Sea Level Rise Driving Increasingly Predictable Coastal Inundation in Sydney, Australia

As global mean sea level continues to rise, thresholds corresponding to coastal inundation impacts are exceeded more frequently. This paper aims to relate sea level rise (SLR) observations and projections to their physical on‐the‐ground impacts. Using a large coastal city as an example, we show that in Sydney, Australia, frequencies of minor coastal inundation have increased from 1.6 to 7.8 days per year between 1914 and present day. We attribute over 80% of the observed coastal inundation events between 1970 and 2015 to the predominantly anthropogenic increases in global mean sea level. Further, we find that impact‐producing coastal inundation will occur weekly by 2050 under high‐ and medium‐emission/SLR scenarios and daily by 2100 under high emissions. The proportion of tide‐only coastal inundation events (i.e., where no storm surge is required to exceed flood thresholds) will increase with SLR, such that most coastal inundation events, including those considered historically severe, will become a predictable consequence of SLR and astronomical tides. These findings are important for coastal managers as frequency, severity, and predictability of inundation impacts can all now be related to the amount of SLR (e.g., a planning allowance or SLR projection). By incorporating known historical inundation events, this allows contextualization, visualization, and localization of global SLR and the changing nature of future coastal inundation risk.


Introduction
Global mean sea level (GMSL) continues to rise at an accelerating rate due to anthropogenic climate change (IPCC, 2019). Specifically, increased greenhouse gas emissions are responsible for 70% of the observed global sea level rise (SLR) since 1970 (Slangen et al., 2016). This leads to increasingly frequent extreme sea level events due to these events occurring against a background SLR trend . Sea level variability observed at tide gauges comprises multiple components, including SLR, astronomical tides (e.g., as presented in tide tables), the effects of climatic, meteorological and oceanographic phenomena, and vertical land motion (Woodworth et al., 2019). Furthermore, there is large regional variability in the meteorological and climatological processes, as well as in astronomical tides, that contribute to extreme sea levels around the Australian coast (McInnes et al., 2016). Storm surges (Callaghan & Power, 2014), tsunami (Beccari, 2009), meteotsunami (Pattiaratchi & Wijeratne, 2015), and sea level anomalies coinciding with high astronomical tides (Hanslow et al., 2019;Maddox, 2018a) all have been associated with past impact-producing extreme sea level events.
In many low-lying locations, SLR has led to a reduction in the gap between typical high tide marks and inundation thresholds (freeboard), causing smaller and more frequent sea level anomalies (i.e., with respect to the changing mean) to result in inundation (Sweet & Park, 2014). This occurrence of typically minor or "nuisance" (Moftakhari et al., 2018) inundation and its impacts are expected to become more frequent into the future (Jacobs et al., 2018;Moftakhari et al., 2018). Recent studies in Australia (Hague et al., 2019;Hanslow et al., 2018Hanslow et al., , 2019 and from the United States (Ray & Foster, 2016;Sweet et al., 2016Sweet et al., , 2018 have documented frequent, typically minor, coastal inundation impacts, occurring multiple times per year and at elevations that can now be reached by the day-to-day astronomical tides. However, the causes, trends, future projections, and economic and environmental impacts of these frequently occurring coastal inundation events remain largely unstudied in the Australian context and, to a lesser extent, globally. Notably, Ray and Foster (2016) were first to attribute specific coastal inundation events (via the exceedance of an impact-based threshold) as being due to astronomical tides alone. It is worth noting that all harmonic-based estimates of astronomical tides include all signal at the frequencies of astronomical tide generating forces, regardless of the underlying physics, which means these estimates can include annual and semiannual weather effects (Parker, 2007). Henceforth, we adopt the terminology of Ray and Foster (2016) and refer to this phenomenon as "tide-only" inundation. We deliberately avoid the terminology of "tidal inundation" and "high tide flooding" as these terms have been used in the Australian and international contexts to mean minor coastal inundation, occurring predominantly but not exclusively, due to astronomical tides (e.g., Dahl et al., 2017;Habel et al., 2020;Hanslow et al., 2018Hanslow et al., , 2019Hino et al., 2019;Moore & Obradovich, 2020;Sweet et al., 2016Sweet et al., , 2018. Critical environmental thresholds in natural and human systems, including for coastal inundation, are typically fixed (although may change as human developments create different exposures to inundation) rather than relative to a changing background signal (Harris et al., 2018). Habel et al. (2020) state that for sea level projections to be useful for planning, they must consider local coastal inundation impacts including those due to astronomical tides. Ultimately, this means to monitor coastal inundation due to extreme sea levels, one must consider metrics that are defined based on consequence rather than likelihood. Coastal flood warning thresholds are defined for many locations in United States by National Oceanographic and Atmospheric Administration , thus, considering the impacts these water levels elicit. Unfortunately, Australia does not have a comparable service, with flood levels only defined by the Bureau of Meteorology (2013) for areas predominantly affected by riverine (not coastal) floods. Hence, most studies on sea level extremes in the Australian domain (Church et al., 2006;Department of Environment Climate Change and Water, 2010;Manly Hydraulics Laboratory, 2011;McInnes et al., 2009McInnes et al., , 2013 do not directly consider their impacts, instead utilizing annual recurrence intervals (ARIs) or annual exceedance probabilities without specific reference to observed coastal impacts. Here we adapt a recently developed impact-based methodology (Hague et al., 2019), like those used in the United States, to analyze historical and projected future coastal inundation events in Sydney, Australia. By considering a variety of inundation thresholds, including the current highest-on-record observation, we show that the occurrence of coastal inundation in Sydney will become increasingly predictable and almost entirely driven by astronomical tides rather than storm surges.

