Introduction

The 2015 Paris Agreement1 sets the specific target of holding the global-mean temperature increase below 2 °C compared to pre-industrial levels, with a further effort to limit it to 1.5 °C. One of the ways to achieve this goal is to remove CO2 from the atmosphere2,3,4. Such carbon dioxide removal (CDR) is a necessary component of mitigation strategies to achieve net zero CO2 emissions and is considered in all emission scenarios, limiting global warming to 2 °C or lower by 2100. To assess their potential effects on the Earth’s climate system, idealized CDR model experiments have typically been conducted by varying CO2 concentrations in the atmosphere5,6. An example is the CDR Model Intercomparison Project (CDRMIP)7, which coordinates the design of CDR experiments with state-of-the-art climate models. In CDRMIP, CO2 concentrations are increased at a constant rate (ramp-up simulation) until quadrupled, and then decreased at the same rate to the initial level (ramp-down simulation). Such idealized climate model simulations, while hypothetical, are useful for qualitatively assessing the extent to which the projected climate changes return to the current states after removing CO2 perturbation and for a better understanding of climate responses to socioeconomic scenarios requiring CDR7,8. The results often show asymmetric responses of global and/or regional climate systems to symmetric CO2 changes. These include surface temperature5,9, precipitation5,9,10,11,12, sea-ice13, ocean acidification6,14, and ocean stratification15. Their changes are largely reversible, although additional time is needed. However, some of them (e.g., Greenland ice sheet, ocean stratification) exhibit irreversibility on century-to-millennium timescales15,16, particularly if critical thresholds are exceeded.

How would mid-latitude weather systems change in a warming climate? How would they respond to CDR? These questions are critical to better understanding future climate risks. However, there is little research on the response of mid-latitude weather systems, including atmospheric blocking, to a changing CO2 pathway. The case of atmospheric blocking is particularly important since it is associated with extreme events in mid-latitudes. Being defined as a quasi-stationary high-pressure system in mid- and high-latitudes17, blocking often causes warm extremes and drives droughts through the associated subsiding motion and enhanced incoming shortwave radiation18,19,20,21,22,23,24. By prompting meridional flows and low-pressure systems upstream and downstream, blocking is also responsible for cold extremes and heavy precipitation25,26,27,28. As such, understanding future changes in blocking frequency is of utmost importance to prepare for the associated weather and climate extremes.

Future changes in Northern Hemisphere (NH) blocking have already been reported in the literature29,30,31. In boreal winter, blocking frequency is projected to decrease in both the North Atlantic (NA) and North Pacific (NP) basins, despite a large uncertainty29,30,31,32. However, the possible response of blocking frequency to CDR has yet to be examined. It is uncertain whether the projected blocking frequency changes would recover when high CO2 concentrations in a warming climate are restored to the present-day levels.

The present study addresses how NH blocking frequency responds to CDR in an idealized experiment by focusing on changes during the winter season when blocking events occur most frequently. A large-ensemble CDR experiment with 28 ensemble members (hereafter CDR-LE), in which CO2 concentrations in the atmosphere are linearly increased and then decreased over time as in CDRMIP, is carried out and compared with a control simulation with fixed present-day CO2 concentrations. The responses of NH blocking frequency to CDR and their inter-basin differences are explained in terms of barotropic energy conversion between the mean flow and high-frequency eddies. The implications of blocking frequency changes to weather extremes are also discussed.

Results

Blocking frequency change to time-varying CO2 concentrations

Figure 1a illustrates the time series of global-mean surface air temperature in boreal winter (SAT; red line) with respect to CO2 concentrations (black line) in CDR-LE. The SAT time series is shown as the differences from the control simulation which mimics the current climate with fixed present-day CO2 concentrations (dashed line; Methods). As CO2 concentrations increase in the ramp-up period, SAT increases gradually until it becomes ~5 °C warmer than the initial state at year 2140 (Fig. 1a). In the ramp-down period of CDR, SAT decreases, but the cooling rate is weaker than the warming rate of the ramp-up period. In turn, after the CDR (year 2280), SAT is still significantly warmer (~1 °C) than the initial state11,33. This result indicates that surface climate change is not a linear function of CO2 change, suggesting that blocking may also exhibit asymmetric changes to a symmetric CO2 change.

