Relative sea level rise (RSLR) has driven large increases in annual water level exceedances (duration and frequency) above minor (nuisance level) coastal flooding elevation thresholds established by the National Weather Service (NWS) at U.S. tide gauges over the last half‐century. For threshold levels below 0.5 m above high tide, the rates of annual exceedances are accelerating along the U.S. East and Gulf Coasts, primarily from evolution of tidal water level distributions to higher elevations impinging on the flood threshold. These accelerations are quantified in terms of the local RSLR rate and tidal range through multiple regression analysis. Along the U.S. West Coast, annual exceedance rates are linearly increasing, complicated by sharp punctuations in RSLR anomalies during El Niño Southern Oscillation (ENSO) phases, and we account for annual exceedance variability along the U.S. West and East Coasts from ENSO forcing. Projections of annual exceedances above local NWS nuisance levels at U.S. tide gauges are estimated by shifting probability estimates of daily maximum water levels over a contemporary 5‐year period following probabilistic RSLR projections of Kopp et al. (2014) for representative concentration pathways (RCP) 2.6, 4.5, and 8.5. We suggest a tipping point for coastal inundation (30 days/per year with a threshold exceedance) based on the evolution of exceedance probabilities. Under forcing associated with the local‐median projections of RSLR, the majority of locations surpass the tipping point over the next several decades regardless of specific RCP.

1 Introduction Sea level has been rising for well over 10,000 years, although the last 4000 years have been remarkably stable with changes less than a few meters and on the order of half a meter over the last 2000 years [Fleming et al., 1998, Milne et al., 2005, Kemp et al., 2011]. Human population, on the other hand, has experienced exponential growth over the last 2000 years with the establishment of expansive coastal population centers [U.S. Department of Commerce (USDOC), 2013]. Given the nearly imperceptible change in mean sea level (MSL) on generational timescales, it is natural that humans associate sea level change with tides and storms rather than climate. Nonetheless, the current scientific consensus is that anthropogenically forced climate change is warming the planet and contributing to sea level rise [Cazenave and Le Cozannet, 2013]. This climate warming has contributed to a global mean sea level rise (SLR) rate of ˜1.7 mm/year over the last century with higher rates of ˜3.2 mm/year over the last couple of decades [Church and White, 2011; Merrifield et al., 2013]. Superimposed upon this global rise are regional sea level dynamics driven by ocean–atmosphere interactions with intra‐annual, annual, interannual, and decadal timescales. This includes storm surge events that are influenced by changes to seasonal storm track tendencies [Hirsch et al., 2001; Sweet and Zervas, 2011; Thompson et al., 2013], and longer term sea level anomalies coherent with modes of ENSO, the Pacific Decadal Oscillation (PDO), and the Atlantic Multidecadal Oscillation (AMO). Dependent upon their state, these climate patterns can regionally exacerbate or suppress storm surge frequencies and SLR rates [Park et al., 2010; Bromirski et al., 2011; Merrifield et al., 2012]. From the perspective of a specific location on land, such as a human dwelling, intertidal habitat, or water level (tide) gauge, vertical land motion also contributes to changes in sea level [Zervas et al., 2013], and it is this relative sea level rise (RSLR) that is of interest to coastal infrastructure and its inhabitants. Relative sea level is normally specified with respect to the tidal datum of MSL, whereas coastal inundation and flooding are best described relative to Mean Higher High Water (MHHW; http://tidesandcurrents.noaa.gov/datum_options.html). The National Tidal Datum Epoch (NTDE) used in the United States is a 19‐year period over which tidal datums specific to each tide gauge are determined and as sea level rises, the tidal datums also rise. The current NTDE for the United States is 1983–2001 and all historic and future‐projected water level information in our study reference this period since it is the relative changes compared to today's condition that we are interested. Consequences of RSLR include an increased frequency or probability of coastal inundation relative to fixed elevations from a combination of storms, tides, and climatic forcings [Hunter 2010; Park et al., 2011; Tebaldi et al., 2012]. This is simply understood by the reduced freeboard or gap between MSL and the flood elevation threshold as the sea level rises, such that smaller storm surges or sea level anomalies will increasingly exceed the flood level threshold as time progresses. As exemplified by Hurricane Katrina in 2005 and Superstorm Sandy in 2012 [Sweet et al., 2013], the Intergovernmental Panel on Climate Change (IPCC) recognizes that societal impacts of sea level change primarily occur via extreme events rather than as a direct consequence of MSL changes, and the panel also expects that the majority of global coastlines will be affected by RSLR by the end of the 21st century [Seneviratne et al., 2012]. In this context, there have been significant investigations of extreme event probabilities and future SLR [Zervas, 2013; Church et al., 2013; Miller et al., 2013; Kopp et al., 2014; Jevrejeva et al., 2014] along with region‐specific recognition [Boon, 2012; Ezer and Corlett, 2012; Sallenger et al., 2012; Kopp, 2013] and detection [Chambers et al., 2012; Haigh et al., 2014] of SLR acceleration. Considering a probability density function (PDF) of coastal water level measured at a tide gauge, the focus has been on evolution of MSL near the center of the density, or on assessment of extreme events in the upper tail. Less attention has been paid to the transition region between these regimes, but it is this transition region that exhibits a highly nonlinear portion of water level probability and holds the most relevance for identifying a tipping point in the change of coastal inundation impacts as sea levels rise. To illustrate this, Figure 1a shows an example of a water level time series measured at a tide gauge with the current (1983–2001 epoch) tidal datum elevations of mean lower low water (MLLW), mean low water (MLW), MSL, mean high water (MHW), and MHHW. Every station also has a station, or a standard datum, defined as the elevation of zero water level. Also shown in the figure is a flood level threshold at a fixed height above MHHW, but whose gap decreases with RSLR. Figure 1b plots probability density estimates of year‐long hourly water levels at New York City (The Battery), NY, and reveals how they have changed over an 80‐year span relative to the current (1983–2001) tidal datums. Comparison of the probability density estimates of MHW or MHHW in 1930 or 1950 to those in 1980 or 2010 reveals a significant increase. Integration of the density above an exceedance threshold (Figure 1c) quantifies the total probability of exceedance allowing one to quantify changes over time. As an example, the increase in annual probability of exceedance of MHW from 1930 to 2010 was 2% to 19%, respectively. Figure 1 Open in figure viewer PowerPoint (a) Schematic illustrating water level measured at a tide gauge, tidal datums and how RSLR closes the gap between a location's flood level threshold and high tide. Probability density estimates in (b) and probability of exceedance in (c) are shown for annual records of hourly water level at New York City (The Battery). Water levels are with respect to the tidal station datum (STND datum). Tidal datums are indicated with the solid vertical lines for the 1983–2001 epoch. The vertical dashed line represents the elevation threshold for minor (nuisance) coastal flood impacts. (1) The probability of exceedance is the complement of the cumulative distribution function (CDF), 1 – CDF, and shares sigmoidal characteristics across water level distributions whether the distributions are wavelike (Rayleigh), nontidal (Gaussian), or tidal (bimodal). The relevant features are: 1) accelerated growth over the transition region between very high water with near‐zero probability (extremes) and MHW, 2) approximately linear growth between MHW and MLW, and 3) decay and saturation below MLW (Figure 1 c). A generic expression of these behaviors can be captured with a logistic function where P(w) is the probability of exceedance, w the water level, and s represents the slope at the midpoint, w 0 . In the accelerated transition regime, exceedance rate changes following equation 1 will be nonlinear regardless of whether the water level densities are moving toward higher levels at a steady or at an accelerated rate dictated by RSLR. We, therefore, expect that as sea levels rise against habitats and infrastructure with fixed flood elevations and cross through this critical transition regime, coastal water level exceedances will accelerate. Sweet et al. [2014] and Ezer and Atkinson [2014] recently discussed the concept of accelerating lesser extreme (nuisance tide) impacts and they highlighted the U.S. East Coast as a region with accelerated impacts. However, both the studies neither recognized the inherent evolution in exceedance probabilities nor elucidated the primary response mechanism of exceedance‐rate acceleration changes that, and will continue to, occur as sea levels rise. In this paper, we show that acceleration in local tidal flooding within a range of elevation thresholds will continue and are largely driven by secular SLR. First, we assess how water level exceedances above the societally relevant thresholds are changing in time. Specifically, we use a common set of elevation thresholds from MHHW to 60 cm above MHHW, as well as local minor coastal flooding threshold levels established by the U.S. National Oceanic and Atmospheric Administration (NOAA) NWS, to provide estimates of annual duration (cumulative hours) and annual event frequency (days with an exceedance) at long‐term NOAA water level gauges around the United States. These measures define nuisance level impacts as compared to the NWS moderate and major impact elevation thresholds recently examined by Kriebel and Gieman [2013]. We also account for interannual variability driven by ENSO through multiple regression analysis. Lastly, we define tipping points and track their likely occurrence in the future dependent upon the RCP‐forced local RSLR projections of Kopp et al. [2014], which account for local change from non‐climatic background subsidence, oceanographic/dynamic effects, and spatially variable responses from shrinking land ice to the geoid and the lithosphere.

