The sea surface temperature (SST) contrast between the Northern Hemisphere (NH) and Southern Hemisphere (SH) influences the location of the intertropical convergence zone (ITCZ) and the intensity of the monsoon systems. This study examines the contributions of external forcing and unforced internal variability to the interhemispheric SST contrast in HadSST3 and ERSSTv5 observations, and 10 models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) from 1881 to 2012. Using multimodel mean fingerprints, a significant influence of anthropogenic, but not natural, forcing is detected in the interhemispheric SST contrast, with the observed response larger than that of the model mean in ERSSTv5. The forced response consists of asymmetric NH–SH SST cooling from the mid-twentieth century to around 1980, followed by opposite NH–SH SST warming. The remaining best-estimate residual or unforced component is marked by NH–SH SST maxima in the 1930s and mid-1960s, and a rapid NH–SH SST decrease around 1970. Examination of decadal shifts in the observed interhemispheric SST contrast highlights the shift around 1970 as the most prominent from 1881 to 2012. Both NH and SH SST variability contributed to the shift, which appears not to be attributable to external forcings. Most models examined fail to capture such large-magnitude shifts in their control simulations, although some models with high interhemispheric SST variability are able to produce them. Large-magnitude shifts produced by the control simulations feature disparate spatial SST patterns, some of which are consistent with changes typically associated with the Atlantic meridional overturning circulation (AMOC).
The north–south interhemispheric surface temperature contrast is an important influence on the location of the intertropical convergence zone (ITCZ) and the strength of the African and Asian monsoons (Folland et al. 1986; Mantsis and Clement 2009; Chiang and Friedman 2012; Hwang et al. 2013; Sun et al. 2013; Schneider et al. 2014), as well as the extratropical circulation (Xue et al. 2018). Previous studies have identified the role of different forcings that have contributed to changes in the interhemispheric temperature contrast over the instrumental period (Drost and Karoly 2012; Friedman et al. 2013). For combined land and ocean surface temperatures, stronger Northern Hemisphere (NH) than Southern Hemisphere (SH) warming is a robust transient climate response to greenhouse gas (GHG) forcing, largely due to the greater NH landmass extent and thus smaller thermal inertia (Stouffer et al. 1989; Xu and Ramanathan 2012). Arctic amplification processes also contribute to greater transient NH warming (Serreze and Barry 2011). In contrast, the transient warming in the Southern Ocean is limited by upwelling, the thermal isolation of Antarctica from the Antarctic Circumpolar Current, and the Southern Ocean meridional overturning circulation (Hutchinson et al. 2013; Marshall et al. 2014; Armour et al. 2016). Northward heat transport by the Atlantic meridional overturning circulation (AMOC) is the main cause of the mean positive NH–SH temperature contrast (Feulner et al. 2013; Kang et al. 2014), and a decreasing AMOC is projected to weaken the interhemispheric temperature contrast in moderate-emissions future climate projections (Feulner et al. 2013).
Due to their sources mainly in the NH and their relatively short atmospheric residence times, anthropogenic aerosol emissions contribute to North Atlantic cooling and a decreased NH–SH interhemispheric temperature contrast (Kiehl and Briegleb 1993; Rotstayn and Lohmann 2002; Chang et al. 2011; Allen et al. 2015; Chung and Soden 2017). Although the magnitude of mid-twentieth century aerosol forcing remains uncertain (Stevens 2015; Kretzschmar et al. 2017; Booth et al. 2018), historical climate model simulations suggest that the positive NH–SH surface temperature imbalance from GHG forcing overtook the aerosol-related NH–SH decrease around 1980 (Drost and Karoly 2012; Friedman et al. 2013; Wilcox et al. 2013; Undorf et al. 2018), with uncertainty in exact timing due to internal variability and intermodal differences (Schurer et al. 2018). This reflects North American and European clean air legislation in the 1970s and continued GHG emissions. Asian sulfate aerosol emissions have also steadily increased since the 1950s, although present-day global emissions do not exceed 1970s estimates (Lamarque et al. 2010; Hoesly et al. 2018). Asian and African black carbon aerosol emissions have also increased during this period; their overall radiative forcing is uncertain but estimated to be positive, spatially and less hemispherically asymmetric compared to sulfate (Bond et al. 2013; Boucher et al. 2013; Wang et al. 2016). Future anthropogenic aerosol declines are projected to expose even larger NH warming in the coming decades (Rotstayn et al. 2013; Rotstayn et al. 2015). Another interhemispheric forcing is stratospheric ozone depletion, which may have stalled SH high-latitude warming (Marshall et al. 2014).
Despite the above progress in physical understanding of the interhemispheric temperature contrast, key questions remain about the roles of forced and unforced interhemispheric temperature variability during the instrumental period. Notably, studies have identified a shift in the interhemispheric temperature difference from the late 1960s through the early 1970s, which had wide-ranging hydrological impacts particularly on Asian and West African monsoon rainfall (Baines and Folland 2007; Dima and Lohmann 2010; Thompson et al. 2010; Liu and Chiang 2012). Thompson et al. (2010) do not find any instrumental SST biases at the time of the shift, and use an analytical adjustment methodology to show that the drop was unrelated to El Niño–Southern Oscillation (ENSO) fluctuations, volcanic eruptions, or advection by wintertime atmospheric circulation. Due to the rapid time scale of the drop and association with a rapid freshening known as the Great Salinity Anomaly (Dickson et al. 1988), it has been proposed that the interhemispheric shift was caused by internal ocean variability, notably a shift in the AMOC (Dima and Lohmann 2010; Thompson et al. 2010), possibly as part of a longer-term decline over the twentieth century driven by Greenland and Arctic meltwater (Rahmstorf et al. 2015; Caesar et al. 2018). However, this period also coincides with strong sulfate aerosol forcing (Terray 2012; Friedman et al. 2013; Wilcox et al. 2013; Hodson et al. 2014; Allen et al. 2015). Since the magnitude of interhemispheric temperature shifts has not been explicitly quantified, it is difficult to express how unusual the late 1960s–early 1970s shift was compared to earlier periods, or if climate models are able to produce comparable shifts. At the millennial time scale, there have been indications that climate models may underestimate interhemispheric temperature variability in paleoclimate reconstructions, although some of the discrepancies may be due to data uncertainties (Neukom et al. 2014, 2018).
