Irreversible climate changes driven by degree-years of temperature overshoot

Irreversible climate changes driven by degree-years of temperature overshoot | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Irreversible climate changes driven by degree-years of temperature overshoot Mitchell Dickau, Kirsten Zickfeld, H. Damon Matthews This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7603499/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract It is becoming increasingly likely that meeting the long-term temperature goal of the Paris Agreement will involve a period of temperature overshoot. Understanding the differences in climate outcomes between overshoot and non-overshoot scenarios requires an assessment of the reversibility of climate changes along an overshoot pathway. Using an intermediate-complexity Earth system model, we quantify the reversibility of a suite of climate variables and investigate the factors driving differences in reversibility across an ensemble of 42 pairs of overshoot and non-overshoot scenarios. For highly irreversible climate variables like permafrost and ocean changes, we show that the long-term outcome is linearly related to the time-integrated overshoot magnitude, which we define here as the degree-years of temperature overshoot. Our results show that degree-years of overshoot can be used to predict the changes of a range of irreversible ocean and permafrost variables in overshoot scenarios, therefore offering important insights into the difference in climate outcomes of overshoot compared to non-overshoot scenarios. Climate Analysis and Modeling Climatology Overshoot climate impacts AMOC permafrost Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 INTRODUCTION Current climate policies have global emissions on track to push global warming well beyond 2.0°C 1 . As a result, it is becoming increasingly likely that if we are to meet the 1.5°C to well-below 2.0°C temperature goal of the Paris agreement, there will first be a period of prolonged temperature overshoot (OS). The increasing likelihood of OS highlights the importance of understanding the climate outcomes of OS compared to non-OS scenarios that achieve the same temperature target by the end of the century. A key question is how the severity of climate changes will differ as a function of the duration and magnitude of OS across a range of policy-relevant 1.5°C to 2.0°C scenarios. Previous work has shown that OS leads to additional climate changes and associated impacts due to hysteresis (or irreversibility) in the climate system 2,3 . These changes can be broadly categorized into two groups: those affecting slow-responding variables, which exhibit significant hysteresis or are sensitive to tipping points, and those affecting fast-responding variables, which tend to exhibit less or no hysteresis. Slow-responding climate variables that show pronounced hysteresis following OS include permafrost carbon loss, ocean temperature, ocean oxygen content, ocean pH, thermosteric sea level rise (SLR), and ice sheet loss along with the associated SLR 3–13 . These variables exhibit hysteresis because they involve large thermal or physical inertia. For instance, once permafrost thaws during OS, the carbon loss is irreversible from a policy perspective since carbon buildup in soils and vegetation and subsequent refreezing would take millennia 12 . Ocean temperature and thermosteric SLR are governed by the slow penetration of heat into the deep ocean, which takes centuries to equilibrate even if surface temperatures are reduced 9 . Similarly, changes in ocean oxygen content and pH that occur during the period of OS can become effectively locked in when surface waters are downwelled, transporting these altered conditions into the deep ocean 10,11 . Once subducted, this water is isolated from the atmosphere for centuries, preventing rapid re-equilibration and delaying recovery of the deep ocean for centuries after surface temperatures have stabilized. Ice sheet loss is marked by threshold behavior and self-reinforcing feedbacks, such as the ice-albedo effect, which make ice sheet recovery impossible on timescales of centuries after substantial loss has occurred 12 . Fast-responding climate variables that exhibit little to no hysteresis following OS include surface air temperature, precipitation, Arctic sea ice, and sea surface pH 3,8,13,14 . Surface air temperature is closely tied to radiative forcing – as CO₂ concentrations decline, temperatures begin to decrease rapidly due to the relatively low thermal inertia of the atmosphere and upper ocean 2,15 . Precipitation also adjusts relatively quickly as surface temperatures change, with reversal occurring slightly after changes in temperature 13 . However, for both temperature and precipitation, even though global mean values show high reversibility, there is evidence that the regional response following OS can exhibit more path dependence 16,17 . Arctic sea ice, while sensitive to warming, can regrow rapidly during cooler periods because it is driven by short-term surface energy fluxes 13 . Sea surface pH, which reflects the balance of CO₂ between the surface ocean and atmosphere, also responds relatively quickly as well – when atmospheric CO₂ levels decline, the surface ocean can begin to outgas CO₂ and partially recover its pH due to rapid gas exchange and mixing in the upper ocean layers 3,13 . These variables tend to lack the deep memory, physical inertia, or strong reinforcing feedbacks that characterize slower components of the climate system, allowing them to more closely track changes in forcing and exhibit minimal hysteresis. Finally, some climate variables do not fit neatly into the categories of fast- or slow-responding. One such example is the Atlantic Meridional Overturning Circulation (AMOC), which is sensitive to rate of temperature change during OS, and can substantially influence both global and regional climate patterns, particularly in the North Atlantic and surrounding areas 18 . In some models, the AMOC recovers within two to three centuries after the peak of OS, suggesting it exhibits less hysteresis than slower-responding variables like permafrost carbon release or deep ocean heat content 3 . At the same time, this recovery time is slower and more path-dependent than that of fast-responding variables such as surface temperature or precipitation. As such, the AMOC occupies an intermediate position – demonstrating a moderate level of hysteresis that depends on both the magnitude and duration of OS, as well as the rate of temperature change 18,19 . Existing modelling studies on the climate impacts of OS have used: 1) idealized CO 2 only scenarios that are concentration driven or driven by emission pulses 3,8,13–16,20–22 , 2) a limited number of scenarios (e.g., SSP5-3.4OS and/or SSP1-1.9 10,17,23–25 ), or 3) an ensemble of realistic scenarios that are simulated in a climate emulator rather than a more complex and spatially explicit Earth system model (ESM) 26 . There has yet to be a study that investigates climate outcomes of OS in relation to the magnitude and duration of OS across an ensemble of policy-relevant (i.e., 1.5° to 2.0°C) multi-gas scenarios in a spatially explicit Earth system model. In this study, we investigate the climate outcomes of OS occurring this century in the University of Victoria intermediate complexity Earth System Climate Model (UVic-ESCM). We simulate 42 pairs of scenarios – one non-OS reference scenario and one OS scenario – with peak temperatures ranging from ~1.5 to ~2.0°C (Fig. 1). To explore how the duration and magnitude of OS affects the climate outcomes, we calculate the degree-years of OS, which we define here as the time integrated difference in global surface air temperature (GSAT) between an OS scenario and its non-OS pair. We then quantify the reversibility of a suite of different climate variables and show that the degree-years of OS are a robust predictor of the changes that occur across a range of highly irreversible climate variables. RESULTS The climate outcomes of OS are often defined in terms of reversibility/irreversibility 3,11,13,17 . For a given climate variable, if there is a difference between the OS and non-OS reference scenario values during the period of OS, and if there is no difference between the scenarios after the period of OS, then this climate variable would be considered fully reversible and OS would be considered to have no impact on long-term change. Conversely, if there is still a difference in a given variable following OS, then the variable would be considered to have some degree of irreversibility. Here, we define the reversibility of a suite of climate variables relative to that of global mean temperature in a series of OS scenarios that return to a target global temperature of between ~ 1.4 and ~ 1.9°C before the end of the century. We quantify reversibility for each climate variable at the return year, which is defined as the year that global mean temperature in the OS scenario returns to the same temperature as in the paired non-OS scenario. In the scenarios used here, the return years fall between 2086 and 2100. Despite pairs of scenarios having equal cumulative CO 2 emissions by the end of the century, return years do not necessarily align with the year when cumulative CO 2 emissions become equal because non-CO 2 forcing in all OS scenarios falls below levels found in the non-OS scenarios after 2090 (SM Fig. 1 ). To calculate reversibility, we first calculate the maximum difference ( \(\:{diff}^{max}\) ) for each variable between the OS and non-OS value during the period of OS. Second, we calculate the difference between the OS and non-OS values of a variable at the return year ( \(\:{diff}^{return\:year}\) ). Using the \(\:{diff}^{max}\) and \(\:{diff}^{return\:year}\) we define the reversibility of a given climate variable at the return year as: $$\:reversibility=\:\frac{{diff}^{max}-{diff}^{return\:year}}{{diff}^{max}}$$ 1 We calculated the reversibility of 30 globally-averaged climate variables simulated by the UVic-ESCM, in addition to the spatial pattern of surface air temperature. Given our representation of reversibility (illustrated in Fig. 2 A), global mean temperature itself is by definition 100% reversible. In addition to the magnitude of temperature OS, we further calculated the time-integral of the global mean temperature OS, which we define here as the degree-years of OS (Fig. 2 B). REVERSIBILITY OF CLIMATE OUTCOMES Across the 30 globally-averaged climate variables simulated by the UVic ESCM, the median reversibility across scenarios ranged from 0% (fully irreversible) to 120% (more reversible than global average temperature) (Fig. 3). Slow responding climate variables are the least reversible, particularly those associated with the ocean and with permafrost (boxplots 1-6 Fig. 3). Climate variables with median reversibility above 100% include the atmospheric concentration of CO 2 , surface ocean carbon cycle variables that follow atmospheric CO 2 levels closely, and global average ocean alkalinity (boxplots 27-30 Fig. 3). For atmospheric CO 2 , sea surface pH and sea surface dissolved inorganic carbon (DIC), greater than 100% median reversibility reflects the understanding that, due to carbon cycle inertia, the ocean continues to take up CO 2 following peak OS as temperatures decline, resulting