Fast high-fidelity flood inundation map generation by super-resolution techniques

Flooding stands out not only as the most prevalent natural hazard (Parhi 2018; Rentschler & Salhab 2020), but also as the natural hazard that produces more annual damage than any other weather-related occurrence in the United States (NOAA 2016). From 1998 to 2017, flooding affected over two billion people, claiming the top spot among all natural hazards in terms of its impact on population (Cred 2018). The consequences of severe floods can be dire, encompassing substantial economic losses and endangering human lives (Haltas et al. 2021). Hurricane Harvey hit Houston in August 2017, resulting in over $125 billion of economic loss (Kousky et al. 2020). Similarly, a record-breaking rainstorm struck Henan, China, in July 2021, claiming 398 lives and causing an economic setback of $17.8 billion (He et al. 2023). More recently, in August 2023, Typhoon Doksuri slammed northeast China, triggering a severe flood that displaced over a million individuals. Apart from the direct threats to both human lives and commerce (Alexander et al. 2019), floods contribute to environmental and public health risks (Okaka & Odhiambo 2018; Rivett et al. 2022). Moreover, the increasing impact of global warming and climate change has amplified the occurrence and intensity of heavy rainfall events (Donat et al. 2016; NASA 2017), leading to a higher frequency of severe floods in recent decades (Popescu & Bărbulescu 2023). Thus, fast and accurate flood prediction holds immense significance in preserving lives, minimizing economic damages, and reducing environmental and public health risks.

In recent years, numerical methods have been widely used in the field of hydrology and hydraulics for flood inundation map generation. Prominent models and software applications, such as HEC-RAS (USACE 2018), FLO-2D (FLO-2D 2018), and SRH-2D (Lai 2010), have been developed to numerically solve the two-dimensional (2D) shallow water equations. These models and software have been extensively utilized by researchers to simulate multiple flood scenarios across various floodplains (Rangari et al. 2019; Ongdas et al. 2020; Iroume et al. 2022; Pathan et al. 2022; Shaikh et al. 2023). Although numerical methods are widely accepted because of their high accuracy and reliability, it is important to acknowledge that achieving high-fidelity simulations can be computationally intensive and time-consuming (He et al. 2023). This is mainly due to the nature of the numerical methods, which often involve considerations of scheme complexity, mesh convergence, and sometimes the requirement of a full momentum solver instead of a diffusion wave solver.

With the current era of big data, in recent years deep learning models have also achieved remarkable success in hydrology and hydraulics (Assem et al. 2017; Hosseiny et al. 2020; Cai et al. 2022; Jiang et al. 2022; Park et al. 2022; Shi et al. 2023; Yin et al. 2023). These models all concentrate on predicting water depths at specific observation points, as these points serve as their training dataset. However, due to the 2D nature of flood mapping outputs, acquiring an appropriate training dataset solely from observational data at water stations is challenging. This issue fundamentally poses a barrier to the effective implementation of deep learning models for the flood mapping problem. As a consequence, the utilization of deep learning models for generating spatially varied flood maps remained largely unexplored until around 2022, with only a limited number of studies delving into this area (Bentivoglio et al. 2022). To overcome the issue, some earlier research attempted to transform the problem into a classification task, employing geographic information system digital elevation data to predict the likelihood of flooding for individual cells or pixels (Bui et al. 2020; Nemni et al. 2020; Muñoz et al. 2021). Although this approach may overcome the issue and simplify the problem, it also results in a substantial reduction in the significance of the information conveyed by the flood maps.

A novel approach has emerged in the field of fluid dynamics, gaining rapid popularity, which involves the integration of super-resolution networks with numerical modeling (Pourbagian & Ashrafizadeh 2022; Bao et al. 2023; Long et al. 2023; Xu et al. 2023; Yasuda & Onishi 2023). However, the application of this innovative super-resolution method in the domains of hydrology and hydraulics remains almost nill. In the context of flood map prediction, the work of He et al. (2023) stands as the only paper that employs this cutting-edge methodology. He et al. (2023) employ 2D hydrodynamic models to generate data for both coarse and fine grids, subsequently utilizing a deep learning model to enhance the resolution of results from the coarse grid to match the fine grid. However, there are two noteworthy limitations in their current approach. First, the grid resolution utilized in their 2D hydrodynamic model is too coarse, even in the finest grid setting of 30m resolution. The authors themselves acknowledge that such coarse grids might fail to capture certain important flow physics, potentially leading to gaps in the precision of their super-resolution outcomes. Second, the study area of this paper is a medium-sized watershed in a rural region, characterized by an elevation difference exceeding 900 m. Despite this considerable topographic variation, the study still encounters notable prediction errors. However, it is worth noting that in most urban areas, elevation differences are considerably smaller. Hence, whether this method can still accurately capture the high resolution of a street-level flood map is worth further investigation. Therefore, the exploration of super-resolution techniques for generating high-fidelity flood maps in urban areas remains incomplete.

