Data-driven methods to estimate the committor function in conceptual ocean models

Abstract

Abstract. In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general, and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare events algorithms like TAMS (trajectory-adaptive multilevel sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called the committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (analog Markov chains, neural networks, reservoir computing, dynamical Galerkin approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analog Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

Potential effect of the marine carbon cycle on the multiple equilibria window of the Atlantic Meridional Overturning Circulation

“…In this study we focused on slow, bifurcation induced tipping of the AMOC, while the AMOC is also able to tip due to faster processes (e.g. density changes related to temperature variations) resulting in noise-induced tipping (Castellana et al, 2019;Jacques-Dumas et al, 2023). The mechanisms presented here might influence these noise-induced transitions as well.…”

“…The model provides a simple framework to study AMOC dynamics and has already been used to show both slow (Cimatoribus et al, 2014) and fast, noise-induced (Castellana et al, 2019;Jacques-Dumas et al, 2023) tipping of the AMOC.…”

Extreme heat wave sampling and prediction with analog Markov chain and comparisons with deep learning

“…This is because knowing the probability of an event gives a prior information to the rare event algorithm (Chraibi et al, 2021). A recent work (Jacques-Dumas et al, 2023) compares SWG and CNN in computing importance functions for two simple Atlantic meridional overturning circulation models. We believe that providing similar benchmarks is important; thus, in this manuscript, we concentrate on the comparisons between deep learning and analog forecasting.…”

AMOC Stability Amid Tipping Ice Sheets: The Crucial Role of Rate and Noise

“…As an illustration, we note that the previously found critical value of GIS tipping duration at In this section, we evaluate the relevance of the stabilization effect of WAIS meltwater fluxes on the AMOC when natural variability is added to the surface freshwater flux. To do so, we redefine the asymmetric component of the surface freshwater flux E a in the following way (Castellana et al, 2019;Jacques-Dumas et al, 2023)…”

“…The time evolution of salinities S i for i ∈ {t, ts, n, s, d} and the pycnocline depth D are given by differential equations identical to those used earlier (Cimatoribus et al, 2014;Castellana et al, 2019;Jacques-Dumas et al, 2023), except for the addition of time-dependent meltwater fluxes F N,S (t) defined by equations ( 1)-(2) (or equations (1)-( 3)), as follows…”