# Framework for Offline Flood Inundation Forecasts for Two-Dimensional Hydrodynamic Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Framework for Offline Flood Inundation Forecast

_{RP1}), only the discharge forecast is shown to the end users. Coupled hydrological-hydrodynamic forecast is activated if the forecasted discharge exceeds the threshold. The threshold of Q

_{RP1}, which is less than the bankful discharge, is carefully selected to ensure that all the maps begin with the similar initial inundation extent and are not over-spilling the river banks. To select the optimal map from the database, the forecasted hydrograph for the next 12 h is compared to the discharge database and the index of the best match is recorded. Furthermore, the inundation maps corresponding to the recorded index are published for the next 12 h with 15-min intervals and can be accessed by end users via a webgis server. The maps are updated every three hours and the forecasted discharge is matched with the discharge database repeatedly for the next 12 h.

#### 2.2. Evaluation Metrics

^{2}) [22]. The metrics are calculated as in Table 1.

^{2}values of more than 0.85. The value of 0.85 was based on the review for model evaluation criteria between the simulated and measured discharge [22,23]; however, the value can be changed depending on the case study. Furthermore, if no optimal match is found, it selects the best NSE and a warning note is issued to the end-user along with the NSE value reported.

## 3. Study Area, Data and Models

#### 3.1. Study Area

#### 3.2. Case Study Data

#### 3.3. Pre-Calibration and Validation of the 2D Flood Inundation Model

^{2}), c

_{f}is the bottom friction coefficient (/s), R is the hydraulic radius (m), |V| is the magnitude of the velocity vector (m/s) and n is the Manning’s roughness coefficient (s/m

^{(1/3)}).

^{−1}was used for distributing the discharge over the cells that integrate the boundary. Table 2 shows the model properties and information of the cell size. The roughness parameter was selected based on a sensitivity analysis. Table 3 shows the calibrated parameter for each land use class (Figure 2a).

## 4. Results and Discussion

#### 4.1. Discharge Comparison

^{2}of 0.87 were selected at the twelfth hour in May 2013. Figure 7 presents the discharge hydrographs that are resulted from the rainfall scenario at the virtual gauge and the optimal ID for the 12-h forecast window with the three-hour update interval of the four events. The selection of new maps (ID) can be seen in the figure. It also shows the different databases for the advective and convective events. It is worth mentioning that the excellent agreement between the offline and online discharge hydrographs is a result of the suitability of the variety of synthetic scenarios generated from the KOSTRA and PEN rainfall simulation to fit the observed data. The quality of the database is therefore considered equally important as the methodology for selecting the maps, as presented in order to cover possible future events.

#### 4.2. Inundation Forecast Comparison

#### 4.2.1. Convective Events

#### 4.2.2. Advective Events

#### 4.3. Update Map Selection

^{3}/s). This value was decided on the river overflowing the banks. Since the inundation extents are within the main channel, they are not affected by this initial discharge. It would be possible to reduce this value and optimise the forecasts. The optimal maps were selected from 3–12 h.

## 5. Framework Performance

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Framework of the offline flood inundation forecast including the pre-recorded and real time component. The coupled hydrological-hydrological forecast is activated once a one-year return period (Q

_{RP1}) is exceeded.

**Figure 2.**Study area (

**a**) Land use and (

**b**) digital elevation model of the city Kulmbach. Data source: Water Management Authority Hof.

**Figure 3.**Precipitation values in mm for various durations (in min) and various return periods. PEN method used to extrapolate precipitation values above 100-year return period. Data source: KOSTRA-DWD 2000 (Kulmbach: Column 47, Row 67).

**Figure 4.**Discharge hydrographs at the upstream gauging stations (

**a**) Ködnitz and (

**b**) Kauerndorf. Data source: Bavarian Hydrological Service (www.gkd.bayern.de).

**Figure 5.**Error in m between the water levels resulting from the calibrated model and the measured water levels on 14 January 2011 at eight sites.