The primary objective of this study is to introduce an approach capable of fast and accurate modeling of urban riverine flood maps with water depth information. It is crucial to have a rapid and accurate response when preparing for a real hurricane or flood event. The proposed methodology will combine the strengths of numerical methods and neural networks to establish a framework that consistently enhances low-fidelity simulation results to attain high-fidelity outcomes. To achieve this, first, we will construct a U-Net architecture and assess its performance in urban flooding scenarios. Second, since the generative adversarial network (GAN) model showed superior performance in the field of computer vision, we will adapt and evaluate the GAN model's performance in the context of urban flooding. Lastly, we will undertake an investigation of the model's sensitivity to input resolution, probing whether our proposed methods can maintain high accuracy and effectiveness with lower-resolution input data.

Both low-resolution and high-resolution simulation results are computed by 2D HEC-RAS in this paper. The location of the boundary conditions is explained in the previous section, and all time-series boundary conditions and validation data are acquired on DBHYDRO from the SFWMD. In this study, we planned to use 40 training cases to ensure the size of the training dataset; however, finding such a comparable quantity of significant flooding events from the past 10 to 20 years is challenging. Therefore, we decided to artificially generate certain boundary conditions for training purposes. For three upstream flow conditions, we selected the 10 largest flow rate hydrographs at each location from the past 10 years and applied the Gaussian distribution to generate 40 sets of different flow rate hydrograph inputs. Notably, the length of the 10 flow hydrographs is not the same because the event is defined by their corresponding rainfall data. Regarding the downstream water stage conditions, manipulating the time series pattern is not feasible as it reflects the actual tide wave. Thus, we chose the highest annual tide stage from the past 10 years. These tide stage hydrographs are then replicated three times and randomly distributed across the 40 training sets. In the testing dataset, we used two historical hurricane events: Hurricane Irma from 2017 and Tropical Storm Isaias from 2020. Both the high-resolution test case simulations are validated at water station S1.

The mesh size used for the low-resolution simulations is 150 ft, while the mesh size for the high-resolution simulations is set as 20 ft. This results in a significant difference in the total cell count, with the high-resolution count being 56 times larger than the small-resolution cell count. Additionally, we added a refinement along the riverbank to enhance the reliability of our high-resolution simulation. Regarding the setup of the numerical solver, it is essential to utilize a full momentum equation solver for situations impacted by tidal conditions (USACE 2018). Therefore, we used the full momentum equation solver to uphold the high-fidelity nature of our high-resolution case, while we used the diffusion wave equation solver in our low-resolution simulations to ensure computational efficiency. The outputs of the 2D HEC-RAS simulations at nodes and faces are automatically stored in HDF5 format by default. Therefore, we employed a Python script to retrieve the saved simulation results from all cases.

As presented in Figure 3, the lower-resolution water depth data derived from low-fidelity simulations have the dimensions of ⁠, whereas the elevation data from DEM and the slope data calculated from the elevation data exhibit dimensions of ⁠. The elevation and slope data have an even higher resolution than the resolution of the high-fidelity simulation. Therefore, it becomes imperative to perform an interpolation to establish consistent dimensions, as indicated by the blue arrow. Following this interpolation, the three input variables are combined into three channels, akin to the concept of RGB (red, green, and blue) channels within the field of computer vision. During the training phase, the high-resolution water depth data serve as labeled data to compute the loss with the model predicted values so that the model can keep updating its learning parameters.

The U-Net architecture, known for its encoder–decoder structure, consistently demonstrates its ability to produce favorable results efficiently and swiftly across a range of vision tasks. A major advantage of the U-Net lies in its capacity to perform well without the need for a large training dataset or extensive graphics processing unit (GPU) memory. A key factor contributing to the success of the U-Net is its incorporation of data augmentation techniques, such as elastic deformation, enabling the deep neural network to effectively learn from diverse input data variations, even when working with a limited number of annotated images.

