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Changes in ENSO amplitude under climate warming and cooling


The response of ENSO amplitude to climate warming and cooling is investigated using the Community Earth System Model (CESM), in which the warming and cooling scenarios are designed by adding heat fluxes of equal amplitude but opposite sign onto the ocean surface, respectively. Results show that the warming induces an increase of the ENSO amplitude but the cooling gives rise to a decrease of the ENSO amplitude, and these changes are robust in statistics. A mixed layer heat budget analysis finds that the increasing (decreasing) SST tendency under climate warming (cooling) is mainly due to an enhancement (weakening) of dynamical feedback processes over the equatorial Pacific, including zonal advective (ZA) feedback, meridional advective (MA) feedback, thermocline (TH) feedback, and Ekman (EK) feedback. As the climate warms, a wind anomaly of the same magnitude across the equatorial Pacific can induce a stronger zonal current change in the east (i.e., a stronger ZA feedback), which in turn produces a greater weakening of upwelling (i.e., a stronger EK feedback) and thus a larger thermocline change (i.e., a stronger TH feedback). In response to the climate warming, in addition, the MA feedback is also strengthened due to an enhancement of the meridional SST gradient around the equator resulting from a weakening of the subtropical cells (STCs). It should be noted that the weakened STCs itself has a negative contribution to the change of the MA feedback which, however, appears to be secondary. And vice versa for the cooling case. Bjerknes linear stability (BJ) index is also evaluated for the linear stability of ENSO, with remarkably larger (smaller) BJ index found for the warming (cooling) case.

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We thank two anonymous reviewers for their helpful comments and suggestions that have enabled us to significantly improve this article. This work is supported by National Science Foundation of China (41676002 and 41376009) and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA11010302). J. Lu is supported by the Office of Science of the U.S. Department of Energy as part of Regional and Global Climate Modeling program.

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Correspondence to Yiyong Luo.


Appendix A: meridional volume transport

The associated change in the meridional volume transport across the tropical ocean is largely determined by the wind-stress driven Ekman transport. Following McPhaden and Zhang (2002), the meridional Ekman transport per unit longitude is calculated by the equation:

$${M_E}= - {\tau _x}/{\rho _0}f$$

where \({\tau _x}\) is the zonal wind stress, and \(f\) is the Coriolis parameter. The transports are confined approximately to the upper 50 m in the tropical oceans (Ralph and Niiler 1999). The Ekman transport divergence between 9°N and 9°S can be estimated as:

$${M_{\text{1}}}=\int\limits_{A}^{B} {{M_E}} [{9^ \circ }{\text{N}}] - \int\limits_{C}^{D} {{M_E}} [{9^ \circ }{\text{S}}]$$

where A and B give the longitudinal range along 9°N (between 126°E and 83°W) and C and D the range along 9°S (between 148°E and 78°W), respectively. The net surface layer divergence is obtained by Ekman transports minus the opposing surface layer geostrophic transports, which is obtained from an integration of geostrophic velocity over the upper 50 m. The water depth of 900 m is used as the reference level for geostrophic calculations.

The calculation of the STC transport for the interior ocean across 9°N and 9°S follows Luo et al. (2009). The interior transport is the sum of the equatorial geostrophic transport integrated from 140°E to 83°W in 9°N and from 160°E to 78°W in 9°S. The mixed layer depth (0.125 kg m−3 criterion) is considered as the upper boundary for the calculation of interior transport when it is denser than the top layer of the STC. For RFS, the top and bottom of the STC layer are marked by 22.0 and 26.0 kg m−3 isopycnals at 9°N, and by 22.5 and 26.2 kg m−3 isopycnals at 9°S, respectively. Because the mean state is changed significantly under both warming and cooling scenarios, the density classes defined are generally \(2{\text{1.5}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}<{\text{ }}{\sigma _{\text{0}}}<{\text{ }}2{\text{5.5}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}\) at 9°N and \(22.{\text{0}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}<{\text{ }}{\sigma _{\text{0}}}<{\text{ }}2{\text{5.7}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}\)at 9°S for WMS, and \(22.{\text{5}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}<{\text{ }}{\sigma _{\text{0}}}<{\text{ }}2{\text{6}}.{\text{5}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}\) at 9°N and \(2{\text{3.0}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}<{\text{ }}{\sigma _{\text{0}}}{\text{ }}<{\text{ }}2{\text{6}}.{\text{7}}\;{\text{kg}}\;{{\text{m}}^{ - 3}}\) at 9°S for CLS.

