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Title Page:
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From the Extreme to the Mean:
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Acceleration and Tipping Points of Coastal Inundation from Sea Level Rise
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*William V. Sweet (William.Sweet@noaa.gov), corresponding author
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Joseph Park (Joseph.Park@noaa.gov)
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NOAA National Ocean Service
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Center for Operational Oceanographic Products and Services
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1305 East West Highway, Silver Spring, MD, USA
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From the Extreme to the Mean:
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Acceleration and Tipping Points of Coastal Inundation from Sea Level Rise
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William V. Sweet and Joseph Park
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NOAA’s Center for Operational Oceanographic Products and Services
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Abstract
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Relative sea level rise (RSLR) has driven large increases in annual water level exceedances
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(duration and frequency) above minor (nuisance level) coastal flooding elevation thresholds
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established by the National Weather Service (NWS) at U.S. tide gauges over the last half
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century. For threshold levels below 0.5 m above high tide, the rates of annual exceedances are
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accelerating along the U.S. East and Gulf Coasts, primarily from evolution of tidal water level
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distributions to higher elevations impinging on the flood threshold. These accelerations are
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quantified in terms of the local RSLR rate and tidal range through multiple regression analysis.
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Along the U.S. West Coast annual exceedance rates are linearly increasing, complicated by sharp
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punctuations in RSLR anomalies during El Niño Southern Oscillation (ENSO) phases, and we
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account for annual exceedance variability along the U.S. West and East Coasts from ENSO
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forcing. Projections of annual exceedances above local NWS nuisance levels at U.S. tide gauges
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are estimated by shifting probability estimates of daily maximum water levels over a
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contemporary 5-year period with probabilistic RSLR projections of Kopp et al. (2014) for
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representative concentration pathways (RCP) 2.6, 4.5 and 8.5. We suggest a tipping point for
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coastal inundation (30 days/per year with a threshold exceedance) based on the evolution of
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exceedance probabilities. Under forcing associated with the local-median projections of RSLR,
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the majority of locations surpass the tipping point over the next several decades regardless of
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specific RCP.
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Introduction
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Sea level has been rising for well over 10,000 years, although the last 4,000 years have been
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remarkably stable with changes less than a few meters and on the order of a half meter over the
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last 2 thousand years (Fleming et al., 1998, Milne et al., 2005, Kemp, 2011). Human population
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on the other hand, has experienced exponential growth over the last 2,000 years with
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establishment of expansive coastal population centers (USDOC, 2013). Given the nearly
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imperceptible change in mean sea level (MSL) on generational timescales, it is natural that
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humans associate sea level change with tides and storms rather than climate. Nonetheless,
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current scientific consensus is that anthropogenic forced climate change is warming the planet
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and contributing to sea level rise (Cazenave and Le Cozannet, 2013).
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This climate warming has contributed to a global mean sea level rise (SLR) rate of ~1.7 mm/year
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over the last century with higher rates of ~3.2 mm/year over the last couple decades (Church and
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White, 2011; Merrifield et al., 2013). Superimposed upon this global rise are regional sea level
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dynamics driven by ocean-atmosphere interactions with intra-annual, annual, interannual and
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decadal timescales. This includes storm surge events which are influenced by changes to
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seasonal storm track tendencies (Hirsch et al., 2001; Sweet and Zervas, 2011; Thompson et al.,
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2013), and longer term sea level anomalies coherent with modes of ENSO, the Pacific Decadal
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Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO). Dependent upon their
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state, these climate patterns can regionally exacerbate or suppress storm surge frequencies and
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SLR rates (Park et al., 2010; Bromirski et al., 2012; Merrifield et al., 2012).
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From the perspective of a specific location on land, such as a human dwelling, inter-tidal habitat
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or water level (tide) gauge, vertical land motion also contributes to changes in sea level (Zervas
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et al., 2013), and it is this relative sea level rise (RSLR) that is of interest to coastal infrastructure
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and its inhabitants. Relative sea level is normally specified with respect to the tidal datum of
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MSL, whereas coastal inundation and flooding are best described relative to Mean Higher High
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Water (MHHW; http://tidesandcurrents.noaa.gov/datum_options.html). The National Tidal
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Datum Epoch (NTDE) used in the United States is a 19-year period over which tidal datums
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specific to each tide gauge are determined and as sea level rises, tidal datums also rise. The
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current NTDE for the United States is 1983-2001 and all historic and future-projected water level
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information in our study reference this period since it is relative changes compared to today’s
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condition that we are interested.
