1. Introduction
Climatological zonal-mean surface temperatures decrease from the equator toward both poles, a hemispherically symmetric signature much larger than the antisymmetric deviations therefrom. By symmetric or antisymmetric we refer to the average or difference, respectively, of each latitude with its mirror about the equator: for a given field χ, χ(φ) = χsym(φ) + χasym(φ), where φ is latitude,
(a) Climatological annual-mean, zonal-mean surface air temperature in a preindustrial control simulation, the hemispherically symmetric component thereof, the global mean thereof, and the global mean plus the hemispherically antisymmetric component, as indicated in the legend. The simulation was performed in a low-resolution configuration of CESM version 1.0.4, with results averaged over years 701–800. (b) Anomalous zonal-mean surface air temperature in an abrupt 4 × CO2 simulation in the same model, averaged over four time periods as indicated in the legend. Solid curves are the full fields, and dotted curves are the corresponding symmetric component. Both panels have units in K.
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
Conversely, CO2-forced zonal-mean surface warming—henceforth simply T—starts out appreciably antisymmetric: prevailing Southern Ocean upwelling (e.g., Armour et al. 2013; Marshall et al. 2015) impedes Antarctic warming for decades (likely reinforced by resulting changes in local lapse rates and clouds; Senior and Mitchell 2000; Rugenstein et al. 2020), while weakly negative to slightly positive radiative feedbacks in northern high latitudes (e.g., Stuecker et al. 2018) among other processes (Feldl et al. 2017; Russotto and Biasutti 2020; Henry et al. 2021) promote Arctic warming. This fast response typically gives way to a more symmetric warming pattern over subsequent centuries (Held et al. 2010), with Antarctic warming partially catching up to the Arctic in century-scale CMIP5 (Andrews et al. 2015) and CMIP6 (Dong et al. 2020) simulations. On longer time scales, polar amplification is comparable in the two hemispheres in multimillennial simulations in fully coupled GCMs (e.g., Danabasoglu and Gent 2009; Li et al. 2013; Rugenstein et al. 2019) and in runs to equilibrium in slab-ocean GCMs (e.g., Manabe et al. 1991; Armour et al. 2013) and diffusive moist energy balance models (MEBMs) (e.g., Merlis and Henry 2018; Armour et al. 2019). Figure 1b illustrates these behaviors via T and Tsym from an abrupt 4 × CO2 simulation in CESM1 over each of four time periods (years 1–10, 21–100, 701–800, and 2901–3000): T and Tsym differ markedly in the first decade when Tasym is largest but gradually become more similar, with T ≈ Tsym and Tasym ≈ 0 to first approximation in the final period.
On millennial time scales changes in deep-ocean circulation become relevant (and can be non-monotonic, cf. Jansen et al. 2018), perturbing the prevailing antisymmetric transport of heat from the southern to the Northern Hemisphere by the Atlantic meridional overturning circulation. For example, in a 3000-yr GCM simulation with perturbed cloud albedos yielding a surface climate resembling the early Pliocene (∼4 Ma), a Pacific meridional overturning circulation emerges after ∼1500 years, increasing the heat convergence into the Northern Hemisphere (Burls et al. 2017).
Nevertheless, past studies indicate that T normalized by its global average—henceforth T*—partially collapses toward a shared pattern at different time scales (cf. Fig. 4a of Armour et al. 2013). Such pattern scaling (e.g., Tebaldi and Arblaster 2014) also largely holds for zonally varying surface temperature responses across CO2 values [e.g., Heede et al. (2020), though there is also considerable evidence for state-dependent climate sensitivity; e.g., Rohrschneider et al. (2019)]. Essentially, the present study combines pattern scaling and the symmetric/antisymmetric decomposition for T under 4 × CO2, arguing that GCM-simulated
We found these behaviors somewhat inadvertently in the aforementioned 4 × CO2 simulation in CESM1 (which is described along with the other models and methodological choices in section 2), and this manuscript constitutes an attempt to better understand them. To assess their robustness, we analyze 11 additional GCMs from the LongRunMIP (Rugenstein et al. 2019) repository (section 3). To clarify their underlying physical mechanisms, we use an MEBM to first emulate the results from CESM1 and then identify the predominant factors determining
2. Methods
a. LongRunMIP and CESM1 4 × CO2 simulations
LongRunMIP (Rugenstein et al. 2019) comprises increased-CO2 simulations from CMIP5-class GCMs spanning from one thousand to several thousand years. We analyze 11 of the 12 available with ≥1000-yr integrations under 4 × CO2, which are listed in Table 1. CESM104 from LongRunMIP was omitted because it is nearly the same as the above-noted CESM1 that we analyze separately. Nine of the LongRunMIP models ran under an abrupt 4 × CO2 and two under a 1% increase per year to 4 × CO2. The latter two (ECHAM5MPIOM and MIROC32) also ran shorter abrupt 4 × CO2 simulations, and so for the first century when forcing and global-mean warming are modest under 1% yr−1 we use the abrupt 4 × CO2 simulation, switching to the 1% to 4 × CO2 simulation for subsequent periods. Output was available regridded to a common 2.5° × 2.5° grid (cf. Table 2 of Rugenstein et al. 2019).
