Cloud radiative effects significantly increase wintertime atmospheric blocking in the Euro-Atlantic sector

Domain: earth_science
Published: 2025-11-05
Editorial outcome: major_revision

Abstract
Reliable simulation, prediction, and complete theoretical understanding of atmospheric blocking remain challenging despite its significant socio-economic impacts. Generations of climate models have notoriously underestimated blocking frequency, particularly over the Euro-Atlantic sector. Identifying factors controlling blocking frequency and dynamics is therefore essential for improving its simulation. Here, using a cloud-locking experiment, we show that cloud radiative effects (CREs) significantly increase the frequency of Euro-Atlantic blocking. CREs enhance upstream diabatic source of wave activity, both directly through longwave heating and indirectly through their feedback on latent heating, with the latter playing the dominant role. The resulting increase in the upstream diabatic source feeds into local wave activity downstream and promotes blocking formation. Qualitatively similar results are shown by multi-model experiments with radiatively inactive clouds to longwave radiation, albeit with a larger impact from mean-state changes. The results underscore the necessity of accurately representing cloud-radiation interactions in weather and climate models for improved prediction of blocking events.

Introduction
One of the main characteristics of the Earth’s mid-latitude troposphere is the jet stream, a fast, narrow band of winds blowing from west to east around the globe. The jet stream occasionally meanders over thousands of kilometers over a certain region, favoring the formation of a quasi-stationary high-pressure system that disrupts the mean westerly flow. This condition is known as blocking1–5. A blocking event can persist for an extended period of time, from a few days to more than a week3–5. Due to their persistence and size, blocks often bring about anomalous, sometimes extreme, weather in the mid-latitudes, including heat waves, cold spells, droughts, and heavy rainfalls, depending on the season and region4,6–11. For example, the unprecedented heatwave in the Pacific Northwest during the summer of 2021 was due at least partially to strong anticyclonic blocking, which caused a significant number of deaths and billion of dollars in damage12,13. Despite its importance, simulating and predicting blocking events is notoriously challenging due to the lack of a comprehensive dynamical theory and because blocks are rare and localized14. Therefore, it is essential to understand the mechanisms and factors contributing to the formation of blocks.

Generations of climate models mostly underestimate the frequency of blocking, casting doubt on future projections of blocking’s impacts on climate extremes4,15,16. This significant negative bias in blocking frequency is pronounced over the Euro-Atlantic sector and has continued across three generations of climate models (CMIP3 to CMIP6)15,16. Such underestimation has been known to be associated with the biases in the model’s mean state and/or the wave source at the lower boundary, which are linked to the processes that drive or damp blocking15–18. Previous studies have suggested that there are several factors contributing to these biases, which include (1) the near-surface temperature gradient19,20, (2) the strength and pattern of the sea surface temperature (SST) and the oceanic front in the Gulf Stream18,21–26, (3) the North Atlantic current positions23,27, (4) the remote influence of tropical convection22,28,29, (5) the intensity of the orographic drag30, and (6) latent heating (LH) in ascending air masses upstream of the block12,31–35. While improving the representation of these factors in climate models has partially increased the accuracy of blocking frequency15,16, fully solving the problem of atmospheric blocking biases remains challenging. This is partly attributed to the other unknown sources of bias, and to compensating errors from various factors, such as the effects of horizontal and vertical model grid resolutions36.

Over the past decades, blocking dynamics were mostly presumed to be predominantly dry, and moist processes were thought to be only of secondary importance. However, by applying back trajectory analysis to observational data, recent studies showed that latent heating (LH) from cloud formation can make a leading order contribution to the anticyclonic potential vorticity (PV) through the strongly ascending warm conveyor belt (WCB) airstreams upstream of the blocks31,32,34,35. By simulating observed blocking events in the Integrated Forecast System, Steinfeld et al.32 showed that artificially turning off LH tendencies upstream of blocking events can substantially reduce the occurrence, duration, and size of blocks. Neal et al.12 also found that cloud LH upstream of the block feeds the wave activity downstream, contributing to block formation. More recently, Hauser et al.34,35 corroborated the significance of moist processes in the formation and maintenance of blocking over the Euro-Atlantic sector. They suggested that accurately representing these moist processes could help reduce forecast errors related to blocking in weather prediction models. This highlights the crucial role of diabatic heating associated with moist processes in blocking formation.

Among diabatic processes, the role of Cloud Radiative Effects (CREs)—the radiative heating resulting from the presence of a cloud—in the dynamics and formation of atmospheric blocking is poorly understood. While much research has focused on the impact of diabatic heating associated with LH release on the blocking31,32,34,35, the influence of CREs remains largely unexplored. CREs can be as important as other diabatic processes, as they significantly affect large-scale circulation and eddies through increased baroclinicity owing to changing meridional temperature gradients and static stability37–42. CREs can also cause a robust precipitation increase over the tropical and extratropical oceans across models40,43, suggesting that cloud-radiative impact might operate via changes in condensation and LH. A recent study showed that CREs influence forecast error growth in the WCB and Rossby wave activity through modifications of latent heating, which in turn governs diabatic PV generation44. Given the significant influence of CREs on moist processes and their interaction with large-scale circulation, it is reasonable to hypothesize that they could also affect blocking formation.

To test this hypothesis, we utilize a “cloud locking” technique in the U.S. DOE’s Energy Exascale Earth System Model (E3SM)45,46, in which interactive cloud-radiation interactions are decoupled from the circulation with minimal disruption to the mean state. Isolating the role of CRE in this way provides greater clarity into its impact on blocking formation. While cloud locking has previously been applied to studies of climate variability39,42,47, extratropical storms38, and extreme precipitation43, its application to atmospheric blocking is novel. We further compare the cloud-locking results with those from an experiment where clouds are transparent (radiatively inactive) to longwave radiation as well as with similar experiments from other models participating in the Cloud-Feedback Model Intercomparison Project (CFMIP). As will be shown later, cloud-radiative feedbacks substantially increase blocking frequency, indicating that CRE-related model biases can directly influence blocking formation. Finite-amplitude local wave activity (LWA) budget analysis5,12,48 further reveal how CRE-induced diabatic heating shapes blocking dynamics and formation, providing a distinct pathway by which diabatic processes modulate blocking. Overall, these findings underscore the necessity of accurately representing CREs to improve the simulation and projection of blocking events in weather and climate models.

Results
Impact of CREs on occurrence of atmospheric blocking
Figure 1 shows the spatial distribution of blocking frequency in the reanalysis and E3SM experiments. The control experiment with prescribed present-day SST forcing (CTL, hereafter; Fig. 1a) generally captures the observed Euro-Atlantic blocking frequency distribution, although the simulated blocking frequency is relatively lower and the maximum center in the mid-latitudes is shifted southward to ~55∘N compared to the MERRA2 reanalysis climatology in winter (December to February). The relatively low blocking frequency in CTL may result from the absence of interactive lower-boundary SST forcing, which is known to modulate Euro-Atlantic blocking formation22,23,25,26. The evolution of Euro-Atlantic blocking events in the CTL run is also found to be comparable to that of blocking events in the reanalysis (see Supplementary Fig. S1). These results indicate that E3SM performs relatively well in capturing Euro-Atlantic blocking.

To investigate the impact of interactive CREs on blocking climatology, we perform a cloud-locking (CLOCK) experiment in which cloud-radiation feedback is disabled while maintaining mean state similar to that in the CTL. As such the cloud properties received by the radiative transfer scheme are taken from the CTL simulation that is independent of the flow field (see details in the Method section). Although this technique has been shown to effectively preserve the spatial, seasonal, and diurnal structure of CREs, it instantaneously removes the interaction between the atmospheric state and the clouds as seen by the radiative transfer38,43,46.

Figure 1b shows the effect of disabling the interactive CRE on the blocking frequency climatology. It is shown that disabling the interactive CRE decreases the blocking frequency over the Euro-Atlantic regions, including the North Atlantic Ocean and West/Central Europe (Fig. 1b, d). Notably, the CLOCK experiment simulates a much lower blocking frequency over the mid-latitude Euro-Atlantic (with the areal mean of 6.06 ± 1.52% blocked days per winter in CLOCK vs 7.73 ± 1.50% blocked days per winter in CTL). In other words, removing the interactive CRE reduces the mid-latitude Euro-Atlantic blocking frequency by up to 21.60 ± 2.14% (see Fig. 1b, d). This result suggests that the interactive CREs can increase the blocking occurrence beyond the mean state.

While the cloud-locking methodology essentially explains the impact of interactive CREs on the blocking formation (with minimal disruption to the mean state), one might wonder whether the changes in the mean state due to radiatively inactive clouds could have a direct or indirect impact on the mean blocking frequency. To investigate this, we conduct another experiment in which clouds do not interact with longwave radiation, i.e., longwave cloud radiative effects (LWCRE) are deactivated. This configuration is similar to the Clouds On/Off Klima Intercomparison Experiment phase 2 (COOKIE-2) methodology within CFMIP; however, here, the underlying SSTs and sea ice are held constant for each year based on climatological monthly varying SSTs from year 200046. We refer to this as the LWOFF experiment. The key difference between the LWOFF and CLOCK simulations is that LWOFF modifies the mean climatic state by removing a major atmospheric heat source (longwave radiative heating from clouds), whereas CLOCK only removes interactive cloud radiative effects with minimal disruption to the mean state38,43,46.

Figure 1c shows the response of blocking frequency climatology in the LWOFF. By disabling LWCRE, blocking frequency is reduced notably over the mid-latitude Euro-Atlantic, with the areal mean dropping to 4.85 ± 1.25% blocked days per winter in the LWOFF, compared to 7.73 ± 1.50% blocked days per winter in the CTL. This suggests that removing LWCRE reduces the mid-latitude Euro-Atlantic blocking frequency by roughly 37.26 ± 3.42%. Moreover, the decrease in blocking frequency affects not only central and western Europe but also a larger portion of the North Atlantic Ocean. The stronger response in the LWOFF simulation compared to CLOCK suggests that changes in mean LWCRE significantly influence the mean states, which, in turn, largely affects the blocking formation. Furthermore, we also compare these results with those from other models in the CFMIP that follow a similar experimental protocol (Table 1 and Fig. 2). The results indicate that disabling LWCRE generally reduces the frequency of blocking events over the mid-latitude Euro-Atlantic region, as demonstrated in most model simulations, similar to E3SM’s LWOFF run (Fig. 2). This reduction is statistically significant in all models except one AMIP experiment (MRI), which shows only a slight decrease (Fig. 2b, c). On average, disabling LWCRE lowers the climatological value by about 15, 19% from the corresponding multi-model mean of AMIP runs (Fig. 2b–c and Tables S1–S2 in Supplementary Information). These results confirm that the impact of removing LWCRE on blocking formation is robust and independent of the specific models used. In the following section, we will explain how the CREs enhance Euro-Atlantic blocking.

Influence of CREs on the dynamical processes of blocking formation
Previous studies have demonstrated that diabatic heating can act as a direct source of wave activity, which influences blocking formation5,12. Additionally, changes in the large-scale mean state, such as the location and structure of the jet and the strength of stationary waves, can influence the conditions that favor blocking formation and development15,49,50. Building upon these insights, we propose two hypotheses to explain how CREs influence the dynamical processes of blocking formation:

1. Cloud-radiation interactions promote blocking formation by enhancing upstream diabatic source of wave activity throughout the blocking lifecycle.
2. CREs alter the background mean state, which in turn affect the environment in which blocks form.