This study aims to characterize the decadal variability of the interhemispheric temperature contrast (focusing on SST only) in a quantitative framework so that the magnitude of the late 1960s–early 1970s shift and other changes can be evaluated more rigorously. We employ a regression-based climate change detection and attribution approach (Hegerl et al. 1997; Allen and Stott 2003) to extract the forced and unforced components of the interhemispheric SST contrast. We also examine NH and SH SST separately to understand their respective contributions to interhemispheric SST variability. Furthermore, we quantify decadal interhemispheric SST shifts using running linear trends and examine the spatial patterns associated with the largest-magnitude trends, analogous to the approach used in recent studies to quantify the early-2000s global mean surface temperature slowdown or hiatus (Meehl et al. 2011; Schurer et al. 2015; Marotzke and Forster 2015; Medhaug et al. 2017).
The paper is organized as follows: In section 2, we present the datasets and simulations investigated. Section 3 describes the characteristics of decadal interhemispheric SST variability. The detection and attribution analysis is applied to the interhemispheric SST contrast in section 4. The separate NH and SH components of interhemispheric SST variability are examined in section 5. Section 6 focuses on decadal shifts in the interhemispheric SST contrast. Finally, section 7 concludes with the implications of our work plus some open questions.
2. Data and models
We define the interhemispheric SST contrast anomaly as the anomaly of mean NH minus mean SH SST; the annual mean is shown in Fig. 1a (top). We examine SST monthly fields from the Met Office Hadley Centre SST dataset (HadSST3) (Kennedy et al. 2011a,b) and the NOAA Extended Reconstructed SST dataset, version 5 (ERSSTv5) (Huang et al. 2017). HadSST3 and ERSSTv5 are both constructed from in situ data using many of the same sources, but apply different quality control, bias corrections, and homogenization. One difference is that ERSSTv5 infills missing data using empirical orthogonal teleconnections, whereas the HadSST3 data are not infilled. Annual means are taken from December–November, which better fit climatological seasons and the ENSO annual cycle, and are calculated from 3-month seasonal means (constructed if there is at least one month of data): December–February, March–May, June–August, and September–November.
Previous studies on the interhemispheric temperature contrast have often examined the combined land surface and SST interhemispheric temperature contrast (Drost and Karoly 2012; Friedman et al. 2013; Feulner et al. 2013; Wilcox et al. 2013). In comparison to the interhemispheric SST contrast, the interhemispheric contrast in land surface temperature, shown using the Climatic Research Unit database (CRUTEM4) (Morice et al. 2012) and the NASA GISS Surface Temperature Analysis (GISTEMP) (Hansen et al. 2010) (250-km smoothing version) (Fig. 1a, bottom), has larger interannual variability and a stronger long-term trend. As our focus is decadal variability, we hereafter investigate the interhemispheric SST contrast. While using SST minimizes the direct response of the land surface, we still expect some contribution from advection from land, especially over the NH (Thompson et al. 2009).
We also examine output from phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Taylor et al. 2012), listed in Table 1. We select all model realizations for which both historical natural forcing (solar and volcanic, referred to as historicalNat) and the corresponding historical all-forcing (natural and anthropogenic, including GHGs, aerosols, ozone, and land use; referred to as historical) experiments are available from 1881 to 2012 to allow the longest possible period for the detection and attribution analysis. In total, 36 historical and historicalNat realizations from 10 different models are investigated. For six models, output was available from the historical or the historical extension (historicalExt) experiments from 2006 to 2012. For four models (IPSL-CM5A-LR, IPSL-CM5A-MR, CSIRO-Mk3.6.0, and one realization of HadGEM2-ES), the historical experiments end in 2005, so the representative concentration pathway 4.5 (RCP4.5) experiment output (van Vuuren et al. 2011) is used from 2006 to 2012.
We investigate SST from the corresponding preindustrial control (piControl) runs of each CMIP5 model, whose lengths are also indicated in Table 1. Control simulations from two additional models, NCAR CCSM4 and GFDL CM3, are also examined in some analyses. Although model drift has been found to affect some variables in CMIP5 models (Sen Gupta et al. 2013), our results for the interhemispheric SST contrast are not affected by linear detrending of the control runs (not shown).
The 2° × 2° ERSSTv5 data and differing-resolution CMIP5 model output are interpolated onto the 5° × 5° HadSST3 grid. In computing hemispheric means, the datasets and models are masked where HadSST3 contains no data in more than 15 of the first 60 years of the study (1881–1940), shown in Fig. 1b. [The land surface temperature data in Fig. 1a (bottom) are masked using a similar threshold based on the 1881–1940 CRUTEM4 coverage.] Hemispheric means are calculated poleward of 5° latitude, as modes of interhemispheric SST variability are generally not centered directly on the equator (Servain et al. 1999; Xie and Carton 2004; Baines and Folland 2007).
3. Observed and modeled interhemispheric SST variability
As our focus is on decadal and multidecadal variability, we apply a 3-yr running mean to the annual data to suppress high-frequency variations such as ENSO (Wang et al. 2012; Dai 2013). The 3-yr mean 1881–2012 observational interhemispheric SST anomaly time series are shown in Fig. 1c, along with those of the CMIP5 historical realizations and their ensemble mean. The observational datasets are highly correlated (r = 0.92) and generally remain within the envelope of the historical simulations. The ensemble mean has a long-term negative trend until around 1980 followed by a rebound, similar to the combined interhemispheric land and SST difference due to opposing GHG and anthropogenic aerosol forcings (Friedman et al. 2013; Wilcox et al. 2013) albeit with a smaller trend since 1980. The amplitude of the ensemble mean variations is expectedly smaller than that of the observations; the latter show a rapid north–south increase in the 1920s and north–south decrease from the late 1960s to early 1970s.
The 1881–2012 standard deviation of the 3-yr mean interhemispheric SST contrast of the observations and historical simulations is shown in Fig. 1d. The standard deviation of ERSSTv5 (0.13°C) is larger than that of HadSST3 (0.12°C); both are larger than the multimodel mean of standard deviations (0.11°C), although still within the intermodel range. An outlier is GISS-E2-H, whose standard deviations cluster between 0.07° and 0.08°C. The single-realization models (particularly BCC-CSM1.1) also have low standard deviations, although we would need more realizations to evaluate their spread. Similar results are found with further smoothing, with a relatively larger spread of model standard deviations (not shown).
