Recent advances in earth observation and machine learning have enabled rapid estimation of flooded areas following catastrophic events such as torrential rains and riverbank overflows. However, estimating the actual inundation depth remains a challenge since it often requires detailed numerical simulation. This paper presents a methodology for predicting the inundation from remote sensing derived information by coupling deep learning and numerical simulation. We generate a large dataset of flood depth inundations considering several heavy rain conditions in four independent target areas. We propose a CNN-based regression framework. Our experiment demonstrates that our methodology can predict inundation depth on a separate target area not included during training, demonstrating great generalization ability.
extent, represented as binary mask images. A CNN-based
regression model links remote sensing-derived
informaFlood disasters can generate significant socioeconomic tion such as digital elevation model (DEM) and flood
impacts [
In this paper, we propose a methodology for estimat- of this work are threefold, which are as follows.
ing inundation depth in the case of flood disasters, using
an integration of numerical simulation and convolutional
neural networks (CNNs) technologies. Our method is an
extension of the framework presented in [
…
… DEM
SAR (RGB)
2.1. Flood mapping via remote sensing
…
vanced CNN-based frameworks. Recently, [
Flood detection is a well-studied topic in the remote sensing community. Pioneer methods are based on moderate and high-resolution optical imagery, exploiting their multi-spectral information. These methods primarily uti- 2.2. Flood Analysis via Numerical lize the near-infrared band to compute spectral indexes Simulation such as the well-known Normalized Diference Vegetation Index (NDVI). For instance, [5] analyzed images from In general, methods based on numerical simulation give the Terra-ASTER and Ikonos sensors to estimate the flood better accuracy for estimating flood extent and its correextent after the 2004 Indian Ocean Tsunami. They ac- sponding inundation depth. These methods often involve curately detected the flood areas in southern Thailand. expensive computation to solve complex physical-based However, one drawback of using optical sensors is that governing equations [11]. As such, numerical simulation they are susceptible to weather and day-light conditions. methods are primarily used to develop risk maps considThus cloudy skies render optical images almost unusable. ering extreme scenarios [12] as preparation for future
With advances in earth observation technologies, such disaster events. as Synthetic Aperture Radar (SAR), several researchers have developed eficient algorithms to detect flooded 3. Methodology areas using change detection analysis of images acquired before and after the disaster. For instance, [6] evaluated This study integrates two advanced technologies, namely the ability of fully-parametric SAR data to detect flooded numerical simulation and deep learning. The numeriareas after the 2011 Tohoku Tsunami. [7] presented an cal simulation generates suficient training samples, and index-based analysis using multi-temporal statistics of deep learning maps the nonlinear relationship present in SAR images. the training data. Our proposed methodology presents
Following the success of modern machine learning two main modules. First, in the development stage, we algorithms, several end-to-end methods have been pro- synthesize a suficient amount of training samples of posed using either optical imagery of SAR data. For in- flood inundation using a physical-based numerical model. stance, [8, 9, 10] developed techniques for assessing flood Then, we train a CNN model in a regression setting to extent using SAR intensity and coherence data and ad- map a binary mask representing the flooded area and DEM to the corresponding inundation depth. Second, deployment stage, we assume that following a significant lfood disaster, it is possible to obtain the flooded area (binary mask) through the analysis of remote sensing imagery (e.g., Synthetic Aperture Radar, optical imaging).
Then, using the binary mask and DEM as inputs, we can infer the associated inundation depth based on the CNN model trained in the first stage. Fig. 1 depicts an overview of our proposed framework. In this paper, we primarily focus on testing the concept of the first stage and present a preliminary evaluation of the second stage. 3.1. Flood simulation In this work, we use the Rainfall-Runof-Inundation (RRI) Model developed by the International Center for Water Hazard and Risk Management (ICHARM). The RRI model is capable of simulating rainfall-runof and flood inundation simultaneously in a two-dimensional configuration [13]. The RRI model handles the terrain slope and river channels separately. In its 2D configuration, the channels are discretized as the center line of the overlying slop grid cell. The flow on the grid terrain slope is calculated using the 2D difusive wave model, while the river channel flow uses a 1D difusion wave model.
