Sampling Rare Climate Events – SAMPRACE

One approach is based on stochastic weather generators based on observations (so called “analog stochastic weather generators”), which are Markov chains with realistic physical features. We define procedures of test of the simulated probability density functions of key climate variables. This allows evaluations on recent cases of heatwaves and cold spells. Another approach is based on ”guided” simulations of climate models towards an extreme of interest. The “guide” is designed by a so-called “committor function” (which is the probability of reaching a given state of the system) that can be obtained through machine learning techniques.
Those theoretical approaches need to be adapted to climate constraints, namely, the seasonal cycle, decadal variability (e.g., due to the ocean) and climate change.
As a result, SAMPRACE will simulate large ensembles of “ultimate” heatwaves and cold spells, conditional to ocean large-scale conditions, and to climate change scenarios.

Application of rare event simulation to a GCM (CESM, NACR) with seasonal cycle to study extreme heat waves over Europe. Thanks to the unprecedented dataset, we have shown that composite maps of extreme heat waves have a hemispheric scale teleconnection pattern with wave number three, and that extreme seasonal heatwaves are the succession of subseasonal heatwaves with high amplitudes. Publication #3. Milestone 1.

Tests and experiments of the coupling of rare event algorithms and stochastic weather generators in a feedback loop way, on simple models. We have demonstrated that rare event simulations are much more efficient when the score function is learnt using an analogue Markov chain. Publication #4. Milestone 2. We have illustrated the structure of the committor function (the probability of a rare event conditioned on the observed state of the system) on a simple toy model of El Nino Southern Oscillation (ENSO). Publication #5. Milestone 2.

Using deep neural networks to make a probabilistic forecast of extreme heat waves. The optimal score function for rare event simulation is called a committor function. Estimating a committor function is equivalent to making a probabilistic forecast for the occurrence of the extreme events $\tau$ days in advance. We have developed a methodology to make a probabilistic forecast of extreme heat waves $\tau$ days in advance and demonstrated its effectiveness and efficiency. The prediction is much better than climatology even with a long lead time $\tau$ and seamlessly uses the predictability potential of fast dynamical drivers (geopotential height) and slow physical drivers (soil moisture). This is a subpart of Milestone 3. Publications #6 and #7.

Systematic tests of the forecast of extreme heat waves (committor function) using the analogue Markov chain This is a subpart of Milestone 3. PhD manuscript of D. Lucente.

Analyses of test cases to define sets of extreme event simulations. We have identified tests cases of extreme events since 2000 (cold spells and heatwaves in France, heatwave in Western North America). The analyses focus on the features of the atmospheric circulation during those events. Milestone 4. Publication #1.

Application of ruin theory to trees. An unforeseen study focused on the impact of climate extremes like heatwaves on the growth of trees in Europe. This study couples a simple version of a heatwave emulator (WP2) and a tree growth model, in order to evaluate the probability of collapse of forests in Europe. This is based on the statistical theory of ruin. This is a proof of the applicability of the methodological developments of SAMPRACE to concrete environmental issues. Part of Milestone 5. Publication #2.

A data base of extreme heatwaves and cold spells, with realistic physical features.
A methodology to simulate GCM with a rare event algorithm.

1. Yiou, P.; Faranda, D.; Thao, S.; Vrac, M. Projected Changes in the Atmospheric Dynamics of Climate Extremes in France. Atmosphere 2021, 12, 1440. doi.org/10.3390/atmos12111440
2. Yiou, P. and Viovy, N.: Modelling forest ruin due to climate hazards, Earth Syst. Dynam., 12, 997–1013, doi.org/10.5194/esd-12-997-2021, 2021.
3. F Ragone, F Bouchet, 2021, Rare event algorithm study of extreme warm summers and heat waves over Europe, Geophysical Research Letters, 48, e2020GL091197., arXiv:2009.02519.
4. D. Lucente, J. Rolland, C. Herbert and F. Bouchet, 2022, Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain, J. Stat. Mech. 083201, arXiv:2110.05050.
5. D. Lucente, C. Herbert and F. Bouchet, 2022, Committor Functions for Climate Phenomena at the Predictability Margin: The example of El Niño Southern Oscillation in the Jin and Timmerman model, published online on Journal of Atmospheric Sciences in June 2022, DOI, arXiv:2106.14990.
6. V. Jacques-Dumas, F. Ragone, P. Borgnat, P. Abry, and F. Bouchet, 2022, Deep Learning based Extreme Heatwave Forecast, Front. Clim., 4, arXiv:2103.09743.
7. G. Miloshevich, B. Cozian, P. Abry, P. Borgnat, and F. Bouchet, 2022, Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data, submitted to PR Fluids, arXiv:2208.00971.
8. Noyelle, R., Faranda, D., & Yiou, P. (2022). Modeling the Northern eddy-driven jet stream position and wind speed variability with stochastic coupled non-linear lattices. J. Atmos. Sci., subjudice, hal.archives-ouvertes.fr/hal-03545111/document

Understanding the statistics and patterns of extreme events is a key issue for the adaptation to climate changes. The more fatal events will most likely be extreme heat waves. Because of the lack of empirical data, model biases, and model sampling issue, studying extremely rare events, for instance events that have not been observed yet, is especially challenging. This project gathers the expertise of two groups that independently made advances solving the model sampling issue (using rare event algorithms), and using empirical data for sampling statistical weather generators (circulation analogues). The aim of this project is to couple these two approaches in order to built the first statistical models able to deal with the model sampling issue, while using empirical data at the same time. With this tool, we will study the first physically relevant worst case scenario for Europe extreme heat waves, and open a new range of extreme event studies, which was impossible so far.