In this paper, we adopt the structure of Res-U-Net, which employs ResBlockss to enhance information flow, addressing the issue of gradient vanishing. Our implementation is organized into four distinct resolution steps on each side, denoted by the blue-colored layers in Figure 4. Each ResBlock in this structure consists of a pair of consecutive 3 × 3 convolutions. On the right side, each layer includes a 2 × 2 transpose convolution layer along with two 3 × 3 convolutions. Rectified Linear Unit (ReLU) serves as the activation function for the entire framework.

As Figure 6(c) and 6(d) presents, both the U-Net and GAN models can successfully enhance the solution resolution and accurately fill up the missing information. The difference between the flood map generated by the machine learning model and the high-resolution simulations (considered ground truth) is extremely small. It is even challenging for the human eye alone to distinguish this distinction. Furthermore, the machine learning model has successfully captured all the intricate details of flood depths at the street level, making it feasible to identify which streets are affected by flooding in the machine learning-generated map.

There is a significant difference between the low-resolution simulation results and the high-resolution results, particularly noticeable in two of the tributaries. The water depth data produced by the low-resolution simulation tend to exhibit instability due to the limited number of grid points. This issue is apparent when examining Figures 6 and 7, which reveal that there are only one to two computational cells spanning the river. However, the elevation changed rapidly in these one to two computational cells. This is the major reason for the significant mismatch. Nevertheless, our machine learning models effectively addressed this issue. As shown in Figure 8, both the U-Net and GAN models can provide water depth results that are closely aligned with those from the high-resolution simulation.

Table 1 presents the performance of the proposed method in various test scenarios. The GAN model exhibited superior performance compared with the U-net model in terms of mean absolute error (MAE) and root mean square error (RMSE). This is expected since the GAN model's generator is based on the U-Net architecture, and the discriminator network could provide the additional information that helped the generator perform better. However, it is worth noting that the GAN model lagged behind the U-Net model in terms of precision, indicating that the GAN model tends to slightly overestimate the flood area. This overestimation may not necessarily be detrimental in engineering practice, as it can provide higher safety factors.

The performance of the proposed method with different coarse-grid sizes under the Hurricane Irma event is summarized in Table 2. Both the U-Net and GAN models exhibit reduced performance as the input low-resolution mesh becomes coarser. Notably, the performance of U-Net declined more pronouncedly compared with the GAN model. The MAE and RMSE of using the coarsest mesh size as input is around four times higher than using the original mesh size. While the GAN model's performance drops initially when coarse-grained, it stays stable as the grid coarsens further.

The biggest advantage of our proposed approach lies in its ability to combine speed and high accuracy. As Table 3 shows, conducting a low-resolution simulation takes around 40 s, but it lacks accuracy and reliability. By contrast, performing a high-fidelity and high-resolution simulation consumes 7–8 h, which may significantly reduce decision-making and execution time when a huge stormwater event is approaching. Thus, when only using numerical methods, it is almost impossible to achieve both speed and accuracy at the same time. Our proposed method could be considered a ‘convertor’ that can consistently transform low-resolution simulation outcomes into high-resolution results. The total time required to obtain high-fidelity results using our method equals the time spent generating the low-resolution simulation plus the neural network processing time, which amounts to approximately 50 s in our case. This means our method makes it feasible to attain a millionth-level resolution within a minute, opening the door to real-time predictions and digital twins after further development.

Another notable advantage of our proposed method is its efficient information representation. Unlike conventional neural networks that require a large number of boundary conditions and operational variables, our method relies on just three matrices of physical variables as input. More specifically, boundary conditions and operational variables such as rainfall patterns, tide patterns, and hydraulic structure operation states typically exhibit extremely high variability. Training a neural network to accurately capture and learn all possible patterns within these variables is an exceedingly challenging task. To overcome this challenge, a huge amount of data is usually needed to feed the neural network in the training phase. As we know, high-quality data in the hydrology and hydraulic fields are limited. Attempting to train the neural network with billions of input samples, as is commonly done in computer vision or natural language processing, is impractical for our hydrology and hydraulic problems. However, in our framework, the input to the neural networks can be understood as ‘preprocessed input’ by HEC-RAS, resulting in a significant reduction in variability. The coarse HEC-RAS model took care of these high-variability variables and processed them into a low-variability flood map information. The range of possible flood map patterns along the riverine is limited and follows certain physical rules. For instance, water consistently accumulates at lower elevation locations. The neural networks could rapidly capture these simpler patterns and provide results with a high level of accuracy. This is also the major reason for the success achieved with just 40 sets of training data, a quantity typically deemed extremely insufficient in conventional deep learning frameworks.