The spatial patterns corresponding to the interhemispheric SST contrast in observations are shown in Figs. 2a and 2c, obtained by ordinary least squares (OLS) regression of the 3-yr mean gridded observations onto the interhemispheric SST time series from 1881 to 2012. Slope significance is evaluated using a two-tailed t test, adjusting for temporal autocorrelation by increasing the regression standard error by a factor of assuming 1 degree of freedom for every 3 years of length (Santer et al. 2000; Biasutti et al. 2008). We additionally apply a false discovery rate (FDR) procedure to test for field significance (Genovese et al. 2002; Wilks 2016), stippling the grid points with p values satisfying the FDR criterion αFDR = 0.05. Both datasets have prominent significant positive slopes over the subpolar North Atlantic and significant negative slopes in the extratropical South Atlantic and south Indian Oceans. ERSSTv5 has more significant grid boxes, presumably due to its reduced spatial noise. Negative Indian Ocean slopes extend into the NH, similar to the interhemispheric SST mode in Parker et al. (2007). There are also positive slopes in the midlatitude North Pacific, albeit not significant in either dataset.
Figure 2e shows the 1881–2012 ensemble mean spatial pattern of the 3-yr mean CMIP5 historical interhemispheric SST contrast, calculated as the ensemble mean of the regression slopes of each gridded realization’s SST field onto its own interhemispheric SST contrast time series (the thin lines in Fig. 1c). The slopes are stippled where at least 30 of the 36 realizations agree on the sign of the slope. In contrast to the observations, the strongest amplitudes and model agreement are in the midlatitude North Pacific, with maximum slopes over the Kuroshio Extension. The models show consistent negative slopes in the extratropical SH, particularly the midlatitude Atlantic and Indian Oceans around 40°–45°S.
To illustrate the hydrologic impacts of interhemispheric SST variability, we show the spatial patterns of tropical rainfall associated with the interhemispheric SST contrast. Figures 2b and 2d show the regression slopes of 3-yr mean rainfall over land using the Global Precipitation Climatology Centre (GPCC) 2.5° spatially infilled full data monthly product, version 2018 (Becker et al. 2013; Schneider et al. 2018) onto the interhemispheric SST contrast. The observed slopes are calculated from 1930 to 2012 due to insufficient gauge coverage beforehand (Polson et al. 2016). Slopes are stippled where significant at p < 0.05 using a two-tailed t test, adjusted for temporal autocorrelation and applying the FDR procedure similarly as the SST data in Figs. 2a and 2c. The right panels show the zonal mean slopes. Figure 2f shows the 1930–2012 ensemble mean slope of CMIP5 historical precipitation over land and ocean regressed onto the interhemispheric SST contrast, with the precipitation fields regridded onto a common 2.5° grid. Stippling indicates sign agreement of at least 30 of 36 realizations as in Fig. 2e. The zonal mean slopes in Fig. 2f are shown both globally and for land regions only (masked to the GPCC grid), with the distribution of the middle 30 realizations indicated.
Both the observations and the models show displacement of tropical rainfall into the warmer SST hemisphere (Chung and Ramanathan 2007; Chiang and Friedman 2012; Sun et al. 2013), with observational slope significance and high model agreement found in the ITCZ and monsoon regions, emphasizing the strong imprint of the interhemispheric SST contrast on these rainfall features. However, almost all the realizations underestimate the zonal mean slope magnitudes in northern tropical land region around 10°N (largely reflecting Africa), consistent with larger-magnitude observed twentieth-century changes compared to most CMIP3 and CMIP5 models (Hwang et al. 2013; Polson et al. 2014; Hegerl et al. 2015).
4. Attribution of interhemispheric SST variability to forcing
In this section, we conduct a detection and attribution analysis to identify the forced components of the 3-yr running mean interhemispheric SST contrast shown above.
a. Detection and attribution methodology
The detection and attribution framework provides a rigorous approach to separate the components of observed climate changes driven by external forcing and internal variability (e.g., Hegerl et al. 1997; Allen and Stott 2003). A typical assumption of regression-based detection and attribution studies such as used here is that the spatiotemporal response pattern of an external forcing is much better known than the response magnitude (Bindoff et al. 2013). Here, we apply total least squares (TLS) regression for detection and attribution of the interhemispheric SST contrast (Allen and Stott 2003). We use multimodel ensemble mean fingerprints, which have often been found to perform better than any individual model (Knutti et al. 2010; Hegerl and Zwiers 2011), although they may underestimate the role of model uncertainty (Schurer et al. 2018). Equal weight is given to each of the 36 realizations in constructing the multimodel ensemble mean. Calculating the mean over the available simulations rather than among individual models results in a greater signal-to-noise ratio; however, it means that some models are given greater weight due to having more realizations.
We apply a two-signal analysis with historical and historicalNat fingerprints to detect net anthropogenic forcing, which has been found to be more robust than detecting aerosol and GHG forcing separately (Bindoff et al. 2013; Jones et al. 2016). The observations and fingerprints are shown in Fig. 3a. As in Schurer et al. (2013), the fingerprints are not optimized. The scaling coefficients β1 and β2, which determine the magnitude of the fingerprints from observations, are calculated as follows:
where y is the observed interhemispheric SST contrast time series of length L (130 years excluding endpoints due to smoothing 132 years); XhistoricalNat and Xhistorical are the length-L multimodel mean fingerprints; εhistoricalNat and εhistorical are the length-L internal variability of each fingerprint; and εobs is the unforced residual variability. We assume that taking the mean over n ensemble members (36 realizations) reduces the internal variability by a factor of .
We rearrange β1 and β2 into natural (βNat) and anthropogenic (βAnt) scaling coefficients, as described in Tett et al. (2002):
We construct the 5%–95% confidence intervals accounting for uncertainty in the internal variability of βNat and βAnt by adding 16 000 random L-yr samples from the control simulations onto the noise-reduced fingerprints and observations. For each iteration, we select three segments without replacement from the 42 nonoverlapping 132-yr segments available from the 10 control simulations corresponding to the fingerprints (Table 1), taking 3-yr means (and excluding endpoints). The best-estimate coefficients and 5%–95% confidence intervals are shown in Table 2 (top). Anthropogenic forcing is detected at the 5% one-sided significance level, whereas natural forcing is not significantly detectable. The best-estimate values of βAnt greater than the multimodel mean (scaling of 1) suggest a larger response to anthropogenic forcing in observations than in models, particularly for ERSSTv5 where the multimodel mean is outside the 5%–95% uncertainty range.
b. Forced and unforced components of the interhemispheric SST contrast
The best-estimate 3-yr mean noise-reduced, or forced, component of y, ỹ, is shown for HadSST3 in Fig. 3b and ERSSTv5 in Fig. 3c, with the 5%–95% confidence intervals constructed from the 16 000 random samples from the control runs. The anthropogenic and natural contributions to the forced components are also shown; the anthropogenic component is calculated by subtracting historicalNat from historical component; see Eqs. (2) and (3). The anthropogenic component dominates the forced response for both datasets. The forced signal consists of a negative trend to around 1980 followed by a partial recovery. The negative trend is overlaid with an increase from around 1920 to 1950.
