1 Introduction

As the prominent interannual mode in the Earth climate system, the El Niño–Southern Oscillation (ENSO) exerts great influence on the climate and weather across the globe (e.g., Wallace and Gutzler 1981; Rasmusson and Carpenter 1982; Philander 1990; Feng and Li 2011, 2013). There is widespread concern regarding the potential change in ENSO behaviors under global warming. Yet jury is still out regarding how the ENSO variability would respond to the future warming climate (e.g., Latif and Keenlyside 2009; Collins et al. 2010; Li et al. 2017). Actually, the Earth climate system has responded and is continuing to respond to the varying external climate forcing. Investigating the physical mechanism of the ENSO variability change in the past climate provides an alternative way to understand the ENSO response to the changing climate in future (Braconnot et al. 2012a, b; Harrison et al. 2015).

The climate during the mid-Holocene (hereafter MH; 6 ka BP) offers a unique frame to study the linkage between the changes in ENSO variability and the background mean state. Based on the paleoclimate archives (e.g, the corals, molluscs, ice cores, and seafloor and lake sediments), a number of studies have documented that the level of ENSO variability is lower in MH than present-day climate (e.g., Tudhope et al. 2001; Cobb et al. 2003; Woodroffe and Gagan 2000; Koutavas and Joanides 2012; Mcgregor et al. 2013; Karamperidou et al. 2015; Emile-Geay et al. 2016; Pausata et al. 2017; White et al. 2018; and many other studies), although few studies (e.g., Cobb et al. 2013) argued that due to the high level of internal variability, it is challenging to discern the ENSO behavior change throughout the Holocene. With the aid of climate models with different complexities, many modeling studies (e.g., Clement et al. 2000; Liu et al. 2000; Kitoh and Murakami 2002; Otto-Bliesner et al. 2003; Brown et al. 2008; Zheng et al. 2008; Chiang et al. 2009; Braconnot et al. 2012; An and Choi 2014; Luan et al. 2012, 2015; Roberts et al. 2014; Emile-Geay et al. 2016; see the review by; Chen et al. 2018; Lu et al. 2018) also presented evidence about the reduction in the ENSO variability in MH compared to present-day climate, albeit showing a large spread in the level of the reduction among the model simulations.

Although the ENSO activity in MH has been widely studied, there is not a consensus on the interpretation of its reduction. Since the end of twenty century, some pioneering studies (e.g., Bush 1999; Clement et al. 1999, 2000; Otto-Bliesner 1999; Liu et al. 2000) have conducted modeling simulation to explore the ENSO response to the MH climate condition. The early work by Clement et al. (2000) suggested that the suppression of ENSO intensity was attributed to the orbital driven changes in the annual cycle over the tropical region in MH. Clement et al. (2000) also pointed out that the model employed in their study was highly idealized, and thus they could not rule out the likelihood that there are some other contributing factors that also played a role in suppressing the ENSO activity in MH. With the aid of a coupled ocean–atmosphere model, Liu et al. (2000) suggested that the reduced ENSO activity in MH was caused by the strengthened Asian summer monsoon and the altered thermocline due to the subduction of warm water from the extratropics to the equatorial thermocline. It was inferred that the reduced ENSO variance might be caused by the nonlinearity associated with frequency entrainment (Liu 2002; Timmermann et al. 2007). Such inference implied an anti-correlation between intensities of the ENSO variability and seasonal cycle; however, other modeling studies argued that both the ENSO and seasonal cycle intensities were reduced during MH (e.g., Braconnot et al. 2012) and the ENSO reconstruction records did not show such inversed relationship (Emile-Geay et al. 2016). Through conducting idealized simulations with an intermediate coupled model, Chiang et al. (2009) found that the aforementioned factors (e.g., the tropical mean state changes associated with the strengthened Asian monsoon, and the frequency entrainment’s effect) did not appear to be operating. Rather, they suggested that the MH ENSO variability reduction was induced by the suppression of the atmospheric activity in the North Pacific extratropic region. Using a coupled model with an ensemble of perturbed physics versions, Brown et al. (2008) suggested that the weakened ENSO variability in MH was associated with the strengthened mean easterly wind in the western and central Pacific equatorial region. Concurrently, Zheng et al. (2008) also suggested that the suppressed ENSO variability in MH was attributed to the strengthened trade wind in Pacific equatorial region, on the basis of PMIP2 model simulations. Consistently, Luan et al. (2012) found that the reduced ENSO intensity in MH simulated by a CGCM developed by IPSL arose from the counteractive effect due to the change in the seasonality of the equatorial thermocline depth, and they further linked the altered seasonality of thermocline depth to the enhanced Asian summer monsoon and intensified trade wind. However, these studies have not fully pointed out the key physical processes behind the strengthened equatorial easterly, i.e., how the strengthening in the background mean easterly modulated the interannual variability.

The diversity in the interpretation of the reduced ENSO intensity among the aforementioned modeling studies probably arises from that their conclusions may be model-dependent. This implies that analyzing the modeling results from multi-model simulations may reduce the uncertainty and make the conclusions relatively more credible. Another possibility is that all the aforementioned factors may contribute to the suppression in ENSO intensity in MH; however, the contribution from some factors may be greater while the contribution from the other factors may be less. Therefore, it is necessary to refine the interpretations proposed by previous studies and identify the key factors that dominate the reduced ENSO variance in MH.

To achieve this goal, this study intended to reinvestigate the mechanisms of the decrease in ENSO intensity in MH through analyzing the multi-model simulations derived from PMIP2 (Braconnot et al. 2007a, b) and PMIP3 models (Braconnot et al. 2012a, b; Taylor et al. 2012). To probe the linkage between the background mean state change and ENSO variability in MH, this study intended to quantitatively diagnose the air-sea feedback processes associated with ENSO intensity in the MH and PI simulations. This is because many ENSO studies have suggested that the ENSO variability is determined by the dynamic and thermodynamic air-sea feedback processes (e.g., Jin et al. 2006; Li 1997; Bellenger et al. 2014; Li et al. 2015, 2017). Understanding the key air-sea feedbacks responsible for the ENSO variability change could help bridge the gap between the background mean state change and interannual variability change.

