1. Introduction
El Niño–Southern Oscillation (ENSO) accounts for most of the interannual variability in global temperature and has links to global hydrological cycling and weather patterns (Philander 1989; Ropelewski and Halpert 1987; Hoerling et al. 1997; Cai et al. 2011). Nonlinear responses to ENSO have been seen in crop yields (Porter and Semenov 2005), ocean chlorophyll concentrations (Park et al. 2011), and the number of tropical cyclones formed (Wang and Chan 2002), among other things. Changes in ENSO amplitude produce changes in the long-period average behavior of environmental systems around the world. Therefore, it is important to understand how the amplitude of ENSO varies with time.
Representation of the variability of ENSO can differ widely between models, due to either differences in model formulation or climate change (e.g., Battisti and Hirst 1989; Timmermann et al. 1999). Differences in model parameterizations are one major source of intermodel differences in the mean state of the tropical Pacific—that is, the mean strength of the tropical Pacific zonal winds and SST gradients. An example is whether the model includes cumulus momentum transport (CMT), which tends to shift the mean convection and trade winds eastward and enhance ENSO variability (Kim et al. 2007). Another source of intermodel differences is the varying strengths of the coupled atmosphere–ocean feedback loops that sustain ENSO. Van Oldenborgh et al. (2005) used a linear regression of SST changes (based on Burgers and van Oldenborgh 2003) in order to determine the strength of these processes in different models. A comprehensive review of the differences in the representation of ENSO in the models in phases 3 and 5 of the Coupled Model Intercomparison Project (CMIP3 and CMIP5) was performed by Bellenger et al. (2014).
It has been shown that ENSO behavior has large intrinsic, unforced variability, occurring on decadal and longer time scales, in both observations (Wang and Ropelewski 1995; Allan et al. 1996; Wang and Wang 1996; Kestin et al. 1998; Gershunov and Barnett 1998; Power et al. 1999; Mann et al. 2000; Hasegawa and Hanawa 2003; Kiem and Franks 2004; Kiem et al. 2003; Verdon et al. 2004) and coupled climate models (Knutson and Manabe 1998; Walland et al. 2000; Vimont et al. 2002; Hunt and Elliott 2003; Power and Colman 2006; Wittenberg 2009). It is unclear what causes this long-period variation and what length of time is adequate to constrain this variability. In evaluating a 2000-yr control simulation of the Geophysical Fluid Dynamic Laboratory (GFDL) Climate Model, version 2.1 (CM2.1) coupled global climate model (GCM), Wittenberg (2009) determined that ENSO amplitude varies on centennial time scales. He found that centennial spectra have extremes spanning a factor of 2 in power in the interannual band, with an even larger spread of spectra for 20-yr epochs. In the 4000-yr GFDL CM2.1 1860 control run, the variance in the Niño-3b region (3°S–3°N, 150°–90°W) ranges over a factor of 3 between different 40-yr epochs (Fig. 1a). In the 500-yr control run of the GFDL CM2 with Modular Ocean Model version 4p1 (MOM4p1) at coarse resolution (CM2Mc)—a lower-resolution descendant of CM2.1 described in Galbraith et al. (2011)—the variance ranges over a factor of 2 on 20-yr time scales (Fig. 1b).
Variance of Niño-3b SST anomalies in °C2 in (a) CM2.1 on 40-yr time scales and in (b) CM2Mc on 20-yr time scales, where dashed lines mark the mean plus/minus the standard deviation, and (c) the 40-yr variance vs the 40-yr average of the Niño-3b SST anomalies in CM2.1.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
The consequences of inherent long-period ENSO variability are not confined to the equatorial Pacific. ENSO has impacts on weather patterns around the globe, referred to as teleconnections (e.g., Ropelewski and Halpert 1987; Hoskins and Karoly 1981; Lau 1997; Trenberth et al. 1998). The teleconnections with ENSO are often nonlinear in nature (Hoerling et al. 1997). Figure 2 shows the regression of the log of the 40-yr smoothed precipitation onto the log of the 40-yr Niño-3 variance, which gives an idea of where ENSO holds sway over nontropical climates. A one-to-one relationship would imply that the threefold range in Niño-3b variance (Fig. 1a) would produce a threefold change in precipitation, which is largely the case in the equatorial Pacific Ocean. A 0.1 value would imply that this change would be 30%, which is still potentially important for areas like Australia and Indonesia. For example, Power et al. (2006) found that the observed average rainfall over Australia exhibits a correlation with the Niño-4 SST anomaly index of −0.53, which ranges higher and lower with interdecadal variability. In addition, the zonal pattern of ENSO-related SST anomalies influences global circulation and precipitation. For example, Kim et al. (2009) showed that tropical storm tracks in the North Atlantic basin are differently affected by central Pacific warming than by eastern Pacific warming. Ashok et al. (2007) found that ENSO-like events with a warm central tropical Pacific flanked by cooler waters to the east and west (referred to as El Niño Modoki) can, depending on the season, produce teleconnections that are the opposite of those from a conventional El Niño.
