evidence: To avoid bias, we therefore recommend, and here use, the approach of Jevrejeva et al.12,24, (also applied in refs 25 and 26), which systematically estimates quadratic coefficients and their uncertainty (95% confidence) for all possible start dates and data lengths of our artificially extended records (see Methods). For just the historic records, our results (Fig. 3a,b), like ref. 26, show that accelerations (that is, two times the quadratic coefficient) are rarely diagnosed to be statistically different from zero in individual tide gauge records, particularly in records shorter than about 130 years. In tide gauge records, both the magnitude and sign of the acceleration are dominated by interannual to multidecadal variability: to a greater extent for sites with large variability such as Fremantle; and to a lesser but still significant extent for sites with smaller variability such as Newlyn. Note that large accelerations observed over shorter timescales are real. However, they are mainly due to natural internal variability and mask any externally forced accelerations (see Discussion).