Hysteresis of European summer precipitation under a symmetric CO2 ramp-up and ramp-down pathway

This study investigates the mechanism of the hysteresis of European summer mean precipitation in a CO2 removal (CDR) simulation. The European summer mean precipitation exhibits robust hysteresis in response to the CO2 forcing; after decreasing substantially (∼40%) during the ramp-up period, it shows delayed recovery during the ramp-down period. We found that the precipitation hysteresis over Europe is tied to the hysteresis in the Atlantic Meridional Overturning Circulation (AMOC). During the ramp-down period, an anomalous high surface pressure circulation prevails over Europe. The anomalous high pressure system is a baroclinic response of the atmosphere to strong North Atlantic cooling associated with a weakened AMOC. This anomalous circulation suppresses summertime convective activity over the entire Europe by decreasing near-surface moist enthalpy in Central and Northern Europe while increasing lower free-tropospheric temperature in Southern Europe. Our findings underscore the need to understand complex interactions in the Earth system for reliable future projections of regional precipitation change under CDR scenarios.


Introduction
In recent decades, Europe has faced an increasing number of extreme hydrological events, such as droughts and floods, which have emerged as significant hazards across the continent (Svetlana et al 2015).These events have resulted in substantial socioeconomic losses, with cumulative damages totaling approximately EUR 520 billion during 1980during -2020during (EEA 2022)).Drought-related annual losses in the European Union and the UK have been estimated at around EUR 9 billion (Cammalleri et al 2020).Previous studies have indicated that climate change severely affects the hydrological cycle in Europe (Donnelly et al 2017).In a warmer climate, the Mediterranean region and most of continental Europe (excluding Scandinavia) are anticipated to undergo prolonged dry spells and notable reductions in summer precipitation with more frequent and/or severe agricultural and ecological droughts expected at 2 • C or higher (Giorgi and Lionello 2008, Sánchez et al 2011, Coumou et al 2015, Kröner et al 2017, Zappa 2019, Boé 2021, IPCC 2023).While these risks are closely connected to social-ecological systems including public water supply and rainfed farming systems, the European Union is yet vulnerable to such risks, as evidenced by the impactful droughts in 2018, 2022, and 2023 (Rossi et al 2023).
To enhance preparedness for mitigating and adapting to increasing climate risks and impacts, the global community strives to achieve the targets outlined in the Paris Agreement, aiming to limit global warming to 1.5 • C.However, while most studies about future precipitation changes have focused on projections for the 21st century under diverse emission scenarios such as shared socio-economic pathways (also known as SSPs), there is a growing interest in assessing and understanding the response of climate systems to carbon dioxide removal (CDR) scenarios.Recently, CDR experiments have been substantially conducted to understand the hysteretic behavior of the climate system, which refers to the path-dependent response during increases and decreases in atmospheric greenhouse gas concentra-  Oh et al (2022a) observed hysteresis in the Indian and North African summer monsoon precipitation regarding the ramped-up and ramped-down CO 2 concentrations in a CDR experiment.However, the extent to which the European summer mean precipitation exhibits hysteresis in response to symmetric CO 2 forcing has not yet been systematically investigated.Understanding the underlying mechanisms behind the projected changes in European summer precipitation also remains an ongoing challenge.Moreover, these drivers are more complex than those influencing changes in winter precipitation (Frei et al 2006, Kröner et al 2017).Therefore, deepening our understanding of these dynamics and obtaining reliable future projections of summer precipitation in Europe are essential.
This study aims to fill the gap by examining the hysteresis of European summer mean precipitation in a CDR experiment.Specifically, we have addressed the following questions: (i) how does summer mean precipitation respond to symmetric increases and decreases in CO 2 concentration?(ii) What causes the precipitation changes?To accomplish this, we have analyzed a 28-member ensemble CDR simulation in terms of changes in precipitation and large-scale environments, including thermodynamic instability.It will be demonstrated that the European summer mean precipitation exhibits substantial hysteresis, which can be understood based on hysteresis in atmospheric and oceanic mean state changes.
The remainder of this study is structured as follows: section 2 describes the model, experimental setup, and analysis methods used.Section 3 presents an assessment of the hysteresis in summer mean precipitation over Europe (section 3.1) and discusses the associated physical mechanisms (section 3.2).
Section 4 summarizes the results and presents conclusions of the study.S1).A 900-year-long single-member simulation was performed with a fixed atmospheric CO 2 concentration of 367 ppm, which is referred to as the PD simulation.Subsequently, 28-member ensemble simulations were performed by branching off the PD simulation (Im et al 2024).The initial conditions of the atmosphere and ocean for the 28 ensemble members were selected to cover different phases of the Atlantic Multidecadal Oscillation (Trenberth and Shea 2006) and Pacific Decadal Oscillation (Mantua et al 1997) during the PD period.Note that all ensemble members started from January 1st and the start year was set to 2001.In each simulation, the CO 2 level was increased by 1% annually over 140 years until it quadrupled to 1468 ppm (ramp-up period, RU hereafter), then it was symmetrically decreased to its initial level (ramp-down period, RD hereafter).

