Low-rank tensor structure of precipitation and its application to satellite-reference merging
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.
Related
- GPROF-IR: An Improved Single-Channel Infrared Precipitation Retrieval for Merged Satellite Precipitation Products
- A Sensor-Adaptive Incremental Learning Framework for Artifact Detection in Satellite Precipitation Data
- Improving global precipitation forecasts with an AI weather model trained on satellite observations
- Composable multi-satellite precipitation estimation for evolving observing systems
- Added value of integrated satellite precipitation products for event-based flood modeling in semi-arid regions
BibTeX
@misc{solgi2026lowrank,
title = {{Low-rank tensor structure of precipitation and its application to satellite-reference merging}},
author = {Ryan Solgi and Rohan Shankar and Hugo A. Loaiciga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11000},
eprint = {2610.11000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11000},
}
RIS
TY - UNPB
TI - Low-rank tensor structure of precipitation and its application to satellite-reference merging
AU - Ryan Solgi
AU - Rohan Shankar
AU - Hugo A. Loaiciga
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.11000
UR - https://arxiv.org/abs/2610.11000
AB - 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.
ER -