Journal of Geodesy

, Volume 93, Issue 12, pp 2605–2620 | Cite as

Precipitable water vapor fusion: an approach based on spherical cap harmonic analysis and Helmert variance component estimation

  • Bao Zhang
  • Yibin YaoEmail author
  • Linyang Xin
  • Xingyu Xu
Original Article


Precipitable water vapor (PWV) is an important parameter in Earth’s atmosphere, and its spatiotemporal variations influence Earth’s energy transfer and weather changes. PWV can be monitored and retrieved by plenty of techniques with varying spatiotemporal resolutions, accuracies, and systematic biases. In this study, we fused PWVs from global navigation satellite system (GNSS), moderate resolution imaging spectroradiometer (MODIS), and European Centre for Medium‐Range Weather Forecasts ERA-5 reanalysis to generate PWV maps with combined resolution and accuracy. Before fusing the data, we apply a bias correction to remove the systematic biases among the three datasets. Then, the fusion is performed by an approach based on the spherical cap harmonic (SCH) analysis and the Helmert variance component estimation (HVCE). The core idea is that the SCH model represents the combined PWV field on the sphere, and the HVCE determines the weights of different datasets. We generate more than 300 combined PWV maps in North America in 2018, which are then validated by a different set of GNSS PWV. Results show that the combined PWVs have mean bias of 0.2 mm, standard deviation of 1.9 mm, and root mean square error of 2.0 mm. The fused PWVs present better accuracy than the MODIS and ERA-5 PWVs. In addition, our proposed approach effectively suppressed regional biases among different datasets. The fused PWV exhibits a better and unified accuracy compared with the MODIS and ERA-5 PWVs.


Precipitable water vapor Data fusion Spherical cap harmonic analysis Helmert variance component estimation 



We thank University Corporation for Atmospheric Research (UCAR) for providing the GNSS PWV data, National Aeronautics and Space Administration (NASA) for providing the MODIS PWV products, and the European Centre for Medium-Range Weather Forecasts (ECMWF) for providing the ERA5 reanalysis data. This work is supported by the National Natural Science Foundation of China (41704004).

Author contributions

BZ and YY together designed the research and proposed the solutions; BZ performed the research and wrote the paper. YY revised the paper; LX and XX helped process and analyze data.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Geodesy and GeomaticsWuhan UniversityWuhanChina

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