Adaptive and accurate trend estimation of the sea level record is critically important for characterizing its nonlinear variations and its study as a consequence of anthropogenic climate change. Sea level change is a nonstationary or nonlinear process. The present modeling methods, such as least squares fitting, are unable to accommodate nonlinear changes, including the choice of a priori information to help constrain the modeling. All these problems affect the accuracy and adaptability of nonlinear trend estimation. Here, we propose a method called EMD‐SSA, that effectively combines adaptive empirical mode decomposition (EMD) and singular spectrum analysis (SSA). First, the sea level change time series is decomposed by EMD to estimate the intrinsic mode functions. Second, the periodic or quasiperiodic signals in the intrinsic mode functions can be determined using Lomb‐Scargle spectral analysis. Third, the numbers of the identified periodicities/quasiperiodicities are used as embedding dimensions of SSA to identify possible nonlinear trends. Then, the optimal nonlinear trend with the largest absolute Mann‐Kendall rank is selected as the final trend for the sea level change. Based on a comprehensive experiment using simulated sea level change time series, we concluded that the EMD‐SSA method can adaptively provide better estimate of the nonlinear trend in a realistic sea level change time series with consistency or high accuracy. We suggest that EMD‐SSA can be used not only to robustly extract nonlinear trends in sea level data, but also for trends in other geodetic or climatic records, including gravity, GNSS observed displacements, and altimetry observations.

中文翻译：

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结合EMD和SSA的非线性海平面趋势估计的自适应方法。

对海平面记录进行自适应且准确的趋势估计对于表征其非线性变化以及作为人为气候变化的结果进行的研究至关重要。海平面变化是一个非平稳或非线性过程。当前的建模方法，例如最小二乘拟合，不能适应非线性变化，包括选择先验信息以帮助约束建模。所有这些问题都会影响非线性趋势估计的准确性和适应性。在这里，我们提出了一种称为EMD-SSA的方法，该方法有效地结合了自适应经验模式分解（EMD）和奇异频谱分析（SSA）。首先，通过EMD分解海平面变化时间序列，以估计固有模式函数。第二，可以使用Lomb-Scargle频谱分析确定本征模式函数中的周期或准周期信号。第三，所识别的周期性/准周期性的数量用作SSA的嵌入维度，以识别可能的非线性趋势。然后，选择具有最大绝对Mann-Kendall秩的最佳非线性趋势作为海平面变化的最终趋势。基于使用模拟海平面变化时间序列进行的综合实验，我们得出结论，EMD-SSA方法能够以一致或高精度的方式自适应地更好地估计实际海平面变化时间序列中的非线性趋势。我们建议EMD-SSA不仅可用于可靠地提取海平面数据中的非线性趋势，而且还可用于其他大地或气候记录中的趋势，包括重力，