Regional temperature extremes and vulnerability under net zero CO₂ emissions

The ZECMIP, a sub-project of CMIP6 (Eyring et al 2016), was designed to quantify temperature change following a complete cessation of CO₂ emissions (i.e. the ZEC), and to investigate the geophysical drivers behind the climate response to CO₂ emissions cessation (Jones et al 2019). Note, ZEC can be evaluated from emissions cessation of only CO₂ (MacDougall et al 2020), non-CO₂ gases such as CH₄ or N₂O (Matthews and Zickfeld 2012), or all anthropogenic emissions (Hare and Meinshausen 2006). However, on decadal timescales, ZEC from ceasing emission of all forcing agents tends to converge to ZEC values from cessation of only CO₂ emissions which makes ZECMIP a reasonable choice given the simulation lengths of participating ESMs.

In this work, ZECMIP experiment esm-1pct-brch-1000 PgC (called experiment A1 from hereon) was used, which corresponds to about 2 °C CO₂-induced warming relative to pre-industrial (Jones et al 2019). Experiment A1 sets CO₂ emissions to zero once cumulative CO₂ emissions reach 1000 PgC, after which models are allowed to freely evolve for at least 100 years. Table S1 shows the ESMs included in the analysis with expanded model descriptions available in Table A1 of MacDougall et al (2020); note, GFDL-ESM2M was the original submission to ZECMIP but has since been replaced by results from GFDL-ESM4. The models included in this analysis are the nine that were available on the Earth System Grid Federation Australian node as of January 2022.

ZEC is defined as the change in global temperature projected to occur following a complete cessation of CO₂ emissions (Matthews and Weaver 2010, MacDougall et al 2020). In this report, ZEC is quantified over multi-decadal intervals on a global average and an individual grid level (latitude–longitude) basis. Figure 1 shows a simple schematic which illustrates how ZEC is quantified using data from the MIROC-ES2L model as an example. In figure 1, the 1pctCO2 portion of the experiment is represented by the blue curve, which is initialized at the pre-industrial condition for each model. The red curve represents the temperature evolution following a complete cessation of carbon dioxide emissions, which occurs at time ${t_{NZ}}$ in figure 1. The near-surface air temperature (tas) variable is used.

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The CMIP variable for near surface air temperature (tas) is used for all temperature calculations. For each model in the ensemble, the baseline net zero climatology, ${\overline {{\text{tas}}} _{NZ}}$ from figure 1, is computed using a 20 year window centered at the time of branching denoted ${t_{NZ}}$; the 20 year baseline climatology is computed as the mean climate bounded by upper and lower bounds illustrated by the blue shaded time frame along the 1pctCO2 curve in figure 1. Once the baseline climatology is known, global ZEC time series are then computed for each model using equation (1):

$$\begin{equation}{\text{ZEC}}\left( t \right) = \overline {{\text{tas}}} \left( t \right) - {\overline {{\text{tas}}} _{NZ}}\end{equation} \tag{ 1 }$$

where ${\text{ZEC}}\left( t \right)$ is the time series representing the difference in global mean surface temperature evaluated at time $t$ and the baseline climatology ${\overline {{\text{tas}}} _{NZ}}$. Figures S1 and S2 in the supplementary information show the global mean surface temperature anomalies and global ZEC time series for the nine ESMs, respectively. Comparable ZEC time series can be found in MacDougall et al (2020) figure 2(b).

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To compute regional changes in ZEC, 20 year climatologies are computed for three unique time periods following emissions cessation. In this research, 20 year climatologies are centered at 25, 50, and 90 years after emissions cessation, consistent with previous research (MacDougall et al 2020, 2022). The three ZEC time frames are centered about ${t_{25}}$, ${t_{50}}$, and ${t_{90}}$, respectively as shown in figure 1; the three ZEC time frames are illustrated by the red shaded portions of the net zero CO₂ portion (red curve) shown in figure 1. Regional (lat, lon) distributions of ZEC for each ZEC time window (ZEC₂₅, ZEC₅₀, ZEC₉₀) are then computed using equation (2):

$$\begin{equation}{\text{ZE}}{{\text{C}}_Y}\left( {{\text{lat,lon}}} \right) = {\overline {{\text{tas}}} _Y}\left( {{\text{lat,lon}}} \right) - {\overline {{\text{tas}}} _{NZ}}\left( {{\text{lat,lon}}} \right)\end{equation} \tag{ 2 }$$

