1 Title Page: 2 3 From the Extreme to the Mean: 4 Acceleration and Tipping Points of Coastal Inundation from Sea Level Rise 5 6 *William V. Sweet ([email protected]), corresponding author 7 Joseph Park ([email protected]) 8 9 NOAA National Ocean Service 10 Center for Operational Oceanographic Products and Services 11 1305 East West Highway, Silver Spring, MD, USA 12 13 1 14 From the Extreme to the Mean: 15 Acceleration and Tipping Points of Coastal Inundation from Sea Level Rise 16 17 William V. Sweet and Joseph Park 18 NOAAβs Center for Operational Oceanographic Products and Services 19 20 21 Abstract 22 23 Relative sea level rise (RSLR) has driven large increases in annual water level exceedances 24 (duration and frequency) above minor (nuisance level) coastal flooding elevation thresholds 25 established by the National Weather Service (NWS) at U.S. tide gauges over the last half 26 century. For threshold levels below 0.5 m above high tide, the rates of annual exceedances are 27 accelerating along the U.S. East and Gulf Coasts, primarily from evolution of tidal water level 28 distributions to higher elevations impinging on the flood threshold. These accelerations are 29 quantified in terms of the local RSLR rate and tidal range through multiple regression analysis. 30 Along the U.S. West Coast annual exceedance rates are linearly increasing, complicated by sharp 31 punctuations in RSLR anomalies during El Niño Southern Oscillation (ENSO) phases, and we 32 account for annual exceedance variability along the U.S. West and East Coasts from ENSO 33 forcing. Projections of annual exceedances above local NWS nuisance levels at U.S. tide gauges 34 are estimated by shifting probability estimates of daily maximum water levels over a 35 contemporary 5-year period with probabilistic RSLR projections of Kopp et al. (2014) for 36 representative concentration pathways (RCP) 2.6, 4.5 and 8.5. We suggest a tipping point for 37 coastal inundation (30 days/per year with a threshold exceedance) based on the evolution of 38 exceedance probabilities. Under forcing associated with the local-median projections of RSLR, 39 the majority of locations surpass the tipping point over the next several decades regardless of 40 specific RCP. 41 2 42 Introduction 43 44 Sea level has been rising for well over 10,000 years, although the last 4,000 years have been 45 remarkably stable with changes less than a few meters and on the order of a half meter over the 46 last 2 thousand years (Fleming et al., 1998, Milne et al., 2005, Kemp, 2011). Human population 47 on the other hand, has experienced exponential growth over the last 2,000 years with 48 establishment of expansive coastal population centers (USDOC, 2013). Given the nearly 49 imperceptible change in mean sea level (MSL) on generational timescales, it is natural that 50 humans associate sea level change with tides and storms rather than climate. Nonetheless, 51 current scientific consensus is that anthropogenic forced climate change is warming the planet 52 and contributing to sea level rise (Cazenave and Le Cozannet, 2013). 53 54 This climate warming has contributed to a global mean sea level rise (SLR) rate of ~1.7 mm/year 55 over the last century with higher rates of ~3.2 mm/year over the last couple decades (Church and 56 White, 2011; Merrifield et al., 2013). Superimposed upon this global rise are regional sea level 57 dynamics driven by ocean-atmosphere interactions with intra-annual, annual, interannual and 58 decadal timescales. This includes storm surge events which are influenced by changes to 59 seasonal storm track tendencies (Hirsch et al., 2001; Sweet and Zervas, 2011; Thompson et al., 60 2013), and longer term sea level anomalies coherent with modes of ENSO, the Pacific Decadal 61 Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO). Dependent upon their 62 state, these climate patterns can regionally exacerbate or suppress storm surge frequencies and 63 SLR rates (Park et al., 2010; Bromirski et al., 2012; Merrifield et al., 2012). 64 65 From the perspective of a specific location on land, such as a human dwelling, inter-tidal habitat 66 or water level (tide) gauge, vertical land motion also contributes to changes in sea level (Zervas 67 et al., 2013), and it is this relative sea level rise (RSLR) that is of interest to coastal infrastructure 68 and its inhabitants. Relative sea level is normally specified with respect to the tidal datum of 69 MSL, whereas coastal inundation and flooding are best described relative to Mean Higher High 70 Water (MHHW; http://tidesandcurrents.noaa.gov/datum_options.html). The National Tidal 71 Datum Epoch (NTDE) used in the United States is a 19-year period over which tidal datums 72 specific to each tide gauge are determined and as sea level rises, tidal datums also rise. The 3 73 current NTDE for the United States is 1983-2001 and all historic and future-projected water level 74 information in our study reference this period since it is relative changes compared to todayβs 75 condition that we are interested. 76 77 Consequences of RSLR include an increased frequency or probability of coastal inundation 78 relative to fixed elevations from a combination of storms, tides and climatic forcings (Hunter 79 2010; Park et al., 2011; Tebaldi et al., 2012). This is simply understood by the reduced freeboard 80 or gap between MSL and the threshold flood elevation as sea level rises, such that smaller storm 81 surges or sea level anomalies will increasingly exceed the flood level threshold as time 82 progresses. As exemplified by Hurricane Katrina in 2005 and Superstorm Sandy in 2012 (Sweet 83 et al., 2013) the Intergovernmental Panel on Climate Change (IPCC) recognizes that societal 84 impacts of sea level change primarily occur via extreme events rather than as a direct 85 consequence of MSL changes, and expect that the majority of global coastlines will be affected 86 by RSLR by the end of the 21st century (Seneviratne et al., 2012). Appropriately, there has been 87 significant investigation of extreme event probabilities and future SLR (Zervas, 2013; Church et 88 al., 2013; Miller et al., 2013; Kopp et al., 2014; Jevrejeva et al., 2014) along with region-specific 89 recognition (Boon, 2012; Ezer and Corlett, 2012; Sallenger et al., 2012; Kopp, 2013) and 90 detection (Chambers et al., 2012; Haigh et al., 2014) of SLR acceleration. 