# Long-Term Temporal Flood Predictions Made Using Convolutional Neural Networks

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Description

#### 2.1. Study Area

^{2}, as illustrated in Figure 1. The drainage was designed under the assumption of a 10-year flood recurrence interval. No bank revetment is present in some river sections, and box culverts are insufficient in the area prone to flooding. Blocking weirs have been erected in some river sections, which has raised the water level and affected upstream drainage. All these factors contribute to flooding in the Dongmen drainage.

#### 2.2. Rainfall Data

#### 2.3. Flooding Data

#### 2.4. Strategy of Data Selection from the Database

## 3. Methods

#### 3.1. Convolutional Neural Networks

^{−6}. We used the optimizer Adam [30] with a learning rate of 5 × 10

^{−4}to train the network from scratch without utilizing pretrained model weights.

#### 3.2. Data Combination for Training

_{0}, the most recent hour; t

_{−1}, the second most recent hour; t

_{−2}, the third most recent hour; t

_{−3}, the fourth most recent hour; t

_{−5}, the sixth most recent hour; t

_{−7}, the eighth most recent hour; t

_{−9}, the tenth most recent hour; and t

_{−11}, the twelfth most recent hour. A dataset contained rainfall data and grid and elevation information, as illustrated in Figure 5. To test the ability of the multichannel CNN model to memorize past rainfall data, the accumulated rainfall of different past periods was input into different channels for testing: these periods included t

_{0}, the most recent hour of rainfall; t

_{−1,0}, t

_{−3,−2,−1}, t

_{−3,−2,…0}, t

_{−5,−4,…0}, t

_{−7,−6,…,0}, t

_{−9,−8,…,0}; and t

_{−11,−10,…,0}, the most recent 2, 3, 4, 6, 8, 10, and 12 h of accumulated rainfall. The dataset contained accumulated rainfall data from the same data source as in Figure 5, grids, and the elevation information, as shown in Figure 6. The effects of the hourly versus accumulated rainfall data types on the CNN learning results were determined. It can be observed that several zero parts in the digital terrain model (DTM) map are used when simulating using the SOBEK model. These zero values indicate areas that have never been flooded or they are impossible to be. Henceforth, during the simulation, the elevation values are set to NaN, which is why the value seen in the graph is zero.

#### 3.3. Evaluation Methods

#### 3.3.1. SSIM

#### 3.3.2. Comparisons of Differences in Location for the Maximum Flooding Depth, Maximum Flooding Depth, and Total Flooding Volume

## 4. Result Analysis

#### Model Comparison

- The training data not containing spatial information resulted in no convergence during the training process (Figure 9a), and the result obtained with the validation data was also divergent, as illustrated in Figure 9b. However, when spatial information was included, regardless of whether it was XY coordinates orYZ coordinates (including terrain elevation), convergence was gradually achieved in the training process;
- For both deep learning architectures and for both series hourly and accumulated rainfall data, the convergence obtained when XYZ spatial information was included was better than that achieved when XY spatial information only was included. Thus, elevation information is vital in CNN models used for flooding prediction;
- When the same data were used for training both architectures, convergence in the training was much better when using the Inception architecture than when using the SCNN architecture. We attribute this to the Inception architecture parameters being more numerous, which meant that more information was learned after separate training and merging of various training branches;
- For a given deep learning architecture and type of spatial information, the convergence achieved using the series hourly rainfall data was slightly better than that achieved using the accumulated rainfall data. For the training data, the effects of CNN architecture and spatial information type are stronger than that of rainfall data type.

## 5. Discussion

#### 5.1. Similarity

- For both the SCNN and Inception architectures, when the accumulated rainfall data were used, the luminance, contrast, structure, and final synthesis (SSIM) results were more favorable than those obtained when the hourly time-series rainfall data were employed;
- The similarity at a small flooding depth was not ideal because in the initial stage of flooding, few grids were flooded. The few numbers of flooded grids severely affected the similarity results. A possible way to improve this is to increase the amount of training data with a small flooding depth;
- When using the hourly time-series rainfall data as the training data, the similarity at various maximum flooding depths fluctuated and was nonuniform, regardless of whether the spatial information contained terrain elevation. Thus, neither architecture could stably learn the time-series rainfall data;
- Regardless of the deep learning architecture that was employed and whether hourly time-series or accumulated rainfall were used, the use of spatial information, including terrain elevation, led to much more favorable results than the nonuse of this information;
- A divergence was discovered near the maximum flooding depth. This was because when high-order polynomial regression is used, oscillation occurs at the edge of the interval; this is called the Runge phenomenon [34]. The phenomenon occurs when using polynomial interpolation with high-degree polynomials over a set of equally spaced interpolation points.

#### 5.2. Comparison of Locations at Which Maximum Flooding Occurred

- The result obtained using the training data containing spatial information XYZ was far more accurate than that obtained using the training data containing only spatial information XY;
- The maximum position was found to be correct approximately 47% of the time. The grid position was within five grids of the actual position approximately 60% of the time; this percentage was much higher than 1/(360 × 201) = 1.38 × 10
^{−5}, indicating that the model could learn the flooding position and did not simply guess the location randomly.