The best-estimate unforced residual or effective residual time series is estimated as follows:
where the scaling factor in the denominator is applied to account for the small component of internal variability in the fingerprints (Schurer et al. 2015). We use both β1 and β2 in Eq. (4) since physically we expect some contribution from both natural and anthropogenic forcing types of forcing, even though natural forcing is not found to be significant. The best-estimate residual time series (Fig. 3d) has prominent north–south maxima in the 1930s and mid-1960s, with the latter followed by a rapid north–south decrease to the early 1970s. We will further examine these decadal changes in section 6.
Figure 3e shows the standard deviations of the observational best-estimate residuals, the control segments, and the historical best-estimate residuals. The observational best-estimate residuals (dashed lines) are within the control simulation range (purple squares), suggesting consistency in magnitude between the internal variability of the observations and the models. For example, the GISS-E2-H control simulation variability is more consistent in magnitude to the observational residuals than the GISS-E2-H historical variability compared to observations (Fig. 1d). The historical best-estimate residuals are estimated by applying the detection and attribution methodology to each historical realization, described in the appendix (black diamonds). Note that this estimate of the internal variability includes an unknown forced component of each model that differs from the multimodel mean fingerprint. This historical best-estimate residual variability is generally within the range of the control simulations, indicating that the multimodel mean fingerprints reasonably capture much of the forced variability in the individual models.
5. Northern and southern components of the interhemispheric SST contrast
Building on the previous section, we apply a detection and attribution analysis to NH and SH SST separately. The NH and SH fingerprints and observations are shown in Figs. 4a and 4b. Both hemispheric observations show a long-term positive trend after cooling from 1881 to around 1910. NH SST shows strong warming from around 1910 to 1940, described as early twentieth-century warming (Hegerl et al. 2018), followed by a slight decrease to around 1980, and then a warming trend until around 2005. SH SST has a short-term increase around World War II (WWII), followed by long-term warming. ERSSTv5 and HadSST3 have the largest overall differences following WWII in the SH, with ERSSTv5 lower by about 0.2°C in the early 1950s (Fig. 4b), potentially related to differences in bias corrections for the transition from bucket to engine room intakes (Kennedy 2014; Huang et al. 2017).
Using the methodology described in section 4a, we obtain the best-estimate scaling coefficients and 5%–95% confidence intervals, shown in Table 2 (bottom). We allow for different NH and SH scaling coefficients to extract the maximum forced variability in each hemisphere; this differs from studies using combined scaling coefficients, such as Schurer et al. (2018). We choose this approach to extract the maximum forced variability in each hemisphere.
Anthropogenic forcing is detected at the 5% one-sided significance level in both the NH and SH. Natural forcing is detected in both hemispheres for HadSST3 (with βNat < 1) but not in ERSSTv5. In both datasets, the best-estimate values of βAnt are greater than 1 for both hemispheres, with the multimodel mean outside the 5%–95% range for the SH. The best-estimate hemispheric forced components (Figs. 4c,d) are dominated by an upward trend from GHG forcing, with aerosol-related NH cooling from 1950 to 1970 (Wilcox et al. 2013; Allen et al. 2015; Undorf et al. 2018).
The best-estimate residual NH and SH time series, and , are calculated similarly to Eq. (4) (Figs. 4e,f). As expected, the best-estimate residual interhemispheric SST contrast, from Eq. (4), is very strongly correlated with the difference of and (HadSST3: r = 0.98; ERSSTv5: r = 0.93). The observed cooling from 1881 to around 1910 is present in both and ; likewise, much of the early twentieth-century NH warming, as warms relatively steadily from 1910 to 1940 and later undergoes a decrease in the late 1960s; increases rapidly in the late 1930s, then drops in the 1940s followed by decadal-scale variations, with minima in the mid-1960s and after the early 2000s. Both and have large standard deviations relative to NH and SH SST of the control simulations and the historical realization best-estimate residuals (calculated following the appendix; Fig. 4g). Interestingly, and are more positively correlated (HadSST3: r = 0.63; ERSSTv5: r = 0.62) than NH and SH SST of any of the control segments or historical realization best-estimate residuals (Fig. 4h). [This is not the case for the direct NH and SH SST observations, whose standard deviations and correlation are within the range of the historical realizations (not shown)]. The large amplitudes and strong correlations of the observational NH and SH SST best-estimate residuals could be due to incomplete removal of the forcing using the multimodel mean fingerprints, or possibly errors in the observations or incorrect climate model decadal variability. We discuss these possibilities in section 7.
6. Decadal shifts in the interhemispheric SST contrast
In this section, we examine decadal shifts in the interhemispheric SST contrast. Several methodologies for identifying climate shifts exist (Overland et al. 2008). Here, we examine running linear trends (Trottini et al. 2015), which have been typically used to quantify the early-2000s global mean surface temperature slowdown or hiatus (Meehl et al. 2011; Schurer et al. 2015; Marotzke and Forster 2015; Medhaug et al. 2017). As our focus is on decadal-scale shifts, we examine 9-yr running OLS trends applied to the 3-yr running mean time series. Similar results are obtained using running trend lengths of 7 to 13 years (not shown).
a. Late 1960s – early 1970s and early 1920s shifts
Figure 5a shows the 3-yr mean interhemispheric SST contrast along with the respective 9-yr running trend. In both observational datasets, the largest-magnitude trend is the rapid drop centered around 1970, consistent with previous qualitative identification (Dima and Lohmann 2010; Thompson et al. 2010) (HadSST3: 1965–73: −0.63°C decade−1, 1966–74: −0.61°C decade−1; ERSSTv5: 1965–73: −0.60°C decade−1, 1966–74: −0.64°C decade−1). Hereafter, we focus on the 1966–74 trends in both datasets for simplicity of comparison. Both NH cooling and SH warming contribute comparable magnitudes to the 1966–74 shift (Table 3). The most positive observational NH–SH trend is centered in 1922 (1918–26) in both datasets, also with contributions from both hemispheres (Table 3).
