Boosting Ensembles for Statistics of Tails at Conditionally Optimal Advance Split Times

Climate science needs more efficient ways to study high-impact, low-probability extreme events. Ensemble boosting, a form of rare event sampling, offers a novel strategy to extract more information from those occasional simulated events, by perturbing them slightly to probe alternative scenarios immediately instead of waiting many simulation-years for the next event. But statistical accuracy and efficiency depend on the perturbation details. In particular for sudden and transient events like precipitation, performance of boosting depends sensitively on the \emph{advance split time} (AST), which must be long enough before the event to let the ensemble diversify, but not so much as to destroy the event. In pursuit of principled guidelines, we study the effect of AST for sampling tracer fluctuations in a quasigeostrophic flow, an idealized but informative model of midlatitude storm track dynamics. We formulate AST selection as an optimization problem for statistical fidelity with a ground truth. Since ground truth is not known in practice, we propose a proxy objective function of \emph{thresholded entropy}, which rewards ensembles with both a high mean and a large spread. We show that ensemble boosting, when given a well-chosen AST and equipped with methods to estimate probabilities, can accurately sample extremes at long return periods. We furthermore find evidence that thresholded entropy successfully identifies an optimal AST, which is roughly 1-3 eddy turnover timescales in the quasigeostrophic system. Moreover, this proxy captures the \emph{variation} of AST with the target location of the tracer within the flow field, suggesting generalizability to climate models. Large-scale deployment of our method will require further development in adaptive optimization strategies, but our work here is an essential first step for establishing what must be optimized.