The Atlantic Multidecadal Oscillation as a dominant factor of oceanic influence on climate
Abstract
A multiple linear regression analysis of global annual mean near-surface air temperature (1900–2012) using the known radiative forcing and the El Niño–Southern Oscillation index as explanatory variables account for 89% of the observed temperature variance. When the Atlantic Multidecadal Oscillation (AMO) index is added to the set of explanatory variables, the fraction of accounted for temperature variance increases to 94%. The anthropogenic effects account for about two thirds of the post-1975 global warming with one third being due to the positive phase of the AMO. In comparison, the Coupled Models Intercomparison Project Phase 5 (CMIP5) ensemble mean accounts for 87% of the observed global mean temperature variance. Some of the CMIP5 models mimic the AMO-like oscillation by a strong aerosol effect. These models simulate the twentieth century AMO-like cycle with correct timing in each individual simulation. An inverse structural analysis suggests that these models generally overestimate the greenhouse gases-induced warming, which is then compensated by an overestimate of anthropogenic aerosol cooling.
1 Introduction
During the past century the Earth has experienced considerable warming due to anthropogenic as well as natural causes. Although a substantial body of research suggests that most of the warming has been due to an increasing atmospheric concentration of CO2 and other greenhouse gases, an exact partitioning of the magnitude of the global warming due to the natural and anthropogenic causes remains uncertain. Most climate research has centered on the use of coupled AOGCMs (atmosphere-ocean general circulation models) to elucidate the climate system from near first principles representing physical, chemical, and biological processes.
Empirical statistical models have been used recently [Lean and Rind, 2008; Foster and Rahmstorf, 2011; Mascioli et al., 2012; Zhou and Tung, 2013; Canty et al., 2013; Chylek et al., 2013] to complement physics-based models and are contributing to our understanding of anthropogenic and natural components of climate variability. The method assumes a linear relation between the observed temperature and a set of selected physically plausible explanatory variables (predictors). A typical set of explanatory variables includes the known radiative forcing and an additional factor characterizing the oceanic influence on climate [Compo and Sardeshmukh, 2009; Zhou and Tung, 2013].
Major radiative forcing includes solar variability (SOL), volcanic eruptions (VOLC) [Douglass and Clader, 2002; Haigh, 2003; Scafetta and West, 2006; Camp and Tung, 2007; Lean and Rind, 2008], anthropogenic greenhouse gases (GHG), and anthropogenic aerosols (AER). The oceanic influence is usually characterized by the El Niño–Southern Oscillation (ENSO) index [Lean and Rind, 2008; Foster and Rahmstorf, 2011]. However, the AMO (Atlantic Multidecadal Oscillation) [Schlesinger and Ramankutty, 1994; Delworth and Mann, 2000; Gray et al., 2004] also exerts a considerable influence on the global and regional climate [Polyakov and Johnson, 2000; Chylek et al., 2006, 2009; Chylek et al., 2010; Chylek et al., 2013; Zhang et al., 2007; Mahajan et al., 2011; Frankcombe and Djikstra, 2011; Zhou and Tung, 2013; Canty et al., 2013; Muller et al., 2013; Kavvada et al., 2013].
In this note we show that the observed annual mean global temperature variability is captured more fully by a regression model when the AMO is added to the set of explanatory variables. Considering a compromise between accuracy and complexity, the minimal regression model that accounts for 93% of the observed annual mean global temperature variance contains only two explanatory variables: anthropogenic greenhouse gases (GHG) and the AMO. Adding all other predictors increases the fraction of accounted for global temperature variance to 94%.
2 Data
In our analysis we use the global mean annual temperatures from 1900 to 2012 as compiled by the NASA GISS (Goddard Institute for Space Studies) available at http://data.giss.nasa.gov/gistemp/. The NASA GISS temperature time series uses spatial correlations to extrapolate temperature data to regions where there are no measurements available. This avoids a possible underestimation of recent global warming due to missing Arctic data as may possibly occur in other temperature data sets [Cowtan and Way, 2013].
Radiative forcing by anthropogenic greenhouse gases, solar variability, and volcanic aerosol (Figure 1a) are from Hansen et al. [2007, 2011], including updates as described on the NASA GISS website (http://data.giss.nasa.gov/modelforce/Fe.1880-2011.txt). The annual average ENSO index is obtained by averaging monthly data from http://jisao.washington.edu/data/cti, and the Atlantic Multidecadal Oscillation (AMO) index is an annual average of smoothed monthly values provided by the NOAA. A detailed description on how the AMO is calculated can be found at the NOAA website http://www.esrl.noaa.gov/psd/data/timeseries/AMO/.
