# Integrated Flood Forecasting and Warning System against Flash Rainfall in the Small-Scaled Urban Stream

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Integrated Flood Forecasting and Warning System

#### 2.1. Short-Term Inundation Prediction

#### 2.2. Very Short-Term Inundation Prediction

#### 2.2.1. Rainfall Forecasting by Radar

^{1.19}) has applied as an optimal radar Z-R relation, which is confirmed that the accuracy is improved over 20 mm/h heavy rainfall [23]. In order to predict the direction of rainfall in weather radar data, TREC is used. TREC is the first kind of radar-based nowcasting method, proposed by Rinehart and Garvey [24]. It is an image processing algorithm that calculates correlation coefficients between successive images of radar echoes and uses the maximum values to obtain the motion vectors of different regions. During calculations, if the regions for determining the correlation coefficient is set too large, the average moving direction and moving speed of the entire rainfall are obtained. On the contrary, if the regions are set too small, it is not easy to obtain meaningful results. In addition, the spatial position (calculation radius) between the two regions reflects the maximum distance of rainfall, so it must be determined within a physically meaningful range. Therefore, in this study, the size of the region was set to 21 km, and the size of the calculated radius was set to 7 km, reflecting the values suggested in the study by Kim and Kim [25]. Through this process, the linear motion of the rainfall during the targeted prediction time was predicted using the calculated motion vector field and reflectivity data. The function of the Z-R relationship algorithm is written as:

^{6}/m

^{3}); R, rainfall intensity (mm/h); a and b, experienced constants.

#### 2.2.2. Construction of the Rainfall-Runoff Model

## 3. Study Area and Data Processing

#### 3.1. Study Area and Runoff Model

^{2}and the Dorim stream has a length of 14.51 km (Figure 4). Upstream catchments of watersheds in Dorim stream are mountainous with steep land slopes, the surface runoffs concentrate rapidly to channel flowing into the downstream urban area once the storm rainfall starts. So, flash flood frequently causes loss of human life and property in this area. Figure 5 shows the rainfall–runoff model of drainage networks in Dorim basin. In result of the constructing drainage networks (all basin of Dorim area), the number of conduits is 32,471 (Figure 5a). After simplification, the number of conduits is 243 (Figure 5b). Although the number of conduits substantially decreases as the criteria of the cumulative drainage area, it was presented that SWMM parameters was calculated automatically and basin area was the same as before the simplification.

#### 3.2. Hydrological Time Series Data

## 4. Application and Evaluation of Integrated System

#### 4.1. Model Application

#### 4.1.1. Application of Short-Term Inundation Prediction

^{2}are 0.9695, 0.9653, and 0.9823, respectively due to lead time. The LSTM has high values of R

^{2}indicating that this model could well reflect the relationship between observed and forecasting depth so that forecasting model with lead time 90 min is quite possible to predict and warning stream flooding. It is sufficiently can warn and evacuate the resident if accurate water level prediction with 90 min lead time is led in flash rainfall.

#### 4.1.2. Application of Very Short-Term Inundation Prediction

^{2}and NSE of the upstream where Seoul University is located were relatively low, but the predictive performance of the downstream, Gwanak Dorim, and Guro 1 bridge was 0.80 and 0.81, respectively, at 40 min lead time which presented good prediction performance. After 50 min lead time, the values of MAE and RMSE are all increased sharply. These cases illustrate that the 40 min lead time is the most appropriate time to forecast and warn urban flooding.

#### 4.1.3. Evaluation of the Integrated Flood Forecasting and Warning System

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic structure of the integrated flood forecasting and warning system for urban basin.

**Figure 5.**The simplified result of drainage networks in rainfall–runoff model of Dorim basin (

**a**) before simplification; (

**b**) after simplification.

**Figure 6.**Locations of the Dorim basin. (

**a**) Location map of water level stations in Dorim stream; (

**b**) water level data with quality control in Dorim stream.

**Figure 7.**Building of hydrologic time series data sets (training set, validation set, test set) in the short-term inundation prediction module.