Details of the LongRunMIP models and simulations used. (from left to right) Model name following Rugenstein et al. (2019) conventions, control simulation duration in years, simulation for which data over years 701–800 is taken, and simulation for which data over years 2901–3000 are taken (or “none” if not available for any simulation in that model).
We include with the LongRunMIP models the 3000-yr 4 × CO2 simulation in CESM1 referred to in the Introduction. This is version 1.0.4 of the model in its low-resolution configuration (Shields et al. 2012). It consists of the Community Atmosphere Model, version 4 with its spectral dynamical core truncated at T31 resolution (∼3.75° × 3.75°) and with 26 vertical levels coupled to the Parallel Ocean Program version 2 (POP2) with ∼3° horizontal resolution and 60 vertical levels.
We focus on temporal averages over four time periods (similar to those of Armour et al. 2013): years 1–10 and 21–100 (during which both the atmosphere and ocean are rapidly responding), 701–800 (during which the atmosphere is in a nearly statistically steady state but the ocean remains slowly varying), and 2901–3000 (at which time the deep ocean has nearly equilibrated). All 12 GCMs extend through year 800 and 5 through year 3000. We refer to the final period as near-equilibrium, recognizing that the climate response would likely meaningfully evolve beyond three millennia in most models given the deep ocean’s multimillennial, diffusive equilibration time scale (Jansen et al. 2018); the box model in section 5 highlights this.
We account for climate drift in each model’s preindustrial control simulation as follows. For the 11 LongRunMIP GCMs, for each time period we compute anomalies as the difference between the 4 × CO2 simulation and the control at that time period if the control simulation extends that long. Otherwise, we subtract an average over the entire control simulation. For CESM1, drift in the control simulation is modest relative to the forced temperature responses, and so for convenience we report anomalies in all periods as differences with the control averaged over years 701–800. All major results presented are insensitive to reasonable methodological choices regarding control drift.
The five GCMs extending to year 3000 include the three farthest on the ends of the full 12-GCM distribution at years 701–800: FAMOUS on one end (highest global-mean warming, and second-weakest changes in both the symmetric and antisymmetric polar amplification indices defined below), versus GISSE2R and CESM1 (respectively, lowest and third lowest mean warming, largest and second-largest increase in symmetric amplification, and second-largest and largest decrease in antisymmetric amplification) on the other. Most likely then this subset usefully approximates the range generated by all 12 models had the others also run to year 3000.
b. Moist energy balance model
To clarify the processes determining the GCM
c. Additional CESM1 simulations under different forcings
To assess how robust the behaviors of
d. Physical meaning of symmetric/antisymmetric decomposition
Arguably, the decomposition of T into a sum and difference of its mirror values about the equator—though always permissible mathematically—gains physical meaning only to the extent that mirror latitudes influence one another. Otherwise, if for example each latitude was in local radiative-convective equilibrium independent of all others, summing or differencing about the equator merely convolves two independent signals. But it is well understood that perturbed atmospheric and oceanic energy flux divergences do strongly influence polar amplification (e.g., Alexeev and Jackson 2013; Armour et al. 2019; Henry et al. 2021), mitigating this concern, at least over sufficiently long time scales.