Although the CMIP5 historical ensemble mean interhemispheric SST contrast has a negative trend in the 1960s and 1970s, the 1966–74 trend magnitude is less than 10% of that in the observations (−0.051°C decade−1), suggesting only a modest role of forcing in the observed trend. As shown in Fig. 5c, the 1966–74 observational trends are larger than any of the 36 historical realizations over this period. The 1918–26 observational interhemispheric SST trends are also much larger than the CMIP5 historical ensemble mean (0.008°C decade−1), but not as far outside the distribution of the 36 individual realizations as the late 1960s–early 1970s shift (Fig. 5b).
The observational spatial SST trends are shown for the two periods in Figs. 5d–g. The 1966–74 trends (Figs. 5e,g) have a prominent north–south SST dipole pattern in the Atlantic, with pronounced cooling in the subpolar North Atlantic and warming in the extratropical South Atlantic, extending to the other midlatitude basins. There is also strong cooling in the central equatorial and northeast Pacific, and a warming in the northwest Atlantic offshore the northeast United States. The 1918–26 trends (Figs. 5d,f) have pronounced cooling from 35° to 50°S in the Atlantic and Indian sectors. There is strong warming in the equatorial Atlantic, the Labrador Sea, the northeast Pacific, and the northern Nordic and Barents Seas (where not masked in ERSSTv5). The spatial trend patterns are very similar if the historical multimodel mean SST is regressed out at each grid box (not shown).
b. Forced and unforced contributions to the late 1960s–early 1970s and early 1920s shifts
We examine the contributions of forced and unforced variability to the late 1960s–early 1970s and early 1920s shifts, based on the detection and attribution best-estimate residuals from section 4. Figure 6a shows (from Fig. 3d) and the corresponding 9-yr running trend. The 1966–74 shift remains the most prominent in both best-estimate residuals, with 87% and 77% of the respective magnitudes of the trends in HadSST3 and ERSSTv5 (Table 3). The 1918–26 interhemispheric trend has nearly the same magnitude in the best-estimate residual HadSST3 as the full dataset (94% unforced) but is more reduced in ERSSTv5 (71% unforced).
We also examine the (Fig. 6b) and (Fig. 6c) contributions to the interhemispheric SST shifts. Both shifts result from additive trends of the NH and SH best-estimate residuals: NH cooling plus SH warming from 1966 to 1974, and NH warming plus SH cooling from 1918 to 1926. Over 1966–74 has pronounced cooling trends (Table 3), with the largest magnitude 9-yr trend over the entire record for HadSST3, and the second-largest in ERSSTv5 after cooling around 1900; also has large warming over this period in ERSSTv5. Warming in and cooling in also interfere constructively to produce the 1918–26 interhemispheric SST trend.
Figure 7a compares the 1966–74 trends in observations and best-estimate residuals with the largest-magnitude negative (SH–NH) 9-yr interhemispheric SST trends in each of the nonoverlapping 132-yr control segments. The 1966–74 observed interhemispheric SST trends (solid lines) exceed all trends from the control simulations; however, the reduced-magnitude trends (dashed lines) are comparable to some of the largest-magnitude control trends. The largest-magnitude negative trend segments are found in HadGEM2-ES, CSIRO-Mk3.6.0, IPSL-CM5A-LR, and GFDL CM3, which are among the high-standard-deviation models in Fig. 3e. (Several control segments exceed the 1918–26 observational and trend magnitudes; not shown.)
Figures 7b–f show the spatial patterns associated with the five largest-magnitude negative interhemispheric SST trends in the control simulations indicated in Fig. 7a. The trends have general agreement with an interhemispheric dipole in the in the tropical and subtropical Atlantic, with cooling in the NH and warming in the SH. HadGEM2-ES years 114–122 (Fig. 7d) and GFDL-CM3 years 14–22 (Fig. 7f) show strong subpolar Atlantic cooling with warming extending off the northeast United States, and GFDL CM3 years 14–22 also show prominent subpolar SH warming in the Weddell Sea region. In contrast, IPSL-CM5A-LR years 608–616 have subpolar North Atlantic warming south of Greenland (Fig. 7c). CSIRO-Mk3.6.0 years 310–318 (Fig. 7b) and HadGEM2-ES years 364–372 (Fig. 7e) have a horseshoe pattern of midlatitude cooling associated with North Atlantic SST variability (Gastineau and Frankignoul 2015) but are less prominent in the central subpolar region. In the Pacific, CSIRO-Mk3.6.0 years 310–318 (Fig. 7b) show a triangle-shaped pattern resembling the transition to the negative phase of the Pacific decadal oscillation (PDO)/interdecadal Pacific oscillation (IPO) (Zhang et al. 1997; Mantua et al. 1997; Power et al. 1999), with the other model episodes generally showing the opposite phase.
7. Summary and discussion
In this study, we quantify the variability of the interhemispheric SST contrast, motivated by its importance for tropical rainfall. We examine the variability of the 3-yr mean interhemispheric SST contrast from 1881 to 2012 in the HadSST3 and ERSSTv5 datasets, applying a detection and attribution analysis using multimodel mean fingerprints from 36 total realizations of 10 CMIP5 models to identify the contributions from natural and anthropogenic forcing. We also investigate the constituent Northern Hemisphere (NH) and Southern Hemisphere (SH) SST variability. Our key findings include the following:
The temporal magnitude of observed interhemispheric SST variability is within the range of the historical CMIP5 simulations examined. The observed spatial pattern of the interhemispheric SST contrast projects most strongly over the subpolar North Atlantic and the extratropical South Atlantic and Indian Oceans. The historical model mean spatial pattern also has strong amplitudes over the extratropical South Atlantic and Indian Oceans, but is much stronger over the North Pacific than the North Atlantic. The tropical rainbands shift toward the relatively warmer SST hemisphere in both observations and models, although most models underestimate the precipitation response over northern tropical land regions.