**Figure 8.**Prediction results of Long Short-Term Memory (LSTM) due to varying lead times on Guro Digital Complex station and scatter plot of the observed and the simulated stream depth in training 3 water level stations. (

**a**) Lead time 30 min. (

**b**) Lead time 60 min. (

**c**) Lead time 90 min.

**Figure 9.**Predicted areal average rainfall by radar due to forecast lead time in Dorim basin. (

**a**) Forecast (10 min). (

**b**) Forecast (20 min). (

**c**) Forecast (30 min). (

**d**) Forecast (40 min). (

**e**) Forecast (50 min). (

**f**) Forecast (60 min). (

**g**) Forecast (70 min). (

**h**) Forecast (80 min). (

**i**) Forecast (90 min). (

**j**) Forecast (100 min). (

**k**) Forecast (110 min). (

**l**) Forecast (120 min).

**Figure 10.**Rainfall–runoff results of SWMM, the predicted water level by radar forecast rainfall across Dorim stream. (

**a**) Seoul University. (

**b**) Sillim 3 bridge. (

**c**) Gwank Dorim bridge. (

**d**) Guro Digital Complex station.

**Figure 11.**Integrated flood forecasting and warning system in web page Ref [29]. (

**a**) Main page. (

**b**) Rainfall prediction page by radar. (

**c**) Stream depth prediction page. (

**d**) Inundation map page.

Step | Detail Process |
---|---|

1st step Checking of the initial condition | Searching the initial conduit and node Calculating the cross-sectional area of flow Checking the branch conduits and nodes Checking the outlet |

2nd step Calculating of the drainage area | Calculating the cumulative drainage area of all nodes from upstream point |

3rd step Calculating of the branch line and mainline | User can define the cumulative drainage area to distinguish branch line and main line |

4th step Calculating of the parameter | Calculating the parameters of nodes and conduits to be deleted in simplification process |

5th step Building of the drainage network | Building the simplified drainage network(.inp) |

Step | Detail Process |
---|---|

1st step | Define DDS input: Neighborhood perturbation size parameter, $\mathsf{\gamma}$ (0.2 is default) Maximum # of function evaluation, $\U0001d4c2$ Vectors of lower, ${\mathrm{X}}^{\mathrm{min}}$, and upper, ${\mathrm{X}}^{\mathrm{max}}$, bounds for all D decision variables Initial solution, ${\mathrm{X}}^{0}=\left[{\mathrm{X}}_{1},\cdots ,{\mathrm{X}}_{\mathrm{D}}\right]\text{}$ |

2nd step | Set counter to 1, i − 1, and evaluate objective function F at initial solution, F(${\mathrm{X}}^{0})$: ${\mathrm{F}}_{\mathrm{best}}=\mathrm{F}\left({\mathrm{X}}^{0}\right),\text{}\mathrm{and}\text{}{\mathrm{X}}^{\mathrm{best}}={\mathrm{X}}^{0}$ |

3rd step | Randomly select J of the D decision variables for inclusion in neighborhood, {$\mathsf{{\rm N}}$}: Calculate probability each decision variable is included in {$\mathsf{{\rm N}}$} as a function of the current iteration count: P(i) = 1 − ln(i)/ln($\U0001d4c2$) FOR d = 1, $\text{}\cdots \mathrm{D}\text{}\mathrm{decision}\text{}\mathrm{variables},\text{}\mathrm{add}\text{}\mathrm{d}\text{}\mathrm{to}\text{}${$\mathsf{{\rm N}}$} with probability P IF {$\mathsf{{\rm N}}$} empty, select one random d for {$\mathsf{{\rm N}}$} |