in lower atmospheric CO 2 at the return year relative to non-OS scenarios 15 . As a result, temperature reversal lags changes to atmospheric CO 2 concentration in OS scenarios, so achieving 100% reversible temperature requires more than a 100% reversal of atmospheric CO 2 concentration. Many of the climate variables presented here exhibit high uncertainty in reversibility across scenarios (Fig. 3). To investigate the drivers of uncertainty in reversibility for variables with high uncertainty – defined as those with an interquartile range in reversibility exceeding 10% (SM Table 1) – we calculated the linear correlation between the absolute values of each variable at the return year in individual OS and non-OS scenarios (i.e., without taking the difference between OS and non-OS) and several potential explanatory variables: peak and return-year for temperature and atmospheric CO₂ concentration, the rates of change in temperature and atmospheric CO₂ concentration during the OS period, and the average temperature and atmospheric CO₂ concentration over the OS period (SM Table 2 and SM Fig. 2). Variables with high uncertainty in reversibility fall into two general groups. The first group includes atmospheric CO 2 as well as most carbon cycle variables: global average ocean DIC, total ocean carbon, total land carbon, total soil carbon, total vegetation carbon, and global average sea surface DIC and pH (boxplots 11, 12, 15-17, 27, 28, 30 Fig. 3). Sea surface DIC and pH are almost perfectly correlated with atmospheric CO 2 at the return year (R 2 = 0.99) because the rapid exchange of CO 2 between the sea surface and the atmosphere allows for these variables to respond to changes in atmospheric CO 2 with almost no delay. Uncertainty in the reversibility of the other carbon cycle variables mentioned here – global average ocean DIC, total ocean carbon, total land carbon, total soil carbon, and total vegetation carbon – are most highly correlated with average CO 2 concentrations during the OS period, indicating that they are more sensitive to the pathway of atmospheric CO 2 than to its present value alone (SM Table 2). The range in atmospheric CO 2 reversibility is driven by varying contributions to temperature change from non-CO 2 forcing between OS and non-OS pairs, and this uncertainty is propagated to carbon cycle variables that respond directly to atmospheric CO 2 changes. We would expect greater reversibility of atmospheric CO 2 in scenarios where non-CO 2 forcing in the OS and non-OS pair are equal and where the reduction in temperature following OS is caused by net-negative CO 2 emissions because, if the reduction in temperature is caused by net negative CO 2 emissions rather than a reduction in non-CO 2 forcing, more carbon would be removed from the atmosphere 15 . Alternatively, if temperature reduction following OS is caused by a reduction in non-CO₂ forcing in the OS scenario relative to the non-OS scenario, temperature can be reversed before cumulative CO₂ emissions in the OS scenario are equal to those of the non-OS scenario. This results in higher atmospheric CO₂ concentrations in the OS scenario at the point of temperature return, and thus reduced CO₂ concentration reversibility. This relationship between the CO₂ and non-CO 2 forcing fraction and the reversibility of atmospheric CO₂ and related carbon cycle variables becomes clear when comparing two key milestones: the return year – when temperature in the OS scenario matches that of the non-OS scenario – and the year when cumulative CO₂ emissions in the OS scenario equal those in the non-OS scenario. When these two milestones occur at the same time, or when cumulative CO₂ emissions in the OS scenario are equal to the non-OS scenario before the return year, reversibility of atmospheric CO₂ and related carbon cycle variables is highest (SM Fig. 3). Conversely, as the cumulative emissions year occurs increasingly after the return year due to lower non-CO 2 forcing in OS scenarios relative to their non-OS pairs, reversibility declines (SM Fig. 3). Reversibility in atmospheric CO₂, sea surface DIC, and sea surface pH show the strongest correlations with the difference between the return year and the cumulative emissions year. Global average ocean DIC and ocean total carbon also correlate strongly with this difference, though their reversibility is notably lower, reflecting the greater reversibility of surface ocean changes compared to those in the deep ocean. Finally, carbon cycle variables associated with the land reservoir also show a clear relationship, but with lower correlations, reflecting the understanding that these variables are also strongly influenced by temperature, and that less of their reversibility can be explained by a metric tied to differences in CO 2 and non-CO 2 forcing fractions between scenario pairs. The second group of variables with high uncertainty in reversibility across scenarios includes those strongly influenced by temperature: permafrost global area, global total sequestered frozen carbon, and global snow volume (boxplots 9, 10, 14 in Fig. 3). In individual OS and non-OS scenarios, these variables show strong linear correlations between their values at the return year and the average temperature over the OS period (R² = 0.95–0.97; SM Table 2). Return year values in these temperature-sensitive variables also correlate strongly with peak and return year temperatures, which is expected given the high inter-correlation among the temperature metrics themselves. However, peak and return year temperatures exhibit lower correlations than average OS-period temperature (SM Table 2), suggesting that reversibility in these variables has a significant inertial component. Since average temperatures across individual scenarios vary widely – from 1.4°C to 2.0°C – we can conclude that the high uncertainty in the reversibility of permafrost area, frozen carbon, and snow volume is driven by differences in average temperatures between OS and non-OS scenario pairs. Two other variables with high uncertainty in reversibility – global average ocean alkalinity and salinity – do not fit neatly into one of the above two groups of variables. For global ocean alkalinity, the absolute changes following OS are small – the median impact of OS on ocean alkalinity at the return year is only an increase of 2.4x10 -7 mol m -3 (range: -4.8x10 -7 to 1.6x10 -6 mol m -3 ). Similarly, the absolute changes in global average ocean salinity following OS are also small – the median impact of OS on salinity at the return year is an increase of 7.0 × 10⁻⁶ grams of salt per 1000 grams of water (psu), with range of 7.2 × 10⁻⁸ to 1.2 × 10⁻⁵ psu. For ocean alkalinity, there is no strong correlation with any of the independent variables considered here (SM Table 2). In contrast, average ocean salinity shows a strong linear correlation (R² = 0.90) with average temperature (SM Table 2). Since OS and non-OS scenarios differ in their average temperatures during this period, it is unsurprising that variables like average ocean salinity, which are strongly correlated with average temperature, exhibit a wide range of reversibility outcomes. However, because changes in average ocean alkalinity and salinity are small in absolute terms, the associated uncertainty in reversibility – when expressed as a percentage – is amplified, making it difficult to interpret. As a result, findings related to these variables should be interpreted with caution. REVERSIBILITY OF THE SPATIAL WARMING PATTERN A grid-cell by grid-cell analysis surface air temperature reversibility shows that regional temperatures vary in their level of reversibility relative to the reversibility of global mean temperature change (which is 100% reversible based on the definition of reversibility used here) (Fig. 3 A). Reversibility values range from about 80% at high latitudes to about 110% across tropical continental regions. In other words, OS scenarios lead to warmer high latitudes and cooler equatorial and middle latitudes compared to non-OS scenarios at the same global warming level. Increased warming in high latitudes is consistent with spatial changes in SAT following OS in idealized simulations 20 , as well as with long-term averages in some CMIP6 models simulating SSP5-3.4OS and SSP1-1.9 scenarios 17 . In agreement with previous work 16,17 , our results show that the lower reversibility at high latitudes is slightly more pronounced in the Southern Hemisphere, where hemispheric average temperature is slightly less than 100% reversible, compared to the Northern Hemisphere, where temperature reversibility is slightly above 100% on average (boxplots 21 & 26 Fig. 3). Irreversible warming at high latitudes is related to polar feedbacks such as the ice albedo feedback. Based on our definition of reversibility, irreversible warming at the poles necessitates greater than 100% reversible changes to temperature in the middle and lower latitudes. The ranges in reversibility values across scenarios are generally low (<=10% range between 5 th and 95 th percentiles over 82% of grid cells; Fig. 3 B), which demonstrates that the spatial distribution of SAT reversibility is relatively independent of the peak temperature or the magnitude of OS for most regions in the scenarios used here. Ranges of reversibility tend to be lower over the oceans than over land which reflects how land surfaces experience higher rates of warming from transient climate change due to the continental and maritime effects. Ranges in reversibility are high (i.e., >15%) in the North Atlantic, high elevation regions of the central United States, and in the Southern Ocean, particularly near the West Antarctic (Fig. 4 B). We would expect these areas to experience regional changes that act as feedbacks on temperature change – the slowdown of AMOC reducing the rate of heat transport to the North Atlantic, the disappearance of ice and snow in the central United States, and the melting of sea ice as in the western Southern Ocean – which explains higher ranges in reversibility in these regions. PREDICTING THE OUTCOME OF IRREVERSIBLE VARIABLES USING DEGREE-YEARS OF OS Simulated changes in many of the most irreversible variables in our study can be well characterized by the time-integrated temperature difference – the degree-years of overshoot – associated with each OS/non-OS scenario pair. In the pairs of scenarios used in this study, degree-years of OS range from approximately 1°C-yr to 9°C-yr (Fig. 1 C). We investigated the relationship between the magnitude of irreversibility in climate variables and the degree-years of OS by performing a linear regression between degree-years of OS and the difference between OS and non-OS for each variable at the return year. We found robust relationships (R 2 > 0.9) between degree-years of OS and the magnitude of irreversibility for several permafrost and ocean variables (Fig. 5). Interestingly, for variables in which there is a strong relationship between degree-years of OS and the magnitude of irreversibility, the relationship appears to be fairly independent of the peak temperature achieved in the OS scenario, which demonstrates that degree-years of OS is a good predictor of the effect of OS on highly irreversible climate variables across a range of OS scenarios compatible with the Paris Agreement (Fig. 5). For globally averaged ocean variables – ocean