The El Niño–Southern Oscillation (ENSO) is the dominant mode of interannual variability in the equatorial Pacific. Its influence spreads across the globe through teleconnections, shaping droughts, floods, and temperature anomalies in various regions. A key question about ENSO's nature—whether it damps on its own and is sustained by random weather noise, or whether it can exist without external forcing—remains open. Simple conceptual models, such as the recharge oscillator, are widely used to estimate ENSO parameters from observational and climate model data. However, these estimates almost always yield a negative growth rate, which is interpreted as a damped regime. This work fits into research that applies the recharge oscillator to diagnose ENSO stability, but it focuses on testing the fitting method itself rather than producing new estimates for the real system.
The authors generated time series of sea surface temperature (SST) anomalies and thermocline depth using a nonlinear recharge oscillator model with known parameters. Two regimes were considered: a damped regime (with a damping time of 1.7 years) and a self-sustaining regime (with a growth time of 11 years), both reproducing observed ENSO characteristics, including a period of about 3.7 years and amplitude distributions. Then they applied the standard procedure to these synthetic data: multivariate linear regression of monthly increments of T and h on the anomalies themselves to estimate parameters R, ε, F1, F2. They also estimated a nonlinear version of the model with quadratic and cubic terms. Additionally, they ran 10,000 simulations with random parameters to cover a wide range of possible regimes. To check sources of error, they varied the temporal resolution of the data (monthly or daily), the type of noise (correlated or white), and the match between the generating and fitting models.
The main result: fitting the linear recharge oscillator model systematically underestimates the growth rate. For the self-sustaining regime (true growth rate positive), in all 100 simulations the estimate was negative, indicating damping. The error is mainly associated with the parameter R (Bjerknes feedback), which is estimated with large bias. The oscillation period is estimated more accurately: most estimates fall within ±6 months of the true value. When using the nonlinear model, the bias decreases but remains significant: the mean growth rate estimate for the self-sustaining case is still negative. Only under ideal conditions (exact match between generating and fitting models, daily data, uncorrelated noise) do the estimates become unbiased. Analysis of 10,000 random regimes showed that when the true growth rate is positive, the estimate is almost always negative, around −0.27 yr⁻¹. For comparison, the estimate from the ORAS5 reanalysis data gives −0.53 yr⁻¹.
The results cast doubt on the conclusion that ENSO is damped, which was based on fitting the recharge oscillator to observations. It is possible that the real growth rate of ENSO is close to zero or even positive, and the negative estimates are an artifact of the method. This is consistent with earlier analytical estimates that gave less damping. The work shows that the distinction between a weakly damped and a weakly self-sustaining regime is fundamentally difficult to capture with standard regression fitting. Compared to neighboring studies that applied the same methodology and obtained negative growth rates, this work is the first to systematically demonstrate the estimation bias on synthetic data with known truth.
In the future, it would be worth exploring other variants of the recharge oscillator model, such as with multiplicative noise or with the parameter F1 depending on the sign of the thermocline anomaly. Alternative estimation methods, such as Bayesian inference or filtering, might yield less biased results. It is also important to check how the bias persists when fitting to full climate model data, where model mismatch is even larger.
The results will affect the interpretation of ENSO stability in climate models and estimates of predictability. They are also important for understanding how ENSO might respond to climate change.
The next step is to apply the same tests to CMIP climate model data and compare estimates with analytical formulas. Also, it would be worthwhile to develop an estimation method that is robust to bias, for example, using simulations with known parameters for calibration.
The work directly relates to a long-standing problem in climatology: whether ENSO is a stochastically excited damped oscillator or a self-sustaining chaotic regime. This distinction matters for ENSO forecasting and for understanding its sensitivity to external forcing. The bias in growth rate estimates means we may be underestimating the system's internal instability, which has implications for interpreting paleoclimate data and projecting future climate.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors tested the standard method for estimating recharge oscillator model parameters on synthetic data with known properties. They showed that even for a self-sustaining regime, the fit almost always yields a negative growth rate, indicating decay. This implies that the conclusion about the damped nature of ENSO from observations may be an artifact of the method.
Where its strength is
The strength of the work lies in challenging the interpretation of a widely used method for assessing ENSO stability, demonstrating a systematic bias toward decay. This opens the possibility of revisiting conclusions about ENSO's nature and underscores the need for caution when diagnosing from limited data.
Where it could go next
Worth trying
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.49, against a usual 0.64. It looks like few have drilled nearby.
The ENSO damping time estimated from standard fitting is about 1.9 years, but analytical formulas give 3 years. This discrepancy may be a consequence of the very bias that the authors uncovered.