Data Requirements and Sources
In order to examine trends in coastal inundation, both reports of impacts of coastal inundation and long sea level height records are required. While the methodology and analysis could be applied anywhere the relevant data exist, Sydney, Australia, provides an excellent case study due to the abundance of both impact and tide gauge data. Note that the method of Hague et al. (2019), which is employed here, has some broad similarities to other contemporaneous studies that have sought to define impact-based sea level thresholds or models for coastal inundation due to high still water levels (Habel et al., 2020;Hino et al., 2019;Moore & Obradovich, 2020). Coastal inundation impacts around Sydney have also been well documented in the scientific literature (Hanslow et al., 2019), government reports (Jacobs, 2012(Jacobs, , 2014(Jacobs, , 2015(Jacobs, , 2016Maddox, 2018bMaddox, , 2019Watson & Frazer, 2009), on social media (e.g., Witness King Tides, 2020), and by local coastal scientists (P. Watson Earth's Future 2020). Table 1 documents the dates of occurrence and the nature of coastal inundation impacts and the source of the information. Figure 1 shows a map of the locations and a small selection of images of inundation events documented in Table 1.
The detection of linear and nonlinear changes due to SLR against long-period climatic variability is improved with increasing length of the sea level time series (Haigh, Wahl, et al., 2014;Watson, 2018). The Sydney region has one of the longest tide gauge records in the Southern Hemisphere (Marcos et al., 2015;Watson, 2011) with digitized hourly data available since 1914 at Fort Denison (Hamon, 1987). Data for Fort Denison, Camp Cove, and Botany Bay were sourced from the Bureau of Meteorology Tides Unit databank, of which portions are available from GESLA-2 (Woodworth et al., 2017) and/or University of Hawaii Sea Level Center (Caldwell et al., 2015). The primary data set used in this study, from Fort Denison, can be wholly reproduced by concatenating the GESLA record with the UHSLC Research Quality data to the end of 2018. These data have temporal resolution of 1 hr and consist of digitized historical records and, more recently, Lanczos-Cosine filtered data, all referenced to a common datum (Hamon, 1987;Holgate et al., 2013;PSMSL, 2020). To account for changes in reporting precision throughout the digitized record and the implications this may have on the consistency of event threshold exceedances through time, all observations have been rounded to the nearest centimeter. Data for Patonga, Port Jackson, Port Hacking, and Bundeena were provided by Manly Hydraulics Laboratory, which was filtered, using a Lanczos-Cosine filter to hourly frequency for comparability to the Bureau of Meteorology data. The Manly Hydraulics Laboratory data, along with Camp Cove and Botany Bay, were only used for the purposes of establishing whether Fort Denison data were representative of regional (defined for this purpose as within 100 km of the gauge) sea level.