91 92 Considering a probability density function (PDF) of coastal water level measured at a tide gauge, 93 the focus has been on evolution of MSL near the center of the density, or on assessment of 94 extreme events in the upper tail. Less attention has been paid to the transition region between 95 these regimes, but it is this transition region which exhibits a highly non-linear portion of water 96 level probability, and holds the most relevance for identifying a tipping point in the change of 97 coastal inundation impacts as sea levels rise. To illustrate this, Figure 1a shows an example of a 98 water level time series measured at a tide gauge with the current (1983-2001 epoch) tidal datum 99 elevations of mean lower low water (MLLW), mean low water (MLW), MSL, mean high water 100 (MHW) and MHHW. Every station also has station, or standard datum, defined as the elevation 101 of zero water level. Also shown is a flood level threshold at a fixed height above MHHW, but 102 whose gap decreases with RSLR. Figure 1b plots probability density estimates of year-long 103 hourly water levels at New York City (The Battery), NY and reveals how they have changed 4 104 over an 80-year span relative to the current (1983-2001) tidal datums. Comparison of the 1930 105 or 1950 probability of MHW or MHHW to those of 1980 or 2010 reveals a significant increase. 106 Integration of the density above an exceedance threshold (Figure 1c) quantifies the total 107 probability of exceedance allowing one to quantify changes over time. As an example, the 108 increase in annual probability of exceedance at MHW from 1930 to 2010 was 2% to 19%. 109 110 The probability of exceedance is the complement of the cumulative distribution function (CDF), 111 1 β CDF, and shares sigmoidal characteristics across water level distributions whether the 112 distributions are wave-like (Rayleigh), non-tidal (Gaussian) or tidal (bi-modal). The relevant 113 features are: 1) accelerated growth over the transition between very high water with near-zero 114 probability (extremes) to MHW, 2) approximately linear growth between MHW and MLW and 115 3) decay and saturation below MLW (Figure 1b). A generic expression of these behaviors can 116 be captured with a logistic function 117 118 (1) π(π€) = 1 1+ππ₯π[βπ (π€0 βπ€)] 119 120 where P(w) is the probability of exceedance, w the water level and s represents the slope at the 121 mid-point, w0. 122 123 In the accelerated transition regime, exceedance rate changes following equation (1) will be 124 nonlinear regardless of whether the water level densities are moving toward higher levels at a 125 steady or accelerated rate dictated by RSLR. We therefore expect that as sea levels rise against 126 habitats and infrastructure with fixed flood elevations and cross through this critical transition 127 regime, coastal water level exceedances will accelerate. Sweet et al. (2014) and Ezer and 128 Atkinson (2014) recently discussed the concept of accelerating lesser extreme (nuisance tide) 129 impacts and both highlighted the U.S. East Coast as a region with accelerated impacts. 130 However, neither study recognized the inherent evolution in exceedance probabilities nor 131 elucidate the primary response mechanism of exceedance-rate acceleration changes that are, and 132 will continue to occur as sea levels rise. 133 5 134 In this paper we show that acceleration in local tidal flooding within a range of elevation 135 thresholds has, and will continue to result from secular SLR. First, we assess how water level 136 exceedances above societally relevant thresholds are changing in time. Specifically, we use a 137 common set of elevation thresholds from MHHW to 60 cm above MHHW, as well as local 138 minor coastal flooding threshold levels established by the U.S. National Oceanic and 139 Atmospheric Administration (NOAA) NWS to provide estimates of annual duration (cumulative 140 hours) and annual event frequency (days with an exceedance) at long-term NOAA water level 141 gauges around the U.S. These measures define nuisance level impacts as compared to NWS 142 moderate and major impact elevation thresholds recently examined by Kriebel and Grieman 143 (2013). We also account for interannual variability driven by ENSO through multiple regression 144 analysis. Lastly, we define tipping points and track their future likely occurrence dependent 145 upon the RCP-forced local RSLR projections of Kopp et al. (2014), which account for local 146 change from non-climatic background subsidence, oceanographic/dynamically effects and 147 spatially variable responses from shrinking land ice to the geoid and the lithosphere. 148 Exceedance Observations 149 150 Verified hourly water levels are available from the NOAA Center for Operational Oceanographic 151 Products and Services (CO-OPS; http://tidesandcurrents.noaa.gov/) and are shown relative to the 152 current (1983-2001) tidal datum of MHHW unless noted otherwise. We focus on NOAA water 153 level gauges with defined nuisance levels and hourly data prior to 1950 (Figure 2). Nuisance 154 flood elevation thresholds are obtained from the NOAA Advanced Hydrological Prediction 155 Systems (AHPS; http://www.nws.noaa.gov/oh/ahps). Land regions at or below nuisance level 156 elevations and susceptible to inundation are mapped under the βFlood Frequencyβ tab of the 157 NOAA Sea Level Viewer (http://csc.noaa.gov/slr/viewer; Marcy et al., 2011) and shown in 158 Figure 2 as red land elevation contours. Honolulu, HI is also included but its elevation threshold 159 is not defined by the NWS, but rather by the Pacific Islands Ocean Observing System (PacIOOS; 160 http://oos.soest.hawaii.edu/pacioos). 