Long-range dependence in North Atlantic sea level

Sea level is an important parameter in climate and oceanographic applications. In this work the scaling behavior of sea level is analyzed from time series of sea level observations. The wavelet domain is particularly attractive for the identification of scaling behavior in an observed time series. The wavelet spectrum from a scale-by-scale wavelet analysis of variance reproduces in the wavelet domain the power laws underlying a scaling process, allowing the estimation of the scaling exponent from the slope of the wavelet spectrum. Here the scaling exponent is estimated in the wavelet domain for time series of sea level observations in the North Atlantic: at coastal sites from tide gauges, covering 50 years of monthly measurements, and in the open ocean from satellite altimetry, covering 12 years of satellite measurements at 10 days intervals. Both tide gauge and altimetry time series exhibit scaling behavior. Furthermore, the degree of stochastic persistence is spatially coherent and distinct at the coast and in the open ocean. Near the coast, the stochastic structure of the sea level observations is characterized by long-range dependence with a moderate degree of persistence. Larger values of the scaling exponent, consistent with weaker persistence, are concentrated in the northern Atlantic. At mid-latitudes the stochastic dependence of sea level observations is characterized by strong persistence in the form of strong long-range and 1/f dependence.