Radiative forcing by atmospheric aerosols continues to be poorly constrained. The large temporal and spatial variability makes global averages of the aerosol optical depth and composition difficult to compute accurately. Although the direct aerosol effect (aerosol interaction with solar and terrestrial radiation) is reasonably well understood, the aerosol's indirect effect (interaction affecting cloud microstructure and cloud life cycle) is one of the major unknowns in the current state of climate science. Therefore, the aerosol radiative forcing in climate models varies considerably, with some of the CMIP5 (Coupled Models Intercomparison Project Phase 5) models restricting their treatment to a direct aerosol effect, while others include an indirect effect as well [e.g., Booth et al., 2012; Wilcox et al., 2013].
In order to encompass a wide range of aerosol radiative forcing possibilities and to show their effect on global mean temperature, we consider four different aerosol radiative forcing models (Figure 1b). The AER 1 model takes the aerosol radiative forcing as prescribed by Hansen et al. [2007, 2011] including sulfate, black carbon, and the indirect aerosol effect available on the NASA GISS website; the AER2 model uses the aerosol radiative forcing as provided by the Intergovernmental Panel on Climate Change (IPCC) fifth assessment report (Climate Change 2013: The Physical Science Basis (Chapter 8) available at http://www.climatechange2013.org/images/report/WG1AR5_Chapter08_FINAL.pdf); the AER3 is the estimate according to Mascioli et al. [2012]; and the AER4 is a hypothetical radiative forcing that simulates the effect of a sulfate aerosol decrease in the atmosphere after the 1980s.
Multiple regression analysis can lead to ambiguous results when explanatory variables are significantly correlated [Wilks, 2006]. Although the aerosol radiative forcing is correlated with the GHG forcing (the correlation coefficient is r = −0.99 for the AER1, r = −0.80 for AER2 and AER3, and r = −0.30 for AER4), we consider the GHG and aerosol forcing separately in regression models and sum up their contributions to temperature variability to obtain the combined GHG and AER effect. This differs from earlier analyses [Lean and Rind, 2008; Chylek et al., 2013] which used the sum of the GHG and AER forcings, combined into one forcing, denoted as GHGA.
3 Structural Analysis of the Observed Annual Mean Global Temperature
(1)The regression model with the above listed explanatory variables accounts for 88% to 90% of the temperature variance (Table 1) depending on which aerosol model (AER1 to AER4) is used. The residuals are found to be correlated (r = 0.52 for AER2) with the AMO index (Figure 1d), suggesting that the AMO should be considered as an additional explanatory variable. When the AMO is added to the above set of explanatory variables, the fraction of accounted for temperature variance increases to 94% (Figure 1c) regardless of the aerosol model used. The model improvement gained by adding the AMO to the set of predictors is highly statistically significant (p < 0.01). The differences among the models with different aerosol radiative forcings are found to be insignificant (Table 1). For definiteness, we consider the AER2 model in the following analysis.
| Model # | Explanatory Variables | R2adj | R2adj + AMO | RSE (K) | RSE (K) + AMO |
|---|---|---|---|---|---|
| 1 | GHG + SOL + VOLC + ENSO + AER1 (Hansen) | 0.884 | 0.942 | 0.1004 | 0.0710 |
| 2 | GHG + SOL + VOLC + ENSO + AER2 (IPCC fifth AR) | 0.895 | 0.942 | 0.0955 | 0.0711 |
| 3 | GHG + SOL + VOLC + ENSO + AER3 (Mascioli) | 0.897 | 0.942 | 0.0949 | 0.0711 |
| 4 | GHG + SOL + VOLC + ENSO + AER4 (Hypothetical) | 0.887 | 0.944 | 0.0991 | 0.0701 |
| 5 | Mean of the above models | 0.891 | 0.943 | 0.0975 | 0.0708 |
| CMIP5 ensemble mean | R2 = 0.870 | ||||
| 6 | GHG + AMO | 0.934 | 0.0758 | ||
| 7 | GHG + ENSO | 0.853 | 0.1132 | ||
| 8 | GHG + AMO + ENSO | 0.938 | 0.0737 | ||
| 9 | GHG + AMO + ENSO + VOLC | 0.939 | 0.0730 | ||
| 10 | GHG + AMO + SOL + VOLC + ENSO | 0.942 | 0.0710 | ||
| 11 | GHG + AMO + GHGxAMO | 0.934 | 0.0757 |
- a The R2adj is the square of adjusted multiple linear correlation coefficient, and RSE is the Residual Standard Error. The better model will have a higher R2adj and a lower RSE. The 100 × R2adj is the percent of the observed temperature variance accounted for by the model. An introduction of the AMO as an explanatory variable increases explanatory power of the regression model on average from 89% to 94% and decreases the average RSE from 0.0975 K to 0.0708 K (line 5). The improvements due to the AMO are highly statistically significant (p < 0.01). The regression model with just the GHG and AMO as explanatory variables (line 6) accounts for 93% of the observed temperature variance, which is significantly higher than any of the models without the AMO. When the AMO is replaced by the ENSO, the fraction of accounted for temperature variance decreases to 85% (line 7). The interaction term GHGxAMO between the GHG and the AMO (line 11) turns out to be negligible and not statistically significant, suggesting no significant interaction (GHG level does not affect the AMO) between these explanatory variables.