161 162 Figure 3 presents annual counts of daily maximum water levels that have exceeded the threshold 163 level for nuisance flooding beginning in year 1920 or when data becomes available. The data (in 6 164 Figure 3 and elsewhere) are binned by meteorological year (May-April) as to not decouple the 165 stormy winter season, which is important for interannual variability diagnosis. As noted by 166 Sweet et al. (2014), the number of days currently impacted by nuisance level flooding is highly 167 correlated to the height of the flood threshold elevation itself and helps explain the lower 168 exceedance values at gauge locations 1-2 (Boston, MA and Providence, RI) and 21-22 (St 169 Petersburg, FL and Galveston, TX). There is clear evidence of increasing frequencies around the 170 U.S. over the last century and particularly since the 1980s. 171 172 When comparing 5-year average exceedances at locations over the last 50 years (1956-1960 to 173 2006-2010; Table 1), we find that frequencies have increased by a factor of 10 or more at 174 Atlantic City, Baltimore, Annapolis, Wilmington, Port Isabel and Honolulu, and by a factor of 5 175 at and Sandy Hook, Philadelphia, Norfolk and Charleston. In addition to the number of days per 176 year with an exceedance, the total hourly duration per year of water level above the flood level is 177 a useful, and in some cases more relevant metric. Linear regression between the two at each 178 station is presented in Table 1 with fit coefficients denoted βDays:Hrsβ. All fits are significant at 179 the 99% level (p-value < 0.01), and the generally high R2 values suggest that a linear scaling 180 provides a reasonable link between the two metrics. 181 Historical Exceedance Characterization 182 183 Figure 3 provides compelling evidence of a nonlinear increase in coastal water level exceedance 184 over the last half-century and is consistent with a logistic evolution of exceedance probabilities. 185 To examine these observations in a temporal framework, the exponential nature of the logistic 186 function suggests a growth model: 187 (2) πΈ(π‘) = πΈ0 + πΌ(π‘ β ππΏ ) + (1 + π) 188 (π‘βππΊ ) π 189 190 where E0 is the exceedance at time t = 0, Ξ± the linear rate of exceedance, r the growth rate, TL and 191 TG the start time of linear and exponential growth, and Ο the growth time constant. This model is 192 fit to yearly exceedance data with maximum likelihood estimation over a wide parameter space 7 193 of initial conditions (Table 2), and the best-fit model from the parameter search is selected based 194 on the minimum Akaike information criteria. 195 196 Figure 4 plots daily exceedance data and model fits at elevation thresholds 10, 20, 30, 40 and 50 197 cm above MHHW at four stations that typify the range of behaviors observed across all regions: 198 New York City (NYC; Battery gauge), Norfolk (Sewells Point gauge), Galveston (Bayside 199 gauge) and San Francisco. The temporal exceedance growth at these four stations encapsulates 200 three types of behaviors observed collectively across all stations. The first type is characterized 201 by linear growth (San Francisco) associated with sites that have either large interannual 202 variability, small RSLR, a high threshold elevation such that the exponential transition region 203 has yet to be reached, or a combination of these factors. East coast stations with linear growth 204 include Charleston, Fernandina Beach and Fort Pulaski. The second type are stations where 205 exponential growth initiated more than several decades ago (prior to 1980) as exemplified by 206 Norfolk and Galveston. The third type is characterized at sites where the inception of 207 exponential growth has been within the last few decades such as at New York City. This latter 208 type is predominantly located on the upper Mid-Atlantic Coast and includes Boston, Kings Point, 209 and Lewes. We suspect that Norfolk, New York City and other Mid-Atlantic locations are 210 experiencing higher growth rates (i.e., Ezer and Atkinson, 2014) from the recent βhot spotβ of 211 SLR acceleration associated with fluctuations of the Gulf Stream and interannual variability 212 (Boon, 2012; Ezer and Corlett, 2012; Sallenger et al., 2012; Kopp, 2013). 213 214 Values of R2, TG and Ο along with standard errors at exceedance thresholds of 10 and 30 cm are 215 shown in Table 3. At a threshold of 10 cm above MHHW most stations are found to have 216 initiated nonlinear growth in the early or mid-twentieth century. As elevations increase the 217 values of TG tend to stay nearly stable at stations where the nonlinear transition is recent, such as 218 New York City, whereas at stations where growth was initiated earlier, there is a progression of 219 TG to later years. TG and Ο characterize the temporal evolution of nonlinear growth, and can be 220 used as metrics to assess a tipping point in exceedance behavior (discussed below). However, 221 since the growth rate is not well-constrained by this model with standard errors as large as the 222 rates themselves, we turn to a polynomial model for rate estimates. 