Defining Impact-Based Thresholds for the Sydney Region
An assumption of the approach of Hague et al. (2019), and indeed all other studies that define impact-based thresholds, is that the water levels recorded at the tide gauge are representative of the water levels at the locations where impacts are reported. Hague et al. (2019) argued that broadscale events with similar regional impacts implied that the tide gauge heights were locally representative. However, the high data density of the Sydney region allows this assumption to be examined empirically. We find that very strong correlations (R > 0.95) exist between the daily minimum, mean, and maximum sea levels at Fort Denison and other nearby tide gauges, as well as in the monthly mean and maximum time series (R > 0.90). This indicates that wind-driven impacts and freshwater contributions are not substantially different across the region. We also find that the same high sea level events elicit impacts in multiple locations around the Sydney region, indicating that inundation is not localized and hence not likely due to local effects. Notably, the 6 December 2017 coastal inundation event saw impacts right along the New South Wales coast including at Coffs Harbour, Newcastle, Gosford, Woy Woy, Moruya, and Batemans Bay (P. Watson, personal communication, 3/5/2020), as well as in the Sydney region (Table 1). This is expected from a physical perspective as the Sydney region comprises predominantly drowned river valley estuaries which have only mild attenuation of the tidal signal away from the oceanic source of sea level variability (Hanslow et al., 2018). Tides are

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Earth's Future the dominant driver of sea level variations in Sydney, with a tidal range of approximately 2 m (highest to lowest tide of the 18.6-year nodal cycle) and an average nontidal residual of 6 cm. Hence, variations in water levels recorded at the Fort Denison tide gauge are highly representative of those in the broader Sydney region. Sydney is also considered to have negligible vertical land motion-thus, the differences between absolute and relative sea levels have been historically small (Burgette et al., 2013) and projected to remain small into the future (Kopp et al., 2014). Therefore, impact-based thresholds can be determined by matching historical and modern records of documented instances of coastal inundation at various sites around Sydney ( Figure 1) to the synchronous Fort Denison tide gauge observations.
Minor and moderate thresholds were defined so that impacts associated with exceeding these thresholds align with impacts prescribed to the minor and moderate classifications used by the Australian Bureau of Meteorology (2013) for riverine flood warnings. Moderate level impacts include flooding of major roads and flooding of buildings above the floor level. Minor level impacts are typically analogous to those of "nuisance" or "high tide" flooding discussed in the international coastal literature (Moftakhari et al., 2018;Ray & Foster, 2016;Sweet & Park, 2014;Sweet et al., 2016) where low-lying residential streets, paths, jetties, carparks, and parklands are submerged. Finally, low-impact inundation was defined to encompass inconvenient coastal floods that cause disruption by impacting bicycle and walking paths, jetties, and boat ramps but without the road closures and property damage impacts of minor floods. The lowest sea level value associated with each impact is defined as the impact-based threshold for that inundation classification. With reference to Table 1, the lowest sea level associated with inconvenient floods of paths and gardens is 1.96 m, the lowest level at which flooding of roads is reported is 2.07 m, and the lowest level associated with flooding of buildings and/or major roads is 2.20 m. Hence, these levels correspond with the low-impact, minor, and moderate impact-based thresholds, respectively.

Historical Inundation Frequencies
The exceedance of impact-based thresholds is commonly used as a proxy for the occurrence of historical coastal inundation (e.g., Dahl  A key aim of this study is to investigate the changing frequency and predictability of these coastal inundation events. To do this, we define "tide-only inundation" quantitatively as when the daily highest astronomical tide exceeds a coastal inundation threshold (Ray & Foster, 2016;Sweet et al., 2018). Tide-only inundation frequencies are calculated the same way as for coastal inundation, except it is the daily hourly maximum predicted tide height, rather than the observed (still water) sea level height, that is compared to the impact-based threshold.
There are two main data completeness criteria utilized in this study, and they are applied sequentially. The first relates to the computation of the daily maximum sea level value, and the second relates to the computation of the yearly number of days above said daily maximum. For a daily maximum sea level value to be defined, there must be no missing hourly sea level observations on that (UTC) day. If a day is missing one or more hourly sea level values, the whole day was assigned a null value and is considered missing for purposes of computing the daily maximum. The second criterion is that, for an annual count exceeding the impact-based threshold, WMO (2017) states that for a count parameter (e.g., exceedance of a threshold) to be calculated for a given time period, at least 70% of the data must be available. Furthermore, the guidelines advise that if the data are not 100% complete, counts should be calculated using ratios of available data in the averaging period. Based on this, an adjusted exceedance count is applied to all years with at least 70% data completeness. In practice, this means that if a year has 10% missing data and has 9 days where the daily maximum sea level exceeds the impact-based threshold throughout remainder of the year (i.e., the 90% of the record where data are not missing), then the adjusted exceedance count is 10. If a year has less than 70% data completeness, it is not considered further in the analysis. It is this adjusted exceedance count that is reported and analyzed in this study. These adjusted annual counts are then rounded to the nearest whole number. Astronomical tides are highly predictable (Pugh & Woodworth, 2014) and thus can be generated many years, even decades or centuries, in advance, provided local changes in astronomical tides (e.g., as described by Haigh et al., 2019) are small. Astronomical tide predictions were generated using R's TideHarmonics package (Stephenson, 2016), to hourly resolution with default options. We compared results from several common

