The Rise and Fall of ENSO in a Warming World: Insights from a Lag-Linear Model

Abstract

The El Niño-Southern Oscillation (ENSO) is a fluctuation in sea surface temperature (SST) and pressure across the equatorial Pacific Ocean with a period of 2-7 years. As the largest mode of interannual variability on Earth, ENSO shapes global weather and climate patterns ranging from monsoons in southern Asia to hurricanes in the Atlantic and droughts in South America. Predicting and understanding ENSO's response to greenhouse warming is essential for mitigating the impacts of climate change, yet model ensemble projections are prohibitively expensive to generate across emission scenarios and remain incompletely understood. Here, we use a hierarchy of models to show that ENSO strength undergoes a transient rise followed by a long-term fall under greenhouse warming. An East Pacific energy budget reveals that the initial increase in ENSO variability is due to enhanced upper-ocean stratification, while its subsequent decrease arises from a slowing Walker circulation and stronger surface flux damping. Building on these mechanisms, we derive a linear model which predicts the evolution of ENSO variability from only East Pacific temperature and stratification. We further show that subsurface warming, and therefore stratification, is connected to surface warming with a lag, enabling us to create a lag-linear model that explains $\sim$90\% of simulated changes in ENSO variability from only global mean SST and its history. This efficient predictor can forecast ENSO strength over time in any warming scenario, and reveals that faster emissions lead to stronger peak ENSO variability even with identical total emissions.

Figures (5)

• Figure 1: ENSO changes with warming and our lag-linear model for predicting these changes. The globes show an El Niño event from ERA5 (a) and the MITgcm idealized simulation (b). Panels c-e show $\Delta \mathrm{M}_{\mathrm{ENSO}}$, i.e., the normalized change in ENSO strength smoothed with a 20 year moving mean, and predictions based on the lag-linear model from ERA5 (c, dashed line), CESM2 under scenario SSP3-7.0 (c, solid line, $R^2=0.97$), CMIP models under an abrupt quadrupling of CO$_2$ (defined to occur in 1980, d, $R^2=0.97$), and idealized MITgcm simulations (e, $R^2=0.99$). The top right of the figure shows the equation for the lag-linear model, where $\langle \bar{T} \rangle_{\mathrm{global}}$ is the global mean SST and $\alpha$, $\beta$, and $t_{\mathrm{lag}}$ are constant parameters. Panel f shows the relationship between the lag-linear prediction and the simulated changes in ENSO strength in all simulations studied (a CMIP ensemble, four MITgcm scenarios with differing warming timescales $\Delta t$, and three CESM2 scenarios). The combined $R^2$ values across warming timescales are 0.67 for CESM2 and 0.93 for the MITgcm. The lag-linear parameters are allowed to vary across models, but are held constant across warming scenarios. The same quantities without the 20-year moving mean are shown in Extended Data Fig. \ref{['ed:UnsmoothedMENSO']}.
• Figure 2: The simulations used in this study and how relevant quantities change with warming. The top row shows the change in climatological (20-year moving mean) SSTs under warming in the full climate model simulations (left) and the idealized MITgcm simulations (right), as well as indicating the warming scenarios. Panel a shows changes in East Pacific moving mean, minima, and maxima temperatures over time for each simulation, and panel b shows how the moving minima and maxima warming relate to changes in the moving mean temperature of the tropical ocean surface.
• Figure 3: Using energy balance to study how the magnitude of El Niño events changes under warming in the MITgcm $\Delta t=$ 50 years simulations. Panel a shows the mean temperature (color) and currents (arrows) in the pre-warming climate (a.i), the transient warming state (a.ii), and the (mostly) equilibrated warmed state (a.iii). Panel b shows the volume averaged anomalous temperature (b.i) and vertical velocity (b.ii) from a composite El Niño structure in the reference climate. Panel c shows the predicted $\Delta \mathrm{M}_{\mathrm{ENSO}}$ from energy balance and compares it to the simulated results. Panel d shows how specific terms affect the predicted ENSO magnitude.
• Figure 4: Our first linear model for ENSO variability. Panel a shows the relationship between three of the energy budget terms and mean temperature in the MITgcm $\Delta t=50$ year simulations, while panel b shows the relationship between the stratification term and mean stratification. Panel c shows the simulated ENSO strength from the MITgcm, the empirically fit linear model and its prediction as a function of time, as well as the predictions if only mean temperature or stratification were allowed to change. Panel d compares the simulated ENSO magnitude to that predicted by the linear model for all MITgcm simulations, where color corresponds to mean temperature and point outlines correspond to different warming rates. Panel e illustrates how this linear model predicts ENSO magnitude would change as a function of the two controlling variables, with the $\Delta t=50$ year simulation data shown as a scatterplot.
• Figure 5: Developing a lag-linear model for ENSO variability in terms of global mean surface temperature. (a) Currents as a function of latitude and depth, with the characteristic latitude of descent (solid) and rough uncertainty range (dashed) indicated with vertical lines. (b) The year after warming begins that temperature maxima (red) and temperature minima (blue) reach three quarters of their final warming, and the same for temperature at depth (green) as a function of mean surface tropical temperature warming timescale. The solid black line represents no delay between surface warming and the quantity in question (i.e., x=y), the dashed black lines represent delays in intervals of 50 years, the solid green line represents a delay of $t_{\mathrm{STC}}=41$ years, and the dashed green lines represent an uncertainty around this value (calculated from the range of downwelling latitudes). Below panels a and b is the lag-linear model equation. (c) ENSO magnitude changes predicted from the lag-linear model in various warming scenarios, the temperature trajectories are shown in Extended Data Fig. \ref{['ed:TempTrajectories']}. (d) How peak ENSO magnitude predicted by the lag-linear model depends on the total amount of warming ($\Delta T_{\infty}$) and the warming timescale ($\tau_W$), with the common SSP scenarios marked.