To test the first hypothesis, we analyze the composite evolution of Euro-Atlantic blocking events based on the finite-amplitude LWA budget. We choose to use the budget of LWA instead of PV because LWA is a positive-definite quantity, as being proportional to the square of (QG) PV anomaly, that directly measures wave amplitude and captures the growth and decay of blocking events. Decomposition of LWA budget and corresponding attribution to the driving physical processes are straightforward without ambiguity from change in the sign of metric, as demonstrated in previous relevant studies5,12,51. The column budget of LWA5,12,48 reads:

∂/∂t hAicosϕ = | - ∇H · hF i + fcosϕ ∂vθ~e/∂zθe + hA_icosϕ | (1)

where the right-hand side terms are (I) horizontal convergence of the LWA flux representing the redistribution of wave activity (the sum of zonal and meridional convergences of the LWA flux), (II) meridional eddy heat flux at the lower boundary (i.e., low-level baroclinic source), and (III) nonconservative (diabatic) source or sink of LWA (see Methods for the definitions of variables). Term III is backed out as residual from Eq. (1). It includes the overall contributions from both the diabatic source/sink of wave activity due to diabatic heating and other dissipation mechanism such as mixing, radiative and Ekman damping.

Equation (1) partitions the contribution of dynamical processes to the growth of LWA hAicosϕ indicating the formation of a block (the occurrence of a “wave activity congestion”5) and allows us to quantify the impacts of diabatic processes via term III. The influence of CREs on blocking formation can be directly assessed by explicitly calculating the contributions of diabatic effects and other processes involved in the LWA budget (see Eq. 12 in Methods).

The development of the blocking events (centered at 45∘–55∘N and 10∘W–10∘E) in the CTL run during the onset period (days -3 to -1) basically captures the observed blocking evolution in the reanalysis (Fig. 3 and Figs. S1–2 in the Supplementary Information). The onset of blocking is marked by a successive increase in LWA (shading in Fig. 3a–d) over Europe. This rise in LWA signifies stronger deceleration of the zonal flow, which slows atmospheric circulation and promotes the development of blocked flow. This is consistent with previous studies showing that blocks are often associated with persistent, large-valued wave-activity anomalies5,12,52,53.

The block-related change in LWA during the onset is primarily driven by the horizontal convergence of LWA flux (Term I) and by nonconservative (diabatic) source or sink of LWA (Term III), whereas contributions from the low-level baroclinic source (Term II) are relatively small and secondary (Fig. 3e–p). Specifically, the downstream growth of the LWA over Europe (positive values in Fig. 3a–d) is predominantly associated with the horizontal convergence of wave activity flux (positive values in Fig. 3e–h), which is partially offset by negative values of Term III (Fig. 3m–p). The positive values in Term I are mainly dominated by the zonal convergence of LWA flux (Fig. S3), consistent with previous studies showing that the zonal LWA flux is the dominant driver of the LWA tendency and a predictor for atmospheric blocking5,50,53. Specifically, when the zonal LWA flux exceeds the carrying capacity of the jet stream, blocking would manifest like a traffic congestion5. On the other hand, the low-level eddy heat flux (Fig. 3i–l) makes only a minor contribution to the downstream enhancement of LWA.

The downstream growth of horizontal LWA convergence is closely linked to enhanced eastward wave-activity flux (zonal LWA flux) originating from the upstream region (see vectors in Fig. 3e–h and Fig. S3). As shown in Fig. 3m-p, positive values of low-level sources and non-conservative (diabatic) processes are collocated with the emergence and growth of wave activity fluxes, acting as LWA sources, with non-conservative processes being of primary importance. This suggests that the upstream hA_icosϕ acts as the main diabatic source of wave activity, which is then advected by the zonal flow downstream and converges to form blocks, as indicated by the LWA convergence downstream (cf. 12).

Such a large positive values in the upstream nonconservative sources of LWA were also found in a previous study12, likely arising from diabatic heating associated with moist ascent along the WCB. Looking closely at Fig. 3m–p, it is evident that the positive values are located between the low-(trough) and high-pressure (ridge) centers, where moist air converges in the WCB. This pattern is also observed in the reanalysis data (see Fig. S2m-p), where the positive values of the low-level and high-pressure centers, where moist air converges in the WCB, and the position of the WCB, are collocated with the local maxima of nonconservative LWA sources (Fig. S4). In addition, both the low-level and high-pressure centers, where moist air converges in the WCB, and the position of the WCB, are collocated with the local maxima of nonconservative LWA sources (Fig. S4). These overall characteristics suggest that the positive hA_icosϕ anomaly upstream is predominantly driven by diabatic heating associated with cloud processes. This finding is confirmed by our further direct calculations of diabatic source of wave activity (ΔΣ), showing that cloud diabatic heating (both LWCRE and LH) significantly contributes to the positive values of the nonconservative sources of LWA in the upstream region, with the most significant contribution coming from latent heat release (Figs. S5–S6 and later in Figs. 6–7). These results support the findings of Neal et al.12 and other studies, highlighting the major role of diabatic heating in the onset of blocking formation31,32,34,35.

Taken together, the results indicate that the formation of the Euro-Atlantic blocking event in both reanalysis and CTL is associated with persistent, large-amplitude wave activity, primarily driven by zonal convergence of LWA flux downstream. This enhanced convergence downstream is fueled by upstream wave activity sources from diabatic heating, with only a minor contribution from the upstream low-level baroclinic generation.

To investigate how the interactive CRE and changes in the mean LWCRE affect the dynamical processes of blocking formation discussed above, we quantify the column LWA and its budget across all three simulations during the onset period, averaged over day -3 to day -1. Figure 4 compares the LWA and its tendency during the onset period of blocking events (days -3 to -1) in the reanalysis and across the three experiments. CTL and MERRA2 exhibit similar LWA and LWA tendency values, with no significant differences between them (Fig. 4d). Among the model experiments, CTL shows the largest LWA tendency (~2.8 ms−1 day−1), followed by CLOCK (~1.9 ms−1 day−1) and LWOFF (~0.8 m s−1 day−1) (Fig. 4d), consistent with stronger wave activity and growth during the blocking onset period in CTL compared to CLOCK and LWOFF (Fig. 4a–d). Given that stronger LWA enhances blocking formation, these results confirm our earlier findings that blocking events occur more frequently in CTL than in CLOCK and LWOFF.

To further understand which processes are responsible for the LWA increases in response to CREs, we compare the LWA budget terms during the onset of the blocks, as shown in Fig. 5. We define the upstream (downstream) region to the west (east) relative to the block to better quantify the contribution of different processes. CTL captures the budget reasonably well compared to MERRA2 (Fig. 5d) (note that the results remain insensitive to the precise location of the polygon). In the upstream region (Fig. 5d), the contribution of hA_icosϕ to the increase in LWA is highest in the CTL (~7 ms−1 day−1), with a significant reduction in CLOCK (~4 ms−1 day−1) and in LWOFF (~2 ms−1) (Fig. 5a–d). This indicates stronger non conservative sources of LWA with interactive CRE. Additionally, the low-level source term remains weakly positive across all experiments, with the largest values found in CTL. The stronger low-level source upstream in the CTL is consistent with the stronger anticyclonic circulation (i.e., block amplitude) in this region (see the contour lines in Fig. 5a–c), resulting in stronger southerly flow (v > 0) and perturbation potential temperature (θ > 0). In contrast, the contribution of the horizontal LWA flux convergence (-∇ · hF i) is negative in all experiments, signifying that the divergence of H LWA partially offset the surplus hA_icosϕ from the upstream region.

In the downstream region (Fig. 5e), the horizontal LWA flux convergence exhibit the highest positive values in CTL (~10 ms−1 day−1), with CLOCK and LWOFF showing low values (~6 ms−1 day−1 and ~3 ms−1 day−1, respectively), indicating 40% and 70% reductions relative to CTL. The substantial increase in horizontal LWA flux convergence in the CTL is consistent with the significant increase of hA_icosϕ in the upstream region (Fig. 5d), which is mainly dominated by diabatic processes (Figs. S5–S6 and later in Figs. 6–7). This suggests that the upstream diabatic source increases horizontal convergence of LWA flux downstream, consistent with Neal et al.12. In contrast, the contribution of hA_icosϕ downstream is negative in all experiments, with CTL showing the greatest negative value (~-6 ms−1 day−1). The large negative values are associated with the dissipation of wave activity due to radiative damping, irreversible mixing, and surface friction downstream of the block (Fig. S6). Overall, the results suggest that CRE increases LWA primarily by enhancing the upstream diabatic wave activity source hA_icosϕ. LWA is then advected by the zonal flow downstream and converges to form localized blocking structures.

Next, we examine which diabatic processes associated with changes in interactive CREs contribute to the enhanced hA_icosϕ upstream. To quantify these contributions, we explicitly calculate the diabatic source and sink of wave activity (ΔΣ) due to different diabatic heating rates (θ_ ) in the reanalysis and across the three experiments (Fig. 6). A comparison between CTL and MERRA2 shows that CTL captures the vertical structure and column-averaged ΔΣ reasonably well, albeit with a few differences (Fig. 6). The LH contribution to ΔΣ in CTL is maximized upstream (i.e., to the west) of the block center between 500–400 hPa (Fig. 6b, c), while the LWCRE contribution to the diabatic wave source is centered between 600–300 hPa upstream of the block (Fig. 6g, h). This region of enhanced diabatic forcing corresponds to the ascending branch of the warm conveyor belt (WCB), which is characterized by strong vertical and poleward transport of moist air (see later in Fig. 7a, e, b, f). However, the upstream diabatic (LH) forcing at lower levels (950–800 hPa) is not adequately captured by CTL (Fig. 6b, c), which may stem from the model’s limitation in representing low-level clouds and the associated LH upstream during the blocking onset (see later in Fig. 7a, b).

By comparing the ΔΣ across all model experiments, we find that the contributions of longwave cloud radiative heating and LH to hA_icosϕ are largest in CTL, with LH making the dominant contribution (Fig. 6). In CLOCK, the LWCRE contribution is significantly reduced by ~57% (-0.15 ms−1 day−1 compared to 0.35 ms−1 day−1 in CTL), and the diabatic wave source upstream between 500-300 hPa is inactive (Fig. 6i). This reduction in LWCRE contribution to ΔΣ is expected because by design, the covariation between CRE and individual weather systems are decoupled. As a result, the modulation of LWCRE by blocking in CLOCK is suppressed. Similarly, the LH contribution to ΔΣ in CLOCK is reduced by ~46% when the CRE is locked (1.3 ms−1 day−1 in CLOCK compared to ~2.4 ms−1 day−1 in CTL) (Fig. 6c, d), further highlighting the role of interactive CRE in amplifying wave activity during blocking onset. Making clouds transparent to longwave radiation eliminates the impact of LWCRE on ΔΣ (Fig. 6a, j) and significantly weakens the LH contribution (Fig. 6a, f). This is consistent with the reduced LWA in LWOFF (Fig. 4), indicating the importance of LWCRE in amplifying wave activity during blocking onset.