We apply structural model analysis in the forward (Figure 2a) as well as in the backward (Figure 2b) direction. In the forward direction, we consider first a set of all the explanatory variables. After that we remove explanatory variables one by one [e.g., Wilks, 2006] until we get a minimum set with still high explanatory power (Table 1). We end up with just two explanatory variables (GHG and AMO), while the reduction in the accounted for fraction of temperature variance decreases only by 1% (from 94 to 93%). A partial covariance between the predictors (especially between the GHG and AER) plays no role in this two-predictor model. For comparison, if the AMO is replaced by the ENSO, the fraction of accounted for temperature variance decreases from 93% to 85% (Table 1).
The function of the AMO as a moderator within a structural model is shown in Figure 2c. It serves as a full moderator [Baron and Kenny, 1986; MacCallum and Austin, 2000; Wu and Zumbo, 2008] of the AMOC (Atlantic Meridional Overturning Circulation) and as a partial moderator of other influences that affect significantly the North Atlantic sea surface temperature.
To investigate a possible interaction between increasing GHG and the AMO, we modify the two predictor models (GHG and AMO) by including an interaction term (Table 1, model #11) in the form of a product of GHG forcing and the AMO index (GHGxAMO). We find the interaction term to be negligible and not statistically significant, failing to detect an interaction between these explanatory variables (the GHG level does not currently affect the AMO; although, this does not exclude a possible future interaction).
Contributions of individual explanatory variables to the twentieth century global temperature variability is shown for the case of a regression model with a full set of statistically significant predictors (Figure 1e), and for a minimal model with just the GHG and the AMO as predictors (Figure 1f). We note that relative contributions of the GHG and the AMO change very little between the models.
The origin of the Atlantic multidecadal oscillation is not yet fully understood [Dima and Lohmann, 2007; Gulev et al., 2013]. Some authors suggested anthropogenic aerosol radiative forcing as a possible origin of the twentieth century AMO-like temperature cycle [e.g., Chylek et al., 2007; Ottera et al., 2010; Booth et al., 2012], while others [Zhang et al., 2013] disagreed. An analysis of long time series records from tree rings and ice cores [Delworth and Mann, 2000; Gray et al., 2004; Chylek et al., 2010, 2012] shows the existence of AMO-like cycles for a long time before anthropogenic effects were of any significance. The AMO-like oscillations were also found in long control runs of some climate models [e.g., Mahajan et al., 2011; Delworth et al., 2012; Wei and Lohmann, 2012; Yang et al., 2013; Zhang et al., 2013], suggesting that the origin of the AMO multidecadal cycle is related to the AMOC. The use of the AMO as an explanatory variable is the subject of an ongoing discussion; additional justification of its use can be found in recent publications [Ting et al., 2009; Wei and Lohmann, 2012; Zhang and Tung, 2013; Muller et al., 2013; Canty et al., 2013; Chylek et al., 2013; Tung and Zhou, 2013; Kavvada et al., 2013].
4 Inverse Structural Analysis of Observed and Model (AOGCMs)-Simulated Temperature
None of the CMIP3 climate models used in the IPCC fourth (2007) assessment report was able to simulate the AMO-like twentieth century cycle with proper timing in individual simulations. Therefore, it was suggested [Wang et al., 2007] that the AMO cycle was due to an intrinsic climate variability that could not be simulated by climate models with correct timing, and accordingly, the cycle was averaged out when the ensemble mean of the model simulations was calculated.
This, however, is not true anymore for the CMIP5 models used in the IPCC fifth assessment report. We find that some models (e.g., GFDL-CM3, HadGEM-ES, and CanESM2) reproduce the AMO-like cycle in each individual simulation with the correct timing (Figures 3a, 3c, and 3e). Here the AMO-like cycle can no longer represent intrinsic climate variability, but instead a forced response to some of the prescribed radiative forcing. These models (with direct and indirect aerosol effect) significantly overestimate the 1960s cooling as well as the cooling due to the Mount Pinatubo eruption of 1991. The models without an active aerosol-cloud interaction (GISS-E2-Hp1 and CCSM4) do not show such large overestimates (Figures 3b and 3d).