Fig. 1: Global surface air temperature and NH blocking frequency response during CO2 pathway.
Fig. 1: Global surface air temperature and NH blocking frequency response during CO2 pathway.
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a Time series of global-mean boreal winter surface air temperature (orange, in K, left y-axis) and CO2 concentrations (black, in ppm, right y-axis) in the CDR experiment; Same as a but for blocking frequency in b Northern Hemisphere, c North Atlantic, and d North Pacific (red, in percentage with respect to the number of winter blocking days) in control (in blue) and ramp-up and -down (in red) simulations. Displayed values are 11-year running means, except for CO2 concentrations. Solid line and shading indicate the ensemble mean and its spread (±1 standard deviation), respectively, except for the control simulation in b–d, where they denote the time-mean and its interdecadal variability (±1 standard deviation of 11-year running means). Vertical lines denote the end of the ramp-up and ramp-down periods, which are followed by the stabilization simulation.

Figure 1b shows the time evolution of the NH-winter blocking frequency, defined as the fraction of winter days with local blocking conditions over 40°–70°N (for the blocking definition, see Methods). With increasing CO2 concentrations, NH blocking frequency is projected to decrease, consistent with previous studies29,31. The time of emergence34, when anthropogenic signal emerges from the internal variability, appears within ~50 years. At the year of maximum CO2 concentrations (year 2140), blocking frequency becomes ~30% lower than in the control simulation. As CO2 concentrations are reduced in the ramp-down period, blocking frequency slowly returns to its initial state. However, it does not fully recover. It instead shows a reduced blocking frequency at the end of CDR, consistent with the SAT change (Fig. 1a). Blocking frequency keeps increasing during a stabilization period of CDR (i.e., after the original CO2 levels have been restored; see Methods), until it returns to the initial state.

The asymmetric NH-winter blocking frequency response to the symmetric CO2 change largely results from NP blocking (160°–240°E, 40°–70°N; Fig. 1d). Although NP blocking frequency slowly increases during the ramp-down period, it does not return to the initial state even during the stabilization period. These features contrast with NA blocking (50°W–30°E, 40°–70°N; Fig. 1c), whose frequency almost recovers during the ramp-down period.

We obtain qualitatively similar results when different blocking indices are used (Supplementary Fig. 1). Although an alternative blocking index30 shows some under-recovery of NA blocking frequency at the end of CDR, it eventually returns to its initial state within ~30 years of stabilization (Supplementary Fig. 1c). Differently, NP blocking does not return to its original state in the 120 years of the stabilization period. This result indicates a basin-dependent blocking frequency change to CDR, which is robust to the choice of blocking detection methods.

To elaborate on the zonally asymmetric NH blocking responses to CDR, the spatial distributions of blocking frequency change in the ramp-up and ramp-down periods are illustrated in Fig. 2a, b. The differences from the early ramp-up (2001–2040) to the CO2 peak (2121–2160) periods and those from the CO2 peak to the late ramp-down (2241–2280) periods are compared. As a reference, the climatological blocking frequency in the control simulation is contoured. The climatology of NH blocking frequency is reasonably well captured by the CDR-LE, showing the two preferred regions of blocking occurrence29,35,36 (Supplementary Fig. 2). During the warming period (Fig. 2a), both NA and NP blocking frequencies decrease, accounting for a large fraction of the total NH blocking frequency decline (see also Fig. 1b). The reduced blocking frequency over the central NA is accompanied by an increase in Ural blocking frequency. This indicates an eastward shift and weakening of NA blocking activity in a warming climate30,31,37. In the cooling period (Fig. 2b), NA blocking frequency largely but not fully recovers, whereas NP blocking frequency remains lower than in the early ramp-up periods (see also Fig. 1c, d). This result reaffirms the distinct responses of the NA and NP blocking frequency to CDR.

Fig. 2: Spatial distribution of NH-winter blocking frequency and duration response during CO2 pathway.
Fig. 2: Spatial distribution of NH-winter blocking frequency and duration response during CO2 pathway.
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Ensemble-mean Northern Hemisphere winter blocking frequency differences between a CO2 peak (2121–2160) and early ramp-up (2001–2040), b late ramp-down (2241–2280) and CO2 peak, and c late ramp-down and early ramp-up periods. Blocking frequency is expressed in the percentage of winter days. Statistically significant differences at the 95% confidence level (two-tailed t-test) are dotted. Contours indicate the wintertime climatology of blocking frequency in control simulation (contour interval of 2%); d–f Number of blocking events as a function of duration in d Northern Hemisphere, e North Atlantic, and f North Pacific for the early ramp-up (red), CO2 peak (black), and late ramp-down (blue) periods. The bottom plots show the difference between the late ramp-down and the early ramp-up period for each blocking duration, with filled bars denoting statistical significance at a 95% confidence level (two-tailed t-test).