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Consequences of RSLR include an increased frequency or probability of coastal inundation
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relative to fixed elevations from a combination of storms, tides and climatic forcings (Hunter
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2010; Park et al., 2011; Tebaldi et al., 2012). This is simply understood by the reduced freeboard
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or gap between MSL and the threshold flood elevation as sea level rises, such that smaller storm
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surges or sea level anomalies will increasingly exceed the flood level threshold as time
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progresses. As exemplified by Hurricane Katrina in 2005 and Superstorm Sandy in 2012 (Sweet
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et al., 2013) the Intergovernmental Panel on Climate Change (IPCC) recognizes that societal
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impacts of sea level change primarily occur via extreme events rather than as a direct
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consequence of MSL changes, and expect that the majority of global coastlines will be affected
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by RSLR by the end of the 21st century (Seneviratne et al., 2012). Appropriately, there has been
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significant investigation of extreme event probabilities and future SLR (Zervas, 2013; Church et
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al., 2013; Miller et al., 2013; Kopp et al., 2014; Jevrejeva et al., 2014) along with region-specific
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recognition (Boon, 2012; Ezer and Corlett, 2012; Sallenger et al., 2012; Kopp, 2013) and
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detection (Chambers et al., 2012; Haigh et al., 2014) of SLR acceleration.
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Considering a probability density function (PDF) of coastal water level measured at a tide gauge,
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the focus has been on evolution of MSL near the center of the density, or on assessment of
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extreme events in the upper tail. Less attention has been paid to the transition region between
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these regimes, but it is this transition region which exhibits a highly non-linear portion of water
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level probability, and holds the most relevance for identifying a tipping point in the change of
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coastal inundation impacts as sea levels rise. To illustrate this, Figure 1a shows an example of a
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water level time series measured at a tide gauge with the current (1983-2001 epoch) tidal datum
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elevations of mean lower low water (MLLW), mean low water (MLW), MSL, mean high water
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(MHW) and MHHW. Every station also has station, or standard datum, defined as the elevation
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of zero water level. Also shown is a flood level threshold at a fixed height above MHHW, but
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whose gap decreases with RSLR. Figure 1b plots probability density estimates of year-long
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hourly water levels at New York City (The Battery), NY and reveals how they have changed
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over an 80-year span relative to the current (1983-2001) tidal datums. Comparison of the 1930
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or 1950 probability of MHW or MHHW to those of 1980 or 2010 reveals a significant increase.
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Integration of the density above an exceedance threshold (Figure 1c) quantifies the total
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probability of exceedance allowing one to quantify changes over time. As an example, the
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increase in annual probability of exceedance at MHW from 1930 to 2010 was 2% to 19%.
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The probability of exceedance is the complement of the cumulative distribution function (CDF),
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1 – CDF, and shares sigmoidal characteristics across water level distributions whether the
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distributions are wave-like (Rayleigh), non-tidal (Gaussian) or tidal (bi-modal). The relevant
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features are: 1) accelerated growth over the transition between very high water with near-zero
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probability (extremes) to MHW, 2) approximately linear growth between MHW and MLW and
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3) decay and saturation below MLW (Figure 1b). A generic expression of these behaviors can
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be captured with a logistic function
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(1)
𝑃(𝑤) =
1
1+𝑒𝑥𝑝[−𝑠(𝑤0 −𝑤)]
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where P(w) is the probability of exceedance, w the water level and s represents the slope at the
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mid-point, w0.
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In the accelerated transition regime, exceedance rate changes following equation (1) will be
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nonlinear regardless of whether the water level densities are moving toward higher levels at a
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steady or accelerated rate dictated by RSLR. We therefore expect that as sea levels rise against
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habitats and infrastructure with fixed flood elevations and cross through this critical transition
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regime, coastal water level exceedances will accelerate. Sweet et al. (2014) and Ezer and
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Atkinson (2014) recently discussed the concept of accelerating lesser extreme (nuisance tide)
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impacts and both highlighted the U.S. East Coast as a region with accelerated impacts.
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However, neither study recognized the inherent evolution in exceedance probabilities nor
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elucidate the primary response mechanism of exceedance-rate acceleration changes that are, and
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will continue to occur as sea levels rise.
