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The authors have declared that no competing interests exist.

Rising sea levels increase the probability of future coastal flooding. Many decision-makers use risk analyses to inform the design of sea-level rise (SLR) adaptation strategies. These analyses are often silent on potentially relevant uncertainties. For example, some previous risk analyses use the expected, best, or large quantile (i.e., 90%) estimate of future SLR. Here, we use a case study to quantify and illustrate how neglecting SLR uncertainties can bias risk projections. Specifically, we focus on the future 100-yr (1% annual exceedance probability) coastal flood height (storm surge including SLR) in the year 2100 in the San Francisco Bay area. We find that accounting for uncertainty in future SLR increases the return level (the height associated with a probability of occurrence) by half a meter from roughly 2.2 to 2.7 m, compared to using the mean sea-level projection. Accounting for this uncertainty also changes the shape of the relationship between the return period (the inverse probability that an event of interest will occur) and the return level. For instance, incorporating uncertainties shortens the return period associated with the 2.2 m return level from a 100-yr to roughly a 7-yr return period (∼15% probability). Additionally, accounting for this uncertainty doubles the area at risk of flooding (the area to be flooded under a certain height; e.g., the 100-yr flood height) in San Francisco. These results indicate that the method of accounting for future SLR can have considerable impacts on the design of flood risk management strategies.

The warming climate is causing sea levels to rise around the globe [

Future projections of sea-level rise (SLR) are deeply uncertain [

Many studies evaluate potential future flood risks (e.g., [

We demonstrate the effect of accounting for uncertainty in the SFB area of California. We choose California as an area of interest, because California has more than 2,000 miles of coastline with roughly 32 million people living in coastal watershed counties [

The black dots represent the monthly mean sea level at the SFB tide gauge [

To demonstrate the effect of representing SLR uncertainty, we approximate the methods found in an existing analysis of the California coastline [_{0},

Following a Bayesian approach (as described in detail in [_{t} as the sum of the semi-empirical model simulations _{t}, residuals _{t} (i.e., approximating the effects of unresolved internal variability and model error), and observation errors _{t},
_{t} is a stationary first-order autoregressive process. It is characterized by an annual autoregression coefficient _{t} with zero mean and constant variance _{t} represents the observation errors (also known as measurement errors) with time-varying known variance _{0}, and _{0}) and the statistical parameters (_{AR1}) with uniform prior distributions using the Markov chain Monte Carlo method and the Metropolis Hastings algorithm [^{7} iterations. We assess convergence using visual inspection and the potential scale reduction factor [^{4} for the analysis [

We approximate the baseline (current) 100-yr (i.e., the 1-in-100 year) storm surge for the SFB area using a Generalized Extreme Value (GEV) analysis [

Shown are (panel a) the maximum recorded sea-level anomaly in a year, the annual block maxima, and (panel b) the return levels for the San Francisco Bay tide gauge (in meters).

We approximate the potential future 100-yr flood height (storm surge including SLR) by accounting for the mean sea-level anomaly and SLR uncertainty in the year 2100. For the 100-yr flood height accounting for mean SLR, we add the mean sea-level anomaly (compared to the year 2000) to the baseline 100-yr storm surge. We use several steps to approximate the effects of future SLR uncertainty, extrapolate a flood survival function, and approximate the 100-yr flood height accounting for SLR uncertainty. First, we add each SLR estimate from the distribution for the year 2100 to the baseline survival function. This results in 2 × 10^{4} simulations of the future flood survival function (shown as the gray lines in ^{4} probability estimates for a specific flood height. We then average the 2 × 10^{4} probability estimates for a specific flood height to approximate the actual probability for that return level. We replicate this process of estimating the return period for a range of flood heights from 1.1–3.3 m (see Caveats). This method produces a new flood survival function where the return level corresponding to a 1% probability of occurring in the year 2100 is taken to be the 100-yr flood height accounting for SLR uncertainty (the dark red curve and point in

In panel a, the dark red line represents the sea-level distribution in the year 2100, whereas, the orange and red points display the mean and Heberger et al. [

We assess the area at risk of flooding (the area to be flooded under a certain height; e.g., the 100-yr flood height) with a geographic information system (ESRI ArcGIS Desktop) using 1/9-arc second (nominal resolution of ∼3 m) topobathy digital elevation models [

Future changes in sea level increase the return level for the 100-yr flood height in the SFB area. Our application of the global mean sea-level model [

Accounting for mean SLR underestimates the probability of flood occurrence in this specific case study. When we consider just the mean SLR, the 100-yr return period occurs at 2.2 m. If we account for the 90% SLR, the 100-yr return period occurs at 2.5 m (

Our results are broadly consistent with some previous findings (e.g., [^{4} values) and repeat the process for multiple flood heights to produce a new survival function accounting for uncertainty. For the example, consider using three samples from the SLR distribution (i.e., the mean SLR—1 standard deviation, the mean SLR, and the mean SLR + 1 standard deviation). Adding those sea-level values to the baseline storm surge survival function results in three new survival functions with 100-yr flood heights of roughly 2.0, 2.2, and 2.5 m (^{−6} (mean SLR—1 standard deviation), 0.01 (mean SLR) and 0.4 (mean SLR + 1 standard deviation). The results from averaging the three samples produces a higher return period for a specific flood height when compared to estimates that neglect uncertainty (i.e., accounting for the mean estimate). In this specific case, the probability of flood occurrence at the 2.2 m flood height when considering uncertainty shortens the return period from a 100-yr to a roughly 7-yr return period (

