Little evidence of hysteresis in regional precipitation, when indexed by global temperature rise and fall in an overshoot climate simulation

Climate change is still a major problem for society, particularly the need for a limit on greenhouse gas (GHG) emissions to prevent dangerous alterations to weather conditions. Upper levels of temperature change that should not be exceeded have been defined—specifically, 2.0 °C (or, in some cases, 1.5 °C [1]) of global warming since preindustrial times. However, achieving these targets requires rapid reductions in future emissions, which poses serious sociological, political and technical challenges [2]. For example, systems providing energy have long lifetimes [3], and even with the most ambitious transitions to non-fossil fuel sources, GHG emissions will likely take decades to reduce massively [4]. Hence, it is likely that prescribed global temperature thresholds will be breached [5, 6]. If society still wants to achieve stabilisation at lower levels, there may be a period of climate overshoot, when global mean temperatures are greater than the stabilization target. This raises a concern about whether a return to a lower temperature threshold (potentially by pervasive carbon capture and storage methods) will provide a safe climate. Specifically, during the overshoot period, the temporary high warming levels may trigger some parts of the climate system to switch to a different state that persists despite falling global temperatures. This is an example of hysteresis—the dependence of the state of a system on its history. Our focus here is whether patterns of rainfall are different as global temperatures decline compared to when they are increasing in an overshoot scenario.

Hysteresis is a type of nonlinearity and can be seen to be caused by system inertia which governs the response of components of the system to external forcings, resulting in a delayed system response as forcing increases and decreases. Hence, hysteresis may cause different rainfall features for the same amount of global warming during the heating and cooling overshoot phases. Moreover, hysteresis may be such that large global thermal overshoot causes components of the climate system to cross tipping points [7], which in turn could generate a stronger form of hysteresis where climate features are locked into a new state and stay there, even as global temperatures decline. The climate system is known to contain many feedbacks [8], where rising atmospheric GHG levels may affect parts of the Earth system in a way that slows or accelerates climate change.

The need for a temporary period of global warming above a desired threshold and a better understanding of the effect of hysteresis on the return to a safer climate is focussing attention on the simulation of overshoot scenarios using Earth System Models (ESMs)—see e.g. [9]. ESM components facilitate the investigation of the processes which influence the Earth's climate, and project their interactions with future scenarios of atmospheric GHG levels (see section 2 below for more details). Boucher et al [10] used the HadGEM2-ES model to examine hysteresis within an ESM, finding that most Earth system metrics exhibit hysteresis with respect to global temperature levels and atmospheric CO₂ concentration. Using the UVic Earth System Climate Model [11], MacDougall [12] examined the climate response to CO₂ removal and the effect of hysteresis in the global carbon pool. The hysteresis characteristics of the global carbon cycle depend on the rate of removal and climate sensitivity [13].

According to Mitchell et al [14], ESM results for the CMIP5 RCP2.6 scenario [15] indicate that the global precipitation rate keeps increasing after surface temperature has been stabilized at order 2.0 °C above pre-industrial levels (see their figure 1(a)). That analysis illustrates that the global Earth system has strong inertial characteristics, with an invigorated global hydrology cycle even for fixed global warming. Specifically, they demonstrate that there is not a unique one-to-one mapping between the level of global warming and global precipitation as climate remains in a transient state even after temperature is stabilised. By contrast, in their analysis of the results from the CMIP6 ScenarioMIP experiments [16], Tebaldi et al [17] find that an overshoot in temperature of a few decades around mid-century, as represented in the overshoot scenario SSP5-3.4-OS, does not influence the final result for temperature and precipitation changes in 2100. These quantities return to the same levels as those reached by SSP4-3.4, although Tebaldi et al acknowledge that other aspects of the system may not be as easily reversible.

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Mondal et al [18] recently made an assessment of the way extreme precipitation is affected by hysteresis, using the CESM1.2 ESM [19] to simulate a scenario where CO₂ is ramped up and then down again. They measure hysteresis by calculating the area under a curve which shows how the climate responds to changing forcing [20]. The curve is different for increasing and decreasing forcing, particularly in monsoon regions.