2 Exceedance Observations Verified hourly water levels are available from the NOAA Center for Operational Oceanographic Products and Services (CO‐OPS; http://tidesandcurrents.noaa.gov/) and are shown relative to the current (1983–2001) tidal datum of MHHW unless noted otherwise. We focus on NOAA water level gauges with defined nuisance levels and hourly data prior to 1950 (Figure 2). Nuisance flood elevation thresholds are obtained from the NOAA Advanced Hydrological Prediction Systems (AHPS; http://www.nws.noaa.gov/oh/ahps). Land regions at or below nuisance level elevation thresholds and susceptible to inundation are mapped under the “Flood Frequency” tab of the NOAA Sea Level Viewer (http://csc.noaa.gov/slr/viewer; Marcy et al., 2011) and shown in Figure 2 as red land elevation contours. Honolulu, HI, is also included but its elevation threshold is not defined by the NWS, but rather by the Pacific Islands Ocean Observing System (PacIOOS; http://oos.soest.hawaii.edu/pacioos). Figure 2 Open in figure viewer PowerPoint NOAA water level (tide gauge) locations numbered as listed in Table 1 and showing NWS defined nuisance flood levels above the 1983–2001 MHHW datum (colored dots) and coastal areas below the nuisance elevations and potentially at risk during nuisance flood events (red contours) provided by http://www.csc.noaa.gov/digitalcoast/tools/slrviewer Figure 3 presents the annual counts of daily maximum water levels that have exceeded the threshold level for nuisance flooding beginning in year 1920 or when data become available. The data (in Figure 3 and elsewhere) are binned by meteorological year (May–April) as to not decouple the stormy winter season, which is important for interannual variability diagnosis. As noted by Sweet et al. [2014], the number of days currently impacted by nuisance level flooding is highly correlated to the height of the flood threshold elevation itself and helps explain the lower exceedance values at gauge locations 1‐2 (Boston, MA, and Providence, RI) and 21‐22 (St Petersburg, FL, and Galveston, TX). There is clear evidence of increasing frequencies around the United States over the last century and particularly since the 1980s. Figure 3 Open in figure viewer PowerPoint Number of daily exceedances per year above the local NOAA NWS nuisance flood level (elevation threshold). When comparing 5‐year average exceedances at locations over the last 50 years (1956–1960 to 2006–2010; Table 1), we find that frequencies have increased by a factor of 10 or more at Atlantic City, Baltimore, Annapolis, Wilmington, Port Isabel, and Honolulu, and by a factor of 5 at Sandy Hook, Philadelphia, Norfolk, and Charleston. In addition to the number of days per year with an exceedance, the total hourly duration per year of water level above the flood level is a useful, and in some cases more relevant, metric. Linear regression between the two at each station is presented in Table 1 with fit coefficients denoted “Days:Hrs”. All fits are significant at the 99% level (p‐value <0.01), and the generally high R2 values suggest that a linear scaling provides a reasonable link between the two metrics. Table 1. Station Number and Name; RSLR Linear Trends for 1950–2013 Annual MSL (Asterisks Signify MSL Acceleration Detected, Significant Above 95% Level Accounting for Autocorrelation) and R2; Nuisance Flood Level Above MHHW, 1956–1960 and 2006–2010 Average Observed Nuisance Flood Days/Year, Nuisance Flood Days‐to‐Hours Conversion Factor and R2; R2 From a Quadratic Regression Between Annual MSL and Annual Daily Exceedances > 0.3 m (*Except for La Jolla Which Is a Linear Model) and R2 From a Model of Multiple Quadratic Regression That Includes Annual Daily Maximum Variance; 2006–2010 Variance of Hourly and Daily Maximum Water Levels and Root Mean‐Square Error (RMSE) Between Observed Days and Hours of Nuisance Flooding/Year and Estimates Based Upon 2006–2010 Probability Densities Shifted Backward in Time by the Local RSLR Trend (e.g., Purple Dash Lines, Figures a and 10c) St. No. Station Name RSLR Nuisance Flooding Increases Attribution Fixed Variance and RSLR Rates RSLR Trend (mm/yr) Trend (R2) Nuisance Level (m) Average Observed Nuisance Days Conversion Factor R2: MSL and Day/Year Above 0.3 m (Quadratic) R2: MSL, Var and Days/Year Above 0.3 m (Quadratic) 2006‐2010 Observed Variance (m2) Historical RMSE of Annual Nuisance Floods (1956–60) (2006–10) (Days:Hrs) (R2) (Hourly) (Daily Max) (Days) (Hours) 1 Boston, MA 2.4* 0.69 0.68 2.6 5.2 1.5 0.90 0.83 0.88 1.04 0.07 2.2 4.4 2 Providence, RI 2.4* 0.62 0.66 1.8 2.0 1.6 0.82 0.85 0.88 0.22 0.05 1.1 2.5 3 New London, CT 2.5* 0.68 0.60 1.2 1.6 3.0 0.73 0.86 0.93 0.10 0.03 1.1 4.6 4 Montauk, NY 3.3* 0.80 0.60 1.5 2.2 3.1 0.74 0.86 0.91 0.07 0.03 1.1 4.8 5 Kings Point, NY 2.3 0.65 0.52 6.2 14.8 2.6 0.89 0.92 0.94 0.76 0.07 4.5 19.0 6 New York City, NY 3.0 0.77 0.65 1.8 4.0 2.4 0.76 0.92 0.95 0.28 0.05 3.6 13.4 7 Sandy Hook, NJ 3.9* 0.83 0.45 2.6 21.4 2.1 0.92 0.96 0.96 0.29 0.05 4.5 20.3 8 Atlantic City, NJ 4.5 0.85 0.43 2.0 20.6 2.2 0.88 0.95 0.97 0.23 0.05 4.6 21.0 9 Philadelphia, PA 3.3* 0.64 0.49 1.7 10.6 2.2 0.92 0.90 0.95 0.43 0.05 4.2 12.3 10 Lewes, DE 3.4 0.75 0.41 4.8 20.0 2.7 0.89 0.92 0.95 0.23 0.05 5.3 23.5 11 Baltimore, MD 3.0 0.75 0.41 0.8 12.4 4.5 0.90 0.88 0.94 0.06 0.04 3.6 24.7 12 Annapolis, MD 3.4 0.80 0.29 2.8 34.4 5.0 0.95 0.87 0.94 0.06 0.04 7.3 77.8 13 Washington D.C. 3.0 0.65 0.31 6.8 28.6 4.2 0.88 0.91 0.93 0.14 0.05 7.7 57.4 14 Norfolk, VA 4.7 0.83 0.53 1.2 7.4 5.5 0.87 0.91 0.97 0.11 0.04 2.6 18.7 15 Wilmington, NC 2.2 0.56 0.25 1.3 32.6 2.1 0.92 0.81 0.88 0.26 0.02 11.2 31.2 16 Charleston, SC 2.9 0.76 0.38 3.6 21.6 1.7 0.95 0.88 0.93 0.35 0.05 4.7 17.6 17 Fort Pulaski, GA 3.3 0.83 0.46 4.8 13.2 1.6 0.96 0.87 0.89 0.59 0.05 4.3 11.9 18 Fernandina Beach, FL 2.4 0.62 0.59 0.6 1.4 1.3 0.75 0.79 0.85 0.46 0.05 1.1 2.0 19 Mayport, FL 2.6 0.67 0.44 0.2 4.8 1.8 0.92 0.76 0.86 0.27 0.03 1.9 4.3 20 Key West, FL 2.6 0.83 0.33 0.0 4.0 2.0 0.88 0.45 0.71 0.04 0.02 1.7 3.2 21 St. Petersburg, FL 2.7 0.86 0.84 0.0 0.0 4.3 0.64 0.71 0.88 0.07 0.02 0.3 1.3 22 Galveston_Bay, TX 6.6 0.92 0.79 0.2 0.8 14.9 0.90 0.82 0.87 0.06 0.03 0.7 9.4 23 Port Isabel, TX 4.3 0.88 0.34 1.6 18.4 7.2 0.90 0.78 0.89 0.04 0.02 5.2 47.8 24 La Jolla, CA 2.0 0.53 0.51 0.6 6.8 1.5 0.96 0.80* 0.84* 0.26 0.06 2.6 5.0 25 San Francisco, CA 1.6 0.38 0.35 2.6 9.6 1.8 0.95 0.81 0.85 0.31 0.04 5.8 14.2 26 Seattle, WA 1.7 0.48 0.65 0.6 2.0 1.5 0.95 0.77 0.86 1.22 0.05 1.8 3.2 27 Honolulu, HI 1.3 0.35 0.22 2.2 19.4 2.00 0.98 0.51 0.67 0.04 0.01 9.8 22.7

