Using total Kalman filter to extract time-varying signals in PWV time series

There has been considerable research in the literature focused on the extraction and analysis of trends and periodic signals in historical precipitable water vapor (PWV) time series. The conventional approach uses an ordinary least-square estimator (OLS) to resolve a time-constant harmonic model with constant trend, amplitude, and phase. However, due to various climatic factors, PWV signals may contain time-varying fluctuations, which should also be contained in signals. In this paper, we propose a novel time-varying harmonic model accounting for fluctuations in both trend and periodic signals. For this, the novel model is expressed in a state-space form and resolved by the Total Kalman Filter (TKF), along with an estimation of the noise parameters. This approach is referred to as the TKF-based approach. The performance of the novel TKF-based approach is demonstrated using homogeneous PWV time series from 2000 to 2018 over 91 GNSS stations and compared with a time-varying model resolved by Kalman smoother (KS) and the time-constant model resolved by OLS. Results show that the newly proposed TKF-based approach can effectively identify time-varying signals, yielding Gaussian-like modeling residuals. Furthermore, the mean standard deviations of the residuals are 4.27 and 3.92 mm for OLS-based and KS-based approaches. In contrast, the value of the new approach is 3.04 mm, indicating a 29 % and 22 % reduction relative to the aforementioned approaches. Finally, for climatical interpretations, an analysis of the correlation between El Niño-Southern Oscillation (ENSO) and time-varying signals over TOW2 suggests ENSO as one contributor to time-varying signals.