Abstract 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.

中文翻译：

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最小二乘法和全最小二乘法在海平面观测时间序列分析和质量控制中的比较研究

摘要 本研究采用最小二乘法(LS-HE)和总最小二乘法估计(TLS-HE)两种方法对测潮仪观测的质量控制进行研究。特别展示了如何处理意外异常，包括海平面高度时间序列中的异常值、偏移和间隙。为此，首先构建时间序列，然后使用基于方差阈值的方法来消除观察中可能的异常值。随后，实施噪声评估算法并对信号进行处理以找到可能的偏移时间并从时间序列中消除它们对应的观测值。最后，检查信号以找到时间序列内的间隙周期，然后用正确的观测值预测间隙区域。间隙填充分析在两种情况下进行。在第一种情况下，在建模过程中只考虑了潮汐的重要频率，而在第二种情况下，包括了根据观测周期的所有可能的频率。我们的结果表明，在建模和间隙填充方面，TLS-HE 方法与 LS-HE 方法相比具有更好的性能。尽管对于偏移和异常值检测，建议使用 LS-HE。这也表明 TLS-HE 方法为间隙填充分析提供了正则解决方案，而 LS-HE 方法需要使用 LSQR 正则化的正则化方案。我们的结果表明，在建模和间隙填充方面，TLS-HE 方法与 LS-HE 方法相比具有更好的性能。尽管对于偏移和异常值检测，建议使用 LS-HE。这也表明 TLS-HE 方法为间隙填充分析提供了正则解决方案，而 LS-HE 方法需要使用 LSQR 正则化的正则化方案。我们的结果表明，在建模和间隙填充方面，TLS-HE 方法与 LS-HE 方法相比具有更好的性能。尽管对于偏移和异常值检测，建议使用 LS-HE。这也表明 TLS-HE 方法为间隙填充分析提供了正则解决方案，而 LS-HE 方法需要使用 LSQR 正则化的正则化方案。