Streamflow model’s benchmark edge came with extra input

A Penn State study found that its hourly streamflow model, h-Diffusion, scored modestly higher than two LSTM benchmarks in one test across 516 U.S. river basins. But h-Diffusion used daily simulated hydrologic states as prior information, while the two comparison models did not. The authors say that difference may help explain the gain.

In the single-forcing test, the median Nash–Sutcliffe Efficiency (NSE) was 0.780 for h-Diffusion, compared with 0.763 for MTS-LSTM and 0.756 for MF-LSTM. The paper reports statistically significant differences among the results at p < 0.01. In an ablation that removed h-Diffusion’s daily simulation input, its median NSE was 0.728.

Results changed with the test setup

The research team includes Penn State researchers based at University Park, Pennsylvania. The study evaluated h-Diffusion and an inpainting-based data-assimilation version, h-Diffusion-DA, using the CAMELS-US dataset. Models were trained on data from Oct. 1, 1990, through Sept. 30, 2003. The single-forcing test covered Oct. 1, 2008, through Sept. 30, 2014; the multiple-forcing test covered Oct. 1, 2003, through Sept. 30, 2008.

The multiple-forcing test produced a different ranking: both LSTM models had higher median NSE scores than h-Diffusion. The paper reports no statistically significant differences among the three models in that comparison. The single-forcing result therefore did not hold across both test configurations.

Assimilating recent observations improved a separate test

A separate single-forcing experiment examined whether recent gauge observations could improve a 24-hour prediction window. When observations were assumed to be available five hours before that window, the median NSE rose from 0.780 for h-Diffusion to 0.832 for h-Diffusion-DA. The approach uses inpainting to incorporate observations without additional model training. This result compares the diffusion model with and without data assimilation; it is not a comparison with the LSTM benchmarks.

The paper also reports probabilistic scores for high flows in its inpainting comparison: a median Continuous Ranked Probability Skill Score (CRPSS) of 0.37 for the top 10% of flows and 0.21 for the top 1%. These figures describe the inpainting comparison, not performance against the LSTM models.

The study reports retrospective tests on U.S. basin data, not an operating public flood-warning service or Pennsylvania-specific forecast accuracy. The authors identify computational optimization and integration with physical process-based models as future research directions. The journal article first appeared in Water Resources Research on July 21, 2026; Penn State’s account of the research is marked last updated Oct. 6, 2026.