The remainder of the paper is organized as follows: we outline the models, the experiment design, and the BJ index used in the study in Sect. 2; we present the changes in the ENSO variability in Sect. 3; we then explore the dominant air-sea feedback processes responsible for the MH ENSO variability change in Sect. 4; lastly, a summary is given in Sect. 5 and a discussion is provided in Sect. 6.

2 Model, experiments, and method

2.1 PMIP models and the experiments

The model outputs utilized in this study were taken from 28 CGCMs, including 15 PMIP2 models and 13 PMIP3 models. According to the experiment protocol of PMIP2 and PMIP3, two suites of experiments were mainly investigated in this study. The first is the pre-industry simulation (hereafter PI), which was employed to represent the modern-day climate, and the second is the MH simulation. In the MH simulation, the topography and ice sheets were the same as those set for the PI simulation. The concentrations of greenhouse gases set for MH simulation was also the same as those prescribed for the PI simulation, except that CH4 was changed from 760 to 650 ppb. The major difference of the forcing and boundary conditions between the two simulations lies in the difference in the orbital parameters: the eccentricity is 0.0167724 (0.018682) in PI (MH), the obliquity is 23.446° (24.105°) in PI (MH), and the angular precession is 102.04° (0.87°) in PI (MH). For more details about the PMIP models and the experiment design, please refer to Braconnot et al. (2007a, b), Taylor et al. (2012), or/and the introduction in the website of http://pmip3.lsce.ipsl.fr/. In this study, the last 100 years’ monthly datasets from the PMIP2 and PMIP3 models were utilized, and all the interannual anomaly fields were obtained through removing the climatological annual cycle from the raw monthly datasets. It is worth mentioning that the analyses associated with the quantitative diagnoses of air-sea feedback processes are conducted based on 11 PMIP3 models. This is because the PMIP2 outputs only provided the annual mean cycle for three-dimensional oceanic variables while the monthly resolution variables were needed when calculating the air-sea feedbacks, and two PMIP3 models (say, CSIRO-Mk3L-1-2 and EC-EARTH-2-2) did not provide the whole required fields.

2.2 BJ index

Based on the recharge oscillator framework (Jin 1997), Jin et al. (2006) developed a simple tool which is termed as the Bjerknes stability index (BJ index), for analyzing the ENSO-related thermodynamic and oceanic dynamic processes in coupled models. Building on the framework in Jin et al. (2006), Kim and Jin (2011a, b) further completed the tool of BJ index. Recently, the BJ index has been widely used to study the scientific issues associated with the ENSO variability change (e.g., Kim et al. 2014a, b; Liu et al. 2014; Chen et al. 2016a, b; Lu et al. 2016; Zhu et al. 2017; Chen et al. 2018; Wang et al. 2018). Following Kim and Jin (2011a, b), the specific formulations of BJ index employed in this study are shown below:

$${\text{BJ = }}\frac{{R - \varepsilon }}{2}$$
(1)
$$R= - \underbrace {{({a_1}\frac{{{{\left\langle {\Delta \overline {u} } \right\rangle }_E}}}{{{L_x}}}+{a_2}\frac{{{{\left\langle {\Delta \overline {v} } \right\rangle }_E}}}{{{L_y}}})}}_{{{\text{MA}}}} - \underbrace {{{\alpha _s}}}_{{{\text{TD}}}}+\underbrace {{{\mu _a}{\beta _u}{{\left\langle { - \frac{{\partial \overline {T} }}{{\partial x}}} \right\rangle }_E}}}_{{{\text{ ZA}}}}+\underbrace {{{\mu _a}{\beta _w}{{\left\langle { - \frac{{\partial \overline {T} }}{{\partial z}}} \right\rangle }_E}}}_{{{\text{EK }}}}+\underbrace {{{\mu _a}{\beta _h}{a_h}{{\left\langle {\frac{{\overline {w} }}{{{H_1}}}} \right\rangle }_E}}}_{{{\text{ TH }}}}$$
(2)
$$\frac{{\partial {{\left\langle h \right\rangle }_w}}}{{\partial t}}= - \varepsilon {\left\langle h \right\rangle _w} - \widetilde {F}[{\tau _x}]$$
(3)
$${\text{ }}\left\langle {\text{Q}} \right\rangle {{\text{ }}_E}= - {\alpha _s}{\left\langle T \right\rangle _E}$$
(4)
$${\text{[}}{\tau _x}]={\mu _a}{\left\langle T \right\rangle _E}$$
(5)
$${\left\langle h \right\rangle _E} - {\left\langle h \right\rangle _W}={\beta _h}[{\tau _x}]$$
(6)
$${\left\langle {{\text{H(}}\overline {w} ){T_{sub}}} \right\rangle _E}={a_h}{\left\langle h \right\rangle _E}$$
(7)
$$\langle u{\text{ }}{\rangle _E}={\beta _u}[{\tau _x}]+{\beta _{uh}}\langle h{\rangle _w}$$
(8)
$${\left\langle {{\text{H(}}\overline {w} )w} \right\rangle _E}= - {\beta _w}[{\tau _x}]$$
(9)

where Eq. (1) depicts the BJ index, which measured the ENSO’s growth rate discussed in this study; Eq. (2) describes the corresponding dynamic and thermodynamic feedbacks; and Eq. (3) denotes the heat content recharge/discharge process. In particular, the overbar denotes the climatological annual mean, T represents the ocean temperature anomaly and (u, v, w) denote the oceanic current anomalies. Here, the anomaly fields (e.g., u, v, w and T) are obtained through removing their corresponding climatological annual cycle. 〈 〉E and 〈 〉 w denote the volume integration above the mixed layer depth (\({H_1}\)) in the eastern and western boxes, respectively. Lx and Ly are the longitudinal and latitudinal lengths of the eastern box, respectively. a1 and a2 are obtained by linear regression using mixed layer temperature anomalies zonally or meridionally averaged at the eastern box boundaries and area-averaged temperature anomalies over the eastern box. \({\text{H}}\left( {\overline {w} } \right){\text{ }}={\text{ }}\left\{ {\begin{array}{*{20}{c}} {1,}&{\overline {w}>0} \\ {0,}&{\overline {w} \leqslant 0} \end{array}} \right.\) is a step function to guarantee only upward vertical motion is considered. \(\Delta\) in Eq. (2) represents the ocean current change between two boundaries; and [] in the BJ index denotes the anomaly averaged across the entire equatorial Pacific basin. From Eq. (4) to Eq. (9), \({\alpha _s}\) indicates the response of the thermodynamic damping to the sea surface temperature anomalies (SSTAs), \(\rho\) and \({C_p}\) denotes the density of seawater and the specific heat capacity, respectively; \({\mu _a}\) represents the response of zonal wind stress anomaly (\({\tau ^{\prime}_x}^{{}}\)) to SSTAs; \({\beta _h}\) denotes anomalous zonal slope of the equatorial thermocline adjusting to \({\tau ^{\prime}_x}^{{}}\); \({a_h}\) represents the impact of thermocline depth change on anomalous ocean subsurface temperature; \({\beta _u}\) indicates the response of upper-ocean zonal current anomaly to \({\tau ^{\prime}_x}^{{}}\); and \({\beta _w}\) indicates a response of anomalous upwelling to \({\tau ^{\prime}_x}^{{}}.\)

The factor R in formula (2) collectively represents the five main contributing terms of BJ index, which will be mainly analyzed in this study. For convenience, the abbreviation of these five terms are marked beneath formula 2; from left to right, they comprise two negative feedbacks [i.e., the dynamic damping by the mean advection (MA term; \(- ({a_1}\frac{{{{\left\langle {\Delta \overline {u} } \right\rangle }_E}}}{{{L_x}}}+{a_2}\frac{{{{\left\langle {\Delta \overline {v} } \right\rangle }_E}}}{{Ly}})\)) and the thermodynamic damping feedback (TD term; \(- {\alpha _s}\))] and three positive feedbacks [i.e., the zonal advection feedback (ZA term; \({\mu _a}{\beta _u}{\left\langle { - \frac{{\partial \overline {T} }}{{\partial x}}} \right\rangle _E}\)), Ekman feedback (EK term; \({\mu _a}{\beta _w}{\left\langle { - \frac{{\partial \overline {T} }}{{\partial z}}} \right\rangle _E}\)) and thermocline feedback (TH term; \({\mu _a}{\beta _h}{a_h}{\left\langle {\frac{{\overline {w} }}{H}} \right\rangle _E}\))]. The two negative feedbacks act to dampen the SST perturbation’s increase, while the positive feedbacks favor the SST perturbation’s increase. For more detailed description about the BJ index, please refer to Kim et al. (2011a, b).

In this study, we chose the commonly-used broad eastern box (180°–80°W, 5°S–5°N) when calculating the BJ index, in a similar manner to that applied by some recent studies (Liu et al. 2014; Lübbecke and McPhaden 2014; Lu et al. 2016; Hua et al. 2018), because such a broad eastern box generally contains the core region of ENSO variability, despite of location differences in the maximum center of ENSO intensity change among the models. It is worth mentioning that in the broad eastern box, the direction of the change in ENSO variability is consistent in the majority of the model simulations, which will be described more in the following section. Note that the main conclusions in the present study are not sensitive to a slight change in longitudinal boundaries of the box.

3 ENSO variability change in MH compared to PI

Figure 1 shows the spatial pattern of the changes in the standard deviation (STD) of SSTA from the 13 PMIP3 model simulations (Fig. 1a–m) and 15 PMIP2 model simulations (Fig. 1n–ab). Note that the change denotes the difference between PI and MH (MH minus PI) throughout the remaining paper. It is found that most of the PMIP3 models (10 out of 13) and most of the PMIP2 models (13 out of 15) show a decrease in the SSTA variability over the eastern Pacific, although the level of the decrease varies greatly across the model simulations. As clearly shown in the multi-model ensemble (MME) result (Fig. 1ac), the SSTA variability become weakened in the eastern equatorial Pacific, indicating that the simulated ENSO intensity is reduced in MH relative to PI. Furthermore, we added the dots in Fig. 1ac to show the specific area where the change in ENSO intensity goes to the same direction in more than 75% of the models. As indicated by the dotted areas, the consistent direction in terms of ENSO intensity change mainly locates in the broad eastern equatorial Pacific, indicating the majority of the models shows an agreement in the simulation of reduced ENSO intensity in MH. The suppressed ENSO intensity simulated by the majority of the PMIP2 and PMIP3 models naturally raises a question, are there any common contributing factors responsible for the suppressed ENSO intensity?

Fig. 1
figure 1

The difference (MH minus PI) of the standard deviation (STD) of sea surface temperature anomaly (SSTA) from a–m 13 PMIP3 models and n–ab 15 PMIP2 models (unit: K). ac presents the multi-model ensemble result from the 28 PMIP2 and PMIP3 models. The dots indicate the area where the change in ENSO intensity goes to the same direction in more than 75 percent of the models. Unit: K

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4 Dominant air-sea feedback processes for the reduced ENSO variability in MH

4.1 Changes in BJ index in MH and its relationship with ENSO variability change

Since ENSO growth involves various air-sea feedback processes, it is necessary to firstly shed light on the key air-sea feedback processes contributing to the suppressed ENSO variability in MH compared to PI. We first calculated the BJ index for the PI and MH simulations from 11 PMIP3 models. As mentioned in Sect. 2.1, the BJ index calculation and the analyses associated with ENSO-related air-sea feedbacks below are based on 11 PMIP3 model results, due to the data availability. Figure 2 shows the relationship between the ENSO variability changes and the BJ index changes among the 11 PMIP3 models. Note that the change in the STD of SSTA averaged over Niño3 region is used to indicate the ENSO intensity change in this study. As clearly seen from Fig. 2, the ENSO intensity changes in MH are positively correlated with the BJ index changes (the correlation coefficient equals to 0.81, which exceeds the significance of 95% based on t-test). The intermodel relationship that the ENSO variability and the BJ index vary in unison indicates that the BJ index could serve as an effective tool to study the issues related to ENSO variability change in MH. Physically, the decrease in BJ index in MH relative to PI indicates that the ocean–atmosphere coupled system becomes more stable in MH, and vice versa. This more stable ocean–atmosphere coupled system is unfavorable for the ENSO perturbation’s growth and therefore leads to a weakening in ENSO variability in MH than that in PI.

Fig. 2
figure 2

The scatter diagram illustrating the relationship between the ENSO intensity change (X-axis; unit: K) and the BJ index change (Y-axis; unit: year−1) among the 11 PMIP3 models. The correlation coefficient is 0.81, which is above the 95% t-test significance level. Note that the models presented here are the models that have provided all the required monthly datasets for BJ-index calculation

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Also, as shown in Fig. 3, the MME mean shows a decrease in the BJ index in MH compared to PI, which corresponds to the MME mean ENSO variability change (Fig. 1ac). From the perspective of MME mean, what physical processes are dominant for the decrease in BJ index and the resultant more stable coupled system in MH than that in PI? Among the five main contributing terms of BJ index (see the second column to the sixth column in Fig. 3), the decrease in BJ index in MH relative to PI primarily induced by the weakened TH term, followed by the weakened ZA term and EK term. Note that the change in TD term (i.e., thermodynamic damping process) makes a negative contribution to the changes in BJ index and ENSO variability during MH. This is because the TD term is a passive response to SST changes during the ENSO cycle, i.e., when a warm (cold) SSTA signal of ENSO starts to grow, the thermodynamic coupling at the ocean surface tends to damp it by releasing more (less) heat into the atmosphere. As such, when the ENSO intensity became weaker in MH than that in PI, the TD damping term would become weaker, accordingly. Therefore, the decrease of ENSO variability in MH compared to PI is attributed to the weakening in the oceanic dynamic terms (including the TH term, ZA term and EK term).

Fig. 3
figure 3

The 11 PMIP3 model ensemble result of the changes in the BJ index and its five contributing terms (unit: year−1), including the mean advection feedback (MA term), thermodynamic damping feedback (TD term), zonal-advection feedback (ZA term), thermocline feedback (TH term), and Ekman feedback (EK term). The whiskers indicate 25 and 75 percentiles, respectively

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In addition to the MME mean results shown above, the individual model results were also investigated. As presented in Fig. 4a–c, we further plotted scatter diagrams to show the relationship between the ENSO variability change and each oceanic dynamic term change individually. It is found that the ENSO variability change is highly correlated with the change in the three terms (TH, ZA, and EK). Here the correlation coefficients between the changes in the aforementioned three terms and the ENSO amplitude change are significant at the 95% confidence level, but the correlation coefficients between the changes in the other two terms (MA and TD) and ENSO amplitude change are insignificant (not shown). The individual model results further lend support to the above conclusion building on the MME mean results, that is, the weakening in the TH, ZA and EK terms gave rise to the decrease in BJ index and thus the suppressed ENSO variability in MH.

Fig. 4
figure 4

a Scatter diagram illustrating the relationship between the ENSO intensity change and the TH term change. b same as a but for the ZA term. c same as a but for the EK term. Here the correlation coefficients are, respective, 0.86, 0.73, and 0.78, which are above the 95% significance level

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It is worth mentioning two points below in terms of the MME average analyses. Firstly, the BJ index and its main contribution terms were calculated for each model and each simulation, and then the MME average was obtained. As seen from the whiskers in Fig. 3, the model dispersion was considered. However, our objective is to distinguish the most dominant drivers in the framework of multi-models. Using the MME average allowed us to identify the common drivers of ENSO intensity change in MH compared to PI. Meanwhile, the individual model results presented by the scatter diagrams (Fig. 4) further revealed the relationship between the ENSO intensity change and the changes in the dominant drivers among multi-models. Secondly, such MME average approach has been employed by some recent studies for investigating the causes of ENSO intensity change in response to external forcing change (e.g., Kim et al. 2014a, b; Chen et al. 2017). For instance, Kim et al. (2014a, b) investigated the ENSO variability change in response to future warming, via analyzing the multi-model ensemble average of the BJ index change and the ensemble average of the corresponding air-sea feedback changes derived from nine “better” CGCMs (despite of a certain spread of ENSO intensity changes among the nine samples). But we applied an unweighted multiple model average here, rather than the weighted average as was done in Kim et al. (2014a, b). This is because it is difficult to distinguish the better and worse models due to that different models show different strengths and weaknesses regarding the present-day simulation, and the better/worse present-day simulation does not mean the better/worse simulated response and changes for MH.

It is also noted that a few studies suggested a caution for applying the diagnostic tool of BJ index, as some assumptions were applied in BJ index. Thus, we particularly employed an alternative diagnostic method (i.e., mixed layer heat budget, hereafter MLHB) to re-examine the key air-sea feedback processes in causing ENSO intensity change in MH compared to PI. For detailed results, please refer to the supplementary material, which provided the specific steps of MLHB analyses and the main conclusions based on the MLHB diagnostic results. Generally speaking, the diagnostic results based on the MLHB analyses in the supplementary material are consistent with the BJ index diagnostic results above. This result supports that BJ index can be a useful tool for investigating ENSO intensity change in response to the external forcing change, which is also found in a relevant study by Wang et al. (2018). Additionally, through conducting the MLHB analyses step-by-step, we found that the nonlinear processes (e.g., the term 3, term 6 and term in Eq. 1 in the supplementary material) did not play a role in causing the reduced ENSO intensity change in MH compared to PI, as demonstrated by the individual model results (Fig. S6) and the multi-model ensemble results (Fig. S7). Based on the consistent diagnostic results derived from different diagnostic methods, we therefore will explore the physical reasons for the weakening in TH term, ZA term and EK term in MH relative to PI in the following sections.

4.2 Cause of the change in TH term

The TH term (i.e., \(TH={\mu _a} \times {\beta _h} \times {a_h} \times {\left\langle {\frac{{\overline {W} }}{{{H_1}}}} \right\rangle _E}\)) is referred to as the thermocline feedback. The thermocline feedback is a positive feedback that tends to cause the air-sea coupled system’s instability (i.e., favoring the SST perturbation’s development). The idea of this positive feedback loop is stated below. In the air-sea coupled system, assuming there is a perturbed warm SSTA signal in the eastern equatorial Pacific (EEP), it would induce an eastward zonal wind stress anomaly (\({\tau ^{\prime}_x}^{{}}\)); the eastward \({\tau ^{\prime}_x}^{{}}\) would then induce a deeper-than-normal thermocline in EEP; and the deepened thermocline would cause an anomalous warming in the ocean subsurface temperature. Through the effect of mean upwelling (\(\overline {W}\)) in EEP, the anomalous subsurface warming would feed back to the mixed layer temperature, which ultimately intensifies the initial warm SSTA signal. Here, the aforementioned response of \({\tau ^{\prime}_x}^{{}}\) to the SSTA is represented by \({\mu _a}\), the response of thermocline depth change to \({\tau ^{\prime}_x}^{{}}\) is denoted by \({\beta _h}\), and the response of anomalous subsurface temperature to the thermocline depth change is denoted by \({a_h}\).

Table 1 shows the MME mean of the strength of the air-sea feedbacks (\({\mu _a}\), \({\beta _h}\), and \({a_h}\)) associated with TH term in the PI and MH simulations, as well as the change and the change rate. It is noted that the strength of \({\beta _h}\) was reduced in MH compared to those in PI, while the strength of \({\mu _a}\) and \({a_h}\) marginally decreased in MH. Additionally, only a slight difference in the mean upwelling between PI and MH was found (not shown). Thus, the change in TH term is primarily determined by the change in the response of thermocline depth anomaly (Dʹ) to \({\tau ^{\prime}_x}^{{}}\) (i.e., \({\beta _h}\)).

Table 1 The 11 PMIP3 model ensemble result of the air-sea feedback sub-processes associated with the BJ index derived from the PI and MH simulations, as well as the corresponding change (MH minus PI) and the change rate (change/PI × 100%)
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Figure 5 shows the spatial pattern of the response of sea surface height anomaly (\(SSH^{\prime}\), a proxy of Dʹ) to \({\tau ^{\prime}_x}^{{}}\), derived from PI, MH and their difference (Fig. 5a–c). Note that a linear Dʹ–SSH relationship has been applied here, and such a relationship was also employed in many previous studies (e.g., Kim et al. 2011a, b, 2014a, b; Chen et al. 2015; Zhu et al. 2017). In both the PI and MH simulations (Fig. 5a, b), in response to a unit eastward \({\tau ^{\prime}_x}^{{}}\) in equatorial Pacific, the the thermocline slope would be less, i.e., a deeper-than-normal thermocline (positive D, ) in EEP and a shallower-than-normal thermocline (negative Dʹ) in the western equatorial Pacific (hereafter WEP). Although both the PI and MH simulations replicated the general features of \({\beta _h}\), the strength of the Dʹ response to \({\tau ^{\prime}_x}^{{}}\) was different between MH and PI. Specifically, a weakening in the Dʹ response appears in MH compared to PI (Fig. 5c). The change in Dʹ response presented in Fig. 5c agrees well with the change in the strength of \({\beta _h}\) as illustrated in Table 1.

Fig. 5
figure 5

The 11 PMIP3 model ensemble result of the response of the thermocline depth anomaly (Dʹ) to zonal wind stress anomaly (\({\tau ^{\prime}_x}\)) from a the PI simulation, b the MH simulation, and c the corresponding change. Here the Dʹ response to \({\tau ^{\prime}_x}^{{}}\) is obtained through regressing the SSHʹ field onto the equatorial Pacific \({\tau ^{\prime}_x}^{{}}\). The unit is m (N m−2)−1

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What causes the weakening in the SSHʹ or Dʹ response to \({\tau ^{\prime}_x}^{{}}\) in MH relative to PI? On the basis of the Sverdrup balance (Neelin 1991; Jin 1997), the relationship between Dʹ and \({\tau ^{\prime}_x}^{{}}\) can be expressed as

$$\frac{{\partial D^{\prime}}}{{\partial x}}=\frac{{{{\tau ^{\prime}}_x}}}{{{\rho _0}g\overline {H} }}$$
(10)

where \(\overline {H}\) denotes the mean thermocline depth; \({\rho _0}\) and \(g\) denote the seawater density and the reduced gravity, respectively. We thus firstly investigated whether the equatorial mean thermocline depth is different between PI and MH. As shown in Fig. 6, the mean thermocline depth along the equator appears nearly no change in MH compared to PI. Not that the unchanged mean thermocline depth from multi-model mean result is not due to the cancellation (i.e., the opposite changes), as the mean thermocline depth appears nearly no change in nearly all the models (not shown). This promotes us to focus on whether there exists a difference in the meridional structure of \({\tau ^{\prime}_x}^{{}}\), because recent studies (Chen et al. 2015, 2017) pointed out that if there is a change in the meridional structure of \({\tau ^{\prime}_x}^{{}}\) in a CGCM, there would be a change in the Dʹ response to \({\tau ^{\prime}_x}^{{}}\). Figure 7 depicts the meridional structure of \({\tau ^{\prime}_x}^{{}}\) from the PI and MH simulations. It is noted that the meridional structure of \({\tau ^{\prime}_x}^{{}}\) is flatter and wider in MH compared to PI. This marked change in the meridional structure of \({\tau ^{\prime}_x}^{{}}\) indicates that the distribution of \({\tau ^{\prime}_x}^{{}}\) would be less confined at the equator in MH, given the same box-averaged \({\tau ^{\prime}_x}^{{}}\) forcing in the equatorial region. Consequently, the less confined \({\tau ^{\prime}_x}^{{}}\) corresponds to a weaker \({\tau ^{\prime}_x}^{{}}\) at the equator (Fig. 7b), which would lead to a smaller Dʹ response in MH in relative to PI. Figure 8 further shows the meridional structure of SSTA derived from the two simulations. Likewise, the meridional structure of SSTA also became flatter and wider in MH than that in PI, in a similar manner to the change in the meridional structure of \({\tau ^{\prime}_x}^{{}}\). Physically, since ENSO is a coupled ocean–atmosphere system, the ENSO-related fields (SSTA and \({\tau ^{\prime}_x}^{{}}\)) naturally experienced a consistent change in the meridional structure.