The variations in the strength of upstream diabatic wave sources discussed above are closely tied to the amplitude and vertical extent of anomalous diabatic heating during the development of the block (Fig. 7a–h). In CTL, similar to MERRA2, enhanced ΔΣ (Fig. 6c, h) is associated with intensified LH and CRE within the WCB region (Fig. 7a–b, e, f; Figs. S7–S8), consistent with stronger vertical aloft and poleward moisture transport in this region. Comparison of diabatic heating terms across model experiments reveals a stronger positive LH anomaly upstream (west of the block center) in CTL relative to CLOCK and LWOFF (Fig. 7b–d, S9). This is consistent with stronger LH-induced ΔΣ upstream in CTL compared to the other experiments (Fig. 6b). Similarly, the longwave cloud radiative heating anomaly is stronger in CTL than in other experiments, with positive heating between 850-550 hPa concentrated west of the block center (Fig. 7e–h and Fig. S9). The stronger positive anomalies in LH and LWCRE in the experiment with interactive CRE align with our findings in Fig. 6, which show that LH and LWCRE contribute most to the diabatic source of wave activity upstream, leading to stronger zonal LWA convergence downstream (Fig. 5e and Figs. S3, S5).

The reduction of LH in CLOCK and LWOFF in the absence of CREs can be explained by the lack of LWCRE impacts on large-scale ascent and moisture transport. During the onset period, LWCRE significantly warms the mid-troposphere (850-450 hPa) in the WCB region upstream in CTL (Fig. 7f), whereas this warming is weaker in CLOCK (Fig. 7g) and absent in LWOFF (Fig. 7h). In the absence of LWCRE-induced warming, cooler mid-tropospheric temperatures steepen the vertical temperature gradient, enhancing static stability and weakening large-scale ascent. This weaker ascent is consistent with reduced negative vertical velocity (ω) anomalies in CLOCK (Fig. 7i) and LWOFF (Fig. 7j) in the WCB region with enhanced LH (see green box), indicating less efficient lifting of moist air into the mid-troposphere. This reduction in ascent is accompanied by weaker vertically integrated moisture transport (IVT) into the WCB (Figs. 7k–l, S10), confirming that less moisture is being advected poleward upstream of the block. The weakening of moisture transport in both CLOCK and LWOFF is consistent with the reduced mean moisture flux upstream (over the eastern North Atlantic) (see later in Fig. 8g, h). As a result, condensation is suppressed, leading to a decline in LH. This is consistent with previous studies showing that LWCRE plays an important role in intensifying vertical motion and LH37,40,41,54.

Another possible pathway is that LWCRE enhances LH through an evaporation feedback. Using observational-based MERRA2 data, we show that during the onset period, positive anomalies in longwave cloud radiative heating, LH, and surface evaporation are partially colocated in the upstream region of the block (green box, Fig. S11). This positive LWCRE anomaly upstream in the WCB is primarily associated with increased high cloud cover, with a secondary contribution from low-to-mid-level clouds (Fig. S12). An increase in high clouds can effectively trap downward LW radiation, which could lead to enhanced surface temperature and latent heat flux (LHF). Positive LHF indicates increased moisture transfer from the surface to the atmosphere, supporting enhanced LH aloft. This increase in LHF (Fig. S11e) is primarily driven by stronger surface wind and enhanced near-surface vapor gradient (qs - qa) upstream of the block region (Figs. S11g, h). The latter can be associated with surface warming linked to CRE during the blocking onset (Fig. S11f), which increases the saturated specific humidity (qs) and hence the moisture gradient (Fig. S11g). Removing this effect would suppress LHF and consequently weaken LH, consistent with previous studies40. While these reanalysis-based diagnostics support the plausibility of this pathway, they cannot fully isolate the role of LWCRE from other contributing processes. Currently, our model simulations were conducted with prescribed SSTs, which limits this surface feedback, and the necessary surface diagnostic variables were not archived to directly evaluate this pathway. Therefore, future investigation in a separate modeling study, particularly those using interactive SSTs, is needed to robustly evaluate this mechanism.

In summary, interactive CREs promote blocking formation mainly by enhancing upstream diabatic wave source, both through its direct influence through LWCRE and indirectly via its impact on LH in the WCB region upstream of the block, with the latter playing a dominant role. The LWA from the upstream diabatic source is then advected by the zonal flow and converges downstream to form blocks. The significant reduction in blocking frequency in the CLOCK and LWOFF experiments underscore the importance of CREs in these processes.

Influence of CREs on blocking through background circulation
One might question whether changes in CREs could induce changes in background mean state that affects blocking formation. Previous studies have found that blocking prevalence is influenced by the strength and latitude of the jet5,49, as well as the intensity of background stationary waves5,22,50. In particular, reduced blocking frequency is often linked to a poleward jet shift and a weakened quasi-stationary ridge5,22,49,50. Figure 8a–d shows the responses of the mean jet (Fig. 8a–b) and background stationary wave (Fig. 8c–d) in CLOCK and LWOFF relative to CTL. The CLOCK experiment exhibits a weak poleward jet shift (Fig. 8a) and a partial weakening of the planetary-scale anticyclonic ridge associated with stationary waves over Europe (Fig. 8c). In contrast, LWOFF exhibits a more pronounced poleward jet shift (Fig. 8b) and a stronger weakening of the quasi-stationary ridge over Europe. These background circulation changes in response to CREs are consistent with previous studies showing that CREs play an important role in shifting the jet poleward by modifying meridional temperature gradients and static stability37–39,42. The poleward shift of the jet and weaker quasi-stationary ridge provide unfavorable conditions for blocking to form over Europe22,49. This finding broadly supports previous studies showing that the weaker quasi-stationary ridge and stronger PV gradients, associated with a poleward-shifted jet, increase the jet’s carrying capacity for wave activity, making a block more difficult to form for a given level of incident transient wave-activity flux53,55. As a result, downstream LWA flux convergence is reduced, consistent with weaker wave activity and lower blocking frequency in these two experiments relative to CTL (Figs. 1, 5e).

The reduction in blocking formation in the CLOCK and LWOFF experiments is consistent with weaker climatological low-level baroclinicity over the storm-track region (eastern North Atlantic), as indicated by the Eady growth rate (EGR) (Fig. 8e–f). Although both experiments show reduced EGR, the decrease over this region is much larger in CLOCK than in LWOFF. This suggests that disabling LWCRE causes a pronounced weakening of low-level baroclinicity, thereby reducing the atmosphere’s capacity to generate and sustain transient eddy activity, which in turn diminishes blocking formation. The reduction in the climatological mean of low-level baroclinicity is also consistent with weaker low-level baroclinic source (i.e., eddy heat flux divergence) in CLOCK and LWOFF relative to CTL during blocking onset (Fig. 5d, e).

In addition to the baroclinicity changes, removing CREs also significantly weakens climatological moisture transport upstream (eastern North Atlantic) in CLOCK and LWOFF relative to CTL (Fig. 8g, h). This reduced moisture transport is likely related to weaker stationary wave ridge that modulates poleward moisture transport from low latitudes (Fig. 8c, d). This weakening of climatological moisture transport, in turn, accounts for the reduced poleward moisture transport anomaly upstream during the blocking lifecycle (Fig. 7k, l), leading to reduced LH upstream and ultimately less blocking formation in CLOCK and LWOFF.

Taken together, changes in CREs can influence blocking formation indirectly by modifying the background mean state, including the jet, quasi-stationary ridges, mean baroclinicity, and moisture transport. These mean-state modifications explain the stronger reduction in LWA and blocking frequency in LWOFF, where the background circulation is substantially modified, compared to CLOCK, where it is only minimally altered.

Methods
Numerical experiments
We use the U.S. DOE’s Energy Exascale Earth System Model v1 (E3SM45) to investigate the contribution of cloud radiative effects (CREs) on the midlatitude atmospheric blocking. All experiments are run in the “AMIP” configuration with realistic land-sea geography, an active land model, and prescribed annually repeating sea surface temperatures (SSTs) and sea-ice concentrations (based on a 20-year monthly climatology centered on year 2000 of the real world)46. The SST pattern is repeated annually, so that interannual variability (e.g., El Niño–Southern Oscillation) is not included. Decoupling cloud radiative forcing from SST-driven changes allows for a clearer isolation of the impact of CREs on blocking dynamics, with minimal interference from lower-boundary SST-related forcing. The control run (CTL) uses the atmospheric forcing representative of the present-day climate conditions (using the initial condition of the year 2000 of the free-running E3SMv1 DECK AMIP simulation)46. The CTL run lasts 20 years following a 30-year spin-up to ensure global soil moisture equilibrium.

The cloud-locking experiment (CLOCK) is identical to CTL, except the cloud properties are “locked" to isolate the interactive CRE. Specifically, we prescribe the cloud optical properties from the first three years of CTL simulation in the CLOCK simulation46. This choice follows the common practice in cloud-locking experiments38,47 and is intended to retain a realistic and internally consistent CRE climatology while reducing computational burden46. Prior studies have shown that even a single year of cloud properties can be sufficient for a cloud-locking configuration (e.g., Middlemas et al.47), so we do not anticipate issues related to undersampling when using three years. In this way, the CLOCK experiment possesses a nearly identical CRE climatology to CTL, but the CREs are decoupled from the dynamics and other physical processes. This means no high-frequency covariance between CREs and circulation affect the blocking. This cloud-locking technique is similar to that used in previous studies38,47. The CLOCK run is also integrated for 20 years.

Because the cloud-locking experiment fundamentally differs from the complete CRE denial experiments, such as those conducted in the COOKIE project60,61, we also perform one CRE denial experiment in the E3SM where LWCRE is disabled (referred to as LWOFF hereafter). In this setup, SSTs and sea ice conditions are kept the same as in the CTL experiment. However, unlike the CLOCK experiment, the LWCRE is deactivated so that the average CRE heating in the atmosphere changes, which then alters the mean circulation and the climate regimes46.

Finally, we also compare the LWOFF experiment to the COOKIE-2 simulations of the Cloud-Feedback Model Intercomparison Project (CFMIP) Tier 2 in two different configurations: standard Earth-like configurations (AMIP) with interactive CREs and AMIP with disabled LWCRE (AMIP-LWOFF). The COOKIE-2 experimental protocol specifies that only the LWCRE is deactivated, while SSTs and sea-ice concentrations are prescribed and held identical between the control run and LWCRE-off simulations61. We analyze daily Z500 fields from these simulations at a spatial resolution of 2.5∘×2.5∘. These simulations have been conducted by four modeling groups so far and are listed in Table 1.

Reanalysis datasets
Daily gridded horizontal velocity, geopotential height, temperature, surface pressure, and temperature tendencies of the NASA MERRA-2 dataset62, covering the period from 1980 to 2020 with a spatial resolution of 0.5∘×0.625∘ and 29 vertical levels, were obtained to assess the ability of the CTL run to simulate the large-scale circulation features, heating rates, and blocking activity. MERRA-2 was chosen here because it provides different diabatic heating rates (a fully gridded 3D heating derived from the assimilation of satellite observations and the GEOS-5 model), making it particularly well-suited for process-level diagnostics involving diabatic influences on wave activity42. Cloud radiative heating rates are diagnosed as all-sky radiative heating rates minus clear-sky radiative heating rates.

