The color of sea level: Importance of spatial variations in spectral shape for assessing the significance of trends

We investigate spatial variations in the shape of the spectrum of sea level variability based on a homogeneously sampled 12 year gridded altimeter data set. We present a method of plotting spectral information as color, focusing on periods between 2 and 24 weeks, which shows that significant spatial variations in the spectral shape exist and contain useful dynamical information. Using the Bayesian Information Criterion, we determine that, typically, a fifth-order autoregressive model is needed to capture the structure in the spectrum. Using this model, we show that statistical errors in fitted local trends range between less than 1 and more than 5 times of what would be calculated assuming \textquotedblleftwhite\textquotedblright noise and that the time needed to detect a 1 mm/yr trend ranges between about 5 years and many decades. For global mean sea level, the statistical error reduces to 0.1 mm/yr over 12 years, with only 2 years needed to detect a 1 mm/yr trend. We find significant regional differences in trend from the global mean. The patterns of these regional differences are indicative of a sea level trend dominated by dynamical ocean processes over this period.