# Do Tensorized Large-Scale Spatiotemporal Dynamic Atmospheric Data Exhibit Low-Rank Properties?

arXiv: https://arxiv.org/abs/2507.03289 · HTML: https://mlsanity.com/paper/2507.03289/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 39 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 3 of 3)

- [Missing Data Reconstruction in Remote Sensing image with a Unified Spatial-Temporal-Spectral Deep Convolutional Neural Network](https://mlsanity.com/paper/1802.08369/) (2018)
- [Long time-series NDVI reconstruction in cloud-prone regions via spatio-temporal tensor completion](https://mlsanity.com/paper/2102.02603/) (2021)
- [Spatiotemporal Estimation of TROPOMI NO2 Column with Depthwise Partial Convolutional Neural Network](https://mlsanity.com/paper/2204.05917/) (2022)

## Abstract (arXiv)

In this study, we investigate for the first time the low-rank properties of a tensorized large-scale spatio-temporal dynamic atmospheric variable. We focus on the Sentinel-5P tropospheric NO2 product (S5P-TN) over a four-year period in an area that encompasses the contiguous United States (CONUS). Here, it is demonstrated that a low-rank approximation of such a dynamic variable is feasible. We apply the low-rank properties of the S5P-TN data to inpaint gaps in the Sentinel-5P product by adopting a low-rank tensor model (LRTM) based on the CANDECOMP / PARAFAC (CP) decomposition and alternating least squares (ALS). Furthermore, we evaluate the LRTM's results by comparing them with spatial interpolation using geostatistics, and conduct a comprehensive spatial statistical and temporal analysis of the S5P-TN product. The results of this study demonstrated that the tensor completion successfully reconstructs the missing values in the S5P-TN product, particularly in the presence of extended cloud obscuration, predicting outliers and identifying hotspots, when the data is tensorized over extended spatial and temporal scales.