where ${\overline {{\text{tas}}} _Y}\left( {{\text{lat,lon}}} \right)$ is the near-surface air temperature at each grid point (lat, lon) averaged over a 20 year window centered at the year defined by subscript Y (subscripted years include 25, 50, and 90). ${ }{\overline {{\text{tas}}} _{NZ}}\left( {{\text{lat,lon}}} \right)$ is the baseline climatology defined as an averaged 20 year window centered at the time associated with the net zero branch, ${t_{NZ}}$. Figure S3 shows baseline climatologies for each of the nine participating ESMs. Equation (2) is applied for each model within the ensemble (n = 9). Figures S4–S6 show the spatial distribution of ZEC₂₅, ZEC₅₀, and ZEC₉₀ for the nine models included in the ensemble, respectively. As highlighted in MacDougall et al (2022), there are significant differences in regional projections of ZEC especially in high-latitudes. The significant differences in regional ZEC projections are noteworthy when considering ensemble mean results, especially in areas such as Arctic latitudes where the largest spread between the models in the ensemble exists.

We assess how high temperature extreme events will evolve after net zero carbon dioxide emissions are achieved by investigating how temperatures during location-specific hottest months change after CO₂ emissions cessation. Local monthly hot temperature extreme thresholds are calculated using the means and standard deviations of the local monthly maximum temperature determined from the pre-industrial control simulation. Monthly temperature data was used so that all nine models could be included in the analysis. Similar methods have been used to study the historical precedence of the 2021 Pacific Northwest heatwave (Neal et al 2022). To compute extreme thresholds for local monthly maximum temperature extremes, first, the calendar month associated with local maximum monthly temperature was determined for each model using the pre-industrial control runs. Figure 2(A) shows a map with the distribution of months associated with maximum near surface air temperature using the MIROC-ES2L model as an example. Maps of the month associated with maximum temperature were also created for the other models and can be found in figure S7.

After determining the month associated with monthly maximum temperature for each grid cell, ensemble means and standard deviations ($\sigma$) are computed for each grid cell's month of maximum temperature. Distributions of mean and standard deviation of local monthly maximum temperature from the piControl simulation are shown in figures 2(B) and (C), respectively. Peak mean temperatures are primarily located over tropical and mid latitude land surfaces. Standard deviation, which is indicative of natural variability in the unforced pre-industrial control experiment, is largest over land surfaces, with generally lower variability in the tropical latitudes. Thresholds of local monthly temperature extrema are then computed for each standard deviation level ($\sigma$-level) using equation (3):

$$\begin{align}&{\text{ta}}{{\text{s}}_{N\sigma }}\left( {{\text{mo}}{{\text{n}}_{{\text{max}}}},{\text{lat, lon}}} \right)\nonumber\\ & \quad = \overline {{\text{tas}}} \left( {{\text{mo}}{{\text{n}}_{{\text{max}}}}{\text{, lat, lon}}} \right) + N*{\sigma _{{\text{tas}}}}\left( {{\text{mo}}{{\text{n}}_{{\text{max}}}}{\text{, lat, lon}}} \right)\end{align} \tag{ 3 }$$

where ${\text{ta}}{{\text{s}}_{N\sigma }}$ represents monthly extreme temperature distribution at a given $\sigma$-level,${ }\overline {{\text{tas}}}$ represents the local (lat, lon) mean near surface air temperature for the month of maximum temperature, and ${\sigma _{{\text{tas}}}}$ is the standard deviation of local (lat, lon) monthly maximum temperature. In the standard deviation term (second term, right hand side), the multiplier $N$ is used to compute specific $\sigma$-level extreme thresholds. For this research, $1\sigma$ through $3\sigma$ extreme thresholds are considered for hot temperature extremes ($N$ = 1, 2, or 3). As an example of a grid-based extreme temperature calculation, figure 2(D) depicts the mean and extreme thresholds $1\sigma$–$3\sigma$ for the closest grid cell over Melbourne, Australia (38° S, 144° E) using the MIROC-ES2L model. The data is specific to the pre-industrial control simulation restricted to the local month of maximum temperature (computed as February over Melbourne for the MIROC-ES2L ESM).