Methodology
To compare the atmospheric and oceanic states between the RU and RD periods at identical CO 2 concentration, we chose two 31 year periods during which the CO 2 concentration doubled compared to the PD: 2055-2085 (2CO2 up ) and 2195-2225 (2CO2 dn ).The difference between the 2CO2 up and 2CO2 dn periods (2CO2 dn -2CO2 up ) was considered as the degree of hysteresis.Statistical significance was determined using Student's t-test with 95% confidence interval.Most analyses were conducted during the boreal summer months (June-July-August) within Europe, encompassing areas within

Moist thermodynamic instability
To understand the changes in summer mean precipitation, we calculated deep convective inhibition (DCIN), which measures environmental thermodynamic stability with respect to deep convection originating within the boundary layer (Fuchs et al 2014, Weber et al 2021).In this study, the DCIN is defined as the difference between the moist enthalpy at the surface (h s ) and saturation moist enthalpy at 700 hPa (h * 700hPa ): where h and h * are the moist enthalpy and saturation moist enthalpy, respectively, C p is the specific heat capacity, T is the temperature, L v is the latent heat of vaporization, and q is the specific humidity.The DCIN can be considered as a proxy for the buoyancy of a non-entraining plume originating near the surface when it reaches the lower free-troposphere, with its sign flipped (Raymond et al 2003).Therefore, a higher DCIN value indicates more stable atmospheric conditions.

Changes in the mean precipitation
Figure 1(a) illustrates the changes in the summer mean precipitation spatially averaged over Europe, along with the corresponding CO 2 concentrations during the RU (red) and RD (blue) periods.The mean precipitation decreased by approximately 40% as the CO 2 concentration increased during the RU period, it then recovered during the RD period (figure 1(a)).
A reduction during the RU period was evident over most of Europe (supplementary figure S3).
While precipitation decreased almost linearly with CO 2 concentration during the RU period, it exhibited a delayed recovery during the RD period, indicating hysteresis in the mean precipitation regarding to CO 2 forcing.Therefore, the amount of mean precipitation during the 2CO2 dn period was approximately 16.1% lower than that during the 2CO2 up period.The mean precipitation only recovered to the level of the 2CO2 up period after the CO 2 concentration was further decreased to approximately 470 ppm. Figure 1(b) confirms that mean precipitation during the 2CO2 dn period was substantially lower than that found during the 2CO2 up period across Europe, with a particularly pronounced decrease observed over the United Kingdom and Ireland.
Subsequently, to better characterize the response of mean precipitation to CO 2 forcing, we examined changes in the convective precipitation (PRECC) and large-scale precipitation (PRECL) separately.Studies have shown that the partitioning of the total precipitation into PRECC and PRECL is highly modeldependent, and that it heavily influences modelsimulated precipitation characteristics (Dai 2006, Neale et al 2012, Rulfová et al 2017, Yang et al 2021).In our simulations, PRECC accounted for approximately 67% of the total mean precipitation, which is comparable to the corresponding values in the fifth generation of ECMWF atmospheric reanalysis (ERA5) (supplementary figure S4).Spatially, the farther south and inland it goes, the larger the PRECC ratio.The PRECL dominated along the west coast of Scandinavia and over the United Kingdom and Ireland throughout the study period.
We observed that the mean PRECC exhibited pronounced hysteresis (figure 2(a)), which was even stronger than that of the mean precipitation.After a substantial decrease during the RU period, the mean PRECC declined further during the RD period until the CO 2 concentration decreased to approximately 800 ppm.The results shown in figures 1 and 2 strongly suggest that the hysteresis in the mean total precipitation is primarily induced by that the mean PRECC.The hysteresis in the mean PRECC appeared to be partially offset by the mean PRECL, which was higher during the RD period than that during the RU period at the same CO 2 concentration (figure 2(b)).Therefore, it appears that explaining the hysteresis in the mean PRECC is necessary to better understand the hysteresis in the mean total precipitation.

