Using a rare event sampling technique to quantify extreme El Niño event statistics

TL;DR

This paper addresses the challenge of characterizing rare extreme El Niño events by applying TEAMS, a rare-event sampling method, to the intermediate-complexity Zebiak-Cane ENSO model. TEAMS creates a branched ensemble of trajectories with targeted perturbations to efficiently sample extreme events, and returns statistics are computed with trajectory weights comparable to DNS. The study demonstrates that TEAMS reproduces DNS return-time distributions and tail behavior at about 20% of the DNS cost, suggesting strong potential for applying the approach to higher-fidelity climate models. The work provides practical guidance on hyperparameter choices and highlights the method's ability to reveal dynamical mechanisms leading up to extremes, offering a valuable tool for informing climate risk in a warming world.

Abstract

Extreme El Niño events, such as occurred in 1997--1998, can induce severe weather on a global scale, with significant socioeconomic impacts that motivate efforts to understand them better. However, extreme El Niño events are rare, and even in a very long direct numerical simulation (DNS) occur too infrequently for robust statistical characterization. This study seeks to generate extreme El Niño event model data at a lower cost, while preserving statistical fidelity, using a rare event sampling technique, which preferentially devotes computational resources toward extreme events by generating a large, branched ensemble of interrelated trajectories through successive targeted perturbations. We specifically use the ``trying-early adaptive multi-level splitting'' (TEAMS) algorithm, which is well-suited for El Niño's relative timescales of predictability and event duration. We apply TEAMS to the Zebiak-Cane model, an intermediate-complexity ENSO model for which it is feasible to run a long DNS (500000 years) for validation. We compare extreme El Niño event return time estimates from TEAMS to those from the long DNS to assess TEAMS' accuracy and efficiency. We find that TEAMS accurately reproduces the return time estimates of the DNS at about one fifth the computational cost. Therefore, TEAMS is an efficient approach to study rare ENSO events that can be plausibly applied to full-complexity climate models.

Figures (8)

• Figure 1: Schematic overview of a TEAMS ensemble. Thick, black line across the top represents a short DNS. Yellow nodes on the DNS represent the beginnings of distinct runs of TEAMS. (A) At the start of each run, $N$ ancestors (yellow offshoots) of duration $T$ are created by taking an initial condition from a DNS, applying a small perturbation, and running the simulation forward for $N \times T$ years. The $k$ lowest-scoring ancestors (lowest maximum NINO3 SST indices, y-axis) are killed (black X's), and $k$ new offspring are produced (green offshoots). (B) Subsequent TEAMS generations. In each generation, the threshold NINO3 level $\ell$ is raised ($\ell_1<\ell_2<\ell_3<...<\ell_J$), the $k$ ensemble members with the lowest scores are killed, and $k$ offspring are produced from randomly selected parents.
• Figure 2: Quantification of advance split time ($\delta$) with a maximum perturbation amplitude $\sigma = 0.1$ ° C. (A) Example divergence of NINO3 of child trajectories (thin red lines) from parent DNS (black line). (B) Example distances between child trajectory and parent DNS as a function of time (thin red lines). Black line: the ensemble-averaged $\epsilon = \text{RMSE}(t) /\text{RMSD}$, which exceeds ${3}/{8}$ after 7.5 years (blue lines).
• Figure 3: Maximum achieved NINO3 SST anomaly averaged across $M=50$ runs of TEAMS as a function of the maximum allowed computational cost $T_{\text{max}}$ (total model years). Ancestor simulations (cost $<400$, left of black dashed line) have a range of scores; once level raisings begin (cost $>400$ years), scores increase and the error estimate (variance between TEAMS runs) decreases.
• Figure 4: Return level as a function of return time, calculated from a DNS (500,000 years) using the modified block maxima method (Poisson approximation) for a range of block sizes (20, 30, 50, 100, 150, 200). The return level $y$ axis is stretched as $-\log(1-\text{NINO3 SST} / 4.3$ ° C), which serves to highlight the tail end of the distribution of NINO3 SST maxima. The figure shows that all block sizes result in similar return time estimates for periods that are larger than the block size.
• Figure 5: Distributions of block maximum NINO3 SSTs (block size $T= 25$ years). Blue: DNS, $5\times10^4$ years in length. Red: TEAMS, $1.2 \times10^4$ years in length. (A) counts of extreme El Niño block maxima. Note that the TEAMS cost, and therefore count, is five times smaller than the DNS. (B) Unweighted PDF of extreme block maxima, showing TEAMS preferably generates high block maxima. (C) Weighted TEAMS PDF, matching the DNS fairly closely, particularly at extremely high values.