ℎ + + = −
+ + = − ℎ − + + = − ℎ − (1) (2) (3)
The model’s governing equations (Eqs. 1, 2, and 3) are derived from a mass balance and momentum conservation conditions. Where ℎ is the height of water from the 3.2. Deep-learning-based regression local surface, and are the unit width discharges in and directions, and are the flow velocities in and Recently, CNN models have achieved excellent success directions, is the rainfall intensity, is the infiltration in mapping nonlinear features as regression tasks [4, rate, is the height of water from the datum, is the 15]. Here, we define the regression problem from DEM density of water, is the gravitational acceleration, and and flooded area to corresponding simulated inundation and are the shear stresses in and directions, depth. respectively. As described in the previous section, the inundation
The RRI model generally uses rainfall and DEM to fore- depth images are built using a numerical simulator uscast the corresponding inundation depth. Our method- ing DEM and rainfall information as input. Further, we ology generates the synthetic flood inundation depth can generate the flooded area (binary mask) using the images using several precipitation scenarios generated computed inundation depth by a straightforward threshrandomly. For each target site, we defined thirty rainfall olding approach. Here, we define flooded areas with an scenarios ranging from 0 /ℎ to 20 /ℎ. The inundation depth greater than 0.2 m. Then, our regresmaximum rain amount was set based on the historical sion models learn the nonlinear mapping from input record from all target sites. , which is consist of binary mask and DEM images, to
In addition, we use a standard method [14] to derive output (inundation depth): : →
the inundation depth based on the DEM and binary mask. As suggested by [
Training & validation areas
Testing area Omachi Omachi
Hijikawa
Ibaraki
Okayama
This straightforward method finds the maximum floodwater level in the flooded area and subtracts it from the local inundated land elevation. This inundation depth ( ) represents a theoretical assumption of a steady horizontal floodplain. We use this theoretical floodplain as a baseline to compare the performance of our methodology. (Huber loss) (Eq. 4, where = − () and = 1) to optimize our CNN regression models. The Huber loss combines the advantage of the L2 loss (gradient decreases when the loss gets close to local minima) and the L1 loss (less sensitive to outliers).
ℒ () = {︃ 21 ()2,
|| ≤ 1 2, otherwise. || − 2 (4)
M E Dm 50 15 llf a ina mm/hr R 20
For the regression tasks, we investigate a wellestablished encoder-decoder architecture (U-Net [16]), which has consistently shown high performance in se- 0 mantic segmentation tasks [17], and two of its varia- thp m 2.5 tions. First, the Attention U-Net [18] incorporates a self- de attention mechanism in U-Net with contextual informa- iton 0 tion extracted at a coarser scale. The attention mod- nda ule emphasizes accurate features for a given task and Iun suppresses irrelevant features when concatenating features extracted by the encoder with those of the decoder Figure 3: Examples of the inputs (DEM and rainfall) and through the skip connections. Second, the LinkNet [19] outputs (maximum inundation depth) of the RRI model. also has an encoder–decoder structure with residual blocks and skip connections, but it shares the information learned by the encoder with the decoder through addi- For the inundation depth simulation, we used the tive operations. In the U-Net model and its variations, DEM released by the Geospatial Information Authorthe overall design of each encoder block is two convolu- ity of Japan (GSI). GSI provides DEM of 5 m and 10 m tional layers, each followed by batch normalization and grid size. In this study, to reduce the computational time, a rectified linear unit (ReLU). we construct the input DEM raster using a re-sampled
Finally, we use the Adam solver [20] for optimization ground sampling distance of 45 m. In addition to the with a learning rate of 0.0001. Xavier initialization is DEM input, the RRI model requires the flow accumulaused to initialize the weights. The batch size is 64, and tion and flow direction that are directly calculated from the number of epochs is 120. We use the PyTorch frame- the DEM. We use the ArcGIS 10.5 software to derive the work [21] to implement our CNN models in two NVIDIA later flow parameters.
