Development of an Observational Encoder for Data Assimilation in the Latent Space of a Variational Autoencoder (with Sea Surface Temperature)

High-dimensional ocean datasets, e.g. of global sea surface temperature, provide crucial insight to the dynamic of physical ocean characteristics such as seasonal cycle, ENSO, and global trend, but the dimensionality often results in computational complexity. Deep learning methods, such as variational autoencoders (VAEs), offer dimension reduction techniques that retain nonlinearities while expressing the system state in a meaningful lower-dimensional latent space. We explore whether encoded spatially limited observations, such as from satellites, buoys, or ship tracks, could be assimilated in the latent space. First, we developed a VAE to create a low-dimensional representation of a global sea surface temperature anomalies dataset. Next, we built a sample environment to demonstrate data assimilation within the latent space by creating spatially incomplete observations from the global dataset by selecting specific regions and adding noise. Accordingly, we developed an observational encoder to map these observations into the latent space of the VAE. For the latent data assimilation, we created a Bayesian update (e.g. Kalman filter) and decoded assimilated observations to evaluate results. We report on the assimilation of encoded limited observations within the latent space and discuss possible applications and future development of this approach.