Detection time for global and regional sea level trends and accelerations

Many studies analyze trends on sea level data with the underlying purpose of finding indications of a long-term change that could be interpreted as the signature of anthropogenic climate change. The identification of a long-term trend is a signal-to-noise problem where the natural variability (the noise) can mask the long-term trend (the signal). The signal-to-noise ratio depends on the magnitude of the long-term trend, on the magnitude of the natural variability, and on the length of the record, as the climate noise is larger when averaged over short time scales and becomes smaller over longer averaging periods. In this paper, we evaluate the time required to detect centennial sea level linear trends and accelerations at global and regional scales. Using model results and tide gauge observations, we find that the averaged detection time for a centennial linear trend is 87.9, 76.0, 59.3, 40.3, and 25.2 years for trends of 0.5, 1.0, 2.0, 5.0, and 10.0 mm/yr, respectively. However, in regions with large decadal variations like the Gulf Stream or the Circumpolar current, these values can increase up to a 50%. The spatial pattern of the detection time for sea level accelerations is almost identical. The main difference is that the length of the records has to be about 40-60 years longer to detect an acceleration than to detect a linear trend leading to an equivalent change after 100 years. Finally, we have used a new sea level reconstruction, which provides a more accurate representation of interannual variability for the last century in order to estimate the detection time for global mean sea level trends and accelerations. Our results suggest that the signature of natural variability in a 30 year global mean sea level record would be less than 1 mm/yr. Therefore, at least 2.2 mm/yr of the recent sea level trend estimated by altimetry cannot be attributed to natural multidecadal variability.