Detection of blocking
We employ a Dole and Gordon’s blocking index63, which is based on finding strong, stationary, and persistent positive daily 500-hPa geopotential height (Z500) anomalies. This index is also known as an anomaly-based blocking index4,64,65 and has outperformed a few other Z500-based indices in identifying heatwave-causing weather patterns10. For this index, the Z500 anomalies are calculated for each grid point as the difference with respect to the climatological mean daily values of the analyzed period. Blocks are identified daily as the two-dimensional areas of at least 2x106 km2 extensions with Z500 anomalies exceeding the threshold. The threshold is defined based on the 90th percentile of the Z500 anomaly distribution between 50∘ and 80∘N4. This threshold is applied to all grid points, and can be varying with the calendar month based on three-month centered distributions. To ensure the quasi-stationarity and persistence, the blocking events must persist for at least 5 days, with a minimum of 50% of the area blocked during the period. Note that any two blocking episodes that are separated by only one non-blocked day are counted as one blocking event, and any blocking events with less than 5 days are ignored. Here, we focus on the blocking events in winter (December–February, DJF) over the Euro-Atlantic sector.

Finite-amplitude local wave activity budget
Following the formalism of Huang and Nakamura51, the local finite-amplitude wave activity (LWA) is defined as the line integral of the eddy component of quasi-geostrophic potential vorticity qe along the meridional displacement of contour q from its equivalent latitude ϕ as:

A(λ,ϕ,z,t) = ∫0η -a qe cos(ϕ+ϕ0)dϕ0, ϕ0 ∈ [0,η], (2)

where
q(λ,ϕ,z,t) = f + 1/acosϕ ∂v/∂λ - 1/acosϕ ∂(u cosϕ)/∂ϕ + f/ρ0 ∂(ρ0 θe/∂zθe)/∂z (3)

is quasi-geostrophic potential vorticity, and
qe(λ,ϕ,ϕ0,z,t) = q(λ,ϕ+ϕ0,z,t) - QREF(ϕ,z,t), (4)

is the eddy component of the q contour relative to a zonally symmetric reference state at the latitude where q = QREF51. λ is longitude, ϕ is latitude, and z = -H ln(p/p0), with p0 = 1000 hPa and H is the reference scale height (7 km), θ is potential temperature, and u and v are the zonal and meridional component of velocity field, respectively. θ~ is the area-mean of potential temperature over the hemisphere, and f is the Coriolis parameter. The QREF is calculated by zonalizing the wavy potential vorticity contour on the z-surface with an area-preserving map5. The integral bounds denote a domain of integration from the given latitude ϕ0=0 to the meridional displacement ϕ0 ∈ [0,η]. By definition, the local wave activity A quantifies the amplitude of finite-amplitude wave disturbance in the atmosphere51,66,67. The density-weighted column mean of LWA budget reads as5,48,51:

∂/∂t hAicosϕ = | - ∇H · hF i + fcosϕ ∂vθ~e/∂zθe + hA_icosϕ | (5)

where,
∇H · hF i = 1/acosϕ ∂/∂λ hFλ i + 1/acosϕ ∂/∂ϕ (hFϕ i cosϕ), (6)

hFλ i = hu e Aicosϕ - a u e q e cos(ϕ+ϕ0)dϕ0 * 0 + 1/2 Re kz=H θ2 e - 1/2 v2 e - u2 e - H ∂θ~/∂z e cosϕ, (7)

hFϕ i = -hu e v e i cosϕ, (8)

where R is the gas constant for dry air (287 J K−1 kg−1). The angle bracket denotes density-weighted vertical average of LWA. The eddy components are defined as:

u(λ,ϕ,ϕ0,z,t) = u(λ,ϕ+ϕ0,z,t) - uREF(ϕ,z,t), (9)

v(λ,ϕ,ϕ0,z,t) = v(λ,ϕ+ϕ0,z,t), (10)

θ(λ,ϕ,ϕ0,z,t) = θ(λ,ϕ+ϕ0,z,t) - θREF(ϕ,z,t). (11)

The data is interpolated onto a regular pseudo-height (z) grid with dz = 1 km before the computation of vertical integral. The upper limit of the integral is taken to be z = 48 km (~1 hPa). Details of the calculation for REF states are discussed in previous studies5,12,48,51,66.

Terms I in Eq. (5) represent the sum of the zonal and meridional convergences of the column-mean horizontal fluxes of wave activity. Term II is the upward LWA flux at the lower boundary (i.e., the vertical component of the generalized Eliassen-Palm flux). Term III represents diabatic sources and sinks of wave activity associated with non-conservative processes. The term includes both the diabatic effect due to diabatic heating and the residual effect due to wave dissipation. In this study, we calculated directly the diabatic wave sources/sinks of wave activity using the diabatic heating rates (θ_ ) output from the model simulation as:

ΔΣ = -a f/ρ0 ∂(ρ0 θ_ /∂zθe/∂z)/∂z cos(ϕ+ϕ0)dϕ0, (12)

so that the total diabatic sources/sink of wave activity due to diabatic heating (ΔΣ) can be decomposed as,

ΔΣ = ΔΣLWCRE + ΔΣSWCRE + ΔΣLH + ΔΣCLR, (13)

where LWCRE is longwave CRE, SWCRE is shortwave CRE, LH is latent heating, and CLR is clear-sky radiative heating. The longwave and shortwave cloud heating rates are defined as the difference between all-sky and clear-sky rates. In this framework, the blocked flow forms as a result of the saturation in the zonal distribution of LWA5. Thus, quantifying each term in Eq. (5) help to elucidate which force drives changes in LWA and, thus, the formation of the block. We use version 2.2.0 of the Python package falwa68,69, which computes finite-amplitude Rossby wave activity and fluxes with snapshots of weather variables as input. The class falwa.oop_interface.QGFieldNHN22, which solves reference states with the boundary conditions as in Neal et al.12 (see Eqs. 14–16 in the study), encapsulates the LWA and flux calculations presented in this study.

Eady growth rate
To understand how rapidly baroclinic eddies can grow in a baroclinic environment, the maximum Eady growth rate (EGR)70 is computed as:

σ = 0.31 g N−1 T−1 | ∂T/∂y |, (14)

Here, σ is the maximum Eady growth rate, the Brunt-Väisälä frequency, denoted as N = g/θ ∂θ/∂z, and g is the acceleration due to gravity. Higher Eady growth rates indicate faster growth of baroclinic eddies and, therefore, more seeding to the blocking formation.

Diagnostics for quasi-stationary waves
The propagation of quasi-stationary planetary-wave activity is analyzed through the horizontal component of the Plumb flux71 in a spherical coordinate system as follows:

FS = p cos(ϕ) [ 1/2a2cos2(ϕ) (∂ψ0/∂λ)2 - ψ0 ∂2ψ0/∂λ2, 1/2a2cos2(ϕ) ∂ψ0/∂λ ∂ψ0/∂ϕ - ψ0 ∂2ψ0/∂λ∂ϕ ] (15)

here, stream function ψ = Z/2Ω sinϕ, where Z is geopotential, and Ω denotes Earth’s rotation rate. The stationary wave in the stream function is calculated as ψ* = ψ - [ψ], where overbars and square brackets denote the monthly and zonal means, respectively.

Data availability
MERRA-2 data are publicly available from NASA GES DISC (https://doi.org/10.5067/A7S6XP56VZWS; https://doi.org/10.5067/9NCR9DDDOPFI). The simulation output from this study is made available at https://portal.nersc.gov/archive/home/b/beharrop/www/e3sm_cre_denial_overview_data/Data_Overview_CRE_denial_in_E3SM.tar. The COOKIE2 data are publicly available via the Earth System Grid Federation, which can be accessed at https://esgf-node.llnl.gov/search/cmip6/. The raw data underlying the figures are available at https://doi.org/10.5281/zenodo.17138125.