Here, we study the projections of annual mean temperature and rainfall as determined by five ESMs for SSP5-3.4-OS, a CMIP6 scenario involving a large overshoot in GHG concentrations and global warming. We differ from Mondal et al by analysing how rainfall levels change at the global and regional scale for the same levels of global warming—one during the period of rising temperatures, and one when temperature is falling. This does not explicitly consider any hysteresis effects in the relationship between GHG level and global mean temperature, as noted above, but we believe that using the degree of global warming is easier to relate to climate policy, since this often focusses on global warming levels and associated thresholds.

Our scenario of interest, SSP5-3.4-OS [16], prescribes CO₂ emissions associated with SSP5-8.5 up until the year 2040. Beyond 2040, SSP5-3.4-OS incorporates aggressive mitigation which reduces CO₂ emissions from a peak of approximately 70 Gt CO₂ in 2040 to zero in circa 2070, and to net negative levels thereafter. These emissions are converted [16, 21] into global mean atmospheric CO₂ concentrations using the MAGICC simple climate model. Hence, land-atmosphere and ocean-atmosphere feedbacks that affect atmospheric CO₂ are as simulated by MAGICC. It is these concentrations (along with the ScenarioMIP-provided concentrations for other long-lived GHGs such as CH₄ and N₂O) which force the ESM simulations whose results we assess here.

ESMs solve partial differential equations which emulate Earth's atmosphere, ocean, cryosphere and land, and include energy exchanges between these components. They predict how these exchanges are expected to change with varying amounts of GHGs. Importantly for climate adaption planning, ESMs also estimate how near-surface meteorology will change—both globally and regionally—in response to altered levels of radiatively-active gases. The most obvious 'weather' variation is increased temperatures as GHGs rise, which all ESMs project [22], but they also project substantially altered rainfall features in a warmer world [23], and this quantity is the focus of our investigations here.

SSP5-3.4-OS is classified [16] as a Tier 2 experiment—that is, it is not a requirement for modelling centres participating in ScenarioMIP. Hence only a subset of centres have run this scenario using their ESM. Furthermore, we consider only the (relatively small number of) SSP5-3.4-OS simulations which have been extended to 2300. The extension assumes [16, 21] that forcings continue to decline beyond 2100, eventually reaching the (low) levels associated with the extension to SSP1-2.6. It also assumes that the level of negative CO₂ emissions reached in year 2100 remains constant until 2140, when it is increased linearly to reach zero by 2170. Similarly, CO₂ emissions from land use are linearly increased [24] from their negative value at 2100 to zero at 2170, whilst aerosol emissions fall sharply at 2040 to a low value in 2070, decreasing to zero in 2250 [24]. Hence, the balance between aerosol and CO₂ forcings remains qualitatively constant throughout the scenario. Since GHGs are well-mixed whilst aerosols often generate more localised spatial temperature effects, the near-constancy of this ratio suggests that our findings of precipitation hysteresis effects are not caused by a difference in atmospheric gas composition in the warming and cooling phases of the overshoot. Using the extension allows us to more fully capture features in climatological response beyond the standard endpoint of 2100 specifed for many CMIP6 scenarios. This longer timeframe is likely to be important, as climate stabilisation after a mid-century overshoot may not occur until after the end of the century.

We have used the SSP5-3.4-OS extended run's results for UKESM1.0 [9, 25], IPSL-CM6A [26, 27], CESM2-WACCM [28, 29], MRI-ESM2-0 [30, 31] and MIROC-ES2L [32, 33] (see table 1), with a focus on near-surface temperature and precipitation rate (i.e. the CMIP database variables named tas and pr respectively). These quantities are presented as ΔT and ΔP, time-evolving anomalies with respect to the IPCC pre-industrial period (1850–1900). We consider the areal-average value of ΔT which acts as our forcing metric for global warming, and analyse ΔP at global and regional scales, examining their time series for evidence of hysteresis.