Anthropogenic, but not natural forcing, is detected at the 95% significance level in the interhemispheric SST contrast. The anthropogenic scaling factors are consistent with the multimodel mean in HadSST3, but results with ERSSTv5 suggest a larger interhemispheric SST response to forcing than simulated in the multimodel mean. We find a significantly larger amplitude of the anthropogenic influence on SH SST than the multimodel mean in both datasets. Natural forcing is detected (p < 0.05) in the NH and SH in HadSST3 only.
After removing the multimodel mean forced signal, the HadSST3 and ERSSTv5 best-estimate residual unforced interhemispheric SST variability is largely consistent in magnitude with that of the control simulations (and the historical realization best-estimate residuals). However, the observational best-estimate residual individual NH and SH SST are more positively correlated than in any of the control simulations examined.
Using 9-yr running trends, we determine that the NH–SH interhemispheric SST decrease around 1970 is the most prominent shift over the instrumental period, corroborating previous identification (Baines and Folland 2007; Dima and Lohmann 2010; Thompson et al. 2010). Based on the multimodel mean detection and attribution analysis, we find that the shift was largely unforced, and due to both unforced NH cooling and SH warming. Interhemispheric SST shifts of comparable magnitude as the best-estimate residual late 1960s–early 1970s shift are found in the control simulations of some of the high-variability models (CSIRO-Mk3.6.0, IPSL-CM5A-LR, HadGEM2-ES, and GFDL CM3).
Here, we consider some potential caveats and issues raised by our analysis. In the same way that the early twenty-first-century global mean surface temperature slowdown or hiatus motivated further research into the global energy balance and ocean heat content (Xie 2016; Yan et al. 2016; Medhaug et al. 2017), we hope that examination of interhemispheric SST variability can underlie future mechanistic insights.
1) Fingerprint uncertainties
One caveat is that we do not consider intermodel differences in the multimodel mean fingerprints in our detection and attribution framework, which would add to the scaling factor uncertainties (Hannart et al. 2014; Schurer et al. 2018). First, there is intermodel spread in the GHG-only response, which may be due to non-CO2 forcings as well as different feedbacks (Jones et al. 2016). Figure 8a shows the 3-yr mean interhemispheric SST contrast anomaly time series in 35 historical GHG-only (historicalGHG) realizations (all historical realizations in Table 1 except for IPSL-CM5A-MR). The multimodel mean time series has a positive 1881–2012 trend of 0.10° ± 0.02°C per 100 years (slope ±2 adjusted standard errors, widened by a factor of as described in section 3). There are still considerable differences among the individual model mean trends, which provide an estimate of the range of the forced response: from −0.04° ± 0.04°C per 100 years in CSIRO-Mk3.6.0 to 0.31° ± 0.05°C per 100 years in IPSL-CM5A-LR (Fig. 8b). (Model mean trends are calculated for the seven models with more than one realization.) The spread of individual realizations is wider, from −0.21° to 0.38°C per 100 years, as it includes a larger contribution of model internal variability (with each realization combining forced and internal variability comparable to the actual climate). We compare the 1881–2012 historicalGHG interhemispheric SST trends with those of global mean SST (including grid points from 5°S–5°N) for each realization in Fig. 8c. The trends are strongly positively correlated (r = 0.58), suggesting that the interhemispheric SST contrast scales with global mean SST in the GHG-forced response.
Anthropogenic aerosol forcing also remains a large uncertainty in the multimodel mean anthropogenic fingerprint. Although all models examined except BCC-CSM1.1 do contain some representation of sulfate aerosol indirect effects, intermodel differences in aerosol parameterization result in different magnitudes and spatial patterns of aerosol forcing (Ekman 2014; Guo et al. 2015; Allen et al. 2015; Rotstayn et al. 2015), particularly related to aerosol–cloud interactions (Chung and Soden 2017). As only a subset of the CMIP5 modeling groups archived specific-forced historical anthropogenic-aerosol-only (historicalAA) realizations, we approximate the historicalAA interhemispheric contrast anomaly by subtracting the respective historicalGHG and historicalNat interhemispheric SST contrast time series from the historical interhemispheric SST contrast for each of the 35 realizations with historicalGHG output (Fig. 8d). Note that the internal variability of the approximate historicalAA time series will typically be larger than for an individual experiment due to it being derived from multiple experiments (historical–historicalGHG–historicalNat), which contributes to some of the intermodel spread.
For a sense of the magnitude of the aerosol response, we examine the interhemispheric SST contrast during the mid-twentieth century period of maximum interhemispheric aerosol forcing (Rotstayn and Lohmann 2002; Hwang et al. 2013; Wilcox et al. 2013), using the 1950–85 trend as in Allen et al. (2015), shown in Fig. 8e. The ensemble mean time series has a significant trend of −0.068° ± 0.014°C decade−1 (slope ±2 adjusted standard errors), and the model mean trends range from −0.16° ± 0.04°C decade−1 in HadGEM2-ES to −0.012° ± 0.032°C decade−1 in CNRM-CM5. For comparison, the observed trends over this period are −0.11° ± 0.05° and −0.16° ± 0.039°C decade−1 in HadSST3 and ERSSTv5 respectively. Improvements in spatiotemporal aerosol emission patterns and better treatment of aerosol probabilities may reduce some of the uncertainties (Schurer et al. 2018; Haustein et al. 2019). Another partially anthropogenic influence on the interhemispheric SST contrast is African dust emissions from land use change, which are poorly simulated by CMIP5 models (Evan et al. 2014; Allen et al. 2015).
Detection of natural forcing in the HadSST3 (which, as it is not infilled, is generally preferred for attribution) individual hemispheres, yet not the interhemispheric SST contrast, suggests that natural forcing over the twentieth century does not show a pronounced enough hemispheric SST contrast to be detectible, despite some hemispheric asymmetry in volcanic forcing (Haywood et al. 2013; Iles and Hegerl 2014). Recent studies increasingly show a volcanic influence on large-scale climate modes, including the AMOC, but the responses may not be well represented across models due to their complex lagged processes and limited eruption observations over the historical period (Swingedouw et al. 2017). For instance, the 1963 Agung eruption may have forced part of the North Atlantic cooling that contributed to the late 1960s–early 1970s interhemispheric SST shift (Swingedouw et al. 2013; Hodson et al. 2014). Some observational analyses also suggest that solar variability may modulate the interhemispheric SST contrast (Rajesh and Tiwari 2018), although detection and attribution studies have so far not found a significant solar influence on large-scale surface temperatures (Schurer et al. 2014).
