Scientific objectives of the extreme and climate communities
Impacts of extreme temperatures. Extreme events such as the summer heat waves of 2003 (France) or 2010 (Russia) were unprecedented in the past 500 years, and were outliers in the probability distribution of temperature (Barriopedro et al., 2011; Schaer et al., 2004). Climate projections expect heat waves to become more severe toward the end of the 21st century (Seneviratne et al., 2012). Therefore, there is a challenge to the scientific community to investigate and simulate events that have never occurred before.
Objectives for extreme event studies. Studies of extreme climate events try to determine the relation between their intensity (or return level) and probability (or return time also called return period), how this relation evolves with global climate change, and their physical features and precursors. As a consequence, it is possible to perform an extreme event attribution (National Academies of Sciences Engineering and Medicine, 2016) that links the probability of events to external forcings. The design of “storylines” (Hazeleger et al., 2015) of extreme events has become important for impact studies. A necessary step to achieve those general objectives is to obtain reliable large samples of low probability events. This is the core of the SAMPRACE proposal, which goes from methodological developments to concrete applications.
Context: difficulty of studying extreme events
Current scientific limitations for studying extreme events. Rare and extreme event statistics are characterized by the average time between two occurrences, called return time. Estimating the return times of a heatwave with a surface temperature exceeding a high threshold (return level) during a month, is a crucial question for public agencies. In order to predict impacts, one also needs maps of physical quantities or patterns, associated to extreme events and their precursors, for instance the temperature pattern of extreme heat waves and the associated atmospheric circulation. The current methodologies for estimating long return times and extreme patterns suffer from three major deficiencies: lack of empirical data, model sampling issues, and model limitations.
The lack of empirical data and the sampling issues. Some extreme events are not necessarily stronger versions of usual ones, but events resulting from unusual dynamics, unobserved so far. How to estimate the return time and the atmospheric patterns of extreme hot or cold seasons that are stronger than any that happened in the recorded history? For example, if a sample of 10 centennial events is necessary for a robust investigation of their properties, one needs at least 1000 years of observations, which is impossible because of the lack of meteorological measurements. Statistical models of extremes can be used to extrapolate large return values (Naveau et al., 2005; Parey et al., 2010), but an issue is to obtain physical constraints. Global Climate Models (GCMs) are also suitable candidates, because they are constrained by the laws of physics. In order to sample correctly the tail of some heatwave distribution, one has to simulate thousands of years of climate. This requires huge computational and storage resources. This sampling issue is a severe limitation. Modelling experiments like the weather@home system (Massey et al., 2015) provide tens of thousands of simulations with a state-of-the-art climate model, but most of those experiments simulate years without extremes, so that rare events are still undersampled. This hinders investigating the most extreme events and prohibit inter model comparison. Therefore, there is a need of a methodology to simulate efficiently such extremes, in order to avoid simulating 107 years of data (the return period of the 2003 heatwave (Schaer et al., 2004)) to sample just a few interesting events.
Model limitations. GCMs can be used to determine return times of extreme events or the evolution of their records (Bador et al., 2017). However, these reflect the dynamics of the GCM, with possible biases, rather than the Earth atmosphere. The relevance of current GCMs to assess large return times is an open question. The only way to assess GCM quality and their bias is to use empirical data.
Faced with these three major limitations, one needs to find a method that would at the same time allow using empirical data to deal with model errors and solve the sampling issue for GCMs. No such approach exists so far, and the aim of SAMPRACE is to make a major step in this direction.
Proposed approach
Rare event algorithms for climate models. The group of F. Bouchet proposed a way to compute return times using rare event algorithms based on importance sampling ideas (Lestang et al., 2018) (see Figure 1 for an example of a rare event algorithm). With this methodology, they have been able to compute return time plots for extreme heat waves over Europe, in a simplified climate GCM (Ragone et al. 2017, see Figure 2). Several hundred times as many extreme heat waves as with the direct numerical simulation were obtained, with the same numerical cost, improving drastically the study of the dynamical and physical processes leading to extreme events, and of their atmospheric patterns and precursors. This breakthrough partially solves the rare event sampling issue and opens the door for new ranges of studies. However, this approach lacks the use of empirical data, and thus suffers from uncontrolled model errors, which we aim to correct with SAMPRACE.
Stochastic weather generators. The group of P. Yiou has designed stochastic weather generators (SWG) based on circulation analogues (Yiou, 2014). This approach produces stochastic models that are sampled through the study of pattern analogues in a set of data (SLP, Z500 and/or temperature). The data set can be composed of observations (E-OBS (Haylock et al., 2008)), reanalysis data (Kistler et al., 2001) or GCM simulations (Taylor et al., 2012). This SWG was designed to perform “conditional” attribution of extreme events (Yiou et al., 2017), which is linked to rare event sampling (National Academies of Sciences Engineering and Medicine, 2016). This SWG was modified in order to be nudged towards extreme events that yield physically plausible features of atmospheric structures and temporal variations (including a seasonal cycle) (Yiou and Jézéquel, 2020). Optimizing this SWG with the experience of F. Bouchet’s team and comparing with GCM simulations would propose an alternative “low cost” approach to simulate extremes with realistic physical features.
SAMPRACE is divided into two work packages (WP), in which both groups are involved. Each WP contains two or three tasks that are interdependent, but with “control points” (section c below). Even though general ideas have been formulated in two seminal papers (Ragone et al., 2017; Yiou and Jézéquel, 2020), many theoretical and practical issues remain to be treated by SAMPRACE.
Expected results for this project
A procedure to simulate realistic extremes with GCMs. Although straightforward for simple and stationary systems, the implementation of rare event algorithms for realistic climate models requires developments and tests to consider seasonality and long-term variability. In practice, this implies a modification of an optimization function (see Figure 1) that depends on anomalies with respect to a seasonal cycle, rather than absolute values, as done for SWGs (Yiou and Jézéquel, 2020).
A statistical model to simulate rare events. We will couple analogue SWG approaches with rare event algorithms. The main idea is to make a stochastic weather generator that will use empirical data, model and reanalysis data providing typical evolutions, but also classes of extremes events that will be simulated using rare event algorithms in GCMs. This is a way to develop statistical models that address, for the first time, the three major deficiencies of the current analysis of extremes in the same framework.
A database of simulated extreme events for impact studies. Within this framework, we aim to simulate unprecedented extreme events that are physically plausible. This will allow us constructing large samples of extreme events and investigate their physical properties (in terms of large-scale patterns). We will focus on long lasting climate events like summer and winter heat waves or cold spells (i.e., from one week to a whole season), and their link with the large-scale atmospheric circulation. As an example, the proposed outcome will be an investigation of worst-case scenarios, in the present climate and future climate toward the end of the 21st century, using RCP scenario simulations (Gidden et al., 2019). We will first focus on European events, for which extensive studies have been performed (Schaer et al., 2004), and recent events like the 2018 summer heatwave or 2018 cold winter in Italy (D’errico et al., 2019). Such simulations will allow evaluating the response of extreme events to climate change and decadal variability.
SAMPRACE 