LAUSR

Time series with strong periodicity and non-stationary character in terms of magnitude and frequency which are changing over measurement period can be decomposed into time-varying trend, seasonal and cyclical components by dynamic harmonic regression (DHR) modeling in the state-space framework. The time-variable parameters of the components are first associated with a generalized random walk process, and then, state parameters are estimated by the recursive Kalman filtering and fixed interval smoothing algorithms. Missed points are filled by the DHR interpolation, and change points are detected by both visual inspection and the Pettitt test. Sea level series at tide gauges, which consist of accelerated trend and strong periodicity, are therefore suitable for DHR modeling. Time-varying trend, seasonal and cyclical components are extracted by the DHR modeling from the monthly mean sea level series longer than 15 years at seven stations within the Arabian Gulf. The DHR model accounts for 90–96% of variation of the monthly series, while the seasonal and cyclical components account for 64–85% and 2–7%, respectively. Average relative sea level rate (RSLR) and absolute sea level rate (ASLR) over the Arabian Gulf are found $$1.67 \pm 0.05$$ 1.67 ± 0.05  mm/year and 1.93 ± 0.05 mm/year, respectively.