# Understanding Uncertainty in Probabilistic Floodplain Mapping in the Time of Climate Change

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}and flows through several cities in the Greater Toronto Area (GTA), including Brampton, Mississauga, and Toronto (Figure 1). The creek’s length is 33 km and is drained into Lake Ontario. About 5 km

^{2}of the watershed’s area is covered with parks, conservation areas and trails, while the rest of the watershed is almost completely urbanized. The Mimico Creek watershed is divided into a total of 70 sub-catchments (67 developed and 3 undeveloped), with areas ranging from 0.18 km

^{2}to 3.3 km

^{2}. The watershed includes 34 channels with lengths varying between 623 m to 2574 m, and slopes between 0.001 and 0.01.

#### 2.2. Data Requirements and Collection

## 3. Methodology

#### 3.1. Integrated Flood Modeling and Floodplain Mapping

#### 3.2. Hydrologic Modeling: HEC-HMS

#### 3.2.1. Hydrologic Model Calibration

#### 3.2.2. Sensitivity Analysis to Identify Uncertain Parameters

#### 3.3. Hydraulic Modeling: HEC-RAS

#### Sensitivity Analysis to Identify Uncertain Parameters

#### 3.4. Floodplain Mapping

#### 3.5. Probabilistic Floodplain Mapping: GLUE

## 4. Results

#### 4.1. Hydrologic Model Calibration

^{3}/s and 97.7 m

^{3}/s. Rainfall hyetographs corresponding to these events were used as the HEC-HMS model input. The model was linked with the OSTRICH framework in a MATLAB interface. The DDS single objective optimization algorithm with the objective function defined in Equation (1) was used with 5000 generations to obtain at least 500 behavioral solutions. Following obtaining the optimized set of parameters (the set that corresponds to the lowest value for the objective function) for each individual calibration storm, each set of parameters was used against the other calibration events. Then, performance of the storm simulation was measured. The results showed that four sets of the parameters perform considerably better than the other sets. These parameters’ sets correspond to event numbers 7, 13, 19 and 27 (Table 1). The set of parameters for these four events resulted in PFC less than 0.3, and NSE more than 0.5 for 7 out of 9 validation events (Table 2).

#### 4.2. Validation of the Hydrologic—Hydraulic Modeling to Generate Floodplain Maps

#### 4.3. Uncertainty Analysis

#### Identifying Sensitive Parameters in Hydrologic and Hydraulic Modeling

#### 4.4. Developing Floodplain Maps

#### 4.4.1. Probabilistic Floodplain Mapping Considering Different Uncertainties

#### 4.4.2. Future Probabilistic Floodplain Mapping under Climate Change

^{2}, while for the 2050s under RCP8.5, the average of potential flooding area for the 100-year event is increased to 4.76 km

^{2}. The predicted flood extents for 2050s under RCP8.5 based on different data sources (Figure 7b–d) are similar, but the flooding probability related to the non-stationary IDF is higher for the potential flood area than the other two scenarios, implying that the flood risk is greater when rainfall non-stationarity is fully accounted for. Figure 8 is the same as Figure 7 but for one example location from upstream. The same findings are observed, but the flooding probability difference between stationary and non-stationary scenarios is less significant for the upstream location. The increasing flood risk under climate change is also reflected by the increased water level as shown in Table 6. For the future period of the 2050s under RCP8.5, the mean water level is projected to rise 0.54–0.98 m (from different data sources, Figure 8b–d) compared with the current period for the upstream sample cross section, and is projected to rise 1.21–1.55 m for the downstream sample cross section. The water level increase is largest for the scenario of Figure 8d when non-stationary IDF is considered.

## 5. Concluding Remarks

^{2}compared to the baseline period, and the water depth for the selected upstream and downstream cross sections are projected to increase by 0.75 m and 1.43 m (average of future projection scenarios), respectively. The flooding probability related to non-stationary IDF is higher for the flood area compared with stationary IDF method, suggesting that flood risk is greater when rainfall non-stationarity is fully accounted for.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Mimico Creek watershed and location of the streamflow station (Mimico Creek at Islington) on the map of Ontario.

**Figure 3.**Comparison of the observed hydrographs for the validation events with the simulated hydrographs from the calibration events.

**Figure 4.**Location of the characteristic points to compare recorded water level from the flood event of July 2013 with the simulated water level.

