# Assessing Coastal Road Flood Risk in Arctic Alaska, a Case Study from Hooper Bay

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Goals and Objectives

^{−1}) x consequences (USD). However, given the model-based flood exposure available to us, we chose to directly tie probability and consequences to flood exposure. Fourth, we estimate the total community road flooding protection costs for 2020–2050 for three possible mitigation approaches. The fourth objective allows us to assess the efficacy of the flood-rise estimate produced under the third objective.

## 3. Materials and Methods

#### 3.1. Objective 1: Determine the Road Flood Exposure of Hooper Bay in Different SLR Scenarios

#### 3.1.1. Storm Modeling

#### 3.1.2. Return Period Calculation

_{T}is the total number of storm events during the period of observation. For this study, it is assumed that we have analyzed all major storms between 1992 and 2011: N

_{T}is the number of storms (9). Constants α and $\beta $ are defined by the assumed distribution, according to Table 1 below. These constants require definition of the shape parameter k for the Fréchet and Weibull distributions. For this analysis, k values of 2.5, 3.33, 5, and 10 were tested for the Fréchet distribution, and of 0.75, 1, 1.4, and 2 were tested for the Weibull distribution, with the fixed values recommended by Goda.

_{(m)}, we calculate the reduced variate (the flooded area expected to have the calculated non-exceedance value for each distribution). The correlation between the peak water level in a given storm (x

_{(m)}) and the reduced variate values (y

_{(m)}) is calculated, with the correlation closest to 1 indicating the best-fitting distribution.

_{(m)}data vs. the reduced variate y

_{(m)}data for the Weibull distribution and creating a trend line with Equation (2).

^{2}is 0.92.

#### 3.1.3. Flood Mapping

#### 3.1.4. Annual Flood Exposure

#### 3.2. Objective 2: Approximate the Unit Cost of Road Flood Exposure (USD/km hr) from the Hooper Bay Airport Improvements Project Access Road Elevation from 2020–2050

#### 3.3. Objective 3: Estimate the Total Community Road Flooding Protection Costs for 2020–2050 for Three Possible Mitigation Approaches and Compare Them

#### 3.3.1. Rough Design of Mitigation Measures

#### 3.3.2. Cost Estimation of Mitigation Measures

#### 3.3.3. AFE following Mitigation Measures

## 4. Results

#### 4.1. Objective 1 Results: Determine the Road Flood Exposure of Hooper Bay in Different Sea Level Rise Scenarios

#### 4.1.1. Return Period Analysis Results

^{2}correlation values for the return-period analysis are summarized in Table 5.

^{2}value of 0.92, scale parameter A of 0.87, and location parameter B of 2.9. Applying this distribution results in the flood extent return periods summarized in Table 6. Also included is the Chapman 2009 storm ranking, based on storm surge heights between 1954 and 2004, for storms that both studies shared.

#### 4.1.2. Annual Flood Exposure

#### 4.2. Objective 2 Results: Approximate the Unit Cost of Road Flood Exposure (USD/km hr) from the Hooper Bay Airport Improvements Project across Road Elevation form 2020–2050

#### 4.3. Objective 3 Results: Estimate the Total Community Road Flooding Protection Costs for 2020–2050 for Three Possible Mitigation Approaches and Compare Them

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Distribution | α | β | Reduced Variate Equation |
---|---|---|---|

Gumbel | 0.44 | 0.12 | y_{(m)} = −ln[−ln(F_{(m)})] |

Fréchet | 0.4 4+ 0.52/k | 0.12 − 0.11/k | y_{(m)} = k[(−ln(F_{(m)})^{−1/k}−1] |

Weibull | $0.2+0.27/\sqrt{k}$ | $0.2+0.23/\sqrt{k}$ | y_{(m)} = [−ln(1−F_{(m)})]^{1/k} |

Constant | Value or Equation |
---|---|

a_{1} | 2.24 |

a_{2} | 11.4 |

$\kappa $ | 1.34 |

c | 0.5 |

$\alpha $ | 0.54 |

$\nu $ | 1 |

a | ${a}_{1}\mathrm{exp}[{a}_{2}{N}^{-1.3}+\kappa {\left(-\mathrm{ln}\nu \right)}^{2}]$ |

Name | Latitude (Y, deg) | Longitude (X, deg) | Estimated Road Length (m) |
---|---|---|---|