3 Historical Exceedance Characterization (2) Figure 3 provides compelling evidence of a nonlinear increase in coastal water level exceedance over the last half‐century and is consistent with a logistic evolution of exceedance probabilities. To examine these observations in a temporal framework, the exponential nature of the logistic function suggests a growth model: where E 0 is the exceedance at time t =0; α the linear rate of exceedance; r the growth rate; T L and T G the start time of linear and exponential growth, respectively; and τ the growth time constant. This model is fit to yearly exceedance data with maximum likelihood estimation over a wide parameter space of initial conditions (Table 2), and the best‐fit model from the parameter search is selected based on the minimum Akaike information criteria. Table 2. Initial Parameter Values for Maximum Likelihood Regression of Exceedance Growth Models Parameter Values Increment E o 1 0 α 1 0 T L 1920–2010 10 T G 1920–2010 10 r 00–200 10 τ 20–80 10 Figure 4 plots daily exceedance data and model fits at elevation thresholds 10, 20, 30, 40, and 50 cm above MHHW at four stations that typify the range of behaviors observed across all regions: New York City (NYC; Battery gauge), Norfolk (Sewells Point gauge), Galveston (Bayside gauge), and San Francisco. The temporal exceedance growth at these four stations encapsulates three types of behaviors observed collectively across all stations. The first type is characterized by linear growth (San Francisco) associated with sites that have either large interannual variability, small RSLR, a high threshold elevation such that the exponential transition region has yet to be reached or a combination of these factors. East coast stations with linear growth include Charleston, Fernandina Beach, and Fort Pulaski. The second type are stations where exponential growth initiated more than several decades ago (prior to 1980) as exemplified by Norfolk and Galveston. The third type is characterized at sites where the inception of exponential growth has been within the last few decades such as at New York City. This latter type is predominantly located on the upper Mid‐Atlantic Coast and includes Boston, Kings Point, and Lewes. We suspect that Norfolk, New York City, and other Mid‐Atlantic locations are experiencing higher growth rates (i.e., Ezer and Atkinson, 2014) from the recent “hot spot” of SLR acceleration associated with fluctuations of the Gulf Stream and interannual variability [Boon, 2012; Ezer et al., 2013; Sallenger et al., 2012; Kopp, 2013]. Figure 4 Open in figure viewer PowerPoint Temporal evolution of exceedances (days/year) and growth model fits (solid lines) above elevation thresholds of 10, 20, 30, 40 and 50 cm above MHHW shown for (a) New York City, (b) Galveston, (c) Norfolk and (d) San Francisco. Values of R2, T G , and τ along with standard errors at exceedance thresholds of 10 and 30 cm are shown in Table 3. At a threshold of 10 cm above MHHW, most stations are found to have initiated nonlinear growth in the early or mid‐twentieth century. As elevations increase, the values of T G tend to stay nearly stable at stations where the nonlinear transition is recent, such as New York City; whereas at stations where growth was initiated earlier, there is a progression of T G to later years. T G and τ characterize the temporal evolution of nonlinear growth, and can be used as metrics to assess a tipping point in exceedance behavior (discussed below). However, since the growth rate is not well constrained by this model with standard errors as large as the rates themselves, we turn to a polynomial model for rate estimates. Table 3. Exponential Growth Model Fit Parameters With Standard Errors, Units Are Years. Stations With Linear Exceedance Growth Are Not Shown 10 cm above MHHW 30 cm above MHHW R2 T G τ R2 T G τ 1 Boston 0.84 1991 ± 5 31 ± 23 0.77 1995 ± 5 29 ± 72 2 Providence 0.62 1958 ± 15 49 ± 29 0.60 1985 ± 8 46 ± 38 3 New London 0.84 1924 ± 14 101 ± 37 0.59 1976 ± 8 61 ± 124 4 Montauk 0.85 1920 ± 15 107 ± 22 0.66 1971 ± 8 54 ± 17 5 Kings Point 0.82 1975 ± 9 44 ± 32 0.75 1972 ± 7 62 ± 62 6 NYC (Battery) 0.86 1986 ± 6 36 ± 21 0.79 1983 ± 5 48 ± 6 7 Sandy Hook 0.91 1964 ± 10 66 ± 33 0.86 1954 ± 17 78 ± 50 8 Atlantic City 0.89 1933 ± 12 83 ± 16 0.80 1943 ± 10 80 ± 25 9 Philadelphia 0.84 1966 ± 11 55 ± 32 0.67 1970 ± 10 62 ± 61 10 Lewes 0.79 1976 ± 11 59 ± 70 0.69 1962 ± 11 87 ± 58 11 Baltimore 0.87 1945 ± 13 86 ± 34 0.72 1972 ± 7 66 ± 105 12 Annapolis 0.88 1928 ± 13 86 ± 34 0.72 1969 ± 40 58 ± 38 13 Washington DC 0.75 1942 ± 19 86 ± 61 0.55 1956 ± 107 88 ± 204 14 Norfolk 0.86 1920 ± 14 113 ± 22 0.75 1950 ± 10 83 ± 45 15 Wilmington 0.82 1939 ± 21 95 ± 50 0.67 1965 ± 9 79 ± 41 19 Mayport 0.72 1967 ± 14 55 ± 49 0.65 1965 ± 8 61 ± 153 20 Key West 0.82 1954 ± 10 80 ± 66 0.51 1991 ± 5 49 ± 106 21 St Petersburg 0.79 1968 ± 14 54 ± 78 0.55 1982 ± 10 44 ± 65 22 Galveston Bay 0.91 1920 ± 8 98 ± 13 0.74 1948 ± 9 80 ± 57 23 Port Isabel 0.84 1922 ± 16 123 ± 29 0.55 1950 ± 16 106 ± 34