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In this paper we show that acceleration in local tidal flooding within a range of elevation
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thresholds has, and will continue to result from secular SLR. First, we assess how water level
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exceedances above societally relevant thresholds are changing in time. Specifically, we use a
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common set of elevation thresholds from MHHW to 60 cm above MHHW, as well as local
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minor coastal flooding threshold levels established by the U.S. National Oceanic and
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Atmospheric Administration (NOAA) NWS to provide estimates of annual duration (cumulative
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hours) and annual event frequency (days with an exceedance) at long-term NOAA water level
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gauges around the U.S. These measures define nuisance level impacts as compared to NWS
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moderate and major impact elevation thresholds recently examined by Kriebel and Grieman
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(2013). We also account for interannual variability driven by ENSO through multiple regression
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analysis. Lastly, we define tipping points and track their future likely occurrence dependent
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upon the RCP-forced local RSLR projections of Kopp et al. (2014), which account for local
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change from non-climatic background subsidence, oceanographic/dynamically effects and
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spatially variable responses from shrinking land ice to the geoid and the lithosphere.
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Exceedance Observations
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Verified hourly water levels are available from the NOAA Center for Operational Oceanographic
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Products and Services (CO-OPS; http://tidesandcurrents.noaa.gov/) and are shown relative to the
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current (1983-2001) tidal datum of MHHW unless noted otherwise. We focus on NOAA water
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level gauges with defined nuisance levels and hourly data prior to 1950 (Figure 2). Nuisance
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flood elevation thresholds are obtained from the NOAA Advanced Hydrological Prediction
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Systems (AHPS; http://www.nws.noaa.gov/oh/ahps). Land regions at or below nuisance level
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elevations and susceptible to inundation are mapped under the “Flood Frequency” tab of the
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NOAA Sea Level Viewer (http://csc.noaa.gov/slr/viewer; Marcy et al., 2011) and shown in
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Figure 2 as red land elevation contours. Honolulu, HI is also included but its elevation threshold
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is not defined by the NWS, but rather by the Pacific Islands Ocean Observing System (PacIOOS;
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http://oos.soest.hawaii.edu/pacioos).
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Figure 3 presents annual counts of daily maximum water levels that have exceeded the threshold
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level for nuisance flooding beginning in year 1920 or when data becomes available. The data (in
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Figure 3 and elsewhere) are binned by meteorological year (May-April) as to not decouple the
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stormy winter season, which is important for interannual variability diagnosis. As noted by
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Sweet et al. (2014), the number of days currently impacted by nuisance level flooding is highly
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correlated to the height of the flood threshold elevation itself and helps explain the lower
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exceedance values at gauge locations 1-2 (Boston, MA and Providence, RI) and 21-22 (St
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Petersburg, FL and Galveston, TX). There is clear evidence of increasing frequencies around the
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U.S. over the last century and particularly since the 1980s.
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When comparing 5-year average exceedances at locations over the last 50 years (1956-1960 to
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2006-2010; Table 1), we find that frequencies have increased by a factor of 10 or more at
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Atlantic City, Baltimore, Annapolis, Wilmington, Port Isabel and Honolulu, and by a factor of 5
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at and Sandy Hook, Philadelphia, Norfolk and Charleston. In addition to the number of days per
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year with an exceedance, the total hourly duration per year of water level above the flood level is
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a useful, and in some cases more relevant metric. Linear regression between the two at each
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station is presented in Table 1 with fit coefficients denoted “Days:Hrs”. All fits are significant at
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the 99% level (p-value < 0.01), and the generally high R2 values suggest that a linear scaling
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provides a reasonable link between the two metrics.
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Historical Exceedance Characterization
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Figure 3 provides compelling evidence of a nonlinear increase in coastal water level exceedance
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over the last half-century and is consistent with a logistic evolution of exceedance probabilities.
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To examine these observations in a temporal framework, the exponential nature of the logistic
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function suggests a growth model:
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(2) 𝐸(𝑡) = 𝐸0 + 𝛼(𝑡 − 𝑇𝐿 ) + (1 + 𝑟)
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(𝑡−𝑇𝐺 )
𝜏
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where E0 is the exceedance at time t = 0, α the linear rate of exceedance, r the growth rate, TL and
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TG the start time of linear and exponential growth, and τ the growth time constant. This model is
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fit to yearly exceedance data with maximum likelihood estimation over a wide parameter space
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of initial conditions (Table 2), and the best-fit model from the parameter search is selected based
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on the minimum Akaike information criteria.