Code availability
The source code needed to run the E3SM experiments is available at https://github.com/beharrop/E3SM. Template bash scripts for setting up and running cloud-locking E3SM are included in the supplementary material of Harrop et al.46. The data in this study are analyzed with NCAR Command Language (NCL). To detect a blocking event, the Contour Tracking (ConTrack) algorithm is employed. The ConTrack is a Python package designed to simplify the process of automatically tracking and analyzing synoptic weather features in weather and climate datasets. The code is publicly available online at https://github.com/steidani/ConTrack. Code to compute finite-amplitude local wave activity, fluxes and non-conservative force contribution via calling falwa68,69 is publicly available at https://github.com/csyhuang/hn2016_falwa/tree/master/scripts/lubis_et_al_2025. The scripts for analyses and generating figures are available at https://doi.org/10.5281/zenodo.17138125.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study presents results that estimate the cloud-radiative effects (CREs) on the frequency of Euro-Atlantic blocking during boreal winter by using climate model simulations with a technique that isolates the interactive CRE. While it is increasingly accepted within the community that the role of upstream latent heating (or moist processes in general) accompanied by synoptic-scale disturbance is pivotal in triggering and maintaining atmospheric blocking systems, the authors stress that it has yet been largely unexplored how the CREs, specifically, affect the genesis of atmospheric blocking. This missing piece of the mechanism becomes a motivation for the study to further investigate the linkage between CREs and atmospheric blocking.\n\nThe authors aim to evaluate the quantitative contribution of CREs in the column-integrated local wave activity (LWA) budget diagnostics. This objective is addressed by comparing the cloud locking (CLOCK) experiment, where interactive CREs have been disabled, to the control simulation, and by explicitly computing the diabatic sources/sinks of LWA from the residual term. As a result, the authors argued that the CREs contribute to the increase of atmospheric blocking frequency by 1) directly increasing the diabatic wave source, as well as by 2) enhancing the amount of latent heat release through longwave CRE (LWCRE) and its feedback on surface evaporation and the subsequent moisture content. They also noted that 3) changes in mean CREs indirectly are capable of substantially modulating blocking frequency by changing the background mean states.\n\nFrom my reading, the topic of this study – causally linking CREs to atmospheric blocking frequency – is quite novel. To my knowledge, no modeling study has used CLOCK experiments (or even a subset of CFMIP experiments) to investigate this detailed aspect. The key argument of the study that CREs increase the blocking frequency is clearly presented, and it is relevant for many fields of atmospheric sciences and weather community.\n\nNevertheless, regarding their physical interpretation of the results, I have some serious concerns. For instance, there is a distinct discrepancy between the location of LWCRE and condensational heating relative to the center of the block, which makes the suggested feedback of LWCRE on condensational heating questionable. I also found the argument that the CLOCK experiment does not significantly alter the mean state to be not very convincing. The credibility of the statement is further weakened by the barely visible white stippling that denotes statistical significance. In addition, even if the methodology of LWA budget analysis has been quite established now, estimating the diabatic process contribution from the residual of the budget entails some key assumptions and thus needs caution. Specifically, it does not provide any information on the vertical structure of CREs, which is obviously a very important component for wave source (not necessarily with respect to ‘column-integrated’ LWA diagnostics). Another concern that counteracts the strengths of the study is some of the conclusions drawn from the results sound too strong, despite some uncertainties in the proposed mechanism (e.g., Lines 272-273). With that said, I hope the authors address these concerns through major revisions.\n\nSpecific major comments\n1) Figure 6, LWCRE within blocking: There has now been much evidence that upstream diabatic heating is critical for downstream blocking development, as seen from the references. A novel finding of this study is that longwave CRE (LWCRE) regulates the amount of condensational heating at the upstream of blocking center, based on the composited results in Fig. 6. Although not described clearly, the authors mentioned that such feedback by LWCRE may be realized through surface evaporation (caption in Fig. 8; note that the description in Lines 274-278 is to explain the LWOFF response). However, the composited LWCRE heating anomaly is situated within atmospheric blocking, whereas the condensational heating anomaly occurs mostly upstream of the blocking center, or along the northwestern boundary of the geopotential height isolines. Given that these heating anomalies are not collocated, it seems unclear how LWCRE could influence the farther upstream latent heat release remotely through the suggested feedback. The fact that the mechanism of the suggested feedback itself remains uncertain (e.g., Lines 272-273) further complicates understanding this causal linkage. Can the authors add more supporting evidence?\n2) Figure 6, physical meaning of positive LWCRE: It is quite surprising (and interesting) for me that the contribution of long-wave cloud-radiative effect is positive, not negative, despite that low-level clouds are dominant in the midlatitudes. I wonder if this physically makes sense and provides an insight. As noted in the introduction, the warm conveyor belt airstreams that trigger this life cycle of blocking occur mostly at mid-to-low troposphere, and there is radiative cooling from low-level clouds tops and heating at cloud bottoms (e.g., Cesana et al. 2019 and many others). Does it mean that radiative warming at the cloud bottom (peaks at the surface) outweighs its atmospheric cooling effect and acts as a positive diabatic source of wave activity? Providing a physical explanation of positive LWCRE in the discussion of Fig. 6 would help readers understand its importance more comprehensively.\n3) Lines 472-484, Methodology-the validity of estimating radiative heating contribution of wave activity from equation (12): Related to the comment above, I am a bit confused of how the contribution of cloud radiative heating can be accurately estimated from the current methodology. If the results in Fig. 6a are taken at face values, it basically suggests that near-surface warming by upstream longwave radiative heating drives mid-tropospheric circulation anomaly. However, as we all know, change in atmospheric circulation is not simply driven by diabatic heating at near surface or certain height only. The vertical structure of radiative heating is complex and can sometimes induce counteracting responses in midlatitude circulation (e.g., Voigt et al. 2023). From my understanding, because of the height scaling factor in Eq. (12), it puts more (perhaps too much) weight to the near surface radiative heating values by construction, and limitedly reflects the rich vertical structure of cloud-radiative effects. I think this is conceivable a potential caveat of the residual approach of the LWA diagnostics. Can the authors show that this estimated LWCRE from Eq. (12) well represents the LWCRE in a more general condition (not particularly associated with blocking onset)? Otherwise, adding a discussion on some methodological limitations may provide further insights into the study.\n4) Lines 472-484, Methodology-implicit assumption on model representation of longwave heating: This study calculated the diabatic sources/sinks of wave activity using the simulated diabatic heating rates, which is different from previous studies (e.g., Neal et al. 2022) who estimated the total diabatic heating effects by suppressing positive diabatic forcing term in the LWA budget integration. While this explicit calculation thus adds a uniqueness to the study, it also hinges on an implicit assumption that the model simulates the diabatic heating rates in a reasonable quality, which is not shown or mentioned at all in the manuscript. To put it another way, it seems important to ascertain whether the control experiment well simulates the horizontal and vertical structure of climatological diabatic heating and does not exhibit obvious errors.\n5) Figure 7, significance of changes in mean states: It is repeatedly emphasized in the manuscript that the CLOCK experiment does not significantly change the mean states at all (particularly in the conclusion section), and thus any notable difference between CLOCK and control simulations is attributable to interactive CREs. However, I am not sure if this is entirely true, considering that there are still some hints of poleward displacement of the North Atlantic jet, weakening of the southwest-northeast tilt of stationary eddies, and reduced maximum Eady growth rate over the Gulf Stream and the entrance of the North Atlantic storm track. I feel these features will be more pronounced if colored stippling is used for statistical significance. Can the authors quantitatively show these mean state changes in CLOCK are negligible compared to LWOFF? In any case, the authors need to tone down statements that overstate the absence of significant change in the mean state for CLOCK throughout the manuscript, as there are actually some significant changes.\n6) Figures 5, 6, 7, differences in moisture transport: Changes in the climatological mean states from the CLOCK experiment are seemingly small (Fig. 7), but it does not necessarily mean that such changes are trivial in modulating atmospheric blocking frequency. One possible pathway of their impacts is a reduction of poleward moisture transport over the upstream of Euro-Atlantic blocking. If the climatological moisture transport is reduced in CLOCK, compared to the control run, it indicates that the moist processes driven by stationary eddies are weaker and therefore contribute to the reduction of condensational heating (Fig. 6a), in addition to the contribution from interactive CREs.\n7) Figure 8, schematic diagram and figure caption: The diagram is reminiscent of Figure 1 in Steinfeld et al. (2022) and seems to build upon previous findings. However, I am somewhat skeptical about whether this schematic illustration accurately reflects the results presented in this study.\nThe first step, ‘moist air injection’, is not explicitly shown in this study but used without any reference being provided in the caption. Regarding the third step, as noted in the earlier major comments, LWCRE is not located upstream of the blocking center, but rather within it. This differs from illustration. Moreover, the process described in the figure caption (i.e., ‘The enhanced LWCRE in turn amplifies LH by boosting evaporation) is not clearly demonstrated in this study, resulting in an unsubstantiated statement. The term ‘divergent outflow’ at the upper troposphere also abruptly appears without any context. Lastly, it feels a bit strange to see the vertical structure of the proposed mechanism for the first time in this study as a schematic diagram. I recommend the authors either replace it with a new diagram based on the results of the study within the framework of LWA diagnostics, or provide a list describing the chain of processes in order.\n\nMinor comments\n1. Line 36: ‘there is no comprehensive dynamical theory’\n2. Lines 35-36: ‘simulating and predicting blocking events … are rare and localized’. This sentence could flow better. I recommend rephrasing it.\n3. Line 10, 39: ‘notoriously underestimate’. I understand that the authors want to strongly motivate the study by pointing out the systematic model biases, but it sounds too strong. Also, in terms of the anomaly method for blocking detection, note that some regions show overestimating biases (Woollings et al. 2018). I recommend an expression like ‘mostly underestimate’.\n4. Line 46: ‘SST’. This acronym is not defined beforehand.\n5. Line 53: ref. 34. Information of ref. 34 is missing in the reference.\n6. Line 101: ‘climatology in winter (December to January)’. There seems a mismatch between this expression and the figure caption. I guess ‘(December to February)’?\n7. Figure 1 caption: It would be helpful to expand all acronyms at their first usage in captions.\n8. Hatches in Fig. 2a: What does this black hatch mean?\n9. Line 242: ‘stronger southerly flow (Ve < 0)’. Is this sign error? I think Ve > 0 represents southerly flow, not Ve < 0.\n10. Line 244: ‘) in the upstream’ -> ‘in the upstream’\n11. Lines 275-276: ‘Reduction in latent heat release … evaporation’. Alternatively, this could be simply due to a weaker warm conveyor belt airstream and the associated moisture transport. See major comment 6.\n12. Line 300: ‘is minimal’ -> ‘are minimal’.\n13. Lines 308-311: This sentence states that there is a ‘partial weakening’ of the climatological ridge over Europe, but then it is followed by an expression ‘Despite no change in the mean state’. Based on the results in Fig. 7, further investigation seems necessary. See major comment 5.\n14. Line 321: ‘the observed reduction … over the region’. It sounds like the authors are describing observational results. I recommend rephrasing it.\n15. Figure 7 caption: Is the unit of the streamfunction correct? It seems a factor of 10 is missing.\n16. Color of stippling: I strongly recommend changing the color of the stippling. It is very difficult to identify.\n17. Lines 377-378: ‘the distinctive role of diabatic wave activity injection … anticyclone’. I feel this sentence could flow better, and its structure also looks somewhat too similar to the original sentence in Neal et al. I recommend rephrasing it.