4 Nuisance Level Exceedance Acceleration (3) The general exponential model (equation 2 ) provides good estimates for the temporal initiation and doubling period of accelerated exceedance, but poorly constrains the growth rate. To obtain improved estimates of the growth rate, we employ a quadratic growth model regressed against annual exceedances above the nuisance flood level of each station from 1950 through 2013: where Nuisance Flooding exceedances, E, represents either days with an impact or cumulative hours per year; t is in years starting at 1950; b 0 the initial exceedance; b 1 the linear rate; and b 2 the quadratic acceleration coefficient. Annual exceedance values are included only if hourly water levels for that year are more than 80% available with results presented in Table 4 for fits with acceleration coefficients above the 90% significance level (p‐value <0.1). We find that acceleration is apparent along most of the U.S. East Coast as well as one location in the Gulf of Mexico (Port Isabel, TX). Nuisance flooding acceleration is not apparent at a few East and Gulf Coast locations (blank cells in Table 4) where the nuisance flood level threshold is higher than that in most other locations (e.g., St. Petersburg and Galveston). In fact, these locations do not have linear regression coefficients above the 90% significance level (p‐value <0.1) for the same reason – namely, that an insufficient amount of exceedances have occurred to establish any discernible pattern. Along the U.S. West Coast, nuisance exceedances are not accelerating but are linearly increasingly (equation 3 with no acceleration term), except at Seattle where the threshold is high. We suspect that this linear response is related to the PDO‐forced stagnation in MSL rise over the last couple of decades [Bromirski et al., 2011, NRC, 2012], the small downward subsidence rates [Zervas et al., 2013], and the large (>0.2 m) ENSO‐driven interannual MSL anomalies comparable in magnitude to the amplitude of the RSLR trend over the last half‐decade. Along the West Coast, large waves also seasonally contribute to coastal flooding [Ruggiero, 2013], but are not generally measured by water level gauges [Hoeke et al., 2013] or associated with nuisance tidal flooding. Table 4. Annual Observed Flood Days and Hours Per Year Above the Nuisance Flood Level From 1950 to 2013 Fit by Quadratic or Linear Regression With Coefficients and Their Standard Error Shown if the Leading Coefficients Are Above the 90% Significance Level (p‐Value < 0.1); Coefficients and Their Standard Error From Multiple Regression Analysis Incorporating ONI as an ENSO Climate Index (CI) Shown for Locations With a CI Coefficient Above the 90% Significance Level (p‐Value < 0.1) Flood Days = b 2 t2 + b 1 t + b 0 Flood Hours = b 2 t2 + b 1 t + b 0 Flood Days = b 2 t2 + b 2(CI) CI2 + b 1 t + b 1(CI) CI + b (1,CI) tCI + b 0 Station Name Nuisance Level (m) b 2 b 1 b 0 R2 b 2 b 1 b 0 R2 b 2 b 2(CI) b 1 b 1(CI) b 1,CI b 0 R2 1 Boston, MA 0.68 0.0037 ± 0.0009 −0.187 ± 0.057 3.24 ± 0.81 0.35 0.0051 ± 0.0014 −0.242 ± 0.095 4.36 ± 1.34 0.31 2 Providence, RI 0.66 0.0013 ± 0.0007 −0.091 ± 0.055 2.58 ± 0.88 0.06 0.0023 ± 0.0013 −0.155 ± 0.095 4.13 ± 1.53 0.07 3 New London, CT 0.60 4 Montauk, NY 0.60 0.0012 ± 0.0006 −0.055 ± 0.039 1.23 ± 0.55 0.15 0.066 ± 0.037 1.40 ± 1.40 0.06 0.0015 ± 0.0006 0.0214 ± 0.2859 −0.069 ± 0.039 −0.611 ± 0.541 0.030 ± 0.014 1.35 ± 0.54 0.26 5 Kings Point, NY 0.52 0.0073 ± 0.0019 −0.317 ± 0.126 7.03 ± 1.76 0.40 0.0194 ± 0.0057 −0.916 ± 0.382 20.22 ± 5.35 0.30 6 New York City, NY 0.65 0.0021 ± 0.0008 −0.096 ± 0.052 1.96 ± 0.73 0.23 0.0052 ± 0.0022 −0.267 ± 0.146 5.46 ± 2.06 0.14 7 Sandy Hook, NJ 0.45 0.0102 ± 0.0021 −0.335 ± 0.141 4.74 ± 1.97 0.66 0.0217 ± 0.0057 −0.796 ± 0.381 12.64 ± 5.33 0.49 0.0115 ± 0.0020 0.6138 ± 0.9820 −0.406 ± 0.134 −2.626 ± 1.822 0.129 ± 0.049 5.13 ± 1.87 0.72 8 Atlantic City, NJ 0.43 0.0095 ± 0.0022 −0.288 ± 0.145 4.22 ± 2.03 0.64 0.0171 ± 0.0064 −0.437 ± 0.426 7.87 ± 5.95 0.45 0.0104 ± 0.0022 0.0390 ± 1.0521 −0.338 ± 0.143 −1.520 ± 1.998 0.095 ± 0.053 4.62 ± 2.00 0.68 9 Philadelphia, PA 0.49 0.0049 ± 0.0019 −0.182 ± 0.127 3.73 ± 1.82 0.31 0.0130 ± 0.0044 −0.596 ± 0.297 10.59 ± 4.28 0.25 10 Lewes, DE 0.41 0.0095 ± 0.0025 −0.388 ± 0.169 8.01 ± 2.49 0.49 0.0234 ± 0.0079 −0.951 ± 0.544 19.47 ± 8.02 0.36 0.0114 ± 0.0022 1.7079 ± 1.0106 −0.501 ± 0.154 −2.678 ± 2.077 0.141 ± 0.054 8.32 ± 2.26 0.62 11 Baltimore, MD 0.41 0.0059 ± 0.0014 −0.221 ± 0.096 3.69 ± 1.35 0.51 0.0310 ± 0.0073 −1.376 ± 0.492 21.68 ± 6.93 0.43 0.0065 ± 0.0014 0.8903 ± 0.7016 −0.262 ± 0.095 −1.375 ± 1.312 0.059 ± 0.035 3.67 ± 1.34 0.55 12 Annapolis, MD 0.29 0.0152 ± 0.0036 −0.428 ± 0.239 7.08 ± 3.40 0.65 0.0924 ± 0.0189 −3.262 ± 1.272 44.97 ± 18.04 0.63 13 Washington D.C. 0.31 0.0071 ± 0.0037 −0.084 ± 0.249 6.68 ± 3.48 0.41 1.366 ± 0.309 6.74 ± 11.38 0.25 0.0092 ± 0.0037 1.5290 ± 1.7999 −0.207 ± 0.244 −4.652 ± 3.324 0.202 ± 0.090 7.11 ± 3.40 0.48 14 Norfolk, VA 0.53 0.0020 ± 0.0011 −0.036 ± 0.073 1.37 ± 1.03 0.35 0.0132 ± 0.0070 −0.413 ± 0.466 8.06 ± 6.57 0.23 0.0030 ± 0.0009 1.3984 ± 0.4585 −0.093 ± 0.062 −1.017 ± 0.857 0.065 ± 0.023 1.23 ± 0.88 0.56 15 Wilmington, NC 0.25 0.0150 ± 0.0034 −0.387 ± 0.225 3.24 ± 3.21 0.68 0.0292 ± 0.0086 −0.688 ± 0.575 5.37 ± 8.18 0.58 0.0168 ± 0.0032 2.8896 ± 1.5995 −0.496 ± 0.217 −1.398 ± 2.977 0.117 ± 0.079 2.80 ± 3.10 0.73 16 Charleston, SC 0.38 0.0058 ± 0.0023 −0.011 ± 0.158 2.04 ± 2.26 0.63 0.0109 ± 0.0042 −0.096 ± 0.288 3.99 ± 4.11 0.59 17 Fort Pulaski, GA 0.46 0.0042 ± 0.0023 −0.048 ± 0.155 2.63 ± 2.12 0.42 0.0071 ± 0.0036 −0.106 ± 0.240 3.40 ± 3.27 0.45 18 Fernandina Beach, FL 0.59 0.024 ± 0.001 0.14 ± 0.36 0.09 0.028 ± 0.015 0.39 ± 0.57 0.06 19 Mayport, FL 0.44 0.0031 ± 0.0008 −0.133 ± 0.055 1.27 ± 0.77 0.41 0.0054 ± 0.0017 −0.231 ± 0.111 2.31 ± 1.57 0.33 20 Key West, FL 0.33 0.0017 ± 0.0006 −0.072 ± 0.043 0.64 ± 0.63 0.28 0.0034 ± 0.0014 −0.142 ± 0.095 1.23 ± 1.39 0.25 21 St. Petersburg, FL 0.84 22 Galveston_Bay, TX 0.79 23 Port Isabel, TX 0.34 0.0061 ± 0.0023 −0.181 ± 0.154 1.76 ± 2.13 0.41 0.0327 ± 0.0189 −0.679 ± 1.260 7.21 ± 17.43 0.30 24 La Jolla, CA 0.51 0.102 ± 0.022 −0.72 ± 0.84 0.28 0.150 ± 0.032 −1.27 ± 1.25 0.27 0.114 ± 0.019 2.078 ± 0.501 −1.18 ± 0.75 0.45 25 San Francisco, CA 0.35 0.128 ± 0.044 3.08 ± 1.63 0.12 0.200 ± 0.083 5.24 ± 3.11 0.09 0.146 ± 0.035 5.511 ± 0.885 2.43 ± 1.29 0.46 26 Seattle, WA 0.65 27 Honolulu, HI 0.22 0.257 ± 0.074 0.18 ± 2.77 0.17 0.490 ± 0.151 −0.31 ± 5.65 0.15