Frequencies of local (lat, lon) monthly hot temperature extreme exceedance are computed for the net zero baseline climatology (20 year window centered at the time of branching denoted ${t_{NZ}}$ from figure 1), and for the ZEC₂₅ and ZEC₉₀ 20 year windows. The frequencies of monthly temperature extremes for the 20 year ZEC time frames and the 20 year baseline climatology express the percentage of years (out of 20) that a local grid cell exceeds local $\sigma$-level thresholds. Changes in frequency of local monthly hot temperature extremes are computed for the ZEC₂₅ and ZEC₉₀ 20 year time frames using equations (4) and (5):

$$\begin{align}&\Delta {f_{{\text{ZEC}}{{25}_{N\sigma }}}}\left( {{\text{lat, lon}}} \right) = {f_{{\text{ZEC}}{{25}_{N\sigma { }}}}}\left( {{\text{lat, lon}}} \right) - {f_{NZ}}_{N\sigma }\left( {{\text{lat, lon}}} \right)\end{align} \tag{ 4 }$$

$$\begin{align}&\Delta {f_{{\text{ZEC}}{{90}_{N\sigma }}}}\left( {{\text{lat, lon}}} \right) = {f_{{\text{ZEC}}{{90}_{N\sigma { }}}}}\left( {{\text{lat, lon}}} \right) - {f_{NZ}}_{N\sigma }\left( {{\text{lat, lon}}} \right)\end{align} \tag{ 5 }$$

where ${f_{{\text{ZEC}}{{25}_{N\sigma { }}}}}$ and ${f_{{\text{ZEC}}{{25}_{N\sigma { }}}}}$ are local (lat, lon) frequencies of $\sigma$-level (N = 1, 2, or 3) monthly temperature extremes for the ZEC₂₅ and ZEC₉₀ 20 year time windows, respectively. ${f_{NZ}}_{N\sigma }$ represents local (lat, lon) frequencies of $\sigma$-level (N = 1, 2, or 3) monthly temperature extremes for the 20 year net zero baseline climatology (centered at t_NZ from figure 1). Differences in extreme frequency over the century after emissions cessation are computed by subtracting the frequencies during the ZEC₉₀ time window by frequencies during the ZEC₂₅ time window.

Changes in local monthly cold extremes were also investigated. The methodology for defining cold extremes follows a similar approach as determining hot extremes, however for cold extremes, the $\sigma$-level thresholds are based on local minimum monthly temperatures determined for each grid cell. Additionally, extreme thresholds are computed using −0.25$\sigma$, −0.5$\sigma$, and −1$\sigma$ for cold extremes because comparable thresholds to those used for the hot extremes analysis are rarely achieved after the simulated warming from the 1pctCO2 phase of the idealized experiment. Changes at these $\sigma$-levels are not always considered as extreme, however trends in −0.25$\sigma$, −0.5$\sigma$, and −1$\sigma$ sigma level events will suggest changes in frequency of 'colder-than-average' cold months following net zero. Additionally, although the extreme level thresholds used for cold extremes here are less than thresholds used for heat extremes, cold extreme events at $- 1\sigma$ thresholds can cause damage and are still studied in current research (Dai et al 2021). For consistency with the local monthly hot extreme convention used in this research, we refer to changes in cold month frequencies as 'cold extremes' throughout the paper. The supplemental material includes an analysis and illustration that shows the method for computing local monthly cold extreme thresholds using a similar approach to the local monthly heat extreme analysis captured in figure 2. Figure S8 in the supplementary material shows the distribution of local coldest months for the nine ESMs. Using the MIROC-ES2L ESM as an illustrative example, figure S9 in the supplementary material shows distribution of months associated with minimum local near surface air temperatures, mean near surface air temperature distribution from pre-industrial control associated with local minimum month, standard deviation distribution of near surface air temperatures from pre-industrial control associated with local minimum month, and pre-industrial control mean near surface air temperature and computed extreme levels—$0.25\sigma$ through −$1\sigma$ for grid cell over Melbourne, Australia.

