Hypergraph neural networks for cross-basin flood-forecast knowledge transfer: a climate-analytics evaluation of negative-transfer risk in ungauged tropical catchments

Cross-basin knowledge transfer is the central obstacle to flood forecasting in ungauged tropical catchments, where hydrological models cannot be calibrated locally and must borrow structure from gauged donor basins. Hypergraph neural networks (HGNNs) have been proposed as a transfer architecture because they encode higher-order relations among sub-basins rather than pairwise adjacency alone, but the conditions under which such transfer degrades rather than improves forecast skill remain unformalised. It formalises a hypergraph hydrological operator, defines a transfer-risk functional that decomposes forecast error into donor-fit, structural-mismatch and hyperedge-interference components, and derives a bound on the excess risk of a transferred HGNN relative to a locally trained model. The bound identifies three measurable quantities — hypergraph spectral gap, hyperedge label divergence and catchment-response heterogeneity — that jointly determine whether transfer is beneficial. The paper then specifies an evaluation protocol that operationalises these quantities for ungauged tropical catchments and reports a climate-analytics diagnostic using NASA POWER monthly reanalysis for Lagos, Nigeria (6.52° N, 3.38° E), 2000–2023, comprising 312 monthly observations with a mean air temperature of 26.414 °C, a standard deviation of 0.943 °C and a warming trend of 0.1553 °C per decade. The diagnostic illustrates how a non-stationary climatic covariate shifts the transfer-risk functional over time. The contribution is a formal account of when hypergraph transfer helps, a diagnostic that can be computed before deployment, and a set of boundary conditions that delimit the claim that HGNNs are a general solution to ungauged flood forecasting.