Extreme heatwave sampling and prediction with analog Markov chain and comparisons with deep learning

TL;DR

The paper tackles predicting and sampling extreme, prolonged heatwaves using two data-driven approaches: an analog Markov chain-based stochastic weather generator (SWG) and a convolutional neural network (CNN), benchmarked on PlaSim-based simulations. SWG extends classic analog forecasting by including temperature and soil moisture predictors, dimensionality reduction, and a committor-function framework for probabilistic forecasting, while comparing its performance to a CNN and a generalized extreme value (GEV) EVT baseline. Key findings show that CNN generally achieves higher probabilistic forecasting skill than SWG for moderate datasets and lead times, while SWG excels at efficiently sampling extreme return times (up to thousands of years) and generating teleconnection patterns consistent with long-control runs; dimensionality reduction speeds computation but does not consistently improve skill. The work demonstrates SWG as a valuable inexpensive baseline for rare-event climate risk assessment and highlights the potential for combining analog methods with modern dimensionality reduction and rare-event algorithms for robust extreme-event analysis.

Abstract

We present a data-driven emulator, stochastic weather generator (SWG), suitable for estimating probabilities of prolonged heatwaves in France and Scandinavia. This emulator is based on the method of analogs of circulation to which we add temperature and soil moisture as predictor fields. We train the emulator on an intermediate complexity climate model run and show that it is capable of predicting conditional probabilities (forecasting) of heatwaves out of sample. Special attention is payed that this prediction is evaluated using proper score appropriate for rare events. To accelerate the computation of analogs dimensionality reduction techniques are applied and the performance is evaluated. The probabilistic prediction achieved with SWG is compared with the one achieved with Convolutional Neural Network (CNN). With the availability of hundreds of years of training data CNNs perform better at the task of probabilistic prediction. In addition, we show that the SWG emulator trained on 80 years of data is capable of estimating extreme return times of order of thousands of years for heatwaves longer than several days more precisely than the fit based on generalised extreme value distribution. Finally, the quality of its synthetic extreme teleconnection patterns obtained with stochastic weather generator is studied. We showcase two examples of such synthetic teleconnection patterns for heatwaves in France and Scandinavia that compare favorably to the very long climate model control run.

Figures (13)

• Figure 1: The map shows relevant areas. Blue: North Atlantic -- Europe (NAE). The dimensions of this region are 22 by 48. Red+Blue: North Hemisphere (above 30 N). The dimensions of this region are 24 by 128. Green: France; Purple: Scandinavia.
• Figure 2: Schematics of different methodologies used for probabilistic forecasting and estimates of extreme statistics. On the left we show the three input fields which are labeled directly on the plot. On the right the target of the inference is displayed (for instance probabilistic prediction as described in \ref{['sec:SWGcommittor']}). On top we have the direct CNN approach. In the middle we show the analog method (SWG), which is the main topic of this work and which is compared to CNN for this task. At at the bottom the option is presented to perform dimensionality reduction of the input fields and pass them as the input on which SWG is "trained". Subsequently, SWG can be used to generate conditional or unconditional synthetic series (green boxes). This synthetic data can be used for make probabilistic prediction or estimating tails of distribution, such as return time plots
• Figure 3: The schematics of the flow of analogs. When applying the algorithm for estimation of committor (equation \ref{['eq:committor']}) the first step consists of starting from the state in the Validation Set (VS), finding the analog in the Training Set (TS) and applying the time evolution operator. All subsequent transition occur within the TS.
• Figure 4: Basic SWG (blue curve) vs CNN. (orange curve) All three panels display NLS (equation \ref{['eq:NLS']}) on the $y$ axis. Left panel has $\tau$ on the $x$ axis, central panel has $\alpha_0$ (a hyperparameter of SWG, see equation \ref{['eq:metric']}) on the $x$ axis and right panel has $n$-nearest neighbors (also hyperparameter of SWG) on the $x$ axis. On the central and the right panels the choice for $\tau = 0$ was made. The dots show data points corresponding to the mean of the cross-validation, whereas the thickness of the shaded area represents two standard deviations. These conventions will be re-used in the subsequent figures.
• Figure 5: Basic SWG vs VAESWG: On the $y$ axis we have NLS (equation \ref{['eq:NLS']}) as a function of lead time $\tau$ and hyper-parameters of SWG (see caption of Figure \ref{['fig:tau_simple_analog']}). SWG is indicated by the same (identical) blue curve as in Figure \ref{['fig:tau_simple_analog']} while orange and green curves correspond to VAESWG where geopotential was passed through two different autoencoders (equation \ref{['eq:vae_ZG']}) (orange and green curves).