Sea level trajectories and recent records at Australian tide gauges

2.1 Data

We obtained tide gauge data from the Australian National Collection of Homogenised Observations of Relative Sea Level (ANCHORS, Hague et al. 2021). Routine updates of ANCHORS have appended new quality-controlled data to the existing homogenised timeseries. Periods of lower confidence were removed from the tide gauge timeseries as these are not suitable for trend or extremes analysis (Hague et al. 2021). ANCHORS was chosen as it is homogenised, with raw data corrected for non-geophysical artefacts in the data, such as those induced by equipment upgrades and site moves.

Future MSL is obtained from the global MSL projection from the 6th Assessment Report (AR6) of the Intergovernmental Panel on Climate Change (IPCC) (Fox-Kemper et al. 2021) to compare to observation-based trajectories. Vertical land motion in Australia is generally small compared to other regions globally, or if present, occurs at local scales due to local processes (Burgette et al. 2013; Rezvani, Watson and King 2022). Further, increases in MSL around Australia are expected to closely follow changes in the global mean (Zhang et al. 2017). This justifies the use of global MSL for comparative purposes in this study.

2.2 Site-based mean and record sea levels

Annual and monthly MSLs were computed as the average of all hourly observations in each calendar year or month at each site with the requirement of 70% completeness. This completeness criterion follows previous studies (Hague et al. 2022), and balances the need to have enough data for the annual mean to be representative of the experienced conditions but for the completeness requirement to not be so onerous that years that are largely complete are discarded. We performed a test of how sensitive our results are to different completeness criteria (Section 3.1). The highest hourly observations at each gauge are considered ‘record floods’ as these maxima exceed published impact-based thresholds for all assessed stations (Hague et al. 2022, 2023). We also estimated the theoretical rate of record setting without a changing climate or variability by assuming that the likelihood of setting a record is equal to the reciprocal of the timeseries length each year (Power and Delage 2019). For example, the probability of a record occurring in each year of a 20-year timeseries is 0.05 (i.e. 1/20). This simplified analysis requires no assumptions around base rates.

2.3 National composite mean sea levels, trends and extrapolation

A national composite MSL timeseries (anomaly relative to 1995–2014 mean) was produced following the process described in Hague et al. (2022) (see their section 3.1.1) for years 1966–2022. This maximal period was used as it is long enough for acceleration to be robustly detected (Haigh et al. 2014b) and to lessen possible contamination by the IPO signal (White et al. 2014).

It is well acknowledged that SLR is accelerating (e.g. Dangendorf et al. 2019; Frederikse et al. 2020; Hamlington et al. 2024), with numerous studies using quadratic or other non-linear representations for SLR contributions to observed changes in mean and extreme sea levels (e.g. Li et al. 2022; Thiéblemont et al. 2023; Treu et al. 2024). Quadratic trends can also be used to generate a future trajectory for SLR, based on these historical accelerations (Church and White 2006; Nerem et al. 2018; Wang et al. 2021; Hamlington et al. 2022). We show by comparison to other SLR representations (Section 3.1) that such an approach is justified for Australia. Regardless, we note (Section 4) that future extrapolations may be unreliable into the far future as conditions may deviate from their past trajectory.

The quadratic trend was estimated by fitting an ordinary least-squares model to the composite annual MSL anomaly timeseries using statsmodels (ver. 0.13.2, see https://www.statsmodels.org/stable/index.html; Seabold and Perktold 2010) in Python. The acceleration in sea level is computed as twice the quadratic coefficient (Church and White 2006; Wang et al. 2021). We consider the 5th, 50th and 95th percentile estimates of acceleration and extrapolate these out to 2100 by solving the differential equation of motion under uniform acceleration:

where t is the time in years after 2022 and α is the acceleration; s_t is the total increase in mean sea level relative to the 1995–2014 national averaged MSL at time t, for example, t = 3 corresponds to the estimate of national averaged MSL in 2025, above the 1995–2014 value, hence s₀ is the amount of SLR for the year 2022 estimated from the regression of observed annual MSL; and u₀ is the velocity at year 2022, estimated as the (first) difference of the 2022 and 2021 values of the quadratic regression of observed annual MSL. Based on our results in Section 3.1, we take s₀ as 0.068 m, u₀ as 0.00534 m year⁻¹ and α as 0.000178 m year⁻². These extrapolations are compared to global MSL projections from the IPCC AR6 (Fox-Kemper et al. 2021).

