TY - JOUR

T1 - Modeling trends and periodic components in geodetic time series

T2 - a unified approach

AU - Kermarrec, Gaël

AU - Maddanu, Federico

AU - Klos, Anna

AU - Proietti, Tommaso

AU - Bogusz, Janusz

N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. This study is supported by the Deutsche Forschungsgemeinschaft under the project KE2453/2-1 for correlation analysis within the context of optimal fitting. FM gratefully acknowledges financial support from the CY Initiative of Excellence (grant “Investissements d’Avenir" ANR-16-IDEX-0008), Project “EcoDep" PSI-AAP2020-0000000013. AK and JB are supported by the National Science Centre, Poland, grant no. UMO-2021/41/B/ST10/01458.

PY - 2024/3/4

Y1 - 2024/3/4

N2 - Geodetic time series are usually modeled with a deterministic approach that includes trend, annual, and semiannual periodic components having constant amplitude and phase-lag. Although simple, this approach neglects the time-variability or stochasticity of trend and seasonal components, and can potentially lead to inadequate interpretations, such as an overestimation of global navigation satellite system (GNSS) station velocity uncertainties, up to masking important geophysical phenomena. In this contribution, we generalize previous methods for determining trends and seasonal components and address the challenge of their time-variability by proposing a novel linear additive model, according to which (i) the trend is allowed to evolve over time, (ii) the seasonality is represented by a fractional sinusoidal waveform process (fSWp), accounting for possible non-stationary cyclical long-memory, and (iii) an additional serially correlated noise captures the short term variability. The model has a state space representation, opening the way for the evaluation of the likelihood and signal extraction with the support of the Kalman filter (KF) and the associated smoothing algorithm. Suitable enhancements of the basic methodology enable handling data gaps, outliers, and offsets. We demonstrate the advantage of our method with respect to the benchmark deterministic approach using both observed and simulated time series and provide a fair comparison with the Hector software. To that end, various geodetic time series are considered which illustrate the ability to capture the time-varying stochastic seasonal signals with the fSWp.

AB - Geodetic time series are usually modeled with a deterministic approach that includes trend, annual, and semiannual periodic components having constant amplitude and phase-lag. Although simple, this approach neglects the time-variability or stochasticity of trend and seasonal components, and can potentially lead to inadequate interpretations, such as an overestimation of global navigation satellite system (GNSS) station velocity uncertainties, up to masking important geophysical phenomena. In this contribution, we generalize previous methods for determining trends and seasonal components and address the challenge of their time-variability by proposing a novel linear additive model, according to which (i) the trend is allowed to evolve over time, (ii) the seasonality is represented by a fractional sinusoidal waveform process (fSWp), accounting for possible non-stationary cyclical long-memory, and (iii) an additional serially correlated noise captures the short term variability. The model has a state space representation, opening the way for the evaluation of the likelihood and signal extraction with the support of the Kalman filter (KF) and the associated smoothing algorithm. Suitable enhancements of the basic methodology enable handling data gaps, outliers, and offsets. We demonstrate the advantage of our method with respect to the benchmark deterministic approach using both observed and simulated time series and provide a fair comparison with the Hector software. To that end, various geodetic time series are considered which illustrate the ability to capture the time-varying stochastic seasonal signals with the fSWp.

KW - Fractional noise

KW - Fractional sinusoidal waveform process

KW - Geodetic time series

KW - Kalman filter

KW - Long memory

KW - Random walk

KW - State space models

KW - Stochastic sinusoidal signals

UR - http://www.scopus.com/inward/record.url?scp=85186610059&partnerID=8YFLogxK

U2 - 10.1007/s00190-024-01826-5

DO - 10.1007/s00190-024-01826-5

M3 - Article

AN - SCOPUS:85186610059

VL - 98

JO - Journal of geodesy

JF - Journal of geodesy

SN - 0949-7714

M1 - 17

ER -