Runoff Potential Index (RPI): 3D modelling of surface-driven hydrological dynamics for drought resilience

Dynamic modelling of water redistribution across 3D surfaces drives understanding from landscape hydrology to microscale flow patterns. Drought vulnerability assessment in agricultural systems remains increasingly critical under climate change. Yet current frameworks lack explicit integration of terrain-mediated hydrological processes with dynamic agricultural impacts-an opportunity for advancing vulnerability assessments. Existing topographic indices-particularly the widely-used Topographic Wetness Index (TWI)-exhibit numerical instability in low-gradient terrains and fail to detect microtopographic variations controlling water retention. These indices treat terrain as static geometry rather than capturing the divergence-driven dynamics that govern water redistribution across 3D surfaces. This study introduces the Runoff Potential Index (RPI), a divergence-based terrain metric: RPI(x, y) = ∇ 2 z/(|∇z| + ε), integrating local terrain curvature (via Laplacian of elevation) with slope magnitude. The Laplacian operator (∇ 2 z) quantifies flow convergence and divergencetransforming static terrain into a dynamic representation of water redistribution governed by surface morphology. The framework combines: (1) RPI terrain analysis using satellite-derived elevation data for upland-lowland differentiation based on water redistribution patterns, and (2) CERES-Rice dynamic crop modeling driven entirely by Earth observation data to evaluate drought stress across varying crop growth cycles. The RPI maintained analytical sensitivity across subtle elevation gradients (0.7-1.8 m variations) where TWI becomes unstable, successfully detecting centimeter-scale microtopographic variations critical for water retention. Terrain analysis revealed lowland areas achieving 200 kg/ha higher yields than uplands. CERES-Rice simulations (2000-2019) identified optimal sowing windows minimizing drought stress, with delayed sowing causing yield reductions exceeding 1,500 kg/ha. This Earth observation framework enables drought vulnerability mapping without in-situ environmental measurements, supporting global climate adaptation. The approach provides field-specific sowing recommendations preventing 45-73% yield losses and satellite-based drought risk assessment accessible to smallholder farmers, directly supporting SDG 13.1 and 13.3. The divergence-based formulation extends beyond agriculture to any system where surface flow dynamics govern spatial heterogeneity-from watershed hydrology to cellular environments where substrate gradients drive biological dynamics.