5 Annual Variance, MSL Characteristics, and Attribution to Threshold Exceedances Location‐specific differences in annual variance are evidenced in probability densities of hourly (Figure 5a) and daily maximum (Figure 5b) water levels for 2006–2010. The probability densities, shown here and throughout our study unless otherwise noted, are constructed using a nonparametric kernel density estimator with location‐specific optimized bandwidths between 0.04 and 0.08. Hourly water level variance (2006–2010 values, Table 1) is dominated by, and scales linearly with, the great diurnal tidal range (GT), defined as the difference between MHHW and MLLW (Figure 5c). The shapes of the hourly probability densities reflect the tide‐cycle characteristics. For instance, San Francisco has a large mixed tide (two highs and two lows that are unequal in magnitude) range, a wide hourly density, and less probability of exposure to water levels above MHHW. On the other hand, Galveston (and much of the Gulf of Mexico Coast) with its small diurnal (one high and one low tide a day) tide range and normal‐like distribution has the narrowest hourly density and higher probability of exceeding MHHW. The distributions of daily maximum water levels are similar and approximately Gaussian with higher probabilities in the tail at locations that experience large storm surges such as the Battery in New York City (Figure 5b). The annual series of hourly water level variance (Figure 6b) do reveal time‐varying patterns associated with the 18.6‐year lunar nodal cycle. However, time series of annual hourly and daily maximum water level variances (not shown) are effectively trend‐stationary and similar to the findings of Zhang et al. [2000] for the U.S. East Coast over the 20th century, which suggests that exceedance increases (Figure 4) are not directly forced by storminess trends. Figure 5 Open in figure viewer PowerPoint Probability density estimates of 2006–2010 (a) hourly and (b) daily maximum water levels and (c) 2006–2010 hourly water level variance in black (1983–2001 hourly variance in grey) linearly regressed against the 1983–2001 GT tidal range. Figure 6 Open in figure viewer PowerPoint Time series of (a) annual MSL and (b) annual variance of hourly water level are shown for four representative stations. Annual MSL in (c) and annual variance of daily maximum water levels in (d) are regressed with annual daily exceedances above 0.1 m and 0.3 m MHHW. Daily maximum water level from Norfolk over 1956–1960 and 2006–2010 are fit in (e) by a normal probability density function and (f) shows their probability of exceedances. On the other hand, annual MSL time series in Figure 6a show large increases over time. Long‐term RSLR trends in Table 1 are computed using annual MSL, with linear coefficients above the 95% significance level (p‐value <0.05) and are consistent with the official NOAA RSLR trends (http://tidesandcurrents.noaa.gov/sltrends/sltrends). A measure of interannual MSL variability is inferred through the R2 values, with low values indicating higher variability along the West Coast and Honolulu largely due to ENSO and PDO influences. RSLR trends with asterisks in Table 1 signify locations with significant acceleration (coefficients – not shown – above the 95% significance level accounting for serial autocorrelation as described in Zervas [2009]) occurring since 1950 in their annual MSL. These stations are located along the upper Mid‐Atlantic Coast where the inception of exponential growth in annual threshold exceedances initiated within the last few decades (Table 3). (4) In order to quantify the relative contribution of variance and MSL to annual exceedances above the nuisance level over time, we fit multiyear series of daily maximum water level with a normal PDF defined by: f is the probability density at a water level height, w, and μ and σ2 are the mean and the variance of the distribution, respectively. The probability of exceedance (P) at a particular water level, w, is defined as 1 – CDF, where the CDF of the normal distribution is defined as: (5) whereis the probability density at a water level height,, and μ and σare the mean and the variance of the distribution, respectively. The probability of exceedance (P) at a particular water level,, is defined as 1 – CDF, where the CDF of the normal distribution is defined as: with the parameters the same as in equation 4 and erf is the error function. In Figure 6e, we show the PDFs and in Figure 6f, the probability of exceedance for the 1956–1960 and 2006–2010 periods at Norfolk with the nuisance flood level highlighted. The mean and variance of the PDF (both in meters) are listed above Figure 6e and 6f as are the number of estimated annual nuisance flood days (P*365 days) on average during 1956–1960 (0.1 day) and 2006–2010 (5.8 days). Readily apparent is the large change in the mean of the distribution between these periods from RSLR with only a small change in variance. Using the variance value from 2006–2010 (0.044) and the mean from 1956–1960 (−0.141) provides an estimate of 0.3 nuisance flood days and confirms that RSLR is the major factor involved in the large exceedance increases observed over this time period (Table 1). We provide further evidence that RSLR is the major factor as compared to variance driving the increases in nuisance flood days in Figure 6c and 6d where annual MSL and annual variance of daily maximum water levels, respectively, are regressed against observed annual daily exceedances above a 0.3 m and 0.5 m MHHW threshold at New York City and San Francisco over the 1950–2013 period. The regressions using annual MSL are fit with a quadratic model (except for La Jolla, which uses a linear fit), whereas fits for annual variance are all linear (all significant at the 95% level; p‐value <0.05) with R2 indicated. In all cases, the amount of the annual exceedance variation (R2) partially explained by the annual MSL is much higher than that by annual variance. In Table 1 under the “Attribution” heading, the R2 values are listed from quadratic fits between annual MSL and annual exceedances above 0.3 m MHHW for all locations. The next column (MSL, Var) lists the total variation in annual exceedances explained (R2) from multiple quadratic regression (not necessarily significant at the 95% level) using both annual MSL and variance. In all cases, it can be seen that annual MSL is the leading factor driving the growth of annual exceedances in time.

