While there is scientific consensus that global and local mean sea level (GMSL and LMSL) has risen since the late nineteenth century, the relative contribution of natural and anthropogenic forcing remains unclear. Here we provide a probabilistic upper range of long-term persistent natural GMSL/LMSL variability (P=0.99), which in turn, determines the minimum/maximum anthropogenic contribution since 1900. To account for different spectral characteristics of various contributing processes, we separate LMSL into two components: a slowly varying volumetric component and a more rapidly changing atmospheric component. We find that the persistence of slow natural volumetric changes is underestimated in records where transient atmospheric processes dominate the spectrum. This leads to a local underestimation of possible natural trends of up to B1mm per year erroneously enhancing the significance of anthropogenic footprints. The GMSL, however, remains unaffected by such biases. On the basis of a model assessment of the separate components, we conclude that it
is virtually certain (P=0.99) that at least 45% of the observed increase in GMSL is of anthropogenic origin.