An orchestra of a thousand musicians plays in harmony as long as the conductor keeps the tempo. But the moment he changes the score, the violins in one corner start playing louder, while the brass in another come in late. This is roughly how climate indices like El Niño reshape the behavior of extreme weather events: drought in one region and heat in another cease to be independent random occurrences and start happening together.

For a long time, scientists struggled to capture this connection. Classical models assumed that the dependence structure between locations is fixed, as if the orchestra always plays the same piece. The new work introduces a conditional variational autoencoder (cXVAE), a neural network that compresses a spatial field into a latent representation and then reconstructs it conditioned on the climate state. The climate index is fed into the latent space via a linear mapping and interleaved with latent variables before being passed to a convolutional decoder.

The results are striking. On synthetic data, the model reproduces the extremal dependence coefficient between pairs of locations at any distance with almost no bias. Incorporating a real climate index instead of white noise noticeably improves reconstruction quality, and learnable basis functions provide an additional gain. A counterfactual experiment with a flipped ENSO index leads to shifts in the distributions of emulated extremes, confirming the model's sensitivity to the climate driver.

The practical value lies in the model's ability to assess how important a given climate factor is for the joint occurrence of extremes, without running full-scale climate simulations. This is the first demonstration that a climate index can be directly embedded into the latent space of an autoencoder, thereby controlling tail dependence.

Now the conductor can not only wave the baton but also play alternative scores. If El Niño is flipped, the orchestra of extremes will sound different, and the neural network will show exactly how. The orchestra remains the same, but the music changes, and we can finally hear it in advance.