Physical mechanism of the hysteresis in european summer mean precipitation
In this subsection, we investigate the physical mechanisms underlying the hysteresis in the mean PRECC and hence the mean total precipitation.First, we examine the changes in DCIN (section 2) for insights into the asymmetric response of convective precipitation to the symmetric CO 2 fording.
Figure 3 demonstrates a strong association between changes in DCIN and mean precipitation.The DCIN showed a substantial increase (from 3 kJ kg −1 to 8 kJ kg −1 ) during the RU period (figure 3(a)), which indicates that as the CO 2 concentration increases, the lower troposphere becomes more thermodynamically stable over Europe, providing unfavorable conditions for moist convection.During the RD period, while the DCIN decreases with CO 2 removal, the rate of decrease was slower than that observed during the RU period.Therefore, the DCIN exhibited an asymmetric change with respect to CO 2 forcing, similarly to the hysteretic behavior observed regarding the mean PRECC.
The difference in DCIN between 2CO2 up and 2CO2 dn periods (2CO2 dn -2CO2 up ) revealed a significant increase in DCIN across Europe during the 2CO2 dn period when compared with the 2CO2 up period.Particularly pronounced increases were observed in regions of Europe closer to the Northern Atlantic, such as the North Atlantic coastal areas (figure 3(b)).Interestingly, while the increase in DCIN appears throughout Europe uniformly, there seems to be strong regionality in terms of the mechanisms that drive the DCIN increase.For example, the increase in DCIN in the northern Europe can be largely attributed to a reduction in the nearsurface moist enthalpy (figure 3(c)).On the other hand, the temperature increase in the lower freetroposphere is the main cause of the increase in DCIN in the southern Europe, especially around the Mediterranean Sea (figure 3(d)).
What are the sources of the changes in the near-surface enthalpy in the northern Europe and 700 hPa temperature in the southern Europe?figure 4 illustrates the differences in large-scale circulation between the 2CO2 dn and 2CO2 up periods.The surface air temperature (T s ) over the North Atlantic was approximately 4 • C lower during the 2CO2 dn period (figure 4(a)).This anomalous surface cooling, prevalent throughout the North Atlantic, Greenland, and Northern Europe, can be attributed to weakened AMOC.Using identical model simulations, An et al (2021b) demonstrated that Atlantic Meridional Overturning Circulation (AMOC) steadily weakened until approximately 2180 in the mid-RD period.The weakening of the AMOC was attributed to reduced horizontal salt advection and freshwater hosing in the North Atlantic, caused by ice melting in response to global warming (Kim and An 2013, Bakker et al 2016, An et al 2021a).This weakening is associated with the positive salt advection feedback mechanism (Buckley and Marshall 2016).Such a feedback process, along with a decrease in evaporation leading to freshening, further contributes to the diminishing intensity of the AMOC until the middle of the RD period (Oh et al 2022b).A weakened AMOC led to rapid surface cooling over the North Atlantic during the RD period.
The pronounced anomalous cooling caused by the weakened AMOC appears to influence circulation in the North Atlantic and Europe by inducing anomalous high sea-level pressure over the eastern North Atlantic and Eurasian Continent (figure 4(a)).The widespread anomalous high pressure was consistent with the pattern expected in the steady linear response of a baroclinic atmosphere to shallow thermal forcing (Hoskins and Karoly 1981), with the anomalous anticyclonic circulation located to the east of the cooling region.Figures 4(c) and (d) reveal that the shallow cooling forced over the North Atlantic is associated with a high geopotential height east of the cooling region.
The anomalous high-pressure system near the surface accompanies widespread surface drying over Europe, likely via the anomalous sinking motion (figures 4(b) and S5 for statistical relationships).With a much drier condition near the surface, summertime deep convection would be strongly suppressed (Chen et al 2020, Williams andO'Gorman 2022), leading to the substantial reduction in convective precipitation.The effect of anomalously dry conditions on deep convection is captured in the DCIN (figure 3(c)).In addition, the cooling over the North Atlantic seemed to directly influence the decrease in T s over Central and Northern Europe, further increasing near-surface moist enthalpy (figure 3(c)).
In the southern Europe around the Mediterranean Sea, where the changes in near-surface   1) between 2CO2 dn and 2CO2up (i.e.2CO2 dn -2CO2up).Brown (blue green) means more stable (unstable) conditions during the 2CO2 dn compared to 2CO2up.The dots represent statistical significance at 95% confidence interval.
moist enthalpy are weak (figure 3(c)), the increase in DCIN seems to be mainly caused by the increase in the lower free-tropospheric temperature (figure 3(d)).Located to the south of the anomalous high-pressure system centered around (55 N, 10 W), the southern Europe experiences anomalous easterly and southerly winds, which bring warm air from the east and south.The resulting warming near the surface appears to cancel out the drying effect, yielding only small changes in the near-surface moist enthalpy (figure 3(c)).In the lower free-troposphere, however, the warming causes an increase in the saturation moist enthalpy, dominantly contributing to the increase in DCIN around the Mediterranean Sea.

