| 04 Aug 2026
RiverGraphNet: Physics-Aware Routing of Gridded Runoff Through Directed River Networks
Abstract. River routing provides the critical link between runoff generation and downstream streamflow prediction, yet conventional routing models often rely on simplified hydraulic assumptions, fixed parameters, and conservative transport formulations that may limit performance in heterogeneous river systems. Here, we introduce RiverGraphNet, a physics-aware graph-based routing framework designed to route physically generated gridded runoff through directed river networks. The framework explicitly isolates routing from runoff generation by coupling Noah-MP runoff with a directed river-network graph derived from the NextGen hydrofabric for the Salt–Verde watershed (Arizona, USA). Gridded runoff is transferred from the Noah-MP domain to graph nodes representing hydrologic routing elements, while streamflow propagation is learned using a Graph Attention Network (GAT) informed by physically meaningful node and edge attributes describing drainage structure, terrain, and hydraulic-routing proxies.
RiverGraphNet was evaluated against observed daily streamflow at 23 USGS gauges and compared with RAPID, a widely used physics-based routing benchmark forced with identical Noah-MP gridded runoff inputs. Experiments examined the influence of temporal routing memory (3–30 day runoff lags), temporal convolution, and alternative loss functions (MSE, weighted MSE, and JKGE-based objectives). RiverGraphNet consistently outperformed RAPID across nearly all gauges and configurations. The best-performing experiment (14-day lag weighted MSE) achieved a median KGE{ss} of 0.72, substantially exceeding RAPID performance (median KGE{ss} of 0.0). Event-scale hydrographs and flow-duration analyses demonstrated improved representation of peak timing, event magnitude, and long-term streamflow distributions. Attention analysis further revealed that routing improvements were most strongly associated with channel-width and dominant-pathway metrics rather than travel-time proxies alone, suggesting that adaptive representation of network influence provides predictive value beyond conventional travel-time parameterization. These results demonstrate the potential of physics-aware, topology-constrained graph learning as a flexible alternative for routing gridded hydrologic runoff through complex river networks.
This manuscript presents a graph attention network (GAT) framework for routing Noah-MP-generated runoff through the NGen river-network topology of the Salt–Verde watershed, and compares it against RAPID. The strategy of isolating the routing step from runoff generation is well motivated, and the set of experiments (temporal-lag configurations, loss-function formulations, ablation of the temporal convolutional head, and attention analysis) is thorough and clearly documented. The candid discussion in Sections 4.4 and 4.6, where the authors acknowledge that the framework does not enforce mass conservation and that part of the performance gain may reflect implicit compensation for Noah-MP biases, is a genuine strength and is not common in manuscripts of this kind.
That said, several issues should be addressed before the manuscript is suitable for publication. These are listed below as major and minor comments.
Major comments
RiverGraphNet is trained in a fully supervised manner directly against observed discharge at the gauges (Section 2.8). RAPID, as described, is not locally recalibrated for this basin, but instead relies on a pre-existing CONUS-scale Muskingum parameterization (as the manuscript itself acknowledges in Section 3.5, lines 753–758). This means the comparison does not isolate "routing representation" alone, as repeatedly stated (e.g., lines 518–521), but conflates two distinct effects: (a) the routing architecture and (b) local calibration against the observed gauge record. The reported RAPID performance (mean KGEss = −0.29, minimum −4.88) is low enough to suggest a parameterization problem rather than an intrinsic limitation of the Muskingum approach. I recommend that the authors: (i) discuss this asymmetry explicitly as a central methodological caveat rather than a passing remark, and (ii) if feasible, include a version of RAPID with at least minimal local calibration (e.g., of the Muskingum X and K parameters) as a fairer benchmark or a sensitivity check.
It is not clear whether all 23 gauges appear in both training and test sets (split only by non-overlapping temporal blocks), or whether some gauges are held out entirely to test spatial generalization. If, as it appears, the model observes every gauge-node during training, the strong performance demonstrates temporal interpolation at known nodes rather than generalization to unseen nodes or sub-basins. This should be stated explicitly, since it materially affects the interpretation of claims about "topology-aware learning" and constrains the scope of the transferability discussion in Section 4.6 (point 2).
The title and abstract emphasize the "physics-aware" nature of the framework, yet physical information (channel width, roughness, etc.) enters only as features of a learned attention mechanism, without any explicit physical constraint (neither mass conservation nor monotonicity with respect to hydraulically meaningful variables). I suggest softening this terminology — e.g., "physically-informed" or "topology-aware with physical attributes" — reserving "physics-aware" for frameworks with explicit constraints, consistent with the authors' own discussion in Sections 4.4/4.6.
The correlations reported in Table 4 and discussed in Sections 3.7/4.5 between attention coefficients and channel width, travel-time proxy, etc. are interesting, but these features (channel width, travel-time proxy, conveyance proxy, storage proxy) are likely correlated with one another. Without a collinearity analysis (e.g., variance inflation factors or a correlation matrix among the predictors themselves), it is difficult to conclude with confidence that channel width specifically — rather than a correlated feature — is driving attention. I recommend adding this analysis, or at least discussing it explicitly as a limitation.
It is not stated whether the results in Table 3 and Figure 5 derive from a single training run or from multiple runs with different random seeds. Neural networks carry non-negligible stochastic variability from initialization and training; without a confidence interval on the model's KGEss (analogous to the standard deviation reported across gauges for RAPID), the Wilcoxon test (lines 556–559) captures variability across gauges but not variability arising from the model's own training process.
The "Jawad Kling–Gupta Efficiency" metric is named after a co-author of the present manuscript (Muhammad Jawad) and cites a work that appears to be unpublished or in press in the same year. Please verify that this citation is complete and verifiable by reviewers and readers, and consider whether the naming convention could give an impression of insufficiently transparent self-citation.
Minor comments
Summary for the authors
This is a methodologically interesting and unusually candid piece of work regarding its own limitations, but Major Comment 1 (the asymmetric comparison between a gauge-calibrated model and an uncalibrated benchmark) is central and needs to be addressed directly. Otherwise, the paper's headline message — that the GNN substantially outperforms RAPID — risks being more misleading than informative.