The reversibility of blocking frequency to a changing CO2 pathway is summarized in Fig. 2c by comparing blocking frequency changes between the late ramp-down period and the early ramp-up period. Although CO2 concentrations are identical in these two periods, blocking frequencies are not. NA and NP blockings show relatively lower frequencies in the late ramp-down period than in the early ramp-up period, this difference being much larger in the NP. In the NA, the asymmetric responses to opposite CO2 changes result in net (the late ramp-down period minus the early ramp-up period) blocking frequency decreases over the climatological blocking center and downstream increases over eastern Europe and the Ural regions. As a consequence, CDR does not substantially alter NA blocking frequency, but it affects the regions of occurrence, causing an eastward shift of NA blocking. NP blocking frequency change is markedly different from that in the NA, being characterized by net decreases, which are more pronounced on the equatorward side of the climatological blocking center. Therefore, after CDR, NP blocking would be less frequent and slightly poleward shifted as compared to its initial state.

Figure 2d–f depict the frequency of blocking events as a function of blocking duration in the early ramp-up, CO2 peak, and late ramp-down periods. Here, an NA blocking event is subsampled when the maximum 500-hPa geopotential height anomaly at the blocking onset is located in the NA domain (50°W–30°E). The same definition is employed to identify a blocking event in the NP domain (160°-240°E). The blocking frequency distribution shows the well-known exponential decrease with increasing duration29. For all durations, the number of NH blockings is reduced from the early ramp-up to CO2 peak periods (compare red and black lines in Fig. 2d). Blocking activity is restored during the ramp-down period (blue line) but exhibits regional differences. NA blocking frequency shows a weak under-recovery with statistically insignificant differences between the late ramp-down and the early ramp-up periods for most blocking durations (open green bar in Fig. 2e). Differently, NP blocking frequency in the late ramp-down period largely remains as in the CO2 peak state (compare black and blue lines in Fig. 2f). As a result, the number of NP blockings tends to be significantly lower in the late ramp-down period than in the early ramp-up period (filled green bars in Fig. 2f). Overall, the basin-dependent blocking frequency change to CDR is robust regardless of the duration of blocking episodes. However, CDR may result in a significant decrease of persistent blockings (those with durations longer than 15 days) in both basins (last green bars in Fig. 2d–f), which would imply a corresponding decrease in the frequency of extreme events induced by persistent blockings.

Possible mechanism

What causes the basin-dependent blocking frequency change to CDR? Previous studies have reported that blocking activities are largely determined by the background flows and their interactions with eddy fluxes29,38,39. In particular, the formation and maintenance of blocking have often been explained by the energy conversion from high-frequency eddies to slowly-varying background flows that embed blocking. Such energy conversion is examined here by calculating the barotropic energy conversion (BTEC), a scalar product of transient eddy fluxes and deformation of mean flows (see Methods). It measures the downscale energy cascade from background flows to high-frequency eddies, a negative (or decrease of) BTEC representing a favorable condition for blocking formation and maintenance. Fig. 3a presents the difference in BTEC between the late ramp-down period and the early ramp-up period. The spatial distribution is qualitatively similar to the blocking frequency change in Fig. 2c, supporting that blocking frequency change can be traced back to BTEC change. The maximum positive differences in BTEC (denoting changes unfavorable for blocking occurrence) appear slightly upstream of the centers of reduced NA and NP blockings. Likewise, a negative difference (i.e., a decreasing BTEC in the late ramp-down period compared to the early ramp-up period) also appears upstream of the increased blocking frequency over Europe. This result suggests that blocking frequency changes are closely associated with BTEC changes: the CO2-induced decrease in blocking frequency is related to an enhanced energy conversion from the slowly-varying background flows to the high-frequency eddies.

Fig. 3: Responses in BTEC and their decompositions during the CO2 pathway.
Fig. 3: Responses in BTEC and their decompositions during the CO2 pathway.
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a Differences of barotropic energy conversion (BTEC; Shading; Unit: 10−5 m2 s−3) between the late ramp-down and the early ramp-up periods. As a reference, the differences in blocking frequency are contoured (1% interval; zero line is omitted; see also Fig. 2c). Here, the zero line is omitted. Time series of regional BTEC (in yellow) with its decomposition terms (BTECx in blue and BTECy in purple) for b North Atlantic and c North Pacific (boxed regions in a) during boreal winter. BTEC and their decomposition terms are expressed as the simulated changes in the CDR experiment with respect to the mean values of the control simulation. Solid lines and shading denote the ensemble mean and spread after taking the 11-year running mean, respectively. Vertical lines in b, c denote the end of the ramp-up and ramp-down periods, which are followed by the stabilization simulation.