oxygen, ocean temperature, and relative sea level height – the difference in absolute values between OS and non-OS scenarios grows before partially reversing as the return year is approached (Fig. 5 B, E, G). As previously discussed, the ocean interior and surface exhibit different responses to net-negative emissions and cooling 3,10,11 . For instance, with thermosteric sea level rise, sea surface water warms, undergoes thermal expansion, and downwells, causing irreversible change in the short-term because the downwelled water can no longer exchange heat with the atmosphere. However, thermosteric sea level rise caused by sea surface warming before downwelling has occurred is easily reversible in the short-term because heat can still be exchange between the sea surface and the atmosphere. The difference in sea surface salinity between OS and non-OS pairs also increases before beginning to decrease as the return year is approached which suggests that there are both more easily and less easily reversible factors influencing change. Some of the decreased salinity in the OS scenario is easily reversed as sea ice refreezes – the loss of sea ice is mostly reversible on short timescales since it responds quickly to changes in temperature (boxplots 18 &19 Fig. 3). However, decreased salinity caused by an influx of fresh water from melting sea ice during OS is not fully reversed because polar regions experience less regional temperature reversibility (Fig. 4). Given that changes in sea surface alkalinity covary with salinity 28,29 , sea surface alkalinity exhibits similar patterns of change as sea surface salinity. Unlike the other variables which exhibit robust relationships between degree-years of OS and the magnitude of irreversibility, maximum meridional overturing, permafrost carbon pool, and total permafrost region carbon all exhibit more linear patterns of irreversibility as it relates to degree-years of OS (Fig. 5 C, D, H). We argue that degree-years of OS can be thought as a proxy for accumulated energy in the Earth system and that these forementioned variables are likely correlated with Earth energy imbalance during OS relative to the non-OS reference scenario. DISCUSSION Due to the lack of progress on reducing emissions, it is increasingly important that we understand the climate effects of OS scenarios across a range of climate variables. An important question in furthering our understanding of the climate outcomes of OS is the question of how the severity of changes relates to the magnitude and duration of OS. Here, we confirm that there are nonnegligible climate effects of OS, especially for slow-responding variables, leading to path dependent climate outcomes. We show that high uncertainty in reversibility is primarily caused by differences in the forcing fractions of CO 2 and non-CO 2 forcers across scenarios (i.e., whether CO 2 or non-CO 2 forcing is what is responsible for OS and its reversal) or by average temperature differences across the pairs of scenarios. We also find that degree-years of OS is linearly related to the outcome of many slow responding irreversible permafrost and ocean variables. Surprisingly, the relationship between degree-years of OS and the outcome of irreversible variable appears to be relatively independent of the peak temperature reached in the 42 pairs of below 2.0°C scenarios simulated here. This finding demonstrates that degree-years of OS could potentially be used to capture the impact of OS for slow responding variables in a range of scenarios compatible with the Paris Agreement. We acknowledge that our definition of reversibility is based on decadal OS timescales that are shorter than the equilibration time for many climate variables. However, defining reversibility at a point in time this century immediately following a period of OS is relevant from climate impact and adaptation planning perspectives. This is particularly important for the practice of communicating climate impacts in terms of global warming levels 30 , which is problematic in OS scenarios given that the path to a given level of warming is an important determinant of climate outcomes. Our finding that degree-years of OS is a strong predictor of the effect of OS for several irreversible climate variables suggests that degree-years of OS could be used to predict the difference in climate outcomes between a stabilization scenario and an OS scenario for the most irreversible set of climate variables. METHODS SCENARIOS We use 42 pairs of scenarios from the ENGAGE project. In the ENGAGE project, Riahi et al. 31 developed pairs of scenarios using several IAMs where one scenario was constrained by a remaining carbon budget (RCB) that cannot be exceeded at any point before 2100 (i.e., the non-OS scenario) and one scenario where the same RCB could be temporarily exceeded but must be returned to by 2100 (i.e., the OS scenario). The RCB constraints in the 42 scenarios used range from 450 Gt CO 2 to 1600 Gt CO 2 . Forcing from non-CO 2 emissions was determined by assumptions embedded in individual IAMs, therefore IAMs simulated different temperature outcomes for the same RCBs. Pairs of scenarios in the ENGAGE ensemble were excluded from our analysis if: 1) annually averaged GSAT in the OS scenario failed to return to GSAT in the non-OS scenario before 2100, or 2) the OS scenario had less than one degree-year of OS. We did not need to control for internal climate variability using multi-year averages, since our results are averaged across an ensemble of scenarios and the intermediate complexity model we use does not exhibit much internal variability 27,32 . MODEL The University of Victoria Earth System Climate Model (UVic-ESCM) is an intermediate complexity climate model with a spatial resolution of 3.8° of longitude and 1.8° of latitude 32 . The model couples atmospheric, oceanic, land surface, and sea ice components while maintaining relatively low computational demands compared to more complex Earth System Models 32 . The atmospheric component uses a two-dimensional single-layer energy-moisture balance model, effectively simulating large-scale heat and moisture transport without detailed atmospheric circulation 32 . Thus, surface wind and cloud albedo are both held static at prescribed values based off observations. In contrast to the atmosphere, the ocean representation is more comprehensive, featuring a three-dimensional general circulation model that resolves major ocean currents and includes dynamic sea ice and marine biogeochemistry modules 32 . The land component incorporates vegetation dynamics by simulating competition between five plant functional types (PFTs) – shrubs, C3 and C4 grasses, and needleleaf and broadleaf trees – and their response to environmental changes 32 . The land model is coupled to carbon cycle models representing the marine terrestrial carbon cycles 27,32 . The interactive carbon cycle includes physical and biological ocean carbon cycling, sedimentary carbon cycling, and a representation of land carbon via the forementioned PFTs, permafrost carbon storage, and soil carbon storage 27,33–35 . The UVic-ESCM's coarse resolution and simplified atmosphere enable computationally efficient century-long simulations of ensembles of scenarios, making it well-suited for this study. However, two key limitations should be noted: 1) the non-dynamic atmosphere means changes in precipitation are not well captured, and 2) only thermosteric sea-level rise is represented. Therefore, changes in precipitation are ignored in this study and all sea-level rise results in this study refer exclusively to thermosteric changes. SIMULATIONS Future simulations in the UVic-ESCM were driven by fossil and land use change CO2 emissions as well as aggregated non-CO2 forcing from the ENGAGE project, the latter being estimated using MAGICC31. Given that the scenarios from the ENGAGE project do not include spatially explicit land cover change 31, land cover in our simulations was held static at preindustrial values. Similarly, the scenarios used here do not include spatially explicit changes to aerosol emissions, so only the aggregate globally averaged forcing of aerosols is included. For consistency, the historical simulation used to calculate temperature anomalies in Fig. 1 A was emissions driven with static land cover and prescribed globally-averaged aerosol forcing. The combined non-CO2 greenhouse gas and aerosol forcing for the historical simulation was harmonized with the future scenarios non-CO2 GHG and aerosol aggregated forcing in the year 2015. Solar forcing was held constant in both the historical and future simulations. Volcanic forcing was included in the historical simulations, but was held constant at the average historical value after the year 2015. References UNEP. Emissions Gap Report 2023: Broken Record – Temperatures Hit New Highs, yet World Fails to Cut Emissions (Again) . (United Nations Environment Programme, Nairobi, 2023). doi:10.59117/20.500.11822/43922. Schleussner, C.-F. et al. Overconfidence in climate overshoot. Nature 634 , 366–373 (2024). Schwinger, J., Asaadi, A., Steinert, N. J. & Lee, H. Emit now, mitigate later? Earth system reversibility under overshoots of different magnitudes and durations. Earth System Dynamics 13 , 1641–1665 (2022). MacDougall, A. H., Zickfeld, K., Knutti, R. & Matthews, H. D. Sensitivity of carbon budgets to permafrost carbon feedbacks and non-CO2 forcings. Environmental Research Letters 10 , 125003 (2015). Gasser, T. et al. Path-dependent reductions in CO2 emission budgets caused by permafrost carbon release. Nat Geosci 11 , 830–835 (2018). de Vrese, P. & Brovkin, V. Timescales of the permafrost carbon cycle and legacy effects of temperature overshoot scenarios. Nat Commun 12 , 2688 (2021). Comyn-Platt, E. et al. Carbon budgets for 1.5 and 2 °C targets lowered by natural wetland and permafrost feedbacks. Nat Geosci 11 , 568–573 (2018). Tokarska, K. B. & Zickfeld, K. The effectiveness of net negative carbon dioxide emissions in reversing anthropogenic climate change. Environmental Research Letters 10 , 094013 (2015). Ehlert, D. & Zickfeld, K. Irreversible ocean thermal expansion under carbon dioxide removal. Earth System Dynamics 9 , 197–210 (2018). Mathesius, S., Hofmann, M., Caldeira, K. & Schellnhuber, H. J. Long-term response of oceans to CO2 removal from the atmosphere. Nat Clim Chang 5 , 1107–1113 (2015). Li, X., Zickfeld, K., Mathesius, S., Kohfeld, K. & Matthews, J. B. R. Irreversibility of Marine Climate Change Impacts Under Carbon Dioxide Removal. Geophys Res Lett 47 , (2020). MacDougall, A. H. Reversing climate warming by artificial atmospheric carbon‐dioxide removal: Can a Holocene‐like climate be restored? Geophys Res Lett 40 , 5480–5485 (2013). Boucher, O. et al. Reversibility in an Earth System model in response to CO2 concentration changes. Environmental Research Letters 7 , 024013 (2012). Zickfeld, K., MacDougall, A. H. & Damon Matthews, H. On the proportionality between global temperature change and cumulative CO2 emissions during periods of net negative CO2 emissions. Environmental Research Letters 11 , 055006 (2016). Tokarska, K. B., Zickfeld, K. & Rogelj, J. Path Independence of Carbon Budgets When Meeting a Stringent Global Mean Temperature Target After an Overshoot. Earths Future 7 , 1283–1295 (2019). Kim, S.