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Figure 4 plots daily exceedance data and model fits at elevation thresholds 10, 20, 30, 40 and 50
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cm above MHHW at four stations that typify the range of behaviors observed across all regions:
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New York City (NYC; Battery gauge), Norfolk (Sewells Point gauge), Galveston (Bayside
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gauge) and San Francisco. The temporal exceedance growth at these four stations encapsulates
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three types of behaviors observed collectively across all stations. The first type is characterized
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by linear growth (San Francisco) associated with sites that have either large interannual
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variability, small RSLR, a high threshold elevation such that the exponential transition region
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has yet to be reached, or a combination of these factors. East coast stations with linear growth
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include Charleston, Fernandina Beach and Fort Pulaski. The second type are stations where
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exponential growth initiated more than several decades ago (prior to 1980) as exemplified by
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Norfolk and Galveston. The third type is characterized at sites where the inception of
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exponential growth has been within the last few decades such as at New York City. This latter
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type is predominantly located on the upper Mid-Atlantic Coast and includes Boston, Kings Point,
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and Lewes. We suspect that Norfolk, New York City and other Mid-Atlantic locations are
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experiencing higher growth rates (i.e., Ezer and Atkinson, 2014) from the recent “hot spot” of
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SLR acceleration associated with fluctuations of the Gulf Stream and interannual variability
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(Boon, 2012; Ezer and Corlett, 2012; Sallenger et al., 2012; Kopp, 2013).
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Values of R2, TG and τ along with standard errors at exceedance thresholds of 10 and 30 cm are
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shown in Table 3. At a threshold of 10 cm above MHHW most stations are found to have
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initiated nonlinear growth in the early or mid-twentieth century. As elevations increase the
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values of TG tend to stay nearly stable at stations where the nonlinear transition is recent, such as
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New York City, whereas at stations where growth was initiated earlier, there is a progression of
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TG to later years. TG and τ characterize the temporal evolution of nonlinear growth, and can be
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used as metrics to assess a tipping point in exceedance behavior (discussed below). However,
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since the growth rate is not well-constrained by this model with standard errors as large as the
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rates themselves, we turn to a polynomial model for rate estimates.
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Nuisance Level Exceedance Acceleration
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The general exponential model (equation 2) provides good estimates for the temporal initiation
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and doubling period of accelerated exceedance, but poorly constrains the growth rate. To obtain
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improved estimates of the growth rate, we employ a quadratic growth model regressed against
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annual exceedances above the nuisance flood level of each station from 1950 through 2013:
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(3) 𝐸(𝑡) = 𝑏2 𝑡 2 + 𝑏1 𝑡 + 𝑏0
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where Nuisance Flooding exceedances, E represents either days with an impact or cumulative
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hours per year, t is in years starting at 1950, b0 the initial exceedance, b1 the linear rate, and b2
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the quadratic acceleration coefficient. Data are included only if hourly water levels for the year
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are more than 80% available with results presented in Table 4 for fits with acceleration
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coefficients above the 90% significance level (p-value < 0.1). We find that acceleration is
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apparent along most of the U.S. East Coast as well as one location in the Gulf of Mexico (Port
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Isabel, TX). Nuisance flooding acceleration is not apparent at a few East and Gulf Coast
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locations (blank cells in Table 4) where the nuisance flood level threshold is higher than most
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(e.g., St. Petersburg and Galveston). In fact, these locations do not have linear regression
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coefficients above the 90% significance level (p-value < 0.1) for the same reason – namely that
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an insufficient amount of exceedances have occurred to establish any discernable pattern. Along
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the U.S. West Coast nuisance exceedances are not accelerating but are linearly increasingly
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(equation 3 with no acceleration term), except at Seattle where the threshold is high. We suspect
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this linear response is related to the PDO-forced stagnation in MSL rise over the last couple
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decades (Bromirski et al., 2011, NRC, 2012), small downward subsidence rates (Zervas et al.,
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2013) and large (>0.2 m) ENSO driven interannual MSL anomalies comparable in magnitude to
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the amplitude of the RSLR trend over the last half decade. Along the West Coast large waves
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also seasonally contribute to coastal flooding (Ruggiero, 2013), but are not generally measured
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by water level gauges (Hoeke et al., 2013) or associated with nuisance tidal flooding.