The temporal evolution of BTEC in the NA subdomain (boxed in Fig. 3a) is depicted in Fig. 3b (yellow line). It resembles NA blocking frequency change with an opposite sign (compare Figs. 3b and 1c). An increasing BTEC is consistent with decreasing blocking frequency in the ramp-up period (~51% less than the initial state at year 2140; Fig. 1c). It indicates a progressive decline in upscale energy cascade40,41, due to weakened absorption of high-frequency eddies by the deformation of slowly-varying background flows. The opposite is true in the ramp-down period when NA blocking and BTEC trends are reversed. A close relationship between blocking frequency and BTEC changes is also observed in the NP (compare Figs. 3c and 1d). The NP blocking frequency keeps decreasing until the late ramp-down period (~42% reduction; Fig. 1d) and remains reduced afterward. Such temporal evolution is again well captured by BTEC with an opposite sign (yellow line in Fig. 3c).

The BTEC can be decomposed into two types of eddy-mean flow interactions: those related to stretching deformation (BTECx; blue) and to shear deformation (BTECy; purple) of background flows (see Methods for details). In the NA, BTEC changes are equally determined by BTECx and BTECy (Fig. 3b). These two components constructively contribute to NA BTEC change and, thus, NA blocking frequency change. In contrast, NP BTEC is dominated by BTECy (Fig. 3c) with a negligible contribution of BTECx. It suggests that different eddy-mean flow interactions are associated with regionally distinct blocking frequency responses to CO2 changes.

To elucidate the relative contributions of transient eddy and slowly-varying background flow changes, BTECx and BTECy are further decomposed into changes in transient eddies, background flows, and nonlinear interactions between the two (Methods; Fig. 4). In the NA, BTECx changes are primarily attributed to background flow changes (BTECxca; navy line in Fig. 4a) with a secondary contribution of nonlinear interaction changes (BTECxaa; green). Changes in the eddy component (BTECxac; light blue) slightly attenuate BTECx throughout the simulation. This suggests that background flow changes (BTECxca + BTECxaa) are mainly responsible for BTECx changes. This is in contrast to the BTECy changes, which are largely accounted for by eddy component changes. While changes in mean flow (BTECyca; orange in Fig. 4c) are marginal, nonlinear interaction (BTECyaa; pink) and eddy (BTECyac; red) components contribute comparably to BTECy changes. Combining these results, it is concluded that both eddy and mean flow changes are important for NA blocking frequency changes.

Fig. 4: BTEC response due to changes in transient eddies, background flows, and their interactions during the CO2 pathway.
Fig. 4: BTEC response due to changes in transient eddies, background flows, and their interactions during the CO2 pathway.
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Time series of BTECx (Unit: 10−5 m2 s−3) induced by eddies (BTECxca; navy), background flows (BTECxac; green), and their nonlinear interaction (BTECaa; light blue) changes for a the North Atlantic and b the North Pacific (see Eqs. 8, 9 in Methods for the definition of each term). Panels in c, d are the same as in a, b, but for BTECy (BTECyca in orange; BTECyac in red; BTECyaa in pink). Solid lines and shading denote the ensemble mean and spread, respectively. The results are shown with an 11-year running average. Vertical lines denote the end of the ramp-up and ramp-down periods, which are followed by the stabilization simulation.

In contrast to the NA, the changes in NP BTEC, which are mostly explained by BTECy (Figs. 3, 4b, d), are dominated by those in the eddy component. The changes in BTECyac (red in Fig. 4d), a product of transient eddy momentum fluxes changes and climatological shear deformations, exhibit a local maximum in the middle of the ramp-down period. Despite its rapid decline in the late ramp-down period, it remains larger than the initial state at the end of CDR, limiting blocking recovery through a weakened upscale energy cascade. Comparatively, the background flow changes (BTECyca; orange) and its nonlinear interactions with transient eddies (BTECyaa; pink) are negligible throughout the simulation, although they partly contribute to the slow recovery of NP blocking frequency during the stabilization period.

These results indicate that blocking frequency changes in the two basins are controlled by different mechanisms. While both transient eddy and background flow changes are important for NA blocking frequency changes, transient eddy changes are crucial for NP blocking frequency changes, in agreement with different blocking dynamics in the two basins42. These further suggest that background flow changes play a different role in the two basins. While blocking frequency changes in the NA are primarily modulated by stretching deformation changes (BTECxca in Fig. 4a), those in the NP are marginally influenced by mean flow changes. The changes in stretching deformation in the NA are mainly due to the zonal stretching changes39 (purple in Fig. 5a). As shown in Fig. 5b, NA jet extends eastward in the late ramp-down period compared to the early ramp-up period, with enhanced zonal stretching to the east of the climatological jet (contoured in Fig. 5b). The NA domain, boxed in Fig. 5b, is affected by these zonal stretching changes. Note that although the NP jet also responds to CO2 forcing (a southeastward extension), it plays a minor role in blocking BTEC changes in the NP domain.