-K. et al. Widespread irreversible changes in surface temperature and precipitation in response to CO2 forcing. Nat Clim Chang 12 , 834–840 (2022). Pfleiderer, P., Schleussner, C.-F. & Sillmann, J. Limited reversal of regional climate signals in overshoot scenarios. Environmental Research: Climate 3 , 015005 (2024). Schwinger, J., Asaadi, A., Goris, N. & Lee, H. Possibility for strong northern hemisphere high-latitude cooling under negative emissions. Nat Commun 13 , 1095 (2022). Herrington, T. & Zickfeld, K. Path independence of climate and carbon cycle response over a broad range of cumulative carbon emissions. Earth System Dynamics 5 , 409–422 (2014). Jeltsch-Thömmes, A., Stocker, T. F. & Joos, F. Hysteresis of the Earth system under positive and negative CO2 emissions. Environmental Research Letters 15 , 124026 (2020). Wei, T., Chen, Y. & Wang, H. Hysteresis of Northern Hemisphere permafrost to carbon dioxide emissions. Environmental Research Letters 19 , 094032 (2024). Keller, D. P. et al. The Carbon Dioxide Removal Model Intercomparison Project (CDRMIP): rationale and experimental protocol for CMIP6. Geosci Model Dev 11 , 1133–1160 (2018). Asaadi, A. et al. Carbon cycle feedbacks in an idealized simulation and a scenario simulation of negative emissions in CMIP6 Earth system models. Biogeosciences 21 , 411–435 (2024). Melnikova, I. et al. Carbon Cycle Response to Temperature Overshoot Beyond 2°C: An Analysis of CMIP6 Models. Earths Future 9 , (2021). Koven, C. D. et al. Multi-century dynamics of the climate and carbon cycle under both high and net negative emissions scenarios. Earth System Dynamics 13 , 885–909 (2022). Drouet, L. et al. Net zero-emission pathways reduce the physical and economic risks of climate change. Nat Clim Chang 11 , 1070–1076 (2021). Mengis, N. et al. Evaluation of the University of Victoria Earth System Climate Model version 2.10 (UVic ESCM 2.10). Geosci Model Dev 13 , 4183–4204 (2020). Millero, F. J., Lee, K. & Roche, M. Distribution of alkalinity in the surface waters of the major oceans. Mar Chem 60 , 111–130 (1998). Lee, K. et al. Global relationships of total alkalinity with salinity and temperature in surface waters of the world’s oceans. Geophys Res Lett 33 , (2006). IPCC, 2022: Summary for Policymakers. in Climate Change 2022 – Impacts, Adaptation and Vulnerability (eds. H.-O. Pörtner et al.) 3–34 (Cambridge University Press, Cambridge, UK and New York, NY, USA, 2022). doi:10.1017/9781009325844.001. Riahi, K. et al. Cost and attainability of meeting stringent climate targets without overshoot. Nat Clim Chang 11 , 1063–1069 (2021). Weaver, A. J. et al. The UVic earth system climate model: Model description, climatology, and applications to past, present and future climates. Atmosphere-Ocean 39 , 361–428 (2001). Schmittner, A., Oschlies, A., Matthews, H. D. & Galbraith, E. D. Future changes in climate, ocean circulation, ecosystems, and biogeochemical cycling simulated for a business‐as‐usual CO 2 emission scenario until year 4000 AD. Global Biogeochem Cycles 22 , (2008). Matthews, H. D., Weaver, A. J. & Meissner, K. J. Terrestrial Carbon Cycle Dynamics under Recent and Future Climate Change. J Clim 18 , 1609–1628 (2005). MacDougall, A. H. & Knutti, R. Projecting the release of carbon from permafrost soils using a perturbed parameter ensemble modelling approach. Biogeosciences 13 , 2123–2136 (2016). Additional Declarations The authors declare no competing interests. Supplementary Files Dickauetal2025SMsubmission.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7603499","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":514397555,"identity":"1b6df26d-d580-4bf8-8d22-b1ef53007438","order_by":0,"name":"Mitchell Dickau","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-5061-1331","institution":"Concordia University","correspondingAuthor":true,"prefix":"","firstName":"Mitchell","middleName":"","lastName":"Dickau","suffix":""},{"id":514397556,"identity":"322e96a4-e4a1-4bbb-ab0f-9424986264b1","order_by":1,"name":"Kirsten Zickfeld","email":"","orcid":"","institution":"Simon Fraser University","correspondingAuthor":false,"prefix":"","firstName":"Kirsten","middleName":"","lastName":"Zickfeld","suffix":""},{"id":514397557,"identity":"25178abf-1c76-4fd6-87d9-7ada06f87eb0","order_by":2,"name":"H. Damon Matthews","email":"","orcid":"","institution":"Concordia University","correspondingAuthor":false,"prefix":"","firstName":"H.","middleName":"Damon","lastName":"Matthews","suffix":""}],"badges":[],"createdAt":"2025-09-12 21:21:49","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7603499/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7603499/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91459958,"identity":"31eb0bb9-f069-4492-abba-42cc9ba5f41d","added_by":"auto","created_at":"2025-09-16 16:56:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":384984,"visible":true,"origin":"","legend":"\u003cp\u003ePaired OS and non-OS scenarios used in this study which achieve a long-term temperature target of less than 2°C with peak temperatures in the OS scenarios ranging from 1.5 to 2.0°C. Panel (A) shows the average global surface air temperature (GSAT) anomalies in OS (red lines) and their paired non-OS (blue lines) scenarios with respect to a 1850-1900 baseline. Panel (B) shows the magnitude of OS relative to the paired non-OS reference scenarios. Panel (C) shows the degree-years of OS (i.e., the time integrated difference in temperature change between an OS and non-OS scenario pair).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/96ed5e682bbf5a543fc965dd.png"},{"id":91460409,"identity":"97395b19-728d-42e2-9ab4-0cc8485a65a4","added_by":"auto","created_at":"2025-09-16 17:04:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":210661,"visible":true,"origin":"","legend":"\u003cp\u003eA) illustrates how reversibility is defined for climate variables. Figure B) illustrates degree-years of OS, which is the time-integrated difference in global surface air temperature (GSAT) between an OS and non-OS pair of scenarios.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/5594490167a86f9d8b65de17.png"},{"id":91459965,"identity":"41abc302-a07e-4581-a364-a1d2db216f86","added_by":"auto","created_at":"2025-09-16 16:56:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":270960,"visible":true,"origin":"","legend":"\u003cp\u003eReversibility of variables in the UVic-ESCM. Median reversibility across all pairs of scenarios for each variable is represented by red lines. Each box represents the 1\u003csup\u003est\u003c/sup\u003e and 3\u003csup\u003erd\u003c/sup\u003e quartiles of reversibility for a given variable. The whiskers represent the 5\u003csup\u003eth\u003c/sup\u003eand 95\u003csup\u003eth\u003c/sup\u003e percentiles of reversibility.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/49a2904f3f5060116c430359.png"},{"id":91461209,"identity":"16fc132a-599f-457f-be02-b00de3aed096","added_by":"auto","created_at":"2025-09-16 17:12:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":674177,"visible":true,"origin":"","legend":"\u003cp\u003eA) shows the mean reversibility of surface air temperature (SAT) across all pairs of scenarios at each grid cell. The equatorial latitudes and the middle latitudes show greater than 100% reversibility which demonstrates that, following OS, temperature is lower in those regions relative to non-OS scenarios. At the poles, temperature is less than 100% reversible which demonstrates that, following OS, temperatures remain higher in these regions relative to non-OS reference scenarios. Figure B) shows the range of the 5\u003csup\u003eth\u003c/sup\u003e and 95\u003csup\u003eth\u003c/sup\u003e percentiles of SAT reversibility across all pairs of scenarios at each grid cell. Most regions show low ranges in reversibility (\u0026lt;10%). Regions where this range is higher (i.e., \u0026gt; 15%) include the North Atlantic, Northern Europe, the central United States, and the Southern Ocean, particularly in the Western Hemisphere.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/417b7d5de2497fbc6d2bc594.png"},{"id":91459962,"identity":"aa50e759-43a2-4574-a79b-63b9022721f6","added_by":"auto","created_at":"2025-09-16 16:56:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":452814,"visible":true,"origin":"","legend":"\u003cp\u003eThe difference between ocean and permafrost variables in the OS and non-OS pairs of scenarios plotted against degree-years of OS. The difference between OS and non-OS of a given variable at the return year is represented by the coloured points in which the colours indicate the peak temperature anomaly reached in the OS scenario. Grey lines represent the relationship between the difference between OS and non-OS of a given variable and degree-years of OS from 2015 until the return year.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/b430d288e7d9c2afecdcf2bd.png"},{"id":91461953,"identity":"90b4ef33-c792-4a57-be96-cdca4c83b26a","added_by":"auto","created_at":"2025-09-16 17:28:46","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2284295,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/b2976f21-6eaa-4293-9158-c6bb63354846.pdf"},{"id":91459961,"identity":"a59dd0b2-7fb9-44bd-938d-4b575cc9a756","added_by":"auto","created_at":"2025-09-16 16:56:44","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":455803,"visible":true,"origin":"","legend":"","description":"","filename":"Dickauetal2025SMsubmission.docx","url":"https://assets-eu.researchsquare.com/files/rs-7603499/v1/417b100ab5a36144e09bc675.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eIrreversible climate changes driven by degree-years of temperature overshoot\u003c/p\u003e","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eCurrent climate policies have global emissions on track to push global warming well beyond 2.0\u0026deg;C \u003csup\u003e1\u003c/sup\u003e. As a result, it is becoming increasingly likely that if we are to meet the 1.5\u0026deg;C to well-below 2.0\u0026deg;C temperature goal of the Paris agreement, there will first be a period of prolonged temperature overshoot (OS). The increasing likelihood of OS highlights the importance of understanding the climate outcomes of OS compared to non-OS scenarios that achieve the same temperature target by the end of the century. A key question is how the severity of climate changes will differ as a function of the duration and magnitude of OS across a range of policy-relevant 1.5\u0026deg;C to 2.0\u0026deg;C scenarios.