Regression of the logarithm of the 40-yr smoothed precipitation onto the logarithm of the 40-yr Niño-3 variance in GFDL CM2.1.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
Because the ENSO system exhibits multidecadal to centennial variability in its amplitude as well as its zonal pattern, it will likely require multicentury model runs to detect changes in the normal ENSO behavior due to anthropogenic forcing. Stevenson et al. (2012) evaluated Community Climate System Model, version 4 (CCSM4) CMIP5 model simulations and found that there are no statistically significant changes in ENSO variability with increases in CO2, except at the highest CO2 levels. They postulated that this lack of significance is due to the short length of the twenty-first-century simulations. In a more encompassing analysis of 27 CMIP5 models, Stevenson (2012) showed that the climate change signal is closely comparable to the naturally occurring centennial variations in ENSO in all the models. Therefore, it is important to characterize the long-period natural variability before we can try to tease out a climate change signal.
Wittenberg (2009) hypothesized that the slow variation of ENSO results from Poisson statistical behavior owing to seasonal phase locking in addition to interannual memory on short-term scales of up to 10 yr. Similar variability of the ENSO amplitude can be produced in delayed oscillator models simply as a result of integrating noise (e.g., Penland and Sardeshmukh 1995; Newman et al. 2011). This would lead one to expect the coupling between the ocean and the atmosphere to be constant in a control simulation, even as the amplitude changes. If, however, the coupling is not constant over different time periods, it might imply that there is a driving force behind the changes in coupling strength with time. Therefore, one of the goals of this paper is to identify potential driving mechanisms for long-period changes in ENSO amplitude.
There are a few possible simple explanations for the long-period variability of ENSO. One possibility is that the changes in Niño-3b anomalous SSTs are due to changes in the mean SSTs. Battisti and Hirst (1989) proposed that under climate change the zonal asymmetries across the equatorial Pacific would reduce, which they argued would decrease ENSO variability. If true, this would have important implications for understanding the response of ENSO to climate change. However, in CM2.1 the temporal range of the 40-yr mean Niño-3b SST anomalies is small compared to the overall spatial variance of SSTs (Fig. 1c). This raises the question of whether such small changes in temperature can really drive the large changes in variance. Moreover, it is evident by looking at Fig. 1c that there is not a strong relationship between the average SST and variance of the 40-yr Niño-3b SST anomalies (correlation coefficient of 0.374). Therefore, the mean temperature is not a particularly good predictor of the changes in variance. Timmermann et al. (1999) also rejected this possibility as the mechanism for enhanced interannual variability in favor of changing ocean dynamics. They argued that the strengthening of the thermocline is the most important change in the mean state of the tropical Pacific Ocean under climate change and that it enhances interannual variability. Along similar lines, Anderson et al. (2009) proposed that decreased stratification due to increased shortwave penetration would reduce ENSO-related interannual variability.
Another possibility is that the changes in Niño-3b variance are the result of a change in the shape of ENSO (Fedorov and Philander 2000), which has implications for teleconnections like those shown by Kumar et al. (2006). We would expect from Fedorov and Philander’s (2000) mechanism that epochs with low ENSO amplitude would see variance concentrated in the central tropical Pacific, while epochs with higher ENSO amplitude would be concentrated more in the eastern tropical Pacific. Instead, we see that the shapes are quite similar (Fig. 3). In this paper, high (low) variance periods are defined as periods with Niño-3b variance greater than (less than) the mean plus (minus) the standard deviation of the Niño-3b variance time series over the total 4000-yr run (e.g., epochs above/below the dashed lines in Fig. 1a). Insofar that there is a difference between high and low amplitude ENSO epochs, it is that the low-amplitude epochs seem to show two distinct peaks, a phenomenon that does not map neatly onto the Fedorov and Philander theory.
(a) Variance of SST anomalies (averaged over 3°S–3°N) during high (red) and low (blue) variance 40-yr periods and (b) variance normalized by its zonal mean in CM2.1.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
The changes in SSTs (Fig. 1c), precipitation (Fig. 2), and ENSO shape (Fig. 3) are difficult to interpret in part because it is unclear whether they result from or drive changes in ENSO amplitude. Distinguishing between cause and effect requires an examination of the changes in the response of the ocean to the atmosphere as well as changes in the response of the atmosphere to the ocean. This paper examines these responses by building upon the framework proposed by van Oldenborgh et al. (2005) for examining intermodel differences in oceanic temperature responses. This is an extremely useful method for characterizing the long-period variability in ocean–atmosphere coupling strengths.
