Effects of different seasonal fitting methods on the spatial distribution characteristics of common mode errors

This study investigated the effects of various seasonal fitting techniques on the spatial distribution of the common mode errors taking the coordinate time series of the continuous GPS reference stations of the Crustal Movement Observation Network of China (CMONOC) as an example. First, the seasonal term of coordinate time series was calculated using constant amplitude harmonic fitting (CAF), continuous wavelet transform (CWT), and smoothing spline fitting (SPF). The seasonal term and linear trend were then removed to obtain the residual time series. Finally, to determine the common mode errors of residual time series, principal component analysis (PCA) was applied. The results indicate that 1) smoothing spline fitting is superior to constant amplitude harmonic fitting and continuous wavelet transform in its ability to fit short-term irregular seasonal signals. In comparison to constant amplitude harmonic fitting, N/E/U has root mean square error (RMSE) values of smoothing spline fitting that are lower by 25%, 20%, and 14.4%, respectively. Smoothing spline fitting also has a higher coefficient of determination than continuous wavelet transform and constant amplitude harmonic fitting. The coefficient of determination in the U direction is larger than that in the N and E directions. 2) Each order PC of the residual series fitted by smoothing spline fitting exhibits apparent spatial aggregation characteristics, with PC1 having a uniform spatial distribution and presenting a largely positive response. Nevertheless, the residual series obtained by constant amplitude harmonic fitting and continuous wavelet transform exhibits scattered spatial response distribution features in each order PC. Compared to N and E, U's spatial response distribution is distinct. From north to south, the spatial response of PC1 in the U direction progressively diminishes. In addition to being much lower than that in other locations, the Sichuan-Yunnan region's spatial response value of PC1 and PC3 also exhibits a clear negative reaction. The root mean square error value of the residual series after smoothing spline fitting is the least, and the filtering effect is the best when comparing the spatial filtering effect based on the three fitting methods. We also compared the root mean square error reduction ratio before and after spatial filtering, and the results showed that the root mean square error reduction ratio before and after the residual series obtained by smoothing spline fitting is slightly larger than that obtained by other methods.

Automated summary

This study examined the effects of different seasonal fitting techniques on the spatial distribution of common mode errors using the coordinate time series of GPS reference stations in China. The results showed that smoothing spline fitting outperformed constant amplitude harmonic fitting and continuous wavelet transform in fitting short-term irregular seasonal signals. Additionally, the residual time series obtained from smoothing spline fitting had the lowest root mean square error and exhibited the best spatial filtering effect.