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Future coastal flood risk will be strongly influenced by sea-level rise (SLR) and changes in the frequency and intensity of tropical cyclones. These two factors are generally considered independently. Here, we assess twenty-first century changes in the coastal hazard for the US East Coast using a flood index (FI) that accounts for changes in flood duration and magnitude driven by SLR and changes in power dissipation index (PDI, an integrated measure of tropical cyclone intensity, frequency and duration). Sea-level rise and PDI are derived from representative concentration pathway (RCP) simulations of 15 atmosphere–ocean general circulation models (AOGCMs). By 2080–2099, projected changes in the FI relative to 1986–2005 are substantial and positively skewed: a 10th–90th percentile range 4–75 times higher for RCP 2.6 and 35–350 times higher for RCP 8.5. High-end FI projections are driven by three AOGCMs that project the largest increases in SLR, PDI and upper ocean temperatures. Changes in PDI are particularly influential if their intra-model correlation with SLR is included, increasing the RCP 8.5 90th percentile FI by a further 25%. Sea-level rise from other, possibly correlated, climate processes (for example, ice sheet and glacier mass changes) will further increase coastal flood risk and should be accounted for in comprehensive assessments.

Sea-level rise (SLR) and tropical cyclones (TCs) influence coastal flood risk in fundamentally different ways¹. Although TC-driven storm surges can have amplitudes of up to several metres, they are highly localized and infrequent; changes in their statistical properties, particularly the number of high-magnitude events, drive the flood hazard^{1, 2, 3}. In contrast, SLR raises the baseline on which all shorter-period sea-level variability is superimposed⁴. Effectively managing dynamic risk requires flood hazard assessments that fuse uncertain projections of changes in SLR and TCs in a consistent manner.

Although recent assessments have begun to develop projections of coastal flood risk that reflect uncertainty in SLR, most assume that the statistical properties of storm surges remain unchanged^{5, 6}; if changes in TCs and their associated surges are assessed, SLR is ignored or included as a constant^{2, 7, 8, 9}. Others have included limited sensitivity analyses to changes in both drivers, without considering an underlying correlation^{10, 11, 12}.

In such assessments, the ‘oceanographic component’ of SLR (that is, ignoring geoid changes, vertical land motion, and net freshwater exchange)^{13, 14, 15} is generally derived from an atmosphere–ocean general circulation model (AOGCM) ensemble, such as the Coupled Model Intercomparison Project Phase 5 (CMIP5) RCP simulations¹⁶. The ensemble spread is due to, among other factors, the rate and locations of heat uptake and changes in wind stress^{13, 17, 18}. Uncertainty in oceanographic SLR can be locally large, notably along the Northeast US coastline^{5, 13, 19, 20, 21, 22}. Little et al.²⁰ find a 16-member AOGCM ensemble range of approximately 20–70 cm in New York City by 2090 relative to a 1986–2005 base period; in a probabilistic analysis, this component drives most of the variance in Northeast US SLR projections through the twenty-first century⁵. The small scale of TCs, and uncertainty in the dependence of their properties on large-scale climate, pose difficulties for model-based assessment^{1, 23, 24}. As even the highest resolution AOGCMs are unable to simulate the inner core of tropical cyclones (or represent storm statistics)²⁵, various statistical and dynamical techniques have been applied to AOGCMs to project future changes in TCs (refs 7, 26, 27, 28, 29, 30). In conjunction with these efforts, aggregated metrics have been developed to describe ocean basin-wide TC activity, such as the power dissipation index (PDI).

These approaches indicate a twenty-first century increase in North Atlantic PDI, driven largely by an increase in the intensity of the largest storms, that is often attributed to sea surface warming of the tropical North Atlantic^{23, 31}. Beyond this general result, there remains substantial uncertainty in future TC frequency and intensity, much of which originates in the AOGCM representation of the large-scale climate variables^{1, 2, 7, 25, 26, 27}. For example, a six-member CMIP5 AOGCM ensemble has been used to generate projections of twenty-first century global PDI change ranging from 8 to 80% for RCP 8.5 (a substantial difference from CMIP Phase 3 models)⁷; a 17-member CMIP5 ensemble—analysed using a different methodology—provides a range of −30 to 450% for North Atlantic PDI (ref. 29).

At present, there has been little analysis of the co-variability of SLR and PDI and its implications for the coastal flood hazard. However, multimodel mean CMIP5 RCP simulations show robust, geographically widespread warming in the upper water column (Fig. 1a). Such changes in upper ocean heat content drive seawater expansion and also fuel TCs, potentially implying a strong physical linkage between sea-level changes and TC-driven surges^{7, 13, 32}. The relationship between these quantities within and across models has not been established.

a, Shading indicates the ensemble mean SST change (2080–2099 mean − 1986–2005 mean); contours indicate the ensemble standard deviation. Blue boxes highlight the regions used in the statistical model of PDI (ref. 29). The solid black box highlights the region included in this analysis. This region is shown in detail in b along with the location of the sites used to develop the FI.

First, we present the ensemble spread in PDI anomaly and site-averaged SLR over the 2080–2099 period (Fig. 2). In RCP 2.6, which requires drastic emission reductions over the twenty-first century, the 15-member ensemble mean projections are 0.21 m SLR (five-site average) and 1.1 × 10¹¹ m³ s⁻² PDI anomaly (representing an absolute PDI > 75% higher than the 1986–2005 mean). Even under relatively weak forcing, these values exceed the mean rate of SLR and the range of 20-year-mean PDI experienced in the twentieth century^{29, 40}. Most ensemble members are relatively tightly clustered around these values. However, the GFDL-CM3, MIROC-ESM and MIROC-ESM-CHEM project high SLR and PDI relative to the ensemble mean.