2) Spatial and basin interhemispheric SST variability
While the basic time series diagnostics (Figs. 1c,d) suggest that the CMIP5 models effectively reproduce the temporal characteristics of the interhemispheric SST contrast, comparison of the observed (Figs. 2a,c) and model mean (Fig. 2e) spatial patterns points to some differences in the mechanisms involved. In particular, the model-mean spatial pattern has much stronger positive slopes over the North Pacific, whereas the observations have the most pronounced positive amplitudes over the subpolar North Atlantic. However, we note that the relatively short observational record and uneven SST observational data distribution, with much more data from the North Atlantic, make it difficult to evaluate the significance of these spatial pattern differences.
Examination of intramodel interhemispheric SST pattern variability suggests that the extratropical North Atlantic may be more important than suggested by the multimodel mean pattern. Figure 9 shows the ensemble standard deviation of the 36 CMIP5 historical SST regression slopes averaged in Fig. 2e. The large intermodel variability over the extratropical North Atlantic north of 40°N contrasts with the weak model-mean slopes in this region in Fig. 2e, suggesting that the different patterns cancel out in the multimodel mean.
There are similar questions about the importance of different ocean basins in the large-magnitude interhemispheric SST shifts. The spatial patterns of the early 1920s and late 1960s–early 1970s interhemispheric SST shifts (Figs. 5d–g) could result from linked ocean basin SST variability, as proposed between Atlantic and Pacific SST (Zhang and Delworth 2007; Chafik et al. 2016). On the other hand, the different ocean basins may be independent, as Goosse (2017) cautions that interhemispheric SST shifts can result from the superposition of unrelated processes. Among the control shifts, the sign difference in the eastern Pacific in CSIRO-Mk3.6.0 years 310–318 (Fig. 7b) suggests different representations linking Pacific and Atlantic SST variability, or possibly that that IPO-related Pacific variability is not important for the interhemispheric SST contrast as it extends into both hemispheres. The eastern Pacific is much less prominent in the observed shifts than in the large-magnitude control shifts, although the late 1960s–early 1970s shift does show strong central and northeast Pacific SST cooling extending to southwest North America.
Next, we discuss the subpolar North Atlantic and potential AMOC contribution to interhemispheric SST shifts. The mechanism of cross-equator ocean heat transport via the AMOC is thought to explain the interhemispheric “bipolar seesaw” SST pattern in glacial–interglacial paleoclimate records (Crowley 1992; Broecker 1998) and has been found in many modeling experiments (Vellinga and Wu 2004; Latif et al. 2006; Stouffer et al. 2007; Sun et al. 2013, 2018). Some studies have thus used the interhemispheric SST contrast as a proxy for the AMOC (e.g., Dima and Lohmann 2010), although the Atlantic interhemispheric SST pattern has been found to be a weaker AMOC indicator than North Atlantic SST in most CMIP5 models (Muir and Fedorov 2015)
An observational limitation is that continuous direct measurements of the AMOC only began in 2004 (with altimetry extending the record to 1993), which is not nearly long enough to resolve decadal and multidecadal variability. Recently, it has been proposed that the century-long SST cooling trend in the subpolar North Atlantic, sometimes referred to as the “warming hole,” indicates a long-term decrease in the AMOC over the twentieth century (Drijfhout et al. 2012; Rahmstorf et al. 2015; Caesar et al. 2018), although the relationship between these surface changes and the AMOC remains contested (Josey et al. 2018). Negative trends in subpolar Atlantic surface salinity and density since the early twentieth century are consistent with an AMOC decrease, although other factors could also be responsible (Friedman et al. 2017; Reverdin et al. 2019). Oceanographic proxy reconstructions also suggest a longer-term AMOC decline since the end of the Little Ice Age (Thibodeau et al. 2018; Thornalley et al. 2018).
As an indirect index of the AMOC, we calculate an AMOC proxy SST time series following Rahmstorf et al. (2015) and Caesar et al. (2018) as the difference of the North Atlantic subpolar gyre (SPG; 50°–15°W, 50°–60°N) and global mean SST, using 3-yr running annual means and masked as shown in Fig. 1b. First, we examine the long-term GHG-forced trends of the AMOC proxy SST index. The 1881–2012 historicalGHG multimodel mean trend of the AMOC proxy SST index (of the models examined in Figs. 8a–c) is −0.50° ± 0.07°C per 100 years (slope ± 2 adjusted standard errors), consistent with the GHG-forced AMOC slowdown simulated by the models (Caesar et al. 2018). We find that the 1881–2012 AMOC proxy SST index trends are very strongly correlated with the respective interhemispheric SST trends across the historicalGHG simulations (r = 0.77).
Next, we examine the observed and historical SST AMOC proxy time series variability. Figure 10a shows the observed 3-yr mean interhemispheric SST contrast and SST AMOC proxy time series anomalies. Although they are strongly correlated (HadSST3: r = 0.63; ERSSTv5: r = 0.58), the AMOC proxy SST time series shows stronger variability on longer decadal time scales, and the interhemispheric SST contrast lacks the long-term twentieth-century trend in the AMOC proxy SST time series. Figure 10b compares the observed correlations of the interhemispheric SST contrast and the AMOC SST proxy index with the historical models. The observed correlations are stronger than nearly all of the historical realizations, with some models showing zero or negative correlations. This is consistent with the discrepancy between Fig. 2e and Figs. 2a and 2c, indicating that the Atlantic SPG plays a much larger role in the observed interhemispheric SST contrast than in most models. This suggests that many models could be misrepresenting some processes of Atlantic interhemispheric SST variability related to the AMOC, or a common response to forcings.
Looking forward, simulation of Atlantic interhemispheric SST variability may improve with increasing model resolution. For example, Hutchinson et al. (2015) find a larger interhemispheric temperature response in an Atlantic-sector coupled climate model using an eddy-permitting 0.25° ocean resolution compared to a 1° resolution, which is typical of CMIP5 models. North Atlantic decadal variability may also improve with correction of North Atlantic mean state biases, particularly salinity, related to AMOC variability (Menary et al. 2015; Park et al. 2016; Liu et al. 2017).
