Peak shaving with solar radiation modification would shorten global temperature overshoot

Abstract

Projected rates of emissions reductions are unlikely to keep global temperatures from crossing the Paris Agreement temperature targets. Large-scale carbon dioxide removal (CDR) could help recover a target temperature after it has been exceeded, producing an overshoot scenario. Solar radiation modification (SRM) is the idea to cool the planet by increasing the reflection of incoming solar radiation. SRM could be used in an overshoot scenario for ‘peak shaving’, where SRM is deployed to maintain a temperature target during the overshoot. Here, we quantify the effect of SRM peak shaving on the duration of the overshoot using an adapted extension of the SSP2-4.5 scenario and an ensemble of variants of the FaIR simple climate model. We find a substantial reduction in overshoot duration, which ranges from approximately 5% for multi-decade overshoots up to approximately 20% for multi-century overshoots. The shortening is predominantly driven by the ocean response to peak shaving. Peak shaving results in lower ocean temperatures relative to the overshoot scenario, inducing a stronger surface temperature response to decreasing and negative emissions, driving overshoot shortening. Thus, SRM, when deployed as a complement to emissions reductions and CDR, could end overshoot decades earlier than otherwise.

Introduction

Through the Paris Agreement in 2015, almost every nation agreed to limit global average temperature increases to well below 2°C above pre-industrial levels, while pursuing efforts to not exceed 1.5°C [1]. By the end of 2024, global surface temperatures have risen approximately 1.31°C above the 1850 to 1900 baseline, according to the real-time global warming index from Haustein et al. [2]. The planet is projected to surpass the 1.5°C target in less than a decade [3], and temperatures are expected to warm further, reaching an estimated 2.7°C by the end of this century under a moderate emissions (SSP2-4.5) scenario [4]. This is significantly above the upper limit of the Paris Agreement, motivating research into novel climate policy options, including carbon dioxide removal and solar radiation modification [5].

Carbon dioxide removal (CDR) is the anthropogenic removal of CO₂ from the atmosphere to long-term storage [6]. CDR in some form is required to drive the reduction in temperature under an overshoot scenario. Several approaches are being explored. Direct air carbon capture and storage (DACCS), which involves extracting CO₂ from ambient air using chemical sorbents [7], is arguably the leading technology for large-scale CDR [8]. DACCS is primarily limited by the costs associated with its high energy demand [9], with cost estimates ranging from $100 to $1,000 per ton of carbon removed [10]. CDR technologies such as DACCS currently remove 1.35 MtCO₂ per year [11], less than 0.01% of current annual global CO₂ emissions [12]. However, large-scale CDR is expected to play a more significant role in future climate strategies [13]. Two of the five illustrative scenarios from the latest IPCC Working Group 1 Assessment Report [4] feature net negative emissions (requiring CDR): SSP1-1.9 and SSP1-2.6, with roughly –14 and –9 GtCO₂ per year by 2100, respectively. The maximum potential of global CDR has been estimated to be about 35 GtCO₂ per year [14]. The global capacity for underground CO₂ storage for CDR, while deeply uncertain [15], has been estimated at between 5,000 and 25,000 GtCO₂, which is greater than the expected long-term global demand [16].

Solar radiation modification (SRM), also known as solar geoengineering, is the idea to cool the planet by increasing the reflection of incoming solar radiation back out to space [17]. Stratospheric aerosol injection (SAI) is a leading approach for SRM deployment [18]. It would aim to mimic the cooling effect of large volcanic eruptions by creating a layer of reflective aerosols in the stratosphere [19]. The leading engineering approach for SAI deployment suggests using a fleet of specially designed aircraft to loft aerosols (or their precursor gases) into the stratosphere [20]. The cost of this has been estimated at about $18 billion per year for each 1°C of cooling, which is inexpensive relative to mitigation, adaptation, and CDR technologies [21].