**Figure 7.**Comparison of discharge hydrographs at the virtual gauge: (

**a**,

**c**) advective events in February 2005 and January 2011, (

**b**,

**d**) convective events in May 2006 and May 2013.

**Figure 8.**Goodness of fit (

**a**) Fit Statistics and (

**b**) Absolute Error between offline and online flooded cells for each time step for the forecast duration of 12 h.

**Figure 9.**Water depth error between offline and online maps for May 2006. Positive values indicate over-prediction and negative values indicate under-prediction: (

**a**) T = 3 h, (

**b**) T = 6 h, (

**c**) T = 9 h and (

**d**) T = 12 h.

**Figure 10.**Water depth error between offline and online maps for May 2013: (

**a**) T = 3 h, (

**b**) T = 6 h, (

**c**) T = 9 h and (

**d**) T = 12 h.

**Figure 11.**Water depth error between offline and online for February 2005: (

**a**) T = 3 h, (

**b**) T = 6 h, (

**c**) T = 9 h and (

**d**) T = 12 h.

**Figure 12.**Water depth error between offline and online for January 2011: (

**a**) T = 3 h, (

**b**) T = 6 h, (

**c**) T = 9 h and (

**d**) T = 12 h.

**Figure 14.**Update of the map selection for the advective events: (

**a**) February 2005 and (

**b**) January 2011.

Evaluation Metrics | Equation | Terms |
---|---|---|

Nash-Sutcliffe efficiency (NSE) | $1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{({O}_{i}-{P}_{i})}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{({O}_{i}-\overline{O})}^{2}}$ | $n$—the number of samples $O$—the forecasted discharge $P$—the discharge of the database $b$—the gradient of the regression line $\mathrm{x}=\{\begin{array}{l}\left|b\right|\text{\hspace{1em}}\mathrm{if}\text{}b\le 1\\ {\left|b\right|}^{-1}\text{\hspace{1em}}\mathrm{if}\text{}b1\end{array}$ $\mathrm{b}=\frac{{{\displaystyle \sum}}_{i=1}^{n}({O}_{i}-\tilde{O})({P}_{\dot{i}}-\tilde{P})}{\overline{{{\displaystyle \sum}}_{\dot{i}=1}^{n}{({O}_{i}-\tilde{O})}^{2}}}$ |

Weighted coefficient of determination (wr^{2}) | $\mathrm{x}{\left(\frac{{{\displaystyle \sum}}_{i=1}^{n}({O}_{i}-\tilde{O})({P}_{\dot{i}}-\tilde{P})}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{({O}_{i}-\tilde{O})}^{2}}\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{({P}_{i}-\tilde{P})}^{2}}}\right)}^{2}$ | |

Fit Statistic (F) | $\frac{{A}_{0}}{{A}_{\mathit{offline}}+{A}_{\mathit{online}}-{A}_{0}}$ | ${A}_{0}$—the overlap of flooded cells in the online (${A}_{\mathit{online}}$) and offline (${A}_{\mathit{offline}}$) maps $\mathit{nf}$—the number of flooded cells ${d}_{}^{\mathit{offline}}$ and ${d}_{}^{\mathit{online}}$—the water depth in the offline and online maps |

Absolute Error (e) | $\frac{{{\displaystyle \sum}}_{i=1}^{\mathit{nf}}|{d}_{i}^{\mathit{offline}}-{d}_{i}^{\mathit{online}}|}{\mathit{nf}}$ |

Data | Value |
---|---|

Model area | 11.5 km^{2} |

Total number of cells | 430,485 |

Number of cells in results domain | 193,161 |

Δt | 20 s |

Minimum cell area | 6.8 m^{2} |

Maximum cell area | 59.8 m^{2} |

Average cell area | 24.8 m^{2} |

Land Use | Calibrated Manning’s n [s/m^{(1/3)}] | Ranges of Manning’s n [s/m^{(1/3)}] |
---|---|---|

Water bodies | 0.022 | 0.015–0.149 |

Agriculture | 0.043 | 0.025–0.110 |

Forest | 0.189 | 0.110–0.200 |

Transportation | 0.014 | 0.012–0.020 |

Urban | 0.074 | 0.040–0.080 |

Duration | No. of Data Samples | Goodness of Fit [-] | |||
---|---|---|---|---|---|

February 2005 | May 2006 | January 2011 | May 2013 | ||

0–3 h | 13 | 0.98 (NSE) | 0.91 (NSE) | 0.96 (NSE) | 0.97 (NSE) |

0–6 h | 25 | 0.99 (NSE) | 0.95 (NSE) | 0.97 (NSE) | 0.96 (NSE) |

0–9 h | 37 | 0.99 (NSE) | 0.95 (NSE) | 0.95 (NSE) | 0.91 (NSE) |

0–12 h | 49 | 0.94 (NSE) | 0.95 (NSE) | 0.97 (NSE) | 0.87 (wr^{2}) |

**Table 5.**Average Fit Statistics and absolute error for the four events at the end of the forecast update interval of three hours.

