (Myhre et al., 2024). The H term is calculated as a residual and is driven by changes in dry static energy in addition to changes in horizontal and vertical winds.

To prevent long-term thermal drift in the pre-industrial control climate, the CMIP models are constrained to achieve a global-mean, annual-mean net top-of-atmosphere (TOA) radiation balance, thereby maintaining the balance expressed in Eq. (1) (Muller and O'Gorman, 2011). Most of the CMIP6 models achieve approximate energy budget closure, and show an improvement compared to CMIP5 models (Irving et al., 2021). There are several methods to achieve radiative balance (or close to radiative balance), some models stabilize at a level of imbalance (drift) in their spin-up simulations e.g. for ACCESS-CM2 and ACCESS-ESM1-5 they gradually stabilize around 0.35 and -0.25 W m⁻², causing the models to have a continuous ocean heat uptake or loss (Bi et al., 2020; Ziehn et al., 2020). Others tune the parameters for AMIP (Atmospheric Model Intercomparison Project) simulations to keep conservation (Döscher et al. 2022). In this study, the H term is calculated as a residual and may therefore also include changes in energy storage (Muller and O'Gorman, 2011). The reanalysis models, although they aim to represent the atmosphere, are not constrained to conserve energy. As a result, the H term is not physically consistent in Eq. (1). For the CMIP models that are constrained, Appendix Fig. A1 shows the H term from the NorESM2-MM model, from June, July and August (JJA) 2015–2020. The dry static energy flux divergence is calculated using data at 3 h temporal resolution, interpolated from terrain-following coordinates to pressure levels and then integrated in the vertical. With a top-of-the-atmosphere radiative imbalance of -0.065 W m⁻² (Seland et al., 2020), the large-scale differences in H between the model calculations and the residual from monthly mean output that is available from the CMIP6 models are comparable, even though the residual term exhibits a smoother field. To calculate a direct H term with the eddy contribution, high temporal data (e.g. 3 h used for the NorESM2 calculations) on pressure levels is needed, and this is unfortunately not available for the other CMIP6 models. Although models do not achieve perfect radiative balance, comparing them with the atmospheric balance equation provides valuable insight into the causes of model spread in European precipitation and how the hydrological cycle responds to global warming.

Here, we evaluate the energy balance equation over Europe (-10 to 30° W and 35 to 75° N) and three sub regions; the Mediterranean (-10 to 30° W, 35 to 48° N), a Central European region (-5 to 15° W and 48 to 66° N) and a Northern European region (10 to 30° W and 64 to 74° N), see Fig. 3b). Individual models are analysed on their native grid over land only. Multi-model means are constructed by interpolating model data to a common grid of 1×1° in latitude and longitude using bilinear interpolation. The results are presented as the change in summer (JJA) averages between the reference period 1980–1999 and a recent period (2004–2023), which includes both reanalysis and observational datasets. For future projections, we show changes relative to the same reference period and two time periods, the mid-century (2040–2059) and the end-of-century (2080–2099).

Figure 1 shows precipitation change over Europe between the reference period (1980–1999) and the recent period (2004–2023), where E-OBS show drying over the Mediterranean, except southern Italy and Greece. Ukraine, Belarus and the Baltic Countries also show a drying since the 1980s. Relative increase for the same data is shown in Fig. A2. The signal is less clear over Central Europe, and an increase over Ireland, the UK, Denmark and Southern Sweden and Norway is found. ERA5 reanalysis generally shows the same tendencies, although with a more pronounced drying over the western Mediterranean and Eastern Europe. Precipitation changes in MERRA-2 reanalysis show a larger area of increase over France and in eastern parts of the Mediterranean, however no large changes over southern Italy.

The CMIP6 model mean shows much weaker precipitation changes and only shows statistical significance over the Northern Sea. For the rest of Europe, the model mean either shows a small decrease or no change, with no statistical significance. Figure 2 shows the model mean change in regional atmospheric energy budget for the same period, to investigate how the different terms evolve.

There is a larger model agreement for the SW, LW SH and H terms in the regional energy budget compared to the precipitation term. For SW atmospheric radiative cooling, the models show an increase in atmospheric radiative cooling over Central Europe with statistical significance, and a decrease in the North Europe over ocean and land. The CMIP6 models generally agree on an increase in LW atmospheric radiative cooling (positive contribution to precipitation change) over the oceans, with less change over Central Europe. An increase in SH contributes negatively to a change in precipitation (Eq. 1), therefore results are presented as a negative to reflect the resulting precipitation response. Models show that SH over land contributes to reducing precipitation except over Northern Scandinavia. The change in dry static energy (H) shows a model mean where there is a positive contribution to precipitation over land and a negative contribution over the oceans.

To further study the spread in the models and how they compare to the reanalysis and observational data over Europe, the fluxes are spatially averaged over land in the European region as well as in the three additional regions (see Fig. 3b and methods). These additional regions include a Mediterranean region where Fig. 1 indicates a general drying, a Central European region where the change from drying to wetter conditions is likely to be located, and a Northern European region which is expected to get wetter. Figure 3a shows the spread between CMIP6 models for the different terms in the regional atmospheric energy budget equation, compared with reanalysis datasets and observations over the four regions. The fluxes are only evaluated over land because of the higher societal importance compared to values over the ocean, and because E-OBS is only available over land.

