(a) Shown are three recent reconstructions of GMSL based on CW11 (ref. 2), J14 (ref. 3) and H15 (ref. 4) over the period 1900–2009. The shadings show their 1σ uncertainties. Their linear trends are given in the legend. All reconstructions suffer, with respect to their temporal variability, from sampling problems related to the temporally and spatially unevenly distributed location of tide gauge measurements23. Therefore, the temporal GMSL variability and the resulting naturally forced centennial trends (P=0.99) have been assessed using spatial average of the LMSLsyn fields (SSH, glacier, Greenland ice sheet and hydrology), which are available over the entire global ocean over the period from 1871 to 2008. The resulting fluctuation function derived from a DFA2 is shown in (b). The fluctuation function yields an α value of 1.28. Following the approach described in refs 8, 13, 14, 15 this implies an upper bound of naturally forced centennial trends (1900–2009) of 0.73 mm per year (P=0.99). This suggests that the observed twentieth century GMSL rise is already outside the range of natural variability with a minimum external contribution (dependent on the reconstruction) of 0.60–1.25 mm per year (P=0.99).