SAI has the potential to offset temperature changes caused by global warming [22], but it would not affect temperature in isolation. It would cause a reduction in global mean precipitation [23], potentially causing worsened droughts in some areas already particularly vulnerable to climate hazards [24]. There would also be several other side effects, including worsened acid rain in some regions [25] and delayed ozone hole recovery [26]. There are several other issues related to the advancement and potential deployment of SRM in general, including concerns over its governability [27], mitigation deterrence or ‘moral hazard’ [28], and termination shock—the harms associated with its sudden cessation [29]. These issues pose significant challenges relating to the feasibility and risks of SRM.

Net negative emissions through CDR would enable temperature overshoot scenarios, in which a temperature target is exceeded but later recovered [30]. Temporary overshoot came to relevance given the apparent inevitability of exceeding the 1.5°C temperature target of the Paris Agreement; most scenarios assessed by the IPCC which achieve 1.5°C by the end of the century initially overshoot that threshold [31]. Even if temperatures return gradually to a given target level, the higher temperatures during the overshoot period would have lasting effects and irreversible consequences, such as extinctions [31]. ‘Peak shaving’ refers to the deployment of SRM to cap temperatures at a certain threshold while greenhouse gas concentrations are reduced [32]. This is commonly framed as a method of ‘buying time’ for mitigation and adaptation [33]. It has been argued to be the only acceptable form of SRM deployment [34], since indefinite deployment would, among other issues, substantially increase the risk of termination shock [35]. However, the plausibility of peak shaving is not guaranteed [36]—it requires the implementation of large-scale and long-term CDR and SRM in tandem, a prospect some consider a high-risk speculation [37]. Acknowledging this, it remains important to explore scenarios involving these emerging technologies to allow for a more holistic analysis of potential pathways to mitigate climate risks.

Previous studies [38, 39] modelling a peak-shaving scenario have shown, but not discussed, that the SRM deployment can be ended before the threshold temperature would have been recovered without peak shaving. We term this phenomenon ‘overshoot shortening’, and this study aims to both quantify this effect and analyse the mechanisms behind it. We consider two potential drivers of overshoot shortening, both related to the broader climatic effects of avoided increases in temperature under peak shaving.

Firstly, the carbon cycle response to peak shaving is proposed as a potential driver. Most models agree that there is a positive carbon–climate feedback due to climate change reducing the net efficiency of carbon sinks [40]. The land and ocean have each removed about a quarter of anthropogenic CO₂ emissions from the atmosphere [41], but the efficacy of these sinks is changing as the climate changes. The response of the land carbon sink to climate change is obscured by uncertain compensatory effects [42], while global warming causes a clear reduction in the efficiency of the ocean carbon sink due to strengthened ocean stratification and reduced thermohaline circulation [43]. The avoided increases in temperature following SRM deployment would strengthen carbon sinks through several mechanisms [44, 45]. For example, the relatively lower temperatures would reduce the rate of heterotrophic respiration (i.e. decomposition), increasing soil carbon retention [46]; suppress permafrost thaw, limiting the associated carbon releases [47]; and cool the ocean surface, increasing ocean CO₂ solubility [48]. As a result, atmospheric carbon dioxide would likely be reduced under a peak-shaving scenario compared the overshoot scenario, which would drive overshoot shortening.

Secondly, a relative reduction in ocean heat content as a result of peak shaving is another potential driver of overshoot shortening. The ocean plays a key role in regulating climate changes, dampening surface warming by absorbing and storing vast amounts of both heat and CO₂ [49]. Ocean warming has accounted for 91% of global heat content increases since 1971 [4]. Ocean heat uptake is controlled by the interaction of several processes, including ocean circulation (currents driven by wind and buoyancy), stratification (layering due to density differences), and ventilation (downwelling from near-surface to deep ocean) [50]. Although literature on the effect of peak shaving on ocean heat content is lacking, large volcanic eruptions have been found to have long-term effects on the climate through their impact on ocean heat uptake [51]. We propose that increases in ocean temperatures would be partially avoided under a peak-shaving scenario, which could drive overshoot shortening.

Methods

The model

This study uses version 2.1.4 of the Finite-amplitude Impulse Response (FaIR) model [52]. It is a reduced complexity climate model, comprising a set of six equations, capable of capturing the global mean temperature response to greenhouse gas and aerosol emissions. FaIR is a zero-dimensional model of globally averaged variables, designed to emulate the behaviour of more complex Earth system models, while avoiding their large computational expense. The model features a carbon cycle but does not represent permafrost thaw. The energy balance model in FaIR comprises three layers, corresponding to a surface, upper ocean, and deep ocean.

