Towards High Resolution Probabilistic Coastal Inundation Forecasting from Sparse Observations

TL;DR

This work tackles high-resolution probabilistic coastal inundation forecasting under sparse sensor data by introducing Diff-Sparse, a masked conditional diffusion model that fuses sparse inundation history with elevation and temporal covariates through a CNN and a cross-attention UNet. By training with a novel masking strategy and a context-embedding mechanism, Diff-Sparse can forecast multi-patch inundation distributions without retraining for different sensor placements. Experiments on TideWatch data for Virginia's Eastern Shore show substantial performance and scalability gains over baselines, especially at high sparsity, and ablations confirm the value of elevation and temporal context. The approach enables fast, probabilistic, location-specific flood forecasts and supports scenario-based decision making for emergency response and planning.

Abstract

Coastal flooding poses increasing threats to communities worldwide, necessitating accurate and hyper-local inundation forecasting for effective emergency response. However, real-world deployment of forecasting systems is often constrained by sparse sensor networks, where only a limited subset of locations may have sensors due to budget constraints. To approach this challenge, we present DIFF -SPARSE, a masked conditional diffusion model designed for probabilistic coastal inundation forecasting from sparse sensor observations. DIFF -SPARSE primarily utilizes the inundation history of a location and its neighboring locations from a context time window as spatiotemporal context. The fundamental challenge of spatiotemporal prediction based on sparse observations in the context window is addressed by introducing a novel masking strategy during training. Digital elevation data and temporal co-variates are utilized as additional spatial and temporal contexts, respectively. A convolutional neural network and a conditional UNet architecture with cross-attention mechanism are employed to capture the spatiotemporal dynamics in the data. We trained and tested DIFF -SPARSE on coastal inundation data from the Eastern Shore of Virginia and systematically assessed the performance of DIFF -SPARSE across different sparsity levels 0%, 50%, 95% missing observations. Our experiment results show that DIFF -SPARSE achieves upto 62% improvement in terms of two forecasting performance metrics compared to existing methods, at 95% sparsity level. Moreover, our ablation studies reveal that digital elevation data becomes more useful at high sparsity levels compared to temporal co-variates.

Figures (7)

• Figure 1: Diff-Sparse architecture. It has two main components. The first component involves context learning, where the sparse context inundation data ($\mathbf{y}_{t_0},\mathbf{y}_{t_1},...,\mathbf{y}_{t_{c-1}}$), sensor mask ($\mathbf{M}$), elevation data ($\mathbf{s}$) and temporal covariates ($\mathbf{z}_{t_0:t_{c-1}}$) are used to generate context embedding $\mathbf{h}_{t_0:t_{c-1}}$. The second component involves a diffusion model where the corresponding forecast is sampled by conditioning on the context embedding. $q(\mathbf{x}_{t_c}^n|\mathbf{x}_{t_c}^{n-1})$ denotes the forward diffusion process; $p_{\theta}(\mathbf{x}_{t_c}^{n-1}|\mathbf{x}_{t_c}^n,n,\mathbf{h}_{t_0:t_{c-1}})$ denotes the reverse diffusion process, parameterized by $\theta$.
• Figure 2: Bar-plots showing Diff-Sparse performance at varying sparsity levels in two patch configurations. Ten experiment runs were performed in each setting; mean and standard deviation of the performance metrics are shown.
• Figure 3: Ablation study at varying sparsity levels for two patch configurations. Ten experiment runs were performed in each setting; mean value of the performance metrics are shown using bar-plots.
• Figure 4: Line-plots showing the performance of Diff-Sparse for different prediction lengths with test dataset configuration $(64^2, 10)$, context length of 12 hours, and sparsity level of $95\%$, in terms of two metrics. The dots represent the mean value of the metrics over ten experiment runs with different seeds; the vertical lines represent standard deviation. We observe that Diff-Sparse performs best when prediction length is $1$. This is expected as Diff-Sparse is trained to make predictions for one future timestep. When making predictions for multiple timesteps auto-regressively, we observe that both NACRPS and NRMSE increase with increasing number of prediction timesteps.
• Figure 5: Bar-plots showing the performance of Diff-Sparse (in terms of NACRPS and NRMSE) for two different masking strategies during training (Zero mask and Noise mask), with patch configuration $(64^2, 10)$ and $(64^2, 20)$ and sparsity level $95\%$. Context and prediction lengths are set to 12 hours. The height of the bars represent the mean value of the metrics over ten experiment runs with different seeds; the vertical black lines represent standard deviation. We observe that Diff-Sparse noise masking yields better result in terms of both performance metrics for the two patch configurations.