Deep spatial transformers for autoregressive data-driven forecasting of geophysical turbulence

A deep spatial transformer based encoder-decoder model has been developed to autoregressively predict the time evolution of the upper layer's stream function of a two-layered quasi-geostrophic (QG) system without any information about the lower layer's stream function. The spatio-temporal complexity of QG flow is comparable to the complexity of 500hPa Geopotential Height (Z500) of fully coupled climate models or even the Z500 which is observed in the atmosphere, based on the instantaneous attractor dimension metric. The ability to predict autoregressively, the turbulent dynamics of QG is the first step towards building data-driven surrogates for more complex climate models. We show that the equivariance preserving properties of modern spatial transformers incorporated within a convolutional encoder-decoder module can predict up to 9 days in a QG system (outperforming a baseline persistence model and a standard convolutional encoder decoder with a custom loss function). The proposed data-driven model remains stable for multiple years thus promising us of a stable and physical data-driven climate model.