This study uses a calibrated, constrained ensemble of model parameters [53] that reproduces both historic observations and assessed climate metrics consistent with the IPCC WG1 Sixth Assessment Report [4]. The ensemble comprises an 841-member posterior created from a 1.6 million-member prior ensemble. 199 members were filtered out because their projections either did not exceed the temperature threshold for overshoot by at least 0.1°C or did not return below it by 2500 (within the time frame of this study). A further 39 members were filtered out due to irregular behaviour of the feedback controller (discussed in Supplementary Text S1), leaving the final ensemble for this study with 603 members. For the entire ensemble, the median of the maximum temperature anomaly without SRM under our adjusted SSP2-4.5 scenario was 2.60°C with a 5th to 95th percentile range of 1.87°C to 3.81°C. The corresponding values for the final ensemble are 2.69°C and 2.16°C to 3.51°C.

A key model parameter for this study is the carbon cycle sensitivity to temperature change, which modulates the strength of the carbon sink based on changes in temperature. The value of this parameter varies across the ensemble, with a median of 2.1 K$−1$⁠, and 5th to 95th percentile range of –1.1 to 5.9 K$−1$⁠, where positive values mean a decrease in strength of carbon sink with increasing temperature. See Leach et al. [52] equations 1–4 for the definition of this parameter, labelled $rT$⁠. The upper ocean heat transfer coefficient is a second key parameter in this study. It defines the efficacy of heat transfer at the ocean–atmosphere interface, which is between the first and second layers of our three-layer energy balance model—see equations 1–4 of Cummins et al. [54]. This value also varies across the ensemble, with a median of 1.2 Wm$−2$ K$−1$ and a 5th to 95th percentile range of 0.9 to 1.7 Wm$−2$ K$−1$⁠.

The scenarios

In order to analyse the effect of peak shaving, a scenario with a pronounced overshoot is required. We select the SSP2-4.5 scenario as a moderate scenario, consistent with current climate policies [55]. In order to provide an overshoot, we adapted an extension of this scenario from Meinshausen et al. [56], as shown in Supplementary Fig. S1. We adjust their idealised extension so fossil and industry CO₂ emissions maintain the trajectory of the standard SSP2-4.5 scenario, reaching net zero in 2130, rather than 2250. This divergence is attributed in part to the implementation of more drastic CDR. Beyond 2130, emissions continue to decline at the same rate, reaching –10 GtCO₂ per year in 2155, remaining constant thereafter. This is consistent with the projections for CDR and storage potential detailed in the introduction. These adjustments create an overshoot scenario, where temperatures exceed and recover the upper temperature target of the Paris Agreement [1] within the scenario time frame (up to 2500). Although substantial uncertainties arise when modelling over such an extended time frame [57], this approach allows for a quantitative analysis of peak shaving under one potentially plausible scenario.

Peak shaving requires a threshold temperature at which global temperature anomalies are capped through the use of SRM. For this study, it was set at 2°C of warming relative to the 1850–1900 baseline, corresponding to the upper limit of the Paris Agreement temperature targets [1]. The year-by-year amount of SRM forcing required to keep to the threshold temperature was computed using a feedback controller—the proportional-integral-derivative (PID) algorithm [58]—which is discussed in Supplementary Text S1. SRM was implemented in the model through the volcanic forcing input, which serves as an analogue for SAI forcing. This study compares two scenarios: an overshoot scenario without the deployment of any SRM (‘OS’ from here on), and a peak-shaving scenario where SRM is deployed to maintain the threshold temperature of 2°C during the overshoot (‘PS’ from here on).