Individual AOGCM projections (2080–2099 mean − 1986–2005 mean) of PDI anomaly (y-axis) and mean SLR across the five sites (x-axis) for RCP 2.6 (a) and RCP 8.5 (b). AOGCMs, indicated by numbers, are overlaid on a kernel density estimate of the bivariate probability distribution; shading indicates the normalized probability from 0.9 (darkest) to 0 (white). Red numbers in b are AOGCMs from group 1; blue numbers are group 2 AOGCMs; black numbers show all other AOGCMs (group 3). Dashed lines indicate ensemble mean values.

Capturing the joint influence of PDI and SLR on the coastal flood hazard requires a technique that can account for changes in flooding driven by both factors. To accomplish this, we follow a peak-over-threshold approach³ in which annually integrated hourly exceedances of a threshold (the 99.5th percentile of summer values) across five US East and Gulf coast locations (Fig. 1b) are used to develop a flood index (FI; equations (1) and (2)). The historical relationship between FI and PDI are used together with SLR projections at each of the five sites⁵ to translate CMIP5 AOGCM PDI anomalies²⁹ to end-of-century FI (see Methods, Supplementary Tables 1 and 2, and Supplementary Figs 2–6). The FI is an aggregate measure of the duration and exceedance of high water during the TC season, normalized so that each site contributes equally. A value of 100 implies that the annually integrated flood height over a threshold is 100 times greater than the 1986–2005 annual mean.

To examine the relative importance of PDI and SLR, and the influence of the intra-AOGCM PDI/SLR correlation, we employ Monte-Carlo sampling to examine FI changes for: SLR only (dashed lines in Fig. 4); PDI and SLR selected at random from the ensemble (‘random model’ case; thin solid lines); and PDI and SLR selected as pairs (‘same model’ case; thick solid lines), from each of 15 models. Figure 4 indicates that uncertainty in the future FI is dominated by changes in century-timescale PDI and SLR projections, rather than uncertainty in the PDI/FI regression. The FI, and the difference between RCPs, increases greatly by the end of the century, driven by the wide spread and skew in the CMIP5 model results. The median 2080–2099 FI is approximately 16 for RCP 2.6 and 100 for RCP 8.5 (for the ‘same model’ case), with a 90th percentile projection of 75 and 350. Most of the change in the FI is driven by SLR (generally greater than 70% depending on the quantile considered), with PDI-induced changes in FI fractionally larger in RCP 8.5 and further into the upper tail. The role of the clustered outliers in Fig. 2 is clearly seen in the secondary peaks at higher FI in Fig. 4. High-end projections for both RCPs (that is, those above the 80th percentile) are determined by these outliers. Furthermore, because these models have high PDI and SLR, the ‘same model’ case results in a ~20% increase in FI relative to the ‘random model’ case and a ~25–30% increase relative to the FI if only SLR is included. The FI changes in Fig. 4 do not include several other factors that influence flood risk (for example, extratropical storms⁴⁷, the interaction of SLR and tides⁴, precipitation^{48, 49} and exposure to flooding^{9, 10, 11}). In particular, SLR arising from other climate- and non-climate-related processes that are not incorporated in AOGCMs (ref. 15) will further increase FI; a complete risk assessment would include these processes in a probabilistic manner^{5, 22}. A sensitivity analysis indicates that a 31 cm SLR contribution from non-oceanographic SLR sources (the median RCP 8.5 projection at Charleston, SC from a recent analysis⁵; see Methods and Supplementary Fig. 7) increases the median FI by a factor of four, whereas the 90th percentile projection is approximately doubled. A complete probabilistic treatment of FI, however, requires an understanding of linkages to these other terms. Although some sources are likely to be independent (for example, glacial isostatic adjustment), others (for example, land ice mass changes) will be coupled to ocean–atmosphere processes.

a,b, Probability (a) and cumulative distribution functions (b) for the 1986–2005 (black) and 2080–2099 flood index (FI) subject to RCP 2.6 (blue) and RCP 8.5 (red). For the 2080–2099 period, dotted lines show the FI if PDI is unchanged; thin solid lines (shown only for b) show the FI distribution if PDI and SLR are drawn randomly from one of the 15 models; thick solid lines show the distribution if PDI and SLR are selected from the same model. The insets expand the x-axis in the range 0 < FI < 30. Grey lines in b indicate the median and 90th percentile of the cumulative probability distribution.

In Fig. 4, we use a multi-location flood index^{50, 51} as opposed to local hazard curves². For this analysis, the FI provides a more robust description of historical surge–climate relationships and the incorporation of a larger AOGCM ensemble—which is critical to uncertainty characterization. However, an index does not distinguish between flood events of varying severity and conflates flooding caused by TCs and SLR. Hazard curves provide a local view of the complete spectrum of flood severity that is not possible with an index. In practice, however, hazard curves based on the historical record invoke tenuous assumptions about storm surge statistics. Model-based hazard curves involve uncertainty in downscaling large-scale climate changes and structural errors in surge models. Furthermore, few flood protection strategies are designed around a complete representation of the risk (most efforts are designed around the 100-year event⁵²).

We thus suggest that an index can complement local analyses; however, it is not immediately clear how to reconcile the two. To aid this effort, we present the sensitivity of our FI projections to flood threshold, index formulation, and choice of locations in Fig. 5. These methodological choices can be roughly segregated into those that change the absolute value by which the flood hazard is amplified or influence the importance of changes in PDI and their correlation with SLR. For example, if the FI is weighted towards higher surges (for example, the squared exceedance case in panel b; ref. 50), the effect of changes in PDI is heightened. A higher threshold (URL: