
Figure 1 presents the SST anomaly (SSTA) averaged in the Niño 3 region (5°S–5°N, 150°W–90°W) derived from the observation and the CAMSCSM simulation. The results show that CAMSCSM could capture the obvious observed interannual variability, but it seems more regular. In addition, the simulated standard deviation (STD) is larger than that observed. Further analysis demonstrates that CAMSCSM successfully captures the observed feature of seasonal ENSO phaselocking (Bellenger et al., 2014), with the most significant STD of SSTA in the boreal winter (figure omitted). Although the seasonal variability simulated by CAMSCSM resembles that of observation, the simulated ENSO amplitude is larger (Fig. 1). To explore the relative roles of ENSOrelated feedback processes in producing the overestimated ENSO amplitude, here we employ the BJ index to investigate the corresponding physical causes.
Figure 1. Time series of Niño 3 index (°C) derived from (a) observation and (b) model simulation. The xaxis denotes time in month. (c) Standard deviations (STD; °C) of Niño 3 (blue) and Niño 3.4 indices (red).
Figure 2 shows the total BJ index and the associated five components. We can see that the BJ index in the observation is negative, indicating that the coupled system is damped. The CAMSCSM well represents the stable system just as in observation, but the value is larger in the simulation compared with observation. The deviation in such values is consistent with that in ENSO amplitude (i.e., larger ENSO magnitude in CAMSCSM than in observation, as shown in Fig. 1). By comparing the differences between simulation and observation in the five contributing terms (green bar in Fig. 2), we find that the major simulation biases lie in the underestimation of the thermodynamic feedback (TD) and thermocline feedback (TH) terms. It is noted that the biases of MA (magnitude underestimation) and EK (magnitude overestimation) also contribute to the total bias. However, even though biases are exhibited in the terms of MA and EK, the largest biases refer to effects of TD and TH. Thus, we will mainly investigate the biases of TD and TH in the present study. In addition, the sum of five feedback terms is not equal to the total BJ index; the damping rate of ocean adjustment also involves the calculation of BJ index, but the five feedback terms represent the key ENSOrelated feedback processes (Kim et al., 2011a).
Figure 2. Total BJ index and its associated contributing terms (units: yr^{–1}), derived from observation (black) and model simulation (red). Difference between the model output and observation is indicated by green bar.
The weakened TD term is directly caused by the underestimated
${\alpha _s}$ in the CAMSCSM, as shown in Table 1. Since the TH term is a product of three important regression coefficients and the mean vertical upwelling, we also present the strength of each corresponding coefficient and the mean state in Table 1. It is found that the underestimated TH term is due to the underestimation in both the mean vertical upwelling and μ_{a}, while the parameters β_{h} and α_{h} simulated by the CAMSCSM are generally similar to those observed (Table 1). Therefore, we focus on the physical mechanism for the difference in these two feedbacks (namely,${\alpha _s}$ and μ_{a}) in the following two sections.α_{s} (s^{–1}) μ_{a} (W m^{–2 }K^{–1}) β_{h} [m (N m^{–2})^{–1}] a_{h} (K m^{–1}) $\overline W $ (m s^{–1}) Observation 8.2 × 10^{–8} 0.0040 7.9 28.1 6.1 × 10^{–6} Model 4.5 × 10^{–8} 0.0030 7.2 29.1 4.5 × 10^{–6} Table 1. Important regression coefficients in TD and TH terms, derived from observation and model simulation

In this paper, we presented an overview of ENSO stability through a CGCM study. The CGCM is the CAMSCSM. By investigating the important ENSOrelated feedbacks, we found that the CAMSCSM can represent the stability of the coupled system (damped) just as in observation, but some biases still exist in the thermodynamic (TD) and the thermocline (TH) feedbacks. The physical causes responsible for the differences are as follows.
(1) The CAMSCSM underestimates the TD feedback over the CEEP. The bias in the thermodynamic process mainly arises from the bias in the simulation of the SWF. In addition, the bias in the SWF originates from the cold climatological mean state over the CEEP.
(2) Both
$\overline W $ and μ_{a} are the primary contributors to the bias in the TH feedback. Meanwhile, the relative contributions of$\overline W $ and μ_{a} are nearly identical. The bias of$\overline W $ is attributed to the climatological mean state. In addition, the surface wind stress anomaly converges around the maximum center of the PRF, which is located in the WEP. Owing to the convergence of surface wind, the$\tau _x'$ in response to SSTA (i.e., μ_{a}) is weakened over the CEEP in the CAMSCSM, suggesting that the unreasonable wind stress feedback matches the unreasonable PRF. Considering that the cold mean SST in the CEEP is the original cause of the precipitation bias, it may contribute to the bias of wind stress anomaly.Such a realistic simulation of the climatological mean state including both temperature and vertical velocity fields, especially in the CEEP, is essential to a reasonable simulation of the ENSOassociated feedback processes. The realistic background mean state plays a key role in reasonably representing ENSO features in the CGCM. In addition to the background mean state, we also find out that the “regular” interannual variability in the model simulation merits more attention in improving the CGCM, which is linked to the ENSO phase transition (Lu et al., 2018). Moreover, the biases of MA (magnitude underestimation) and EK (magnitude overestimation) also contribute to the total bias, and even though the biases are relatively slight, they require further research for improving the CGCM. The bias of μ_{a} is an important error source in the thermocline feedback; thus, the role of the individual atmospheric component of CGCM should also be an object of focus in the future. In addition, the bias of SWF, TCCF, and PRF may be also attributed to other factors, such as the convection parameterization schemes and cloud microphysical schemes in the atmospheric component (Li et al., 2014, 2015). Our planned work aims to continuously improve CAMSCSM simulation quality to better understand climate change and predict future weather and climate.
Additionally, in order to examine whether the external forcing during the historical period would impact our conclusions, we also conducted the same analysis of the “historical” simulation. It is found that the simulation biases in the “historical” simulation are similar to those in the piControl simulation, e.g., that similar bias (see online supplementary material) exists in the underestimated SWF (Fig. S1), the underestimated windSST feedback (Fig. S2), and the cold bias in the mean SST (Fig. S3). This means that the ENSOrelated simulation biases revealed in this study are the common biases in the coupled simulations of the CAMSCSM.
Appendix: About the BJ index
Based on some assumptions, Jin et al. (2006) and Kim and Jin (2011a, b) simplified the mixed layer heat budget equation. Ultimately, the areaaveraged SST tendency equation can be estimated as follows:
$$ \dfrac{{\partial {{\left\langle T \right\rangle }_{\rm E}}}}{{\partial t}} = R{\left\langle T \right\rangle _{\rm E}} + F{\left\langle h \right\rangle _{\rm W}}, \tag{A1} $$ (A1) where
$$ \begin{align} R = &  \left( {{a_1}\frac{{{{\left\langle {\Delta \overline u } \right\rangle }_{\rm E}}}}{{{L_x}}} + {a_2}\frac{{{{\left\langle {\Delta \overline v } \right\rangle }_{\rm E}}}}{{{L_y}}}} \right)  {\alpha _s} + {\mu _a}{\beta _u}{\left\langle {  \frac{{\partial \overline T }}{{\partial x}}} \right\rangle _{\rm E}} \\ & +{\mu _a}{\beta _w}{\left\langle {  \frac{{\partial \overline T }}{{\partial z}}} \right\rangle _{\rm E}} + {\mu _a}{\beta _h}{\left\langle {\frac{{\overline w }}{{{H_1}}}} \right\rangle _{\rm E}}{a_h}, \end{align}\tag{A2} $$ (A2) and
$$ F = {\beta _{uh}}{\left\langle {  \dfrac{{\partial \overline T }}{{\partial x}}} \right\rangle _{\rm E}} + {\left\langle {\dfrac{{\overline w }}{{{H_1}}}} \right\rangle _{\rm E}}{a_h}. \tag{A3} $$ (A3) In the above Eqs. (A1)–(A3), u, v, and w represent the zonal current, meridional current and vertical oceanic movement, respectively; and T represents ocean temperature. < >_{E} and < >_{W} denote volume average quantities in the eastern and western boxes (see the definitions below), respectively, from the surface to the base of the surface mixed layer depth. The overbar represents the climatological seasonal mean. L_{x} and L_{y} denote the longitudinal and latitudinal lengths of the eastern box. a_{1} and a_{2} are obtained using anomalous SST averaged zonally or meridionally at the boundaries of an areaaveraged box and areaaveraged SST anomalies (SSTA) in the eastern box. α_{s} denotes the response of the thermodynamic damping to the SSTA; here, the net surface heat flux (Q_{net}) anomaly divided by (ρC_{p}H_{1}) represents the thermodynamic damping, with ρ representing the density of seawater, C_{p} representing the specific heat capacity and H_{1} representing the mixed layer depth. More detailed description can be found in Kim et al. (Kim and Jin, 2011a, b; Kim et al., 2014).
On the right hand side of Eq. (A2), in the order from left to right, the corresponding terms indicate dynamic damping by mean advection feedback (MA), thermodynamic damping (TD), zonal advection feedback (ZA), Ekman feedback (EK), and thermocline feedback (TH). In this study, we chose a broad eastern box (5°S–5°N, 180°–80°W) and the corresponding western box (5°S–5°N, 120°E–180°) when calculating the BJ index.
Some important parameters in the BJ index and their definitions are provided in Table A1.
Parameter Definition α_{s} Response of the thermodynamic damping to the sea surface
temperature anomalies (SSTA)μ_{a} Response of zonal wind stress anomaly to SSTA β_{u} Response of anomalous upperocean zonal current to wind β_{h} Anomalous zonal slope of the equatorial thermocline
adjusting to winda_{h} Effect of thermocline depth change on ocean subsurface
temperature anomaliesβ_{w} Response of ocean upwelling to wind forcing Table A1. Definition of the parameters in the BJ index
α_{s} (s^{–1})  μ_{a} (W m^{–2 }K^{–1})  β_{h} [m (N m^{–2})^{–1}]  a_{h} (K m^{–1})  $\overline W $ (m s^{–1})  
Observation  8.2 × 10^{–8}  0.0040  7.9  28.1  6.1 × 10^{–6} 
Model  4.5 × 10^{–8}  0.0030  7.2  29.1  4.5 × 10^{–6} 