Fig. 5: Responses in SST, AMOC, and 500-hPa zonal wind during CO2 pathway.
Fig. 5: Responses in SST, AMOC, and 500-hPa zonal wind during CO2 pathway.
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Changes in a zonal wind (m s−1) in the CDR simulation (with respect to the mean of the control simulation) upstream (in brown; 60°–40°W, 50°–65°N) and downstream (in blue; 10°W–10°E, 50°–65°N) of the NA region with the largest BTEC changes (green box in b; see also Fig. 3a), and their difference (downstream minus upstream, in purple); c Atlantic meridional overturning circulation (AMOC; Sv) in winter. The strength of the AMOC is defined by averaging the winter-mean Atlantic meridional ocean stream function from 35°N to 45°N at 1000-m depth, where its maximum is found in the control simulation. Dark and light colors indicate the ensemble mean and spread, respectively. Differences in b 500-hPa zonal wind (U500; m s−1) and d sea surface temperature (SST; K) between the late ramp-down and the early ramp-up periods. For reference, the climatological U500 in the control simulation is superimposed in b (contour interval 7 m s−1), and the regions displaying the largest BTEC changes are boxed in green. Statistically significant differences at the 95% confidence level (two-tailed t-test) are dotted in b, d.

The eastward extension of the NA jet is primarily caused by the weakening of the Atlantic meridional overturning circulation (AMOC). Figure 5d shows the sea surface temperature (SST) difference between the late ramp-down and the early ramp-up periods, revealing cold anomalies in NA high latitudes. The cold anomalies result from the delayed recovery of the AMOC (Fig. 5c), which weakens ocean heat transport from low latitudes to NA high latitudes11,33. The resulting enhanced SST gradient has been shown to force an eastward intensification of NA jet43,44,45 (Fig. 5b, d). The time evolution of the AMOC indeed follows the NA stretching deformation change, especially to the zonal wind change downstream of the NA jet (compare Fig. 5c with the blue line in Fig. 5a).

A slowdown of the AMOC in a warming climate has been attributed to reduced surface water density due to increased heat and freshwater fluxes46,47, which is closely related to positive salt advection feedback48. Such feedback further weakens AMOC until the middle of the ramp-down period with a decrease in surface evaporation33. This is followed by a rapid strengthening of the AMOC in the late ramp-down period initiated by a salt advection feedback with changes in salinity gradient and ocean stratification33,49.

Discussion

The present study examines the response of NH-winter blocking frequency to CDR with a large-ensemble simulation. The model simulation reveals that blocking frequency linearly decreases in the ramp-up period when CO2 concentrations increase until quadrupled. The blocking frequency recovers at a slower rate during the ramp-down period as CO2 concentrations return to present-day values. Moreover, the recovery of blocking frequency in the ramp-down period exhibits regional contrasts. While NA blocking frequency almost returns to the initial state (except for an eastward shift), NP blocking frequency remains significantly lower than in its original state even after CDR. An additional CDR experiment with doubling CO2 concentrations further supports this result (Supplementary Fig. 3).

The basin-dependent blocking frequency changes are closely related to both transient eddy and background flow changes. However, different dynamical processes are involved in the blocking frequency changes of the two basins. While blocking frequency changes in the NP are dominated by eddy momentum flux changes, those in the NA are controlled by both eddy momentum flux and stretching deformation changes. Additional analysis shows that the enhanced stretching deformation in the late ramp-down period compared to the early ramp-up period is caused by an eastward intensification of the NA jet, likely due to a weaker AMOC.

Although this study has focused on barotropic processes, baroclinic processes may also play a role in changing blocking frequency50 as regional SST changes are closely associated with background flow changes. In addition to this, changes in diabatic processes51 and land surface conditions52,53,54,55 could also influence blocking frequency changes. Their contributions warrant further investigations.

The NH-winter blocking frequency changes have important implications for extreme events. Fig. 6 presents the changes in blocking-related cold surges (CSs), defined as a fraction of CS days concurring with the blocking during winter, from the early ramp-up to the late ramp-down periods. Even though the long-term trend of SAT is removed to define CS events (Methods), blocking-related CSs are reduced in western Europe with a hint of weak increase in northern Eurasia (Fig. 6a). Such a pattern resembles the eastward shift of NA blocking frequency in the late ramp-down period (Fig. 2c). The decrease in blocking-related CSs over western North America (Fig. 6b) is also consistent with reduced NP blocking frequency (Fig. 2c). These blocking-related CS changes explain a large fraction of the total CS differences between the late ramp-down and the early ramp-up period (~60% in the NA and ~78% in the NP; boxed region in Supplementary Fig. 4).