6 Exceedance Acceleration Patterns Sweet et al. [2014] noted an inverse linear relationship (R2 = 0.59) between acceleration rates of annual nuisance flood days and nuisance flood elevation thresholds along the U.S. East and Gulf Coasts. Here, we generalize and extend that relationship through quantification of the hourly annual exceedance acceleration over a range of common elevation thresholds. Figure 7a shows acceleration coefficients of equation 3 (>90% significance level; p‐value <0.1) for hourly exceedances above elevation thresholds from MHHW to 0.6 m above MHHW. Acceleration coefficients are larger at locations with smaller variance (Table 1) and/or tide range (Figure 5a). For instance, Galveston, Port Isabel, Annapolis, Baltimore, Montauk, and Norfolk, which have more tightly bound hourly probabilities (e.g., Galveston in Figure 5a), have higher acceleration coefficients for elevations ≤0.3 m above MHHW associated with steeper probability of exceedance (1‐CDF) curves across similar elevations (e.g., Norfolk versus New York City in Figure 7a). Figure 7 Open in figure viewer PowerPoint 2 ) above the 90% significance level (p‐value < 0.1) from quadratic regression fits of annual number of hourly exceedances above elevation thresholds from MHHW to 0.6 m above MHHW between 1950 and 2013. Scatter plots of location‐specific b 2 acceleration coefficients for 0.1, 0.3 and 0.5 m elevations and (b) RSLR trend rates (Table 2, (c) GT tide range fit with a quadratic fit and R2 and (d) RSLR trend and GT showing R2 of multiple quadratic regression (significant at 95% level; p‐value < 0.05). (a) Acceleration coefficients (b) above the 90% significance level (p‐value < 0.1) from quadratic regression fits of annual number of hourly exceedances above elevation thresholds from MHHW to 0.6 m above MHHW between 1950 and 2013. Scatter plots of location‐specific bacceleration coefficients for 0.1, 0.3 and 0.5 m elevations and (b) RSLR trend rates (Table 1 ) with linear fit and R, (c) GT tide range fit with a quadratic fit and Rand (d) RSLR trend and GT showing Rof multiple quadratic regression (significant at 95% level; p‐value < 0.05). 2) for exceedances above the 0.1 and 0.3 m thresholds (Figure 2014 (6) Increasing MSL (RSLR) is the leading factor causing annual exceedances (nuisance and other threshold levels) to increase in time since variance changes are essentially trend‐steady. In Figure 7 b–d, we investigate the relative influence of differing rates of RSLR with respect to tide range upon annual exceedance acceleration rates. RSLR rates exhibit a direct positive relationship to hourly acceleration coefficients (hours/year) for exceedances above the 0.1 and 0.3 m thresholds (Figure 7 b), supporting the findings of Ezer and Atkinson [] who detected the highest acceleration in flooding hours for a 0.3 m threshold above MHHW at locations with higher RSLR rates. Unique to this study is quantification of tidal range and its nonlinear relationship to threshold exceedance rates, which allows for an improved estimate of annual acceleration for minor/nuisance‐level thresholds (Figure 7 c). The coupled importance of both RSLR rates and tidal range in relation to acceleration in annual hourly exceedance rates (i.e., Figure 7 a) can be expressed through multiple quadratic regression: where b 2_hours is the acceleration coefficient (hours/year2) from equation 3 with values plotted in Figure 7d; GT is the great diurnal tidal range over the 1983–2001 tidal epoch available online (http://tidesandcurrents.noaa.gov); RSLR are the linear MSL trends in Table 1; and b 0 , b 1 , and b 2 are the regression coefficients. The relationships for 0.1, 0.3, and 0.5 m elevation thresholds are shown in Figure 7d (all significant at 95% level; p‐value <0.05) and define, for instance, the influence of tide range, such that Annapolis and Galveston, which have nearly identical tide ranges but nearly a factor of two RSLR trend difference (Table 1), have similar exceedance accelerations over a range of elevation thresholds (Figure 7a). This type of approach (equation 6) might prove useful to help establish spatial patterns applicable for locations not having an immediately adjacent long‐term water level gauge but with plausible regional estimates of RSLR and modeled tide range information (e.g., http://vdatum.noaa.gov).

7 Interannual Variability Interannual variability can affect and obscure the underlying trends in annual nuisance‐level exceedances (e.g., Figure 4d). Along the West Coast (Figure 8d), regional shifts in MSL during El Niño produce high sea level anomalies [Enfield and Allen, 1980; Chelton and Davis, 1982; Miller et al., 1997], which are associated with higher nuisance‐level exceedances (Figure 8f) primarily during periods of highest astronomical tides [Sweet et al., 2014]. La Niña conditions are typically associated with low sea level anomalies. Along the East Coast, ENSO's global teleconnection can alter winter‐storm track patterns along the Mid‐Atlantic [Hirsch et al., 2001; Eichler and Higgins, 2006] and is coherently related to sea level anomalies [Park and Dusek, 2013]. During strong El Niños (e.g., 1997), there is an increased likelihood for coastal storm surges [Sweet and Zervas, 2011; Thompson et al., 2013] as shown in Figure 8a, which increases nuisance‐level exceedances (Figure 8c). The transition from ENSO cool‐to‐neutral conditions in 2008 to a moderately strong El Niño during 2009 highlights the ENSO effects (increased mean, variance/skew) on probability densities of daily maximum water levels in Norfolk and San Francisco (Figure 8b, e). Figure 8 Open in figure viewer PowerPoint 2 values are from a linear regression significant at the 95% level (p‐value > 0.05). In (b) and (e) are annual probability densities over the transition from the 2008 neutral to 2009 strong El Niño. Regression fits by a (c) quadratic model at Norfolk and a (f) linear model at San Francisco are significantly improved by including ONI into a multiple regression (red line; coefficients in Table 1950 to 2013 annual mean ONI with ENSO warm conditions in red and ENSO cool in blue with (a) daily nontidal residual (NTR) storm surges > 0.3 m per year at Norfolk (green bars), and (d) detrended annual MSL (anomaly) at San Francisco. Rvalues are from a linear regression significant at the 95% level (p‐value > 0.05). In (b) and (e) are annual probability densities over the transition from the 2008 neutral to 2009 strong El Niño. Regression fits by a (c) quadratic model at Norfolk and a (f) linear model at San Francisco are significantly improved by including ONI into a multiple regression (red line; coefficients in Table 4 ) to estimate observed daily exceedances above the nuisance flood level per year (grey). (7) To assess ENSO influence on annually observed nuisance exceedances, we use the Oceanic Niño Index (ONI) in a multiple regression model: where E, t, b 0 , b 1 , and b 2 parameters are the same as in equation 3, and b 1(CI) , b 2(CI) , and b 1,CI represent the fit coefficients related to the inclusion of the ONI climate index (CI). The ONI was utilized since it accounts for the warming trend in the Niño 3.4 region, is thought to better represent interannual variability, and is operationally predicted by NOAA [NOAA, 2014]. At both Norfolk and San Francisco, inclusion of the ONI significantly (CI coefficient(s) >90% level, p‐value <0.1) improves the historical characterization of nuisance exceedances as shown in Figure 8c, f, with higher R2 values shown in Table 4 (Norfolk R2 from 0.35 to 0.56, and San Francisco from 0.12 to 0.46). Results of the multiple regression indicate that the annual number of days with nuisance flooding at San Francisco increase proportionally to ONI at a rate of 5.5 days per unit ONI, whereas at Norfolk, nuisance days increase by a factor of 1.4 times the square of the annual ONI value. Other West and East Coast stations show similar ONI sensitivity (Table 4) with greater influence at lower nuisance‐level elevation thresholds.