\n18. Line 442: ‘a blocking-based anomalies index’. I think the authors meant ‘an anomaly-based blocking index’.\n19. Line 480, Equation 13: Is total diabatic heating composed of only these four terms? I thought there is also a heating term of vertical diffusion (or sometimes referred to as diabatic heating due to turbulent mixing). Also, I guess longwave CRE (LWCRE) is derived from the difference between net longwave heating and clear-sky radiative heating, correct (same for SWCRE)? If so, please add this detail.", "reviewer_2": "Cloud-Radiative Effects Significantly Increase Wintertime Atmospheric Blocking in the Euro-Atlantic Sector (Lubis et al., 2024)\nThis study investigates the radiative impact of clouds on the dynamics and frequency of midlatitude atmospheric blocking during winter. Using two modeling techniques, the authors assess the impact of cloud radiative effects (CREs) on the blocking and show that CREs significantly increase the frequency of blocking over the Euro-Atlantic sector. To gain a process-based understanding of the radiative impact of clouds on the blocking dynamics, a budget analysis of the local wave activity was performed for different simulations. The results indicate that CREs directly affect the onset of blocking by enhancing the diabatic source of wave activity upstream of the blocks. Furthermore, the results indicate that CREs can also indirectly affect the dynamics of blocking through changes in the mean atmospheric state, such as changes in the position of the jet stream and the eddy growth rate.\n\nOverall, this is a well-structured study that highlights the importance of cloud-radiation-circulation coupling for the dynamics of atmospheric blockings that are associated with high impact weather extremes. Over the last decade, the importance of cloud-radiative effects on midlatitude dynamics, either on climate or weather time scales, has gained attention in climate studies, and with it the need to improve the simulation of CREs in models. A better understanding of blocking dynamics and a better simulation of CREs in models are both important aspects of modeling, and therefore I find this study interesting and useful as it provides new insights into midlatitude dynamics.\n\nThe methods used in the study are well established and documented in previous studies. The authors used both well-known cloud locking and COOKIE methods to assess the impact of CREs on blocking. The results were also validated by comparing the impact of CREs from other model simulations, and overall, the authors find a robust result regardless of the model used. In addition, the suitability of the diagnostics used was assessed using reanalysis data. Overall, I consider the study suitable for publication, although I have some remarks, questions and minor revisions.\n\nRemarks:\n1- As mentioned in the preprint, many factors contribute to the formation of blocking. I am interested to know how the impact of CREs compares to the other factors. If possible, some information in the discussion can also help to put the impact of CREs into perspective. Also, since CRE uncertainties are smaller than the CRE itself, can we expect to see a significant impact of CRE uncertainties on blocking frequency? For example, the study of Zhao et al., 2018 (https://www.sciencedirect.com/science/article/pii/S0169809517309122) shows that uncertainties in CREs could affect the mean circulation.\nThis also makes me wonder about the time scale of the impact of CREs. It may be the case that uncertainties in the simulation of CREs affect the blocking frequency on longer climate time scales of years, but do we expect uncertainties in CREs to affect blocking events on time scales of weeks or during the blocking onset period? (This relates to the argument in lines 401-402: \"minimizing CRE-related model biases, could therefore potentially enhance early-warning systems to mitigate damages caused by such events.\").\nFinally, can the authors elaborate on which method is better to quantify the impact of CRE on blocking for medium-range weather forecasts?\n2- Considering that SST and sea ice are fixed in the simulations performed in this study (also preserving the mean state in cloud locking), it seems better to use the term cloud-radiative heating (CRH) rather than cloud-radiative effects (CRE)? CRE is more general and includes the impact of clouds on surface radiative effects. The term Atmospheric Cloud Radiative Effect (ACRE, (K/s)) has also been used before (e.g., Voigt et al., 2020, https://wires.onlinelibrary.wiley.com/doi/full/10.1002/wcc.694), which separates the radiative effect of clouds in the atmosphere from that of the surface. Or perhaps it should be mentioned in the paper that the radiative heating of clouds in the atmosphere is actually being studied? Following on from this, I was wondering if the results might change if the interactive ocean was coupled to the model simulations rather than the SST being prescribed. Can the surface CRE also affect the blocking?\n3- Are all temperature tendencies from the physical parameterization considered in the analysis of the diabatic source of LWA? In Fig. S6 the \"Res\" is attributed to dissipation processes, but in Eq. 13 only the heating rates from radiation and condensation are considered. What about heating from turbulence or convection? I am also confused by the changing notion of latent heating and condensation throughout the text. In your analysis, does condensation heating (COND) include heating from all microphysical processes and heating from convection? If so, I suggest calling this just latent heating.\n4- Regarding the repeated argument of LWCRE feedback on latent heating by enhanced evaporation. Can the authors elaborate on this? The preprint refers to studies that actually show that CRE warming in the tropics is balanced by less latent heating.\nThere are studies that indicate the mechanism of the impact of longwave radiation on clouds and latent heating. For example, Fu et al., 1995 (https://doi.org/10.1175/1520-0469(1995)052>1310:IORACI<2.0.CO;2), showed that LW radiation enhance condensation and droplet growth. Or by affecting the eddies that can promote stronger vertical motion and hence latent heating (Li et al., 2015).\n\nMinor revisions:\nLine 15: ... (CREs significantly increase the formation of) - \"CREs significantly enhance the formation of blocking or increase the frequency of blocking\"\nLine 46: ... sea surface temperature (SST)\nLines 43-44: ... (models mean state) - \"model representation of mean atmospheric state and/or the waves at ...\"\nLine 53: reference 34 is missing.\nLine 54: ... (blocking dynamics were mostly presumed to be predominantly dry) - \"the dynamics of atmospheric blocking is predominantly driven by dry dynamics\"\nLine 68: ... (resulting from the presence of clouds) - \"resulting from cloud-radiation interaction (absorb, emission, ...)\"\nLine 74: ... (over the extratropical ocean across models), I think reference 41 shows the impact of CRE on tropical ocean rather than extratropical ocean, reference 37 talks about the impact of CRE on extratropical ocean\nLine 77: reference 42 do not directly show the impact of CRE on forecast error growth, rather the impact of all-sky radiation on error growth.\nLine 83: ... (greater clarity into), greater than? I believe compared to COOKIE methods? In this section I believe there is a need to shortly explain the difference between the two methods to help smoothly follow the story (even though it is explained later and in the method).\nLine 84: ... \"used cloud locking to study the impact of CRE on\"\nAlso, in reference 39 the cloud locking method is not used rather than just disabling CRH and applying COOKIE method.\nLine 87: ... (to longwave radiation), I understand that the impact of shortwave CRE is negligible but would be good to mention it.\nLine 90: might be helpful to shortly mention here or in the discussion why CRE is biased in weather and climate models.\nFigure 1a: can the contour labels be added to ease the comparison.\nFigure S1: caption: shading (tendency) unit is m day-1\nLine 118: The reference to Fig. 1d with the result of 21% decrease in blocking frequency seemed at first confusing.\nLine 126: \"Clouds On/Off Klimate Intercomparison Experiment (COOKIE)\"\nLine 129, as only the cloud radiative heating is disabled in these simulations, I suggest the term clouds-off LW or CLWOFF or something similar instead of LWOFF\nLine 142: also, please refer to Table 1 here\nFigure 2: caption: remove ((b) As in (a))?\nLine 160: density-weighted vertical average, what is the interval of the vertical integral in this analysis?\nLine 162: remove (RHS), only used once\nLine 169: Is A \"wave activity\" or local wave activity (LWA)?\nFigure 3:\n- (a-d) do these panels show the left-hand side term of Eq. 1 or sum of right-hand side terms?\n- Caption: meridional eddy heat flux at the base of the atmosphere or at the lower boundary? And which level is that?\n- Caption: ((m-p) sources and sinks of wave activity) - \"(m-p) nonadiabatic sources and sinks of the wave activity\"\nFigure S3: ... blocking -in- the CTL ..., also change Lag to days, consistent with Fig 3\nLine 209: OLR change to \"outgoing longwave radiation\", here would be good to also mention that minimum OLR and max water are associated with the position of WCB.\nLine 212-220: nonadvective or nonadiabatic?\nFigure 4: is the \"blocking high center\" refer to the position of maximum geopotential anomaly?\nLine 274: ... (eliminates the LWCRE to LWA) - \"eliminates the impact of LWCRE on LWA\"\nLine 282: ... from LWCRE and COND, (introduced before)\nFigure 6: caption: ... Euro-Atlantic blocking ((remove shading), unit: m s-1day-1), In (remove all) panels (b-g)\nLines 288-289: please refer to Fig. 6a and Fig. S6\nFigure 7 caption: I suggest rewriting the caption, as using phrases such as 'as in (a-b)' does not imply what contours are shown in other panels.\nLine 310: From Figure 7 I tend to say that the mean state is in fact changing in the CLOCK?\nLine 358: ... where clouds are fully transparent to longwave radiation.\nTable 1: Clouds On/Off Klimate Intercomparison Experiment\nEq. 3: maybe better to bring equation 4 before 3 as \"q\" is not in Eq.2\nLine 462: Qref change to QREF, consistent with other terms\nLine 470: revise to \"The density-weighted vertical average of LWA (\"column LWA\") tendency reads as\"\nLine 475: Non-advective or nonadiabatic?\nRef 44: There is newer reference to Harrop et al., 2024 (https://gmd.copernicus.org/articles/17/3111/2024/): (Harrop, B. E., Lu, J., Leung, L. R., Lau, W. K. M., Kim, K.-M., Medeiros, B., Soden, B. J., Vecchi, G. A., Zhang, B., and Singh, B.: An overview of cloud–radiation denial experiments for the Energy Exascale Earth System Model version 1, Geosci. Model Dev., 17, 3111–3135, https://doi.org/10.5194/gmd-17-3111-2024, 2024.)", "reviewer_3": "Review comments on Lubis et al.\nIn this study, the authors present compelling evidence on the critical role of the cloud radiative effects (CREs) in enhancing blocking frequency. By using a suite of idealized simulations and applying local wave activity diagnostic, they show that CREs amplify blocking frequency by strengthening upstream wave activity. Investigating the impact of CREs on blocking dynamics and frequency is novel, and their idealized simulations offer convincing support for the significant influence of CREs on wintertime blocking frequency, employing a solid dynamical framework.\n\nHowever, the manuscript, in its current form, requires substantial refinement. I have several questions and concerns regarding the methodology of their idealized simulation, as well as the interpretation of their results. Particularly, the experimental setup contains inconsistencies that hinder reproducibility, and the interpretation of results lacks sufficient explanations of underlying physical mechanisms.\n\nMy detailed comments are as follows.\n\nMajor Comments:\n1. Methodology:\n  From my understanding, all the idealized simulations run in this work use the same SSTs and SICs computed from a 20-year monthly climatology from 1990 to 2010 (see my second minor comment below). With this choice of the boundary condition, I am concerned that the authors may be underestimating moisture sources from the ocean to the atmosphere, particularly over the Gulf Stream and North Atlantic Current. By averaging out mesoscale ocean eddies, which are prevalent in these regions, the simulations may suppress surface latent heat flux, potentially reducing moisture availability to the atmosphere. Previous studies (e.g., Yamamoto et al. (2021, WCD), Matthews et al. (2024, GRL)) have shown these regions to be critical moisture sources for latent heating associated with Euro-Atlantic blocking events. I recommend that the authors consider using non-averaged boundary conditions. If that is not feasible, please provide a clear justification for the choice of this SST/SIC boundary condition and acknowledge this potential limitation of this work in the main text.\n  For CLOCK experiment, why do authors prescribe the cloud optical properties only from the first three years of the CTL simulation and not the entire 20-year period of the CTL simulation? The authors describe how in this manner they can ensure the similar CRE climatology to CTL, but I am not convinced. Furthermore, the authors write how they loop over the three-year cloud optical property files for the eleven-year cloud locking experiment, which sounds inconsistent with the description that the experiment is run for 20 years. Please rewrite the paragraph to clarify the above points if is my mere misunderstanding. If not, I recommend that the authors undertake the simulation with the use of the CRE file with the entire 20-year period of the CTL simulation to truly ensure that both simulations have the same CRE climatology.\n  The usage of 1979-2020 ERA5 data is not quite consistent with the experimental design where the authors chose to use 20-year integration based on the 20-year climatological SSTs and SICs. In order to make a fair comparison with the model results, please use 1990-2010. Also, please add the results from ERA5 on Figs 4 and 5 as well.