The outline of this paper is as follows. Section 2 presents the models upon which the regression is performed. Section 3 describes the theory underlying the linear regression technique and the methodological application herein. The results of the linear regression on the models are presented and compared in section 4a. To identify potential driving mechanisms of multidecadal variability, section 4b first investigates the connection between the model regression coefficients and ENSO variability (with a focus on the oceanic response to atmospheric forcing). Then the paper extends the regression technique to the individual temperature tendency components associated with specific transport mechanisms. Section 4c examines the atmospheric response to oceanic forcing, while section 5 summarizes our procedure and findings, linking the results to implications for evaluating and using climate models.
2. Models and data
This paper investigates the variability in ENSO amplitude and ocean–atmosphere coupling strengths on multidecadal time scales in three models, two of which are control runs. The first is the 4000-yr preindustrial control run of the GFDL CM2.1, which couples atmosphere, ocean, land, and sea ice components (Delworth et al. 2006). The atmospheric component has a horizontal resolution of 2.0° latitude by 2.5° longitude with 24 vertical levels. The ocean component has a horizontal resolution of 1° in the extratropics, with zonal spacing reducing to ⅓° near the equator. The ocean has 50 vertical levels, the first 22 of which are evenly spaced by 10 m. CM2.1 is ranked among the world’s best GCMs in terms of its simulation of global climate as well as ENSO (van Oldenborgh et al. 2005; Wittenberg et al. 2006; Guilyardi 2006; Reichler and Kim 2008). The model does not use flux adjustments. The control run holds atmospheric composition, insolation, and land cover constant at 1860 values, which means that all variability in the simulation is internally produced, as opposed to being driven by any anthropogenic (greenhouse gas, aerosol, and land use change) or natural (solar variability, volcanic aerosol) climate forcings. The length of the 4000-yr simulation makes it a prime candidate for examining long-period variability.
However, CM2.1 did not save out all of the temperature tendency components associated with radiative fluxes into the ocean’s surface and large eddies within the mixed layer, which are essential for distinguishing between advective and diffusive changes. Therefore, we also present the results of the analogous 1860 control run of the 500-yr GFDL CM2Mc at coarse resolution (Galbraith et al. 2011), which saves out all temperature tendency terms (advective, diffusive, and eddy tendencies). CM2Mc is a lower-resolution version of the GFDL CM2Mc that uses no flux adjustments. It is very similar to the GFDL coupled model CM2.1 (in particular the column physics in the atmosphere are identical), but it has a coarser resolution in both atmosphere and ocean and uses an updated version of the Modular Ocean Model ocean code (MOM4p1) that includes a parameterization of mixed layer eddies as described in Fox-Kemper et al. (2011). The ocean meridional resolution in CM2Mc varies between 3° and ⅔°, with sufficiently high resolution to resolve the equatorial waveguide and produce a reasonable ENSO (Galbraith et al. 2011). Possible mechanisms controlling unforced changes in coupling strengths in these two models are explored in order to provide a baseline for comparison with twentieth-century, twenty-first-century, and future CO2-forced changes.
This paper also analyzes the GFDL Ensemble Coupled Data Assimilation (ECDA) system, which was developed using the same basic model configuration as CM2.1 but strongly constrained by observations. ECDA uses CM2.1 to interpolate in data-poor regions and time periods. Therefore, differences between ECDA and CM2.1 are likely due to the addition of data constraints rather than to some underlying difference in physical parameterizations. The ECDA has been shown to be a good representation of the ocean variability associated with ENSO and other climate modes (Chang et al. 2013). This study uses ECDA reanalyzed ocean temperatures and surface wind stresses for the period 1961–2010 (Zhang et al. 2007) in order to compare the two control runs to the observed variability of the tropical Pacific.
3. Theory and methodology
Several phenomena play a role in the natural fluctuations associated with ENSO in the Niño-3b region: coastal and equatorial upwelling, zonal SST gradients, thermocline depth variations, and atmospheric circulation induced by east–west sea level pressure asymmetry. These various components determine the characteristics of ENSO. In essence, there is a positive feedback loop (Bjerknes 1966) whereby wind anomalies over the central equatorial Pacific cause wave propagation to the east in the top layers of the ocean that generate thermocline depth anomalies (Fig. 4). This results in coastal upwelling that brings cooler seawater from depth up to the surface in the eastern equatorial Pacific, thereby producing a zonal SST gradient, which reinforces the pressure asymmetry along the equator and initiates further atmospheric circulation. The inner loop in Fig. 4 portrays how the zonal winds push the cooler upwelled waters in the east toward the west, which cools the surface of the ocean in the central equatorial Pacific (Wyrtki 1975; Picaut et al. 1996). Given that the ocean is often assumed to modulate climate on long time scales (Hasselmann 1976), it is reasonable to hypothesize that long-period changes in the structure of the ocean might produce changes in the strength of coupling that would modulate ENSO amplitude.