Results

Overshoot shortening

Figure 1 shows the temperature responses for a single model configuration to illustrate the concept of this study. The OS temperature anomaly can be seen to exceed the threshold temperature (at Line 1) and later recover it (at Line 3). The PS temperatures are capped until SRM is no longer required in order to keep below the threshold temperature (at Line 2). This occurs before the threshold temperature is recovered under the OS scenario, demonstrating overshoot shortening, which is quantified by the difference between the years indicated by Lines 2 and 3. For this illustrative case, the overshoot of 340 years is shortened by 60 years—an 18% reduction. The SRM forcing, which is implemented through volcanic forcing, deviates from zero in 2042 when the threshold temperature is reached and PS temperatures separate from OS. After reaching a maximum of approximately –5.4 Wm$−2$⁠, it returns to zero when SRM deployment is ended in 2322, aligning with when PS temperatures decline from the threshold temperature.

Alternative illustrative temperature profiles are presented in Supplementary Fig. S2 for scenarios where net negative emissions do not continue beyond the end of the overshoot. For the case of net zero emissions from the point of the threshold temperature being recovered under OS, temperatures rebound by approximately 0.05°C for the alternative OS scenario, and approximately 0.12°C for the alternative PS scenario.

Figure 2 shows the temperature profiles for the ensemble. The median year for exceeding the 2°C threshold is 2059, which is consistent with the results for the SSP2-4.5 scenario from the Coupled Model Intercomparison Project Phase 6 (CMIP6) simulations [4]. The OS temperatures exhibit a broad range of overshoots, and the PS temperatures display effective peak shaving. However, the threshold temperature is exceeded by up to 0.2 K for some ensemble members at the beginning of SRM deployment. This is due to a slight deficiency in the feedback controller, as discussed in Supplementary Text S1. For the ensemble (median values provided with the 5th to 95th percentile range), the overshoot of 231 years (91–417 years) is shortened by 40 years (7–91 years)—a 17% (8%–22%) reduction.

Figure 3 presents the percentage overshoot shortening under the PS scenario plotted against the OS overshoot duration. Every member of the ensemble has its overshoot shortened under PS compared to OS. Although there is considerable spread, an increasing trend in percentage shortening with overshoot duration can be seen from roughly 5% to 20%. The increasing trend spans from OS overshoot durations of about 60 to 300 years. Judging from this Figure, a 100-year overshoot would be shortened by approximately 8% (2–15%, 5th to 95th percentile range), equivalent to 8 years (2–15 years), and a 300-year overshoot would be shortened by approximately 20% (13–26%), equivalent to 60 years (39–78 years). The colour gradient across the plots displays a horizontal trend, indicating a positive correlation between OS temperature overshoot and overshoot duration. The OS temperature overshoot accounts for approximately 3% of the variance in the vertical spread of data points about the trend line. This suggests the relationship between OS temperature overshoot and PS overshoot shortening is largely indirect, mediated through OS overshoot duration. The PS and OS overshoot durations are compared more directly in Supplementary Fig. S3. OS overshoot durations span a range of 91–417 years (5th to 95th percentile) with median 231 years, which shorten to 84–325 years with median 192 years under the PS scenario.

Carbon cycle response

The atmospheric CO₂ concentration profiles under each scenario are shown in Fig. 4. PS and OS follow closely aligned trends, with PS remaining slightly below OS from the onset of SRM deployment. The average difference between the two scenarios increases up to a maximum of 2.5 ppm in 2143 (shortly after peak OS temperatures), and steadily decreases over time thereafter. By 2500, the average difference between the scenarios is minimal, at approximately 0.1 ppm. This difference between the scenarios is due to the lower PS temperatures causing a relative increase in the efficiency of carbon sinks. This response is controlled by the carbon cycle sensitivity to temperature change parameter. This parameter varies across the ensemble and its influence on CO₂ concentrations is shown in Supplementary Fig. S4. We find no evidence for a significant correlation between the percentage overshoot shortening and the carbon cycle sensitivity to temperature change parameter (P-value: 0.45). A scatter plot is shown in Supplementary Fig. S5. The variation in overshoot shortening across the ensemble in our study therefore does not depend on the carbon cycle response to peak shaving.

Ocean response

Figure 5a shows a negative correlation between the OS overshoot duration and the upper ocean heat transfer coefficient. Figure 5b shows a negative trend between the overshoot shortening and this coefficient, although the spread is fairly broad. The 5th percentile coefficient value of 0.9 Wm$−2$ K$−1$ corresponds approximately to an overshoot duration of 373 years and a shortening of 22%, while the 95th percentile coefficient value of 1.7 Wm$−2$ K$−1$ corresponds approximately to a duration of 115 years and a 10% shortening.

