# A Spatiotemporal Deep Learning Approach for Urban Pluvial Flood Forecasting with Multi-Source Data

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## Abstract

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## 1. Introduction

- High temporal and spatial resolution of flood forecasts;
- Sufficient lead time between prediction and event occurrence.

- Development of a prediction model for pluvial flooding based on deep learning that can predict the spatial and temporal evolution of the flooding situation. In contrast to other studies investigating the use of deep learning to predict pluvial flooding [31,33,34,35], the model output is a flooding sequence for the upcoming time steps instead of the maximum water levels. The chosen model design also allows predictions to be generated at any point in an event and is not limited to specific durations of an event. The accuracy of the results is expected to be as close as possible to that of physically based models, with drastically reduced computation times at the same time.
- Compared to existing studies on predicting pluvial flash floods using deep learning approaches [31,33,34,35], the sewer network is considered as an extra retention volume here. To achieve this, an event-specific overflow forecast is taken as an additional input variable informing whether the sewer network is overloaded or not. In subsequent operational use, this input can be provided either by hydrodynamic sewer network models or data-driven models.
- Different model setups are evaluated. This refers, on the one hand, to the considered model inputs and in the case of overflow prediction, to the data format and the model architecture depending on it. Furthermore, different modern deep learning architectures such as encoder-decoder networks, graph neural networks, or generative adversarial networks are combined and compared with each other in the investigations.

## 2. Methodology

#### 2.1. Modeling Concept

- 1D time series (precipitation information and overflow forecast): These are time series whose values vary along the temporal axis but are assumed to be constant over the spatial extent of the study area (precipitation) or correspond only to a single spatial unit in the study area (overflow).
- 2D raster (spatial information): These are raster data sets whose values vary across the spatial extent of the study area but are assumed to be constant over time.
- 3D raster sequence (predicted inundation areas): These are grid sequences with the same format as video sequences. The values vary both spatially and temporally.

#### 2.2. Considered Layers and Network Architectures

#### 2.2.1. Fully Connected Layers

#### 2.2.2. Convolutional Layer

#### 2.2.3. Recurrent Layer

#### 2.2.4. Graph Neural Networks (GNNs)

_{i}∈ V to node v

_{j}∈ V can be described as (v

_{i}, v

_{j}) ∈ E. For efficient processing of graphs in ML applications, they are usually represented as a matrix. One way of doing this is to use an adjacency matrix A ∈ ℝ

^{N×N}consisting of an N × N matrix in which, for each position i, j (1 ≤ i ≤ N; 1 ≤ j ≤ N), the following is the case:

^{N×D}is considered as input. Here, N describes the number of nodes and D is the number of input features per node. The output at the node Z ∈ ℝ

^{N×F}(F stands here for the number of output features) is accordingly a function f of the adjacency and feature matrix:

#### 2.2.5. Generative Adversarial Networks

## 3. Case Study

#### 3.1. Study Area and Hydrodynamic Model

^{2}in the south of the city of Gelsenkirchen in Germany was selected for the investigations (see Figure 2). The site is primarily urban and drains with a combined sewer system. The terrain has an average slope of 7.5% and is not influenced by rivers or slopes in terms of flooding. A railroad line runs across the area, dividing the catchment area into a northern and southern part. Both parts are connected by two underpasses, which are potentially at risk of flooding and were underwater during past extreme events.

#### 3.2. Pluvial Flood Event Data Sets

#### 3.3. Data Generation and Preprocessing

#### 3.3.1. Data Generation Process

#### 3.3.2. Data Preprocessing

_{-D+1},..., t] for the past time steps and [t

_{+1},..., t

_{H}] for the predicted time steps. D and H were set to 60 min for the studies performed here, corresponding to 12 time steps for the chosen temporal resolution of five minutes. The precipitation forecast for the forecast horizon of 60 min was set to be the measured precipitation of the corresponding time steps for the investigations carried out here. In the future, a forecast generated by a precipitation forecast model will be used. The procedure for generating the training pairs P is shown as an example for one observation time step in Figure 4. The total number of all generated training pairs from the 258 used events was 9045.

#### 3.4. Investigated Model Setups

#### 3.4.1. Experiment 1: Comparison of Different Input Variables

- Model 1: Precipitation;
- Model 2: Precipitation + Overflow forecast;
- Model 3: Precipitation + Spatial information;
- Model 4: Precipitation + Overflow forecast + Spatial information.

#### 3.4.2. Experiment 2: Comparison of Different Preprocessing of the Overflow Data

#### 3.4.3. Experiment 3: Comparison of Different Model Setups

#### 3.5. Performance Evaluation

_{i}for the respective values of the individual cells determined with the neural network NN and the hydrodynamic model HD. The RMSE can assume values in the range [0, ∞], where 0 corresponds to the optimal fit. The absolute error is given as the result. Other metrics for determining the relative error, such as the relative mean squared error (MRSE), were also tested. However, it was found that pixels with low water levels sometimes resulted in extreme relative errors. In the subsequent averaging of error values over all the cells of a flooding grid, this problem led to poor results. However, the affected cells have only a low hazard potential and are thus of minor relevance compared to cells with high water levels.

