As remote sensing technology produces increasingly fine-resolution digital elevation models (DEMs), traditional hydrologic algorithms face computational bottlenecks. Amid rising frequencies of natural disasters due to global warming, efficiently processing this abundant topographical data has become critical. We investigate whether exploiting the structural regularities inherent in topography, such as continuity, local homogeneity, and consistent gradients, can improve computational efficiency. This thesis introduces two works that enable scalable hydrologic modeling by adapting to the inherent topographical structure. First, we present Scalable Terrain-Aware Adaptive Resolution Framework for Flow Modeling (STAAR-FM), which introduces an irregular, terrain-aware mesh that dynamically allocates computational resolution based on topographic complexity. This approach preserves hydrologic fidelity while substantially reducing computational overhead in flow accumulation, achieving 77.69% streamline matching at 30% data reduction. Second, we develop TopoFlowGNN, a Graph Neural Network (GNN) framework that learns hydrologic dynamics on adaptive DEM-derived graphs, demonstrating the broader potential of topology-guided GNNs. TopoFlowGNN extends the concept of an adaptive grid to a more flexible representation. By embedding physical flow directionality as an inductive prior, the model efficiently learns the dynamics of flux transfer. We demonstrate its efficacy on the task of predicting flood depth, achieving Nash-Sutcliffe Efficiency of 0.728 versus 0.224 for baseline methods with real-time inference speeds of 11.68 batches/second. This addresses a problem that has historically been intractable for real-world applications due to the computational cost of numerical solvers, making flood forecasting operationally feasible where physics-based solvers require hours to days. Together, these works demonstrate the potential of adaptive terrain-aware representations for hydrologic modeling.
Deven Biehler (Mon,) studied this question.