Although this approach is statistically robust, we are aware of criticisms of using high order trends in forecasting, which can result in unrealistic values (e.g. Lamberson and Firman 2002). Accordingly, we additionally construct a nonlinear trend from a sequence of linear segments using detrended fluctuation analysis (DFA). To obtain projections from the detrended analysis we use an extended exponential smoothing approach. This involves a linear forecast equation:

where lt=αyt+(1−α)(lt−1+ϕhbt−1) and bt=β(lt−lt−1)+(1−β)ϕhbt−1. Here, l_t and b_t are estimates of level and trend, α and β are smoothing parameters for level and trend at time t, whereas ϕ^h is a dampening parameter to moderate the trend and avoid over-forecasting over long time horizons. The initial values for l_t, b_t and ϕ^h are 0.037, 0.0036 and 0.0391 respectively, and the smoothing parameters α and β are 0.0054 and 0.0056 respectively. These values were calibrated for the Australian data based on a fit between year and SLR in metres above 1995–2014 mean.

3.1 Sea level trend

We compare the quadratic and piecewise linear trends to a Lowess smoothed timeseries generated using an implementation of Cleveland (1979) in statsmodels (Seabold and Perktold 2010) (Fig. 1). Since 1966, nationally averaged MSL has increased 0.124 m based on quadratic ordinary least-squares fitting, 0.127 m based on the Lowess smoothing and 0.117 m based on the piecewise linear regression. The piecewise approach identifies a single estimated break point occurring in 1993 with a distinct shift in slope. This slope estimates a SLR of 3.97 mm year⁻¹ over the 1993–2022 period. Based on our quadratic fit, sea level accelerated at 0.113 mm year⁻² (95% confidence interval: 0.048–0.178 mm year⁻²) over 1966–2022, indicating a statistically significant acceleration. This can be interpreted as SLR increasing by 1.13 mm year^–1 more every decade. Our central estimate for acceleration sits above the upper limit of the confidence interval for global sea level acceleration over 1971–2018 (0.066–0.080 mm year⁻²) (Fox-Kemper et al. 2021). This higher acceleration could be due to the several record-breaking years since 2018 experienced in Australia (Section 3.2). The trend has led to the four highest national composite annual MSLs occurring after 2010 (Fig. 1a). There is strong coherence between each gauge, especially from the mid-1990s (Fig. 1b).

Fig. 1.

(a) Timeseries of national annual average mean sea level (MSL) for 1966–2022 (black), with Lowess smoothing (dashed), quadratic (dark red dash-dot) and piecewise linear (light blue dotted) trends, and (b) annual means for each site along with national annual average MSL.

The increase in MSL since the IPCC baseline period helps decision makers understand how observations are tracking relative to projections and the associated planning benchmarks (Department of Energy Environment and Climate Action 2023). We estimate how much higher MSL is in 2022 compared to its mean value over the 1995–2014 baseline period used by the IPCC. Using the quadratic fit, MSL is 0.067 m higher than the 1995–2014 mean. Similar estimates of 0.064 and 0.063 m were found using Lowess smoothing and piecewise linear regression respectively. For example, this means that as of 2022, 0.067 m out of the 0.20 m being planned for by 2040 in Victoria has already occurred (Department of Energy Environment and Climate Action 2023).

Both quadratic and piecewise linear representations offer a better fit to the observations than a single linear trend over the 1966–present period as used in previous studies (White et al. 2014; Hague et al. 2022), providing strong statistical evidence to support a conclusion that SLR is accelerating. First, the piecewise linear regression indicates a significant acceleration. Second, the quadratic coefficient in the 1966–2022 quadratic model is significant (P = 0.005). Third, including the quadratic coefficient results in a better fit to the data and lower root mean square error (RMSE) of 0.0003 and R² = 0.56 than if it is omitted (R² = 0.49, RMSE = 0.013). Fourth, the Akaike and Bayes Information Criteria are lower if the quadratic coefficient is included than if it is omitted, suggesting that this fit is sufficiently better to justify the additional complexity compared to a linear alternative.

We also tested the sensitivity of the national composite MSL to the minimum completeness criterion applied to identify whether there are sufficient data to compute an annual mean. We find that MSL does not depend greatly on the completeness criterion with RMSE of 0.003 m or less for completeness criteria of 50–90%, compared to the 70% used here. Relaxing the criterion to 50% only allows 35 more site-years to be included (a 2% increase), whereas tightening to 90% completeness reduces the number of site-years by 117 (7%).

3.2 Sea level records

In a stationary climate (i.e. one with no trends and variability), we would expect the current record sea level to have an equal probability of having been set in any previous year when an annual maximum was recorded (Section 3.1; Power and Delage 2019). Based on this principle, the current site-based record annual MSLs were set disproportionately late in the observation period as 36 of 37 locations had their current annual MSL record set in 2010 or after (Fig. 2a), which is 3.5 times greater than would be expected under stationarity. Out of these 36 locations, half set their record annual MSL in either 2021 or 2022. Records set in the last 2 years of the data period were 8.7 and 14.7 times more frequent than would be expected in a stationary climate respectively.

