Nonlinear Sea-Level Trends and Long-Term Variability on Western European Coasts Tal Ezer † * , Ivan D. Haigh ‡ , and Philip L. Woodworth § † Center for Coastal Physical Oceanography Old Dominion University Norfolk, VA 23508, U.S.A. ‡ National Oceanography Centre University of Southampton Southampton, Hampshire SO14 3ZH, U.K. § National Oceanography Centre Liverpool, Merseyside L3 5DA, U.K. ABSTRACT Ezer, T.; Haigh, I.D., and Woodworth, P.L., 2016. Nonlinear sea-level trends and long-term variability on western European coasts. Journal of Coastal Research, 32(4), 744–755. Coconut Creek (Florida), ISSN 0749-0208. Nonlinear trends and long-term variability in sea level measured on the U.K. and western European coasts with long tide-gauge records (~100–200 y) were investigated. Two different analysis methods, a standard quadratic regression and a nonparametric, empirical mode decomposition method, detected similar positive sea-level accelerations during the past ~150 years: 0.014 6 0.003 and 0.012 6 0.004 mm/y 2 , respectively; these values are close to the sea-level acceleration of the global ocean over the same period, as reported by several studies. Ensemble calculations with added white noise are used to evaluate the robustness of low-frequency oscillations and to estimate potential errors. Sensitivity experiments evaluate the impact of data gaps on the ability of the analysis to detect decadal variations and acceleration in sea level. The long-term oscillations have typical periods of 15–60 years and ranges of 50–80 mm; these oscillations appear to be influenced by the North Atlantic Oscillation and by the Atlantic Multidecadal Oscillation. Analysis of altimeter data over the entire North Atlantic Ocean shows that the highest impact of the North Atlantic Oscillation is on sea-level variability in the North Sea and the Norwegian coasts, whereas the Atlantic Multidecadal Oscillation has the largest correlation with sea level in the subpolar gyre and the Labrador Sea, west of the study area. ADDITIONAL INDEX WORDS: Sea-level oscillations, sea-level acceleration, empirical mode decomposition, North Atlantic oscillations. INTRODUCTION Nonlinear variations in sea level may include both oscillatory changes, such as decadal and multidecadal variations, as well as changes in the long-term sea-level rise (SLR) rates because of global sea-level acceleration associated with increased rates of land-based ice melt or climatic changes in ocean circulation or wind patterns. In most regions of the world’s ocean, there are indications for increasing rates of coastal SLR, but detecting statistically significant long-term sea-level acceleration (on century-long scales) is difficult because of the need to remove decadal and multidecadal variations (Calafat and Chambers, 2013; Dangendorf et al., 2014; Haigh, Nicholls, and Wells, 2009; Haigh, et al., 2014; Wahl et al., 2013; Woodworth et al., 2009a,b). There are also significant spatial variations in both linear and nonlinear trends in the sea level (Boon and Mitchell, 2015; Ezer, 2013). Boon (2012) and Sallenger, Doran, and Howd (2012) indicated temporal changes in acceleration along the U.S. East Coast but with marked larger, positive acceleration in recent years, especially north of Cape Hatteras, where the Gulf Stream (GS) separates from the coast. Nonlinear trends make it difficult to assess whether the recent acceleration is part of natural variations or long-term global trends. Detecting sea-level acceleration is especially difficult because of the need to separate between oscillatory changes and long-term trends. Therefore, various different analysis methods have been used to detect acceleration (see Visser, Dangendorf, and Peterson [2015] for a review of a wide range of such methods). Two different analysis methods are used here to detect sea-level acceleration and demonstrate their usefulness: a standard quadratic regression (fitting the data with the simplest polynomial model of an acceleration curve) and a nonparametric empirical mode decomposition (EMD; Huang et al., 1998); the methods will be described in detail later. An attractive characteristic of the EMD is that it is a more- objective method than parametric regression methods because EMD does not assume a specified formula for the trend and the filtering of oscillations of different timescales is done by an empirical sifting process without specifying a particular filter. As discussed later, there are also some shortcomings in the EMD method. An EMD analysis to help study nonlinear variations and the forcing mechanisms of sea level will be demonstrated, using long records of European sea-level tidal gauges. Because nonlinear variations in sea level are regional, the variations on the western European coasts can be compared with global SLR and variations of sea level in other regions. Recent studies focus attention on a ‘‘hotspot’’ in the western part of the North Atlantic Ocean, where SLR and sea-level acceleration are significantly greater than global rates (Boon, 2012; Ezer, 2013; Ezer and Corlett, 2012; Kopp, 2013; Sallenger, Doran, and Howd, 2012; Yin and Goddard, 2013). Studies suggest that the SLR pattern on the western side of the DOI: 10.2112/JCOASTRES-D-15-00165.1 received 31 August 2015; accepted in revision 16 October 2015; corrected proofs received 23 November 2015; published pre-print online 29 December 2015. *Corresponding author: tezer@odu.edu Ó Coastal Education and Research Foundation, Inc. 2016 Coconut Creek, Florida July 2016 Journal of Coastal Research 32 4 744–755