Tide gauge location and the measurement of global sea level rise

The location of tide gauges is not random. If their locations are positively (negatively) correlated with sea level rise (SLR), estimates of global SLR will be biased upwards (downwards). Using individual tide gauges obtained from the Permanent Service for Mean Sea Level during 1807–2010, we show that tide gauge locations in 2000 were independent of SLR as measured by satellite altimetry. Therefore these tide gauges constitute a quasi-random sample, and inferences about global SLR obtained from them are unbiased. Using recently developed methods for nonstationary time series, we find that sea levels rose in 7 % of tide gauge locations and fell in 4 %. The global mean increase is 0.39–1.03 mm/year. However, the mean increase for locations where sea levels are rising is 3.55–4.42 mm/year. These findings are much lower than estimates of global sea level (2.2 mm/year) reported in the literature and adopted by IPCC (2014), and which make widespread use of imputed data for locations which do not have tide gauges. We show that although tide gauge locations in 2000 are uncorrelated with SLR, the global diffusion of tide gauges during the 20th century was negatively correlated with SLR. This phenomenon induces positive imputation bias in estimates of global mean sea levels because tide gauges installed in the 19th century happened to be in locations where sea levels happened to be rising.