The fractional Sinusoidal wavefront Model (fSwp) for time series displaying persistent stationary cycles

In the analysis of sub-annual climatological or geodetic time series such as tide gauges, precipitable water vapor, or GNSS vertical displacements time series but also temperatures or gases concentrations, seasonal cycles are often found to have a time-varying amplitude and phase. These time series are usually modelled with a deterministic approach that includes trend, annual, and semi-annual periodic components having constant amplitude and phase-lag. This approach can potentially lead to inadequate interpretations, such as an overestimation of Global Navigation Satellite System (GNSS) station velocity, up to masking important geophysical phenomena that are related to the amplitude variability and are important for deriving trustworthy interpretation for climate change assessment. We address that challenge by proposing a novel linear additive model called the fractional Sinusoidal Waveform process (fSWp), accounting for possible nonstationary cyclical long memory, a stochastic trend that can evolve over time and an additional serially correlated noise capturing the short-term variability. The model has a state space representation and makes use of the Kalman filter (KF). Suitable enhancements of the basic methodology enable handling data gaps, outliers, and offsets. We demonstrate our method using various climatological and geodetic time series to illustrate its potential to capture the time-varying stochastic seasonal signals.