Summary and discussion
This study has examined the hysteresis of European summer mean precipitation in an idealized CO 2 removal experiment using CESM1.2.2.Our findings showed a remarkable hysteresis in European summer mean precipitation, with a 40% reduction during the RU period and a delayed recovery during the RD period.This hysteresis in the mean precipitation was primarily induced by the mean PRECC, which accounts for most of the mean precipitation.
The change in the mean PRECC was closely associated with that in the mean DCIN.During the RU period, DCIN increased substantially, indicating a more thermodynamically stable atmosphere, which strongly suppresses summertime deep convection.During the RD period, the DCIN recovered but at a slower rate than the rate of increase during the RU period, leading to the asymmetric changes in the mean PRECC observed regarding symmetric CO 2 forcing.With the reduced convective precipitation, PRECL increases and partly compensates the decrease in the mean precipitation.This is presumably because the low-level moisture is not efficiently removed by convective precipitation.
Hysteresis in the DCIN is found to be associated with anomalous surface cooling over the North Atlantic caused by weakening of the AMOC during the RD period (An et al 2021b).This cooling induced an anomalous large-scale anticyclonic circulation over Europe as a response to the thermal forcing (Hoskins and Karoly 1981).The anomalous circulation induced the increase in DCIN over the entire Europe, with a noticeable north-south contrast in the mechanism responsible for the stability increase.In the Central and Northern Europe, near-surface cooling and drying were the main causes of the increase in DCIN.On the other hand, warming in the lower freetroposphere was mainly responsible for the DCIN increase in the Southern Europe.Consequently, the mean PRECC and mean total precipitation decreased during this period over the entire Europe, resulting in pronounced hysteresis.This highlights the essential role of AMOC in influencing atmospheric circulation, surface conditions, and the hysteretic behavior of summer mean precipitation over Europe.
Our results that highlighted pronounced hysteresis in the mean precipitation even at equivalent atmospheric CO 2 concentrations may have profound implications for climate risk reduction, strategic climate mitigation, and prospective understanding of changes in summer precipitation across Europe under scenarios of net positive and negative CO 2 emissions.By deepening our understanding of hysteresis in climate systems and its underlying mechanisms, we will be better equipped to formulate wellinformed decisions that mitigate the impact of shifting precipitation patterns.This study could serve as a crucial step in enhancing our preparedness for water scarcity and energy production, policy development, and increasing our resilience against recurrent hydrological hazards.
A few limitations of our study and possible ways to address them are as follows.Firstly, while CESM1 exhibited a significant reduction and overshoot of the AMOC in this study, the extent of the AMOC weakening and its effect on European summer precipitation differed across different climate models (Jackson et al 2014, Schwinger et al 2022).For instance, Schwinger et al (2022) demonstrated that CESM version 2 also displays substantial hysteresis in the AMOC under the CDR scenario, resulting in pronounced cooling across the expansive North Atlantic region during the RD period, akin to our findings.In contrast, models such as GFDL-ESM4 show different AMOC recovery rates, leading to distinct cooling (and even warming in some cases) patterns over the North Atlantic and Europe.Further investigation is required to evaluate the impacts of different AMOC changes on the hysteresis of European precipitation within the CDR intercomparison project models.Secondly, there are significant differences in the way moist deep convection is parameterized across climate models.Therefore, the partitioning between convective and PRECL needs to be considered when assessing regional precipitation projections in the climate models.Lastly, when assessing climate-related risks, it is crucial to provide reliable projections of both mean and extreme precipitation.Future studies should examine whether and to what extent European summer extreme precipitation shows hysteresis in CDR experiments.