## 4. Results

#### 4.1. Comparison of the Investigated Model Setups

#### 4.2. Assessment of the Prediction Accuracy

#### 4.3. Forecast for a Historical Heavy Rainfall Event

- Predictions with shallow water depths and only a few flooded pixels often lead to large errors. This problem is particularly evident at step t = +15 min with a CSI of 0, the worst possible result. The RMSE also shows the worst value compared to the other time steps. The same problem was also found by Löwe et al. [35]. On the other hand, predicted flood maps with many flooded pixels usually show a high accuracy, as is the case for time steps t = +30 min and + 60 min. Accordingly, the flooding patterns particularly relevant for crisis management are predicted with high accuracy.
- The model reacts with a slight delay to the precipitation load. While increasing flood areas before the peak are underestimated, the extent of areas after the peak is slightly overestimated. This behavior is illustrated by the histogram with the error frequencies, and it is also displayed in other events.
- In the center of the depicted section, there is an underpass where the most considerable differences of up to 25 cm occur. However, it should be noted that the water levels there are sometimes more than two meters high. In this case, the relative error would be in the range of about 10–15% and thus within an acceptable range.

## 5. Discussion

^{2}), an expansion to larger areas and thus a higher number of raster cells to be computed will quickly exceed the available GPU RAM. Considering the currently available technology, this makes training impossible beyond a certain amount of data. One approach to covering entire urban areas is to divide the computational domain into sub-models and merge the results as described in Berkhahn et al. [31]. Another method is to train models in parallel on multiple GPUs. One approach to this is represented by the Python library Mesh-TensorFlow [80], which allows developing large models with extreme memory requirements and training them in parallel on multiple GPU units.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Distribution of events in the data set. (

**a**) The maximum return times T distribution for all 153 natural rainfall events. (

**b**) A schematic representation of the design rainfall events, with the selected durations, model rainfall types, and return periods/scenarios. For scenarios S 1.5 and S 4.0, the number indicates the increase factor by which the values of the 100-year model rains were multiplied.

**Figure 4.**Converting the data into a supervised learning problem using a single training pair as an example.

**Figure 6.**Baseline architecture combined with the corresponding input paths for the overflow forecast and the spatial information.

**Figure 7.**Baseline architecture with the different input paths for the considered formats of the overflow forecast. Baseline architecture with the input paths for the overflow forecast formatted as (

**a**) unstructured hydrographs, (

**b**) raster sequences, and (

**c**) spatiotemporal graphs.

**Figure 11.**Distribution of metrics depending on different recurrence intervals for the threshold value d ≥ 0.5 m.

**Figure 13.**Results and evaluation for three time steps of a single forecast with the T-GCN at the beginning of the event on 3 July 2009 in Gelsenkirchen. Instead of showing the entire study area, a section with a flooded underpass is expanded for better visualization.

**Table 1.**Evaluation results for all models from the three experiments (for each experiment and metric, the best result is bolded).

Model | RMSE ↓ | CSI ↑ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

d ≥ 0.02 | d ≥ 0.05 | d ≥ 0.1 | d ≥ 0.2 | d ≥ 0.5 | d ≥ 0.02 | d ≥ 0.05 | d ≥ 0.1 | d ≥ 0.2 | d ≥ 0.5 | |

Experiment 1: Model Inputs | ||||||||||

Model 1 (Inputs: rain) | 0.039 | 0.052 | 0.074 | 0.140 | 0.553 | 0.504 | 0.488 | 0.399 | 0.299 | 0.122 |

Model 2 (Inputs: rain, manhole spilling) | 0.028 | 0.037 | 0.052 | 0.096 | 0.096 | 0.538 | 0.543 | 0.495 | 0.414 | 0.768 |

Model 3 (Inputs: rain, spatial information) | 0.037 | 0.050 | 0.074 | 0.144 | 0.547 | 0.510 | 0.466 | 0.384 | 0.293 | 0.157 |

Model 4 (Inputs: rain, spatial information, manhole spilling) | 0.026 | 0.035 | 0.051 | 0.092 | 0.118 | 0.595 | 0.574 | 0.511 | 0.421 | 0.746 |

Experiment 2: Manhole Spilling Forecast Format | ||||||||||

Model 5 (Unordered) | 0.026 | 0.035 | 0.051 | 0.094 | 0.118 | 0.595 | 0.574 | 0.511 | 0.421 | 0.746 |

Model 6 (Raster Sequence) | 0.030 | 0.040 | 0.058 | 0.115 | 0.148 | 0.548 | 0.514 | 0.434 | 0.340 | 0.679 |

Model 7 (Graph) | 0.026 | 0.036 | 0.052 | 0.092 | 0.081 | 0.575 | 0.557 | 0.492 | 0.424 | 0.788 |

Experiment 3: Model Architecture | ||||||||||

Model 8 (T-GCN) | 0.026 | 0.036 | 0.052 | 0.092 | 0.081 | 0.575 | 0.557 | 0.492 | 0.424 | 0.788 |

Model 9 (T-GCN cGAN) | 0.027 | 0.037 | 0.055 | 0.113 | 0.158 | 0.623 | 0.602 | 0.545 | 0.440 | 0.723 |

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## Share and Cite

**MDPI and ACS Style**

Burrichter, B.; Hofmann, J.; Koltermann da Silva, J.; Niemann, A.; Quirmbach, M.
A Spatiotemporal Deep Learning Approach for Urban Pluvial Flood Forecasting with Multi-Source Data. *Water* **2023**, *15*, 1760.
https://doi.org/10.3390/w15091760

**AMA Style**

Burrichter B, Hofmann J, Koltermann da Silva J, Niemann A, Quirmbach M.
A Spatiotemporal Deep Learning Approach for Urban Pluvial Flood Forecasting with Multi-Source Data. *Water*. 2023; 15(9):1760.
https://doi.org/10.3390/w15091760

**Chicago/Turabian Style**

Burrichter, Benjamin, Julian Hofmann, Juliana Koltermann da Silva, Andre Niemann, and Markus Quirmbach.
2023. "A Spatiotemporal Deep Learning Approach for Urban Pluvial Flood Forecasting with Multi-Source Data" *Water* 15, no. 9: 1760.
https://doi.org/10.3390/w15091760