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Earth's Future tidal analysis packages-TideHarmonics, UTide (Codiga, 2011), and TTide (Pawlowicz et al., 2002), as well as the Bureau of Meteorology's in-house tidal analysis software. We found the choice of package to have negligible impact on the results, so we chose TideHarmonics for computational efficiency and reproducibility of results. When analyzed against hourly predictions generated by other analysis packages, TideHarmonics had correlations of 0.987 or greater, linear regression coefficients of between 1.0002 and 1.0172, and absolute average differences of between 0.0049 and 0.0553 m. Harmonic constituents were derived using hourly data over an epoch of 1986-2005, the baseline period used for recent climate change projections (IPCC, 2019). As this period is greater than 18.6 years, it is sufficiently long to capture the key variability of the tidal cycle relevant to this analysis (Haigh et al., 2011). Predictions were then propagated from these constituents over the relevant period, 1914-2018 creating a hindcast to be used for the historical analysis.
As tide predictions issued by the Bureau of Meteorology (and many other oceanographic agencies globally) are reported with respect to a temporally invariant datum, changes in mean sea level must be considered. The tide predictions used in this analysis comprise mean sea level in each year and the astronomical tide oscillating about that mean. The exact specification of historical mean sea level can influence results of analysis of tide-only inundation frequencies. Since that mean is changing due to SLR, for this analysis, astronomical tides are derived as per above with the Dangendorf et al. (2019) GMSL reconstruction used to specify the historical mean of each year. Compared to other options such as polynomial or linear fits to the observed tide gauge data, this has the benefit of capturing nonlinear or nonpolynomial variations in GMSL, which have been observed in the Fort Denison tide gauge record (Watson, 2011). Furthermore, global, rather than local, MSL was used because increases in this parameter have been directly attributed to anthropogenic climate change (Slangen et al., 2016). For a geologically stable gauge such as Sydney, the difference between these will reflect the differences between anthropogenic SLR at the global and local scale, oceanographic and meteorological variability at different time scales (e.g., due to El Niño), and sampling issues. Published estimates suggest that SLR in Sydney is likely to be close to the GMSL change in the long term, differing by less than 10% (McInnes et al., 2015). As the global trend continues to increase, the difference between the GMSL and local MSL trend is likely to diminish so the choice matters less as sea levels rise in the future. The reconstruction was expressed with respect to the observed 1986-2005 mean from the Fort Denison sea level records. This allows a more straightforward approach to attribution in the counterfactual analysis (section 5). One downside of using the reconstruction is that it ends in 2015, so predicted historical tides cannot be generated after this year. There is no missing data in the predicted tides, so all years from 1914 to 2015 are included for calculation of tide-only inundation.
The resulting calculations show that all severities of coastal inundation are occurring more frequently, compared to a century ago ( Figure 2). Frequency counts of low-impact and minor inundation increased from averages of 11.6 and 1. If one considers a specific event, the nontidal residual may have raised or lowered the predicted astronomical tide to either exacerbate or mitigate impacts of coastal inundation. However, considering the 13.4 days per year (1996 to 2015) of low-impact tide-only inundation, we find that on average 8.8 (65%), coincided with a day of coastal inundation (i.e., the astronomical tide and observed sea level both exceeded the impact-based threshold). Tide-only inundation occurred at 67% of the rate of coastal inundation over the 1996-2015 period, up from 1.4% over the 1914-1933 period. This indicates that the contribution of tides to impact-producing extreme sea levels, and the associated inundation, has dramatically increased over the last century.