Fig. 6
figure 6

The PMIP model ensemble result of the mean thermocline depth (unit: m) along the equator (averaged for 5°S–5°N) from the PI simulation (blue) and MH simulation (red). Note that the mean thermocline depth is estimated by the position where the maximum vertical gradient of mean temperature locates

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Fig. 7
figure 7

The 11 PMIP3 model ensemble result of the meridional structure of normalized \({\tau ^{\prime}_x}^{{}}\) field [units: N m−2 (N m−2)−1] averaged over Niño4 longitude range (160°E–150°W), derived from a the PI (blue) and MH (red) simulations, and b the corresponding change (black). Following Chen et al. (2017), the normalized \({\tau ^{\prime}_x}^{{}}\) field here was obtained through regressing the \({\tau ^{\prime}_x}^{{}}\) field onto the time series of Niño4-averaged \({\tau ^{\prime}_x}^{{}}\). The light blue (red) in a indicates the intermodel spread which was estimated by the intermodel standard deviation in the PI (MH) simulation

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Fig. 8
figure 8

Same as Fig. 7, but for the meridional structure of the normalized SSTA-STD field (units: K/K) averaged over eastern box longitude range (180°E–80°W). Following Chen et al. (2017), here the SSTA-STD field was normalized by the value of SSTA-STD averaged over eastern Pacific region (180°E–80°W, 10°S–10°N)

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Why does the ENSO meridional structure become flat in MH relative to that in PI? As reported by some recent studies, the ENSO meridional structure is primarily controlled by the surface poleward mean meridional current (Zhang et al. 2009, 2013; Zhang and Jin 2012; Chen et al. 2015). Figure 9 shows the mean meridional currents from the PI simulation (Fig. 9a), the MH simulation (Fig. 9b), and the corresponding change (Fig. 9c). As shown in Fig. 9a, b, the mean meridional currents exhibit the shallow meridional overturning circulation over the Pacific region in the PI and MH simulations, characterized by a poleward flow in surface layer and an equatorward flow beneath the surface layer. As shown in Fig. 9c, the surface poleward mean meridional current become strengthened in MH compared to that in PI. Consequently, the strengthened surface poleward flow results in a wider and flatter meridional structure of ENSO-related SSTA and \({\tau ^{\prime}_x}^{{}}\) in MH than that in PI.

Fig. 9
figure 9

The 28 PMIP model ensemble result of the mean meridional current averaged over the central-eastern Pacific (160°E–90°W), derived from the a PI simulation, b MH simulation, and c the corresponding change

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4.3 Cause of the change in ZA term

The ZA term (\(ZA={\mu _a} \times {\beta _u} \times {\left\langle { - \frac{{\partial \overline {T} }}{{\partial x}}} \right\rangle _E}\)) is referred to as the zonal advection feedback. It consists of the zonal gradient of mean temperature (\(\frac{{\partial \overline {T} }}{{\partial x}}\)) and two air-sea feedback sub-processes (say, \({\mu _a}\) and \({\beta _u}\)). As described above, \({\beta _u}\) represents the response of anomalous oceanic zonal current (hereafter uʹ) to \({\tau ^{\prime}_x}^{{}}\). As shown in Table 1, the strength of \({\beta _u}\) was reduced in MH compared to those in PI, while the strength of \({\mu _a}\) marginally decreased in MH. Additionally, there is only a slight difference in the \(\frac{{\partial \overline {T} }}{{\partial x}}\) between PI and MH (not shown). Thus, the weakened ZA term in MH compared to PI is primarily attributed to the reduction in the air-sea feedback of \({\beta _u}\).

Figure 10 shows the vertical-zonal section of the response of uʹ to \({\tau ^{\prime}_x}^{{}}\) (see the shaded in Fig. 10a–c) across the equatorial Pacific, derived from the two simulations and their difference. As clearly shown in Fig. 10a, b, in both the PI and MH simulations, an eastward uʹ would occur over the equatorial Pacific as a result of a unit eastward \({\tau ^{\prime}_x}^{{}}\) at the equator. However, it is found that the strength of the uʹ response to \({\tau ^{\prime}_x}^{{}}\) was weaker in MH than that in PI (see the shaded in Fig. 10c), which represents the aforementioned decrease of the \({\beta _u}\) in MH relative to PI.

Fig. 10
figure 10

Vertical-zonal section along the equator (averaged between 5°S and 5°N) of the uʹ response to the equatorial Pacific \({\tau ^{\prime}_x}^{{}}\) [shading; units: (m s−1)/(N m−2)] derived from the 11 PMIP3 model ensemble result. Specifically, a is for the PI simulation, b for the MH simulation and c for the corresponding change. The contours in c denote the difference in the wʹ response to the equatorial Pacific \({\tau ^{\prime}_x}^{{}}\) [contour interval is 1.0 × 10−5 (m s−1)/(N m−2); black solid curves denote positive value, black dashed curves denote negative value, and gray curve is the zero line]

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It is suggested by the previous studies (e.g., Su et al. 2010; Chen et al. 2015, 2016) that the uʹ along the equator consists of two main components, including the anomalous geostrophic current (\({u^{\prime}_g}\)) and the anomalous Ekman current (\({u^{\prime}_e}\)). To account for the change of the \({\beta _u}\) in MH compared to PI, we further diagnosed the two components of \(u^{\prime}\) based upon the following equations (Su et al. 2010, 2014).

$${u^{\prime}_g}= - \frac{{g{\partial ^2}D^{\prime}}}{{\beta \partial {y^2}}}$$
(11)
$${u^{\prime}_e}=\frac{1}{{\rho {H_1}}}\frac{{{r_s}{{\tau ^{\prime}}_x}+\beta y{{\tau ^{\prime}}_y}}}{{{r_s}^{2}+{{(\beta y)}^2}}}$$
(12)

where \(\beta\) is the planetary vorticity gradien, \({\tau ^{\prime}_y}\) is the meridional wind stress anomaly, and \({r_s}\) is a constant Rayleigh damping coefficient. As clearly shown in Table 2, in both the PI and MH simulations, the response of \(u^{\prime}\) to \({\tau ^{\prime}_x}^{{}}\) is dominated by the response of \({u_g}^{\prime }\) to \({\tau ^{\prime}_x}\), whereas the contribution of the response of \({u^{\prime}_e}\) to \({\tau ^{\prime}_x}\) is minor. Regarding the \({u_g}^{\prime }\) response to \({\tau ^{\prime}_x}\), previous studies (e.g., Su et al. 2014; Chen et al. 2015, 2016) reported that the change in the \({u_g}^{\prime }\) response is closely linked to the change in the Dʹ response to \({\tau ^{\prime}_x}\). This is because the maximum Dʹ over the EEP is centered at the equator (Fig. 5a, b), the weakened Dʹ response corresponds to a smaller value of \(- \frac{{{\partial ^2}D^{\prime}}}{{\partial {y^2}}}\) and hence weakened \({u_g}^{\prime }\) response (refer to Eq. 11). Therefore, the difference of \({\beta _u}\) between PI and MH is also linked to the aforementioned difference in the \(D^{\prime}\) response to \({\tau ^{\prime}_x}^{{}}\).