This section describes results from our analysis of ΔT and ΔP from UKESM1.0, before discussing the extent to which our findings are applicable to the four other ESMs. For brevity, we reserve the diagrams in the main the text for UKESM1.0, presenting corresponding figures for the other models in the supplementary material for this paper. Summary statistics for all models are presented in tables 1–3.

3.1. Global

Figure 1 displays time series for global area-weighted averages of ΔT and ΔP. Both variables increase with time up to circa 2070, before decreasing. We note from table 1 that y_{ΔT max}, the year at which ΔT peaks, is earlier than the equivalent year for maximum rainfall, y_{ΔP max}. This observation (y_{ΔT max} < y_{ΔP max}) is true for all models considered here (table 1), and is the first indication of a potential inertia in rainfall response to changing levels of global warming.

To proceed further, we determine two years at which there is an almost identical level of global warming: one (y₊) during the period of rising ΔT, and one (y₋) when it is falling. Throughout, when comparing mean properties for two years, we use values extracted from a 21 year rolling mean centred on each year, which obviates the effects of variability at interannual scales. After inspecting the behaviour of all models, we choose y₊ = 2043, since this falls near the rough midpoint of the temperature range during the period of increasing global warming. For UKESM1.0, the 21 year y₊-centred mean (i.e., for the years between 2033 and 2053) value for ΔT is 2.536 °C (see table 1). During the period of decreasing warming, this temperature is passed in the interval centred on y₋ = 2148, at which the 21 year centred mean of ΔT is 2.544 °C (for all models, our selected years are such that the relative difference between these two temperature anomalies is less than 1%). The double-headed horizontal arrow in figure 1 highlights the gap between the two years.

In addition to the lag between y_{ΔP max} and y_{ΔT max}, we see from figure 1 that ΔP has a smaller gradient, so it decreases more slowly than ΔT during its downward phase, again suggesting the potential for inertial effects in precipitation. To quantify whether the difference ΔP(y₋)–ΔP(y₊) is statistically significant, we detrend the precipitation values for each year in the two 21 year intervals by first subtracting the 21 year rolling mean centred on that year and then adding the mean value for the midpoint year of the interval. The detrended values are shown in the inset of figure 1 for increasing and decreasing intervals, with the dashed lines denoting the mean at y₋ and y₊. We then calculate [34] the t statistic and related p value from a t-test for the means of two independent samples of values. This is a test to see if the null hypothesis that the two samples have identical mean values can be rejected. For UKESM1.0 (see table 1), the large (absolute) value for t (−14.01) and the effectively zero value for p (5.17 × 10⁻¹⁷) confirm that the null hypothesis can be rejected. Hence, for global mean changes in precipitation, we conclude that the difference between the average expected values of the two samples is statistically significant. This finding is consistent with the noticable difference between the two curves in the inset of figure 1. The t and p values for the other models in table 1 also show that ΔP(y₋)–ΔP(y₊) is statistically significant. We therefore conclude that, for these models on a global scale, there is an inertia in precipitation response to global temperature changes in an overshoot setting.

We visualize the same data presented in figure 1 differently in figure 2, which shows ΔP plotted against ΔT, including the 21 year centred rolling mean and highlight the same 21 year intervals, centred on y₊ and y₋ used in figure 1. Here, the fact that ΔP both decreases more slowly than ΔT and that its maximum is delayed, implies that after around year 2070, a clear hysteresis loop emerges—that is, for a given ΔT, the value of ΔP post-2070 is greater than the corresponding value on the pre-2070 branch of the curve. The double-headed arrow illustrates the gap between the two branches of the loop at y₊ and y₋, where for almost identical values of global mean ΔT, global mean ΔP differs by ΔP(y₋)–ΔP(y₊) = 0.053 mm d⁻¹ for UKESM1.0 (see table 1). Beyond around 2150, ΔP and ΔT have a smaller dependence on time, (corresponding to the flatter stabilisation period in figure 1), converging to around ΔP = 0.15 mm d⁻¹, ΔT = 2.4 °C for UKESM1.0.