Duration | Average Fit Statistics [-] | Average Absolute Error [m] | ||||||
---|---|---|---|---|---|---|---|---|

February 2005 | May 2006 | January 2011 | May 2013 | February 2005 | May 2006 | January 2011 | May 2013 | |

0–3 h | 0.97 | 0.75 | 0.97 | 0.76 | 0.06 | 0.14 | 0.06 | 0.27 |

0–6 h | 0.96 | 0.84 | 0.97 | 0.80 | 0.07 | 0.11 | 0.06 | 0.22 |

0–9 h | 0.96 | 0.89 | 0.97 | 0.92 | 0.07 | 0.09 | 0.07 | 0.12 |

0–12 h | 0.93 | 0.90 | 0.95 | 0.93 | 0.11 | 0.08 | 0.07 | 0.11 |

Time | Flooded Cells | May 2006 [%] | |||
---|---|---|---|---|---|

<−0.25 m | −0.25–0 m | 0.25–0 m | >0.25 m | ||

T = 3 h | 36,865 | 3 | 48 | 49 | 0 |

T = 6 h | 55,550 | 3 | 96 | 1 | 0 |

T = 9 h | 60,012 | 3 | 11 | 86 | 0 |

T = 12 h | 60,418 | 3 | 13 | 84 | 0 |

Time | Flooded Cells | May 2013 [%] | |||
---|---|---|---|---|---|

<−0.25 m | −0.25–0 m | 0.25–0 m | >0.25 m | ||

T = 3 h | 34,493 | 8 | 92 | 0 | 0 |

T = 6 h | 44,553 | 5 | 4 | 84 | 7 |

T = 9 h | 45,864 | 4 | 6 | 89 | 1 |

T = 12 h | 44,204 | 8 | 88 | 3 | 1 |

Time | Flooded Cells | February 2005 [%] | |||
---|---|---|---|---|---|

<−0.25 m | −0.25–0 m | 0.25–0 m | >0.25 m | ||

T = 3 h | 30,915 | 6 | 7 | 87 | 0 |

T = 6 h | 37,426 | 5 | 2 | 87 | 5 |

T = 9 h | 43,691 | 5 | 12 | 76 | 7 |

T = 12 h | 46,790 | 7 | 91 | 2 | 0 |

Time | Flooded Cells | January 2011 [%] | |||
---|---|---|---|---|---|

<−0.25 m | −0.25–0 m | 0.25–0 m | >0.25 m | ||

T = 3 h | 30,825 | 6 | 70 | 24 | 0 |

T = 6 h | 32,348 | 6 | 69 | 25 | 0 |

T = 9 h | 37,097 | 6 | 3 | 87 | 4 |

T = 12 h | 42,603 | 5 | 4 | 81 | 10 |

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**MDPI and ACS Style**

Bhola, P.K.; Leandro, J.; Disse, M.
Framework for Offline Flood Inundation Forecasts for Two-Dimensional Hydrodynamic Models. *Geosciences* **2018**, *8*, 346.
https://doi.org/10.3390/geosciences8090346

**AMA Style**

Bhola PK, Leandro J, Disse M.
Framework for Offline Flood Inundation Forecasts for Two-Dimensional Hydrodynamic Models. *Geosciences*. 2018; 8(9):346.
https://doi.org/10.3390/geosciences8090346

**Chicago/Turabian Style**

Bhola, Punit Kumar, Jorge Leandro, and Markus Disse.
2018. "Framework for Offline Flood Inundation Forecasts for Two-Dimensional Hydrodynamic Models" *Geosciences* 8, no. 9: 346.
https://doi.org/10.3390/geosciences8090346