Attribution of Coastal Inundation to SLR
In order to consider the role that SLR has played in the increase in coastal inundation frequency, we consider an alternate reality (i.e., a counterfactual analysis) where MSL does not change from its 1914-1933 value-

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Earth's Future that is, the first 20 years of the Fort Denison observations. This was achieved using the following method. Residuals were calculated by subtracting the predicted tides generated using harmonic analysis (as per the above, using the Dangendorf et al., 2019, specification of GMSL changes) from the observed sea levels recorded at the Fort Denison tide gauge. These residuals were then added onto a set of predictions derived using the same harmonic constituents as above but oscillating about the 1914-1933 Fort Denison mean instead of the changing GMSL. This creates a counterfactual time series of sea level observations (i.e., the sum of residuals and predicted tides) without the contribution of rising GMSL. Analysis of exceedance of the new counterfactual time series was carried out in the same manner as for coastal inundation (section 4), as the daily maximum hourly sea level values in the counterfactual were compared to the impact-based thresholds. As the residuals are calculated using the predicted tides, this analysis is constrained by the length of the reanalysis which concludes in 2015.
This paper then follows the methodology of Strauss et al. (2016) by defining the counterfactual sea level time series (i.e., the "no SLR" scenario) as a reference state and the observed Fort Denison time series as the new (i.e., under SLR) state, in the fraction attributable risk (FAR) framework of Stone and Allen (2005). The FAR and Risk Ratio (RR) are calculated as where P without SLR is computed as mean of coastal inundation days in the observed time series over a reference period, divided by the 365 days per year. P without SLR is computed as the mean of coastal inundation days in the counterfactual ("no SLR") time series over the same reference period, divided by the 365 days per year. The period of 1996-2015 is used as it is the last 20 years of the counterfactual time series.
The trend in GMSL has been largely attributed to anthropogenic climate change, especially since 1970 when greenhouse gas emissions are reported to be responsible for 70% of the observed trend (Slangen et al., 2016).
Comparing the exceedance count in the "no SLR" time series to that of the observed sea level time series (Figure 2c) shows the degree to which climate change, via the change in GMSL, has already increased coastal inundation risk in Sydney Figure 1d) did not occur in the "no SLR" scenario, even at a low-impact level. Overall, minor coastal inundation occurred nine times more often between 1996 and 2015 as a direct result of SLR. Considering the FAR framework (Stone & Allen, 2005), we find that 88.9% of minor inundation and 83.3% of low-impact inundation could be attributed to SLR, with RRs of 9.0 and 6.0, respectively. Thus, we can conclude that if a low-impact or minor coastal inundation event happened in the 1996-2015 period, the event was made more likely (Lewis et al., 2019) by SLR. It is worth noting that coastal inundation frequencies have increased over this recent period, and hence, the FAR of an event today is likely higher than the value calculated using this 20-year mean.
Interestingly, we found a decrease in coastal inundation frequency over time in the "no SLR" scenario ( found Sydney's observed tidal range reduction was potentially related to channel dredging rather than SLR. However, overall, the combined effect of these factors was small compared to the effect of SLR and will become increasing less important as the trend accumulates.

Future Projections of Inundation and Extreme Sea Level Frequencies
A key objective of this study was to derive projections of impact-producing extreme sea level event frequencies. For this purpose, a baseline sea level climatology was defined using all daily maximum hourly sea levels

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Earth's Future recorded over the 1986-2005 period (the baseline period used by IPCC, 2019), which is effectively equivalent to an empirical probability density function. This is equivalent to the approach of Sweet et al. (2018) except those authors used a baseline of 1998-2016 rather than the 1986-2005 one used here. For each year in the IPCC (2019) projection period of 2007-2100, a new climatology was defined by increasing every daily maximum hour sea level observation in the baseline climatology by the amount corresponding to a specified RCP projection increment for the year in question. This is equivalent to shifting the mean of the probability