Fig. 6: Response in blocking-related CS frequency during CO2 pathway.
Fig. 6: Response in blocking-related CS frequency during CO2 pathway.
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Difference in the frequency of blocking-related cold surges between the late ramp-down and the early ramp-up periods for a North Atlantic and b North Pacific. The frequency of blocking-related cold surges is expressed in the percentage of winter days. Statistically significant differences at the 95% confidence level are dotted (two-tailed t-test).

The CSs are influenced not only by blocking frequency but also by blocking intensity and size56,57. Recent studies have reported an increasing spatial scale and intensification of blocking in a warming climate58, partly due to enhanced diabatic processes59, which are robust, especially over the NP60. A similar change is found in NP blocking (Supplementary Fig. 5), which shows a zonally-extended and intense blocking pattern in the ramp-up period (Supplementary Fig. 5d). However, this change does not fully recover in the ramp-down period (Supplementary Fig. 5e, f). These increases in blocking size and intensity, particularly in NP blocking, could drive more frequent CSs18, since blocking-related CSs are triggered by the advection of cold air by blocking circulations in the presence of marked background temperature gradients28. However, they are not enough to compensate for the CS decreases induced by the blocking frequency reductions.

The state-of-the-art climate models still have non-negligible biases in reproducing blocking frequency30,31. The model used in this study, CESM1, is not an exception. The model biases are assessed by comparing the reanalysis for the period of 1979–2018 with the control simulation. Although this is not a fair comparison due to the control simulation being equilibrated with a fixed external forcing, it is still useful to characterize the model biases qualitatively. As in most climate models, the control simulation underestimates NA blocking frequency (Supplementary Fig. 2c). The NP blocking frequency is also slightly underestimated on the northwestern flank of the observed blocking center, while it is overestimated on the southeastern flank (Supplementary Fig. 2c). Although the sources of these model biases remain to be determined, the relatively coarse model resolution (~1 degree in this study) may underestimate important processes that govern the formation and maintenance of blocking such as transient eddies (and the associated upscale energy cascade) and diabatic heating51,61. Despite these model biases, the control simulation reproduces qualitatively well the overall distribution of blocking frequency and duration. Moreover, blocking frequency changes to high CO2 concentrations in the ramp-up period are qualitatively similar to those reported in CMIP6 future scenarios runs31. Although NA blocking biases can be locally comparable to the magnitude of blocking responses in the ramp-down and ramp-up periods of CDR, this is not the case for NP blocking, which dominates the delayed recovery of NH-winter blocking. This suggests that the key findings of the present study are not substantially altered by model biases, being useful to qualitatively understand the blocking responses to CO2 changes.

The present study highlights that CDR, as a climate intervention method, may not guarantee the full recovery of atmospheric blocking frequency and related extreme events. To generalize this finding, multi-model analyses with various CDR scenarios are desirable. Such analyses would help better design the CDR policy.

Methods

Model experiment

The Community Earth System Model (CESM) version 1.2.2 with f09_g16 (about 1-degree in the atmosphere) resolution is employed62. As a reference, a control simulation with constant present-day CO2 concentrations (367 ppm) is conducted for 900 years. The last 120 years are utilized to determine internal variability, which is defined as the standard deviation of 11-year running averages. From this simulation, a total of 28 initial conditions are selected to initialize the CDR-LE. Each simulation comprises 280 years of CO2 changes, including successive periods of CO2 increase (ramp-up) and decrease (ramp-down), followed by 120 years of stabilization with constant CO2 concentrations of the control simulation (see ref. 33 for the details). Specifically, CO2 concentrations are increased from the initial value at a rate of 1% per year until quadrupled in the ramp-up period (140 years for 2001–2140). They are then reduced at the same rate in the ramp-down period (140 years for 2141–2280). The fully recovered CO2 concentrations are then maintained for 120 years in the stabilization period (2280–2400). Additional experiments are also conducted by doubling CO2 concentrations instead of quadrupling them. To assess the model biases, the control simulation is compared with the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim)63 for the period of 1979–2018.