Less economically developed regions experience disproportionate loss and damage from climate extremes such as heatwaves, floods, and tropical storms (Gamble et al 2016, Birkmann et al 2022) To improve understanding of how the frequency of temperature extremes might affect populations with different levels of vulnerability following CO₂ emissions cessation, the relationship between local monthly maximum temperature extremes and local HDI was explored. HDI is a unique multidimensional measure of development and serves as an important alternative to some traditional single dimensional measures of development such as gross domestic product (Sagar and Najam 1998). HDI is a composite measure that considers length and health of life, access to education, and standard of living (Kummu et al 2018). HDI was chosen for this study as a measure of socioeconomic development because the HDI includes social indicators as well as economic development. Figure S10 shows the 2015 HDI distribution used in this study. HDI changes over time due to developments such as improvements in regional economic markets, increased access to healthcare, and advancements in local education. However, projections of HDI have not been developed in accordance with the CO₂ emissions cessation scenario used under the ZECMIP framework. Therefore, static regional HDI values based on the recent 2015 dataset from Kummu et al (2018) are used here. The HDI dataset from Kummu et al (2018) has been used in other studies examining inequality of climate change impacts (e.g. Lieber et al 2022).

To provide a comprehensive projection of how ZEC varies spatially within the ensemble, median ZEC distributions for ZEC₂₅ and ZEC₉₀ time windows are shown in figures 3(A) and (B), respectively. The median was chosen here to avoid skewing regional results from the limited sample size (n = 9) towards outliers such as the CESM2 model which shows a strong inter-hemispheric temperature gradient after CO₂ emissions cessation. The inter-hemispheric relationship exhibited by CESM2 is shown in the supplemental material Figures S4–S6, and is also shown in figure 3 of MacDougall et al (2022). Additionally, to evaluate the change in ZEC over the century following carbon dioxide emissions cessation, the regional difference between median ZEC₉₀ and ZEC₂₅ was computed and is shown in figure 3(C). If at least eight of the nine ESMs show agreement in the sign of ZEC (or sign of change in ZEC in the case of figure 3(C)) then this corresponds to p-value <0.05 (calculated using the binomial distribution) and is taken to be statistically significant. Figure S13 in the supplemental material shows an illustration of the fundamental binomial distribution with a nine-model sample size. Although ESMs are not entirely independent (Knutti et al 2013), the ESMs participating in ZECMIP have a large diversity of component sub models as shown in tables A1 and A2 from MacDougall et al (2020).

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The ZEC distributions show cooling or warming responses between −0.5 °C and 0.5 °C with significant regional variation consistent with previous work from MacDougall et al (2022). The global mean surface temperature decline 0.07 °C by the ZEC₂₅ time frame and continues to decline an additional 0.14 °C over the century after CO₂ emissions cessation. An ensemble median global mean surface temperature drop of 0.16 °C over the century after CO₂ cessation is noteworthy considering the scale of global surface temperature goals established in the Paris Agreement (<2 °C above pre-industrial levels with efforts to limit to 1.5 °C). The model-specific global ZEC results are available in table S1 in the supplementary material. The regional ZEC distributions show a rapid cooling response over land with continued cooling as the ZEC time window reaches ZEC₉₀, with the largest land surface cooling occurring in the Northern Hemisphere. The largest warming is projected in the northeast Pacific Ocean, and Southern and Indian Ocean roughly between longitudes 70° W (Cape Horn, Chile) and 175° E (New Zealand). Overall, land exhibits greater cooling than the ocean likely because of differences in oceanic and land heat capacities, where land show quicker recovery to pre-industrial temperatures than ocean areas (MacDougall et al 2022). It is also possible that changes in local feedbacks and the hydrological cycle causes greater cooling over land than the ocean (Joshi et al 2008). There is an initial cooling by ZEC₂₅ followed by a rebound in near-surface air temperature over the century after ZEC₂₅ in the North Atlantic. This is possibly due to the evolution of Atlantic Meridional Overturning Circulation projected by the models; results from MacDougall et al (2022) suggest diverse evolution of AMOC between the models with some models showing an AMOC strengthening by the end of the century after CO₂ emissions cessation.