#### 5.3. Maximum Flooding Depth Prediction

^{2}is 0.78, but the regression line does not pass through the origin. A small value is present in the non-flooded area in the two-dimensional flooding-prediction map (and the minimum flooding depth in space). Thus, a numerical offset may exist in the deep learning regression result. The value shift may be due to the data sampling because we almost did not sample non-flooding data. The data for the first 11 h of each event, with little rain and no flooding, were not selected.

#### 5.4. Total Flooding Volume

#### 5.5. Case Comparison

## 6. Conclusions

- This study used the SCNN architecture, which has few parameters, and the Inception architecture, which has numerous parameters, to make flooding predictions when training with the same data. The results revealed that the Inception architecture achieved excellent results;
- Using multiple and randomization methods, this study employed 21 actual rainfall events to produce 6000 rainfall events of various durations. The physical model we constructed could simulate a flooding situation under extreme rainfall. A total of 218,850 sets of rainfall data were generated from the data of 6000 events. We divided the maximum flooding depth of all data into 20 groups and calculated the amount of data in each group. Only 0.653% of all the data were taken out for training, and this achieved favorable results;
- When spatial information was not included in the training dataset, convergence could not be achieved with either CNN architecture. Inclusion of XYZ information in the training data resulted in optimal results;
- More accurate training results were obtained when using accumulated rainfall data than when using hourly time-series rainfall data;
- This study used the SSIM to compare the flooding results predicted by the AI and physical models. When the water level was low because there were few deep-water grid samples, the similarity was low, and some other errors that occurred were due to the Runge effect. In all the other findings, excellent graphical similarity was discovered. The results obtained using deep learning to predict the flooding range and depth were very similar to the original data. Therefore, the method proposed in this paper obtained favorable results when used to predict flooding caused by heavy rain;
- Because of the sampling of the training data, the overall predicted water depth slightly shifted. In the future, the accuracy for low water levels can be improved by increasing the amount of the low water level or early rainfall data through data resampling.
- The deep learning models proposed in this study were trained with rainfall data and corresponding flooding depth data but without real-time data, which could be used to modify the prediction results. Therefore, the forecasted rainfall data can be input into our models to obtain long-term flooding forecasts, which would aid in disaster prevention and response, and provide responders with more time to prepare.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Original amount of data in various flooding depth ranges and the amount of 25th percentile data.

**Figure 5.**Schematic of the data combination, with the data being 8-h rainfall, X and Y meshes, and a digital terrain model. (

**a**) the most recent hour rainfall; (

**b**) the second most recent hour rainfall; (

**c**) the third most recent hour; (

**d**) the fourth most recent hour rainfall; (

**e**) the sixth most recent hour rainfall; (

**f**) the eighth most recent hour rainfall; (

**g**) the tenth most recent hour rainfall; (

**h**) the twelfth most recent hour; (

**i**) the longitude mesh; (

**j**) the latitude mesh; (

**k**) elevation information.

**Figure 6.**Schematic of the data combination, with data being 8-h accumulated rainfall, X and Y meshes, and a digital terrain model. (

**a**) the most recent hour rainfall; (

**b**) the most recent 2 h of accumulated rainfall; (

**c**) the most recent 3 h of accumulated rainfall; (d) the most recent 4 h of accumulated rainfall; (

**e**) the most recent 6 of accumulated rainfall; (

**f**) the most recent 8 h of accumulated rainfall; (

**g**) the most recent 10 h of accumulated rainfall; (

**h**) the most recent 12 h of accumulated rainfall; (

**i**) the longitude mesh; (

**j**) the latitude mesh; (

**k**) elevation information.

**Figure 7.**Combination classification of: (

**a**) rainfall data in different time series (ser), coordinates (XY), and elevation (Z); and (

**b**) cumulative rainfall data in different periods (acc), coordinates (XY), and elevation (Z). (

**c**) Combination of different physical factors.

**Figure 8.**Data of different combinations are input to two CNN architectures (SCNN and Inception). The obtained results are compared in various ways.

**Figure 9.**Convergence of the loss function for different models: (

**a**) training data; and (

**b**) validation data.

**Figure 10.**Actual data (

**left**) and deep learning predictions (

**right**) of the flooding distribution and depth.

**Figure 11.**Structural similarity index (SSIM) similarity in the flood results produced by various models to the corresponding actual data: (

**a**) luminance comparison, (

**b**) contrast comparison, (

**c**) structure comparison, and (

**d**) SSIM comparison.

**Figure 12.**Difference in the location of the maximum flooding depth between the actual data and the predictions made by the artificial intelligence (AI) models.

**Figure 14.**Total flooding volume predicted by AI versus the actual values: (

**a**) training data and (

**b**) testing data.

**Figure 15.**Use of various deep learning models for a single rainfall event, showing the maximum flooding depth versus time.