The median temperature responses of the three model layers (surface, upper ocean, and deep ocean) are compared in Fig. 6. In a similar format to Fig. 2, the ensemble temperature profiles for each model layer are shown in Supplementary Fig. S6. For OS temperatures, the ocean layers can be seen to follow similar trends as the surface, but with delayed and diminished temperature responses, particularly for the deep ocean. The delay in reaching peak OS temperatures, measured from when surface OS temperatures peak, is 43 years for the upper ocean and 163 years for the deep ocean. PS temperatures remain lower than OS temperatures from the onset of SRM deployment for all three model layers. After 2300, this disparity is more distinct for the ocean layers, particularly the deep ocean, compared to the surface. The ocean layers are also slower to cool than the surface for both OS and PS scenarios. In 2500, the deep ocean layer has greater OS and PS temperature anomalies than the upper ocean layer, which in turn has greater anomalies than the surface layer. Once OS and PS ocean temperatures start to decline, the rate of cooling is greater under OS compared to PS, indicating that the ocean is losing heat less quickly under PS and thus the heat flux to the surface is smaller.

Figure 7a shows the median cooling under PS compared to the OS scenario for each model layer. The magnitude and timing of peak cooling varies between the layers. For the surface, upper and deep ocean layers respectively, the peak cooling is roughly 0.7 K in 2130, 0.6 K in 2140, and 0.4 K in 2210. At the median year of ending SRM deployment (2250), PS cooling is roughly 0.2 K, 0.3 K and 0.35 K. After this point, greater cooling continues to be seen in the ocean layers, particularly the deep ocean, compared to the surface. This is indicated in panel b by the negative cooling difference after the ‘SRM end’ point. The initially positive values here indicate the ocean layers being cooled less than the surface, while the negative values indicate the opposite.

Discussion

This study analysed the effect of peak shaving with SRM on the duration of the overshoot with an ensemble of variants of the FaIR model, using an adapted extension of the SSP2-4.5 scenario. Every member of the ensemble had its overshoot shortened by peak shaving, with longer overshoots having a greater proportional shortening up to about 20% (Fig. 3). Overshoot shortening as a result of peak shaving is exhibited in other studies [38, 39]. While these studies did not quantify the shortening, their findings are qualitatively similar to the results of this study (Fig. 3), despite using different scenarios and climate models.

Overshoot shortening implies a shorter SRM deployment period than would be assumed based on the background emission scenario’s projected overshoot duration. A shorter deployment would, compared to a longer one, reduce the exposure to side effects of SRM, such as the impacts on precipitation, acid rain, and ozone hole recovery, as discussed in the introduction. It would also slightly lessen the risk of termination shock, since there would be less time for disruptions to arise [29]. However, in line with the findings of Baur et al. [59], we stress that peak shaving at 2°C under our extension of SSP2-4.5 could still require a multi-century commitment to SRM, despite overshoot shortening.

With peak shaving ending (in the median case) decades before the overshoot, the cumulative net negative emissions by the end of peak shaving would be hundreds of GtCO₂ lower than by the end of the overshoot. However, as shown by Supplementary Fig. S2, net negative emissions would need to continue beyond the end of SRM deployment in order to stay below the threshold temperature. Peak shaving would bring temperatures to within the threshold in advance of some of the net negative emissions effort and the associated costs.

Carbon cycle response

The carbon cycle response to peak shaving is explored as a potential driver of overshoot shortening. There is a marginal difference between the atmospheric CO₂ concentration profiles of the OS and PS scenarios (Fig. 4). The peak average difference of 2.5 ppm corresponds to emissions of roughly 19.5 GtCO₂ [60], slightly over half current annual CO₂ emissions [12]. According to the IPCC 6th Assessment Report [4], each 1,000 GtCO₂ of cumulative CO₂ emissions induces an estimated warming of 0.45°C, meaning this CO₂ difference corresponds to less than 0.01°C of temperature difference. The cooling effect of the carbon cycle response to peak shaving is therefore being outweighed by another factor in driving the overshoot shortening. This is supported by the lack of correlation between the carbon cycle sensitivity to temperature change parameter and the overshoot shortening (Supplementary Fig. S5), indicating the carbon cycle response has minimal influence on the overshoot shortening in our results.