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Earth's Future density function to higher sea levels and assuming no change to the variance. The average number of days where this adjusted time series exceeds the relevant impact-based threshold is then considered the estimate of coastal inundation days for the year in question. This process is repeated for every year and for each RCP SLR scenario considered-the 5th, 50th (median), and 95th percentiles of RCPs 2.6, 4.5, and 8.5.
The estimation of future frequencies of tide-only inundation was different than the distribution-shifting method used for coastal inundation. As discussed in section 4, the highly predictable nature of tides allowed a tidal hindcast to be derived over a historical period. For the projections of tide-only inundation, we implement a similar process but for future tides, using the GMSL estimates (5th, 50th, and 95th percentiles for RCPs 2.6, 4.5, and 8.5) from IPCC (2019) to specify the future mean sea level about which the astronomical tides oscillate. Future annual counts of tide-only inundation ( Figure 3 and Table 1) can thus be estimated in the same way as historical counts (section 4), as the number of days per year where the highest hourly tide prediction value exceeds the relevant impact-based threshold. A feature of this method is that by using harmonic analysis extending to 2100, key tidal variability on 4.4-, 8.9-, and 18.6-year cycles (Haigh et al., 2011) is included.
As SLR continues, the proportion of coastal inundation events that are due to astronomical tides alone (i.e., "tide-only" inundation) will increase, as demonstrated in the convergence between the coastal inundation and tide-only inundation curves in Figure 3. This represents a shift from coastal inundation events being predominantly due to storm surges to coastal inundation events being predominantly due to high tides exceeding impact-based thresholds with no or minimal input from other sources of sea level variability. This is often conceptualized via the concept of "freeboard" (Sweet & Park, 2014)-the typical distance between high tides and the flood threshold. As SLR occurs, the freeboard reduces, meaning there is a lesser requirement for sea level anomalies (tidal residuals) to elevate water levels above the predicted high tide level and cause flooding. When viewed from a climatological perspective, tides (of all heights) are highly predictable, to the point where dates and times of tide-only inundation can be forecast decades in advance (e.g., Ray & Foster, 2016). Conversely, storm surges can only be forecast days in advance as the physical processes that lead to these happen at (synoptic) meteorological time scales. This means that a change from predominantly storm surge-driven flooding to tide-driven flooding represents a trend toward increasingly predictable coastal floods. Hence, increasing predictability of coastal flooding is expected to occur all around Australia as SLR occurs and freeboard reduces, although the timing of convergence is expected to vary geographically and investigating this will be the subject of future work.
Under RCP 8.5, predicted tides are expected to exceed the low-impact inundation threshold 132 (90% CI: 86-184) days per year by 2050 and daily (90% CI: 359-365) by 2100. For the minor threshold, 69 (90% CI: 28-112) and 365 (90% CI: 314-365) days of exceedance are expected each year, by 2050 and 2100, respectively. Comparing these results to the earlier results presented for coastal inundation projections indicates that effectively all low-impact and minor flooding will be due to astronomical tides alone. For moderate inundation, it takes until after 2050 for inundation to become completely tidally driven, with only 7 (90% CI: 0-32) days' highest tide exceeding the moderate threshold each year by 2050. However, by 2100, we expect 358 (90% CI: 201-365) days per year where the daily high tide exceeds the moderate inundation threshold. As tidal predictions can be generated many years in advance (i.e., out to 2100) through harmonic analysis, coastal inundation frequencies in Sydney therefore become a predictable consequence of SLR and tides with minimal role for ocean, weather, and climate variability (e.g., storm surges and ENSO).
This predictability also extends to much higher inundation thresholds, such as the current highest-on-record observation of 2.40 m (recorded 25 May 1974). Considering RCP 8.5, coastal inundation exceeding this current record is estimated to occur 234 (90% CI: 70 to 359) days per year by 2100. While the 1974 observed sea level was associated with a surge of 54 cm, this level will be exceeded by astronomical tides alone as early as