The ESMs show significant agreement of cooling over land, with increasing area of the planetary surface having significant model agreement by the ZEC₉₀ time frame. There is also significant model agreement of cooling in tropical Atlantic, Indian, and western Pacific Oceans seen in the ZEC₉₀ figure 3(B); this strong cooling agreement is driven by continued temperature changes between ZEC₉₀ and ZEC₂₅ as captured by the cross-hatching in figure 3(C). There is significant warming agreement within the ensemble shown as a sharp band of warm sea surface temperatures in the Southern and Indian Oceans spanning between longitudes 70° W–175° E in the ZEC₂₅ and ZEC₉₀ time windows. The continued warming in the Southern Ocean after CO₂ emissions cessation is possibly due to delayed circumpolar upwelling and equatorward transport (Armour et al 2016). In terms of continued warming between ZEC₂₅ and ZEC₉₀ time frames (figure 3(C)), there is negligible warming agreement between the ESMs in the ensemble. Figure S11 in the supplementary material includes mean ZEC distributions, the additional ZEC₅₀ time frame, and shows the ensemble spread in ZEC for each time window. There is significant spread of ZEC values regionally with the highest spread located in high latitudes quite possibly due to different model representations related to AMOC and sea-ice coverage (MacDougall et al 2022).

Most participating ESMs ran a single ensemble member for the ZECMIP A1 experiment, however two of the nine ESMs ran the experiment with three members (UKESM1-0-LL and CanESM5). As an additional analysis, ZEC regional distributions of the two models with multiple ensemble members were examined to understand how variability within the models compare to mean changes in regional ZEC₂₅ and ZEC₉₀ patterns. Figures S15 and S19 show regional ZEC projections for each model member (n = 3) for CanESM5 and UKESM1-0-LL, respectively. For the CanESM5 data, the three simulations tend to show large land areas with ZEC positive/negative sign agreement during the ZEC₉₀ time frame, but less so in the ZEC₂₅ time frame. The UKESM1-0-LL members show large areas of ZEC positive/negative sign agreement for both ZEC₂₅ and ZEC₉₀ time frames. Further investigation is needed to determine more accurate projections of regional ZEC using larger sets of multi-member ensembles than are currently available.

Once $1\sigma$ through $3\sigma$ local monthly temperature extreme thresholds were computed for each model in the ensemble using methods described in section 2.3, changes in frequencies of local maximum monthly temperature extreme exceedances were computed using the 20 year ZEC₂₅ and ZEC₉₀ time frames using equations (4) and (5). Figure 4 shows frequencies of $1\sigma$ through $3\sigma$ local monthly heat extremes during the net zero baseline climatology, the changes in frequencies of $1\sigma$ through $3\sigma$ local monthly heat extremes during the ZEC₂₅ and ZEC₉₀ time frames, and the change in frequency between ZEC₉₀ and ZEC₂₅ time frames.

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During the 20 year net zero baseline time frame, land-based grids exhibit very high frequency of local monthly heat extremes for the 1$\sigma$ threshold. For 2$\sigma$ and 3$\sigma$ thresholds, highest frequencies of local monthly heat extreme exceedances during the net zero baseline climate time frame are largely shown in tropical latitudes due to low variability in the tropics (Hawkins et al 2020, Mahlstein et al 2011). When the ZEC₂₅ time frame is reached, most land surfaces exhibit either no change or a large-scale initial decline in frequency of local monthly heat extreme following CO₂ emissions cessation with some exceptions such as areas of Northern Asia and midwestern North America. In the ZEC₂₅ time frame, there are greater decreases in frequencies of land-based monthly heat extremes for 2$\sigma$ and 3$\sigma$ thresholds than the decreases in frequencies for the 1$\sigma$ threshold, especially in tropical latitudes. Although land-based initial reductions in frequency of local monthly heat extremes (especially for 2$\sigma$ and 3$\sigma$ thresholds) are evident in many regions, the areas of largest initial decline in frequency of local monthly heat extreme frequency are over land in the Northern Hemisphere. While frequencies of land-based extremes tend to decline during the ZEC₂₅ time frame, large oceanic regions have a projected increase in frequency of local monthly heat extremes after CO₂ emissions cessation; specifically, the South Atlantic, Indian Ocean, and Southern Ocean have areas where frequency of local monthly heat extremes are projected to increase with significant model agreement south of Australia. The pattern of increasing oceanic frequencies in the Southern Hemisphere resembles changes in regional ZEC₂₅ shown in figure 3(A).