The main feedbacks in the ENSO cycle (van Oldenborgh et al. 2005)—licensed under a creative commons license 2.0.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
Van Oldenborgh et al. (2005) evaluated the performance of Eq. (2) on climate models that were prepared for the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) and on observations from the Tropical Atmosphere Ocean (TAO) array. The models exhibit varying sensitivities to the feedback processes captured by the regression coefficients. Of all the models tested, the CM2.1 twentieth-century run was among the top performers in exhibiting a realistic and balanced ENSO cycle as depicted by the regression coefficient strengths when compared to observations. However, the CM2.1 twentieth-century run has climate forcing built in and is relatively short in duration. One of the questions addressed here is how Eq. (2) performs on the model when there is no climate forcing built in.
4. Results
a. Model results and comparison with ECDA
The results of the linear regression (averaged over 3°S–3°N) are shown in Fig. 5 for CM2.1 and in Fig. 6 for CM2Mc. The CM2.1 regression coefficients are shown for 40-yr time scales (Fig. 5, left: thin gray lines), 200-yr time scales (Fig. 5, right: thin gray lines), and the entire 4000-yr duration (Fig. 5: thick black lines). High variance periods are colored red, while low variance periods are colored blue. It is clear that for 40-yr evaluation periods the CM2.1 control run produces widely ranging regression coefficients across epochs. The regression coefficients range within about a factor of 2 from the 4000-yr regressed amplitudes. Thus, the atmosphere–ocean coupling strengths are not constant in the CM2.1 control run but, in fact, change on multidecadal time scales. Over longer evaluation periods, such as 200 yr (Fig. 5, right), the regression coefficients are more well constrained across different epochs.
Regression coefficients α (km−1 month−1)—the thermocline depth parameter, β (kPa−1 month−1)—the wind stress parameter, and γ−1 (months)—the damping time—averaged over 3°S–3°N in CM2.1 (bold black lines), in the ECDA reanalysis (dashed bold black lines), and in time periods of two different durations in CM2.1 (thin gray lines): (left) 40-yr epochs and (right) 200-yr epochs, where red (blue) lines indicate high (low) Niño-3b variance periods.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
Regression coefficients α (km−1 month−1)—the thermocline depth parameter, β (kPa−1 month−1)—the wind stress parameter, and γ−1 (months)—the damping time—averaged over 3°S–3°N, on 20-yr epoch time scales in CM2Mc (thin gray lines), where red (blue) lines indicate high (low) Niño-3b variance periods, and in the ECDA reanalysis (dashed bold black lines).
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
The CM2Mc regression coefficients were only evaluated on 20-yr time scales (Fig. 6) owing to the shorter duration of the model run. Although this produces very few samples (25 to be exact, of which only 2 are low variance and 3 are high variance), evaluating on any shorter time scales would run the risk of capturing interannual variations, which would dilute the longer-term behavior. The CM2Mc regression coefficients exhibit qualitative agreement with those of CM2.1, which gives us some degree of confidence that the CM2Mc can be used to decompose these regression coefficients into the individual temperature tendency terms that drive them.
In looking at the 40-yr CM2.1 regression coefficients in Fig. 5, it is clear that there are large differences between how the system responds to the thermocline depth and wind stress anomalies in times of high and low variance. There are two main regions in the pattern of α where there is a distinguishable difference between high and low variance periods: 170°E–170°W (the αwest region) and 138°–118°W (the αeast region). During high variance 40-yr periods there is weaker response of local SST changes to thermocline depth anomalies in the αwest region and a stronger response in the αeast region. Another way of looking at this is that αeast − αwest (the difference between the 40-yr average α in each of those regions) tends to be negative during low variance periods and positive during high variance periods. In essence, αeast − αwest can be used as a metric of the response of the SST to the slope of the thermocline in this model because it captures the relationship between ENSO amplitude variance and the thermocline depth fluctuations around an inflection point that is somewhere between those two regions. There is also a clear zonal shift in the shape of α between high and low variance periods, evident on both 40-yr and 200-yr time scales. In the CM2Mc, there is a qualitatively similar trend in the αeast region such that there is higher response of local SST changes to thermocline depth anomalies during high variance periods. There does not appear to be a similarly strong separation in the αwest region, but it is difficult to tell given the small number of samples.
The pattern of the 40-yr CM2.1 β exhibits differences in its magnitude between high and low variance periods over much of the equatorial Pacific (180°–90°W). Lower variance periods are associated with higher β in the central equatorial Pacific, indicating a stronger response of the local SST change to wind stress anomalies, and lower β in the eastern equatorial Pacific, indicating a weaker response to wind stress anomalies and of the opposite sign (and vice versa for high variance periods). The pattern of the CM2Mc β shows a similar separation between high and low variance periods in much of the central equatorial Pacific, but the signal becomes ambiguous east of 120°W.