Obs 1 | 61.51978 | −166.13460 | 375 |

Obs 2 | 61.5218901 | −166.1278690 | 375 |

Obs 3 | 61.523828 | −166.1215510 | 375 |

Obs 4 | 61.5251258 | −166.1171688 | 375 |

Obs 5 | 61.5284810 | −166.1059030 | 10 |

Obs 6 | 61.5291370 | −166.104405 | 100 |

Obs 7 | 61.5297640 | −166.103379 | 100 |

Obs 8 | 61.530556 | 166.103056 | 215 |

Obs 9 | 61.524471 | −166.104426 | 140 |

Obs 10 | 61.525671 | −166.094672 | 130 |

Obs 11 | 61.528566 | −166.116316 | 100 |

Obs 12 | 61.530628 | −166.097743 | 330 |

Obs 13 | 61.529957 | −166.094571 | 220 |

Obs 14 | 61.531475 | −166.094842 | 390 |

Obs 15 | 61.532585 | −166.098755 | 220 |

Obs 16 | 61.532774 | −166.103008 | 100 |

Observation Point | Elevation Added (m) |
---|---|

6 | 0.5 |

7 | 1.1 |

8 | 1.1 |

9 | 0.3 |

10 | 0.7 |

11 | 0.5 |

12 | 0.9 |

13 | 2.7 |

14 | 1.1 |

15 | 0.9 |

16 | 0.9 |

Distribution | k | R^{2} |
---|---|---|

Weibull | 2.0 | 0.92 |

Gumbel | n/a | 0.89 |

Weibull | 1.4 | 0.87 |

Fréchet | 10 | 0.85 |

Weibull | 1.0 | 0.79 |

Fréchet | 5.0 | 0.79 |

Fréchet | 3.33 | 0.72 |

Weibull | 0.75 | 0.68 |

Fréchet | 2.5 | 0.65 |

Storm | Max Water Level (m) | Return Period (Years) | Chapman Results (Storm Surge Height) | |
---|---|---|---|---|

Ranking | Return Period (Years) | |||

September 2005 | 4.17 | 17.21 | ||

November 1996 | 4.13 | 15.00 | 4 | 10 |

October 1995 | 4.12 | 14.45 | 3 | 11 |

October 1992 | 3.76 | 5.57 | 2 | 13 |

October 2004 | 3.62 | 4.19 | 1 | 15 |

November 2011 | 3.53 | 3.54 | ||

October 2006 A | 3.35 | 2.76 | ||

October 2006 B | 3.35 | 2.74 | ||

October 1996 | 3.06 | 2.18 | 5 | 7 |

SLR Scenario | Baseline | 30 cm | 60 cm | 90 cm | 120 cm |
---|---|---|---|---|---|

Prior to Elevation | |||||

All observation points | 20.6 | 32.1 | 74.3 | 98.2 | 119.5 |

Access road only (1–4) | 6.8 | 12.3 | 35.6 | 44.7 | 51.3 |

Access road excluded (5–16) | 13.7 | 19.8 | 38.7 | 53.5 | 68.2 |

Post elevation | |||||

All observation points | 13.8 | 20.0 | 40.0 | 57.6 | 79.0 |

Access road only (1–4) | 0.0 | 0.2 | 1.3 | 4.1 | 6.6 |

Cost of the elevation project (USD 2020) | 7,998,500 |

Years of effective protection | 30 |

Average annual flood exposure (km h/year) | 9.57 |

Unit cost of flood exposure (USD/km h) | 27,873 |

Estimated AFE, SLR Scenarios (km h/year) | ||||||
---|---|---|---|---|---|---|

Measure | Cost (USD 2020) | Baseline | 30 | 60 | 90 | 120 |

Do Nothing | 0 | 13.7 | 19.8 | 38.7 | 53.5 | 68.2 |

Elevate Roads | 9,804,600 | 0.0 | 0.0 | 0.9 | 2.6 | 6.7 |

Roadside Dike | 8,334,400 | 0.0 | 0.0 | - | - | - |

Large Dike | 8,429,800 | 0.0 | 0.0 | - | - | - |

Relocate | 272,540,000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

Estimated AFE, SLR Scenarios (km h/year) | ||||||
---|---|---|---|---|---|---|

Measure | Cost (USD 2020) | Baseline | 30 | 60 | 90 | 120 |

Do Nothing | 0 | 13.8 | 20.0 | 40.0 | 57.6 | 79.0 |

Elevate Roads | 9,804,600 | 0.0 | 0.2 | 2.2 | 6.7 | 13.3 |

Roadside Dike | 8,334,400 | 0.0 | 0.2 | - | - | - |

Large Dike | 8,429,800 | 0.0 | 0.2 | - | - | - |

Relocate | 272,540,000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

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## Share and Cite

**MDPI and ACS Style**

Miller, A.C.; Ravens, T.M.
Assessing Coastal Road Flood Risk in Arctic Alaska, a Case Study from Hooper Bay. *J. Mar. Sci. Eng.* **2022**, *10*, 406.
https://doi.org/10.3390/jmse10030406

**AMA Style**

Miller AC, Ravens TM.
Assessing Coastal Road Flood Risk in Arctic Alaska, a Case Study from Hooper Bay. *Journal of Marine Science and Engineering*. 2022; 10(3):406.
https://doi.org/10.3390/jmse10030406

**Chicago/Turabian Style**

Miller, Anna Christina, and Thomas Michael Ravens.
2022. "Assessing Coastal Road Flood Risk in Arctic Alaska, a Case Study from Hooper Bay" *Journal of Marine Science and Engineering* 10, no. 3: 406.
https://doi.org/10.3390/jmse10030406