# Flood Mapping Uncertainty from a Restoration Perspective: A Practical Case Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Site Location

#### 2.2. Digital Elevation Model

#### 2.3. Bathymetric Adjustments

#### 2.4. Rating Curve

#### 2.4.1. Rating Curve Function

#### 2.4.2. Synthetic Stage–Discharge Data

^{3}/s were used. Based on test simulations and field data, the Manning coefficient was set to 0.034 for the channel and 0.04 for the banks. Figure 4 presents a profile of the simulated reach with an indication of the location used as a reference to derive the rating curve.

#### 2.5. Frequency Analysis

#### 2.5.1. Generalized Extreme Values (GEV) Function

_{p}quantile associated with a discharge and its exceedance probability (p) can be computed by the following expressions.

#### 2.5.2. Extreme Flow Data and Drainage Area Correction Factor

_{max}) time series at this location was used to compose the extreme value time series. The drainage area at the reference flow gauge is 512.8 km

^{2}, while the drainage area at the study reach is 173.5 km

^{2}. Figure 6 shows both drainage areas.

_{max}).

#### 2.6. Bayesian Model

#### 2.6.1. Bayesian Rating Curve Model

#### 2.6.2. Fully Bayesian Model

#### 2.6.3. Markov Chain Monte Carlo Simulations

#### 2.7. HEC-RAS Model Set-Up

## 3. Results

#### 3.1. Results of the Synthetic Rating Curve

^{3}/s while the respective elevations are between 308.64 and 310.29 m, a change of 1.65 m. Based on the field survey and the hydraulic simulations, this is considered a reasonable water level oscillation for the magnitude of the simulated discharges and should be confined to the channel banks. The range of discharges was defined to simulate a possible real-world flow measurement interval since extreme flow measurements are not usually collected. This necessitates the need to extrapolate the rating curve when performing the frequency analysis study.

#### 3.2. Results of the Extreme Data Time Series at the Study Site

^{3}/s) of the time with the one that is maintained 99% of the time (1.0 m

^{3}/s). The former is more than four times greater than the latter.

#### 3.3. Results of the Bayesian Approach

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Annual maximum mean daily discharges and associated stages at the rating curve cross-section.

Q USGS (m^{3}/s) | Q Site (m^{3}/s) | H_{max} (m) | Year | Q USGS (m^{3}/s) | Q Site (m^{3}/s) | H_{max} (m) | Year |
---|---|---|---|---|---|---|---|