**Figure 16.**Difference in the maximum flooding depth position when using various deep learning models to make predictions for a single rainfall event.

**Figure 17.**Flooding depth at different locations versus time for a single rainfall event when using the Inception architecture and rainfall data containing XYZ information.

**Figure 18.**Two-dimensional results obtained using the Inception architecture and accumulated rainfall data containing XYZ information in comparison with the physical model results at time points of (

**a**) 16; (

**b**) 20; (

**c**) 28; and (

**d**) 40 h.

**Figure 19.**SSIM and its components’ variation with time in the flooding results for a rainfall event when using the Inception architecture and accumulated rainfall data containing XYZ information.

Event | Start Time | End Time | Duration (h) | Areal Average Rainfall (mm) |
---|---|---|---|---|

1 | 17/07/2005 10:00 | 18/07/2005 18:00 | 33 | 36.4 |

2 | 04/08/2005 09:00 | 06/08/2005 00:00 | 40 | 65.8 |

3 | 31/08/2005 07:00 | 01/09/2005 08:00 | 26 | 55.2 |

4 | 01/10/2005 23:00 | 02/10/2005 18:00 | 20 | 30.3 |

5 | 26/07/2008 22:00 | 28/07/2008 22:00 | 49 | 66.8 |

6 | 12/09/2008 02:00 | 09/15/2008 00:00 | 71 | 235.9 |

7 | 21/10/2010 00:00 | 10/22/2010 13:00 | 38 | 224.7 |

8 | 11/06/2012 21:00 | 12/06/2012 23:00 | 27 | 294.2 |

9 | 14/06/2012 11:00 | 15/06/2012 06:00 | 20 | 42.0 |

10 | 26/08/2012 09:00 | 27/08/2012 08:00 | 24 | 31.5 |

11 | 11/05/2013 01:00 | 13/05/2013 01:00 | 49 | 90.3 |

12 | 12/07/2013 16:00 | 13/07/2013 14:00 | 23 | 26.7 |

13 | 04/10/2013 14:00 | 06/10/2013 23:00 | 58 | 2.3 |

14 | 20/05/2014 20:00 | 22/05/2014 00:00 | 29 | 96.9 |

15 | 22/07/2014 21:00 | 24/07/2014 03:00 | 31 | 36.1 |

16 | 21/09/2014 16:00 | 22/09/2014 12:00 | 21 | 25.2 |

17 | 07/08/2015 08:00 | 08/08/2015 13:00 | 30 | 125.5 |

18 | 27/09/2015 14:00 | 29/09/2015 05:00 | 40 | 99.7 |

19 | 26/09/2016 10:00 | 28/09/2016 04:00 | 43 | 49.4 |

20 | 02/06/2017 10:00 | 04/06/2017 04:00 | 39 | 288.6 |

21 | 12/09/2017 22:00 | 14/09/2017 12:00 | 39 | 9.1 |

Group | Statistical Properties of Rainfall | Number of Events | |
---|---|---|---|

1 | Mean | ${\mathsf{\mu}}_{D}$ | 1000 |

Standard deviation | ${\mathsf{\sigma}}_{D}$ | ||

2 | Mean | $2{\mathsf{\mu}}_{D}$ | 1000 |

Standard deviation | ${\mathsf{\sigma}}_{D}$ | ||

3 | Mean | $3{\mathsf{\mu}}_{D}$ | 1000 |

Standard deviation | ${\mathsf{\sigma}}_{D}$ | ||

4 | Mean | ${\mathsf{\mu}}_{\left(D,2D,3D\right)}$ | 3000 |

Standard deviation | ${\mathsf{\sigma}}_{\left(D,2D,3D\right)}$ |

Model | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Architecture | SCNN | Inception | ||||||||||

Rainfall type | Series hourly (ser) | Accumulated (acc) | Series hourly (ser) | Accumulated (acc) | ||||||||

Space type | None | XY | XYZ | None | XY | XYZ | None | XY | XYZ | None | XY | XYZ |

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**MDPI and ACS Style**

Wang, H.-W.; Lin, G.-F.; Hsu, C.-T.; Wu, S.-J.; Tfwala, S.S.
Long-Term Temporal Flood Predictions Made Using Convolutional Neural Networks. *Water* **2022**, *14*, 4134.
https://doi.org/10.3390/w14244134

**AMA Style**

Wang H-W, Lin G-F, Hsu C-T, Wu S-J, Tfwala SS.
Long-Term Temporal Flood Predictions Made Using Convolutional Neural Networks. *Water*. 2022; 14(24):4134.
https://doi.org/10.3390/w14244134

**Chicago/Turabian Style**

Wang, Hau-Wei, Gwo-Fong Lin, Chih-Tsung Hsu, Shiang-Jen Wu, and Samkele Sikhulile Tfwala.
2022. "Long-Term Temporal Flood Predictions Made Using Convolutional Neural Networks" *Water* 14, no. 24: 4134.
https://doi.org/10.3390/w14244134