8 223 Nuisance Level Exceedance Acceleration 224 225 The general exponential model (equation 2) provides good estimates for the temporal initiation 226 and doubling period of accelerated exceedance, but poorly constrains the growth rate. To obtain 227 improved estimates of the growth rate, we employ a quadratic growth model regressed against 228 annual exceedances above the nuisance flood level of each station from 1950 through 2013: 229 (3) πΈ(π‘) = π2 π‘ 2 + π1 π‘ + π0 230 231 232 where Nuisance Flooding exceedances, E represents either days with an impact or cumulative 233 hours per year, t is in years starting at 1950, b0 the initial exceedance, b1 the linear rate, and b2 234 the quadratic acceleration coefficient. Data are included only if hourly water levels for the year 235 are more than 80% available with results presented in Table 4 for fits with acceleration 236 coefficients above the 90% significance level (p-value < 0.1). We find that acceleration is 237 apparent along most of the U.S. East Coast as well as one location in the Gulf of Mexico (Port 238 Isabel, TX). Nuisance flooding acceleration is not apparent at a few East and Gulf Coast 239 locations (blank cells in Table 4) where the nuisance flood level threshold is higher than most 240 (e.g., St. Petersburg and Galveston). In fact, these locations do not have linear regression 241 coefficients above the 90% significance level (p-value < 0.1) for the same reason β namely that 242 an insufficient amount of exceedances have occurred to establish any discernable pattern. Along 243 the U.S. West Coast nuisance exceedances are not accelerating but are linearly increasingly 244 (equation 3 with no acceleration term), except at Seattle where the threshold is high. We suspect 245 this linear response is related to the PDO-forced stagnation in MSL rise over the last couple 246 decades (Bromirski et al., 2011, NRC, 2012), small downward subsidence rates (Zervas et al., 247 2013) and large (>0.2 m) ENSO driven interannual MSL anomalies comparable in magnitude to 248 the amplitude of the RSLR trend over the last half decade. Along the West Coast large waves 249 also seasonally contribute to coastal flooding (Ruggiero, 2013), but are not generally measured 250 by water level gauges (Hoeke et al., 2013) or associated with nuisance tidal flooding. 251 252 Annual Variance, MSL Characteristics and Attribution to Threshold Exceedances 253 9 254 Location-specific differences in annual variance are evidenced in probability densities of hourly 255 (Figure 5a) and daily maximum (Figure 5b) water levels for 2006-2010. The probability 256 densities, shown here and throughout our study unless otherwise noted, are constructed using a 257 nonparametric kernel density estimator with location-specific optimized bandwidths between 258 0.04 and 0.08. Hourly water level variance (2006-2010 values, Table 1) is dominated by, and 259 scales linearly with the great diurnal tidal range (GT), defined as the difference between MHHW 260 and MLLW (Figure 5c). The shapes of the hourly probability densities reflect the tide-cycle 261 characteristics. For instance, San Francisco has a large mixed tide (two highs and two lows that 262 are unequal in magnitude) range, a wide hourly density and less probability of exposure to water 263 levels above MHHW. On the other hand, Galveston (and much of the Gulf of Mexico Coast) 264 with its small diurnal (one high and one low tide a day) tide range and normal-like distribution 265 has the narrowest hourly density and higher probability of exceeding MHHW. The distributions 266 of daily maximum water levels are similar and approximately Gaussian with higher probabilities 267 in the tail at locations that experience large storm surges such as the Battery in New York City 268 (Figure 5b). The annual series of hourly water level variance (Figure 6b) do reveal time-varying 269 patterns associated with the 18.6-year lunar nodal cycle. However, time series of annual hourly 270 and daily maximum water level variances (not shown) are effectively trend-stationary and 271 similar to the findings of Zhang et al. (2000) for the U.S. East Coast over the 20th century, which 272 suggests that exceedance increases (Figure 4) are not directly forced by storminess trends. 273 274 On the other hand, annual MSL time series in Figure 6a show large increases over time. Long- 275 term RSLR trends in Table 1 are computed using annual MSL, with linear coefficients above the 276 95% significance level (p-value < 0.05) and are consistent with the official NOAA RSLR trends 277 (http://tidesandcurrents.noaa.gov/sltrends/sltrends). A measure of interannual MSL variability is 278 inferred through the R2 values, with low values indicating higher variability along the West 279 Coast and Honolulu largely due to ENSO and PDO influences. RSLR trends with asterisks in 280 Table 1 signify locations with significant acceleration (coefficients β not shown β above the 95% 281 significance level accounting for serial autocorrelation as described in Zervas (2009)) occurring 282 since 1950 in their annual MSL. These stations are located along the upper Mid-Atlantic Coast 283 where the inception of exponential growth in annual threshold exceedances initiated within the 284 last few decades (Table 3). 10 285 286 In order to quantify the relative contribution of variance and MSL to annual exceedances above 287 the nuisance level over time, we fit multi-year series of daily maximum water level with a 288 normal PDF defined by: 289 (4) π(π€, π, π) = 290 1 πβ2π π (π€βπ)2 2π2 291 292 where π is the probability density at a water level height, π€, and µ and Ο2 are the mean and the 293 variance of the distribution, respectively. The probability of exceedance (P) at a particular water 294 level, π€ is defined as 1 β CDF, where the CDF of the normal distribution is defined as: 295 π€βπ (5) π(π€, π, π) = 1/2 [1 + erf ( 296 π β2 )] 297 298 with the parameters the same as in equation (4) and erf is the error function. In Figure 6e we 299 show the PDFs and in Figure 6f the probability of exceedance for the 1956-1960 and 2006-2010 300 periods at Norfolk with the nuisance flood level highlighted. The mean and variance of the PDF 301 (both in meters) are listed above Figure 6e and 6f as are the number of estimated annual nuisance 302 flood days (P*365 days) on average during 1956-1960 (0.1 day) and 2006-2010 (5.8 days). 303 Readily apparent is the large change in the mean of the distribution between these periods from 304 RSLR with only a small change in variance. Using the variance value from 2006-2010 (0.044) 305 and the mean from 1956-1960 (-0.141) provides an estimate of 0.3 nuisance flood days and 306 readily confirms that RSLR is the major factor involved in the large exceedance increases 307 observed over this time period (Table 1). 308 309 We provide further evidence that RSLR is the major factor as compared to variance driving the 310 increases in nuisance flood days in Figure 6c and Figure 6d where annual MSL and annual 311 variance of daily maximum water levels, respectively, are regressed against observed annual 312 daily exceedances above a 0.3 m and 0.5 m MHHW threshold at New York City and San 313 Francisco over 1950-2013. The regressions using annual MSL are fit with a quadratic model 314 (except for La Jolla, which uses a linear fit) whereas fits for annual variance are all linear (all 11 315 significant at the 95% level; p-value < 0.05) with R2 indicated. In all cases, the amount of the 316 annual exceedance variation (R2) partially explained by annual MSL is much higher than by 317 annual variance. In Table 1 under the βAttributionβ heading, the R2 values are listed from 318 quadratic fits between annual MSL and annual exceedances above 0.3 m MHHW for all 319 locations. The next column (MSL, Var) lists the total variation in annual exceedances explained 320 (R2) from multiple quadratic regression (not necessarily significant at the 95% level) using both 321 annual MSL and variance. In all cases it can be seen that annual MSL is the leading factor 322 driving the growth of annual exceedances in time. 323 324 Exceedance Acceleration Patterns 325 326 Sweet et al. (2014) noted an inverse linear relationship (R2 = 0.59) between acceleration rates of 327 annual nuisance flood days and nuisance flood elevation thresholds along the U.S. East and Gulf 328 Coasts. Here, we generalize and extend that relationship through quantification of the hourly 329 annual exceedance acceleration over a range of common elevation thresholds. Figure 7a shows 330 acceleration coefficients of equation (3) (> 90% significance level; p-value < 0.1) for hourly 331 exceedances above elevation thresholds from MHHW to 0.6 m above MHHW. Acceleration 332 coefficients are larger at locations with smaller variance (Table 1) and/or tide range (Figure 5c). 333 For instance, Galveston, Port Isabel, Annapolis, Baltimore, Montauk, Norfolk, which have more 334 tightly bound hourly probability (e.g., Galveston in Figure 5a) have higher acceleration 335 coefficients for elevations β€ 0.3 m associated with steeper probability of exceedance (1-CDF) 336 curves across these elevations (e.g., Norfolk versus New York City in Figure 9). 337 338 Above, we show that increasing MSL (RSLR) is the leading factor causing annual exceedances 339 (nuisance and other threshold levels) to increase in time since variance changes are essentially 340 trend-steady. Also, where the annual exceedance rates are accelerating, they are higher at 341 elevation thresholds nearer MHHW at locations with smaller tide range/variance. In Figure 7b-d 342 we investigate the relative influence of differing rates of RSLR with respect to tide range upon 343 annual exceedance acceleration rates. RSLR rates exhibits a direct positive relationship to 344 hourly acceleration coefficients (hours/year2) for exceedances above the 0.1 and 0.3 m threshold 345 (Figure 7b), supporting the findings of Ezer and Atkinson (2014) who detected the highest 12 346 acceleration in flooding hours for a 0.3 m threshold above MHHW at locations with higher 347 RSLR rates. Unique to this study is quantification of tidal range and its nonlinear relationship to 348 threshold exceedance rates, which allows for an improved estimate of annual acceleration for 349 minor/nuisance-level thresholds (Figure 7c). The coupled importance of both RSLR rates and 350 tidal range in relation to acceleration in annual hourly exceedance rates (i.e., Figure 7a), can be 351 expressed through multiple quadratic regression: 352 (6) π2_βππ’ππ = π2(πΊπ) πΊπ 2 + π2(π ππΏπ ) π ππΏπ 2 + π1(πΊπ) πΊπ + π1(π ππΏπ ) π ππΏπ + 353 π1(πΊπ,π ππΏπ ) πΊπ β π ππΏπ + π0 354 355 356 where b2_hours is the acceleration coefficient (hours/year2) from equation (3) with values plotted in 357 Figure 7a, GT is the great diurnal tidal range over the 1983-2001 tidal epoch and available online 358 (http://tidesandcurrents.noaa.gov), RSLR are the linear MSL trends in Table 1 and b0, b1 and b2 359 are the regression coefficients. The relationships for 0.1, 0.3 and 0.5 m elevation thresholds are 360 shown in Figure 7d (all significant at 95% level; p-value < 0.05) and define, for instance, the 361 influence of tide range, such that Annapolis and Galveston, which have nearly identical tide 362 ranges but nearly a factor of two RSLR trend difference (Table 1), have similar exceedance 363 accelerations over a range of elevation thresholds (Figure 7a). This type of approach (equation 6) 364 might prove useful to help establish spatial patterns applicable for locations not having an 365 immediately adjacent long-term water level gauge but with plausible regional estimates of RSLR 366 and modeled tide range information (e.g., http://vdatum.noaa.gov). 