196.24 | 66.40 | 309.56 | 1924 | 81.27 | 27.50 | 309.08 | 1961 |

194.25 | 65.73 | 309.56 | 1925 | 81.84 | 27.69 | 309.08 | 1962 |

129.41 | 43.79 | 309.30 | 1926 | 110.15 | 37.27 | 309.22 | 1963 |

138.75 | 46.95 | 309.34 | 1927 | 92.03 | 31.14 | 309.13 | 1964 |

107.60 | 36.41 | 309.21 | 1928 | 40.21 | 13.61 | 308.82 | 1965 |

104.21 | 35.26 | 309.19 | 1929 | 78.15 | 26.45 | 309.06 | 1966 |

156.59 | 52.99 | 309.42 | 1930 | 100.24 | 33.92 | 309.17 | 1967 |

77.59 | 26.25 | 309.06 | 1931 | 114.40 | 38.71 | 309.24 | 1968 |

113.55 | 38.42 | 309.23 | 1932 | 136.20 | 46.09 | 309.33 | 1969 |

144.70 | 48.96 | 309.37 | 1933 | 94.01 | 31.81 | 309.14 | 1970 |

65.41 | 22.13 | 308.99 | 1934 | 70.23 | 23.76 | 309.02 | 1971 |

66.83 | 22.61 | 309.00 | 1935 | 155.18 | 52.51 | 309.41 | 1972 |

201.05 | 68.03 | 309.58 | 1936 | 110.15 | 37.27 | 309.22 | 1973 |

147.81 | 50.02 | 309.38 | 1937 | 89.76 | 30.37 | 309.12 | 1974 |

221.72 | 75.03 | 309.65 | 1938 | 71.92 | 24.34 | 309.02 | 1975 |

85.80 | 29.03 | 309.10 | 1939 | 88.63 | 29.99 | 309.11 | 1976 |

112.70 | 38.14 | 309.23 | 1940 | 138.19 | 46.76 | 309.34 | 1977 |

105.91 | 35.84 | 309.20 | 1941 | 92.03 | 31.14 | 309.13 | 1978 |

101.09 | 34.21 | 309.18 | 1942 | 186.89 | 63.24 | 309.53 | 1979 |

100.81 | 34.11 | 309.17 | 1943 | 106.19 | 35.93 | 309.20 | 1980 |

96.28 | 32.58 | 309.15 | 1944 | 108.45 | 36.70 | 309.21 | 1981 |

141.02 | 47.72 | 309.35 | 1945 | 147.53 | 49.92 | 309.38 | 1982 |

53.52 | 18.11 | 308.91 | 1946 | 171.88 | 58.16 | 309.47 | 1983 |

146.96 | 49.73 | 309.38 | 1947 | 150.65 | 50.98 | 309.39 | 1984 |

232.20 | 78.57 | 309.68 | 1948 | 66.54 | 22.52 | 308.99 | 1985 |

123.18 | 41.68 | 309.28 | 1949 | 74.19 | 25.10 | 309.04 | 1986 |

96.28 | 32.58 | 309.15 | 1950 | 159.14 | 53.85 | 309.43 | 1987 |

146.96 | 49.73 | 309.38 | 1951 | 163.95 | 55.48 | 309.44 | 1988 |

106.47 | 36.03 | 309.20 | 1952 | 110.15 | 37.27 | 309.22 | 1989 |

163.67 | 55.38 | 309.44 | 1953 | 104.49 | 35.36 | 309.19 | 1990 |

127.14 | 43.02 | 309.29 | 1954 | 98.83 | 33.44 | 309.17 | 1991 |

111.00 | 37.56 | 309.22 | 1955 | 113.27 | 38.33 | 309.23 | 1992 |

118.65 | 40.15 | 309.26 | 1956 | 159.99 | 54.14 | 309.43 | 1993 |

186.89 | 63.24 | 309.53 | 1957 | 119.78 | 40.53 | 309.26 | 1994 |

180.66 | 61.13 | 309.51 | 1958 | 104.21 | 35.26 | 309.19 | 1995 |

121.20 | 41.01 | 309.27 | 1959 | 131.96 | 44.65 | 309.31 | 1996 |

125.73 | 42.54 | 309.29 | 1960 | 175.85 | 59.50 | 309.49 | 1997 |

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**Figure 3.**Cross-section XS4 (Station 33.98035): (

**a**) comparison between field survey (continuous red line) and DEM (continuous blue line with dots); and (

**b**) resulting cross-section after combining field survey and DEM data.

**Figure 4.**Reach profile with the indication of the surveyed cross-sections and the location of the cross-section used as reference to derive the rating curve.

**Figure 10.**Posteriors distributions for the rating curve parameters and their 95% credible interval.

**Figure 13.**Flood maps and the 95% credible interval for the return periods: 3 years (

**a**); 100 years (

**b**); 1000 years (

**c**); and 10,000 years (

**d**).

**Table 1.**Mean discharges and the thresholds for 2.5% and 97.5% credibility quantiles considering different return periods (RP).

RP | Q (m^{3}/s) 2.5% | Q (m^{3}/s) Med | Q (m^{3}/s) 97.5% |
---|---|---|---|

3 | 41.78 | 44.97 | 48.57 |

100 | 77 | 83.61 | 90.47 |

1000 | 97.22 | 106.76 | 120.98 |

10000 | 105.53 | 129.67 | 161.72 |

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Rampinelli, C.G.; Knack, I.; Smith, T. Flood Mapping Uncertainty from a Restoration Perspective: A Practical Case Study. *Water* **2020**, *12*, 1948.
https://doi.org/10.3390/w12071948

**AMA Style**

Rampinelli CG, Knack I, Smith T. Flood Mapping Uncertainty from a Restoration Perspective: A Practical Case Study. *Water*. 2020; 12(7):1948.
https://doi.org/10.3390/w12071948

**Chicago/Turabian Style**

Rampinelli, Cássio G., Ian Knack, and Tyler Smith. 2020. "Flood Mapping Uncertainty from a Restoration Perspective: A Practical Case Study" *Water* 12, no. 7: 1948.
https://doi.org/10.3390/w12071948