Abstract
The intermittent and variable nature of precipitation makes its accurate estimation over extended domains difficult, yet its spatiotemporal structure suggests that a low-rank representation may be possible. This work represents daily precipitation over the contiguous United States (CONUS) as spatiotemporal tensors and applies CANDECOMP/PARAFAC factorization, showing that preserving the native spatial and temporal modes yields more accurate reconstruction than factorizing independent daily fields or unfolded space--time matrices. Building on this finding, this work presents TMerge, a tensor-based framework that integrates satellite precipitation with sparse reference observations through shared low-rank spatial and temporal factors. TMerge was applied to correct the IMERG Final Run product with climate prediction center reference observations over CONUS. During 2019-2022, TMerge increased correlation from 0.53 to 0.85 and reduced root-mean-square error and mean absolute error by 48.2% and 29.3%, respectively. TMerge consistently outperformed linear bias correction, quantile mapping, and neural networks across seasons, precipitation-intensity regimes, and regions. Improvements were spatially coherent and largest in coastal regions where IMERG errors were greatest. These results demonstrate that low-rank tensor structure parsimoniously approximates the dominant spatiotemporal variability of precipitation and provides a practical mechanism for improving satellite estimates under limited reference observations over extended domains.
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Cite this article
APA 7
Solgi, R., Shankar, R., & Loaiciga, H. A. (2026). Low-rank tensor structure of precipitation and its application to satellite-reference merging. https://omanscience.com/en/articles/low-rank-tensor-structure-of-precipitation-and-its-application-to-satellite-reference-merging
MLA 9
Solgi, Ryan, et al. "Low-rank tensor structure of precipitation and its application to satellite-reference merging." https://omanscience.com/en/articles/low-rank-tensor-structure-of-precipitation-and-its-application-to-satellite-reference-merging.
Chicago (author–date)
Solgi, Ryan, Rohan Shankar, and Hugo A. Loaiciga. 2026. "Low-rank tensor structure of precipitation and its application to satellite-reference merging." https://omanscience.com/en/articles/low-rank-tensor-structure-of-precipitation-and-its-application-to-satellite-reference-merging.
Harvard
Solgi, R., Shankar, R. and Loaiciga, H. A. (2026) 'Low-rank tensor structure of precipitation and its application to satellite-reference merging', Available at: https://omanscience.com/en/articles/low-rank-tensor-structure-of-precipitation-and-its-application-to-satellite-reference-merging.
Vancouver
Solgi R, Shankar R, Loaiciga HA. Low-rank tensor structure of precipitation and its application to satellite-reference merging. https://omanscience.com/en/articles/low-rank-tensor-structure-of-precipitation-and-its-application-to-satellite-reference-merging
IEEE
R. Solgi, R. Shankar, and H. A. Loaiciga, "Low-rank tensor structure of precipitation and its application to satellite-reference merging," https://omanscience.com/en/articles/low-rank-tensor-structure-of-precipitation-and-its-application-to-satellite-reference-merging.