Sparse Space-Time Tokenization for Water-Level Reconstruction on River Networks

Satellite altimeters observe river water levels globally, but their measurements are irregular and extremely sparse in space and time. We introduce a dataset for reconstructing daily water surface elevation (WSE) on 19,172 reaches of the Amazon river network from heterogeneous satellite measurements. Fewer than 1% of reaches are observed per day, causing a dense reach--time representation to consist mostly of missing values. We instead tokenize only observed measurements and requested predictions, sample connected river subgraphs, and process the resulting sequence with a bidirectional selective state space model and topology-aware positional encodings. Masked reconstruction provides self-supervision across both locations and times, and node-independent metadata encodings permit transfer to reaches absent from training. Against held-out in situ gauges, this sparse representation outperforms graph-imputation baselines and a state-of-the-art domain-specific method. These results indicate that, under extreme sparsity, physical topology can be more useful for choosing and encoding tokens than as a message-passing graph.