Blocking index

Blocking is detected by using a hybrid blocking index64,65, which is applied to the daily geopotential height field at 500 hPa (Z500). This hybrid blocking index adopts two distinct features of the classical blocking indices66. One is the anomaly-based index, which emphasizes the quasi-stationary and high amplitude nature of the blocking high67. The other is the reversal-based blocking index, focusing on the morphology of Z50068,69. A blocking candidate is first detected when the daily Z500 anomaly (Z500′) exceeds a seasonally varying threshold. The threshold is set to 1.3 standard deviations of the Z500′ distribution with all grid points poleward of 30 °N and all days within a 3-month centered window. Additional conditions, such as the day-to-day overlapping of blocked areas and duration (≥5 days), are also imposed to account for the large-scale, quasi-stationary, and persistent nature of blocking. Blocking is then identified when the large-scale meridional gradient of Z500 is negative at any grid point satisfying the above criteria64.

The adopted thresholds can be sensitive to the period chosen to define the climatology as well as to the long-term change of background flow. To exclude such effects, \({\rm{Z}}500^{{\prime}}\) is defined as follows:

$${{\rm{Z}}500(\lambda ,\phi )}^{{\prime} }=\left({\rm{Z}}500\left(\lambda ,\phi \right)-{\overline{{\rm{Z}}500\left(\lambda ,\phi \right)}}-{{\rm{Z}}500\left(\lambda ,\phi \right)}^{* }\right)/\sin (\phi )$$
(1)

where \(\overline{{\rm{Z}}500\left(\lambda ,\phi \right)}\) is the 365-day running mean of Z500(λ,ϕ), and Z500(λ,ϕ)* is the calendar-day mean of 30-day running mean of \({\rm{Z}}500\left(\lambda ,\phi \right)-\overline{{\rm{Z}}500\left(\lambda ,\phi \right)}\) (see details in refs. 64,70). The climatological components (i.e., \(\overline{{\rm{Z}}500\left(\lambda ,\phi \right)}\) and \({{\rm{Z}}500\left(\lambda ,\phi \right)}^{* }\)) are obtained by considering the whole period of the simulation from control to stabilization periods. This approach removes the long-term trend and the seasonal cycle of Z500.

Long-term changes in blocking can also be sensitive to the choice of blocking index30,71, since each index seeks different blocking characteristics66. To test the sensitivity of the result to the definition of blocking, anomaly-only (same as the above hybrid index except for Z500 reversal criteria) and reversal-only (same as the one in ref. 30) indices are also utilized.

Barotropic energy conversion

Blocking formation and maintenance are often associated with the interactions between transient eddies and slowly-varying background flows72,73,74,75,76. Such processes can be examined by computing the barotropic energy conversion (BTEC)77,78. The BTEC is the scalar product of eddy-characteristics (E), similar to the Hoskins’ E-vector79, and deformation of mean flows (D)80,81:

$${\bf{E}}=\left({{\rm{E}}}_{{\rm{x}}},{{\rm{E}}}_{{\rm{y}}}\right)=\left(\frac{{{v}^{{\prime} }}^{2}-{{u}^{{\prime} }}^{2}}{2},-{{u}^{{\prime} }v}^{{\prime} }\right)$$
(2)
$${\bf{D}}=\left({{\rm{D}}}_{{\rm{x}}},{{\rm{D}}}_{{\rm{y}}}\right)=\left(\frac{\partial \bar{{{u}}}}{\partial {\rm{x}}}-\frac{\partial \bar{{{v}}}}{\partial {\rm{y}}},\frac{\partial \bar{{{u}}}}{\partial {\rm{y}}}+\frac{\partial \bar{{{v}}}}{\partial {\rm{x}}}\right)$$
(3)
$${\rm{BTEC}}={\bf{E}}\,\cdot\, {\bf{D}}$$
(4)
$${\rm{BTECx}}={{\rm{E}}}_{{\rm{x}}}\,\cdot\, {{\rm{D}}}_{{\rm{x}}},{\rm{BTECy}}={{\rm{E}}}_{{\rm{y}}}\,\cdot\, {{\rm{D}}}_{{\rm{y}}}$$
(5)

where \({u}\) and \(v\) are zonal and meridional winds at 500 hPa, respectively. The prime denotes an 8-day high-pass Lanczos filtered quantity82, and the overbar represents the slowly-varying background flow, defined as the difference of the full field from the high-pass-filtered field65,83. The zonal component of E (Ex) is associated with the zonal and meridional elongation of high-frequency eddies (Eq. 2). Its meridional component (Ey) represents the momentum flux or tilting of high-frequency eddies. In Eq. 3, Dx and Dy represent the stretching and shear deformations of slowly-varying background flows, respectively. The zonal and meridional components of the scalar product in BTEC are referred to as BTECx and BTECy, respectively (Eq. 5).