Fig. 2.

The year when the current annual (a) average MSL record and (b) maximum hourly sea level record was set for Australian tide gauges.

Current record flood levels (i.e. the highest of all hourly observations) were also set disproportionately late in the observation period, albeit less so than for the MSL records (Fig. 2b). The current record flood level was set at 24 locations from 2010 onwards, which is 2.4 times greater than the expected number of current records to have been over this period without a trend. The smaller increases in frequency of record maxima compared to record means is explained by signal-to-noise ratio arguments: the variability between years in annual MSLs is much less than the variability of annual maxima for Australian tide data. The mean standard deviation of annual mean and maximum sea levels across all tide gauges are 0.055 and 0.139 m respectively. As the climate change signal similarly affects mean and extreme sea level elevations in Australia (e.g. Colberg and McInnes 2012), the difference between signal-to-noise ratios for means and maxima is essentially a function of the difference in variability between each metric (i.e. the noise).

Monthly MSL records also occur more frequently in the latter part of the observational timeseries (Fig. 3). The number of current site-based monthly records found in the most recent decade is 7.8 times greater than the number in the first decade. Of all current monthly records, 77% were set during 2010–2022. This is 3.4 times greater than would be expected without a changing climate. This analysis has accounted for lower data density in the early part of the record by computing counts using the ratios of missing data in each year (World Meteorological Organisation 2017). For example, if 1966 only has 70% of the total expected station-months then all record counts are divided by 0.7. In aggregate these data show clearly that across hourly, monthly and annual timescales, record setting is now being strongly influenced by the rise in MSL.

Fig. 3.

The number of current monthly MSL records set in calendar year across all sites in the ANCHORS dataset each year (adjusted for missing data). The shading within the bars shows the breakdown of how records are distributed by calendar month. Austral winter months are shown as darker colours and austral summer months are shown as lighter colours. La Niña year marked with an asterisk (black for single year, red for multi-year), based on classifications by Huang et al. (2024).

The years where the most site-based monthly MSL records were set coincide with multi-year episodes of the La Niña phase of ENSO (Huang et al. 2024). For example, 70 and 83% of locations set at least one monthly MSL record in 2021 and 2022 respectively. Similarly, 42 and 51% of locations set at least one monthly MSL record in 2010 and 2011 respectively. Whereas La Niña increases mean and extreme sea levels at many locations around Australia (Lowe et al. 2021; Viola et al. 2024), the fact that only recent La Niña events have been associated with large numbers of record sea levels (Fig. 3) highlights the accumulating impact of the trend. The recent La Niña may affect estimates of trends, although similarities between the trends computed here and those without the recent record years from earlier studies (White et al. 2014; Hague et al. 2022) suggest that this is not a first-order effect.

3.3 Future mean sea level trajectory

Noting the clear acceleration in Australian MSL, we explore here what a statistical extrapolation tells us about possible Australian sea level changes over coming decades. Extrapolating the observed quadratic trend of 0.113 mm year⁻² [90% confidence interval: 0.048–0.178 mm year⁻²] estimates 2050 MSL as 0.26 ± 0.03 m [90% confidence interval] above 1995–2014 MSL, with further estimates of 0.45 ± 0.07 m for 2070 and 0.83 ± 0.20 m for 2100 (Fig. 4). The linear extrapolation, based on the exponential smoothing on the DFA, predicts 0.15 m SLR [0.09–0.25] by 2050 using an undampened parameter and 0.19 m SLR [0.13–0.27] using a damped parameter. High SLR scenarios (e.g. SSP5–8.5) published by the IPCC are most consistent with a continuation of the SLR trajectory that has been observed in the last 50 years (Fig. 4d), based on differences between the extrapolations and projections. For future MSL to be consistent with median estimate of low scenarios (e.g. SSP1–2.6) the observed acceleration must immediately cease, which seems unlikely given recent global temperatures (Fig. 4a).

Fig. 4.

Comparison of quadratic (dark red lines: median solid, dotted 5 and 95% estimates), linear with damped exponential smoothing (light blue lines: median solid, dotted 5 and 95% estimates) and IPCC AR6 global mean sea level (MSL) projections (median estimate black dashed line, shading representing 66 and 90% range). Four different emission scenarios are presented for the IPCC AR6 projections: (a) SSP1–2.6, (b) SSP2–4.5, (c) SSP3–7.0 and (d) SSP5–8.5. Observed nationally averaged annual MSL timeseries provided for reference (black solid line). Median estimates provided in Bureau of Meteorology (2024).