A related question is the role of the AMOC in the early 1920s and late 1960s–early 1970s interhemispheric SST shifts. The AMOC proxy SST time series of Fig. 10a shows a rapid drop during the late 1960s–early 1970s shift, though not as prominent in the overall record given the larger decadal variability. The spatial SST pattern associated with the late 1960s–early 1970s shift (Figs. 5e,g) shows an Atlantic interhemispheric SST dipole suggested as an AMOC fingerprint (e.g., Dima and Lohmann 2010) as well as the specific AMOC slowdown pattern of subpolar Atlantic cooling and warming offshore the northeast United States (Saba et al. 2016; Caesar et al. 2018). Subsurface salinity and temperature profiles also suggest an AMOC decline during the mid-twentieth century concurrent with the late 1960s–early 1970s interhemispheric SST shift (Hodson et al. 2014). However, determining the role of the AMOC from alternative mechanisms is difficult on such short time scales given the lack of data over the period. For example, Wang et al. (2015) showed that atmospheric teleconnections can also produce an interhemispheric Atlantic SST dipole pattern. In contrast, the 1920s do not have a persistent increase in the AMOC proxy SST record in Fig. 10a, but rather strong interannual variability. Likewise, the spatial SST pattern associated with the early 1920s shift (Figs. 5d,f) does not have an Atlantic interhemispheric dipole; the sign change is around 30°S rather than in the equatorial Atlantic.
Decadal shifts in the subpolar North Atlantic have previously been described in several different unforced simulations involving linkages between blocking, sea ice, and AMOC feedbacks (Drijfhout et al. 2013; Kleppin et al. 2015; Moreno-Chamarro et al. 2015; Sgubin et al. 2017). Understanding how these different processes may contribute to the interhemispheric SST shifts in the control simulations remains a topic of future investigation. Among our sample of large-magnitude model events (Figs. 7b–e), HadGEM2-ES years 114–122 and GFDL CM3 years 14–22 show strong and coherent cooling in the subpolar North Atlantic and warming in the Gulf Stream extension, which are consistent with the spatial fingerprint of an AMOC slowdown (Saba et al. 2016; Caesar et al. 2018); GFDL CM3 in particular has been found to have large-amplitude multidecadal AMOC variability (Cheng et al. 2013). The warming found in GFDL CM3 years 14–22 in the high-latitude SH adjacent to Antarctica has been suggested to be an AMOC slowdown signature (Dima and Lohmann 2010). Although the IPSL-CM5A-LR control shift in years 608–616 shows strong warming in the subpolar North Atlantic, this could potentially be due to the AMOC: as shown in Muir and Fedorov (2015) (their Fig. 4), the IPSL-CM5A-LR AMOC SST spatial pattern has anomalies of opposing sign in the subpolar North Atlantic.
3) NH and SH SST variability
An intriguing finding from our detection and attribution analysis is that the best-estimate residual NH and SST are more positively correlated than in any of the control simulations (Fig. 4h). Likewise, the best-estimate residual NH and SH SST standard deviations are at the upper end of the control simulation variability (Fig. 4g), which is not the case for the interhemispheric SST contrast (Fig. 3e). The positive best-estimate residual NH and SH SST correlation and large-magnitude variability are consistent: the in-phase residual NH and SH SST variations have a canceling influence on the interhemispheric SST contrast.
There are a couple of possibilities that could account for the large positive best-estimate residual NH and SH SST correlation and large-magnitude variability. One explanation, related to the fingerprint uncertainties discussed in section 7b(1), is that there is a common NH and SH forced component that is missing or underestimated by the models. For example, climate models may underestimate the cooling from early-twentieth-century eruptions, such as Katmai (1912) and Colima (1913), accounting for the early-twentieth-century discrepancies between the NH and SH fingerprints and observations in Figs. 4a and 4b.
Common SST data biases in the NH and SH could also artificially inflate the correlation. Recent studies examining geographic biases (Cowtan et al. 2018; Chan and Huybers 2019) and hemispheric and global time series (Folland et al. 2018; Haustein et al. 2019) have found that WWII-era warming and potentially also some cooling around 1900 remain inflated in gridded observational data products. A third possibility is that the models may underestimate common decadal variability in the NH and SH SST. IPO-related Pacific decadal variability, which has been linked to excursions in global mean surface temperature (Kosaka and Xie 2013; Maher et al. 2014; England et al. 2014; Dai et al. 2015; Gastineau et al. 2019), is underestimated by many CMIP5 models (Kociuba and Power 2015; Henley et al. 2017). Pacific decadal variability may account for some of the joint negative values in residual NH and SH SST after around 2000 (Figs. 4e,f), reflecting lower global mean SST than the CMIP5 historical model mean in the so-called hiatus or slowdown (Fyfe et al. 2013; Medhaug et al. 2017).
These discrepancies raise questions about the use of model control experiments to simulate background variability, as in many detection and attribution studies (as well as other analyses such as future projections). Using control simulations with unrealistic variability means that the confidence intervals calculated in analyses using them may be over- or underconfident, which could lead to misleading conclusions. In the future, perhaps the simulation of internal variability should be treated more explicitly in model selection (e.g., Knutti et al. 2010).
A.R.F, G.C.H., and A.S. were supported by the ERC-funded TITAN project (EC-320691). A.R.F. was also supported by the U.S. NSF Grant EAPSI-1311103 and the U.K. NERC-funded SMURPHs project (NE/N006143/1). G.C.H. and A.S. were further supported by the U.K. NERC under the Belmont forum, Grant PacMedy (NE/P006752/1). S.-Y.L. was funded by the Taiwan NSC Grant 102-2611-M-001-006. J.C.H.C was supported by the U.S. DOE Office of Science, Biological and Environmental Research program (DE-FG02-08ER64588). The HadSST3 data were provided by the U.K. Met Office Hadley Center, and the ERSSTv5 data were provided by the U.S. NOAA’s National Centers for Environmental Information. We acknowledge the World Climate Research Program’s Working Group on Coupled Modeling, which is responsible for CMIP and the climate modeling groups for producing and making available their model output. For CMIP the U.S. DOE’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The CMIP5 output was hosted by the U.K. Center for Environmental Data Analysis. We thank Debbie Polson for providing the detection and attribution code and Mike Mineter for valuable assistance. We appreciate the constructive feedback from three anonymous reviewers.
Historical Simulation Residuals
The best-estimate residuals are estimated for each historical realization as follows. Building on Schurer et al. (2015), we modify the denominator scaling in Eq. (4) to account for the component of shared variance of each individual historical realization time series with the model mean fingerprint Xhistorical (the average of all historical realization time series):
where γhistorical is the respective historical realization time series.