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Annual Variance, MSL Characteristics and Attribution to Threshold Exceedances
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Location-specific differences in annual variance are evidenced in probability densities of hourly
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(Figure 5a) and daily maximum (Figure 5b) water levels for 2006-2010. The probability
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densities, shown here and throughout our study unless otherwise noted, are constructed using a
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nonparametric kernel density estimator with location-specific optimized bandwidths between
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0.04 and 0.08. Hourly water level variance (2006-2010 values, Table 1) is dominated by, and
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scales linearly with the great diurnal tidal range (GT), defined as the difference between MHHW
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and MLLW (Figure 5c). The shapes of the hourly probability densities reflect the tide-cycle
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characteristics. For instance, San Francisco has a large mixed tide (two highs and two lows that
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are unequal in magnitude) range, a wide hourly density and less probability of exposure to water
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levels above MHHW. On the other hand, Galveston (and much of the Gulf of Mexico Coast)
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with its small diurnal (one high and one low tide a day) tide range and normal-like distribution
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has the narrowest hourly density and higher probability of exceeding MHHW. The distributions
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of daily maximum water levels are similar and approximately Gaussian with higher probabilities
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in the tail at locations that experience large storm surges such as the Battery in New York City
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(Figure 5b). The annual series of hourly water level variance (Figure 6b) do reveal time-varying
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patterns associated with the 18.6-year lunar nodal cycle. However, time series of annual hourly
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and daily maximum water level variances (not shown) are effectively trend-stationary and
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similar to the findings of Zhang et al. (2000) for the U.S. East Coast over the 20th century, which
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suggests that exceedance increases (Figure 4) are not directly forced by storminess trends.
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On the other hand, annual MSL time series in Figure 6a show large increases over time. Long-
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term RSLR trends in Table 1 are computed using annual MSL, with linear coefficients above the
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95% significance level (p-value < 0.05) and are consistent with the official NOAA RSLR trends
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(http://tidesandcurrents.noaa.gov/sltrends/sltrends). A measure of interannual MSL variability is
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inferred through the R2 values, with low values indicating higher variability along the West
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Coast and Honolulu largely due to ENSO and PDO influences. RSLR trends with asterisks in
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Table 1 signify locations with significant acceleration (coefficients – not shown – above the 95%
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significance level accounting for serial autocorrelation as described in Zervas (2009)) occurring
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since 1950 in their annual MSL. These stations are located along the upper Mid-Atlantic Coast
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where the inception of exponential growth in annual threshold exceedances initiated within the
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last few decades (Table 3).
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In order to quantify the relative contribution of variance and MSL to annual exceedances above
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the nuisance level over time, we fit multi-year series of daily maximum water level with a
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normal PDF defined by:
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(4) 𝑓(𝑤, 𝜇, 𝜎) =
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1
𝜎√2𝜋
𝑒
(𝑤−𝜇)2
2𝜎2
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where 𝑓 is the probability density at a water level height, 𝑤, and µ and σ2 are the mean and the
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variance of the distribution, respectively. The probability of exceedance (P) at a particular water
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level, 𝑤 is defined as 1 – CDF, where the CDF of the normal distribution is defined as:
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𝑤−𝜇
(5) 𝑃(𝑤, 𝜇, 𝜎) = 1/2 [1 + erf (
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𝜎 √2
)]
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with the parameters the same as in equation (4) and erf is the error function. In Figure 6e we
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show the PDFs and in Figure 6f the probability of exceedance for the 1956-1960 and 2006-2010
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periods at Norfolk with the nuisance flood level highlighted. The mean and variance of the PDF
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(both in meters) are listed above Figure 6e and 6f as are the number of estimated annual nuisance
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flood days (P*365 days) on average during 1956-1960 (0.1 day) and 2006-2010 (5.8 days).
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Readily apparent is the large change in the mean of the distribution between these periods from
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RSLR with only a small change in variance. Using the variance value from 2006-2010 (0.044)
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and the mean from 1956-1960 (-0.141) provides an estimate of 0.3 nuisance flood days and
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readily confirms that RSLR is the major factor involved in the large exceedance increases
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observed over this time period (Table 1).