There are two major reasons for our proposed method to achieve such incredible accuracy with a very limited training dataset. The two major reasons are explained as follows.

The primary factor is efficient information representation, as previously discussed. In contrast to traditional super-resolution tasks, such as enhancing the resolution of 10,000 different types of images, our target, the flood map, exhibits significantly lower variability. With the assistance of HEC-RAS, the initially high-variability input data has been transformed into flood map data, which has much lower variability. The potential shapes and dimensions of flood maps are highly constrained. Therefore, if the training data cover a wide range of flood levels and is well distributed, the extrapolation issues could be completely eliminated. Interpolation predictions tend to yield much higher accuracy in almost all machine learning cases.

The second major reason is that we actually converted a super-resolution problem to a denoising problem from the perspective of neural networks’ functionality. In the field of traditional computer science, nearly all conventional super-resolution networks deal with images composed of three channels: RGB. However, our framework manipulates directly on scalar matrices. In many cases, the pixel values in RGB are unsuitable for numerical interpolation, whereas our 2D scalar matrices allow for such operations. Consequently, most super-resolution frameworks require upsampling within the network to enhance resolution, whereas our neural network does not, as the input and output dimensions in our method are identical. By this uniformity in input and output dimensions, we can effectively transfer low-level feature map information to the latter stages of the neural network through skip connections. This step can keep more low-level feature map information and often leads to a significant improvement in model performance.

There are several limitations to this work. First, the study area examined in this research only exhibits a tide-dominant domain, which means the magnitude and gradient of the downstream tide condition influenced more than the magnitude and gradient of the upstream flow rates. The flow rate-dominant domain was not investigated in this paper owing to the content length constraints and time limitations. Such flow rate-dominant domains could potentially yield different model performance outcomes. Second, the methodology employed in this study demands a certain level of GPU memory, even though it offers rapid training and testing speeds. The GPU memory requirement is directly linked to the total number of grid points of the target resolution. Presently, it has been observed that an 8GB GPU can only accommodate up to one million grid points. For conducting super-resolution tasks on very large riverine systems, it is advisable to employ GPUs with larger memory capacities or use other methods. Lastly, the current work falls under the category of ‘small models’ in the field of computer science and artificial intelligence. This implies that each model only works in a specific domain. Generalizing the findings of this study to create a ‘large model’ capable of addressing all types of riverine systems remains a formidable challenge with the existing model architecture. Achieving this ultimate objective of artificial intelligence may require the adoption of ‘large model’ structures such as Swin-Transformer, Vision Transformer (VIT), or diffusion models.

This paper presents a super-resolution-assisted framework that can rapidly and accurately model the riverine system flood map. The proposed method combines the strength of both numerical simulation and neural networks. It can present a high-fidelity numerical simulation result by using low-resolution numerical simulation. This process shortens the total computation time from many hours to approximately 1 min. The drastic reduction in computational time makes real-time prediction feasible, which is significantly important in real hurricane or flood preparation scenarios. The model's performance has been evaluated and a high accuracy is achieved within engineering practices. The findings are as follows:

• 1.

  In our study area, both the U-Net and GAN models have demonstrated the capability to dramatically decrease the computation time required to generate high-fidelity results, reducing it from 7–8 h to 1 min. Furthermore, the accuracy of both models is notably high, as evidenced by the MAE values. The U-Net model yielded MAEs ranging from 0.00048 to 0.00219 ft, while the GAN model produced MAEs within the range of 0.00046–0.00133 ft.

• 2.

  The GAN model displays a lower sensitivity to changes in input resolution when compared with the U-Net model, although both models exhibit a decrease in performance as the input resolution decreases.

• 3.

  The proposed method extends the applications of super resolution beyond its traditional use in computer vision. It effectively recovers lost information because of the large grid size in the low-resolution geometry.

The authors gratefully acknowledge the financial support from the National Science Foundation under Grant CBET 2203292. Also, the authors are grateful to the anonymous reviewers for their constructive comments, which helped to significantly improve the quality of the manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.