Early forecasting of tsunami inundation from tsunami and geodetic observation data with convolutional neural networks

The study addresses the critical need for rapid and accurate tsunami hazard forecasts to support timely evacuations and reduce casualties. Experiences from the 2011 Tohoku tsunami revealed that underestimation of earthquake magnitude and tsunami height, compounded by communication disruptions, led to inadequate evacuation and high loss of life. Although observation networks have improved and several real-time forecasting approaches have been developed, accurately forecasting near-field tsunami inundation immediately after an earthquake remains difficult due to uncertainties in rapid source estimation and the heavy computational cost of nonlinear shallow-water simulations. The authors propose an end-to-end convolutional neural network (CNN) that directly predicts onshore tsunami inundation time series from real-time offshore tsunami and onshore geodetic observations, aiming to deliver fast, accurate early warnings without explicit source inversion or supercomputing resources.

The paper reviews advancements in tsunami early warning since the 2011 Tohoku event: deployment of dense offshore observation networks (e.g., DONET, S-Net) and development of real-time forecasting methods, including rapid source estimation, data assimilation, and high-performance inundation simulations. Prior approaches often rely on estimating the tsunami source from seismic or geodetic data and then running computationally expensive simulations, which introduces delays and uncertainties. Studies have shown inland geodetic data are valuable for source characterization, and data assimilation of offshore pressure data can improve forecasts. However, real-time inundation prediction still faces challenges due to non-unique inversions and computational burdens. Deep learning, particularly CNNs, has achieved strong performance in pattern recognition and has begun to serve as a surrogate for physics-based simulations, motivating its application to tsunami forecasting.

Data generation and simulation: The 2011 Tohoku-Oki source geometry was discretized into 44 subfaults (per Fujii et al.). Slip on each subfault was randomly assigned within defined ranges to synthesize 12,000 earthquake-tsunami scenarios (Mw ~9.0–9.2 assuming 30 GPa rigidity; Mo 4.03×10^22–8.21×10^22 Nm). Initial sea-bottom deformation used Okada’s formulation. Tsunami propagation and inundation were simulated with TUNAMI-N2 (nonlinear shallow-water equations) on nested grids (grid sizes ~1215, 405, 135, 45, 15 m) with Δt = 0.2 s; the 15 m grid covered the Sendai Plain. Each 2 h simulation required ~3 h on a CPU node (2×Intel Xeon Gold 6148, 384 GiB RAM). Observations and targets: Inputs comprised 49 offshore tsunami observation points (ocean-bottom pressure/gauges) at 1 Hz and 5 onshore geodetic (GNSS) points represented as constant ground deformation vectors having the same sample length as the offshore inputs. Several input window lengths were tested (5, 10, 15, 20, 25, 30 min). The forecast target was the onshore inundation waveform (flow depth) at a single site on the Sendai Plain (sampled at 0.5 Hz, length 3600). Dataset split: 10,000 training, 1,000 validation, 1,000 test scenarios. CNN architecture: A compact 1D CNN of 15 layers: nine convolutional layers, three pooling-like convolutional layers, followed by three fully connected layers. Input channels are stacked waveforms from selected observation points (offshore and onshore). Activations: Leaky ReLU (α = 0.01). Dropout p = 0.5 on fully connected layers. Kernel sizes/strides/padding were chosen to preserve array sizes; dimensionality reduction primarily via pooling-like layers. For certain observation lengths (e.g., 5, 15, 25, 35 min), the last conv kernel size was set to 3 to avoid remainder issues. Longer input windows yielded larger networks (more parameters). Training: Loss was mean squared error (MSE) over the forecast time window. Optimizer: Adam with learning rate 1e-4, β1 = 0.9, β2 = 0.999, ε = 1e-8. Implemented in PyTorch with Horovod on ABCI (per node: 2×Intel Xeon Gold 6148 and 4×NVIDIA Tesla V100 SXM2, 384 GiB RAM). Batch size 25 per GPU; 5 nodes; trained for 3000 epochs and selected the checkpoint with minimum validation loss. Training completed within ~2 h for the largest network. Evaluation metrics: Maximum tsunami amplitude (peak flow depth) and tsunami arrival time (time when flow depth first exceeds 10% of the maximum). Sensitivity analysis via occlusion tests: systematically zeroing individual station inputs to evaluate relative MSE change, highlighting influential observation points along tsunami propagation paths. Real-event application: Trained on synthetic scenarios and tested on actual 2011 Tohoku data: three GPS buoys (803, 801, 806) and three GNSS stations (Rifu, Watari, Soumal). Gaps in buoy records were cubic-interpolated to 1 Hz. Geodetic inputs used 5-min post-event displacements (latest available at Soumal). Forecasts were generated for the Sendai Plain site (validated against Arahama Elementary School surveyed trace) and for Sendai New Port (wave gauge recorded first peak before destruction). Robustness to noise was assessed by adding real pre-event short-period noise and synthetic white noise (up to 20% of max amplitude) to inputs; similarity was quantified via variance reduction.