The pattern of the 40-yr CM2.1 γ−1 does not exhibit a clear difference between high and low variance 40-yr periods, except perhaps in the easternmost reaches of the equatorial Pacific basin. However, there does appear to be less damping in the western and central equatorial Pacific during times of low variance on 200-yr time scales. In CM2Mc, there is some evidence of separation in the pattern of γ−1 in the western and central equatorial Pacific, although the high variance periods are not actually very different from normal variance periods (periods within one standard deviation of the mean). In both models in the region around 130°–110°W the low variance periods actually bracket the high variance periods.
These regression coefficients are not directly comparable to those calculated by the original study of van Oldenborgh et al. (2005) from the climate-forced CM2.1 simulation and from observations for three reasons. First, this study uses a constant finite upwelling time δ [from Eq. (2)] as opposed to a variable one. Second, the CM2.1 twentieth-century run has climate forcings built in, while the 4000-yr control run keeps climate parameters constant at 1860 values. Third, van Oldenborgh et al. evaluated a single century, while we evaluate multiple centuries, in addition to multidecadal time scales. From our analysis, we can infer that a single-century regression may produce regression coefficients that have very different amplitudes compared to other centuries.
Comparing the regression coefficients presented in this study to the observationally derived regression coefficients in van Oldenborgh et al. (2005) is also complicated because it would be difficult to determine what amount of the differences is due to model inadequacies in representing the real world and what amount is due to the difference of including or excluding climate forcing, not to mention the differences in measurement locations. In an effort to address this issue, the regression is performed on the ECDA reanalysis, which has been shown to agree well with observations in both climatology and variability for the 50-yr period between 1961 and 2010. Ensemble Coupled Data Assimilation is ideal for comparison because it is essentially assimilating data into CM2.1.
The resulting ECDA regression coefficients, as shown in Figs. 5 and 6 as the bold dashed black lines, display some qualitative similarities to the model-regressed coefficients. The shape of the CM2.1 α is very similar to that of ECDA but with higher amplitude. In addition, there are slight zonal differences in the shape of α between CM2.1 and ECDA. The shape of β differs largely between ECDA and CM2.1, with the CM2.1-regressed β having higher amplitude. The peaks of the CM2.1 γ−1 appear to be shifted slightly to the west when compared to the ECDA γ−1, with higher amplitude in the western equatorial Pacific and lower amplitude in the eastern equatorial Pacific. The CM2Mc regression coefficients exhibit similar biases in zonal shape to those of CM2.1, but the CM2Mc amplitudes are much closer to those of ECDA.
It is difficult to determine a mechanism underlying the biases of the model, given that ECDA does not conserve energy; that is, ECDA adds spurious sources of heat where the CM2.1 diverges from observations. However, we would conjecture that the overly strong response of the CM2.1 local change in SST anomalies to the thermocline depth anomalies (α) is due to either upwelling from too great depths, overly strong upwelling, or too much ocean mixing. The overly strong response of the CM2.1’s ocean surface to a given wind stress anomaly (β) could also be due to turbulent heat fluxes being too strong and/or upwelling coming from too great a depth. This may be because the model does not properly represent ocean eddy fluxes due to tropical instability waves (Jochum and Murtugudde 2006). The biases in the damping time (γ−1) probably result from inadequacies in the parameterization of convection and clouds in the CM2.1 (Wittenberg et al. 2006; Kim et al. 2007, 2011). For instance, Wittenberg et al. (2006) showed that the convective response in the CM2.1 is shifted too far to the west, which may explain the westward shift in the CM2.1 damping time peaks as compared to the ECDA. The regression coefficients lend themselves to understanding why CM2.1 produces an overly vigorous ENSO than has been seen over the past 50 yr, a bias noted by Wittenberg et al. (2006). In the case of the coarser CM2Mc, the ocean’s surface responds more realistically to wind stress and thermocline anomalies, which may produce more realistic ENSO amplitudes.
b. Changes in the oceanic response to the atmosphere
If multidecadal variations in ENSO amplitude are caused by changes in the strength of ocean–atmosphere coupling, they will be reflected in the regression coefficients. In general, one would expect higher ENSO amplitude variance to be associated with an ocean surface that is more responsive to both thermocline depth anomalies (larger α) and zonal wind stress anomalies (larger β) and less strongly damped (smaller γ). Figure 7 shows the correlation between the CM2.1 regression coefficients (the thin gray, blue, and red lines in Fig. 5) and the CM2.1 Niño-3b variance for each 40-yr epoch as a function of longitude. The dashed lines draw the eye to the regions that exhibit correlations above 0.5 and below −0.5, an arbitrary threshold for high correlation. The filled symbols are significant to the p < 0.01 level. The inverse damping time γ is not highly correlated with Niño-3b variance, except in the eastern equatorial Pacific where there is a strongly negative correlation. This is expected because a larger γ (shorter relaxation time) would be associated with more damping of temperature anomalies owing to weaker winds and/or more longwave trapping, thus producing lower Niño-3b variance. The wind stress regression coefficient β is highly anticorrelated with the Niño-3b variance on 40-yr time scales throughout most of the equatorial Pacific. This is the opposite of what one would expect if an increase in ENSO amplitude was due to a more responsive ocean surface. The thermocline depth regression coefficient α has a negative correlation with Niño-3b variance (also in the opposite direction to explain a stronger ENSO) in the αwest region but a positive correlation in the αeast region.