367 368 Interannual Variability 369 370 Interannual variability can affect and obscure the underlying trends in annual nuisance-level 371 exceedances (e.g., Figure 4d). Along the West Coast (Figure 8d), regional shifts in MSL during 372 El Niño produce high sea level anomalies (Enfield and Allen, 1980; Chelton and Davis, 1982; 373 Miller et al., 1997), which are associated with higher nuisance-level exceedances (Figure 8f) 374 primarily during periods of highest astronomical tides (Sweet et al., 2014). La Niña conditions 375 are typically associated with low sea level anomalies. Along the East Coast, ENSOβs global 376 teleconnection can alter winter-storm track patterns along the mid-Atlantic (Hirsch et al., 2001; 13 377 Eichler and Higgins, 2006) and is coherently related to sea level anomalies (Park and Dusek, 378 2013). During strong El Niños (e.g., 1997), there is an increased likelihood for coastal storm 379 surges (Sweet and Zervas, 2011; Thompson et al., 2013) as shown in Figure 8a, which increases 380 nuisance-level exceedances (Figure 8c). The transition from ENSO cool-to-neutral conditions in 381 2008 to a moderately strong El Niño during 2009 highlights the ENSO effects (increased mean, 382 variance/skew) on probability densities of daily maximum water levels in Norfolk and San 383 Francisco (Figure 8b, e). 384 385 To assess ENSO influence on annually observed nuisance exceedances, we use the Oceanic Niño 386 Index (ONI) in a multiple regression models: 387 (7) πΈ(π‘) = π2 π‘ 2 + π2(πΆπΌ) πΆπΌ 2 + π1 π‘ + π1(πΆπΌ) πΆπΌ + π1,πΆπΌ π‘πΆπΌ + π0 388 389 390 where E, t, b0, b1 and b2 parameters are the same as in equation (3), and b1(CI), b2(CI) and b1,CI 391 represent the fit coefficients related to the inclusion of the ONI climate index (CI). The ONI was 392 utilized since it accounts for the warming trend in the Niño 3.4 region, is thought to better 393 represent interannual variability and is operationally predicted by NOAA (NOAA, 2014). At 394 both Norfolk and San Francisco, inclusion of the ONI significantly (CI coefficient(s) > 90% 395 level, p-value < 0.1) improves the historical characterization of nuisance exceedances as shown 396 in Figure 8c, f, with higher R2 values shown in Table 4 (Norfolk R2 from 0.35 to 0.56, and San 397 Francisco from 0.12 to 0.46). Results of the multiple regression indicate that the annual number 398 of days with nuisance flooding at San Francisco increase proportionally to ONI at a rate of 5.5 399 days per unit ONI, whereas at Norfolk nuisance days increase by a factor of 1.4 times the square 400 of the annual ONI value. Other West and East Coast stations show similar ONI sensitivity 401 (Table 4) with greater influence at lower nuisance level elevation thresholds. 402 403 Tipping Points 404 405 In complex systems, a small parameter change can cause a transition from a stable state to a new 406 equilibrium state drastically different from the initial one (Groffman et al., 2006; Lenton et al., 14 407 2008). We believe that at many coastal locations around the globe with critical coastal 408 ecosystems or where humans have established infrastructure at fixed locations over the last 409 century such transitions have begun in response to RSLR. Specifically, the data suggest that 410 RSLR has elevated water levels at many coastal locations such that the nuisance flood levels are 411 no longer confined to the extreme tails of the water level distributions, but have, or will soon 412 enter the transitional phase of exponential growth in exceedances. It is then natural to ask 413 whether physically relevant metrics can be expressed to quantify the evolution of this behavior, 414 and we propose two, one based on the temporal inception of nonlinear exceedance growth, the 415 other on the changing probability of inundation with respect to a specific elevation threshold. 416 The initiation of nonlinear growth was quantified in the parameters TG and Ο (Table 3), indicating 417 that at many coastal locations the transition from linear to exponential growth of exceedances has 418 already occurred. 419 420 Regarding the transitional behavior of exceedance probabilities associated with a specific 421 elevation, Figure 9 shows probability of exceedance curves for year-long hourly water levels 422 during 1930, 1950, 1980 and 2010 at New York City and Norfolk. The MSL and MHHW tidal 423 datums are shown as vertical lines. To illustrate a tipping point for water level exceedance, let 424 us consider MHHW level as the elevation threshold and an exceedance probability of 1/12 (30 425 days/year using the daily-maximum event metric or 720 hours/year using the cumulative-hours 426 duration metric), although different selections of elevation threshold and probability of 427 exceedance would ideally be customized for each specific location to reflect the local 428 communityβs susceptibilities. Figure 9 shows that as sea level has risen, sometime between 1980 429 and 2010 a threshold was crossed such that the probability of exceeding MHHW at both the New 430 York City and Norfolk surpassed 1/12. The corresponding exceedance probabilities and water 431 levels are shown in Table 5. Though the 1/12 probability is arbitrary, it illustrates a 432 duration/frequency threshold to be selected corresponding to a locationβs ability to deal with or 433 recover from the cumulative impacts associated with lesser extreme inundation events. We 434 couple these tipping points with projections of annual exceedance probabilities in the following 435 section. 436 15 437 Projections 438 439 We have shown that annual exceedance rates are changing in time in response to RSLR with 440 increasingly higher rates as flood threshold elevations approach MHHW (Figures 4, 7a). The 441 logical question is then posed: what does the future hold? 442 443 The 30 days/year tipping point is a starting point in defining site specific frequency-duration 444 thresholds. We use nonparametric probability density estimates of daily water level maximums 445 constructed for 2006-2010 (i.e., Figure 5b) to project forward in time by simply shifting their 446 independent variable (water level) by the RSLR projections. The choice of 2006-2010 provides 447 a contemporary climatology, closely aligns with the current GT tide range (R2=0.92, Figure 5c), 448 and occurred when ENSO was on average slightly cool (ONI average of -0.22). We also assume 449 that future water level variance matches that of 2006-2010. To assess this assumption (fixed 450 variance and no interannual variability of annual MSL relative to the locationβs RSLR trend; 451 shown as a purple dashed line in Figure 10a, c), we compute root mean square error (RMSE) 452 from comparison with historical nuisance-level exceedances (last 2 columns of Table 1). The 453 RMSE provide a measure of historic exceedance variability and evidence that the assumptions 454 are satisfied (at least approximately). 455 456 We use RSLR projections of Kopp et al. (2014), who provide separate projections in response to 457 forcing from RCP 2.6, 4.5, and 8.5 conditions (Meinshausen et al., 2011), which correspond 458 respectively to likely global mean temperature increases in 2081β2100 of 1.9β2.3 C, 2.0β3.6 C, 459 and 3.2β5.4 C above 1850β1900 levels (IPCC, 2013). They are probabilistic estimates based 460 upon process modeling and expert assessment/elicitation and account for local subsidence, 461 oceanographic/dynamical effects and spatially variable responses from shrinking land ice to the 462 geoid and the lithosphere. The RSLR projections initiate in 2000 and are location (tide gauge) 463 specific, often substantially differing from the global SLR median (5β95%) estimates of 0.5 m 464 (0.29β0.82 m) under RCP 2.6, 0.59 (0.36β0.93 m) under RCP 4.5 and 0.79 m (0.52β1.21 m) 465 under RCP 8.5 (Kopp et al., 2014). We also provide a projection based solely on the 466 continuation of historical local RSLR with no other future adjustments. This projection initiates 467 in 2008 (mid-point of the 2006-2010 probability density estimate) and is essentially the Low 16 468 Scenario for global SLR provided by the 2013 U.S. National Climate Assessment (NCA; Parris 469 et al., 2013). We refer to this projection as the NCA Low and stress that it is considered unlikely 470 since it assumes no changes in local RSLR trend rates within the 21st century. 471 472 Figure 10 shows projections for the annual number of days impacted by flooding above the local 473 nuisance flood level (Table 1) for Norfolk and San Francisco. Over the next couple of decades, 474 projections based upon the median of the RCP RSLR values at both locations cross the tipping 475 point and are nearly indistinguishable (Figure 10a, c) since the global SLR projections of Kopp 476 et al. (2014) are quite similar between RCPs over the next several decades. The projections 477 using the local 95% RSLR probability of RCP 8.5 crosses the tipping point within the next 478 decade, whereas they cross by 2050 under the NCA Low (Figure 10b, d). Over a 60 year time 479 horizon, the upper saturation (365 days/year) of the logistic function (1-CDF) is realized at both 480 locations under the local 95% RSLR projection of RCP 8.5. We would argue that degradation to 481 public works and critical infrastructure would occur and require mitigation well before 482 saturation. We show the continuation of the historical regression fits (quadratic or linear black 483 dash, quantified in Table 4) of observed annual nuisance flood days only for the next couple 484 decades (Figure 10a, c) since they are a best-fit representation reflecting past interannual MSL 485 and variance variability likely to recur in the near future. However, we would stress that these 486 are not valid projections over the long term since they do not realize the evolution which will 487 occur in exceedance probabilities (i.e., Figure 9). Lastly, we note that the regression fits (black 488 dash) range from slightly higher (Figure 10c) to lower (Figure 10a) when compared historically 489 to the 2006-2010 probability density estimates (purple dash) at all the tide gauge locations, 490 possibly related to regional decadal-scale MSL anomaly and storm variability patterns. 491 492 In Figure 11, we use a consistent elevation threshold of 0.5 m MHHW to examine 493 probabilistically when the crossing dates for the 30 days/year tipping point might occur in the 494 future using the RCP-based RSLR projection probabilities. Tipping point dates are illustrated 495 using the Kopp et al. (2014) local 5%, 20%, 80% and 95% RSLR projection probabilities for 496 RCP 2.6 (Figure 11a), 4.5 (Figure 11b) and 8.5 (Figure 11c). The median and the 5% and 95% 497 probabilities for local RSLR amounts by 2100 are also shown. Accordingly, the majority of 498 locations will cross the 30 days/year (0.5 m above MHHW threshold) tipping point by 2050 17 499 under RSLR projections quite likely to occur (within the local 20% and 80% probability range of 500 RSLR projections) and by 2060 under RSLR projections very likely to occur (between local 5% 501 and 95% probability range of RSLR projections) from all three RCPs. 502 503 A general pattern emerges (Figure 11) of delayed tipping point dates for locations with lower 504 local RSLR projections (e.g., San Francisco and Seattle) or smaller daily maximum variance as 505 listed in Table 1 (Wilmington, Key West, St. Petersburg). Conversely, tipping points occur 506 sooner at locations with higher local RSLR projections (Galveston) or that have larger water 507 level variance and a propensity for more frequent and stronger storm surges (Boston, Kings 508 Point, New York City, Atlantic City). This co-dependency of future tipping point dates upon 509 both future RSLR (black dots in Figure 11) and variance of daily maximum water level (Table 1) 510 can be expressed with a multivariate linear regression as in equation (6) where the tipping point 511 date is the dependent variable and RSLR and water level variance are the independent variables. 512 This coupled model accounts for 73%, 79% and 83% of the variance (p-value < 0.05) in future 513 tipping point dates associated with RCP 2.6, 4.5 and 8.5 respectively for a 0.5 m threshold above 514 MHHW. Taken together with findings based upon annual hourly exceedances in Figure 7, 515 locations with smaller water level variance will generally take longer to surpass 516 duration/frequency tipping points (e.g., 30 flood days/year) for elevation thresholds above 0.3 m 517 MHHW, but are prone for a more rapid transition below this elevation. 