  In meteorology, finding similar weather patterns or analogs in historical
datasets can be useful for data assimilation, forecasting, and postprocessing.
In climate science, analogs in historical and climate projection data are used
for attribution and impact studies. However, most of the time, those large
weather and climate datasets are nearline. They must be downloaded, which takes
a lot of bandwidth and disk space, before the computationally expensive search
can be executed. We propose a dimension reduction technique based on
autoencoder (AE) neural networks to compress those datasets and perform the
search in an interpretable, compressed latent space. A distance-regularized
Siamese twin autoencoder (DIRESA) architecture is designed to preserve distance
in latent space while capturing the nonlinearities in the datasets. Using
conceptual climate models of different complexities, we show that the latent
components thus obtained provide physical insight into the dominant modes of
variability in the system. Compressing datasets with DIRESA reduces the online
storage and keeps the latent components uncorrelated, while the distance
(ordering) preservation and reconstruction fidelity robustly outperform
Principal Component Analysis (PCA) and other dimension reduction techniques
such as UMAP or variational autoencoders.