\n  The decomposition of the total diabatic sources/sinks of wave activity is a great attempt, and I found the results quite interesting. I recommend that the authors use JRA55 reanalysis data, which I believe provides the necessary diabatic terms, to compare and validate their results.\n2. Interpretation of the physical significance of CRE\n  From the model results that are presented in this manuscript, I agree with the authors that CRE does seem to significantly -- although secondarily to latent heating -- contribute to increase the wintertime Euro-Atlantic blocking frequency. However, the specific role of CRE in atmospheric blocking remain unclear. In the introduction, the authors review prior studies on the impact of CRE on large-scale atmospheric circulation, yet they do not discuss the physical processes directly relevant to blocking. Since CRE can induce both cooling and heating effects depending on cloud type, and blocking involves high-pressure systems (clear skies) alongside warm conveyor belts (precipitating clouds), the authors should clarify their hypothesis on how CRE may influence blocking. A more detailed physical explanation would strengthen their argument, especially regarding Figures S5 and 6(b).\n\nMinor Comments:\n1. The authors write that for CTL they use initial condition of the year 2000s, but which exact years do they use precisely? Or do they mean they used the atmospheric condition of year 2000?\n2. In l.127 the authors write that they use SST from year 2000, while in l.425 they describe that they use the same SSTs and SICs as CTL. Please amend this inconsistency accordingly.\n3. Detailed description of the methodology of the COOKIE-2 simulations is completely missing, and the authors need describe it in detail in the Method section. Also, I found it very confusing that the authors use COOKIE-2 and CFMIP interchangeably.\n4. How many blocks are detected in each experiment, and thus included in each composite maps?\n5. The authors attribute the LWA sources almost solely to the diabatic heating term, which is not in line with the previous studies (e.g., Pfahl et al. 2015, Steinfeld and Pfahl 2019, and Yamamoto et al. 2021 all found ~50% associated with diabatic heating, and the rest adiabatic). How can you explain this discrepancy?\n6. I suggest that the authors swap around Sections 3.1 and 3.2, to first show the mean states of the idealized simulations before discussing LWA results.\n7. I would appreciate it if the authors can list limitations of the current study, including the point that I raised in my first comment, in the conclusion.\n8. Fig 1b: interesting tail of negative signature extending all the way to off the east coast of North America. If you extend the area to a broader area, would it extend to the proximity of Gulf Stream? (related to my first major comment)\nOther small comments:\n• L80 “climate feedback modes” -> “climate modes”?\n• Fig S1: Is this a case study, or composite?\n• L.130: Which major atmospheric heat source are the authors speaking about? Please be more specific.\n• L.154-156: Again, please elaborate more, on what bases the authors come up with these two hypotheses, and what they exactly mean by them.\n• Fig 2 caption: Please properly describe what the box-whisker plots in (b) and (c) show. Are they showing interannual variability, or ensemble spread? Please explain. They are clearly different from (a), so please remove “(b) As in (a)”. Also, the circles over the box-whisker plots are misleading, because they are normally used to indicate the presence of anomalies.\n• L.174 “closely resembles”: I would lessen the tone, as there are visible differences, including that there is no clear low-pressure system on the west of blocking in reanalysis.\n• L.176 “stronger deceleration of the zonal flow”: Is this shown anywhere?\n• Fig S3: It reads lag-3 – Lag0 but are they also supposed to read “days -3” – “days 0”?\n• L. 192 “congestion of a traffic jam”: Tautology. Please rewrite.\n• Fig S4: Please change the contours of all the panels to geopotential height anomalies, so it is easier to compare against Fig S2, to see what the authors are trying to show the readers in l.210.\n• Fig S5: “DTCOND” does not match with the description in the caption. Please make them consistent.\n• L.222 “the interactive CRE (CLOCK) and changes in the mean LWCRE (LWOFF)”: The descriptions of what you want to illustrate and the corresponding simulation designs are not quite matching, or more like the opposite. Please rewrite.\n• L.224: its budget “of all three simulations”\n• Figs 4, 5: Stippling is not quite visible. I suggest that the authors change the color range to something like [-5 to 5], [-20, 20] respectively.\n• Fig 4: Please indicate the 10deg x 10deg area used to construct (d) on each map.\n• Figs 4 & 5: please adequately explain what exactly the error bars indicate.\n• Fig 5: Are the encircled regions also 10deg x 10deg?\n• Fig S6: “ΔΣtot” does not match with the description in the caption.\n• L.271 “cloud-radiative impact might operate”: please elaborate more on what you mean by this.\n• L.274: I don’t understand the sentence. Is it “from LWA”? Are you speaking about LWOFF simulation? Please clarify.\n• L.276 “increased nighttime cooling”: Do you mean radiative cooling of the surface?\n• L.279 “discused” -> “discussed”\n• L.284 “larger longwave radiative heating”: By which physical mechanisms? Please explain.\n• L.310 “no change in the mean state”: Just above this sentence, the authors described that there are some differences in the mean state.\n• L.312 “This is consistent with our previous analysis”: please specify which paper/results the authors are referring to.\n• L.317 Please explain how exactly turning off LWCRE change the meridional temperature gradient\n• Fig 7: Indicate what contours of (c)-(f) are, and also the contour intervals for all the panels\n• L.323 “Eady’s growth rate” -> “Eady growth rate”\n• L.442 “blocking-based anomalies index” -> “anomaly-based blocking index”\n• L.463: the definition of q is already written\n• L.465: H=7km is already written\n• L.468: “the meridional displacement of the wavy potential vorticity contour relative to φ”\n• L.485: reference for falwa is missing?\n• L.488 “boundary conditions listed in Neal et al.”: please specify.\n• L.489 “Eddy Growth Rate” -> Eady Growth Rate", "reviewer_1_round_2": "I appreciate the authors’ effort in addressing my previous comments and revising the manuscript accordingly, which I believe has substantially improved the manuscript. In their revision, the authors now propose two hypotheses to causally link CREs to dynamical processes of blocking formation: 1) increasing diabatic heating sources and 2) modifying the background mean state (L155-163). To test these hypotheses, partly in response to the reviewers’ previous comments, they have included new results on the vertical structure of diabatic heating, cloud-related variables, and moisture transport. I find all of them relevant and supportive of their proposed mechanisms. The authors also newly streamlined these mechanisms at the end of the section (L308-330), which adds clarity to understanding how interactive CREs influence blocking frequency.\n\nWhile I enjoyed reading the authors’ detailed response to my previous comments, I have one follow-up comment, which is simply to share my thoughts, along with a minor suggestion on the updated results. I have listed a few other minor suggestions for clarifications.\n- Lines 308-330: The revised manuscript now suggests two (at least) possible pathways based on their original and new findings. They are clearly described and sound convincing for the most part. In particular, I find that the first mechanism provides a clear explanation dynamically linking LWCRE to changes in LH.\nMeanwhile, I would also like to point out that the possibility of the second mechanism, related to high cloud cover and evaporation feedback, has been explored only by MERRA2, not by model experiments. I assume the reason model results are not shown for the same diagnostics in the study is either that the variables relevant to the diagnostics are not available from the current model configuration, or that model results may differ substantially from the MERRA2 results, given that cloud fraction and surface properties are quite challenging to represent accurately in models. In any case, it is less clear whether the second mechanism similarly operates in the CTL simulation.\nThe results from Figs. 7e and 7f also raise the possibility that the second mechanism may not be well captured by the model. Specifically, the positive LWCRE anomaly in MERRA2 is located vertically from 800 hPa to 400 hPa with its peak at 500 hPa, whereas that in CTL is found between 850-550hPa (L304) with its peak at ~800 hPa. This vertical difference may indicate that cloud cover fraction at different altitudes in the model deviates from MERRA2 quite noticeably. If this surface warming through high cloud cover anomaly is not explicitly shown by model experiments, then I believe the suggested causality from MERRA2 is not fully demonstrated as well (as surface warming itself can be induced by many other factors). With that said, I feel this would be a minor point relative to the key arguments of the study. The authors have already provided sufficient new and interesting results, and I do not think it is essential for this study to ascertain whether the proposed second mechanism holds in model experiments. Nevertheless, it would be appreciated if the authors could clarify that the second ‘possible’ pathway proposed in this study is based on reanalysis results, and that further investigation in a separate modeling study would be helpful.\n- Magnitude of vectors: Information on the magnitude of vectors is missing throughout the manuscript. I recommend including reference vectors in the figures or providing their magnitude information in the figure captions.\n- Lines 156-157 ‘changes in the large-scale mean state, …, the strength of stationary waves, influence’-> ‘and the strength of stationary waves’? I recommend revisiting this sentence.\n- Lines 445-446 ‘Therefore, improving … could therefore potentially …’. I suggest removing one of ‘therefore’ in the sentence.\n- Vectors in the second row of Fig. 8: I found the black vectors denoting the Plumb flux appear somewhat smaller compared to the vectors in other figures. Please consider thickening them or changing their color.", "reviewer_2_round_2": "Cloud-Radiative Effects Significantly Increase Wintertime Atmospheric Blocking in the Euro-Atlantic Sector (Lubis et al., 2025)\nThis is my second review of the study. I appreciate the authors' efforts in addressing the previous comments, and the manuscript has really improved following the major revisions. I have only a few minor comments. Addressing these comments, I believe the paper is in good shape to proceed.\n<Minor comments>\nLines 18-19 (also Lines 393-394): The sentence suggests that the main way in which CRE affects the diabatic source of wave activity is through direct impact ('primarily', CRE heating), while the indirect pathway through changes in latent heating is secondary. In fact, this is the opposite. It would be better to say, for example, that CRE affects the diabatic source of wave activity both directly and indirectly, with the indirect pathway playing a significant role.\nLine 86: ‘… its impact on simulated variability,’\nThe term simulated variability here is unclear, -> changing to ‘its impact on blocking formation’\nLine 107: Here, it would be better to refer to the limitations of the experiments discussed later in the method, as Fig. S1 illustrates that notably fewer blocking events are simulated with the E3SM CTL. Is this related to the missing lower-boundary SST-related forcing in E3SM simulations?\nFigures 5, 6, and S6: as the diabatic terms shown in Fig. 6a do not add up to the total diabatic term shown in Fig. 5d, it seems a large contribution comes from clear-sky radiative heating (according to equation 13), right? And if yes, this term does not change a lot between CTL, LWOFF and CLOCK? In other words, the major changes in diabatic source wave activity are due to changes in diabatic heating and specifically the latent heating?\nLine 279: From Fig. 7 (cf. panels a and b), it seems that the limitation mentioned is due to differences in latent heating between MERRA and CTL at lower levels rather than to low-cloud radiative processes. At least, the spatial variability of cloud radiative heating is comparable between MERRA and CTL (panels e and f), but not latent heating. This makes me wonder about latent heating at lower levels by MERRA that is absent in CTL. What could be the reason?\nLine 320: I believe that reference 41 fits better here, as it also shows that the absence of CRE cools the atmosphere and increases static stability within ascending regions of cyclones. However, it also highlights the significant role of LW cooling by low-level clouds in reducing static stability and weakening cyclones, similar to reference 38.\nLine 328 References 37 and 54 show that CRE (warming) results in reduced latent heating (and precipitation) within the tropics. Reference 37 shows that CRE in the mid-latitudes increases precipitation (therefore LH), but this was attributed to enhanced eddies and vertical motion (similar to the first proposed pathway).\nFrom the ref 37:\n‘the heating of the tropical atmosphere by ACRE (Fig. 4c) is primarily balanced by a reduction in the latent heating, consistent with the reduction in tropical precipitation evident in the clouds-on simulation (Fig. 8).’\nTherefore, referencing these studies does not seem correct. A similar reference might be 40, which shows that CRE enhances cloud microphysical heating, although it does not show changes in surface evaporation.