Table 2 The 11 PMIP3 model ensemble result of the responses of zonal current anomaly (\(u^{\prime}\)) averaged over 0–50 m, zonal geostrophic current anomaly (\({u_{\text{g}}}^{\prime }\)) and zonal Ekman current anomaly (\({u_e}^{\prime }\)) along the eastern equatorial Pacific (180°W–80°W, 5°S–5°N) to equatorial \({\tau ^{\prime}_x}^{{}}\), derived from the PI simulation, MH simulation, and the corresponding change
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4.4 Cause of the change in EK term

The EK term (\(EK={\mu _a} \times {\beta _w} \times {\left\langle { - \frac{{\partial \overline {T} }}{{\partial z}}} \right\rangle _E}\)) is referred to as Ekman feedback. It consists of the vertical gradient of mean temperature (\(\frac{{\partial \overline {T} }}{{\partial z}}\)) and two air-sea feedback sub-processes (say, \({\mu _a}\) and \({\beta _w}\)). As described above, \({\beta _w}\) represents the response of anomalous upwelling (hereafter wʹ) to \({\tau ^{\prime}_x}^{{}}\). As shown in Table 1, the strength of \({\beta _w}\) was reduced in MH compared to those in PI, whereas the strength of \({\mu _a}\) marginally decreased in MH. Additionally, there is only a slight difference in the \(\frac{{\partial \overline {T} }}{{\partial z}}\) between PI and MH (not shown). Thus, the weakened EK term in MH compared to PI is induced by the reduced strength in the air-sea feedback of \({\beta _w}\).

Why does the strength of \({\beta _w}\) become weaker in MH than PI? It may be related to the weakened response of uʹ to \({\tau ^{\prime}_x}^{{}}\) (i.e., the weakened \({\beta _u}\)) in MH compared to that in PI, because it has been demonstrated that the change in the wʹ response to \({\tau ^{\prime}_x}^{{}}\) in the equatorial region is generally coherent with the change in the uʹ response to \({\tau ^{\prime}_x}^{{}}\) due to the mass conservation (e.g., Wang et al. 2018). Specifically, in response to a unit eastward \({\tau ^{\prime}_x}^{{}}\), the weakened response of uʹ in MH relative to that in PI would weaken the surface water convergence, and hence causes a weakening in the anomalous downwelling (wʹ < 0) in the EEP (see the contours in Fig. 10c). As a result, the weaker \({\beta _w}\) ultimately results in the reduction in EK term in MH than that in PI.

Our quantitative analyses above elucidated that the change in the \(D^{\prime}\) response to \({\tau ^{\prime}_x}^{{}}\) (i.e., \({\beta _h}\)) could lead to the change in the TH, ZA, and EK terms and thus alter the ENSO variability in MH. To test this hypothesis, we further plotted a scatter diagram to illustrate the relationship between the change in \({\beta _h}\) and the change in ENSO variability. As shown in Fig. 11, it is noted that the change in \({\beta _h}\) is positively correlated with the ENSO variability change (here the correlation coefficient exceeds the 95% significance level). This result further confirms our argument, that is, the change in \({\beta _h}\) holds a key for the weakening in the oceanic dynamic terms and the resultant reduction in ENSO intensity in MH.

Fig. 11
figure 11

Scatter diagram illustrating the relationship between the ENSO intensity change (X-axis; unit: K) and the change in \({\beta _h}\) [Y-axis; unit: m (N m−2)−1] among the 11 PMIP3 models. The correlation coefficient is 0.85, which is above the 95% t-test significance level

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5 Summary

In the present modeling study, we investigated the physical cause of the ENSO intensity change in MH climate compared to present-day climate, through analyzing a suite of simulations from PMIP2 and PMIP3 models. The majority of PMIP2 and PMIP3 models show a decrease in ENSO intensity in MH compared to PI, although the degree of the decrease varies across the models. To identify the dominant factors that lead to the reduced ENSO activity in MH, we employed the BJ index to quantify the strength of the dynamic and thermodynamic air-sea feedback processes associated with the ENSO variability. The quantitative diagnostic results show that the suppressed ENSO variability in MH is primarily caused by the weakened TH term, followed by the weakened ZA and EK terms. In contrast, the change in the thermodynamic term makes a negative contribution to the suppressed ENSO variability. Our analyses further demonstrate that the weakening in the air-sea feedback of \({\beta _h}\) (i.e., the Dʹ response to \({\tau ^{\prime}_x}^{{}}\)) plays a decisive role for the reduction in the TH, ZA and EK terms in MH, and the reduced \({\beta _h}\) is further linked to the enhanced surface poleward mean meridional current.

As shown in the schematic diagram (Fig. 12), the possible explanation for the suppressed ENSO variability in MH was summarized. Among many aspects of the mean state changes under the MH orbital forcing, the enhanced surface poleward mean meridional current was identified as a dominant factor in driving the ENSO variability change in MH. The enhanced mean surface poleward meridional current gave rise to a wider and flatter meridional structure of ENSO-related anomaly fields (i.e., the SSTA and \({\tau ^{\prime}_x}^{{}}\)), which leads to the \({\tau ^{\prime}_x}^{{}}\) at the equator becomes weaker in MH than that in PI. As a result, this weaker \({\tau ^{\prime}_x}^{{}}\) at the equator induced the response of Dʹ less effectively (i.e., the strength of \({\beta _h}\) was weakened in MH relative to PI). Such weakened \({\beta _h}\) directly contributes to the reduction in the TH term. On the other hand, the weakened \({\beta _h}\) or the weakened Dʹ response could cause a weakening in the ugʹ response to \({\tau ^{\prime}_x}^{{}}\), which induces the weakening in the uʹ response to \({\tau ^{\prime}_x}^{{}}\) (i.e., \({\beta _u}\)) and the resulting weakened ZA term in MH. Meanwhile, due to the mass conservation, the weakened uʹ response to \({\tau ^{\prime}_x}^{{}}\) corresponds to a weakening in the wʹ response to \({\tau ^{\prime}_x}^{{}}\) (i.e, \({\beta _w}\)). Consequently, the weakened \({\beta _w}\) leads to the weakened EK term in MH. Eventually, the weakening in the TH, ZA and EK terms collectively suppressed the ENSO variability in MH compared to PI.