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePrevious work has shown that OS leads to additional climate changes and associated impacts due to hysteresis (or irreversibility) in the climate system\u003csup\u003e2,3\u003c/sup\u003e. These changes can be broadly categorized into two groups: those affecting slow-responding variables, which exhibit significant hysteresis or are sensitive to tipping points, and those affecting fast-responding variables, which tend to exhibit less or no hysteresis. Slow-responding climate variables that show pronounced hysteresis following OS include permafrost carbon loss, ocean temperature, ocean oxygen content, ocean pH, thermosteric sea level rise (SLR), and ice sheet loss along with the associated SLR\u003csup\u003e3\u0026ndash;13\u003c/sup\u003e. These variables exhibit hysteresis because they involve large thermal or physical inertia. For instance, once permafrost thaws during OS, the carbon loss is irreversible from a policy perspective since carbon buildup in soils and vegetation and subsequent refreezing would take millennia\u003csup\u003e12\u003c/sup\u003e. Ocean temperature and thermosteric SLR are governed by the slow penetration of heat into the deep ocean, which takes centuries to equilibrate even if surface temperatures are reduced\u003csup\u003e9\u003c/sup\u003e. Similarly, changes in ocean oxygen content and pH that occur during the period of OS can become effectively locked in when surface waters are downwelled, transporting these altered conditions into the deep ocean\u003csup\u003e10,11\u003c/sup\u003e. Once subducted, this water is isolated from the atmosphere for centuries, preventing rapid re-equilibration and delaying recovery of the deep ocean for centuries after surface temperatures have stabilized. Ice sheet loss is marked by threshold behavior and self-reinforcing feedbacks, such as the ice-albedo effect, which make ice sheet recovery impossible on timescales of centuries after substantial loss has occurred\u003csup\u003e12\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFast-responding climate variables that exhibit little to no hysteresis following OS include surface air temperature, precipitation, Arctic sea ice, and sea surface pH\u003csup\u003e3,8,13,14\u003c/sup\u003e. Surface air temperature is closely tied to radiative forcing \u0026ndash; as CO₂ concentrations decline, temperatures begin to decrease rapidly due to the relatively low thermal inertia of the atmosphere and upper ocean\u003csup\u003e2,15\u003c/sup\u003e. Precipitation also adjusts relatively quickly as surface temperatures change, with reversal occurring slightly after changes in temperature\u003csup\u003e13\u003c/sup\u003e. However, for both temperature and precipitation, even though global mean values show high reversibility, there is evidence that the regional response following OS can exhibit more path dependence\u003csup\u003e16,17\u003c/sup\u003e. Arctic sea ice, while sensitive to warming, can regrow rapidly during cooler periods because it is driven by short-term surface energy fluxes\u003csup\u003e13\u003c/sup\u003e. Sea surface pH, which reflects the balance of CO₂ between the surface ocean and atmosphere, also responds relatively quickly as well \u0026ndash; when atmospheric CO₂ levels decline, the surface ocean can begin to outgas CO₂ and partially recover its pH due to rapid gas exchange and mixing in the upper ocean layers\u003csup\u003e3,13\u003c/sup\u003e. These variables tend to lack the deep memory, physical inertia, or strong reinforcing feedbacks that characterize slower components of the climate system, allowing them to more closely track changes in forcing and exhibit minimal hysteresis.\u003c/p\u003e\n\u003cp\u003eFinally, some climate variables do not fit neatly into the categories of fast- or slow-responding. One such example is the Atlantic Meridional Overturning Circulation (AMOC), which is sensitive to rate of temperature change during OS, and can substantially influence both global and regional climate patterns, particularly in the North Atlantic and surrounding areas\u003csup\u003e18\u003c/sup\u003e. In some models, the AMOC recovers within two to three centuries after the peak of OS, suggesting it exhibits less hysteresis than slower-responding variables like permafrost carbon release or deep ocean heat content\u003csup\u003e3\u003c/sup\u003e. At the same time, this recovery time is slower and more path-dependent than that of fast-responding variables such as surface temperature or precipitation. As such, the AMOC occupies an intermediate position \u0026ndash; demonstrating a moderate level of hysteresis that depends on both the magnitude and duration of OS, as well as the rate of temperature change\u003csup\u003e18,19\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eExisting modelling studies on the climate impacts of OS have used: 1) idealized\u0026nbsp;CO\u003csub\u003e2\u003c/sub\u003e only scenarios that are concentration driven or driven by emission pulses\u0026nbsp;\u003csup\u003e3,8,13\u0026ndash;16,20\u0026ndash;22\u003c/sup\u003e, 2) a limited number of scenarios (e.g., SSP5-3.4OS and/or SSP1-1.9\u003csup\u003e\u0026nbsp;10,17,23\u0026ndash;25\u003c/sup\u003e), \u0026nbsp;or 3) an ensemble of realistic scenarios that are simulated in a climate emulator rather than a more complex and spatially explicit Earth system model (ESM)\u003csup\u003e26\u003c/sup\u003e. There has yet to be a study that investigates climate outcomes of OS in relation to the magnitude and duration of OS across an ensemble of policy-relevant (i.e., 1.5\u0026deg; to 2.0\u0026deg;C) multi-gas scenarios in a spatially explicit Earth system model.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this study, we investigate the climate outcomes of OS occurring this century in the University of Victoria intermediate complexity Earth System Climate Model (UVic-ESCM). We simulate 42 pairs of scenarios \u0026ndash; one non-OS reference scenario and one OS scenario \u0026ndash; with peak temperatures ranging from ~1.5 to ~2.0\u0026deg;C (Fig. 1). To explore how the duration and magnitude of OS affects the climate outcomes, we calculate the degree-years of OS, which we define here as the time integrated difference in global surface air temperature (GSAT) between an OS scenario and its non-OS pair. We then quantify the reversibility of a suite of different climate variables and show that the degree-years of OS are a robust predictor of the changes that occur across a range of highly irreversible climate variables.\u0026nbsp;\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eThe climate outcomes of OS are often defined in terms of reversibility/irreversibility \u003csup\u003e3,11,13,17\u003c/sup\u003e. For a given climate variable, if there is a difference between the OS and non-OS reference scenario values during the period of OS, and if there is no difference between the scenarios after the period of OS, then this climate variable would be considered fully reversible and OS would be considered to have no impact on long-term change. Conversely, if there is still a difference in a given variable following OS, then the variable would be considered to have some degree of irreversibility.\u003c/p\u003e\u003cp\u003eHere, we define the reversibility of a suite of climate variables relative to that of global mean temperature in a series of OS scenarios that return to a target global temperature of between ~\u0026thinsp;1.4 and ~\u0026thinsp;1.9\u0026deg;C before the end of the century. We quantify reversibility for each climate variable at the return year, which is defined as the year that global mean temperature in the OS scenario returns to the same temperature as in the paired non-OS scenario. In the scenarios used here, the return years fall between 2086 and 2100. Despite pairs of scenarios having equal cumulative CO\u003csub\u003e2\u003c/sub\u003e emissions by the end of the century, return years do not necessarily align with the year when cumulative CO\u003csub\u003e2\u003c/sub\u003e emissions become equal because non-CO\u003csub\u003e2\u003c/sub\u003e forcing in all OS scenarios falls below levels found in the non-OS scenarios after 2090 (SM Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo calculate reversibility, we first calculate the maximum difference (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{diff}^{max}\\)\u003c/span\u003e\u003c/span\u003e) for each variable between the OS and non-OS value during the period of OS. Second, we calculate the difference between the OS and non-OS values of a variable at the return year (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{diff}^{return\\:year}\\)\u003c/span\u003e\u003c/span\u003e). Using the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{diff}^{max}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{diff}^{return\\:year}\\)\u003c/span\u003e\u003c/span\u003e we define the reversibility of a given climate variable at the return year as:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:reversibility=\\:\\frac{{diff}^{max}-{diff}^{return\\:year}}{{diff}^{max}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWe calculated the reversibility of 30 globally-averaged climate variables simulated by the UVic-ESCM, in addition to the spatial pattern of surface air temperature. Given our representation of reversibility (illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA), global mean temperature itself is by definition 100% reversible. In addition to the magnitude of temperature OS, we further calculated the time-integral of the global mean temperature OS, which we define here as the degree-years of OS (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eREVERSIBILITY OF CLIMATE OUTCOMES\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAcross the 30 globally-averaged climate variables simulated by the UVic ESCM, the median reversibility across scenarios ranged from 0% (fully irreversible) to 120% (more reversible than global average temperature) (Fig. 3). Slow responding climate variables are the least reversible, particularly those associated with the ocean and with permafrost (boxplots 1-6\u0026nbsp;Fig. 3). Climate variables with median reversibility above 100% include the atmospheric concentration of CO\u003csub\u003e2\u003c/sub\u003e, surface ocean carbon cycle variables that follow atmospheric CO\u003csub\u003e2\u003c/sub\u003e levels closely, and global average ocean alkalinity (boxplots 27-30 Fig. 3). For atmospheric CO\u003csub\u003e2\u003c/sub\u003e, sea surface pH and sea surface dissolved inorganic carbon (DIC), greater than 100% median reversibility reflects the understanding that, due to carbon cycle inertia, the ocean continues to take up CO\u003csub\u003e2\u003c/sub\u003e following peak OS as temperatures decline, resulting in lower atmospheric CO\u003csub\u003e2\u003c/sub\u003e at the return year relative to non-OS scenarios\u003csup\u003e15\u003c/sup\u003e. As a result, temperature reversal lags changes to atmospheric CO\u003csub\u003e2\u003c/sub\u003e concentration in OS scenarios, so achieving 100% reversible temperature requires more than a 100% reversal of atmospheric CO\u003csub\u003e2\u003c/sub\u003e concentration.\u003c/p\u003e\n\u003cp\u003eMany of the climate variables presented here exhibit high uncertainty in reversibility across scenarios (Fig. 3).\u0026nbsp;To investigate the drivers of uncertainty in reversibility for variables with high uncertainty \u0026ndash; defined as those with an interquartile range in reversibility exceeding 10% (SM Table 1) \u0026ndash; we calculated the linear correlation between the absolute values of each variable at the return year in individual OS and non-OS scenarios (i.e., without taking the difference between OS and non-OS) and several potential explanatory variables: peak and return-year for temperature and atmospheric CO₂ concentration, the rates of change in temperature and atmospheric CO₂ concentration during the OS period, and the average temperature and atmospheric CO₂ concentration over the OS period (SM Table 2 and SM Fig. 2).