The 95 per cent confidence interval for the mean sea-level change rate derived from tide gauge data

Abstract

Tide gauge (TG) data are crucial for assessing global sea-level and climate changes, coastal subsidence and inundation. Mean sea-level (MSL) time-series derived from TG data are autocorrelated. The conventional ordinary least-squares regression method provides reasonable estimates of relative sea-level (RSL) change rates (linear trends) but underestimates their uncertainties. In order to cope with the autocorrelation issue, we propose an approach that uses an ‘effective sample size’ (Neff) to estimate the uncertainties (±95 per cent confidence interval, or 95 per cent CI for short). The method involves decomposing the monthly MSL time-series into three components: a linear trend, a periodic component and a noise time-series. The Neff is calculated according to the autocorrelation function (ACF) of the noise time-series. We present an empirical model that fits an inverse power-law relationship between 95 per cent CI and time span (T) based on 1160 TG data sets globally distributed, where 95 per cent CI = 179.8T -1.29 . This model provides a valuable tool for projecting the optimal observational time span needed for the desired uncertainty in sea-level rise rate or coastal subsidence rate from TG data. It suggests that a 20-yr TG time-series may result in a 3–5 mm yr-1 uncertainty (95 per cent CI) for the RSL change rate, while a 30-yr data set may achieve about 2 mm yr-1 uncertainty. To achieve a submillimetre per year (< 1 mm yr-1) uncertainty, approximately 60 yr of TG observations are needed. We also present a Python module (TG Rate 95CI.py) for implementing the methodology. The Python module and the empirical model have broad applications in global sea-level rise and climate change studies, and coastal environmental and infrastructure planning, as well as Earth science education.