| 08 Jan 2026
Contrasting different noise models for representing westerly wind bursts in a recharge oscillator model of ENSO
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.
This manuscript describes the role of various noise approximations to the role of Westerly Wind bursts (WWBs) on the development of large amplitude El Nino events. The finding that conditional additive and multiplicative (CAM) noise is a reasonable approximation to intermittent WWBs with impacts on asymmetries between El Nino and La Nina events is perhaps not unsurprising given the literature on applications of noise in linear inverse models (LIMs). However the demonstration within a simplified framework of the recharge oscillator model is somewhat novel. In general, this work is well described, clear and accessible to a wide audience. It is entirely appropriate for NPG.
Given the effort to produce the conditional noise model (CON) I am somewhat confused that this is not at all mentioned in the abstract nor why the paper only has a focus on large amplitude El Nino and not on the ability to reproduce the observed La Nina amplitudes.
Specific comments:
Paragraph 1; Line 1: Reference [1] is to an ECMWF tech. report from 1997. I suggest replacing this with a more up to date reference that takes into account the most recent decades.
Paragraph 2; Line 1: What is the "inferred measure of the time-integrated wind stress associated with WWBs"? Is it simply wind stress anomalies? Please explicitly state what is calculated in Figure 1. Also why use CESM rather than a reanalysis e.g. ERA5. I would further suggest combining the observed time integrated wind stress due to WWBs with the observed NINO3 index and demonstrate i.e. quantify the relationship.
Page 2: regarding Gaussian multiplicative noise on East Pacific SST, please provide references to the "... emerging consensus in the ENSO literature".
Page 3: Last sentence before section"Noise Models": missing section number. i.e., "in section ? we will discuss ..."
Sentence following Equation 8: \nu_{2} is undefined.
Page 6: Combine Fig3 with new Fig1 observed WWBs.
Fig 4: Please quantify the differences between observed and estimated variance and skewness. By eye, it appears that OU is a better fit than either CAM or CON.
Fig5: I do not see the relevance of these timeseries segments. Please provide a quantitative measure or drop the figure.
Fig8: Please provide a table with the dates of the chosen events. Further, it is quite obvious that many of these events are not monotonically increasing until at least t=-6 months. Choosing only the 4 most extreme cases does not strengthen the argument when all chosen cases are exceeding the threshold.