The rapid and accurate forecasting of natural disasters is paramount for effective disaster mitigation and saving lives. The 2011 Tohoku tsunami tragically highlighted the limitations of existing early warning systems. Initial underestimation of the earthquake magnitude and tsunami height led to delayed evacuations and increased casualties. While the warning was updated, communication disruptions hampered information dissemination. The catastrophic impact of the 2004 Indian Ocean tsunami further emphasized the urgent need for improved early warning systems. Current tsunami early warning systems, developed using past events and available technology, face challenges. Real-time inundation forecasting remains difficult due to the complexities of rapid tsunami source estimation and the high computational cost of simulating tsunami propagation. This paper addresses these challenges by proposing a novel tsunami forecasting method utilizing Convolutional Neural Networks (CNNs), a deep learning approach. CNNs offer a computationally efficient way to directly forecast tsunami inundation from real-time observation data without requiring extensive computational resources or complex tsunami source estimation. Deep learning's success in image and pattern recognition and its application in physics-based simulations makes it a promising tool for tsunami forecasting. The study aims to demonstrate the feasibility and effectiveness of a CNN-based approach for end-to-end tsunami inundation forecasting, providing rapid and accurate early warnings.

Existing tsunami early warning systems, particularly those developed since the 2011 Tohoku tsunami, utilize real-time observation data from dense tsunami observation networks. Methods include real-time inundation simulations using supercomputers, coupled with rapid source estimations and data assimilation techniques. However, challenges persist due to uncertainties in tsunami source estimation and the high computational demands of simulating nonlinear tsunami propagation in shallow water. The use of deep learning, and specifically CNNs, is relatively novel in this application, offering a potential solution to these challenges. While deep learning has proven successful in various fields, including image and pattern recognition and physics-based simulations, its application to end-to-end tsunami inundation forecasting represents a significant advancement.

This study employs a CNN to process data from dense tsunami and geodetic observation networks. The methodology involves three primary stages: data preparation, network configuration and training, and performance evaluation. Firstly, 10,000 cases of numerical tsunami propagation and inundation simulations were conducted using the TUNAMI-N2 code. These simulations, based on randomly generated tsunami scenarios, produced synthetic observation data at various points and the resulting tsunami inundation waveforms. Ocean bottom pressure gauge data was simulated as pressure waveforms. Inland geodetic observations of initial ground heights were included as additional inputs, reflecting their usefulness in tsunami source determination. A 1D-CNN with 15 layers was designed for tsunami forecasting due to its suitability for real-time and low-cost applications. The network architecture included convolutional and pooling layers to extract features from the stacked waveform inputs, and fully connected layers to forecast the onshore tsunami inundation waveform. The network's input considered various time windows (5, 10, 15, 20, 25, and 30 min) of tsunami observations to assess the impact of observation length. The training process utilized the mean squared error (MSE) as the loss function and the Adam optimization algorithm. The training was performed on a GPU-accelerated supercomputer using PyTorch and Horovod. The performance of the trained CNN was evaluated using 1000 test scenarios not used in training, using metrics such as maximum tsunami amplitude and arrival time. Further analysis explored the effects of observation length and the inclusion of geodetic data on forecasting accuracy. A sensitivity analysis, employing an occlusion test, determined the importance of specific observation points in the forecasting process. The computational time for tsunami forecasting was also measured to assess the method's suitability for real-time applications. Finally, the CNN's performance was tested using actual observation data from the 2011 Tohoku tsunami event, examining its robustness to noise in real-world data.

The CNN demonstrated excellent performance in forecasting tsunami inundation. Using only 5 minutes of offshore tsunami and inland geodetic observations, the mean absolute errors for maximum tsunami amplitude and arrival time were 0.4 m and 47.7 s, respectively. The average relative errors were 8.1% and 1.2%, respectively. The forecasting process was exceptionally fast, requiring only 0.004 s on average using a single CPU node. Longer observation periods led to improved forecasting accuracy. The inclusion of geodetic observation data significantly enhanced the model's performance, particularly for shorter observation periods, by improving initial ground height estimation, compensating for the limitations of short-term offshore observations. Sensitivity analysis revealed that the CNN primarily utilizes information from observation points along the major tsunami propagation path to the forecasting site. The computational time remained remarkably low even with longer observation periods and the addition of geodetic data. When applied to the 2011 Tohoku tsunami event using real-world data, the CNN provided reasonably accurate inundation forecasts, particularly with longer observation windows (35 and 40 minutes), though the predicted arrival time tended to be slightly earlier than the observed arrival time. This slight discrepancy might be attributed to the simplified assumption of instantaneous slip in the tsunami data generation process, neglecting the effects of rupture propagation which are estimated to have lasted around 2.5-3 minutes. Even with added noise simulating real-world conditions, the CNN maintained high accuracy, demonstrating its robustness to noisy inputs.

This study demonstrates the significant potential of CNNs for rapid and accurate tsunami inundation forecasting. The method addresses key limitations of traditional simulation-based approaches by bypassing the need for complex and time-consuming tsunami source estimations while maintaining high accuracy and computational efficiency. The successful application of the CNN trained only on synthetic data to the 2011 Tohoku tsunami event highlights the model's ability to generalize to real-world scenarios within the range of the training data. The robustness to noise underscores the practicality of the method for real-time applications with potentially imperfect observational data. However, the slight underestimation of arrival time in the 2011 event underscores the need to further improve the model by incorporating the effects of rupture propagation in future studies. The use of geodetic data significantly enhances the model's accuracy, highlighting the value of integrating various data types for improved forecasting. Future research should focus on expanding the training dataset to encompass a wider variety of tsunami generation mechanisms to improve the model's applicability to various tsunami events and enhance its overall accuracy and robustness.

This research presents a novel and highly effective method for early tsunami inundation forecasting using CNNs. The model demonstrates exceptional speed and accuracy, addressing the limitations of conventional methods. The ability to utilize synthetic data for training, coupled with robustness to noise and the incorporation of geodetic data, makes this approach highly practical for real-time early warning systems. Future work should focus on expanding the training data to cover a broader range of tsunami scenarios, including those from non-seismic sources, and refining the model to address the minor arrival time discrepancies observed.

The primary limitation is the reliance on synthetic training data. While the model generalizes well to real-world scenarios, the absence of a comprehensive dataset of real tsunami events could limit its performance in highly unusual scenarios. The slight tendency to underestimate the tsunami arrival time, potentially related to the simplified assumption of instantaneous slip during data generation, is another limitation. The accuracy of the forecast is also contingent on the availability and quality of observation data. Incomplete or noisy data can affect the model's predictive power.