Tensor-based compression of the sea temperature data

Abstract

In this work we investigate efficient data compression for spatiotemporal Black, Azov and Marmara Seas temperature tensors that contain significant number of missing values. These tensors have a complex structure influenced by the coastlines and bathymetry, as well as temporal temperature changes. While such missing data typically provokes utilization of tensor completion algorithms, we demonstrate that standard SVD-based compression approaches (including the Tucker, Tensor-Train (TT) and Quantized-TT formats) are remarkably effective and yield comparable results. We propose a greedy spatial data partitioning algorithm enhancing their performance. We divide the data into the smaller subtensors before compression via exploitation of this trick. Furthermore, our analysis reveals a strong temporal dependency in the data's compressibility caused by its nature. Fixing the level of precision we observe a significant seasonal variation. Investigating this, we find that a temporal partitioning on a scale of approximately two days is nearly optimal for all tested tensor based formats. The combined application of these spatial and temporal strategies with tensor methods ultimately achieves a robust compression ratio of 5 times across the entire dataset.