# A Dataset and Model for Imputing Water Surface Elevation on a Large and Extremely Sparse Spatiotemporal Graph

arXiv: https://arxiv.org/abs/2609.11580 · HTML: https://mlsanity.com/paper/2609.11580/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [INCREASE: Inductive Graph Representation Learning for Spatio-Temporal Kriging](https://mlsanity.com/paper/2302.02738/) (2023)
- [CausalRivers -- Scaling up benchmarking of causal discovery for real-world time-series](https://mlsanity.com/paper/2503.17452/) (2025)
- [KITS: Inductive Spatio-Temporal Kriging with Increment Training Strategy](https://mlsanity.com/paper/2311.02565/) (2023)
- [The Merit of River Network Topology for Neural Flood Forecasting](https://mlsanity.com/paper/2405.19836/) (2024)
- [Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations](https://mlsanity.com/paper/2402.12598/) (2024)
- [FastSTI: A Fast Conditional Pseudo Numerical Diffusion Model for Spatio-temporal Traffic Data Imputation](https://mlsanity.com/paper/2410.15248/) (2024)
- [STA-GANN: A Valid and Generalizable Spatio-Temporal Kriging Approach](https://mlsanity.com/paper/2508.16161/) (2025)
- [Graph Structure Learning for Spatial-Temporal Imputation: Adapting to Node and Feature Scales](https://mlsanity.com/paper/2412.18535/) (2024)
- [DUALFloodGNN: Physics-informed Graph Neural Network for Operational Flood Modeling](https://mlsanity.com/paper/2512.23964/) (2025)
- [AnchorGK: Anchor-based Incremental and Stratified Graph Learning Framework for Inductive Spatio-Temporal Kriging](https://mlsanity.com/paper/2512.21569/) (2025)

## Abstract (arXiv)

Continuous monitoring of water surface elevation across river networks is critical for flood forecasting, water resource management, and understanding the global water cycle. Yet, the scarcity of in situ gauges across much of the globe constrains the development of reliable modeling frameworks. Satellite altimetry has the potential to alleviate this problem but its use is currently hindered by sparse temporal coverage. To this end, we introduce AmazonSWE, a dataset for training and evaluating large-scale spatiotemporal graph imputation methods that integrates processed satellite altimetry measurements from a range of sources, including the recent wide-swath SWOT sensor. The dataset covers over 19K river sections and 10 years (2016-2026) in the Amazon river basin, with in situ gauges held out for evaluation. Besides contributing a novel real-world use case with the potential for societal impact, AmazonSWE introduces significant technical challenges: with fewer than 1% of sections observed per day, the dataset is far sparser than existing imputation benchmarks, and its directed acyclic river topology is both structurally different from and larger than graphs in existing datasets. We show that prior spatiotemporal graph imputation methods are not adapted to this topology, scale and sparsity, and propose a simple bidirectional selective state space model that outperforms them by sampling connected subgraphs and flattening space and time into a single token sequence with topology-aware positional encodings. Compared to the state-of-the-art published method for SWOT-based WSE densification, which integrates statistics with physical modeling, our model reduces RMSE against in situ gauges by 18-39%, while producing predictions for every river section rather than only those with sufficient nearby satellite coverage.