Appendix B: Bjerknes linear stability index

Based on the recharge oscillator framework and with a number of assumptions for simplifications in the mixed layer heat budget equation (Jin et al. 2006; Kim and Jin 2011), the SST tendency over the eastern equatorial Pacific can be estimated as follows:

$$\frac{{d{{\langle T\rangle }_E}}}{{dt}}=R{\langle T\rangle _E}+F{\langle h\rangle _W}$$

where \({\langle \cdot \rangle _E}\) and \({\langle \cdot \rangle _W}\) represent the eastern and western boxed averaged quantity, respectively. With the latitudinal range from 5°N and 5°S, the two boxes are separated based on a nodal line by computing the empirical orthogonal function of detrended SSTA over the tropical Pacific and then regressing ocean heat content anomalies onto the first principal component. Specifically, for this study the nodal line separating the eastern and western boxes is chosen to be 174°W in RFS, 161°W in WMS and 179°E in CLS, respectively. \(T\) is the SSTA, \(h\) is the thermocline depth, and \(F\) is the frequency factor of interannual oscillator. \(R\) is the growth rate of the ENSO oscillator, in this study, we will examine the growth rate measured by the BJ index. \(R\) can be expressed by:

$$R= - \left[{a_1}\frac{{{{\langle \Delta \bar {u}\rangle }_E}}}{{{L_x}}}+{a_2}\frac{{{{\langle \Delta \bar {v}\rangle }_E}}}{{{L_y}}}\right] - {\alpha _s}+{\mu _a}{\beta _u}{\left\langle - \frac{{\partial \bar {T}}}{{\partial x}}\right\rangle _E}+{\mu _a}{\beta _h}{\left\langle \frac{{\bar {w}}}{{{H_1}}}\right\rangle _E}{\alpha _h}+{\mu _a}{\beta _w}{\left\langle - \frac{{\partial \bar {T}}}{{\partial z}}\right\rangle _E}$$

where the \(\bar {u}\), \(\bar {v}\), \(\bar {w}\) and \(\bar {T}\) are climatological currents and temperature, respectively; \({H_1}\) represents the mixed layer depth; \({L_x}\) and \({L_y}\) represent the longitudinal and latitudinal lengths of the eastern box, respectively; \({a_1}\) and \({a_2}\) are estimated using SSTA averaged zonally or meridionally at boundaries and averaged SSTA over the box; \({\alpha _s}\), \({\mu _a}\), \({\beta _h}\), \({\beta _w}\), \({\beta _u}\), and \({\alpha _h}\) reflect atmospheric dynamic sensitivities to ENSO SST forcing as well as the ocean dynamic sensitivities to ENSO wind forcing. Using the least-squares regression method (Jin et al. 2006; An and Bong 2016), these coefficients are computed from approximated balance equations, i.e., \({\langle Q\rangle _E}= - {\alpha _s}{\langle T\rangle _E}\), \([{\tau _x}]={\mu _a}{\langle T\rangle _E}\), \({\langle h\rangle _E} - {\langle h\rangle _W}={\beta _h}[{\tau _x}]\), \({\langle H(\bar {w})w\rangle _E}= - {\beta _w}[{\tau _x}]\), \({\langle u\rangle _E}={\beta _u}[{\tau _x}]+{\beta _{uh}}{\langle h\rangle _W}\), and \({\langle H(\bar {w}){T_{sub}}\rangle _E}={\alpha _h}{\langle h\rangle _E}\), where \(Q\) is the net downward heat flux, \([{\tau _x}]\) is the equatorial trade wind anomaly, \(H(\bar {w})\) is a step function to consider only climatological upwelling, and \({\beta _{uh}}\) refers to geostrophic current adjusted to thermocline.

On the right hand side of Eq. (10), in an order of left to right, the first two negative terms represent the dynamic damping, the third negative term represents the thermodynamic damping, and the next three positive terms represent the effects of the zonal advective feedback, thermocline feedback, and Ekman feedback, respectively.

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Wang, Y., Luo, Y., Lu, J. et al. Changes in ENSO amplitude under climate warming and cooling. Clim Dyn 52, 1871–1882 (2019).

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  • ENSO amplitude
  • Climate warming
  • Climate cooling
  • Dynamical feedbacks
  • BJ index