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

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.