8 Tipping Points In complex systems, a small parameter change can cause a transition from a stable state to a new equilibrium state that is drastically different from the initial one [Groffman et al., 2006; Lenton et al., 2008]. We believe that at many coastal locations around the globe with critical coastal ecosystems or where humans have established infrastructure at fixed locations over the last century, such transitions have begun in response to RSLR. Specifically, the data suggest that RSLR has elevated water levels at many coastal locations such that the nuisance flood levels are no longer confined to the extreme tails of the water level distributions, but have, or will soon, entered the transitional phase of exponential growth in exceedances. It is then natural to ask whether physically relevant metrics can be expressed to quantify the evolution of this behavior, and we propose two metrics, one based on the temporal inception of nonlinear exceedance growth and the other based on the changing probability of inundation with respect to a specific elevation threshold. The initiation of nonlinear growth was quantified in the parameters T G and τ (Table 3), indicating that at many coastal locations, the transition from linear to exponential growth of exceedances has already occurred. Regarding the transitional behavior of exceedance probabilities associated with a specific elevation, Figure 9 shows exceedance probability curves for year‐long hourly water levels during 1930, 1950, 1980, and 2010 at New York City and Norfolk. The MSL and MHHW tidal datums are shown as vertical lines. To illustrate a tipping point for water level exceedance, let us consider MHHW level as the elevation threshold and an exceedance probability of 1/12 (30 days/year using the daily‐maximum event metric or 720 hours/year using the cumulative‐hours duration metric), although different selections of elevation threshold and probability of exceedance would ideally be customized for each specific location to reflect the local community's susceptibilities. Figure 9 shows that as the sea level has risen, sometime between 1980 and 2010, a threshold was crossed such that the probability of exceeding MHHW at both New York City and Norfolk surpassed 1/12. The corresponding exceedance probabilities and water levels are shown in Table 5. Though the 1/12 probability is arbitrary, it illustrates a duration/frequency threshold to be selected corresponding to a location's ability to deal with or recover from the cumulative impacts associated with lesser extreme inundation events. We couple these tipping points with projections of annual exceedance probabilities in the following section. Figure 9 Open in figure viewer PowerPoint Probability of exceedance (1‐CDF) of annual hourly water level records at New York City (NYC) and Norfolk. Tidal datums (vertical solid lines) are with respect to the NTDE 1983–2001 and shown relative to each location's station datum (Water Level = 0). The NWS nuisance flood level is shown (red dash) and the probability of 1/12 of the year (1 month) is shown with the horizontal dashed line. Table 5. Exceedance Probability (P) in Percent With Respect to MHHW Datum (1983–2001) and Water Levels Corresponding to a 1/12 Probability of Exceedance From Yearlong Hourly Water Level Records at the New York City and Norfolk. MHHW at New York City Is 2.54 m and Norfolk Is 2.18 m Above Station Datum Year New York City Norfolk P (%) P = 1/12 Level (m) P (%) P =1/12 Level (m) 1930 0.9 2.25 0.6 1.87 1950 2.2 2.34 1.4 1.99 1980 3.6 2.44 3.5 2.09 2010 12 2.65 19.6 2.33

9 Projections We have shown that annual exceedance rates are changing in time in response to RSLR with increasingly higher rates as flood threshold elevations approach MHHW (Figures 4, 7a). The logical question is then posed: what does the future hold? The 30 days/year tipping point is a starting point in defining site‐specific frequency‐duration thresholds. We use nonparametric probability density estimates of daily water level maximums constructed for 2006–2010 (i.e., Figure 5b) to project forward in time by simply shifting their independent variable (water level) by the RSLR projections. The choice of 2006–2010 provides a contemporary climatology, closely aligns with the current GT tide range (R2 = 0.92, Figure 5c), and occurred when ENSO was on average slightly cool (ONI average of −0.22). We also assume that future water level variance matches that of 2006–2010. To assess this assumption (fixed variance and no interannual variability of annual MSL relative to the location's RSLR trend; shown as a purple dashed line in Figure 10a, c), we compute root mean square error (RMSE) from comparison with historical nuisance‐level exceedances (last two columns of Table 1). The RMSE provides a measure of historic exceedance variability and evidence that the assumptions are satisfied (at least approximately). Figure 10 Open in figure viewer PowerPoint 2014 Future tipping point (red horizontal line) when nuisance level flooding at Norfolk (0.53 m) and San Francisco (0.35 m) occurs more than 30 days/year under the NCA Low (purple line) and the local RSLR projections (median) for RCP 2.6, 4.5, 8.5 and the 95% probability projection of RCP 8.5 from Kopp et al. (). Also shown is the continuation of the historical regression (black dash) of observed annual exceedances (blue columns) as well as historical estimates assuming 2006–2010 probability densities and local RSLR trends (purple dash). We use RSLR projections of Kopp et al. [2014], who provide separate projections in response to forcing from RCP 2.6, 4.5, and 8.5 conditions [Meinshausen et al., 2011], which correspond, respectively, to likely global mean temperature increases in 2081–2100 of 1.9–2.3 C, 2.0–3.6 C, and 3.2–5.4 C above 1850–1900 levels [IPCC, 2013]. They are probabilistic estimates based upon process modeling and expert assessment/elicitation and account for local subsidence, oceanographic/dynamical effects, and spatially variable responses from shrinking land ice to the geoid and the lithosphere. The RSLR projections initiate in 2000 and are location (tide gauge)‐specific, often substantially differing from the global SLR median (5–95%) estimates of 0.5 m (0.29–0.82 m) under RCP 2.6, 0.59 (0.36–0.93 m), under RCP 4.5 and 0.79 m (0.52–1.21 m), and under RCP 8.5 [Kopp et al., 2014]. We also provide a projection based solely on the continuation of historical local RSLR with no other future adjustments. This projection initiates in 2008 (midpoint of the 2006–2010 probability density estimate) and is essentially the Low Scenario for global SLR provided by the 2013 U.S. National Climate Assessment [NCA; Parris et al., 2012]. We refer to this projection as the NCA Low and stress that it is considered unlikely since it assumes no changes in local RSLR trend rates within the 21st century. Figure 10 shows projections for the annual number of days impacted by flooding above the local nuisance flood level (Table 1) for Norfolk and San Francisco. Over the next couple of decades, projections based upon the median of the RCP RSLR values at both locations cross the tipping point and are nearly indistinguishable (Figure 10a, c) since the global SLR projections of Kopp et al. [2014] are quite similar between RCPs over the next several decades. The projections using the local 95% RSLR probability of RCP 8.5 crosses the tipping point within the next decade, whereas they cross by 2050 under the NCA Low (Figure 10b, d). Over a 60‐year time horizon, the upper saturation (365 days/year) of the logistic function (1‐CDF) is realized at both locations under the local 95% RSLR projection of RCP 8.5. We would argue that degradation to public works and critical infrastructure would occur and require mitigation well before saturation. We show the continuation of the historical regression fits (quadratic or linear black dash, quantified in Table 4) of observed annual nuisance flood days only for the next couple of decades (Figure 10a, c), since they are a best‐fit representation reflecting past interannual MSL and variance variability likely to recur in the near future. However, we would stress that these are not valid projections over the long term since they do not realize the evolution, which will occur in exceedance probabilities (i.e., Figure 9). Lastly, we note that the regression fits (black dash) range from slightly higher (Figure 10c) to lower (Figure 10a) when compared historically to the 2006–2010 probability density estimates (purple dash) at all the tide gauge locations, possibly related to regional decadal‐scale MSL anomaly and storm variability patterns. In Figure 11, we use a consistent elevation threshold of 0.5 m MHHW to examine