4th step | For j = 1, $\text{}\cdots $ J decision variables in {$\mathsf{{\rm N}}$}, perturb ${\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{best}}\text{}$ using a standard normal random variable, $\mathsf{{\rm N}}$(0,1), reflecting at decision variable bounds if necessary: ${\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}={\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{best}}+{\mathsf{\sigma}}_{\mathrm{j}}\mathrm{N}\left(0,1\right),{\text{}\mathrm{where}\text{}\mathsf{\sigma}}_{\mathrm{j}}=\mathsf{{\rm Y}}\left({\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{max}}-{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{min}}\right)$ ${\mathrm{IF}\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{min}},\text{}\mathrm{reflect}\text{}\mathrm{perturbation}:$ ${\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}={\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{min}}+\left({\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{min}}-{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}\right)$ ${\mathrm{IF}\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{max}},{\text{}\mathrm{set}\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}={\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{min}}$ ${\mathrm{IF}\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{max}},\text{}\mathrm{reflect}\text{}\mathrm{perturbation}:$ ${\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}={\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{max}}-({\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}-{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{max}})$ ${\mathrm{IF}\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}{\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{min}},{\text{}\mathrm{set}\text{}\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}}={\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{max}}$ |

5th step | Evaluate F(${\mathrm{X}}^{\mathrm{new}})\text{}\mathrm{and}\text{}\mathrm{update}\text{}\mathrm{current}\text{}\mathrm{best}\text{}\mathrm{solution}\text{}\mathrm{if}\text{}\mathrm{necessary}:$ $\mathrm{IF}\text{}\mathrm{F}({\mathrm{X}}_{\mathrm{j}}{}^{\mathrm{new}})\le {\mathrm{F}}_{\mathrm{best}},\text{}\mathrm{update}\text{}\mathrm{new}\text{}\mathrm{best}\text{}\mathrm{solution}:$ ${\mathrm{F}}_{\mathrm{best}}=\mathrm{F}\left({\mathrm{X}}^{\mathrm{new}}\right){\text{}\mathrm{and}\text{}\mathrm{X}}^{\mathrm{best}}={\mathrm{X}}^{\mathrm{new}}$ |

6th step | Update iteration count, i = i+1, and check stopping criterion: IF i = m, STOP, print output (e.g., ${\mathrm{F}}_{\mathrm{best}}\text{}{\text{}\mathrm{X}}^{\mathrm{best}})$ ELSE go to STEP 3 |

Data Set | Station | Min | Max | Avg. | STDEV |
---|---|---|---|---|---|

Training set | Guro Digital Complex station | 0.27 | 3.73 | 0.31 | 0.103 |

Gwanak Dorim bridge | 0.10 | 2.62 | 0.12 | 0.069 | |

Sillim 3 bridge | 0.12 | 2.42 | 0.21 | 0.087 | |

Seoul University | 0.14 | 1.56 | 0.16 | 0.067 | |

Validation set | Guro Digital Complex station | 0.27 | 2.74 | 0.30 | 0.108 |

Gwanak Dorim bridge | 0.08 | 2.20 | 0.13 | 0.086 | |

Sillim 3 bridge | 0.04 | 1.59 | 0.20 | 0.060 | |

Seoul University. | 0.01 | 1.08 | 0.12 | 0.089 | |

Test set | Guro Digital Complex station | 0.23 | 2.57 | 0.29 | 0.091 |

Gwanak Dorim bridge | 0.08 | 1.89 | 0.14 | 0.061 | |

Sillim 3 bridge | 0.08 | 1.43 | 0.16 | 0.049 | |

Seoul University | 0.01 | 0.99 | 0.11 | 0.074 |

Case | Model | Data | Input Variable | Output Variable |
---|---|---|---|---|

Case 1 | LSTM | Water level | W_{se} (t), W_{se} (t − 1), ..., W_{se} (t − τ) | W_{gdc} (t + 3)W _{gdc} (t + 6)W _{gdc} (t + 9) |

Case 2 | W_{se} (t), W_{se} (t − 1), ..., W_{se} (t − τ)W _{sil} (t), W_{sil} (t − 1), ..., W_{sil} (t − τ) | |||

Case 3 | W_{se} (t), W_{se} (t − 1), ..., W_{se} (t − τ)W _{sil} (t), W_{sil} (t − 1), ..., W_{sil} (t − τ)W _{gdb} (t), W_{gdb} (t − 1), ..., W_{gdb} (t − τ) |

_{gdc}= Water level data of Guro Digital Complex station, W

_{gdb}= Water level data of Gwanak Dorim bridge, W

_{sil}= Water level data of Sillim3 bridge, W

_{se}= Water level data of Seoul University. t = Current time, τ = previous time.

