The effect of temporal correlated noise on the sea level rate and acceleration uncertainty

It is well known that sea level variations exhibit temporal correlation. This is sometimes ignored in the estimation process of the sea level rise or taken into account using a first-order autoregressive model. We have verified that this stochastic model is accurate for yearly tide gauge and sea level reconstruction time-series but it underestimates the real rate uncertainty in satellite altimetry and monthly tide gauge data by a factor of 1.3-1.5 and sometimes even 2. Similar results were found for sea level acceleration. An original finding is that in 13-17 per cent of the tide gauge data, we found random walk which increases the rate uncertainty on average by an additional factor of 3. The estimation errors presented in this research should be added to the other sources of uncertainty, such as the vertical land movement, spatial correlation and altimeter drift, to obtain the total sea level rate and acceleration error.