\u003c/p\u003e\n\u003cp\u003eVariables with high uncertainty in reversibility fall into two general groups. The first group includes atmospheric CO\u003csub\u003e2\u003c/sub\u003e as well as most carbon cycle variables: global average ocean DIC, total ocean carbon, total land carbon, total soil carbon, total vegetation carbon, and global average sea surface DIC and pH (boxplots 11, 12, 15-17, 27, 28, 30 Fig. 3). Sea surface DIC and pH are almost perfectly correlated with atmospheric CO\u003csub\u003e2\u003c/sub\u003e at the return year (R\u003csup\u003e2\u003c/sup\u003e = 0.99) because the rapid exchange of CO\u003csub\u003e2\u003c/sub\u003e between the sea surface and the atmosphere allows for these variables to respond to changes in atmospheric CO\u003csub\u003e2\u003c/sub\u003e with almost no delay. Uncertainty in the reversibility of the other carbon cycle variables mentioned here \u0026ndash; global average ocean DIC, total ocean carbon, total land carbon, total soil carbon, and total vegetation carbon \u0026ndash; are most highly correlated with average CO\u003csub\u003e2\u003c/sub\u003e concentrations during the OS period, indicating that they are more sensitive to the pathway of atmospheric CO\u003csub\u003e2\u003c/sub\u003e than to its present value alone (SM Table 2).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe range in atmospheric CO\u003csub\u003e2\u003c/sub\u003e reversibility is driven by varying contributions to temperature change from non-CO\u003csub\u003e2\u003c/sub\u003e forcing between OS and non-OS pairs, and this uncertainty is propagated to carbon cycle variables that respond directly to atmospheric CO\u003csub\u003e2\u003c/sub\u003e changes. We would expect greater reversibility of atmospheric CO\u003csub\u003e2\u003c/sub\u003e in scenarios where non-CO\u003csub\u003e2\u003c/sub\u003e forcing in the OS and non-OS pair are equal and where the reduction in temperature following OS is caused by net-negative CO\u003csub\u003e2\u003c/sub\u003e emissions because, if the reduction in temperature is caused by net negative CO\u003csub\u003e2\u003c/sub\u003e emissions rather than a reduction in non-CO\u003csub\u003e2\u003c/sub\u003e forcing, more carbon would be removed from the atmosphere\u003csup\u003e15\u003c/sup\u003e. Alternatively, if temperature reduction following OS is caused by a reduction in non-CO₂ forcing in the OS scenario relative to the non-OS scenario, temperature can be reversed before cumulative CO₂ emissions in the OS scenario are equal to those of the non-OS scenario. This results in higher atmospheric CO₂ concentrations in the OS scenario at the point of temperature return, and thus reduced CO₂ concentration reversibility.\u003c/p\u003e\n\u003cp\u003eThis relationship between the CO₂ and non-CO\u003csub\u003e2\u003c/sub\u003e forcing fraction and the reversibility of atmospheric CO₂ and related carbon cycle variables becomes clear when comparing two key milestones: the \u003cem\u003ereturn year\u003c/em\u003e \u0026ndash; when temperature in the OS scenario matches that of the non-OS scenario \u0026ndash; and the year when cumulative CO₂ emissions in the OS scenario equal those in the non-OS scenario. When these two milestones occur at the same time, or when cumulative CO₂ emissions in the OS scenario are equal to the non-OS scenario \u003cem\u003ebefore\u003c/em\u003e the return year, reversibility of atmospheric CO₂ and related carbon cycle variables is highest (SM Fig. 3). Conversely, as the cumulative emissions year occurs increasingly \u003cem\u003eafter\u003c/em\u003e the return year due to lower non-CO\u003csub\u003e2\u003c/sub\u003e forcing in OS scenarios relative to their non-OS pairs, reversibility declines (SM Fig. 3).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eReversibility in atmospheric CO₂, sea surface DIC, and sea surface pH show the strongest correlations with the difference between the return year and the cumulative emissions year. Global average ocean DIC and ocean total carbon also correlate strongly with this difference, though their reversibility is notably lower, reflecting the greater reversibility of surface ocean changes compared to those in the deep ocean. Finally, carbon cycle variables associated with the land reservoir also show a clear relationship, but with lower correlations, reflecting the understanding that these variables are also strongly influenced by temperature, and that less of their reversibility can be explained by a metric tied to differences in\u0026nbsp;CO\u003csub\u003e2\u003c/sub\u003e and non-CO\u003csub\u003e2\u003c/sub\u003e forcing fractions between scenario pairs.\u003c/p\u003e\n\u003cp\u003eThe second group of variables with high uncertainty in reversibility across scenarios includes those strongly influenced by temperature: permafrost global area, global total sequestered frozen carbon, and global snow volume (boxplots 9, 10, 14 in Fig. 3). In individual OS and non-OS scenarios, these variables show strong linear correlations between their values at the return year and the average temperature over the OS period (R\u0026sup2; = 0.95\u0026ndash;0.97; SM Table 2). Return year values in these temperature-sensitive variables also correlate strongly with peak and return year temperatures, which is expected given the high inter-correlation among the temperature metrics themselves. However, peak and return year temperatures exhibit lower correlations than average OS-period temperature (SM Table 2), suggesting that reversibility in these variables has a significant inertial component. Since average temperatures across individual scenarios vary widely \u0026ndash; from 1.4\u0026deg;C to 2.0\u0026deg;C \u0026ndash; we can conclude that the high uncertainty in the reversibility of permafrost area, frozen carbon, and snow volume is driven by differences in average temperatures between OS and non-OS scenario pairs.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTwo other variables with high uncertainty in reversibility \u0026ndash; global average ocean alkalinity and salinity \u0026ndash; do not fit neatly into one of the above two groups of variables. For global ocean alkalinity,\u0026nbsp;the absolute changes following OS are small \u0026ndash; the median impact of OS on ocean alkalinity at the return year is only an increase of 2.4x10\u003csup\u003e-7\u003c/sup\u003e mol m\u003csup\u003e-3\u003c/sup\u003e (range: -4.8x10\u003csup\u003e-7\u003c/sup\u003e to 1.6x10\u003csup\u003e-6\u003c/sup\u003e mol m\u003csup\u003e-3\u003c/sup\u003e). Similarly, the absolute changes in global average ocean salinity following OS are also small \u0026ndash; the median impact of OS on salinity at the return year is an increase of 7.0 \u0026times; 10⁻⁶ grams of salt per 1000 grams of water (psu), with range of 7.2 \u0026times; 10⁻⁸ to 1.2 \u0026times; 10⁻⁵ psu. For ocean alkalinity, there is no strong correlation with any of the independent variables considered here (SM Table 2). In contrast, average ocean salinity shows a strong linear correlation (R\u0026sup2; = 0.90) with average temperature (SM Table 2). Since OS and non-OS scenarios differ in their average temperatures during this period, it is unsurprising that variables like average ocean salinity, which are strongly correlated with average temperature, exhibit a wide range of reversibility outcomes. However, because changes in average ocean alkalinity and salinity are small in absolute terms, the associated uncertainty in reversibility \u0026ndash; when expressed as a percentage \u0026ndash; is amplified, making it difficult to interpret. As a result, findings related to these variables should be interpreted with caution.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eREVERSIBILITY OF THE SPATIAL WARMING PATTERN\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA grid-cell by grid-cell analysis surface air temperature reversibility shows that regional temperatures vary in their level of reversibility relative to the reversibility of global mean temperature change (which is 100% reversible based on the definition of reversibility used here) (Fig. 3 A). Reversibility values range from about 80% at high latitudes to about 110% across tropical continental regions. In other words, OS scenarios lead to warmer high latitudes and cooler equatorial and middle latitudes compared to non-OS scenarios at the same global warming level. Increased warming in high latitudes is consistent with spatial changes in SAT following OS in idealized simulations \u003csup\u003e20\u003c/sup\u003e, as well as with long-term averages in some CMIP6 models simulating SSP5-3.4OS and SSP1-1.9 scenarios\u003csup\u003e17\u003c/sup\u003e. In agreement with previous work\u003csup\u003e\u0026nbsp;16,17\u003c/sup\u003e, our results show that the lower reversibility at high latitudes is slightly more pronounced in the Southern Hemisphere, where hemispheric average temperature is slightly less than 100% reversible, compared to the Northern Hemisphere, where temperature reversibility is slightly above 100% on average (boxplots 21 \u0026amp; 26 Fig. 3). Irreversible warming at high latitudes is related to polar feedbacks such as the ice albedo feedback. Based on our definition of reversibility, irreversible warming at the poles necessitates greater than 100% reversible changes to temperature in the middle and lower latitudes.\u003c/p\u003e\n\u003cp\u003eThe ranges in reversibility values across scenarios are generally low (\u0026lt;=10% range between 5\u003csup\u003eth\u003c/sup\u003e and 95\u003csup\u003eth\u003c/sup\u003e percentiles over 82% of grid cells; Fig. 3 B), which demonstrates that the spatial distribution of SAT reversibility is relatively independent of the peak temperature or the magnitude of OS for most regions in the scenarios used here. Ranges of reversibility tend to be lower over the oceans than over land which reflects how land surfaces experience higher rates of warming from transient climate change due to the continental and maritime effects. Ranges in reversibility are high (i.e., \u0026gt;15%) in the North Atlantic, high elevation regions of the central United States, and in the Southern Ocean, particularly near the West Antarctic (Fig. 4 B). We would expect these areas to experience regional changes that act as feedbacks on temperature change \u0026ndash; the slowdown of AMOC reducing the rate of heat transport to the North Atlantic, the disappearance of ice and snow in the central United States, and the melting of sea ice as in the western Southern Ocean \u0026ndash; which explains higher ranges in reversibility in these regions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePREDICTING THE OUTCOME OF IRREVERSIBLE VARIABLES USING DEGREE-YEARS OF OS\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSimulated changes in many of the most irreversible variables in our study can be well characterized by the time-integrated temperature difference \u0026ndash; the degree-years of overshoot \u0026ndash; associated with each OS/non-OS scenario pair. In the pairs of scenarios used in this study, degree-years of OS range from approximately 1\u0026deg;C-yr to 9\u0026deg;C-yr (Fig. 1 C). We investigated the relationship between the magnitude of irreversibility in climate variables and the degree-years of OS by performing a linear regression between degree-years of OS and the difference between OS and non-OS for each variable at the return year.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe found robust relationships (R\u003csup\u003e2\u003c/sup\u003e \u0026gt; 0.9) between degree-years of OS and the magnitude of irreversibility for several permafrost and ocean variables (Fig. 5). Interestingly, for variables in which there is a strong relationship between degree-years of OS and the magnitude of irreversibility, the relationship appears to be fairly independent of the peak temperature achieved in the OS scenario, which demonstrates that degree-years of OS is a good predictor of the effect of OS on highly irreversible climate variables across a range of OS scenarios compatible with the Paris Agreement (Fig. 5).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFor globally averaged ocean variables \u0026ndash; ocean oxygen, ocean temperature, and relative sea level height \u0026ndash; the difference in absolute values between OS and non-OS scenarios grows before partially reversing as the return year is approached (Fig. 5 B, E, G). As previously discussed, the ocean interior and surface exhibit different responses to net-negative emissions and cooling \u003csup\u003e3,10,11\u003c/sup\u003e. For instance, with thermosteric sea level rise, sea surface water warms, undergoes thermal expansion, and downwells, causing irreversible change in the short-term because the downwelled water can no longer exchange heat with the atmosphere. However, thermosteric sea level rise caused by sea surface warming before downwelling has occurred is easily reversible in the short-term because heat can still be exchange between the sea surface and the atmosphere.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe difference in sea surface salinity between OS and non-OS pairs also increases before beginning to decrease as the return year is approached which suggests that there are both more easily and less easily reversible factors influencing change. Some of the decreased salinity in the OS scenario is easily reversed as sea ice refreezes \u0026ndash; the loss of sea ice is mostly reversible on short timescales since it responds quickly to changes in temperature (boxplots 18 \u0026amp;19 Fig. 3). However, decreased salinity caused by an influx of fresh water from melting sea ice during OS is not fully reversed because polar regions experience less regional temperature reversibility (Fig. 4). Given that changes in sea surface alkalinity covary with salinity\u003csup\u003e28,29\u003c/sup\u003e, sea surface alkalinity exhibits similar patterns of change as sea surface salinity.\u003c/p\u003e\n\u003cp\u003eUnlike the other variables which exhibit robust relationships between degree-years of OS and the magnitude of irreversibility, maximum meridional overturing, permafrost carbon pool, and total permafrost region carbon all exhibit more linear patterns of irreversibility as it relates to degree-years of OS (Fig. 5 C, D, H). We argue that degree-years of OS can be thought as a proxy for accumulated energy in the Earth system and that these forementioned variables are likely correlated with Earth energy imbalance during OS relative to the non-OS reference scenario.\u0026nbsp;\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eDue to the lack of progress on reducing emissions, it is increasingly important that we understand the climate effects of OS scenarios across a range of climate variables. An important question in furthering our understanding of the climate outcomes of OS is the question of how the severity of changes relates to the magnitude and duration of OS. Here, we confirm that there are nonnegligible climate effects of OS, especially for slow-responding variables, leading to path dependent climate outcomes. We show that high uncertainty in reversibility is primarily caused by differences in the forcing fractions of CO\u003csub\u003e2\u003c/sub\u003e and non-CO\u003csub\u003e2\u003c/sub\u003e forcers across scenarios (i.e., whether CO\u003csub\u003e2\u003c/sub\u003e or non-CO\u003csub\u003e2\u003c/sub\u003e forcing is what is responsible for OS and its reversal) or by average temperature differences across the pairs of scenarios.\u003c/p\u003e\u003cp\u003eWe also find that degree-years of OS is linearly related to the outcome of many slow responding irreversible permafrost and ocean variables. Surprisingly, the relationship between degree-years of OS and the outcome of irreversible variable appears to be relatively independent of the peak temperature reached in the 42 pairs of below 2.0\u0026deg;C scenarios simulated here. This finding demonstrates that degree-years of OS could potentially be used to capture the impact of OS for slow responding variables in a range of scenarios compatible with the Paris Agreement.\u003c/p\u003e\u003cp\u003eWe acknowledge that our definition of reversibility is based on decadal OS timescales that are shorter than the equilibration time for many climate variables. However, defining reversibility at a point in time this century immediately following a period of OS is relevant from climate impact and adaptation planning perspectives. This is particularly important for the practice of communicating climate impacts in terms of global warming levels \u003csup\u003e30\u003c/sup\u003e, which is problematic in OS scenarios given that the path to a given level of warming is an important determinant of climate outcomes. Our finding that degree-years of OS is a strong predictor of the effect of OS for several irreversible climate variables suggests that degree-years of OS could be used to predict the difference in climate outcomes between a stabilization scenario and an OS scenario for the most irreversible set of climate variables.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003eSCENARIOS\u003c/h2\u003e\u003cp\u003eWe use 42 pairs of scenarios from the ENGAGE project. In the ENGAGE project, Riahi et al. \u003csup\u003e31\u003c/sup\u003e developed pairs of scenarios using several IAMs where one scenario was constrained by a remaining carbon budget (RCB) that cannot be exceeded at any point before 2100 (i.e., the non-OS scenario) and one scenario where the same RCB could be temporarily exceeded but must be returned to by 2100 (i.e., the OS scenario). The RCB constraints in the 42 scenarios used range from 450 Gt CO\u003csub\u003e2\u003c/sub\u003e to 1600 Gt CO\u003csub\u003e2\u003c/sub\u003e. Forcing from non-CO\u003csub\u003e2\u003c/sub\u003e emissions was determined by assumptions embedded in individual IAMs, therefore IAMs simulated different temperature outcomes for the same RCBs. Pairs of scenarios in the ENGAGE ensemble were excluded from our analysis if: 1) annually averaged GSAT in the OS scenario failed to return to GSAT in the non-OS scenario before 2100, or 2) the OS scenario had less than one degree-year of OS. We did not need to control for internal climate variability using multi-year averages, since our results are averaged across an ensemble of scenarios and the intermediate complexity model we use does not exhibit much internal variability \u003csup\u003e27,32\u003c/sup\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eMODEL\u003c/h2\u003e\u003cp\u003eThe University of Victoria Earth System Climate Model (UVic-ESCM) is an intermediate complexity climate model with a spatial resolution of 3.8\u0026deg; of longitude and 1.8\u0026deg; of latitude \u003csup\u003e32\u003c/sup\u003e. The model couples atmospheric, oceanic, land surface, and sea ice components while maintaining relatively low computational demands compared to more complex Earth System Models \u003csup\u003e32\u003c/sup\u003e. The atmospheric component uses a two-dimensional single-layer energy-moisture balance model, effectively simulating large-scale heat and moisture transport without detailed atmospheric circulation \u003csup\u003e32\u003c/sup\u003e. Thus, surface wind and cloud albedo are both held static at prescribed values based off observations. In contrast to the atmosphere, the ocean representation is more comprehensive, featuring a three-dimensional general circulation model that resolves major ocean currents and includes dynamic sea ice and marine biogeochemistry modules \u003csup\u003e32\u003c/sup\u003e. The land component incorporates vegetation dynamics by simulating competition between five plant functional types (PFTs) \u0026ndash; shrubs, C3 and C4 grasses, and needleleaf and broadleaf trees \u0026ndash; and their response to environmental changes \u003csup\u003e32\u003c/sup\u003e. The land model is coupled to carbon cycle models representing the marine terrestrial carbon cycles \u003csup\u003e27,32\u003c/sup\u003e. The interactive carbon cycle includes physical and biological ocean carbon cycling, sedimentary carbon cycling, and a representation of land carbon via the forementioned PFTs, permafrost carbon storage, and soil carbon storage \u003csup\u003e27,33\u0026ndash;35\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe UVic-ESCM's coarse resolution and simplified atmosphere enable computationally efficient century-long simulations of ensembles of scenarios, making it well-suited for this study. However, two key limitations should be noted: 1) the non-dynamic atmosphere means changes in precipitation are not well captured, and 2) only thermosteric sea-level rise is represented. Therefore, changes in precipitation are ignored in this study and all sea-level rise results in this study refer exclusively to thermosteric changes.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eSIMULATIONS\u003c/h3\u003e\n\u003cp\u003eFuture simulations in the UVic-ESCM were driven by fossil and land use change CO2 emissions as well as aggregated non-CO2 forcing from the ENGAGE project, the latter being estimated using MAGICC31. Given that the scenarios from the ENGAGE project do not include spatially explicit land cover change 31, land cover in our simulations was held static at preindustrial values. Similarly, the scenarios used here do not include spatially explicit changes to aerosol emissions, so only the aggregate globally averaged forcing of aerosols is included. For consistency, the historical simulation used to calculate temperature anomalies in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA was emissions driven with static land cover and prescribed globally-averaged aerosol forcing. The combined non-CO2 greenhouse gas and aerosol forcing for the historical simulation was harmonized with the future scenarios non-CO2 GHG and aerosol aggregated forcing in the year 2015. Solar forcing was held constant in both the historical and future simulations. Volcanic forcing was included in the historical simulations, but was held constant at the average historical value after the year 2015.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eUNEP. \u003cem\u003eEmissions Gap Report 2023: Broken Record \u0026ndash; Temperatures Hit New Highs, yet World Fails to Cut Emissions (Again)\u003c/em\u003e. (United Nations Environment Programme, Nairobi, 2023). doi:10.59117/20.500.11822/43922.\u003c/li\u003e\n\u003cli\u003eSchleussner, C.-F. \u003cem\u003eet al.\u003c/em\u003e Overconfidence in climate overshoot. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e634\u003c/strong\u003e, 366\u0026ndash;373 (2024).\u003c/li\u003e\n\u003cli\u003eSchwinger, J., Asaadi, A., Steinert, N. J. \u0026amp; Lee, H. Emit now, mitigate later? Earth system reversibility under overshoots of different magnitudes and durations. \u003cem\u003eEarth System Dynamics\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 1641\u0026ndash;1665 (2022).\u003c/li\u003e\n\u003cli\u003eMacDougall, A. H., Zickfeld, K., Knutti, R. \u0026amp; Matthews, H. D. Sensitivity of carbon budgets to permafrost carbon feedbacks and non-CO2 forcings. \u003cem\u003eEnvironmental Research Letters\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 125003 (2015).\u003c/li\u003e\n\u003cli\u003eGasser, T. \u003cem\u003eet al.\u003c/em\u003e Path-dependent reductions in CO2 emission budgets caused by permafrost carbon release. \u003cem\u003eNat Geosci\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 830\u0026ndash;835 (2018).\u003c/li\u003e\n\u003cli\u003ede Vrese, P. \u0026amp; Brovkin, V. Timescales of the permafrost carbon cycle and legacy effects of temperature overshoot scenarios. \u003cem\u003eNat Commun\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 2688 (2021).\u003c/li\u003e\n\u003cli\u003eComyn-Platt, E. \u003cem\u003eet al.\u003c/em\u003e Carbon budgets for 1.5 and 2\u0026thinsp;\u0026deg;C targets lowered by natural wetland and permafrost feedbacks. \u003cem\u003eNat Geosci\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 568\u0026ndash;573 (2018).\u003c/li\u003e\n\u003cli\u003eTokarska, K. B. \u0026amp; Zickfeld, K. The effectiveness of net negative carbon dioxide emissions in reversing anthropogenic climate change. \u003cem\u003eEnvironmental Research Letters\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 094013 (2015).\u003c/li\u003e\n\u003cli\u003eEhlert, D. \u0026amp; Zickfeld, K. Irreversible ocean thermal expansion under carbon dioxide removal. \u003cem\u003eEarth System Dynamics\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 197\u0026ndash;210 (2018).\u003c/li\u003e\n\u003cli\u003eMathesius, S., Hofmann, M., Caldeira, K. \u0026amp; Schellnhuber, H. J. Long-term response of oceans to CO2 removal from the atmosphere. \u003cem\u003eNat Clim Chang\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e, 1107\u0026ndash;1113 (2015).\u003c/li\u003e\n\u003cli\u003eLi, X., Zickfeld, K., Mathesius, S., Kohfeld, K. \u0026amp; Matthews, J. B. R. Irreversibility of Marine Climate Change Impacts Under Carbon Dioxide Removal. \u003cem\u003eGeophys Res Lett\u003c/em\u003e \u003cstrong\u003e47\u003c/strong\u003e, (2020).\u003c/li\u003e\n\u003cli\u003eMacDougall, A. H. Reversing climate warming by artificial atmospheric carbon‐dioxide removal: Can a Holocene‐like climate be restored? \u003cem\u003eGeophys Res Lett\u003c/em\u003e \u003cstrong\u003e40\u003c/strong\u003e, 5480\u0026ndash;5485 (2013).\u003c/li\u003e\n\u003cli\u003eBoucher, O. \u003cem\u003eet al.\u003c/em\u003e Reversibility in an Earth System model in response to CO2 concentration changes. \u003cem\u003eEnvironmental Research Letters\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 024013 (2012).\u003c/li\u003e\n\u003cli\u003eZickfeld, K., MacDougall, A. H. \u0026amp; Damon Matthews, H. On the proportionality between global temperature change and cumulative CO2 emissions during periods of net negative CO2 emissions. \u003cem\u003eEnvironmental Research Letters\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 055006 (2016).\u003c/li\u003e\n\u003cli\u003eTokarska, K. B., Zickfeld, K. \u0026amp; Rogelj, J. Path Independence of Carbon Budgets When Meeting a Stringent Global Mean Temperature Target After an Overshoot. \u003cem\u003eEarths Future\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 1283\u0026ndash;1295 (2019).\u003c/li\u003e\n\u003cli\u003eKim, S.-K. \u003cem\u003eet al.\u003c/em\u003e Widespread irreversible changes in surface temperature and precipitation in response to CO2 forcing. \u003cem\u003eNat Clim Chang\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 834\u0026ndash;840 (2022).\u003c/li\u003e\n\u003cli\u003ePfleiderer, P., Schleussner, C.-F. \u0026amp; Sillmann, J. Limited reversal of regional climate signals in overshoot scenarios. \u003cem\u003eEnvironmental Research: Climate\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, 015005 (2024).\u003c/li\u003e\n\u003cli\u003eSchwinger, J., Asaadi, A., Goris, N. \u0026amp; Lee, H. Possibility for strong northern hemisphere high-latitude cooling under negative emissions. \u003cem\u003eNat Commun\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 1095 (2022).\u003c/li\u003e\n\u003cli\u003eHerrington, T. \u0026amp; Zickfeld, K. Path independence of climate and carbon cycle response over a broad range of cumulative carbon emissions. \u003cem\u003eEarth System Dynamics\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e, 409\u0026ndash;422 (2014).\u003c/li\u003e\n\u003cli\u003eJeltsch-Th\u0026ouml;mmes, A., Stocker, T. F. \u0026amp; Joos, F. Hysteresis of the Earth system under positive and negative CO2 emissions. \u003cem\u003eEnvironmental Research Letters\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 124026 (2020).\u003c/li\u003e\n\u003cli\u003eWei, T., Chen, Y. \u0026amp; Wang, H. Hysteresis of Northern Hemisphere permafrost to carbon dioxide emissions. \u003cem\u003eEnvironmental Research Letters\u003c/em\u003e \u003cstrong\u003e19\u003c/strong\u003e, 094032 (2024).\u003c/li\u003e\n\u003cli\u003eKeller, D. P. \u003cem\u003eet al.\u003c/em\u003e The Carbon Dioxide Removal Model Intercomparison Project (CDRMIP): rationale and experimental protocol for CMIP6. \u003cem\u003eGeosci Model Dev\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 1133\u0026ndash;1160 (2018).\u003c/li\u003e\n\u003cli\u003eAsaadi, A. \u003cem\u003eet al.\u003c/em\u003e Carbon cycle feedbacks in an idealized simulation and a scenario simulation of negative emissions in CMIP6 Earth system models. \u003cem\u003eBiogeosciences\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 411\u0026ndash;435 (2024).\u003c/li\u003e\n\u003cli\u003eMelnikova, I. \u003cem\u003eet al.\u003c/em\u003e Carbon Cycle Response to Temperature Overshoot Beyond 2\u0026deg;C: An Analysis of CMIP6 Models. \u003cem\u003eEarths Future\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, (2021).\u003c/li\u003e\n\u003cli\u003eKoven, C. D. \u003cem\u003eet al.\u003c/em\u003e Multi-century dynamics of the climate and carbon cycle under both high and net negative emissions scenarios. \u003cem\u003eEarth System Dynamics\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 885\u0026ndash;909 (2022).\u003c/li\u003e\n\u003cli\u003eDrouet, L. \u003cem\u003eet al.\u003c/em\u003e Net zero-emission pathways reduce the physical and economic risks of climate change. \u003cem\u003eNat Clim Chang\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 1070\u0026ndash;1076 (2021).\u003c/li\u003e\n\u003cli\u003eMengis, N. \u003cem\u003eet al.\u003c/em\u003e Evaluation of the University of Victoria Earth System Climate Model version 2.10 (UVic ESCM 2.10). \u003cem\u003eGeosci Model Dev\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 4183\u0026ndash;4204 (2020).\u003c/li\u003e\n\u003cli\u003eMillero, F. J., Lee, K. \u0026amp; Roche, M. Distribution of alkalinity in the surface waters of the major oceans. \u003cem\u003eMar Chem\u003c/em\u003e \u003cstrong\u003e60\u003c/strong\u003e, 111\u0026ndash;130 (1998).\u003c/li\u003e\n\u003cli\u003eLee, K. \u003cem\u003eet al.\u003c/em\u003e Global relationships of total alkalinity with salinity and temperature in surface waters of the world\u0026rsquo;s oceans. \u003cem\u003eGeophys Res Lett\u003c/em\u003e \u003cstrong\u003e33\u003c/strong\u003e, (2006).\u003c/li\u003e\n\u003cli\u003eIPCC, 2022: Summary for Policymakers. in \u003cem\u003eClimate Change 2022 \u0026ndash; Impacts, Adaptation and Vulnerability\u003c/em\u003e (eds. H.-O. P\u0026ouml;rtner et al.) 3\u0026ndash;34 (Cambridge University Press, Cambridge, UK and New York, NY, USA, 2022). doi:10.1017/9781009325844.001.\u003c/li\u003e\n\u003cli\u003eRiahi, K. \u003cem\u003eet al.\u003c/em\u003e Cost and attainability of meeting stringent climate targets without overshoot. \u003cem\u003eNat Clim Chang\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 1063\u0026ndash;1069 (2021).\u003c/li\u003e\n\u003cli\u003eWeaver, A. J. \u003cem\u003eet al.\u003c/em\u003e The UVic earth system climate model: Model description, climatology, and applications to past, present and future climates. \u003cem\u003eAtmosphere-Ocean\u003c/em\u003e \u003cstrong\u003e39\u003c/strong\u003e, 361\u0026ndash;428 (2001).\u003c/li\u003e\n\u003cli\u003eSchmittner, A., Oschlies, A., Matthews, H. D. \u0026amp; Galbraith, E. D. Future changes in climate, ocean circulation, ecosystems, and biogeochemical cycling simulated for a business‐as‐usual CO \u003csub\u003e2\u003c/sub\u003e emission scenario until year 4000 AD. \u003cem\u003eGlobal Biogeochem Cycles\u003c/em\u003e \u003cstrong\u003e22\u003c/strong\u003e, (2008).\u003c/li\u003e\n\u003cli\u003eMatthews, H. D., Weaver, A. J. \u0026amp; Meissner, K. J. Terrestrial Carbon Cycle Dynamics under Recent and Future Climate Change. \u003cem\u003eJ Clim\u003c/em\u003e \u003cstrong\u003e18\u003c/strong\u003e, 1609\u0026ndash;1628 (2005).\u003c/li\u003e\n\u003cli\u003eMacDougall, A. H. \u0026amp; Knutti, R. Projecting the release of carbon from permafrost soils using a perturbed parameter ensemble modelling approach. \u003cem\u003eBiogeosciences\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 2123\u0026ndash;2136 (2016).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Concordia University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Overshoot, climate impacts, AMOC, permafrost","lastPublishedDoi":"10.21203/rs.3.rs-7603499/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7603499/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIt is becoming increasingly likely that meeting the long-term temperature goal of the Paris Agreement will involve a period of temperature overshoot. Understanding the differences in climate outcomes between overshoot and non-overshoot scenarios requires an assessment of the reversibility of climate changes along an overshoot pathway. Using an intermediate-complexity Earth system model, we quantify the reversibility of a suite of climate variables and investigate the factors driving differences in reversibility across an ensemble of 42 pairs of overshoot and non-overshoot scenarios. For highly irreversible climate variables like permafrost and ocean changes, we show that the long-term outcome is linearly related to the time-integrated overshoot magnitude, which we define here as the degree-years of temperature overshoot. Our results show that degree-years of overshoot can be used to predict the changes of a range of irreversible ocean and permafrost variables in overshoot scenarios, therefore offering important insights into the difference in climate outcomes of overshoot compared to non-overshoot scenarios.\u003c/p\u003e","manuscriptTitle":"Irreversible climate changes driven by degree-years of temperature overshoot","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-16 16:56:40","doi":"10.21203/rs.3.rs-7603499/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"acb19930-849e-4b7d-89db-5e57ceb35556","owner":[],"postedDate":"September 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":54652877,"name":"Climate Analysis and Modeling"},{"id":54652878,"name":"Climatology"}],"tags":[],"updatedAt":"2026-01-09T22:05:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-16 16:56:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7603499","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7603499","identity":"rs-7603499","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}