Results show that the two reanalysis datasets have the most extreme values of SW and LW radiative cooling, with ERA5 having a strongly positive and MERRA-2 a strongly negative SW radiative cooling, and MERRA-2 having a strongly positive and ERA5 having a strongly negative LW radiative cooling. The CMIP6 models' SW and LW radiative cooling are mostly located within the spread of these two reanalysis extremes. For the SH contribution to precipitation, the CMIP6 models also mostly lie between the two reanalysis values for the large European region and the Mediterranean region, with MERRA-2 having a large radiative cooling over the Eastern Mediterranean land regions (see Fig. A3, showing energy budget maps for ERA5 and MERRA-2). For the Central European and Northern European regions the SH terms of the reanalysis data are more similar to each other, with CMIP6 models both having a stronger cooling and warming than the reanalysis datasets. While the H term is for the reanalysis is not consistent with Eq. (1), since the reanalysis is not constrained to be energy conservative, they do compare better to the CMIP6 models, with consistently positive contributions. Even with MERRA-2 assimilated precipitation, there is large differences between the reanalysis and the gridded observations, except over Central Europe where the reanalysis data and observations show similar change. MERRA-2 have more mean summer precipitation in the later period for all regions compared to E-Obs, except the Northern Europe. ERA5 have the opposite change in precipitation with lower increases or decreases in the later period compared to E-Obs, and larger change over Norther Europe. The CMIP6 models have a large spread crossing the zero line, but with a positive contribution to precipitation for the model mean (as also seen in Fig. 2).

With the large spread between the models for the individual energy budget terms, the resulting spread in precipitation change is large, underlining the uncertainty in how precipitation is represented in GCMs. One crucial question is the role of the evolution of sea surface temperatures, which is known to vary between models. To test the role of this to European precipitation changes, we utilize simulations from AMIP (Atmospheric Model Intercomparison Project), which are forced with observed sea surface temperature and sea ice evolution to avoid ocean-atmosphere feedback – as such removing this inter-model uncertainty. Figure A4 shows the change in the atmospheric energy budget components for a subset of AMIP models. Here we analyze the linear trend in each component across 1980–2014 since AMIP simulations are only available until the end of 2014. But even with this forced similarity, the models still show a large spread, indicating that the ocean does not explain the model diversity in precipitation change, nor in the different terms of the atmospheric energy budget. The uncertainty connected to natural variability is also shown for two models; UKESM0-1-LL with high ECS, and MIROC6 with low ECS for their ensemble members. The spread between the ensemble members is smaller than the spread shown between the different models indicating that natural variability is also not a large cause of the uncertainty in the atmospheric energy budget.

With the limitations and uncertainties in the historical reanalysis data, it is challenging to constrain the spread in CMIP6 models. Understanding the response to future climate projections in the different models is of importance.

The change in future projections of precipitation is a drying over continental Europe and an increase over Northern Scandinavia, with a decreasing area where models disagree with higher forcing (no statistically significant change in precipitation). The signal in change is also stronger for this high-end forcing scenario, compared to the middle of the road SSP2-4.5 (shown in Fig. A5).

The change in forcing for future projections is clearly seen in the change in SW radiative cooling for the CMIP6 models, where at the end of the century the area where the mean model has insignificant results is reduced to cover the continental Europe, while the other regions show a negative contribution to precipitation increase for SW. LW radiative cooling shows a generally positive contribution to precipitation, that is increasing with time towards the end-of-the century (compare top and bottom row of Fig. 4). The change in SH and H also strengthens from mid-century to end-of-century.

The H term shows that there is a small change that is not statistically significant implying a low model agreement on the sign of change over land compared to the other terms, especially for the end-of-century change with the strongest forcing. To further understand this, the regional mean change for each model over land (similar to Fig. 3) is shown in Fig. 5.

Results show that for all regions except the Northern European region, the H term model results are spread out around zero for both projections, for both the middle and end of century change. Thus, the contribution of dry static energy to CMIP6 precipitation change can be both positive and a negative depending on model, resulting in a model mean close to zero and also explaining the lower model agreement for the H term over continental Europe, compared to the other terms (Fig. 4). The model spread in radiative cooling from SW and LW are lowest among the energy budget terms, but especially for SW stretches across the zero line, making their future contribution to precipitation change highly model dependent. SH, on the other hand, has a larger model spread, but mostly shows a consistently negative contribution to precipitation (indicating increased SH flux) over land for all of the models, except over the Central and Northern European regions where some models show a positive contribution. Given this high model spread in the different energy budget terms, the resulting spread in projected precipitation change is substantial. It should be noted, however, that the change over the different regions gets stronger with forcing and time, even though the spread is similar for the two periods and the two forcings studied.

We have used the atmospheric energy equation over Europe to explain model differences in historical precipitation change. The biggest uncertainty in sign (if the term contributes to increase or decrease in precipitation) is found for the H term. Since the H term accounts for much of the spatial variability of precipitation changes, we investigate the role of model variations in ECS to the dry static energy flux divergence. Figure 6 shows how the changes in the H and precipitation differ with ECS over the different regions. The linear interpolations show that models with higher ECS have a larger contribution from the H term and a larger increase in precipitation for the Northern region, with a statistical significance of ∼ 0.5 for the H term and ∼ 0.4 for precipitation at the end-of-century for both forcing scenarios (see Table B2). Over the Mediterranean there is a drying with higher ECS, however only H shows a statistically significant correlation of around 0.6 at the end-of- century for both forcings. The other regions show little change with the model ECS. To see the effect of temperature on precipitation changes, Fig. 6c and f show the change when precipitation change is normalized with temperature change. The results are similar to only precipitation with reduced correlations.