A Comparative Study Between Least Square and Total Least Square Methods for Time–Series Analysis and Quality Control of Sea Level Observations

In this study, the quality control of tide gauge observations is investigated by two methods of least square (LS-HE) and total least square harmonic estimation (TLS-HE). Particularly, it is shown how to deal with unexpected anomalies, including outliers, offset and gap in the time series of sea level height. To do so, at first the time series is constructed and then a method based on variance threshold is used to eliminate the possible outliers in the observations. Subsequently, a noise assessment algorithm is implemented and the signal is processed to find the possible times of offsets and to eliminate their corresponding observations from the time series. Finally, the signal is checked to find the periods of gap within the time series and then the gap area is predicted with correct observations. Gap filling analysis is performed in two contexts. In the first, only the significant frequencies of tide are considered in the modelling procedure, while in the second, all possible frequencies according to the period of observations are included. Our results show that for modelling and gap filling, the TLS-HE method has a better performance in a comparison with LS-HE method. Although, for offset and outlier detections, the LS-HE is recommended. It also indicates that the TLS-HE method provides a regular solution for gap filling analysis while LS-HE method needs a regularization scheme for which LSQR regularization is used.