TITAN RTX 24-GB GPUs. We generate thirty rainfall scenarios for each target site to build the training samples. Then, the RRI model 4. Experiments simulated each scenario and estimated the maximum inundation depth in meters. Here, we systematically crop, Here, we show the eficiency of our proposed method- using a sliding window, tile where there is at least 0.2 m ology for predicting inundation depth using informa- of inundation depth for each target area. This process tion collected from previous flood disasters in Japan. We eliminates spots with no inundation, such as mountain evaluate the performance of the CNN-based models (e.i., areas. We set the tile size as 5.76 km × 5.76 km (128 × U-Net, Attention U-Net, and LinkNet) using a realistic 128 pixels). Finally, the tiles (samples) are 153, 253, 298, operational scheme. and 327 for Ibaraki, Okayama, Hijikawa, and Omachi, respectively. Fig. 3 shows examples of the simulated inundation depth using the RRI model. 4.1. Dataset Our experiments focus on the flood disasters from four diferent events located at unique sites in Japan: 1) 2015 Floods in Ibaraki, 2-3) 2018 Floods in Okayama and Hijikawa, and 4) 2019 Floods in Omachi. All flood disasters occurred following torrential rainfalls. Fig. 2 shows the location of each event. The morphology of each target site is diferent, where Ibariki and Omachi present a gradually plain surface while Okayama and Hijikawa show mountain terrain. 4.2. Cross-domain evaluation We use the root-mean-square error (RMSE) to evaluate our results. We compute a pixel-wise RMSE using the predicted inundation depths from the trained CNN models and the reference simulation results. Conventionally, machine learning methods evaluate their performance using training and testing samples derived with the same statistical distribution. Although such a scheme benefits model generalization, it does not represent a practical application, especially in analyzing flood disasters where rainfall distribution and topographic features generate a unique pattern of inundation depth.
Thus, we design our experiments considering a realworld deployment. We used three target areas for training and validating our CNN models. Then, we tested the model performance and generalization using an independent test target area. These experiment settings represent a realistic condition during disaster response, where we can derive binary masks (flooded areas) using image analysis of remote sensing imagery or machine learning-based methods [22, 23]. Then, the DEM and binary mask are input for forecasting the expected inundation depth within the flooded area.
In this study, we select the Omachi area for testing our methodology. This area is never used in model training. Thus, we train the CNN models using the other target areas (i.e., Ibaraki, Hijikwa, and Okayama). We randomly split the remaining samples into two subsets, training and validation sets. We analyze the robustness of our framework by conducting three independent experiments using a diferent seed number to control the random operations. We report the mean and standard deviation of the three-fold experiments.
We conduct two training schemes. In the first, we construct the input images by concatenating the DEM and binary mask. This scheme represents a more realistic scenario. In the second training scheme, we also concatenate the theoretical floodplain ( ). Thus the input image is a 3-channels raster. The purpose of the later scheme is to evaluate the accuracy of the CNN model by providing it with more information related to the inundation depth. n o ilt a u m i S n o iit c d e r P . u m i S – . d e r P D w
F (theoretical floodplain) in the input does not significantly modify our models’ performance. One possible reason for such an outcome is that the is almost a linear operation of the DEM and binary mask. Thus, the in4.2.1. Quantitative Results formation that it might input to the network is already Table 1 shows the numerical results of predicting the included in the two other features (i.e., DEM and binary inundation depth on the validation subsets. All three re- mask). gression models perform similarly, with LinkNet slightly Table 2 list the numerical evaluation on the test taroutperforming the other models. These results indicate get area (i.e., Omachi area). Recall that this area was that the networks successfully learn a nonlinear map- never used during training, representing a fully out of ping from diferent binary change and DEM images to the distribution set. We found that the LinkNet again their corresponding inundation maps. These results are shows slightly better performance among the diferent consistent with the training strategy of randomly split CNN-based regression models. However, in general, the training and validation samples from the same statistical models outperform the validation scores, demonstratdistribution, namely training target areas. ing our framework’s great generalization ability. One Furthermore, we also observe that including the possible reason for such results is that the topographic
This work was supported by the Japan Aerospace Exploration Agency (JAXA) 3rd Research Announcement on the Earth Observations, Japan Society for the Promotion of Science through (JSPS) KAKENHI under Grant 22H01741, the Japan Science and Technology Agency (JST), Japan-US Collaborative Research Program, Grant Number JPMJSC2119, and JST, FOREST Grant Number JPMJFR206S.