**Table 5.**Comparison of performances of SWMM for stream depth prediction (lead time from 20 min to 70 min by radar).

Stations | Forecast 20 min | Forecast 30 min | ||||||
---|---|---|---|---|---|---|---|---|

R^{2} | RMSE | NSE | MAE | R^{2} | RMSE | NSE | MAE | |

Seoul University | 0.35 | 0.34 | −1.71 | 0.30 | 0.41 | 0.35 | −1.73 | 0.30 |

Sillim 3 birdge | 0.83 | 0.23 | 0.18 | 0.21 | 0.82 | 0.25 | 0.08 | 0.21 |

Gwank Dorim bridge | 0.94 | 0.14 | 0.86 | 0.13 | 0.82 | 0.21 | 0.69 | 0.15 |

Guro Digital Complex station | 0.93 | 0.40 | 0.48 | 0.35 | 0.85 | 0.46 | 0.31 | 0.38 |

Stations | Forecast 40 min | Forecast 50 min | ||||||

Seoul University | 0.34 | 0.35 | −1.82 | 0.31 | 0.36 | 0.36 | −1.91 | 0.32 |

Sillim 3 birdge | 0.80 | 0.25 | 0.03 | 0.22 | 0.62 | 0.27 | −0.14 | 0.23 |

Gwank Dorim bridge | 0.81 | 0.21 | 0.69 | 0.15 | 0.67 | 0.27 | 0.50 | 0.17 |

Guro Digital Complex station | 0.83 | 0.46 | 0.30 | 0.38 | 0.71 | 0.52 | 0.10 | 0.41 |

Stations | Forecast 60 min | Forecast 70 min | ||||||

Seoul University | 0.36 | 0.35 | −1.89 | 0.31 | 0.37 | 0.35 | −1.80 | 0.31 |

Sillim 3 birdge | 0.61 | 0.27 | −0.15 | 0.22 | 0.68 | 0.27 | −0.09 | 0.22 |

Gwank Dorim bridge | 0.56 | 0.30 | 0.38 | 0.18 | 0.57 | 0.29 | 0.41 | 0.18 |

Guro Digital Complex station | 0.60 | 0.56 | −0.04 | 0.42 | 0.55 | 0.57 | −0.06 | 0.41 |

**Table 6.**Comparison of flood warning time in SWMM, LSTM, and River Emergency Evacuation Notification System (REENS).

Flood Warning | Riverside Caution | Riverside Vacuation |
---|---|---|

Observation | 7:10 | 7:20 |

REENS | 7:10 | 7:10 |

LSTM (30 min lead time) | 6:50 (7:20) | 6:50 (7:20) |

LSTM (60 min lead time) | 6:20 (7:20) | 6:20 (7:20) |

LSTM (90 min lead time) | 5:40 (7:10) | 5:50 (7:20) |

SWMM (20 min lead time) | 7:00 (7:20) | 7:00 (7:20) |

SWMM (30 min lead time) | 7:00 (7:30) | 7:00 (7:30) |

SWMM (40 min lead time) | 6:50 (7:30) | 6:50 (7:30) |

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## Share and Cite

**MDPI and ACS Style**

Lee, J.H.; Yuk, G.M.; Moon, H.T.; Moon, Y.-I.
Integrated Flood Forecasting and Warning System against Flash Rainfall in the Small-Scaled Urban Stream. *Atmosphere* **2020**, *11*, 971.
https://doi.org/10.3390/atmos11090971

**AMA Style**

Lee JH, Yuk GM, Moon HT, Moon Y-I.
Integrated Flood Forecasting and Warning System against Flash Rainfall in the Small-Scaled Urban Stream. *Atmosphere*. 2020; 11(9):971.
https://doi.org/10.3390/atmos11090971

**Chicago/Turabian Style**

Lee, Jung Hwan, Gi Moon Yuk, Hyeon Tae Moon, and Young-Il Moon.
2020. "Integrated Flood Forecasting and Warning System against Flash Rainfall in the Small-Scaled Urban Stream" *Atmosphere* 11, no. 9: 971.
https://doi.org/10.3390/atmos11090971