- Synthetic-scenario performance (1,000 unseen tests; 5-min observations with geodetic data): mean absolute error of maximum tsunami amplitude ≈ 0.4 m (≈8.1% relative error) and arrival time ≈ 47.7 s (≈1.2% relative error). - Computational speed: average inference time ≈ 0.004 s per scenario on a single 40-core CPU node for 5-min input; even for 30-min inputs with geodetic data, ≈ 0.011 s per scenario. - Observation length and geodetic inputs: Longer input windows systematically improved accuracy. Including onshore geodetic data substantially improved forecasts, achieving performance comparable to longer offshore observation windows, primarily by better constraining initial ground deformation (subsidence/uplift). - Sensitivity analysis: The most influential observation points lie along primary tsunami propagation paths and above large-slip source regions. Distant stations had minimal impact. With longer observation windows and inclusion of geodetic data, nearshore sensitivities increased and onshore sensitivities were significant, indicating effective data integration by the CNN. - 2011 Tohoku event (inundation near Arahama ES): With ≤20 min observations, forecasts were unphysical due to lack of tsunami signal. With 30 min input (first positive peak appearing), forecasts became reasonable but underestimated amplitude. With 35 min, forecasted maximum flow depth ≈ 3.88 m at 3974 s; with 40 min, ≈ 5.64 m at 3952 s. These are broadly consistent with the surveyed trace (~4.62 m above the school basement), though forecasted peak arrival was ~3 min early. - 2011 Tohoku event (Sendai New Port): With 30 min input, forecasted first peak ≈ 6.78 m vs observed 6.62 m; with 35–40 min inputs, peaks ≈ 5.77–6.42 m and improved rising-phase matching. Arrival times remained ~3 min early. - Noise robustness: Adding real short-period noise yielded near-identical forecasts (similarity: 99.999% inundation; 99.997% offshore waveform). With large added white noise at 20% of max amplitude, average similarity remained ≈ 99.7% across 1000 tests.

The CNN-based approach directly maps real-time offshore tsunami and onshore geodetic observations to onshore inundation time series, avoiding explicit and uncertain source inversion and the computational expense of nonlinear shallow-water simulations. On unseen synthetic scenarios it achieved low errors in both amplitude and arrival time with millisecond-scale inference, demonstrating suitability for rapid warning issuance. The model effectively integrates heterogeneous data; geodetic inputs compensate for short offshore observation windows by constraining near-field subsidence/uplift that strongly influences inundation. Sensitivity analyses confirm that only a subset of observation points along dominant propagation paths is critical for accurate predictions, informing optimal sensor placement and data prioritization. Application to the 2011 Tohoku event shows the CNN trained solely on synthetic data can generalize to real observations when the event characteristics fall within the training distribution. The systematic ~3 min early-arrival bias is plausibly due to the instantaneous-slip assumption in training data (no rupture propagation), suggesting that incorporating realistic source time histories would further improve timing accuracy. Overall, the results support AI-enabled inundation forecasting as a practical component of early warning systems, particularly where computational resources are limited.

This work introduces an end-to-end 1D-CNN that forecasts onshore tsunami inundation waveforms directly from real-time offshore tsunami and onshore geodetic observations. Trained on 10,000 synthetic scenarios, the model achieves high accuracy and near-instant inference on standard CPUs, outperforming traditional simulation pipelines in speed while maintaining fidelity. It generalizes to the 2011 Tohoku event, providing reasonable inundation and offshore waveform forecasts even with noisy inputs, and highlights the value of integrating geodetic data. Future research should: (1) incorporate rupture propagation and source kinematics to improve arrival-time accuracy; (2) expand training datasets to encompass diverse tsunamigenic mechanisms (e.g., splay and outer-rise faults, tsunami earthquakes, volcanic and landslide sources), potentially by sampling generic sea-surface displacement units; (3) investigate multi-site/multi-output forecasting; and (4) exploit sensitivity insights for optimized sensor network design and data assimilation with AI.

- Training data assumed instantaneous slip on subfaults and did not model rupture propagation, likely causing the ~3 min early-arrival bias in real-event forecasts for large earthquakes. - The CNN was trained exclusively on synthetic scenarios; performance depends on the real event lying within the training distribution. Broader generalization requires more diverse scenario coverage. - With very short observation windows (≤20 min in the 2011 event), forecasts can be unphysical due to insufficient tsunami signal. - Generating large, high-resolution synthetic datasets and training sizable CNNs is computationally demanding, though feasible with modern HPC. - Real-time observations may be incomplete or noisy (e.g., instrument failure), which, while shown to be tolerable in tests, can still pose challenges in extreme cases.