An Improved Principal Component Analysis Method for the Interpolation of Missing Data in GNSS-Derived PWV Time Series

Missing data in precipitable water vapor derived from global navigation satellite systems (GNSS-PWV) is commonly a large hurdle in climatical applications, since continuous PWV is an important prerequisite. Interpolation using principal component analysis (PCA) is typically used to resolve this problem. However, the popular PCA-based interpolating methods, e.g., rank-deficient least squares PCA (RDPCA) and data interpolating empirical orthogonal function (DINEOF), often lead to unsatisfactory results. This study analyzes the relationship between missing data and PCA-based interpolation results and proposes an improved interpolation-based RDPCA (IRDPCA) that can take into account the PWV derived from ERA5 (ERA-PWV) as an additional aid. Three key steps are involved in the IRDPCA: initially interpolating missing data, estimating principal components through a functional model and optimizing the interpolation through an iterative process. Using a 6-year GNSS-PWV over 26 stations and ERA-PWV in Yunnan, China, the performance of the IRDPCA is compared with the RDPCA and DINEOF using simulation experiments based on both homogeneous data (i.e., interpolating ERA-PWV using available ERA-PWV) and heterogeneous data (i.e., interpolating GNSS-PWV using ERA-PWV). In the case of using homogeneous data, the root mean square (RMS) values of the interpolation errors are 3.45, 1.18 and 1.17 mm for the RDPCA, DINEOF and IRDPCA, respectively; while the values are 3.50, 2.50 and 1.55 mm in the heterogeneous case. These results demonstrate the superior performance of the IRDPCA in both the heterogeneous and homogeneous cases. Moreover, these methods are also applied to the interpolation of the real GNSS-PWV. The RMS, absolute bias and correlation of the GNSS-PWV are calculated by comparison with ERA-PWV. The results reveal that the interpolated GNSS-PWV using the IRDPCA is not impacted by the systematic discrepancies in the ERA-PWV and agrees well with the original data.

Automated summary

This study proposes an improved interpolation-based RDPCA method, which takes the PWV derived from ERA5 as an additional aid, to interpolate missing data in precipitable water vapor derived from global navigation satellite systems. The performance of the IRDPCA is compared with RDPCA and DINEOF using simulation experiments, and the results demonstrate the superior performance of the IRDPCA in both the heterogeneous and homogeneous cases. Furthermore, these methods are also applied to the interpolation of the real GNSS-PWV, and the interpolated GNSS-PWV using the IRDPCA is not impacted by the systematic discrepancies in the ERA-PWV and agrees well with the original data.