Correlation between the thermocline regression coefficient α (squares), the wind stress regression coefficient β (circles), and the inverse damping time γ (diamonds) and the Niño-3b variance on 40-yr time scales in CM2.1. Dashed black lines draw attention to the 0.5 correlation coefficient level. Filled symbols are significant to the p < 0.01 level.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
To determine what processes could be driving the long-period variations in the responsiveness of the ocean’s surface, we first examine the conceptual basis for the regression [Eq. (1)]. As stated earlier, β is expected to represent 
Indeed, the vertical temperature stratification in the subsurface equatorial Pacific is highly correlated with the Niño-3b variance on multidecadal time scales in both CM2.1 (Fig. 8a) and CM2Mc (Fig. 8b). For example, in CM2.1 the average β over the region 170°–110°W exhibits a strong negative relationship (correlation coefficient of −0.69) with the average vertical temperature stratification at 45-m depth (Fig. 11). Vertical temperature stratification is defined here as the difference between the ocean temperature at the surface box (5 m) and the temperature at any given depth. In the CM2.1, higher Niño-3b variance is concurrent with stronger vertical temperature stratification in the central equatorial Pacific, representing a shoaling of the thermocline, and weaker stratification in the eastern equatorial Pacific, representing a deepening of the thermocline. Hence, there is a strong indication that multidecadal epochs with high ENSO variance have generally flatter thermoclines and, as would be expected, less upwelling for a given wind stress in the eastern equatorial Pacific (Fig. 9a). The relationship between stratification and ENSO variance in the CM2Mc is not as strong because there are only 12 independent 40-yr epochs in the length of the 500-yr control run, but there is similar overall behavior.
Correlation between the 40-yr average vertical stratification (temperature difference between 5 m and the depth specified on the y axis) averaged over 3°S–3°N and the 40-yr Niño-3b variance in (a) CM2.1 and (b) CM2Mc. Correlation starts at 15 m because the surface bin is at 5 m and next bins are incremented by 10 m. Correlations > 0.2 are significant to the p < 0.01 level.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
CM2.1 regression coefficients averaged over 3°S–3°N of (a) anomalous upwelling speeds at 50 m (w50m) onto anomalous τx, (b) anomalous SSTs regressed onto anomalous Z20, and (c) anomalous τx regressed onto anomalous SSTs in times of high (red) and low (blue) Niño-3b variance 40-yr periods.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
Turning to α, from Eq. (1) α is expected to represent 
Additionally, Fig. 9b demonstrates that the influence of Z20 on SST (as opposed to local SST change) is not necessarily the source of the change in the correlation with Niño-3b variance. We would expect that, if changes in the responsiveness of the ocean’s surface were driving changes in ENSO variance, SST anomalies would be more sensitive to thermocline depth anomalies during high variance periods. However, higher variance periods are associated with a smaller response of SST anomalies to thermocline depth anomalies in the αwest region, while in the αeast region there is not a strong relationship with variance. This implies that the relationship between Z20 and SST is secondary to a more dominant source of variability.
The fact that there is a fairly high correlation between the average β in the central equatorial Pacific and αeast − αwest (Fig. 11) suggests that there may be similar underlying drivers of variability. In fact, the response of the ocean’s surface to thermocline depth anomalies, as indicated by αeast − αwest, is also highly correlated with ocean stratification (Fig. 11). This may point to a relationship whereby higher stratification in the αwest region shields the surface from the impact of thermocline variations. By contrast, higher stratification in the αeast region amplifies the impacts of thermocline variability, thereby increasing the contrast between surface water and the waters upwelling from below.
