  We present a novel machine learning approach to reduce the dimensionality of
state variables in stratified turbulent flows governed by the Navier-Stokes
equations in the Boussinesq approximation. The aim of the new method is to
perform an accurate reconstruction of the temperature and the three-dimensional
velocity of geophysical turbulent flows developing non-homogeneities, starting
from a low-dimensional representation in latent space, yet conserving important
information about non-Gaussian structures captured by high-order moments of
distributions. To achieve this goal we modify the standard Convolutional
Autoencoder (CAE) by implementing a customized loss function that enforces the
accuracy of the reconstructed high order statistical moments. We present
results for compression coefficients up to 16 demonstrating how the proposed
method is more efficient than a standard CAE in performing dimensionality
reduction of simulations of stratified geophysical flows characterized by
intermittent phenomena, as observed in the atmosphere and the oceans.