By the ZEC₉₀ time frame, there are widespread reductions in frequency of 2$\sigma$ and 3$\sigma$ local monthly heat extreme with the largest frequency reductions over land in the Northern Hemisphere. For each extreme threshold, areas of model significance emerge in the ZEC₉₀ time frame over land in the Northern Hemisphere. Changes in local monthly heat extreme frequencies during the ZEC₂₅ and ZEC₉₀ time frames closely follow the mean state regional ZEC₉₀ patterns (figure 3(B)) where large-scale land cooling is accompanied by warming in the Southern and Indian Ocean south of Australia.

There are continued reductions in land-based local monthly heat extreme frequencies for the remainder of the century after ZEC₂₅ shown in figures 4(J)–(l). These continued reductions in local monthly heat extreme frequencies resemble the land response in near-surface air temperature shown in figure 3(C). Despite large land regions showing reductions in heat extreme frequency, there are virtually no areas with significant model agreement. After a small initial decline in frequency of local monthly heat extremes in the northern North Atlantic (especially for 1$\sigma$ and 2$\sigma$), heat extremes in the northern North Atlantic show a rebounding trend after ZEC₂₅ time frame shown in figures 4(J)–(l). This northern North Atlantic rebounding trend is also evident in regional ZEC patterns in figure 3 which is possibly due to evolution in AMOC after CO₂ emissions cessation.

Supplementary analysis was done to analyze regional patterns of local monthly heat extreme changes using the two participating ESMs with multiple simulation members (UKESM1-0-LL and CanESM5). Analysis for the two models was performed using identical methods as for the single member analysis discussed in the methods section, and results are found in supplementary information. The results show similar spatial patterns for extreme frequency changes between the three members of each model ensemble, however there are areas where the members show differences in sign changes of local monthly heat extremes; additional members for each ESM would help improve understanding of changes in heat extremes after CO₂ emissions cessation.

Once 0.25$\sigma$–1$\sigma$ local monthly cold temperature extreme thresholds were computed for each model in the ensemble, the change in frequencies of local minimum monthly temperature extreme exceedances were computed using the 20 year ZEC₂₅ and ZEC₉₀ time frames the same way as above for monthly warm extremes. Figure 5 shows the ensemble median frequencies of local monthly cold extremes, changes in frequencies of local monthly cold extremes after CO₂ emissions cessation, and trends in frequency over the remainder of the century after ZEC₂₅ computed as the difference in frequency during ZEC₉₀ and ZEC₂₅ time frames.

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There are virtually no areas where local monthly cold extreme frequencies are elevated during the net zero baseline climatology because of large-scale warming prior to emissions cessation. Note, maps in figure 5 are based on ensemble medians of local cold monthly frequencies, however, there are areas that show slight increases in ensemble mean local cold monthly extremes during the net zero baseline climatology as shown in figure S14 of the supplemental material; these areas are clearest over high-latitude grids in the Atlantic Ocean possibly due to reduced meridional heat transport from weakening AMOC strength during the 1pctCO₂ emissions phase of the experiments.

After CO₂ emission cessation, local monthly cold temperature extremes become more frequent in many extratropical land areas. The most obvious signals are seen in the −0.25$\sigma$ and −0.5$\sigma$ thresholds over North America, Europe, Northern Asia, Greenland, southern South America, Australia, and Antarctica. At the −1$\sigma$ threshold, changes in frequency are very subtle with small frequency increases over Northern Hemisphere land, Antarctica, the northern North Atlantic, and the Southern Ocean; this is because, for all models, global mean temperatures exceed 1 °C warming relative to pre-industrial levels following the 1pctCO2 ramp-up phase of the experiment (see figure S1 in supplementary material). Areas with significant ensemble agreement (eight or more ESMs) of increased local monthly cold extreme frequency are clearest over Northern Hemisphere land, and over Antarctica for −0.25$\sigma$ and −0.5$\sigma$ threshold. There are negligible areas with significant ensemble agreement at the −1$\sigma$ threshold because it is rare to exceed the 1$\sigma$ threshold at elevated global mean temperature.

Over the remainder of the century after the ZEC₂₅, there are large areas of increasing frequency of local monthly cold extremes, as high as 10%, which are again most evident in the mid-to-high latitudes in North America and northern Asia. There are also regions with reduction in frequency of cold extremes over the remainder of the century after ZEC₂₅; for each $\sigma$ threshold, the northern North Atlantic ocean exhibits decreased frequency of local monthly cold extremes after the initial increased frequency shown in the ZEC₂₅ time frame. Similar to frequencies of local monthly heat extremes, there are very limited areas of significant ensemble agreement (8 or more ESMs) of increasing or decreasing frequency of cold extremes over the remainder of the century after ZEC₂₅.