In the inverse (backward direction) structural analysis (Figure 2b) we project the observed global temperature and climate model simulations of the global mean temperature onto a set of explanatory variables (using equation 1 for model-simulated instead of the observed temperature) and compare the projections to identify structural differences between the projections of the individual climate models and the observed temperature.
The projection of the observed global temperature on a set of explanatory variables suggests that the greenhouse gas induced temperature variability accounts for 0.71°C ± 0.18°C of the warming between the years 1900 and 2012 (Figure 4a). The set of selected climate models (NASA GISS-E2, NCAR/LANL CCSM4, NOAA GFDL-CM3, CanESM2, and the UK Met Office HadGEM-ES) shows a GHG-induced warming varying between 0.94 (GISS-ER2) and 1.76°C (CanESM2).
The model excess warming is compensated by an overestimated cooling effect by anthropogenic aerosols. The projection of the observed global temperature on the aerosol forcing function (explanatory variable) is negligible and not statistically significant (0 ± 0.12°C), while the projected aerosol cooling in the models is up to 0.80°C (Figure 4b). The aerosol cooling is large especially in models with an explicit aerosol-cloud interaction (HadGEM-ES, GFDL-CM3, and CanESM2) while aerosol cooling in models with only aerosol direct effect (CCSM4 and GISS-E2-H1) is much closer to the aerosol component of the observed temperature (Figure 4b).
The anthropogenic component (GHG + AER) of the observed temperature is increasing monotonically with time, while the anthropogenic component of the GFDL-CM3, CanESM2, and HadGEM-ES simulations switches from warming to cooling in the 1950s and back to warming in the 1970s (Figure 4c). A strong aerosol effect explains why the AMO-like behavior is reproduced with a correct timing in each individual simulation by these models. This interpretation agrees with Booth et al. [2012] who state that the twentieth century Atlantic temperature variability in the HadGEM-ES model is due to an aerosol effect.
Considered models also overestimate the effect of solar variability and volcanic aerosols and underestimate the AMO effect (Figure 4). Although the AMO does not contribute to the long-term temperature trend, its 60 to 80 year cycle can be mistaken for a trend when a shorter time span is considered. Thus, our analysis suggests that the AMO contributed about one third to the post-1975 global warming, which could be misinterpreted as a part of anthropogenic warming if the AMO effect would be neglected [see also Zhou and Tung, 2013; Chylek et al., 2013].
The observed structural differences between the observed temperature and temperature simulated by climate models indicate the areas where climate models may benefit from improvement of the physical parameterizations. Our structural analysis suggests that the overestimate of GHG warming and aerosol cooling and the missing AMO cycles are major shortcomings of the climate models considered.
5 Summary and Discussion
A multiple linear regression model that uses the set of explanatory variables composed of radiative forcing due to anthropogenic greenhouse gases and aerosols, solar variability, volcanic eruptions, and ENSO accounts for 89 ± 1% of the global annual mean temperature variance. When AMO is added to the set of explanatory variables, the fraction of explained temperature variance increases to 94%. Just two explanatory variables (GHG and AMO) still account for 93% of the temperature variance. The improvement of the regression model by including the AMO is highly statistically significant (p < 0.01). For comparison, the CMIP5 ensemble mean of all simulations accounts for 87% of the observed temperature variance.
Our analysis suggests that about two thirds of the late twentieth century warming has been due to anthropogenic influences and about one third due to the AMO. This is a robust result independent of the parameterization of the anthropogenic aerosol radiative forcing used or of the considered regression model, as long as the AMO is among the explanatory variables.
An inverse structural analysis shows that all considered climate models (GFDL-CM3, HadGEM-ES, CCSM4, CanESM2, and GISS-E2) overestimate GHG warming that is then compensated by an overestimated aerosol cooling. The overestimates are especially large in models with an indirect aerosol effect. In these models a strong aerosol effect generates the AMO-like 20th century temperature variability. The apparent agreement with the observed temperature variability is achieved by two compensating errors: overestimation of GHG warming and aerosol cooling. This raises a question of reliability of these models' projections of future global temperature. The inverse structural analysis underscores the significance of the AMO-like oscillation and therefore the need to establish its origin and to better simulate it in future climate models.
Acknowledgments
We thank Lily Chylek for discussion and the figure of the structural model (Figure 2). Reported research (LA-UR-13-25010) was supported in part by the Los Alamos National Laboratory Institute of Geophysics, Planetary Physics, and Signatures. All data are publically available from the sources cited.
The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.
