Satellite altimetry and tide gauges are the two main techniques used to measure sea level. Due to the limitations of satellite altimetry, a high-quality unified sea level model from coast to open ocean has traditionally been difficult to achieve. This study proposes a fusion approach of altimetry and tide gauge data based on a deep belief network (DBN) method. Taking the Mediterranean Sea as the case study area, a progressive three-step experiment was designed to compare the fused sea level anomalies from the DBN method with those from the inverse distance weighted (IDW) method, the kriging (KRG) method and the curvature continuous splines in tension (CCS) method for different cases. The results show that the fusion precision varies with the methods and the input measurements. The precision of the DBN method is better than that of the other three methods in most schemes and is reduced by approximately 20% when the limited altimetry along-track data and in-situ tide gauge data are used. In addition, the distribution of satellite altimetry data and tide gauge data has a large effect on the other three methods but less impact on the DBN model. Furthermore, the sea level anomalies in the Mediterranean Sea with a spatial resolution of 0.25° × 0.25° generated by the DBN model contain more spatial distribution information than others, which means the DBN can be applied as a more feasible and robust way to fuse these two kinds of sea levels.

Sea level records exhibit complex nonlinear variability as a result of competing physical processes, some of which are largely unknown, and the available length of the record will also affect the trend estimation, therefore robust methods for determining consistent long-period, nonlinear trends are needed to effectively analyze different sea level records holistically, which is important for timely research and applications to address current and future coastal vulnerability and adaptations due to sea level rise (Ghil et al., 2002; Plattner & GianKasper, 2014; Zhang & Church, 2012). At least 30 methods classified into five categories, have been used to estimate or search for sea level trends (see Visser et al., 2015 for a detailed review), and some methods have been compared in terms of different aspects, including accuracy, standard deviation, computational cost, consistency, capacity to provide temporal information, resolution, complexity, and predictive performance (Watson, 2016a). Although there are differences between the results in terms of which methods are better, one could draw some common conclusions. A simple parabola (Houston & Dean, 2011; Woodworth, 1990) or straight line is commonly used to fit the trend in sea level change time series (Douglas, 1991). However, the trend estimate provides limited, if any, information about transient variations of the trend, and the trend estimate is likely to be influenced by the particular data span (Parker et al., 2013). Some other predefined functions or models, such as piecewise functions (Fenoglio-Marc & Tel, 2010), exponential functions (Parker et al., 2013), and different autoregressive moving average models (Beenstock et al., 2015; Thompson, 1980), used to search for sea level trends are also not sufficiently universal to apply to all sea level change time series. Although the moving average is a simple method, data are lost from the two ends of the averaged record, leading to the absence of re-Abstract 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 optima...

With the global mean sea level rise (Dangendorf et al., 2019) and the increase in the intensity of extreme weather events (Kossin et al., 2020), marine disasters in coastal areas have become increasingly severe. Storm surges caused by hurricanes and typhoons are the main causes of extreme sea-level disasters (Han et al., 2017). During 2000-2019, storms killed nearly 200,000 people (the highest death tolls were in South East Asia) and caused more than $1.39 trillion in economic losses (the Americas experienced 72% of the total losses, most occurred in the U.S.) (CRED & UNDRR, 2020). Storm surge (SS), also termed non-tidal residual, is a rise in sea level resulting from low atmospheric pressure and strong winds (Muis et al., 2016). It can lead to coastal flood events (Resio & Westerink, 2008), especially when the SS encounters astronomical high tides. The spatiotemporal characteristics analysis of extreme sea-level events and robust estimation of their occurrence probabilities are key to designing strategies for disaster prevention and mitigation in coastal areas. To do this, long and high spatial-coverage/temporal-resolution SS records are needed.As the most reliable water level observations, high-frequency data from tide gauge stations have been widely used in extreme sea-level studies (Marcos & Woodworth, 2017;Menéndez & Woodworth, 2010;Wahl & Chambers, 2015). However, the data of most tide gauges are easily affected by environmental factors and are still not long enough (Haigh et al., 2021). In addition, the sparseness and uneven distribution of tide gauge stations limit the in-depth analysis of the spatial characteristics of SSs.Numerical models can resolve physical coastal processes and simulate SSs with high spatial coverage at both the regional scale (