Statistical Response of ENSO Complexity to Initial Condition and Model Parameter Perturbations

TL;DR

This paper develops a statistical-response framework using information theory to quantify how ENSO complexity responds to perturbations in initial conditions and model parameters. It contrasts trajectory-based and distribution-based approaches, derives Gaussian and Fisher-information-based approximations, and demonstrates that perturbation direction and impact depend on ENSO phase and lead time, with variance often dominating under external forcing. Using a six-variable multiscale stochastic ENSO model, the study shows that SST, thermocline depth, and zonal advection contribute differently across short-, medium-, and long-range horizons, and that Gaussian approximations provide accurate, efficient estimates suitable for operational systems. The framework enables robust probabilistic forecasting and scenario analysis for ENSO under variability and climate-change scenarios, highlighting practical implications for predictability and risk assessment.

Abstract

Studying the response of a climate system to perturbations has practical significance. Standard methods in computing the trajectory-wise deviation caused by perturbations may suffer from the chaotic nature that makes the model error dominate the true response after a short lead time. Statistical response, which computes the return described by the statistics, provides a systematic way of reaching robust outcomes with an appropriate quantification of the uncertainty and extreme events. In this paper, information theory is applied to compute the statistical response and find the most sensitive perturbation direction of different El Niño-Southern Oscillation (ENSO) events to initial value and model parameter perturbations. Depending on the initial phase and the time horizon, different state variables contribute to the most sensitive perturbation direction. While initial perturbations in sea surface temperature (SST) and thermocline depth usually lead to the most significant response of SST at short- and long-range, respectively, initial adjustment of the zonal advection can be crucial to trigger strong statistical responses at medium-range around 5 to 7 months, especially at the transient phases between El Niño and La Niña. It is also shown that the response in the variance triggered by external random forcing perturbations, such as the wind bursts, often dominates the mean response, making the resulting most sensitive direction very different from the trajectory-wise methods. Finally, despite the strong non-Gaussian climatology distributions, using Gaussian approximations in the information theory is efficient and accurate for computing the statistical response, allowing the method to be applied to sophisticated operational systems.

Figures (11)

• Figure 1: The statistical response of $T_C$ to the initial value perturbations for events with different starting dates and at different lead times, where a 30% perturbation is added to the initial value of each of the six state variables. Different rows show the resulting statistical response amplitude measured by the relative entropy using different methods. In each row, the x-axis is the starting date on the first day of each month across the 36 years, and the y-axis is the lead time (months). The horizontal lines above the x-axis indicate the event type of that year based on the DJF SSTa.
• Figure 2: The most sensitive direction of perturbation. In Panels (a)--(b), the directions are computed using the quad form w/ mean and variance. Each point in the plot represents the variable associated with the largest component in the 6-dimensional eigenvector, namely the principal coordinate direction (PCD). It approximates the most sensitive perturbation direction if a perturbation is imposed on the corresponding starting date (its x-axis value) that leads to the response at a given lead time (its y-axis value). The two panels show the cases when the statistics of $T_C$ and $T_E$ are adopted, respectively, in computing the relative entropy. Panel (c) shows the PCD based on the statistical response of $T_E$ using the quad form w/ mean only. Panels (d)--(e) summarize the schematic structures of the most sensitive direction for different ENSO events corresponding to the findings in Panels (a)--(b).
• Figure 3: Seasonal statistical response by perturbing the initial conditions using the most sensitive direction (MSD) based on $T_E$. Panels (a)--(c): The response of $T_C$, including the total response and the response in the signal and the dispersion, respectively. Panels (d)--(f): The response of $T_E$.
• Figure 4: Similar as Figure \ref{['SPB_study_RE_T_E_MSD_IC']} but using the most sensitive direction (MSD) based on $T_C$.
• Figure 5: The most sensitive direction (in the form of the PCD) and the statistical response to the perturbations of model parameters. Panels (a)--(b) show the most sensitive directions for the response in $T_C$ and $T_E$, respectively, using the quad form w/ mean and variance. Panel (c) shows that in $T_E$ using the quad form w/ mean only. Panels (d)--(e) show statistical response of $T_E$ by perturbing all the variables by 10% using the exact formula and the Gaussian approximation.