518 519 The decade when the 30 days/year tipping point is surpassed are mapped for local nuisance flood 520 levels (Figure 12a) listed in Table 1 as well as for a common 0.5 m threshold (Figure 12b). 521 Tipping points for nuisance level flooding under the NCA Low projection have already been 522 surpassed (e.g., Annapolis, Washington D.C., Wilmington) or will so in the coming decade at 523 locations with lower elevation thresholds and higher RSLR rates (e.g., Atlantic City, Charleston, 524 Port Isabel). By 2050, the majority of locations surpass their tipping point under the local 525 median (50%) RSLR projection probability for all RCPs except at locations with higher nuisance 526 flood levels (e.g., Boston, New York City, St Petersburg, Galveston, Seattle), whereas under the 527 local 95% probability for RSLR projections of RCP 8.5, the majority of stations surpass the 528 tipping point by 2030. Tipping point dates for the 0.5 m MHHW threshold (Figure 12b) follow 18 529 the same general patterns of Figure 11 and are surpassed at the majority of locations by 2040 530 under the local median (50%) RSLR projection probability of the RCPs. 531 532 Concluding Remarks 533 534 NOAA water level (tide) gauges have been measuring water levels for over a century, 535 quantifying RSLR along most of the continental U.S., Hawaii and Pacific Island Territory 536 coastlines. RSLR exacerbates nuisance flooding impacts relative to todayβs fixed reference 537 frame. At very high thresholds, such as those of the 100-year event experienced during 538 hurricane strikes, RSLR has and will continue to nonlinearly compress recurrence probabilities 539 in the future because smaller storm surges will increasingly impact fixed elevations (Hunter 540 2010; Park et al., 2011; Tebaldi et al., 2012; Sweet et al., 2013). The same is true for impacts 541 from lesser extremes or nuisance flooding occasionally experienced today during high tide. We 542 show that these events (defined as exceedances over local NOAA NWS minor flood thresholds) 543 are increasing in time at the NOAA tide gauges in our study. Moreover, annual event rates for 544 exceedances over thresholds from MHHW to 0.5 m above MHHW are accelerating along the 545 U.S. East and Gulf Coasts. This occurs as rising sea levels evolve the nonlinear portion of a 546 water level distribution against a fixed elevation irrespective of whether the sea level rise is 547 linear or nonlinearly accelerating (Figure 1). 548 549 We show that annual rates of hourly exceedances over elevation thresholds from MHHW to 0.5 550 m above MHHW along the East and Gulf Coasts tend to exhibit higher acceleration rates at 551 locations with higher RSLR rates and smaller tide ranges. Interannual variability in MSL and to 552 a lesser extent water level variance affect annual threshold exceedance rates and make the 553 appropriate time-dependent characterization challenging. This is especially relevant along the 554 U.S. West Coast, where MSL anomaly punctuations from ENSO and multi-decadal MSL trends 555 dampened by PDO overwhelm the underlying RSLR signal. 556 557 Acceleration in RSLR rates, which are projected to occur during the 21st century (Parris et al., 558 2013; Church et al., 2013; Kopp et al., 2014) will further intensify inundation impacts over time, 19 559 and further reduce the time between flood events. We introduce the concept of a tipping point 560 for impacts from future coastal inundation when critical elevation thresholds for various public 561 works or coastal ecosystem habitats may become increasingly compromised by increasingly 562 severe tidal flooding (Grossman et al., 2006). Using NOAA NWS elevation thresholds and 563 future median values of local RSLR projections of Kopp et al. (2014), we find that the majority 564 of locations surpass a 30 days/year tipping point by 2050 except for locations with higher 565 nuisance flood levels (e.g., Boston, St Petersburg, Galveston and Seattle). Under the local 95% 566 projection probability for RSLR under the RCP 8.5, whose global projected rise approximates 567 that of the NCA Intermediate High SLR scenario (1.2 m SLR by 2100), this tipping point is 568 surpassed by the end of the next decade (2030). At all locations, the tipping points are surpassed 569 much earlier than 2100 β the date for which most global mean SLR projections are formulated 570 and publically discussed. 571 572 Impacts from recurrent coastal flooding include overwhelmed stormwater drainage capacity at 573 high tide, frequent road closures, and general deterioration and corrosion of infrastructure not 574 designed to withstand frequent inundation or salt-water exposure. As sea levels continue to rise 575 and with an anticipated acceleration in the rate of rise from ocean warming and land-ice melt, 576 concern exists as to when more substantive impacts from tidal flooding of greater frequency and 577 duration will regularly occur. Information quantifying these occurrences and associated 578 frequency-based tipping points is critical for assisting decision makers responsible for necessary 579 mitigation and adaptation efforts in response to sea level rise. 580 20 581 Acknowledgments 582 We thank Robert Kopp for sharing data from the Kopp et al. (2014) study as well as his and an 583 anonymous reviewerβs review and constructive comments. We thank Jayantha Obeysekera, John 584 Marra, Stephen Gill and Chris Zervas for their helpful discussions and Doug Marcy, Matt 585 Pendleton and Billy Brooks for the high resolution graphics in Figure 2 and the idea to assess 586 impacts above societally relevant thresholds. 21 587 References 588 589 Boon, J.D., J. M. 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