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Earth's Future 2061 (90% CI: 2052-2075) under RCP 8.5. Over the 2081-2100 period, we estimate that tide-only inundation will occur at 97% (90% CI: 79-103%) of the rate of coastal inundation of this severity. This means that it is likely, under RCP 8.5, by 2100, that more that 60% of all days will have a daily high tide exceeding the present-day highest-on-record record observation. This demonstrates that even considering a threshold of highest-on-record sea level, coastal inundation will become almost exclusively driven by daily tides and become highly predictable many years in advance by the late 21st century. While tidal amplitudes are expected to continue decreasing slightly (Devlin et al., 2017;Harker et al., 2019), these changes are negligible compared to SLR projections at Sydney. For example, Devlin et al. (2017) estimate a 2.5 mm decrease in tidal range per meter of SLR. As such, there is very little uncertainty in these coastal inundation estimates beyond the well-quantified and documented uncertainty in mean SLR projections (Kopp et al., 2019).
In order to assess the robustness of the tidal inundation projections derived using the harmonic analysis method, similar time series were derived by applying the distribution-shifting method used for coastal inundation to a tidal prediction distribution over the 1986-2005 period. We derived low-impact, minor, and moderate inundation frequencies under the fifth, median, and 95th percentile estimates of RCP 8.5 projected GMSL, under the distribution-shifting method to allow direct comparison to the nine tide-only inundation curves in Figure 3 (black lines). The distribution-shifting method could not reproduce interannual variability in tidal inundation frequencies due to the periodic nodal cycles not being resolved by resampling the climatology. Aside from this, the results were very similar suggesting that the different and independent methods of calculating coastal and tidal inundation are robust. We found the mean difference in total exceedances between the two methods to average 0.18% over the 2007-2100 period, with the largest difference being 0.42% and the least difference being 0.08%. The Pearson's correlation coefficient between the two methods' resultant time series varies between 0.9969 and 0.9992, and slopes vary between 0.9574 and 1.0011. This reinforces the predictable nature of future coastal inundation, as SLR means inundation becomes increasingly tidally driven.

Implications for Adaptation-Emergence Times, ARIs, Emission Reductions, and Predictability
A key application of this analysis is the ability to estimate emergence times, the first year when coastal inundation will occur at a specific frequency (e.g., weekly, daily, and 100 days per year). This assists in further relating projections to impacts and provides insights into tipping points and the exponential nature of SLR impacts (Taherkhani et al., 2020). Emergence times are intended to be a tool for policymakers and impacts scientists to help contextualize the increasingly frequent coastal inundation that is expected in the next 80 years. The projected emergence year of various inundation frequencies and whether these frequencies have already been reached are presented in Table 2.
Global greenhouse gas emissions are following RCP 8.5 more closely than any other scenario (Hayhoe et al., 2017;Peters et al., 2013). Therefore, considering the differences between high-and low-emissions scenarios may also enable cost-benefit analysis of various adaptation and mitigation strategies (Table 2). For example, we found 8,100 days of moderate coastal inundation will occur in the 2020-2100 period under RCP 8.5 (median estimate). Following the lower-emission scenarios of RCP4.5 or RCP 2.6 resulted in 4,414 and 5,807 fewer days of inundation, reductions of 54% and 72%, respectively, considering median estimates. Crucially, we also found that frequent coastal flooding is inevitable in Sydney, even if rapid reductions of greenhouse gas emissions occur and future emissions track closer to RCP4.5 or RCP2.6. For example, the emergence of weekly minor inundation is expected by the 2070s in the 95th, 50th, and 5th percentile estimates in all RCP scenarios (Table 2). However, considering the median estimates, weekly minor flooding occurs by the 2050s in all scenarios. This means that adaptation, or acceptance of a higher inundation risk, will be necessary even with strong emission reductions.
Analyzing the differences between emergence times shows the acceleration in the frequency of inundation. Considering all minor and moderate inundation scenarios in Table 2, it takes an average of 19.9 years for the annual frequency to increase from 10 to 30 days per year but only another 12.3 years to reach weekly frequency, a 62% increase in rate. The higher the emission scenario, the larger the increase in rate, 85% under RCP 8.5 and 40% under RCP 2.6. These results are consistent with an earlier study (Sweet & Park, 2014)  Earth's Future year frequency, the average ratio of coastal inundation days to tide-only inundation days is 0.76; at 52 days per year, the ratio is 0.84. This further shows that future coastal inundation frequencies are more closely related to predictable tides and SLR than the frequency of large sea level anomaly events (e.g., storm surges).
ARIs are commonly used to assess long-term risks of extreme sea level events to inform policy (Buchanan et al., 2017;DECCW, 2010;McInnes et al., 2015). However, from a risk management perspective, it is also instructive to consider future risks to assets impacted by present-day extreme sea levels. Therefore, we estimate future changes in the frequency of exceedance of 1914-2008 ARI levels (Department of Environment Climate Change and Water, 2010; Figure 4), using the same distribution-shifting methodology as above.   100-year ARI is used to assess 21st century coastal inundation risk under RCP 8.5, the risk is underestimated by a factor of more than 3,600.
When considering lower-emissions scenarios, large reductions are also seen in projections of exceedances of the historical 100-year ARI (Figure 4c). For example, the number of days where the 100-year ARI is exceeded is 39% lower under RCP 4.5 and 43% lower under RCP 2.6 compared to RCP 8.5 between 2020 and 2050, The increasing predictability of the occurrence of coastal impacts demonstrated in this study is important for adaptation, as it will likely necessitate a shift in how society manages coastal risk and inundation events. For example, as illustrated by Ray and Foster (2016), the precise timing and duration of when inundation due to tides will occur can be determined decades in advance. In some parts of the world, including Sydney, it is now not necessary to rely on only short-term sea level forecast models (e.g., Allen et al., 2018;Taylor & Brassington, 2017) to predict when impact-producing extreme sea levels may occur. However, these models will be important in forecasting the severity of inundation, especially in cases where sea level anomalies are large. However, we have shown that even events that have been historically very rare will occur on hundreds of days each year, due to tides alone, by 2100. This means that dealing with the impacts of these events will require greater proactivity or adaptation rather than simply a responsive approach, dealing with consequences of presently unusual, extreme events as they occur.
These important findings for adaptation strategies all support the movement toward an impact-based approach for coastal risk assessments rather than considering sea level allowances (e.g., Hunter, 2012;McInnes et al., 2015) or amplification factors of statistical metrics of extreme sea levels (e.g., Buchanan et al., 2017). In general, sea level allowances tell the policymaker how high they need to elevate coastal assets to keep inundation risk constant. This is impractical for most purposes as elevating all roads, homes, businesses, and recreational spaces is prohibitively expensive or physically impossible. Using amplification factors, the policymaker would typically be confined to considering an event that is statistically extreme (e.g.,

