  We propose a new 'Bi-Reduced Space' approach to solving 3D Variational Data
Assimilation using Convolutional Autoencoders. We prove that our approach has
the same solution as previous methods but has significantly lower computational
complexity; in other words, we reduce the computational cost without affecting
the data assimilation accuracy. We tested the new method with data from a
real-world application: a pollution model of a site in Elephant and Castle,
London and found that we could reduce the size of the background covariance
matrix representation by O(10^3) and, at the same time, increase our data
assimilation accuracy with respect to existing reduced space methods.