NFigure 1 .
Figure 1.Hysteresis of the European summer mean precipitation.(a) Scatter plot of the mean precipitation spatially averaged over Europe (35-70 • N and 13 • W-35 • E) during the CO2 ramp-up (red; RU) and ramp-down (blue; RD) periods.The lime-colored star indicates the value from the present-day (PD) simulation.The red (blue) dots signify annual summer precipitation, whereas the scarlet (sky blue) dots represent the 11 year moving average precipitation for each of the 28 ensemble members.The vertical grey shading shows the 31 year period when CO2 doubles: the model years 2055-2085 during the RU (2CO2up) and 2195-2225 during the RD (2CO2 dn ) periods.The hysteresis intensity is measured by the cut-off area in the diagram in panel (a) (Kim et al 2022).(b) Spatial distribution of the difference in the mean precipitation between 2CO2 dn and 2CO2up (i.e.2CO2 dn -2CO2up).The dots represent statistical significance at 95% confidence interval.

Figure 2 .
Figure 2. Same as figure 1(a) but for (a) the summer mean European convective precipitation (PRECC) and (b) the summer mean European large-scale precipitation (PRECL).

Figure 3 .
Figure 3. Changes in the deep convective inhibition (DCIN).(a) The 21 year moving time evolution of the mean DCIN.The solid line and shading indicate the 28-ensemble mean value and spread (standard deviation), respectively.The vertical grey shadings represent the 2CO2up and 2CO2 dn periods.The vertical dashed grey line shows the year when the CO2 concentration quadrupled from its initial level.(b)-(d) Spatial distribution of the difference in (b) the mean DCIN, (c) negative of near-surface moist enthalpy (the second term on the right hand side of equation (1), and (d) saturation moist enthalpy at the lower free-troposphere (the first term on the right hand side of equation (1) between 2CO2 dn and 2CO2up (i.e.2CO2 dn -2CO2up).Brown (blue green) means more stable (unstable) conditions during the 2CO2 dn compared to 2CO2up.The dots represent statistical significance at 95% confidence interval.
Figure 4. (a)-(b) Spatial distribution of the differences in large-scale atmospheric conditions in the boreal summer (JJA) between the 2CO2 dn and 2CO2up periods for (a) the surface temperature (shading, K) and sea-level pressure (contour; unit: hPa) and (b) surface-specific humidity (shading) and zonal wind at 850 hPa (contour; unit: m s −1 ) The green (purple dashed) contours delineate positive (negative) differences.(c)-(d) Vertical profile of the differences in the wavenumber-1 pattern in the zonal-mean removed meridionally averaged (45-70 • N) (c) vertical temperature and (d) geopotential height.The black arrows on the x-axis in panels (c) and (d) denote the longitude where the strongest SST cooling appears.The stippling represents areas where the difference is statistically significant to the 95% confidence interval.
tions (Wu et al 2010, Boucher et al 2012, Chadwick et al 2013, Jo et al 2022, Kim et al 2022, Kug et al 2022, Oh et al 2022a, Song et al 2022, Yeh et al 2021).For instance, Kug et al (2022) demonstrated the hysteretic behavior of the latitudinal location and strength of the intertropical convergence zone and