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3.2. Regional

We next study the overshoot projections at the regional scale—in particular, the extent to which our global findings remain applicable at more local scales. Figure 3 shows the spatial distribution of the 21 year centred mean of ΔP—as determined by UKESM1.0—for y₊ and y₋ (top and middle panels), and the difference ΔP(y₋)–ΔP(y₊) (bottom panel). Points with the largest absolute values for the difference are mostly concentrated around the tropics, here marked as a full latitudinal band of −20° ⩽ ϕ ⩽ 20°. The tropical Pacific (for which 102°E ⩽ λ ⩽ 56°W) has also been highlighted as a region that contains much of the differences.

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Figures 4 and 5 show the time evolution of the area-weighted average anomalies for global near-surface temperature (as seen previously in figures 1 and 2) and precipitation rate in the tropical Pacific region, from UKESM1.0. A comparison with figures 1 and 2 shows that ΔP still increases with time up to around 2070, but now decreases more slowly. However, the regional data has much more interannual variability than the global, due to the smaller number of grid points in the regional sample, likely resulting in a lower amount of spatial cancelling of anomalies compared to the global statistics (see below). For this region, we note from table 2 that y_{ΔT max} is earlier than y_{ΔP max}—i.e. peak temperature is reached before peak precipitation (as was the case on the global scale) for all models apart from MIROC-ES2L (for which y_{ΔP max} is only slightly smaller than y_{ΔT max}).

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For this region, the size of the difference ΔP(y₋)–ΔP(y₊) as calculated by UKESM1.0 is 0.111 mm d⁻¹ (see table 2), which is greater than that for ΔP averaged over the globe—partly because the region we have selected deliberately contains the largest absolute values for this difference. However, despite these larger differences for regional amounts of rainfall for near-identical temperatures the interannual variability is also substantially larger and overwhelms these differences. This large variability makes it harder to discern the gap between the rising and falling ΔT branches in figure 5 and the overlap between the highlighted intervals centred on y₊ and y₋. Once again, we display the overlap (in the inset to figure 4) as the detrended precipitation values for the two intervals, together with the results of a t-test for the means of the two samples. A comparison with the inset to figure 1 shows that the degree of overlap between the intervals is greater for this region, so generating a smaller (absolute) value for t (−1.45) and larger value for p (0.156). The larger variability prevents rejection of the null hypothesis that there is no statistically significant difference between the average expected values of the two samples. Results from other ESMs for this region are summarised in table 2, and are consistent with those for UKESM1.0 in that t has decreased and p has increased compared to global mean ΔP(y₋) versus ΔP(y₊). The p values range from 0.0252 (IPSL-CM6A) to 0.981 (MIROC-ES2L), indicating moderate to no evidence against the null hypothesis of no difference between ΔP(y₋) and ΔP(y₊) for this tropical Pacific location.

For this overshoot scenario, our analysis shows that we have observed hysteresis in the annual mean precipitation rate averaged over the globe, but not for the tropical Pacific region. We now consider an intermediate region of all points in latitudinal range −20° ⩽ ϕ ⩽ 20°—i.e. the complete tropical zone in figure 3. For brevity, we do not show the equivalent plots, but summarise their characteristics for all models in table 3. We find y_{ΔT max} < y_{ΔP max} for all models, and also see values for t and p which, for each model, fall between those for the globe (table 1) and the tropical Pacific (table 2). They show that, for this larger region, four models show a statistically significant difference between the average expected values of the samples of ΔP centred on y₋ and y₊. The exception is MIROC-ES2L, which has values for t (−1.36) and p (0.18) that are comparable with those for UKESM1.0 in the tropical Pacific—i.e. for this model, there is no statistical significance for ΔP(y₋)–ΔP(y₊) in the tropical region.

