  Climate change exacerbates riverine floods, which occur with higher frequency
and intensity than ever. The much-needed forecasting systems typically rely on
accurate river discharge predictions. To this end, the SOTA data-driven
approaches treat forecasting at spatially distributed gauge stations as
isolated problems, even within the same river network. However, incorporating
the known topology of the river network into the prediction model has the
potential to leverage the adjacency relationship between gauges. Thus, we model
river discharge for a network of gauging stations with GNNs and compare the
forecasting performance achieved by different adjacency definitions. Our
results show that the model fails to benefit from the river network topology
information, both on the entire network and small subgraphs. The learned edge
weights correlate with neither of the static definitions and exhibit no regular
pattern. Furthermore, the GNNs struggle to predict sudden, narrow discharge
spikes. Our work hints at a more general underlying phenomenon of neural
prediction not always benefitting from graphical structure and may inspire a
systematic study of the conditions under which this happens.