Still, it is puzzling that the local SST change is less responsive both to a given wind stress perturbation in the central equatorial Pacific and to a given thermocline depth perturbation in the αwest region during high variance periods. This is not due to changes in the frequency of ENSO because the variance of the change in Niño-3b temperature anomalies 
To better understand the multidecadal variability in the SST changes, we expand the linear regression equation to the individual temperature tendency components in a comparable model: the 500-yr CM2Mc control run. Temperature tendency can be decomposed into three parts: (i) the 3D advective tendency, (ii) the vertical diffusive tendency—defined as the sum of the implicit vertical diffusive temperature tendency, the K-profile parameterization (KPP) nonlocal temperature tendency (Large et al. 1994), and the shortwave heating into the surface of the ocean—and (iii) the tendency due to parameterized subgrid-scale, mesoscale, and submesoscale eddies—collectively referred to as the “eddy tendency.” In Fig. 10, the anomalous temperature tendency terms summed over the top 50 m of the ocean are regressed onto the anomalous thermocline depth, zonal wind stress, and SST on 20-yr time scales in the CM2Mc. Such a decomposition effectively separates out the physical processes that are contributing to α, β, and γ. Not all terms have the same impact on variations. For example, the amplitudes of the eddy term regression coefficients are generally an order of magnitude smaller than those from the other two tendency components, which suggests that the eddy tendency is less important in modulating long-period variability.
Regression coefficients averaged over 3°S–3°N of the anomalous temperature tendency terms: advective tendency, vertical diffusive tendency, and eddy tendency (all summed over the top 50 m of the ocean) onto the anomalous thermocline depth Z20, anomalous zonal wind stress τx, and anomalous SST in CM2Mc on 20-yr time scales, where red (blue) lines indicate high (low) Niño-3b variance.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
Figure 10a reveals that advection responds in the opposite way to thermocline depth anomalies during high and low variance periods in the αeast region, such that a deeper thermocline is associated with advective warming (cooling) during high (low) variance periods. In the αwest region, there may be some distinguishability in the responses of both advective and vertical diffusive tendency to thermocline depth anomalies, but it is not very clear (Figs. 10d,g). In the region 180°–150°W, the eddy and vertical diffusive tendencies exhibit responses of opposite sign, which may account for the weak relationship between α and ENSO variance in that area.
Looking at the β coefficients associated with the individual tendency terms, there is a clear signal in Fig. 10e. During high variance periods there is a weaker response of vertical diffusion to zonal winds in the region 160°E–120°W and a somewhat stronger response but of opposite sign at the far eastern edge of the basin. This result helps explain the puzzling relationship between β and stratification. We had originally expected that higher stratification would mean that mixing and upwelling would work on a larger temperature gradient and produce a larger change in SST. However, the response of mixing to winds actually becomes weaker under higher stratification; that is, all else being equal, the mixing coefficient drops as stratification increases. Hence, stratification is not a driver of variance but appears to respond to it and, to some extent, dampens it.
The γ coefficients show how the individual tendency term anomalies respond to SST anomalies. During low variance periods, there is a stronger response of advection to SSTs in the region 130°–110°W (Fig. 10c) and a stronger response of diffusion to SSTs in the region 150°E–170°W (Fig. 10f). However, the response is of approximately the same magnitude and of opposite sign between advective and vertical diffusive tendencies in those two regions, which explains why there is not a strong relationship between the inverse damping time and ENSO variance in those regions in Fig. 7. There does not appear to be a significant signal in any of the other regions/terms, but that could be partly due to the limited number of samples.
c. Changes in the atmospheric response to the ocean
Figure 9c draws upon the ENSO feedback cycle in order to assess the response of the atmosphere to the ocean. During high variance periods there is a notably stronger response of the atmosphere, represented by zonal wind stress anomalies, to the ocean, represented by SST anomalies, over the central equatorial Pacific from about 170° to 130°W and a weaker response of the atmosphere to the ocean from about 120° to 110°W. This is consistent with Anderson et al. (2009), who found that a warming of the eastern equatorial Pacific results in an increased wind response with a longer fetch, which amplifies ENSO amplitude. Additionally, as the center of action for the wind response moves east, the off-equatorial Rossby waves generated by the equatorial wind stress anomaly will also take longer to propagate to the west. In classical delayed oscillator type models, this acts to increase the amplitude. Accordingly, during high variance periods when the precipitation is higher in the east, the winds penetrate farther into the central part of the basin and the winds are more responsive to SSTs in the central equatorial Pacific. This indirect process provides an additional way in which changes in the atmospheric response to the ocean can feed back on the variance (Fig. 11).
ENSO correlation coefficient network on 40-yr time scales in CM2.1. Except for Niño-3b variance, which is averaged over the Niño-3b region, and αeast − αwest, which is the difference between the average over the αeast and the αwest regions, the other variables are averaged over the central equatorial Pacific (3°S–3°N, 170°–110°W). Correlation coefficients are significant to the p < 0.01 level.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
The shifting state of the atmosphere may also play a role in reducing the responsiveness of the ocean to the atmosphere. There is a strong negative correlation (−0.78) between β and precipitation over the central equatorial Pacific in the CM2.1 (Fig. 11). This is likely due to the eastward shift of the center of convection during El Niño episodes, which produces heavier precipitation over the central and eastern equatorial Pacific and consequently increases the near-surface temperature stratification (e.g., Li et al. 1998).