These underestimated flood occurrences are due to the fact that accounting for the full distribution changes the shape of the survival function. We create a simple test to further investigate how incorporating the full distribution affects the survival function. For instance, we compare how the shape and characteristics of the SLR distribution impact the results by comparing our SLR distribution to a normal, log normal, and Pareto distribution (

Relatively small changes in the return level can impact adaptation strategies [^{2} at risk of flooding (^{2} (using the mean SLR estimate) and roughly 8.0 km^{2} (accounting for uncertain SLR). In comparison, accounting for SLR uncertainty increases the mean SLR flood risk area by roughly a factor of 2 (

The gray area within the inset plot displays the area analyzed in this curve. The area in blue is water, whereas the area in tan is land. The dashed lines represent the elevation associated with the mean sea level (black), the baseline 100-yr storm surge (yellow), and the future 100-yr flood height (orange and dark red). The black curve displays the cumulative density or percentage of the area analyzed at elevations between -2–8 m. For example, ∼42% of the area analyzed has an elevation of 2.7 m (100-yr flood height accounting for uncertain sea-level rise) or lower.

The maps display the baseline 100-yr flood risk area in yellow. In the year 2100, the potential 100-yr flood height includes accounting for the mean sea-level projection (orange), the Heberger et al. [

100-yr Flood risk area in county subdivisions (sq.km) | ||||
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County subdivisions | Baseline storm surge | Flood height accounting for mean SLR | Flood height accounting for Heberger et al. 2009 SLR | Flood height accounting for SLR uncertainty |

1.6 | 3.9 | 5.5 | 8.0 | |

6.3 | 10.9 | 13.7 | 18.0 | |

1.9 | 6.4 | 8.4 | 11.2 |

We use relatively simple models and statistical methods to make a simple point. This simplicity is chosen to provide a hopefully transparent analysis. Yet, this simplicity requires us to make several approximations that lead to caveats and future research needs. For example, we neglect uncertainty associated with the GEV parameters. Additionally, we use a simple interpolation method to estimate the inverse of the survival function using the surrounding values when accounting for SLR uncertainty. If the return level value does not exist, then a value of zero is returned as the probability of flood occurrence. Due to the tight shape, the return level values with probabilities of flood occurrence below the 100,000-yr return period are assigned to have a zero probability of flood occurrence. A simple test suggests the impact of this approximation is relatively small, but can potentially lead to conservative estimates (

As sea levels rise, flood risks are projected to increase. Studies evaluating future flood risks are often silent on the impact of uncertainty in sea-level projections and instead consider the mean, best, or large quantile (i.e., 90%) estimate. We show how accounting for sea-level rise uncertainty can increase the area at risk of flooding and can increase the probability of flood occurrence. Using the San Francisco Bay area as an example, we demonstrate that these effects can be sizable. Specifically, we show how accounting for uncertainty increases the 100-yr return level by 0.5 m, shortens the return period from a 100-yr to a roughly 7-yr return period, changes the shape of the survival function, and roughly doubles the area at risk of flooding in San Francisco over using the mean sea-level rise estimate. Although, we use the San Francisco Bay area as an example the overall results are transferable to many regions and indicate that the method of accounting for sea-level rise can have considerable impacts on the design of flood risk management strategies.

Photograph of the tide gauge (bottom left corner) used in this study. Photograph by KL Ruckert on July 14, 2011.

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Panel a displays the probability density function of global mean sea-level rise in the year 2100 along with the mean ±1 standard deviation projections (green lines). In panel b, the baseline storm surge (light blue) is shifted by sea-level projections of 0.4 m (-1 standard deviation; light green), 0.6 m (mean; green), and 0.9 m (+1 standard deviation; dark green) to represent potential future flood height. The average of the three return periods at 2.2 m is represented as the black square. The pink star is produced when the return period below the 100,000-yr return period is approximated as zero and then averaged with the two other return periods at 2.2 m. Note that (panel b and c) the approximation method for the return period at 2.2 m produces the same return period value as the result from accounting for the return periods below 100,000 years and hence displays little to no flood risk over-or-underestimation.

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Panel a displays the probability density function (pdf) of our global mean sea-level rise in the year 2100 (dark red) along with the normal (light blue), log normal (blue), and Pareto (dark blue) distribution approximations of global mean sea-level rise in the year 2100. In panel b, the survival function accounting for each sea-level rise approximation (light to dark blue) is shown for comparison to the baseline storm surge (yellow) and the survival function accounting for our estimated empirical sea-level rise pdf (dark red).

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Each county subdivision (outlined in brown) is located within the analysis extent. In the analyzed area, the 100-yr flood risk area is displayed in yellow (baseline), orange (flood height accounting for the mean sea-level projection), red (flood height accounting for the Heberger et al. [

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The maps display the baseline 100-yr flood risk area in yellow. In the year 2100, the potential 100-yr flood height includes the addition of sea-level projections. The future 100-yr flood risk area based on the mean sea-level projection is in orange, based on the Heberger et al. [

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The maps display the baseline 100-yr flood risk area in yellow. In the year 2100, the potential 100-yr flood height includes the addition of sea-level projections based on the mean sea-level projection (orange), the Heberger et al. [

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The maps of Oakland, CA display the baseline 100-yr flood risk area in yellow. In the year 2100, the potential 100-yr flood height includes the addition of sea-level projections. The future 100-yr flood risk area based on the mean sea-level projection is in orange, based on the Heberger et al. [

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The maps of Alameda, CA display the baseline 100-yr flood risk area in yellow. In the year 2100, the potential 100-yr flood height includes the addition of sea-level projections based on the mean sea-level projection (orange), the Heberger et al. [

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This table was accessed and modified on 13 June 2016 from

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We thank Stefan Rahmstorf for providing his global sea-level model (