**Figure 5.**Box plots developed for (

**a**) imperviousness and (

**b**) curve number for 70 sub-catchments in the study area.

**Figure 6.**Probabilistic floodplain maps for (

**a**) a selected part of the watershed (area designated with the square) corre-spond to different scenarios (

**b**) no flooding; (

**c**) scenario 1; (

**d**) scenario 2; (

**e**) scenario 3; (

**f**) scenario 4; (

**g**) scenario 5; (

**h**) scenario 6; (

**i**) scenario 7.

**Figure 7.**Probabilistic floodplain maps under future climate change from different data source for one downstream location: (

**a**) current period; (

**b**) 2040–2069 under RCP8.5 from CCDP; (

**c**) 2030–2070 under RCP.8.5 from stationary IDF; and (

**d**) 2030–2070 under RCP8.5 from non-stationary IDF.

**Figure 8.**Probabilistic floodplain maps under future climate change from different data source for one upstream location: (

**a**) current period; (

**b**) 2040–2069 under RCP8.5 from CCDP; (

**c**) 2030–2070 under RCP.8.5 from stationary IDF; and (

**d**) 2030–2070 under RCP8.5 from non-stationary IDF.

Calibration Event ID | C7 | C13 | C19 | C27 |
---|---|---|---|---|

Storm Date | 20 March 1980 | 29 September 1986 | 14 January 1995 | 2 April 2009 |

Cumulative rainfall (mm) | 33.8 | 58.7 | 62.1 | 40.6 |

Peak flow (m^{3}/s) | 31.7 | 62.3 | 38.9 | 28.0 |

Flow volume (mm) | 26.6 | 44.3 | 56.0 | 25.8 |

Validation Event ID | Date | Cumulative Rainfall (mm) | Streamflow Peak (m^{3}/s) | Streamflow Volume (mm) |
---|---|---|---|---|

V1 | 22 February 1975 | 37.9 | 30.3 | 36.2 |

V2 | 10 September 1986 | 76.3 | 77.85 | 58.5 |

V3 | 17 July 1992 | 30.0 | 39.6 | 18.6 |

V4 | 28 August 1992 | 38.2 | 51.8 | 24.1 |

V5 | 20 January 1995 | 41.7 | 32.5 | 36.6 |

V6 | 5 October 1995 | 79.9 | 58.5 | 37.5 |

V7 | 19 August 2005 | 41.3 | 48.23 | 39.0 |

V8 | 19 October 2011 | 49.0 | 40.8 | 32.5 |

V9 | 4 September 2012 | 43.9 | 42.8 | 18.0 |

**Table 3.**Comparison of the observed flood depth from the event of July 2013 with the simulated flood depth from the proposed integrated hydrologic–hydraulic–GIS based modeling for floodplain delineation (datum NAD83CSRS 1983).

Location | Observed Flood Depth (m) | Simulated Flood Depth (m) |
---|---|---|

1 | 162.7 | 163.3 |

2 | 162.1 | 162.1 |

3 | 115.2 | 115.9 |

Scenario | Hydrologic Model Input (Rainfall) | Hydrologic Model Parameters (θ) | Hydrologic Model Input and Parameters (Rainfall and θ) | Hydraulic Model Parameters (Floodplain and Channels’ Manning) |
---|---|---|---|---|

S1 | × | × | × | ✓ |

S2 | × | ✓ | × | × |

S3 | ✓ | × | × | × |

S4 | × | × | ✓ | × |

S5 | × | ✓ | × | ✓ |

S6 | ✓ | × | × | ✓ |

S7 | × | × | ✓ | ✓ |

**Table 5.**Water level variation upstream and downstream of the river due to different sources of uncertainty (std: standard deviation).

Scenario | S1 | S2 | S3 | S4 | S5 | S6 | S7 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Statistic | mean | std | mean | std | mean | std | mean | std | mean | std | mean | std | mean | std |

Upstream | 0.97 | 0.02 | 0.59 | 0.06 | 0.32 | 0.12 | 0.29 | 0.08 | 0.60 | 0.07 | 0.37 | 0.11 | 0.29 | 0.12 |

Downstream | 0.34 | 0.06 | 0.79 | 0.03 | 0.42 | 0.16 | 0.43 | 0.10 | 0.77 | 0.10 | 0.39 | 0.17 | 0.39 | 0.16 |

**Table 6.**Comparison of mean water level of selected upstream and downstream cross section for different scenarios: (

**a**) current period; (

**b**) 2040–2069 under RCP8.5 from CCDP; (

**c**) 2030–2070 under RCP.8.5 from stationary IDF; and (

**d**) 2030–2070 under RCP8.5 from non-stationary IDF.

Scenario | a | b | c | d |
---|---|---|---|---|

Upstream mean water level (m) | 206.99 | 207.73 | 207.53 | 207.97 |

Downstream mean water level (m) | 85.8 | 87.32 | 87.01 | 87.35 |

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## Share and Cite

**MDPI and ACS Style**

Zahmatkesh, Z.; Han, S.; Coulibaly, P. Understanding Uncertainty in Probabilistic Floodplain Mapping in the Time of Climate Change. *Water* **2021**, *13*, 1248.
https://doi.org/10.3390/w13091248

**AMA Style**

Zahmatkesh Z, Han S, Coulibaly P. Understanding Uncertainty in Probabilistic Floodplain Mapping in the Time of Climate Change. *Water*. 2021; 13(9):1248.
https://doi.org/10.3390/w13091248

**Chicago/Turabian Style**

Zahmatkesh, Zahra, Shasha Han, and Paulin Coulibaly. 2021. "Understanding Uncertainty in Probabilistic Floodplain Mapping in the Time of Climate Change" *Water* 13, no. 9: 1248.
https://doi.org/10.3390/w13091248