A positive BTEC indicates the energy conversion from the slowly-varying background flows to high-frequency eddies. It typically occurs upstream of the eddy-driven jet. In contrast, a negative BTEC tends to occur downstream of the jet, where high-frequency eddies accelerate the background flows. The associated upscale energy cascade from high- to low-frequency flows40 provides a favorable condition for the formation and maintenance of blocking41,78. In this regards, decreasing blocking frequency can be qualitatively understood with increasing BTEC.

To assess the contributions of transient eddy and slowly-varying background flow changes to BTEC changes, both BTECx and BTECy are further decomposed as follows:

$$\begin{array}{ll}{\rm{BTECx}}={\rm{BTECxcc}}+{\rm{BTECxca}}+{\rm{BTECxac}}+{\rm{BTECxaa}}\\\qquad\qquad=\overline{{{\rm{E}}}_{{\rm{x}}}}\,\cdot\, \overline{{{\rm{D}}}_{{\rm{x}}}}+\overline{{{\rm{E}}}_{{\rm{x}}}}\,\cdot\, \Delta {{\rm{D}}}_{{\rm{x}}}+\Delta {{\rm{E}}}_{{\rm{x}}}\,\cdot\, \overline{{{\rm{D}}}_{{\rm{x}}}}+{\Delta {\rm{E}}}_{{\rm{x}}}\,\cdot\, {\Delta {\rm{D}}}_{{\rm{x}}}\end{array}$$
(6)
$$\begin{array}{l}{\rm{BTECy}}={\rm{BTECycc}}+{\rm{BTECyca}}+{\rm{BTECyac}}+{\rm{BTECyaa}}\\\qquad\qquad=\overline{{{\rm{E}}}_{{\rm{y}}}}\,\cdot\, \overline{{{\rm{D}}}_{{\rm{y}}}}+\overline{{{\rm{E}}}_{{\rm{y}}}}\,\cdot\, \Delta {{\rm{D}}}_{{\rm{y}}}+\Delta {{\rm{E}}}_{{\rm{y}}}\,\cdot\, \overline{{{\rm{D}}}_{{\rm{y}}}}+{\Delta {\rm{E}}}_{{\rm{y}}}\,\cdot\, {\Delta {\rm{D}}}_{{\rm{y}}}\end{array}$$
(7)

where overbar represents the climatology in the control simulation, and ∆ denotes the projected change from the control simulation. The BTECxcc and BTECycc, which are constant during the simulation, represent an interaction between the time-mean components of transient eddy and background flows. In contrast, the other terms, which vary over time, indicate the contributions explained by background flow changes (i.e., BTECxca and BTECyca), eddy component changes (i.e., BTECxac and BTECyac), and nonlinear interaction changes between the two (i.e., BTECxaa and BTECyaa).

Since the time evolutions of BTECx and BTECy are well captured by the time-varying components of their decompositions by definition, the projected changes in both BTECx and BTECy (i.e., ∆BTECx and ∆BTECy) can be estimated as follows:

$$\begin{array}{ll}\Delta {\rm{BTECx}}\,\approx\, \left({\rm{BTECxca}}-{{\rm{BTECxca}}}_{2001}\right)\\\qquad\qquad\quad +\left({\rm{BTECxac}}-{{\rm{BTECxac}}}_{2001}\right)\\\qquad\qquad\quad +\left({\rm{BTECxaa}}-{{\rm{BTECxaa}}}_{2001}\right)\end{array}$$
(8)
$$\begin{array}{ll}\Delta {\rm{BTECy}}\,\approx\, \left({\rm{BTECyca}}-{{\rm{BTECyca}}}_{2001}\right)\\\qquad\qquad\quad +\left({\rm{BTECyac}}-{{\rm{BTECyac}}}_{2001}\right)\\\qquad\qquad\quad +\left({\rm{BTECyaa}}-{{\rm{BTECyaa}}}_{2001}\right)\end{array}$$
(9)

where ∆ denotes the projected change from the control simulation; the subscript 2001 indicates the time-mean value in the first year of the CO2 ramp-up and –down simulation.

Cold surges

Cold surge (CS) is defined as when the daily minimum surface air-temperature anomaly is below a threshold for at least 2 consecutive days84,85. In this study, −1.5 standard deviation of the daily minimum temperature anomaly distribution for the control simulation is used as a threshold. A running annual mean is first subtracted to remove the long-term trend, and temperature anomalies are then computed as the daily departure from the calendar-day mean of the entire period (considering all years of both control simulation and CDR experiments). The blocking-related CS days are defined as the number of CS days concurring with a regional blocking.