\nLines 414-416: I don’t think that the identified and proposed mechanism of CRE impact is ‘fundamentally’ different. Results show that CRE (directly and indirectly) affect upstream diabatic heating (already later in line 418, the importance of upstream diabatic heating for blocking is mentioned), and changes in LH will translate into changes in PV at upper-levels. (like ref 40 that shows changes in LH by CRE lead to changes in large-scale winds and PV at upper levels and dominate the changes in the tropopause wave that, as also said in the preprint here, is important for blocking formation, e.g., ref 31). The results presented are additive and complementary to some established ideas. The point is that the indirect impact of CRE has a higher weight than the direct impact of CRE heating.\n<Typos>\nLine 480: Table S1 -> Table 1\nLine 487: Table S2 -> Table 1\nLine 496: cloud heating rates, all-sky rates -> cloud radiative heating, all-sky radiative heating, clear-sky radiative heating", "reviewer_3_round_2": "I appreciate the authors’ extensive additional analyses and their point-by-point response to my previous comments. I think the manuscript has improved since the previous round, particularly with the inclusion of diabatic decomposition and cloud cover diagnostics. However, I find the physical interpretation of the diagnosed effects still lacks dynamical depth and clarity, and important diagnostics that support the proposed mechanisms remain underutilized.\nBelow I outline my major concerns in detail:\nMajor Comments\n1. Dynamical explanation\nWhile the manuscript clearly establishes that CREs (especially LWCRE) enhance blocking by increasing upstream wave activity, I find the explanation of the physical mechanisms still remains largely descriptive. The text alludes to CRE-induced enhancements in latent heating and high cloud cover, but does not fully explain the dynamical pathway from cloud radiative forcing to blocking onset. The authors refer to Supplementary Figure S12 showing increased high cloud cover upstream of blocks. However, this key diagnostic is not meaningfully integrated into the main text or used to support the proposed feedback between LWCRE and latent heating. This weakens the causal argument. To improve clarity and support the proposed mechanism, I recommend:\n• Bringing the high-cloud fraction results into the main text\n• Interpreting results within the warm conveyor belt (WCB) framework, which provides a well-established basis for linking moist ascent, diabatic PV generation, and upper-level ridge formation (e.g., Grams et al., 2011; Methven, 2015)\nIn addition, the introduction (lines 70–82) would benefit from a more detailed discussion of prior work on how physically CREs influence large-scale dynamics, to better motivate the study and help interpret later figures, the former of which currently reads rather opportunistic.\nFinally, the discussion around lines 297–307 would be significantly strengthened by explicitly incorporating:\n1. PV-based reasoning — how diabatic heating generates negative PV anomalies aloft and strengthens ridges (Haynes and McIntyre, 1987)\n2. Low-PV air transport via WCBs, which links latent heating with anticyclonic upper-level anomalies (e.g., Pfahl et al., 2015; Steinfeld and Pfahl, 2019)\nBringing these concepts into the discussion would ground the proposed mechanism in current dynamical theory and reinforce the CRE-blocking connection.\n2. Mischaracterization of LWA sources vs. redistribution\nThe manuscript attributes blocking formation primarily to the convergence of horizontal LWA flux. However, this interpretation risks conflating LWA redistribution with LWA generation.\nAccording to previous works (e.g., Nakamura and Huang, 2018; Yamamoto and Martineau, 2024), horizontal fluxes only redistribute LWA—they do not generate or destroy it. The true sources of wave activity are:\n• The non-conservative term ⟨Ȧ⟩ cosϕ, which includes diabatic heating, PV mixing, and numerical diffusion\n• The low-level eddy heat flux, reflecting baroclinic generation.\nYour Fig. 3 clearly shows both terms contributing positively upstream of the block, consistent with the findings of Yamamoto and Martineau (2024) for the Atlantic region. However, the manuscript text does not clearly distinguish these processes from flux convergence. I recommend reframing the interpretation to emphasize that CREs enhance wave activity generation via diabatic and baroclinic processes, which is then redistributed downstream by horizontal fluxes in lines 188–210.\n3. Evaporation Feedback\nIn lines 327–331, the manuscript states that LWCRE-induced surface warming increases evaporation, which then amplifies latent heating. While plausible, I am afraid that this is oversimplified. According to the bulk formula, latent heat flux depends on the moisture gradient between surface and near-surface air, wind speed, and air density. Thus, an increase in surface temperature does not guarantee increased evaporation if near-surface air also becomes more humid. I suggest the authors revise this explanation to clarify under what thermodynamic conditions the proposed feedback would hold.\nMinor Comments:\n- I have mentioned this for the first round, but I still think that the description of COOKIE/COOKIE2 are insufficient. For the sake of reproducibility, please clarify what they are in the main text.\n- L.96 underscores -> underscore\nReferences:\n• Grams, C. M., Wernli, H., Böttcher, M., Campa, J., Corsmeier, U., Jones, S. C., Keller, J. H., Lenz, C. J., and Wiegand, L.: The key role of diabatic processes in modifying the upper-tropospheric wave guide: A North Atlantic case-study, Q. J. Roy. Meteor. Soc.,137, 2174–2193, 2011.\n• Methven, J.: Potential vorticity in warm conveyor belt outflow, Q. J. Roy. Meteor. Soc., 141, 1065–1071, 2015.\n• Haynes, P. H. and McIntyre, M. E.: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and frictional or other forces, J. Atmos. Sci., 44, 828-841, 1987.\n• Pfahl, S., Schwierz, C., Grams, C. M., Wernli, H., Croci-Maspoli, M., Grams, C. M., and Wernli, H.: Importance of latent heat release in ascending air streams for atmospheric blocking,\nNat. Geosci., 8, 610–615, 2015.\n• Steinfeld, D. and Pfahl, S.: The role of latent heating in atmospheric blocking dynamics: a global climatology, Clim. Dynam., 53, 6159–6180, 2019\n• Nakamura, N. and Huang, C.: Atmospheric blocking as a traffic jam in the jet stream, Science, 361, 42-47, 2018.\n• Yamamoto, A. and Martineau, P.: On the driving factors of the future changes in the wintertime Northern-Hemisphere atmospheric waviness, Geophys. Res. Lett., 51, e2024GL108793, 2024", "reviewer_3_round_3": "I appreciate the authors’ effort in expanding the analysis and responding to earlier comments. The manuscript is technically improved, but two major issues of physical interpretation remain unresolved.\nThis is the third time I raise this, and I will be more explicit here. I fully understand that this study uses the LWA framework to diagnose the impact of CREs on blocking. I am also aware of the formal dynamical basis of that framework, and its usefulness. My concern is not about methodology—but about the lack of physical explanation consistent with established dynamical understanding. The authors use LWA to quantify the contribution of diabatic processes to midlatitude wave activity and blocking. However, the manuscript never explains why those processes—particularly latent heating and LWCRE—lead to enhanced wave activity.\nFor example, to me Figure 7 clearly shows the signature of WCB-type ascent—vertical and poleward transport of low-PV air—which amplifies the upper-level ridge. This is a well-established mechanism, yet the manuscript avoids acknowledging it (l.277-288). Similarly, the authors attribute increased waviness to LWCRE but offer no physical mechanism—only a diagnostic association. If the claim is that CREs dynamically influence blocking, then the physical pathway must be explained in terms of PV-based thinking (e.g., via diabatic PV generation, modification of the jet, ridge amplification, etc.). It is not sufficient to show the signal in the LWA budget without interpreting the underlying dynamics. The authors already offered some dynamical explanations in the response to my previous comment, so I am merely asking to add these in the main text where relevant.\nThis omission is especially problematic given that the Introduction (l.75-84) frames the study as addressing the dynamical influence of LWCRE on the jet and storm track, but never follows through with a coherent explanation. To be absolutely clear, I am asking the authors to articulate the physical mechanism by which cloud radiative effects—particularly LWCRE—alter the atmospheric circulation, in terms of known dynamical processes such as diabatic PV generation, ascent in WCBs, or changes in jet structure. This includes explaining the role of cloud height and vertical heating profiles, since LWCRE is not a single uniform effect. Without this physical context, the claim that LWCRE enhances blocking lacks credibility, regardless of what appears in the LWA diagnostics.\nThe LWA formulation, after all, is based on QGPV dynamics—you cannot claim it's a different framework and therefore exclude PV-based interpretation. At this point, I find it disappointing that these core interpretative issues remain unaddressed.\nSecond, the description of LWA sources and redistribution still remains unclear and fragmented, although I see much improvement compared to the previous version. I understand the authors do not want to label zonal LWA convergence as a “sink,” but the current wording does not help the reader clearly understand what is happening dynamically. The mechanism should be presented cleanly: non-conservative forcings (e.g., latent heating and CREs) and low-level eddy meridional heat flux generate LWA upstream of blocking events, which is then redistributed by zonal LWA convergence, forming localized blocking structures. This sequence is physically grounded and fully consistent with Yamamoto and Martineau (2024), which the authors should cite. Right now, the manuscript reads more like a descriptive catalog of LWA differences than a coherent dynamical explanation.", "reviewer_3_round_4": "I appreciate the authors’ effort to address my previous concerns. The manuscript now provides much greater clarity regarding the dynamical context of CREs and diabatic heating. I have a few additional minor comments regarding the newly added paragraphs.\nl.211–l.216:\nThere is some redundancy in the discussion of Figs. 3m–p. You might consider simplifying the whole thing to something like:\n“As shown in Figs. 3m–p, positive values of low-level sources and non-conservative (diabatic) processes are collocated with the emergence and growth of wave activity fluxes, acting as LWA sources, with non-conservative processes being of primary importance.”\nl.375, 439, 451:\nWhat do you mean by “quasi-stationary wave ridge”? Is this different from the “large-scale stationary ridges” mentioned at l.367? I found the expression confusing, since it is unclear whether you are referring to the climatological ridge or to a ridge associated with the blocking itself. Please clarify or rephrase.\nl.377:\nDid you mean “incipient” rather than “incident”?\nl.446–457:\nHere, the authors describe only the \"indirect\" diabatic impact (Hoskins et al. 1985; Steinfeld & Pfahl 2019). However, the \"direct\" diabatic impact — in which WCBs transport low-PV air from lower latitudes and altitudes into higher latitudes and the upper troposphere (e.g., Pfahl et al. 2015; Steinfeld & Pfahl 2019; Yamamoto et al. 2021) — should also be mentioned, as it likely plays a role."}, "author_response": "We thank the editor and reviewers for their constructive comments and positive feedback. Before providing a point-by-point response to the reviewers’ suggestions, we would like to highlight the major revisions made to the manuscript, as summarized below:\n1. Additional supporting evidence has been incorporated, based on observation-based reanalysis data (MERRA-2) and model experiments, to strengthen our conclusion that cloud radiative effects (CREs) significantly increase the blocking frequency over the Euro-Atlantic sector:\n• By analyzing the vertical structure of cloud radiative heating, the diabatic wave source, cloud fraction, evaporation, and moisture transport during the lifecycle of blocking events, using both MERRA-2 reanalysis and model experiments, we confirm that interactive CREs enhance local wave activity (LWA) by strengthening the diabatic source of wave activity upstream of the blocking region. This intensification occurs primarily through the direct effect of longwave CREs and indirectly via their feedback on latent heating (LH). Although the direct contribution of longwave CREs to the diabatic wave source is secondary to their LH-indirect influence, both mechanisms contribute to the overall increase in the upstream diabatic wave source (see updated Figs. 6 and 7).\n• The increase in LH under LWCRE results from strengthened poleward moisture transport, and potentially to increased surface evaporation upstream of the Euro-Atlantic blocking region (see updated Fig. 7 and Figs. S7–S12).\n• In addition to the sizable indirect impact of CREs on blocking via LH, we emphasize that the indirect effects of CRE on the mean state, through the shift of the mean jet and weakening of the stationary waves, mean baroclinicity, and mean poleward moisture transport, influence the blocking formation (updated Fig. 8).\n2. We have now compared the CTL results with reanalysis-based observations from MERRA-2 to validate our findings (see updated Figs. 4-7).\n3. We have included additional details in the model experiment section, particularly the rationale for using a fixed SST lower boundary (see “Numerical Experiments”). A new discussion has also been added to address the limitations of the results in light of this choice (see “Discussion”).\nWe have also addressed all other reviewers’ comments, and finally, we hope the revised version satisfactorily addresses your concerns.\nSincerely,\nOn behalf of all authors,\nSandro W. Lubis"}]

Decision letter