GHG emissions remain sufficiently high that it may be difficult to constrain mean global warming to key targets such as 1.5 °C [5] or 2.0 °C above pre-industrial levels. Hence, if stabilisation of global warming at such targets is still desirable, a period of global temperature overshoot may occur [35]. Alternatively, society may place less initial emphasis on remaining below temperature targets, but global warming could reach levels discovered as dangerous for many populations. Society may then attempt to instigate strong emission cuts, or even initiate negative overall CO₂ emissions, lowering temperatures and following an warming overshoot path. Such overshoots could be large, especially in the latter scenario. Yet it is only recently that the research community has begun to run simulations associated with a substantial peak in temperature.

Understanding the implications of temporary warming peaks is important because the Earth system is believed to include tipping points. Although some tipping points may have high levels of inertia, allowing a temporary change in temperature that would otherwise cause their activation, others could be triggered at substantially higher levels of global warming [36]. Such non-linearity could cause attributes of the climate system to lock into irreversible states, or have inertial features with timescales comparable to overshoot duration. Both possibilities of hysteresis imply that features of the climate system may be different, for the same global temperature, depending on whether the system is in the warming or cooling phase. Many researchers offer evidence of hysteresis effects—for instance, changes to the land surface that cause land-atmosphere feedbacks to lock climate into a new state, even as warming reverses. Examples include the greening of the Sahara [37], the loss of snow cover [38], or the potential inability of the Amazon rainforest to return to its current state [39]. These behaviours will break correlations between local near-surface meteorological conditions and the background level of global warming. Understanding these differences is critical for adaptation planning, if global mean temperatures follow an overshoot trajectory. However, where they exist, these effects introduce an additional dimension to the projection of climate impacts as they are not simply related to the level of global warming.

We have analyzed features of precipitation from simulations by five ESMs forced by SSP5-3.4-OS. This scenario corresponds to a relatively high peak in global warming before subsequent decline. We have focussed on changes in global mean near-surface temperature and precipitation rate at different geographical scales, and the relationship between them. We use global warming as our metric of climate change as it relates strongly to global policy aspirations (i.e. eventual stabilisation levels). Geographical changes to precipitation affect the future probabilities of drought or flood occurrence and freshwater availability. For all models, we have found evidence of hysteresis [18, 20] in the areally-averaged global mean precipitation. For two periods of near-identical levels of global warming, one when temperatures are rising and one when temperatures fall, we find the latter has higher levels of mean precipitation. Put simply, the world has a potential to be wetter on any return path in global temperature after warming has peaked. Both time periods of comparison are of 21 years and the t-test (95% confidence level) suggests that the means of the two periods are different.

A difference map of the 21 year mean rainfall for the same two periods of near-identical global warming provides details about local contributions to global differences, with the largest discrepancies in the tropics. For the entire tropics, we again find a statistically significant higher rainfall for the decreasing global temperature period (in a similar fashion to the global rainfall) for four out of five ESMs assessed, although the significance level is quantitatively lower. If we restrict attention to only a longitudinal sector of the Earth's tropical region centred on the Pacific (which contains the largest differences), we cannot reject the null hypothesis (confidence level of 95%) that mean precipitation is different for rising and falling temperatures. We note that our rainfall change results for the tropical region are more germane for adaption planning than those for the tropical Pacific region, which is mostly oceanic.

