Response of ENSO amplitude to global warming in CESM large ensemble: uncertainty due to internal variability

Abstract

El Niño–Southern Oscillation (ENSO) is the dominant mode of variability in the coupled ocean-atmospheric system. Future projections of ENSO change under global warming are highly uncertain among models. In this study, the effect of internal variability on ENSO amplitude change in future climate projections is investigated based on a 40-member ensemble from the Community Earth System Model Large Ensemble (CESM-LE) project. A large uncertainty is identified among ensemble members due to internal variability. The inter-member diversity is associated with a zonal dipole pattern of sea surface temperature (SST) change in the mean along the equator, which is similar to the second empirical orthogonal function (EOF) mode of tropical Pacific decadal variability (TPDV) in the unforced control simulation. The uncertainty in CESM-LE is comparable in magnitude to that among models of the Coupled Model Intercomparison Project phase 5 (CMIP5), suggesting the contribution of internal variability to the intermodel uncertainty in ENSO amplitude change. However, the causations between changes in ENSO amplitude and the mean state are distinct between CESM-LE and CMIP5 ensemble. The CESM-LE results indicate that a large ensemble of ~15 members is needed to separate the relative contributions to ENSO amplitude change over the twenty-first century between forced response and internal variability.

Appendix: The estimation of the minimum ensemble size N min

In this study, we evaluate the 95% statistical significance of the ensemble mean changes against a null hypothesis of zero using a one-sample t test. We use the statistic for ensemble mean defined as

$$t(N - 1)=\frac{{\bar {x}}}{{{\sigma \mathord{\left/ {\vphantom {\sigma {\sqrt N }}} \right. \kern-0pt} {\sqrt N }}}}$$

where $\bar {x}$ is the ensemble mean change of ENSO amplitude in a specific 50-year running window relative to that in the first window, $\sigma$ is the sample standard deviation of the changes in CESM-LE (CMIP5), N is the ensemble size 40 (23),and t(N − 1) is the t statistic for the degrees of freedom N − 1. When $\bar {x}$ and $\sigma$ satisfy the following relationship

$$\left| {\frac{{\bar {x}}}{\sigma }} \right|>\frac{{t{{(N - 1)}_{p=0.05}}}}{{\sqrt N }}$$

we can reject the hypothesis and the ensemble mean changes are significant at the 95% confidence level.

According to t-distribution, $t{(N - 1)_{p=0.05}}\sim 2$ for 2-sided t test (~1.7 for 1-sided t test) when N > ~20. Therefore, we can estimate the minimum ensemble size as${N_{min}}\sim \frac{4}{{{{\left( {\bar {x}/\sigma } \right)}^2}}}~$ (${N_{min}}\sim \frac{{2.9}}{{{{\left( {\bar {x}/\sigma } \right)}^2}}}~$) for 2-sided (1-sided) t test. In this study, we detect the significance of changes in T _Niño-3 based on 1-sided t test, while detect the significances of ΔT ^* _Niño-3 and ENSO amplitude changes based on 2-sided t test.