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

Abstract

SUMMARYTide 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’ (${N}_{\mathrm{ eff}}$) 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 ${N}_{\mathrm{ eff}}$ 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 $95\ \mathrm{ per}\ \mathrm{ cent}\,\mathrm{ CI} = 179.8{T}^{ - 1.29}$. 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.