Contrasting different noise models for representing westerly wind bursts in a recharge oscillator model of ENSO

TL;DR

Westerly wind bursts (WWBs) strongly modulate ENSO, but their stochastic forcing is not fully captured by conventional Gaussian noise. The authors evaluate a noisy recharge oscillator (RO) model under three forcings—multiplicative Ornstein–Uhlenbeck (OU) noise, additive correlated additive and multiplicative (CAM) noise, and a conditional OU/CAM (CON) model—emphasizing CAM's potential to produce $\alpha$-stable statistics through jump-like fluctuations. CAM noise yields pronounced ENSO asymmetry and a monotonic buildup of large warming events without deterministic nonlinearities; the conditional model combines Gaussian noise for small SST anomalies and CAM noise for larger anomalies to span the full ENSO spectrum. Calibrated to NOAA NINO3 data (1871–2023), all three schemes reproduce the observed statistics of SST, but CAM-based forcing (and CON) better capture the clustering of WWBs before large events and their monotonic pre-peak growth, suggesting CAM-type stochastic forcing is key for extreme ENSO dynamics and should be incorporated in more realistic climate models.

Abstract

Westerly wind bursts (WWBs) have long been known to have a major impact on the development of El Niño events. In particular, they amplify these events, with stronger events associated with a higher number of WWBs. We further find indications that WWBs lead to a more monotonically increasing evolution of warming events. We consider here a noise-driven recharge oscillator model of ENSO. Commonly, WWBs are represented by a state-dependent Gaussian noise which naturally reproduces the amplification of warm events. However, we show that many properties of WWBs and their effects on sea surface temperature (SST) are not well captured by such Gaussian noise. Instead, we show that conditional additive and multiplicative (CAM) noise presents a promising alternative. In addition to recovering the sporadic nature of WWBs, CAM noise leads to an asymmetry between El Niño and La Niña events without the need for deterministic nonlinearities. Furthermore, CAM noise generates a more monotonic increase of extreme warming events with a higher frequency of WWBs accompanying the largest events. This suggests that extreme warm events are better modelled by CAM noise. To cover the full spectrum of warm events we propose a conditional noise model in which the wind stress is modelled by additive Gaussian noise for sufficiently small SSTs and by additive CAM noise once the SST exceeds a certain threshold. We show that this conditional noise model captures the observed properties of WWBs reasonably well.

Figures (10)

• Figure 1: An inferred measure of the time-integrated wind stress due to westerly wind bursts in a global climate model DanabasogluEtAl20. Shown is $\Delta t_{\rm{WWB}}\, U_{\rm{WWB}}^2$, where the WWB duration is given by $\Delta t_{\rm{WWB}}$ (in days) and the surface wind speed strength is $U_{\rm{WWB}}$ (in $m/s$).
• Figure 2: (a) OU process with a characteristic decorrelation decay time of $4.9$ days ($c_1=-1.4$, $c_4=0.7$, $c_2=c_3=0$). (b) CAM noise process with intermittent peaks ($c_1=1.22$, $c_2=1.14$, $c_3=0.65$ and $c_4=0.8$ with corresponding $\alpha=1.88$ and $\beta=0.81$). (c) and (d) show the integrals of (a) and (b), correspondingly.
• Figure 3: Observed NINO3 index from 1871 until 2023. A moving average over 4 months was applied to observations from NOAA-NINO3-2003. The horizontal line demarcates an index of 1.5, which we use to separate large El Niño events from normal ones. The vertical lines denote the years 1997 and 2015, for which the large El Niño events were accompanied by strong WWBs.
• Figure 4: Histograms of the variance and skewness of the SST for different driving noise models. The red dot demarcates the observed variance and skewness from the NINO3 index. The black dot is the average of a $10^8$ month-long simulation of the recharge oscillator model \ref{['eq:Te0']}--\ref{['eq:hw0']}. (a) OU, (b) CAM, (c) CON.
• Figure 5: Typical time series of the SST $T_e$ obtained from the RO model \ref{['eq:Te0']}--\ref{['eq:hw0']}, when driven by different noise models. (a) OU, (b) CAM, (c) CON.