Interestingly, there is a much stronger response of τx to SSTs during El Niño than during La Niña throughout most of the central and eastern equatorial Pacific, as shown by the interannual regression between the wind stress anomalies and SST anomalies during the different phases of ENSO (Fig. 12). Here El Niño (La Niña) is defined as the times when the Niño-3b SST anomalies are greater than (less than) the mean plus (minus) the standard deviation of the respective 40-yr average Niño-3b SST anomalies. Therefore, it seems that much of the variability in Niño-3b SST anomalies is dominated by a stronger response to warming during El Niño periods.
CM2.1 regression coefficients averaged over 3°S–3°N for anomalous τx regressed onto anomalous SST for every 40-yr period during (a) El Niño months and (b) La Niña months: high (low) Niño-3b variance periods are in red (blue).
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00147.1
5. Summary and discussion
ENSO is a dynamic process that exhibits variability over a range of different time scales (e.g., Wittenberg 2009), making it difficult to detect and/or predict externally forced changes (Knutson et al. 1997; AchutaRao and Sperber 2002; Yukimoto and Kitamura 2003; Yeh et al. 2007; Yeh and Kirtman 2004; An et al. 2005a,b; Meehl et al. 2006; Power et al. 2006; Lin 2007). Multidecadal changes in ENSO amplitude variance do not seem to be largely explained by the relatively small changes in mean temperature or by changes in the shape of ENSO, making it difficult to determine what drives such long-period variability. This paper addresses these challenges and makes progress toward isolating the causes of multidecadal variability in Niño-3b variance found in the CM2.1.
A regression of local SST changes based on van Oldenborgh et al. (2005) is applied to the CM2.1 and CM2Mc control runs in order to examine the internal coupling strength variability associated with ENSO. The model regression coefficients are also compared to those produced by ECDA, which gives insight into the physical biases of both models. CM2.1 and CM2Mc exhibit qualitatively similar regression coefficients to those of ECDA, with CM2Mc producing more realistic amplitudes than CM2.1. This analysis demonstrates that not only does ENSO amplitude range widely across multidecadal time periods, but the actual ocean–atmosphere coupling strengths exhibit large internal variability as well. In CM2.1 the regression coefficients change by about a factor of 2 on multidecadal time scales. These results suggest that it will require multiple decades to centuries-long model runs to characterize the internal long-period variability in coupling strengths. In addition, one needs to be careful using only 40 years of data to constrain model physics. This highlights the importance of producing longer proxy records of tropical temperature variability so that the mechanisms proposed here can be evaluated and compared to the real world.
To explain the long-period variability of coupling strengths (with a focus on oceanic responses to atmospheric forcing), the van Oldenborgh et al. (2005) framework was expanded in this paper to the temperature tendency components associated with 3D advection, vertical diffusive processes, and subgrid-scale eddy processes. This expansion revealed that increasing stratification in the central equatorial Pacific damps the response of the ocean to the atmosphere primarily through a decrease in vertical diffusion, highlighting the importance of mixed layer processes and potentially of salinity stratification as noted by Maes et al. (2005). An investigation of the response of the atmosphere to the ocean indicated that eastward shifts in precipitation are associated with a stronger atmospheric response to oceanic forcing in the central equatorial Pacific. Understanding such signatures of ENSO variability may contribute to the predictability of El Niño. Furthermore, the results suggest that, when the CM2.1 has a weaker (putatively more realistic) cold tongue, it ends up with a stronger (putatively less realistic) El Niño. While this result is unlikely to be true for all coupled models, it nonetheless shows how important it is to constrain all parts of the coupling cycle. Simply reducing the mean bias in one part of the system will not necessarily produce a more realistic model overall.
The analysis herein makes the assumption that a linear regression is sufficient to understand these processes. This is supported by the fact that, when we use variable finite upwelling delays, the regression model is in danger of overfitting the data. However, when we look at the interannual regression between the wind stress anomalies and SST anomalies during the different phases of ENSO, some interesting patterns emerge that suggest the picture may not be so simple (Fig. 12). Not only is there a separation in the regression pattern between El Niño and La Niña periods, but there is a strong difference in the behavior of high variance 40-yr epochs between the different ENSO phases, indicating that the coupling may be nonlinear in nature. In summary, this paper confirms previous studies on long-period ENSO variability while extending these results by identifying the driving mechanism as due to changes in coupling and describing the signature of these changes in the long-period mean states of the ocean and atmosphere.
Acknowledgments
The authors gratefully acknowledge NOAA’s and GDFL’s provision of both CM2.1 and the Ensemble Coupled Data Assimilation. The authors thank Andrew Wittenberg for useful discussions and three anonymous reviewers for useful suggestions. AR acknowledges support from NSF through the Water, Climate and Health IGERT at Johns Hopkins University.
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