It is harder to identify hysteresis in local precipitation differences for near-identical global temperature levels because interannual variability is larger at smaller spatial scales. Indeed, when searching for differences in rainfall in individual gridboxes (i.e. over all points in figure 3), for all ESMs, there are no locations where the difference between annual mean precipitation values for rising and falling temperatures is statistically significant. We acknowledge that selecting an averaging interval which is greater than one year would smooth out this variability—for example, using five years would remove effects of the El Niño-Southern Oscillation—and give rise to other potentially stronger conclusions about statistically significant differences. However, we have focussed on interannual variability as it is frequently year-to-year variations which have the strongest societal impacts, and our approach places longer-term hysteresis effects in the context of such yearly fluctuations. The effect of uncertainty caused by interannual variability could also be reduced by performing an ensemble of runs for the SSP5-3.4-OS scenario. A statistically significant difference between average precipitation levels for rising and falling temperatures could be detected with a sufficiently large ensemble. However for many potential overshoot scenarios, the Earth will pass through these periods of similar temperature quickly, and so the high variability can be expected to cause the rainfall levels during the two intervals to be statistically indistinguishable. Hence, regarding annual precipitation, adaptation policy should be predominantly concerned with the background level of global warming, irrespective of whether such warming is rising or decreasing.

We acknowledge three important caveats. Firstly, our analysis is only for a limited set of ESMs, and we hope that our analysis will encourage more model runs within an overshoot-type framework in the planning for CMIP7 [40]. Secondly, our particular scenario peaks and returns relatively quickly—i.e. within decades, rather than over centuries. If a scenario reaches much higher global warming levels and remains there for longer, a more substantial alteration of Earth system components is expected. These changes may involve strong nonlinearities from which the system may not recover during the period of falling temperatures. Major changes in Earth system features which persist during any declining global warming may modulate any links between large-scale global temperature levels and local climate features during the period of rising warming values. Hence, we encourage modelling groups to simulate overshoot scenarios which incorporate different maximum temperatures and a range of durations at peak warming level. Our third caveat is that the link between climate forcings and global temperature may contain hysteresis effects, even if these are not present in a mapping between global warming and local climate. Specifically, if the linkages between regional meteorological conditions and overshoot in GHG levels or radiative forcing are investigated, stronger hysteresis effects may be observed. There are long timescales, especially oceanic, which break any one-to-one link between radiative forcing (i.e. altered overall composition of radiatively-active gases) and global temperature, and so by definition between radiative forcing and precipitation. For instance, substantial ongoing changes in regional temperature and precipitation patterns have been simulated [41] for stabilised global net-zero CO₂ emissions and related slowly-changing CO₂ levels. Indeed, global precipitation may continue to increase even after a peak in CO₂ concentration has been passed [42]. However, our selection in this paper of global mean temperature rather than radiative forcing 'factors out' many of these longer-timescale effects. We reiterate that this focus on global temperature in our background definition of overall change ties in with the basis for most climate policy being eventual stabilisation at key global mean warming thresholds and the identification of pathways to them [6]. Finally, we acknowledge the effect of other forcing components—including aerosol emissions [43]—on precipitation levels. Their variations are similar to those for CO₂ emissions in this overshoot scenario [24]. However, revisiting our analysis using GHG-only overshoot simulations (as they become available) would formally reveal the extent to which aerosols have any additional regional impacts—beyond hysteresis due to other factors—on the mapping between global temperature and regional precipitation.

We have studied ESM simulations which have been forced by a substantial overshoot scenario, causing an large peak in global warming. At the local level, we find little evidence of statistically different annual mean precipitation levels for similar amounts of global warming in the upward and downward temperature phases. Little or no hysteresis during an overshoot period removes an important 'degree-of-freedom' from climate impacts assessments. This simplification is important when trying to determine the implications of initially missing a global temperature threshold, as it allows a simpler mapping to global temperature without having to refer to other aspects of a global warming path such as its history.

J W and C H are both grateful for financial support from the NERC TerraFIRMA project (Grant reference NE/W004895/1). In addition, J W acknowledges support from the Met Office Hadley Centre Climate Programme funded by DSIT. We thank Colin Jones and two anonymous referees for their helpful comments on our work.

The original CMIP6 data for this study is available on the Earth System Grid Federation at https://esgf.llnl.gov [25, 27, 29, 31, 33].

The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.5281/zenodo.10523162 [44].

The authors declare that there is no conflict of interest regarding the publication of this article.