降水的低秩张量结构及其在卫星参考融合中的应用

中文摘要 AI 辅助

降水的间歇性和多变性使得在广阔区域内对其进行准确估算十分困难，但其时空结构表明可能存在低秩表示。本研究将美国本土（CONUS）的日降水量表示为时空张量，并应用CANDECOMP/PARAFAC分解，结果显示，保留原生空间和时间模式的重构效果优于对独立日场或展开的时空矩阵进行分解。基于这一发现，本研究提出了TMerge，这是一种基于张量的框架，通过共享低秩空间和时间因子将卫星降水与稀疏参考观测数据进行整合。TMerge被用于结合气候预测中心的参考观测数据，对美国本土的IMERG最终运行产品进行校正。在2019-2022年期间，TMerge使相关系数从0.53提升至0.85，均方根误差降低48.2%，平均绝对误差降低29.3%。TMerge在不同季节、降水强度区间和区域中，均持续优于线性偏差校正、分位数映射和神经网络方法。其改进效果在空间上具有一致性，且在IMERG误差最大的沿海地区最为显著。这些结果表明，低秩张量结构能够简约地近似降水的主导时空变异性，为在广阔区域内参考观测数据有限的情况下改进卫星估算提供了实用机制。

英文摘要

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.

发表机构

• University of California-Santa Barbara（加利福尼亚大学圣巴巴拉分校）
• Cornell University（康奈尔大学）

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