Nevertheless, a corollary is that this decomposition becomes physically meaningful only beyond the time scale over which a given latitude plausibly influences its mirror. For example, while Previdi et al. (2020) argue convincingly that Arctic amplification emerges in a matter of months after imposed CO2 forcing, for our purposes this Arctic signal is unlikely communicated to the opposite pole on such a subannual time scale. Shin and Kang (2021) show that, in an aquaplanet GCM with radiative forcing confined to one hemisphere’s extratropics, local warming is communicated to the opposite polar cap through a multistep circulation adjustment, manifesting in surface warming over ∼5–10 years. For non-aquaplanets, zonal asymmetries plausibly yield teleconnections mediated by Rossby waves that could potentially transmit the signal across the tropics more rapidly (Ding et al. 2014); nevertheless we take the Shin and Kang (2021) result as a posteriori justification for our choice of the first decade as the earliest and shortest period analyzed.
Though a few prior studies have applied the symmetric/antisymmetric decomposition to related properties of the atmospheric energy budget, to our knowledge none have applied it to surface warming itself. Frierson and Hwang (2012) use the antisymmetric component of zonal-mean net energetic forcing of the atmosphere to interpret tropical precipitation and atmospheric energy fluxes under doubled CO2. In terms of hemispheric averages, observations and GCMs exhibit considerable symmetry in top-of-the-atmosphere (TOA) albedo climatologically (Voigt et al. 2013; Stephens et al. 2015) and in GCMs under hemispherically antisymmetric external forcing (Voigt et al. 2014).
e. Amplification indices
As quantitative bulk measures of
3. 4 × CO2 results in GCMs
Figure 2 shows the 4 × CO2-forced T*,
For 4 × CO2 simulations in 6 of the 12 GCMs analyzed: (left) full, (center) hemispherically symmetric component, and (right) antisymmetric component of zonal-mean surface air temperature change in years 1–10, 21–100, 701–800, and if available years 2901–3000, with each period as indicated in the legend in (e). Printed values at the bottom of each panel are (left) the mean warming during that period, (center) the symmetric polar amplification index for that period, and (right) the northern minus Southern Hemisphere polar amplification index for that period. Values at the top of each panel in the center column are the fractional change in the symmetric polar amplification index from the first to the last period, and at the top of each panel the right column are the same but for the northern–southern difference. (d)–(f) For CESM1, the asterisk signifies that these simulations are not from LongRunMIP (unlike the 11 other models). The remaining six models are shown in Fig. 3.
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
As in Fig. 2, but for the remaining six GCMs.
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
The
The
Given these two robust responses, empirically each model’s PAsym in the initial decade provides a nontrivial albeit approximate lower bound on its near-equilibrium PAsym value—and for models in which
Having established these behaviors in full-physics GCMs, we turn to better understanding them via two simpler models: first with an MEBM to clarify the physical mechanisms underlying the robust
4. Moist energy balance model
Figure 4 shows T, T*,
Surface air temperature response in the CESM1 4 × CO2 simulation at the four selected time periods and in the moist energy balance model simulations meant to reproduce the CESM1 4 × CO2 simulation at each of those time periods, as indicated by the text in (a). Panels show different temperatures: (a) raw (in K), (b) mean-normalized (unitless), (c) mean-normalized symmetric component (unitless), and (d) mean-normalized antisymmetric component (unitless). Note differing vertical axis spans in each panel.
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
To test the role of anti-symmetries in λ and
Mean-normalized (a) full, (b) symmetric, and (c) antisymmetric surface air temperature anomaly fields in MEBM simulations with the antisymmetric components of the radiative feedback parameter and ocean heat uptake fields multiplied by the factor α, with red curves for α = 0, blue for α = 1 (i.e., unchanged), and dark yellow for α = 3. Dotted, dash–dotted, dashed, and solid lines correspond to years 1–10, 21–100, 701–800, and 2901–3000, respectively, of the CESM1.0.4 abrupt 4 × CO2 simulation. Note that the vertical axis range is identical in (a) and (b), but not in (c), while the vertical axis spacing is identical in all three panels.