Figure 6 shows ensemble median frequency of local hot monthly temperature exceedance during net zero baseline climatology (A)–(C), ensemble median change in frequency of local hot monthly temperature extreme exceedance plotted against HDI for land-based grid cells for the ZEC₂₅ (D)–(F), and ZEC₉₀ (G)–(I) time frames and the difference between the two time frames (J)–(L).

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In these results, the Spearman rank correlation is used to understand the overall relationship between changes in local monthly heat extreme frequency and local HDI. The Spearman rank correlation describes statistical dependence between two variables. Spearman rank correlations of −1 or +1 indicate that the relationship between two variables is monotonic. As climate change has been shown to disproportionately impact regions of lower socio-economic development (Harrington et al 2016, King and Harrington 2018), a negative Spearman correlation is found (i.e. higher frequencies of heat extremes for lower HDI regions, lower frequency of heat extremes for higher HDI regions). During the 20 year baseline climate, local monthly heat extremes are shown to disproportionately affect lower HDI regions captured by moderately negative Spearman rank correlations in figures 6(A)–(C). During the ZEC₂₅ and ZEC₉₀ time frames, most land areas experience either no change or reduced frequency of local monthly heat extreme for all $\sigma$-levels (shown before in figure 4). Similarly, most grids show either zero change or continued decrease in frequency of local monthly heat extremes shown in figures 6(J)–(L) which is also consistent with results shown in figure 4.

In the ZEC₂₅ and ZEC₉₀ time frames, $1\sigma$ and $2\sigma$ distributions have a weakly negative change in Spearman rank correlations which suggests that inequality of climate change remains (and is slightly enhanced) after net zero CO₂. The negative change in Spearman correlations in $1\sigma$ and $2\sigma$ thresholds are due to larger reductions in frequencies of heat extremes in high HDI mid- to high-latitudes than the reductions in tropical latitudes which tend to have lower HDI, although this is a weak effect and differs slightly from the $3\sigma$ results. Over the remainder of the century after the ZEC₂₅ time frame, the inequality of climate change for $1\sigma$ and $2\sigma$ thresholds is slightly enhanced suggested by negative changes in Spearman correlations in figures 6(J) and (K). However, for the $3\sigma$ threshold, the inequality of climate change is slightly relaxed based on the positive Spearman correlation in figure 6(l).

In addition to local monthly heat extreme frequency and HDI, we also investigated the relationship between frequency of local monthly cold extremes and HDI. Figure 7 shows the ensemble median change in frequency of local monthly cold temperature extreme exceedance plotted against HDI for land-based grid cells for the 20 year ZEC time frames. Like figure 6, changes in cold temperature extreme frequency were computed as the difference between ZEC₉₀ and ZEC₂₅ frequency distributions, and Spearman rank correlations were computed for each distribution.

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During the net zero baseline climatology, land-based cold extreme frequencies are negligible based on ensemble median and are supported by results in figures 4(A)–(C). During the ZEC₂₅ time frame, increased frequencies in cold extremes are evident across extreme thresholds following CO₂ emissions cessation (figures 7(D)–(F)). Additionally, positive changes in Spearman rank correlations are calculated during the ZEC₂₅ time frame due to the emergence in cold extreme frequency over high-HDI Northern Hemisphere land masses as shown in figures 5(D)–(F). The consistently positive Spearman correlations indicate that local cold monthly temperature extremes tend to impact higher HDI regions following CO₂ emissions cessation, which is opposite to heat extreme trends where lower HDI regions continue to experience higher frequency of local monthly heat extremes for $1\sigma$ and $2\sigma$ thresholds. Over the remainder of the century after the ZEC₂₅ time frame, Spearman rank correlations slightly increase which suggests that high HDI land regions will continue to experience higher frequency cold extremes after CO₂ emissions cessation. In terms of ensemble median frequencies of cold extremes, nearly every populated grid cell experiences either no change or an increase in cold extreme frequency similar to the large-scale land-based cooling shown in the mean state regional climate projections post net zero (figure 3).