10.1029/2020EF001607
Earth's Future the 100-year ARI), regardless of whether this level is associated with the impacts of concern. Emergence times and emission scenarios can provide information on the possible time frames required for adaptation decisions to be made and can also enable the cost-benefit approach used to make these decisions in a more intuitive way. Consider the example of managed retreat of coastal communities (e.g., Alexander et al., 2012;Wrathall et al., 2019). If a local government or community have decided that they plan to enact a policy of coastal retreat in the future, how do they know when the time has come to relocate? Without an impact-based perspective and knowing the current and future frequencies of impacts, there is a risk of relocating too early (unnecessary displacement of a community) or too late (location becomes uninhabitable and community disperses to other places). A solution within the framework of emergence times could be the setting of a threshold of a certain frequency of inundation of a certain severity (e.g., 30 days per year of moderate flooding) and planning for retreat by the time those conditions are projected to occur. This allows the unique circumstances and vulnerability (vertical land offsets, tidal range, and storm frequency) of each location to be fully considered. More broadly, the utilization of the impact-based perspective directly enables a practical cost-benefit analyses of various adaptation and mitigation pathways when combining local asset (e.g., Hanslow et al., 2018) or economic loss (e.g., Hino et al., 2019) information.

Conclusions
We have found that coastal inundation in Sydney, Australia, has increased from 1.6 to 7.8 days per year over the last century and that 88.9% of these minor inundation days would not have occurred without already-observed GMSL rise. Further, we have found that projected SLR will lead to increasingly frequent and increasingly predictable coastal inundation this century, with impacts such as flooding of roads, paths, parks, and private property. Coastal inundation of at least minor level will occur on average weekly by 2050 and, under high-emissions scenarios, every day by 2100. Sea levels occurring during the majority of these inundation events will be higher than any of those observed in 104 years of tide gauge observations at Fort Denison. When considering sea levels associated with low-impact, minor, and moderate inundation, exceedances of these thresholds become a predictable consequence of SLR and tides with minimal role for ocean, weather, and climate variability. This finding is particularly important for considering the applicability of climate change science to adaptation decision to manage the impacts of climate change. While weekly minor inundation is effectively unavoidable by the 2070s without adaptation measures, reduced global emissions can result in large reductions in the frequency of coastal inundation projected for Sydney, especially in the late twentieth century. This analysis has highlighted that while still of some use, many current coastal risk assessment tools such as amplification factors and SLR allowances are inadequate to make and implement evidence-based policy at the local and regional scale. An impact-based perspective, such as that developed in this study, is therefore required to ensure that the on-the-ground impacts of SLR, which provide the motivation for such adaptation, can be more holistically considered in coastal risk assessments.