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
To test the role of the spatial patterns of λsym and
Surface air temperature response in MEBM simulations corresponding to years 1–10 (dotted curves) and years 2901–3000 (solid curves) of the CESM1 4 × CO2 simulation, shown either (a) raw (in K) or (b) mean-normalized (unitless). Colors correspond to simulations with (red) both λ and
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
To distinguish the contributions of λsym versus
To interpret this strong influence of λsym, Fig. 7 shows λ, λsym, and λasym for each time period (as well as, for completeness in interpreting the various MEBM simulations, the corresponding
(a)–(c) Radiative forcing (
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
Summarizing: the MEBM captures the CESM1 warming patterns reasonably well when forced with the latter’s λ and
5. Box model of amplification indices
Having explored the mechanisms underlying the robust responses across the GCMs, we now investigate the cross-GCM discrepancies via a three-box, two-time-scale model applied to two of the end-member GCMs noted above, CESM1 and FAMOUS5 (Smith et al. 2008). Our three-box model is an extension of the well-known two-time-scale box model for global-mean warming (Held et al. 2010; Geoffroy et al. 2013; Rohrschneider et al. 2019) to region-mean warming (see also Geoffroy and Saint-Martin 2014) in the Arctic (60°–90°N), Antarctic (60°–90°S), and lower latitudes (60°S–60°N). Recalling that CESM1 has the second-least mean warming, second-most positive change in PAsym (+22%), and most negative change in PAasym (−109%) whereas FAMOUS has the most mean warming, second-least positive (−5%) change in PAsym, and second-least negative (−27%) change in PAasym, this diagnosis of the regional warming time scales points toward potential causes of the spread in
Time series of 10-yr running mean of Arctic (red), Antarctic (yellow), and low-latitude (blue) box-average temperatures in the abrupt 4 × CO2 simulation in (a),(c) CESM1 and (b),(d) FAMOUS. Overlain gray curves are the fits from the simple two-layer box model for each region. Rows show (top) raw fields and (bottom) the same time series but each normalized by the global-mean warming. The plot in (d) also includes as thin horizontal lines the predictions from the box model under the approximation of horizontally uniform fast and slow warming time scales, as described in the text.
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
Best-fit values of the five parameters in the two-time-scale model for the abrupt 4 × CO2 simulations in CESM1 and in FAMOUS for each of the three regions of our box model and for the global mean. Units are in K for Teq and years for τf and τs; af and as are dimensionless.
For CESM1, Teq is slightly higher for the Antarctic (17.8 K) than Arctic (15.1 K), both of which are ∼3 times higher than for lower latitudes (5.8 K). The fast response time scales for the Arctic (9.4 years) and lower latitudes (12.7 years) are comparable and an order of magnitude less than the Antarctic time scale (85.3 years). Equilibrium warming is weighted fairly evenly between the fast and slow responses (af = 0.59, 0.48, and 0.60 for the Arctic, Antarctic, and lower latitudes, respectively). The slow response time scales are all millennial—2223, 2564, and 1065 years for the Arctic, Antarctic, and lower latitudes, respectively. The two-time-scale fit captures the overall evolution for each region fairly well, though with too sharp a shoulder after the initial decades for the Arctic and lower latitudes (Fig. 8a). CESM1 also exhibits considerable centennial-time-scale variability particularly after ∼1800 years (roughly coinciding with the emergence of the Pacific meridional overturning circulation in the Pliocene-like simulation; Burls et al. 2017). For the fast response, the separation of the Antarctic time scale from the Arctic and lower latitudes is evident. For the slow response, it is evident that both caps would continue warming nontrivially beyond year 3000, which after all is only ∼1.2–1.3 times their slow response time scales. The global-mean-normalized time series (Fig. 8c) show the initial strong Arctic amplification and the Antarctic subsequently catching up by around ∼500–600 years.
The two-time-scale fit is even better for FAMOUS than for CESM1 (Fig. 8b) and highlights the striking result that the Antarctic fast response time scale is slightly shorter than the Arctic’s—τf = 14.1, 15.9, and 15.3 years for lower latitudes, Arctic, and Antarctic, respectively—unlike CESM1 and counter to physical intuition given the retarding influence of Southern Ocean upwelling. The predicted equilibrium warming is over 10 K higher in the Arctic (26.4 K) than Antarctic (16.1 K), which in turn is less than 4 K warmer than the lower latitudes (12.3 K). It is also weighted more toward the fast than slow response for all three regions, with af = 0.78, 0.71, and 0.66 for the Arctic, Antarctic, and lower latitudes, respectively. With comparable time scales and weightings for the fast response but much larger equilibrium warming in the Arctic, initial decades feature much greater Arctic than Antarctic warming. The slow response time scale is similar for lower latitudes and Arctic (433 and 471 years, respectively), and moderately longer for the Antarctic (588 years). As such, the Antarctic continues warming somewhat longer than the rest of the globe, which moderately weakens the antisymmetric amplification. Still, the Antarctic slow time scale is within ∼25%–35% of the others.
