# The Impact of Uncertainties in Ice Sheet Dynamics on Sea-Level Allowances at Tide Gauge Locations

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## Abstract

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## 1. Introduction

## 2. Data and Methodology

#### 2.1. Uncertainty Distributions of Sea-Level Change

#### 2.2. The Statistics of Sea-Level Extremes

^{®}evfit (Mathworks, Natick, MA, USA) function, as described in Hunter et al. [26]. In a comparison of the Gumbel scale parameters obtained from the evfit method to the ismev method as used in Hunter [9] (both methods are extensively described in Hunter et al. [26]), we found that the results are very similar to the extent required for the present analysis and we therefore use the values from the Matlab

^{®}evfit method only. We select all tide gauge records that contain at least 20 years of data and where each year with data is more than 75% complete (Figure 3), which yields a data set of 658 records. Following Hunter et al. [26], we reject four stations that show significant non-Gumbel behaviour, and also leave out two Hudson Bay tide gauges (Canada) as we do not have sea-level projections available there. This leaves 652 records, of which 448 records have ≥30 years of data available, 319 records ≥40 years, 164 records ≥50 years and 94 records ≥60 years.

#### 2.3. Allowances Methodology

## 3. Results

#### 3.1. Sea-Level Projections for 2010–2100

#### 3.2. Allowances for Different Uncertainty Distributions

#### 3.3. Changes in the Frequency of Extreme Events

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

AR5 | Fifth Assessment Report |

CMIP5 | 5th phase of the Climate Model Intercomparison Project |

EAIS | East Antarctic Ice Sheet |

GESLA-2 | Global Extreme Sea Level Analysis Version 2 |

GRIS | Greenland Ice Sheet |

IPCC | Intergovernmental Panel on Climate Change |

RCP | Representative Concentration Pathway |

SLR | Sea-Level Rise |

WAIS | West Antarctic Ice Sheet |

## Appendix A. SEAWISE Methodology

**Figure A1.**An example showing the SEAWISE methodology which step-wise combines different uncertainty distributions into a final uncertainty distribution ${P}_{combined3}$. All y-axes are probability density (dimensionless). This example is for a grid point off the Canadian coast (290W-67N), using the VW15 scenario for the ice sheet dynamics contributions. P(Non-Ice Dynamic SLR) contains the contributions from glaciers, ocean density variations and ocean dynamics, ice sheet surface mass balance, groundwater extraction and glacial isostatic adjustment [12].

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**Figure 1.**The three scenarios for ice sheet dynamics contributions to sea-level rise used in this study, for (

**a**) Greenland, (

**b**) West Antarctica and (

**c**) East Antarctica (cumulative m sea-level change between 2010–2100). Original uncertainty distributions in solid lines, medians in vertical lines, shifted uncertainty distributions (where all medians match the IPCC medians) in dashed lines.

**Figure 2.**Four examples of tide gauge records: (

**a**) Barcelona, (

**b**) Delfzijl, (

**c**) Gan, (

**d**) Willapa Bay. Hourly data (in blue) and their annual maximum values (red) for 2000–2010 (m), where the mean of each time series has been removed. $\lambda =$ the Gumbel scale parameter (m). Locations are indicated in Figure 5a by their first letter.

**Figure 3.**(

**left**) Gumbel scale parameters (m) at 652 tide gauge stations and (

**right**) a zoom on the European region.

**Figure 4.**Example of a skewed sea-level uncertainty distribution (black), broken down into a set of four normal distributions (blue), which together describe the original distribution best (red dash).

**Figure 5.**Projected cumulative sea-level change (m) for 2010–2100; median (left column) and 95th percentile (right column). All projections have the same median for the projected individual dynamical ice sheet contributions to SLR but a different shape of the uncertainty distribution. (

**a**) IPCC; (

**b**) VW15; (

**c**) R15. The locations of the tide gauges in Figure 2 are indicated in (

**a**) by their first letter.

**Figure 6.**Allowances (m) for 2100 (left column), Allowances minus global mean SLR (middle column, m) and Allowances minus local SLR (right column, m), using 2010–2100 sea-level change projections, all projections have the same median for the projected dynamical ice sheet contributions to SLR but a different shape of the uncertainty distribution. (

**a**) IPCC; (

**b**) VW15; (

**c**) R15.

**Figure 8.**Scatter of 2010–2100 change in sea level (m) median (left column) and 95th percentile (right column) vs. the Gumbel scale parameter (m), colourscale indicating allowance (m), for the three scenarios (

**a**) IPCC; (

**b**) VW15; (

**c**) R15.

**Figure 9.**Ratio of the change in the frequency of extreme events (2100 vs. 2010) if allowances are not applied, based on the (

**a**) IPCC (

**b**) VW15 and (

**c**) R15 sea-level change scenario. Note the logarithmic scale. A limit of ${10}^{4}$ has been imposed, as frequency increases above this level mean that a coastal structure effectively would be lost if no allowance is applied.

**Table 1.**Percentage (number) of tide gauge stations for every ${10}^{n}$ increase in the frequency of extreme events by 2100 per ice sheet scenario IPCC, VW15 and R15).

${\mathbf{10}}^{\mathit{n}}$ | IPCC | VW15 | R15 |
---|---|---|---|

0–1 | 1% (6) | 0% (2) | 1% (6) |

1–2 | 11% (73) | 1% (9) | 10% (67) |

2–3 | 21% (139) | 6% (37) | 21% (136) |

3–4 | 17% (109) | 6% (39) | 16% (105) |

>4 | 50% (325) | 87% (565) | 52% (338) |

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## Share and Cite

**MDPI and ACS Style**

Slangen, A.B.A.; Van de Wal, R.S.W.; Reerink, T.J.; De Winter, R.C.; Hunter, J.R.; Woodworth, P.L.; Edwards, T. The Impact of Uncertainties in Ice Sheet Dynamics on Sea-Level Allowances at Tide Gauge Locations. *J. Mar. Sci. Eng.* **2017**, *5*, 21.
https://doi.org/10.3390/jmse5020021

**AMA Style**

Slangen ABA, Van de Wal RSW, Reerink TJ, De Winter RC, Hunter JR, Woodworth PL, Edwards T. The Impact of Uncertainties in Ice Sheet Dynamics on Sea-Level Allowances at Tide Gauge Locations. *Journal of Marine Science and Engineering*. 2017; 5(2):21.
https://doi.org/10.3390/jmse5020021

**Chicago/Turabian Style**

Slangen, Aimée B. A., Roderik S. W. Van de Wal, Thomas J. Reerink, Renske C. De Winter, John R. Hunter, Philip L. Woodworth, and Tamsin Edwards. 2017. "The Impact of Uncertainties in Ice Sheet Dynamics on Sea-Level Allowances at Tide Gauge Locations" *Journal of Marine Science and Engineering* 5, no. 2: 21.
https://doi.org/10.3390/jmse5020021