Fig. 12
figure 12

A schematic diagram that summarized the possible explanation for the reduced ENSO intensity in MH proposed in this study

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6 Discussions

In the current study, we unveiled that the change in the wind-thermocline feedback (i.e., \({\beta _h}\)) is a key factor that regulate the ENSO variability in MH through its impact on ocean dynamics. It is worth noting that a recent study that focused on the response of ENSO variance to global warming also suggested that \({\beta _h}\) is the key factor that determines the ENSO variance change (Kim et al. 2014a, b; Chen et al. 2015, 2017). This indicates that among a number of ENSO-related air-sea feedbacks, the air-sea feedback of \({\beta _h}\) seems to be more susceptible to external forcing change, and that we may need to pay more attention to the \({\beta _h}\) when studying the issues associated with the ENSO variability change. The main difference between Kim et al. (2014a, b) and our current study is discussed below. Their study attributed the change in \({\beta _h}\) to the change in the mean zonal thermocline depth based upon the future projection simulations from nine CMIP5 models; while we found that there is nearly no change in the mean zonal thermocline depth in the MH simulation compared to PI simulation (Fig. 6), and we suggested that the \({\beta _h}\) change is due to the change in the meridional structure of \({\tau ^{\prime}_x}^{{}}\), which is further linked to the change in the surface mean meridional current.

It is noteworthy that understanding the linkage between the mean state change (e.g., the mean meridional current change) and MH orbital forcing is another complex issue. A recent study (Tian et al. 2018) found that the tropical Pacific Walker circulation is strengthened in MH compared to PI in the PMIP2 and PMIP3 simulations. They suggested that in response to the MH orbital forcing, the Asian and North African monsoon precipitation was strengthened due to large-scale surface warming in Northern Hemisphere in boreal warm seasons, which caused the intensified large-scale thermally east–west circulation and the corresponding increase in the surface trade wind over the tropical equatorial Pacific. Meanwhile, some relevant studies (Chen et al. 2015, 2017) have shown that the change in the surface poleward mean meridional current is mainly caused by the change in the mean surface zonal wind due to the Ekman transport effect, through conducting sensitivity experiments with an ocean general circulation model. Therefore, the enhanced surface mean meridional currents under MH orbital forcing revealed in this study is probably associated with the strengthened Pacific trade wind in MH.

Several recent modeling studies have also carried out analyses regarding the ENSO variability change in MH relative to that in PI. The following discussion is about the consistence and difference between the others’ modeling studies and the current study. Using two coupled models from NCAR Climate System Model (CSM3) and Hadley Center Model (HadCM3) that participated in PMIP2, Roberts et al. (2014) pointed out that the reduced ENSO variance was, respectively, attributed to the reduction in the SST-wind feedback (which is analogous to the \({\mu _a}\) as introduced in this study) in CSM3 and the reduction in the oceanic temperature-wind feedback (which is analogous to the integrated effect of \({\beta _h} \cdot {a_h}\)) in HadCM3. Our results also found that all the aforementioned air-sea feedbacks—\({\mu _a}\), \({\beta _h}\) and \({a_h}\) were weakened in MH relative to PI, which is consistent with Roberts et al. (2014). But our quantitative analyses further demonstrated that the weakened \({\beta _h}\) is the key factor for the lower ENSO activity in MH, while the reductions in \({\mu _a}\) and \({a_h}\) are minor, based on the simulations by a range of PMIP3 models. Two recent studies (Tian et al. 2017; Chen et al. 2018) also suggested that the mean STC change is important for the ENSO variability change in MH, which is supported by the current finding based on multi-model simulation results. One major difference between their study and ours is that Tian et al. (2017) only investigated two model simulations (one simulation even adopted the flux adjustment scheme) in details and they only conducted the MLHB analysis, and Chen et al. (2018) only employed a single coupled model even though it exhibits excellent performance in simulating the present-day ENSO behaviors; while our conclusions were mainly based on the 13 PMIP3 models and we conducted two different diagnostic methods (BJ index and MLHB), which allowed us to identify the common drivers of ENSO intensity change in MH. Another recent study (An and Bong 2017) suggested that the reduced ENSO variability was caused by the strengthened dynamic damping (i.e., the MA term), which is due to the enhanced mean meridional currents. Our results also showed that the mean meridional currents and the corresponding MA term were intensified in MH compared to PI (i.e., the negative value of MA term becomes more negative in MH), which is consistent with their finding. However, we found that the role of the MA term change in altering the ENSO variability was relatively smaller than the other three ocean dynamic terms. The discrepancy between their finding and ours might arise from that only the selected growth season (i.e., June-December) was used in their calculation of the BJ index, while the entire 12 calendar months were used in our calculation. It is suggested that the choice of calculating BJ index through using the entire 12 calendar months (i.e., using all the monthly outputs) may be better, because the growth season of ENSO in the PMIP models is not always June–December (figure not shown), especially for the MH; and using all the monthly outputs to calculate the BJ index has been widely used in many relevant studies (e.g., Kim et al. 2011a, b, 2014a, b; Liu et al. 2014; Lübbecke and McPhaden 2014; Lu et al. 2016; Zhu et al. 2017), as the BJ index was created to measure the overall stability of ocean–atmosphere coupled system associated with ENSO.

It is worth mentioning that this study benefits from that the PMIP3 model simulation provided the monthly resolved datasets (including the ENSO-related three-dimensional oceanic variables, such as u, v, w, and T), which allowed us to conduct the quantitative analyses on a series of air-sea feedbacks associated with ENSO variability. But the possible explanation for the suppressed ENSO activity in MH proposed in this study was built on the model world, which is needed to be further tested with the aid of high time–space resolution paleoclimate proxy datasets in future.