This is independent of time. Therefore so too are PAsym and PAasym—imperfect for the −27% decrease in PAasym but capturing the modest −6% change in PAsym well. Figure 8c shows the global-mean-normalized warming for each region for FAMOUS along with their predicted values from (4). The simple approximation (4) is biased low for each region, but in reasonable agreement with (4) the FAMOUS time series vary modestly in time, at most for the Arctic by ∼10% over the 3000 years.
Summarizing, for CESM1 there are three relevant time scales. In the initial decades, the Arctic warms rapidly but not the Antarctic, yielding large values of both PAsym and PAasym. The fast Antarctic warming transpires over subsequent decades to centuries, increasing PAsym but weakening PAasym. Over subsequent millennia, the slow responses emerge continuing to warm both polar caps, comparably to one another but more than lower latitudes, further increasing PAsym while decreasing PAasym. For FAMOUS, a surprisingly short time scale of Antarctic warming combined with much greater Arctic than Antarctic (or low-latitude) equilibrium warming combine to keep changes in both PAsym and PAasym modest from decadal to millennial time scales. These results show that the preferential initial Arctic versus Antarctic amplification, though robust, can arise via rather different processes in different GCMs.
6. Results across CO2 levels and a Pliocene-like simulation in CESM1
Though bounding a GCM’s near-equilibrium PAsym from a short integration would be useful, our ultimate concern is what can be inferred for the real climate system, for which an instantaneous quadrupling of CO2 is not directly relevant to anthropogenic warming—in which the CO2 increase is gradual and (one dearly hopes) remains well below a quadrupling—nor those paleoclimate states for which non-CO2 forcings are of first-order importance. We therefore now present CESM1 simulations at 2–16 × CO2 and the Pliocene-like simulation; these address the sensitivity of the results to CO2 amount and to a strongly meridionally patterned, non-CO2 forcing but do not directly address the issue of gradual rather than abrupt forcings, which we return to in the concluding discussion section below.
The left column of Fig. 9 shows T, T*,
The
The right column of Fig. 9 shows T, T*,
Zonal-mean surface warming in (a),(c),(e),(g) 2, 4, 8, and 16 × CO2 simulations and (b),(d),(f),(h) the Pliocene-like simulation in CESM1. For CO2, colors are according to the legend in (a) and line styles according to the legend in (c). For the Pliocene-like simulation, the legend is in (b). Shown are (a),(b) raw warming (in K) and the mean-normalized (c),(d) full field, (e),(f) symmetric component, and (g),(h) antisymmetric component. Vertical axis range is identical in (c)–(f), which also have the same vertical axis spacing as (g) and (h).
Citation: Journal of Climate 35, 20; 10.1175/JCLI-D-20-0972.1
Summarizing, across CO2 values in CESM1 the
7. Conclusions
a. Summary
We decompose the zonal-mean surface air temperature response to abrupt CO2 quadrupling from decadal to millennial time scales into hemispherically symmetric and antisymmetric components in 12 GCMs—11 from LongRunMIP (Rugenstein et al. 2019) plus a low-resolution version of CESM1.0.4. Normalized by the contemporaneous global-mean warming, the symmetric warming component at a given time differs considerably across GCMs but for a given GCM changes modestly with time; a symmetric polar amplification index changes from the first decade to years 701–800 or (if available) years 2901–3000 by −6% to +8% in 6 of 12, increases by 34% in 1 outlier, and increases by 13%–22% in the remaining 5. The antisymmetric component weakens in time in all 12, but this varies considerably across GCMs—near-equilibrium warming is appreciably antisymmetric in some including FAMOUS versus almost entirely symmetric in some including CESM1. Based on these results, we consider a weak change to modest increase in symmetric polar amplification and modest to complete reduction in antisymmetric polar amplification to be robust responses and subsequently attempt to better understand them.