However, the FaIR model does not capture key processes relevant to the carbon cycle response to peak shaving. For example, permafrost thaw is not accounted for since the majority of the models it was calibrated on do not include it. The latest IPCC report estimates that each 1°C of global warming would release approximately 11–150 GtCO₂ from permafrost thaw [61]. The carbon cycle response to peak shaving would therefore be underestimated, as reasonably significant avoided CO₂ emissions are not accounted for. Judging from the peak PS cooling for the median overshoot and the peak mean difference in CO₂ concentrations, accounting for permafrost thaw would increase the OS–PS atmospheric CO₂ difference by between approximately 40% and 520%. Zhao et al. [45] investigated the carbon cycle response to SAI under a similar scenario (stabilising temperatures under SSP2-4.5 at 1.5$°$C until 2069) using an earth system model with a permafrost component. They found that an SAI cooling of approximately 0.8°C (0.1°C more than the median of this study) increases cumulative carbon uptake by 92 GtCO₂. This value is significantly larger than the corresponding 19.5 GtCO₂ figure from this study but falls within the above-stated range when accounting for permafrost thaw.

Ocean response

The ocean response to peak shaving appears to be the primary factor causing the overshoot shortening. There is a clear correlation between the overshoot shortening and the upper ocean heat transfer coefficient (Fig. 5b). However, there also is a clear correlation between the coefficient and the OS overshoot duration (Fig. 5a), which is in turn correlated with the overshoot shortening (Fig. 3). The coefficient may therefore only have an impact on overshoot shortening through its relationship with the OS overshoot duration.

The ocean response can also be investigated by inspecting the temperature profiles of the ocean layers (Fig. 6). The temperature effects of peak shaving extend beyond the surface to the ocean, which could be driving overshoot shortening through the ocean’s relationship with surface temperatures. Under the OS scenario, ocean temperatures increase and then decrease, implying the ocean changes from a heat sink (energy transfers from the atmosphere to the ocean) to a heat source (energy transfers from the ocean to the atmosphere). While acting as a heat source, the ocean inhibits the decrease in surface temperatures in response to net negative emissions. Under the PS scenario, ocean temperatures remain lower, peak later, and, once they decrease, do so at a slower rate compared to OS. The ocean under PS therefore acts as a heat sink for longer and subsequently as a weaker heat source. This induces a stronger surface temperature response to net negative emissions, as ocean heat uptake is prolonged and a weaker ocean heat source results in a weaker inhibition of decreasing global temperatures. This causes faster cooling, causing overshoot shortening. After the end of SRM deployment, PS surface temperature remains markedly lower than OS for centuries due to the reduced ocean temperatures (Fig. 7).

This can also be understood through the Held et al. [62] framing of fast and slow components of global warming. In the case of SRM deployment, there is a fast component of cooling as the surface quickly responds to the negative forcing. The slow component relates to the ocean heat content, whereby the negative forcing causes an anomaly in ocean heat storage, which affects surface temperatures over a longer time frame. A similar effect is explored by Stenchikov et al. [51], who note that changes in ocean heat uptake caused by large volcanic eruptions affect the climate over decades, separately to the short-term surface temperature response to volcanic forcing. This presents a parallel to SRM deployment, and our results indicate a slow cooling component in addition to the fast surface response.

Our ocean response results are limited by the simplicity of the FaIR model. The energy balance model in FaIR comprises just three layers, representing a surface, upper ocean, and deep ocean. This broad simplification fails to capture many important complexities related to the ocean’s response in this study. For example, changes in ocean circulations, such as the Atlantic Meridional Overturning Circulation (AMOC), are not adequately represented. The AMOC is sensitive to temperature changes and, if disturbed, would impact ocean heat uptake [63] and ocean carbon uptake [64]. The AMOC plays a significant role in the climate’s nonlinear response to an overshoot scenario [65], which would also be relevant to this study.

