Characterizing and minimizing the effects of noise in tide gauge time series: relative and geocentric sea level rise around Australia

We quantify the rate of sea level rise around the Australian continent from an analysis of tide gauge and Global Positioning System (GPS) data sets. To estimate the underlying linear rates of sea level change in the presence of significant interannual and decadal variability (treated here as noise), we adopt and extend a novel network adjustment approach. We simultaneously estimate time-correlated noise as well as linear model parameters and realistic uncertainties from sea level time series at individual gauges, as well as from time-series differences computed between pairs of gauges. The noise content at individual gauges is consistent with a combination of white and time-correlated noise. We find that the noise in time series from the western coast of Australia is best described by a first-order Gauss-Markov model, whereas east coast stations generally exhibit lower levels of time-correlated noise that is better described by a power-law process. These findings suggest several decades of monthly tide gauge data are needed to reduce rate uncertainties to < 0.5 mm yr(-1) for undifferenced single site time series with typical noise characteristics. Our subsequent adjustment strategy exploits the more precise differential rates estimated from differenced time series from pairs of tide gauges to estimate rates among the network of 43 tide gauges that passed a stability analysis. We estimate relative sea level rates over three temporal windows (1900-2011, 1966-2011 and 1993-2011), accounting for covariance between time series. The resultant adjustment reduces the rate uncertainty across individual gauges, and partially mitigates the need for century-scale time series at all sites in the network. Our adjustment reveals a spatially coherent pattern of sea level rise around the coastline, with the highest rates in northern Australia. Over the time periods beginning in 1900, 1966 and 1993, we find weighted average rates of sea level rise of 1.4 +/- 0.6, 1.7 +/- 0.6 and 4.6 +/- 0.8 mm yr(-1), respectively. While the temporal pattern of the rate estimates is consistent with acceleration in sea level rise, it may not be significant, as the uncertainties for the shorter analysis periods may not capture the full range of temporal variation. Analysis of the available continuous GPS records that have been collected within 80 km of Australian tide gauges suggests that rates of vertical crustal motion are generally low, with the majority of sites showing motion statistically insignificant from zero. A notable exception is the significant component of vertical land motion that contributes to the rapid rate of relative sea level change (> 4 mm yr(-1)) at the Hillarys site in the Perth area. This corresponds to crustal subsidence that we estimate in our GPS analysis at a rate of -3.1 +/- 0.7 mm yr(-1), and appears linked to groundwater withdrawal. Uncertainties on the rates of vertical displacement at GPS sites collected over a decade are similar to what we measure in several decades of tide gauge data. Our results motivate continued observations of relative sea level using tide gauges, maintained with high-accuracy terrestrial and continuous co-located satellite-based surveying.