An MEBM prescribed with ocean heat uptake and radiative feedback parameter (λ) fields inferred from four different time periods of the 4 × CO2 CESM1 simulation captures the salient GCM behaviors. In additional MEBM simulations with the antisymmetric components of λ and ocean heat uptake either removed or amplified, despite the antisymmetric warming pattern changing drastically, the symmetric warming pattern hardly changes. Conversely, removing the meridional structure in λ (even with its global mean unchanged) causes three key changes: it reduces mean warming at each time period, it makes the warming pattern more polar amplified at each time period, and it weakens the increase in time of the symmetric polar amplification index. Of these three, the first two are a straightforward consequence of λ being less stabilizing overall at high than low latitudes. The third, we argue, results from the loss after the initial decade of a deep global minimum in λ just equatorward of the Southern Ocean. This imprints onto the symmetric component of λ, and with no comparable change at lower latitudes, the result is that radiative restoring becomes comparatively less stabilizing in the extratropics than tropics, promoting polar amplification.
To clarify causes of differences across the GCMs, a simple three-box, two-time-scale model of warming in the Arctic, Antarctic, and lower-latitude sectors was fitted to 3000-yr time series of annual-mean surface warming in the end-member models CESM1 and FAMOUS. Strikingly, in FAMOUS there is effectively no difference in the fast response time scale between the Antarctic and elsewhere. This runs counter to CESM1 where the Antarctic time scale is an order of magnitude larger and to physical intuition given the delaying effect of Southern Ocean upwelling. Fortuitously, however, it enables an analytical approximate solution that yields a time-invariant symmetric polar amplification index in reasonably good agreement with the GCM.
Finally, we investigate the sensitivity of these behaviors to the radiative forcing via additional CESM1 simulations. The normalized symmetric warming pattern varies moderately across CO2 magnitudes from 2 to 16 times preindustrial, with symmetric polar amplification increasing—and antisymmetric polar amplification decreasing—less in time the higher CO2 is. At least after the first decade, both components change even less in time in a simulation generating an early Pliocene-like surface climate attained through meridionally patterned cloud albedo perturbations. Thus, qualitatively the symmetric component is insensitive in time and to forcing magnitude for a given forcing structure despite, unsurprisingly, depending sensitively on the forcing structure.
b. Discussion
Does the hemispherically symmetric/antisymmetric decomposition of polar-amplified warming add value over more conventional analyses? In terms of the bulk amplification indices defined as the ratio of polar cap-averaged warming to globally averaged warming, admittedly the results are mixed. Across the 12 GCMs under abrupt 4 × CO2, the Arctic amplification index spans 1.79–2.50 in the first decade and changes afterward by −0.53 to +0.04—a larger range than that of PAsym (−0.10 to +0.40) in absolute terms but actually smaller in percentage terms (−23% to +2% for the Arctic versus −6% to +34% for PAsym). The Antarctic amplification index in the first decade spans 0.33–1.15 and changes thereafter from +0.04 to +1.27 (fractionally, +4% to +352%), a larger range than the first-to-last-period change in PAasym of −0.09 to −0.90 (fractionally, −17% to −109%). As such, a complementary view would be that the robust responses are a weak change to modest decrease in Arctic amplification and a weak to large increase in Antarctic amplification. In either case, it is clear that model diversity in evolution of warming patterns across time scales is greatest for the southern extratropics, weakest in the tropics, and intermediate for the northern extratropics.
Further support for the southern high latitudes figuring centrally in model disagreement comes from the three-box, two-time-scale model fitted to the two end members FAMOUS and CESM1. Their most salient discrepancies are the ∼5.5-fold longer Antarctic fast-response time scale in CESM1 and the ∼2.5–4.5-times-longer slow-response time scales in all regions for CESM1. Both involve ocean dynamical processes—prevailing Southern Ocean upwelling and deep ocean equilibration—suggesting a predominant role for ocean model formulation.
Nevertheless, going beyond scalar amplification indices to the full latitude-by-latitude pattern, by eye from Figs. 2, 3, and 9 clearly the mean-normalized symmetric component persists more in time from its values in initial decades over subsequent centuries and millennia than either the full field or its antisymmetric counterpart—and likewise (in CESM1 at least) across CO2 concentrations. We therefore argue that the hemispherically symmetric/antisymmetric decomposition merits further study.
One useful next step would be extending the analyses to additional, higher resolution, and more modern GCMs via the CMIP6 abrupt 4 × CO2 simulations—consider that the end-members CESM1 and FAMOUS are both low-resolution and/or simplified versions of CMIP5-class GCMs. The CMIP abrupt 4 × CO2 runs typically span 150 years, precluding direct investigation of the multi-centennial and longer time-scale behaviors. However, for the 12 GCMs we analyze, values in years 21–100 are well correlated with those for years 701–800 for global mean warming (r = 0.99), Arctic amplification (r = 0.94), Antarctic amplification (r = 0.78), PAsym (r = 0.87), and PAasym (r = 0.84).