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We provide further evidence that RSLR is the major factor as compared to variance driving the
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increases in nuisance flood days in Figure 6c and Figure 6d where annual MSL and annual
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variance of daily maximum water levels, respectively, are regressed against observed annual
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daily exceedances above a 0.3 m and 0.5 m MHHW threshold at New York City and San
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Francisco over 1950-2013. The regressions using annual MSL are fit with a quadratic model
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(except for La Jolla, which uses a linear fit) whereas fits for annual variance are all linear (all
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significant at the 95% level; p-value < 0.05) with R2 indicated. In all cases, the amount of the
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annual exceedance variation (R2) partially explained by annual MSL is much higher than by
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annual variance. In Table 1 under the “Attribution” heading, the R2 values are listed from
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quadratic fits between annual MSL and annual exceedances above 0.3 m MHHW for all
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locations. The next column (MSL, Var) lists the total variation in annual exceedances explained
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(R2) from multiple quadratic regression (not necessarily significant at the 95% level) using both
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annual MSL and variance. In all cases it can be seen that annual MSL is the leading factor
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driving the growth of annual exceedances in time.
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Exceedance Acceleration Patterns
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Sweet et al. (2014) noted an inverse linear relationship (R2 = 0.59) between acceleration rates of
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annual nuisance flood days and nuisance flood elevation thresholds along the U.S. East and Gulf
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Coasts. Here, we generalize and extend that relationship through quantification of the hourly
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annual exceedance acceleration over a range of common elevation thresholds. Figure 7a shows
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acceleration coefficients of equation (3) (> 90% significance level; p-value < 0.1) for hourly
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exceedances above elevation thresholds from MHHW to 0.6 m above MHHW. Acceleration
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coefficients are larger at locations with smaller variance (Table 1) and/or tide range (Figure 5c).
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For instance, Galveston, Port Isabel, Annapolis, Baltimore, Montauk, Norfolk, which have more
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tightly bound hourly probability (e.g., Galveston in Figure 5a) have higher acceleration
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coefficients for elevations ≤ 0.3 m associated with steeper probability of exceedance (1-CDF)
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curves across these elevations (e.g., Norfolk versus New York City in Figure 9).
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Above, we show that increasing MSL (RSLR) is the leading factor causing annual exceedances
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(nuisance and other threshold levels) to increase in time since variance changes are essentially
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trend-steady. Also, where the annual exceedance rates are accelerating, they are higher at
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elevation thresholds nearer MHHW at locations with smaller tide range/variance. In Figure 7b-d
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we investigate the relative influence of differing rates of RSLR with respect to tide range upon
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annual exceedance acceleration rates. RSLR rates exhibits a direct positive relationship to
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hourly acceleration coefficients (hours/year2) for exceedances above the 0.1 and 0.3 m threshold
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(Figure 7b), supporting the findings of Ezer and Atkinson (2014) who detected the highest
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acceleration in flooding hours for a 0.3 m threshold above MHHW at locations with higher
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RSLR rates. Unique to this study is quantification of tidal range and its nonlinear relationship to
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threshold exceedance rates, which allows for an improved estimate of annual acceleration for
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minor/nuisance-level thresholds (Figure 7c). The coupled importance of both RSLR rates and
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tidal range in relation to acceleration in annual hourly exceedance rates (i.e., Figure 7a), can be
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expressed through multiple quadratic regression:
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(6) 𝑏2_ℎ𝑜𝑢𝑟𝑠 = 𝑏2(𝐺𝑇) 𝐺𝑇 2 + 𝑏2(𝑅𝑆𝐿𝑅) 𝑅𝑆𝐿𝑅2 + 𝑏1(𝐺𝑇) 𝐺𝑇 + 𝑏1(𝑅𝑆𝐿𝑅) 𝑅𝑆𝐿𝑅 +
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𝑏1(𝐺𝑇,𝑅𝑆𝐿𝑅) 𝐺𝑇 ∗ 𝑅𝑆𝐿𝑅 + 𝑏0
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where b2_hours is the acceleration coefficient (hours/year2) from equation (3) with values plotted in
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Figure 7a, GT is the great diurnal tidal range over the 1983-2001 tidal epoch and available online
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(http://tidesandcurrents.noaa.gov), RSLR are the linear MSL trends in Table 1 and b0, b1 and b2
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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, ENSO’s 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) 𝐸(𝑡) = 𝑏2 𝑡 2 + 𝑏2(𝐶𝐼) 𝐶𝐼 2 + 𝑏1 𝑡 + 𝑏1(𝐶𝐼) 𝐶𝐼 + 𝑏1,𝐶𝐼 𝑡𝐶𝐼 + 𝑏0
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 τ (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
community’s 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 location’s 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 location’s 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 2081–2100 of 1.9–2.3 C, 2.0–3.6 C,
459
and 3.2–5.4 C above 1850–1900 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 (5–95%) estimates of 0.5 m
464
(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)
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 today’s 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 – 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 reviewer’s 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
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