probabilistically when the crossing dates for the 30 days/year tipping point might occur in the future using the RCP‐based RSLR projection probabilities. Tipping point dates are illustrated using the Kopp et al. [2014] local 5%, 20%, 80%, and 95% RSLR projection probabilities for RCP 2.6 (Figure 11a), 4.5 (Figure 11b), and 8.5 (Figure 11c). The median and the 5% and 95% probabilities for local RSLR amounts by 2100 are also shown. Accordingly, the majority of locations will cross the 30 days/year (0.5 m above MHHW threshold) tipping point by 2050 under RSLR projections quite likely to occur (within the local 20% and 80% probability range of RSLR projections) and by 2060 under RSLR projections very likely to occur (between local 5% and 95% probability range of RSLR projections) from all three RCPs. Figure 11 Open in figure viewer PowerPoint 2014 Tipping point dates (left vertical‐axis) when a location is projected to experience 30 days/year of flooding above 0.5m MHHW in response to local RSLR projections of RCP (a) 2.6, (b) 4.5 and (c) 8.5 from Kopp et al. (). The colored boxes represent dates associated with the 20% and 80% RSLR projection probabilities and the whiskers convey the dates for the 5% and 95% probabilities. Local RSLR amounts by 2100 are shown on the right y‐axis, with dots presenting the 50% and the error bars the 5% and 95% probabilities per RCP. Note: Honolulu, HI is not shown since water levels 0.5 m above MHHW have never been historically observed. A general pattern emerges (Figure 11) of delayed tipping point dates for locations with lower local RSLR projections (e.g., San Francisco and Seattle) or smaller daily maximum variance as listed in Table 1 (Wilmington, Key West, St. Petersburg). Conversely, tipping points occur sooner at locations with higher local RSLR projections (Galveston) or that have larger water level variance and a propensity for more frequent and stronger storm surges (Boston, Kings Point, New York City, Atlantic City). This codependency of future tipping point dates upon both future RSLR (black dots in Figure 11) and variance of daily maximum water level (Table 1) can be expressed with a multivariate linear regression as in equation 6 where the tipping point date is the dependent variable and RSLR and water level variance are the independent variables. This coupled model accounts for 73%, 79%, and 83% of the variance (p‐value <0.05) in future tipping point dates associated with RCP 2.6, 4.5, and 8.5, respectively for a 0.5 m threshold above MHHW. Taken together with findings based upon annual hourly exceedances in Figure 7, locations with smaller water level variance will generally take longer to surpass the duration/frequency of tipping points (e.g., 30 flood days/year) for elevation thresholds above 0.3 m MHHW, but are prone for a more rapid transition below this elevation. The decade when the 30 days/year tipping point is surpassed is mapped for local nuisance flood levels (Figure 12a) listed in Table 1 as well as for a common 0.5 m threshold (Figure 12b). Tipping points for nuisance level flooding under the NCA Low projection have already been surpassed (e.g., Annapolis, Washington D.C., Wilmington) or will so in the coming decade at locations with lower elevation thresholds and higher RSLR rates (e.g., Atlantic City, Charleston, Port Isabel). By 2050, the majority of locations surpass their tipping point under the local median (50%) RSLR projection probability for all RCPs except at locations with higher nuisance flood levels (e.g., Boston, New York City, St Petersburg, Galveston, Seattle), whereas under the local 95% probability for RSLR projections of RCP 8.5, the majority of stations surpass the tipping point by 2030. Tipping point dates for the 0.5 m MHHW threshold (Figure 12b) follow the same general patterns of Figure 11 and are surpassed at the majority of locations by 2040 under the local median (50%) RSLR projection probability of the RCPs. Figure 12 Open in figure viewer PowerPoint 2014 Decade when the 30 days/year tipping point is surpassed for (a) local nuisance flood levels listed in Table 1 and for (b) a common 0.5 m threshold under the local RSLR projections of Kopp et al. (). Particular tipping point decades, e.g. 2021–2030 are specified in the legend as > 2021. Note: Honolulu, HI is not shown since water levels 0.5 m above MHHW have never been historically observed.

10 Concluding Remarks NOAA water level (tide) gauges have been measuring water levels for over a century, quantifying RSLR along most of the continental U.S., Hawaii, and Pacific Island Territory coastlines. RSLR exacerbates nuisance flooding impacts relative to today's fixed reference frame. At very high thresholds, such as those of the 100‐year event experienced during hurricane strikes, RSLR has and will continue to nonlinearly compress recurrence probabilities in the future because smaller storm surges will increasingly impact fixed elevations [Hunter 2010; Park et al., 2011; Tebaldi et al., 2012; Sweet et al., 2013]. The same is true for impacts from lesser extremes or nuisance flooding occasionally experienced today during high tide. We show that these events (defined as exceedances over local NOAA NWS minor flood thresholds) are increasing in time at the NOAA tide gauges in our study. Moreover, annual event rates for exceedances over thresholds from MHHW to 0.5 m above MHHW are accelerating along the U.S. East and Gulf Coasts. This occurs as rising sea levels evolve the nonlinear portion of a water level distribution against a fixed elevation irrespective of whether the sea level rise is linearly increasing or nonlinearly accelerating (Figure 1). We show that annual rates of hourly exceedances over elevation thresholds from MHHW to 0.5 m above MHHW along the East and Gulf Coasts tend to exhibit higher acceleration rates at locations with higher RSLR rates and smaller tide ranges. Interannual variability in MSL and to a lesser extent water level variance affect annual threshold exceedance rates and make the appropriate time‐dependent characterization challenging. This is especially relevant along the U.S. West Coast, where MSL anomaly punctuations from ENSO and multidecadal MSL trends dampened by PDO overwhelm the underlying RSLR signal. Acceleration in RSLR rates, which are projected to occur during the 21st century [Parris et al., 2012; Church et al., 2013; Kopp et al., 2014], will further intensify inundation impacts over time, and further reduce the time between flood events. We introduce the concept of a tipping point for impacts from future coastal inundation when critical elevation thresholds for various public works or coastal ecosystem habitats may become increasingly compromised by increasingly severe tidal flooding [Groffman et al., 2006]. Using NOAA NWS elevation thresholds and future median values of local RSLR projections of Kopp et al. [2014], we find that the majority of locations surpass a 30 days/year tipping point by 2050 except for locations with higher nuisance flood levels (e.g., Boston, St Petersburg, Galveston and Seattle). Under the local 95% projection probability for RSLR under the RCP 8.5, whose global projected rise approximates that of the NCA Intermediate High SLR scenario (1.2 m SLR by 2100), this tipping point is surpassed by the end of the next decade (2030). At all locations, the tipping points are surpassed much earlier than 2100 – the date for which most global mean SLR projections are formulated and publically discussed. Impacts from recurrent coastal flooding include overwhelmed storm water drainage capacity at high tide, frequent road closures, and general deterioration and corrosion of infrastructure not designed to withstand frequent inundation or saltwater exposure. As sea levels continue to rise and with an anticipated acceleration in the rate of rise from ocean warming and land ice melt, concern exists as to when more substantive impacts from tidal flooding of greater frequency and duration will regularly occur. Information quantifying these occurrences and the associated frequency‐based tipping points is critical for assisting decision makers who are responsible for the necessary mitigation and adaptation efforts in response to sea level rise.

Acknowledgments We thank Robert Kopp for sharing data from the study by Kopp et al. [2014] as well as for his and an anonymous reviewer's review and constructive comments. We thank Jayantha Obeysekera, John Marra, Stephen Gill, and Chris Zervas for their helpful discussions and Doug Marcy, Matt Pendleton, and Billy Brooks for the high resolution graphics in Figure 2 and the idea to assess impacts above societally relevant thresholds.

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