Though constraining global-mean warming
The MEBM simulations suggest that, in CESM1 at least,
The ultimate motivation for this work is to infer as much as possible regarding anthropogenic climate change in the real climate system from limited data records. What can be inferred from the real climate system based on these results, bracketing temporarily questions of validity? Historical radiative forcing is characterized by two factors we have yet to consider. First is a gradual rather than abrupt CO2 increase. A useful starting place would be standard 1% per year CO2 increase simulations. In initial years to decades when the radiative forcing is still relatively small, global-mean warming will likely be too small for the mean-normalized fields to be meaningful, and the spatial pattern of warming will likely be strongly influenced by internal variability. For that reason, analyzing these fields in one or more available large ensembles could be useful. Second is a complex spatiotemporal evolution with nontrivial antisymmetric component owing to anthropogenic aerosols, volcanoes, and land-use change. We have not examined forcings with large hemispherically antisymmetric components, and it is possible that the
The 2–16 × CO2 simulation results from CESM1 suggest that, in that model at least, the
We conclude by noting that this analysis depended crucially on the existence of an ensemble of millennial-scale integrations in LongRunMIP (Rugenstein et al. 2019), and that, in attempting to bound longer-time-scale behaviors from shorter integrations, it complements ongoing efforts such as the “fast-forward” technique (Saint-Martin et al. 2019) to attain equilibrium solutions in GCMs more rapidly.
We are using the term “robust” here in two slightly different senses. For PAsym, the robustness refers more to the cross-model spread being small than to the sign of the response (though the sign is shared by 10 of 12 models). For PAasym, the robustness refers to the sign, with all 12 models simulating a decrease with time, despite a much wider range of magnitudes in that decrease.
Modest anti-symmetries stem from the radiative forcing and the climatological surface air temperature used to compute ∂Tqsat; in additional simulations with these also symmetrized (not shown), the warming pattern is very similar to the symmetric pattern shown.
In the MEBM, there is no true distinction between OHU and the radiative forcing, and so imposing the mean OHU uniformly can be equally conceptualized as reducing the global-mean radiative forcing.
Strictly speaking, the λsym signal sits just outside our chosen Antarctic region boundary of 60°S. But the diffusive MSE transport in the MEBM clearly communicates this signal to the adjacent polar cap.
Compare with Table 1 of Rugenstein et al. (2020), FAMOUS is also an outlier in that the equilibrium warming estimated for CO2-doubling differs nearly twofold whether 2 × CO2 or 4 × CO2 simulations are used (4.40 and 8.55 K, respectively).
Acknowledgments.
We thank William Wang for generating several figures that facilitated our analyses. S.A.H. was supported during different periods of this study by an NSF Atmospheric and Geospace Sciences Postdoctoral Research Fellowship (NSF Award 1624740), a Caltech Foster and Coco Stanback Postdoctoral Fellowship, and a Columbia University Earth Institute Fellowship. T.M.M acknowledges support from NSERC. N.J.B. acknowledges support from NSF Award 1844380 and is supported by the Alfred P. Sloan Foundation as a Research Fellow. A.V.F. acknowledges support from the ARCHANGE project (ANR-18-MPGA-0001, France). Three anonymous reviewers provided extremely useful comments and motivated the analyses of LongRunMIP and the box model.
APPENDIX
Moist Energy Balance Model Formulation
For the CO2 radiative forcing [
For the diffusive approximation to atmospheric energy transport convergence, because all quantities are anomalies, surface MSE is linearized as
The MEBM is integrated to equilibrium using a fourth-order Runge–Kutta time-stepping scheme. A second-order finite difference scheme is used for the ∇2 operator (Wagner and Eisenman 2015). There are 60 model grid points evenly spaced in sinφ ≈ 1/30 increments, with gridpoint centers in each hemisphere from sinφ ≈ 0.12 (corresponding to φ ≈ 4.8°) to sinφ ≈ 0.98 (corresponding to φ ≈ 79.5°). The CESM1 fields, which are evenly spaced in latitude over 48 boxes spanning ∼1.8°–87.2° in each hemisphere with ∼3.6° spacing, are spectrally transformed at order 20 to the MEBM grid.
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