Limitations and further research

The complexity of the FaIR model is low, even compared to other simple climate models [52]. While it is able to emulate the behaviour of more complex models, there are drawbacks to its simplicity. It is highly parameterised and simulates globally averaged systems, meaning many processes and regional differences are not captured in the model. Also, the scenario, as shown in Supplementary Fig. S1, follows a single emissions pathway. We expect our findings to remain qualitatively similar across different overshoot scenarios, given the physical mechanisms underlying the response. However, different pathways would lead to overshoots with different OS temperature profiles, likely impacting the quantitative response to peak shaving.

The modelled scenarios depend on large-scale CDR and SRM, neither of which are certain prospects, and both remain distant from large-scale deployment. Furthermore, our scenario spans a multi-century time frame, in contrast to most climate projections, which finish at 2100 [66]. While this is necessary for an analysis of multi-century overshoots, the scenario uncertainty increases substantially over such an extended time frame [57].

Further research could conduct the analysis of this study using more and more complex climate models. This could be carried out in future phases of the Reduced Complexity Model Intercomparison Project (RCMIP) [67] or the Geoengineering Model Intercomparison Project (GeoMIP) [68], which could be achieved by adapting and extending the newly proposed G6-1.5K-SAI experiment [69]. Future studies using earth system models [70] could address many of the limitations of the FaIR model. Future work could also model a broader range of emissions scenarios and threshold temperatures to further explore overshoot shortening. Lastly, further insights regarding the ocean response to peak shaving could be gained from the analysis of energy fluxes into and out of the ocean.

Conclusions

This study has analysed the shortening of global temperature overshoot under a peak-shaving scenario with SRM deployment. We used an ensemble of variants of the FaIR simple climate model and an adapted extension of the SSP2-4.5 scenario. In the absence of SRM, temperature overshoots 2°C in this scenario for 91–417 years (5th to 95th percentile) with median 231 years. With SRM deployed to limit warming to 2°C, this is shortened to 84–325 years with median 192 years. We find that the overshoot shortening ranges from approximately 5% for multi-decade overshoots up to approximately 20% for multi-century overshoots. Our results thus suggest that deploying SRM alongside emissions cuts and CDR would substantially accelerate the end of temperature overshoot.

This study has also explored the mechanisms behind overshoot shortening through peak shaving. The carbon cycle response to peak shaving is relatively minor in this study, and it was determined that its role in driving the overshoot shortening is minimal. Instead, we attribute the overshoot shortening effect primarily to the ocean temperature response. This is due to peak shaving resulting in comparatively lower ocean temperatures, which induces a stronger surface temperature response to decreasing and negative emissions. This causes expedited cooling due to peak shaving, resulting in overshoot shortening. This study provides an initial analysis of overshoot shortening through peak shaving with SRM and serves as a basis for future studies to explore the subject further.

Acknowledgments

The authors would like to thank Chris Smith (Vrije Universiteit Brussel) for his timely and helpful support with FaIR model functionalities and troubleshooting.

Author contributions

Linus Boselius (Data curation [lead], Formal analysis [lead], Methodology [equal], Software [lead], Visualization [lead], Writing—original draft [lead], Writing—review & editing [equal]), Alistair Duffey (Methodology [equal], Project Administration [supporting], Software [supporting], Supervision [supporting], Writing—review & editing [equal]), and Peter J. Irvine (Conceptualization [lead], Methodology [equal], Project administration [lead], Supervision [lead], Writing—review & editing [equal])

Supplementary data

Supplementary data is available at Oxford Open Climate Change online.

Conflict of interest: None declared.

Funding

LB’s contribution was in part funded by the University College London MAPS Summer Research Internship scheme. AD’s contribution was funded by the London Natural Environment Research Council (NERC) Doctoral Training Partnership (DTP) Grant NE/S007229/1.

Data availability

The FaIR model and instructions for its use are publicly available at https://docs.fairmodel.net. SSP scenario data are publicly available at https://tntcat.iiasa.ac.at/SspDb. The Meinshausen et al. (2020) scenario extensions are publicly available at https://greenhousegases.science.unimelb.edu.au

References