A New Class of Monthly Rainfall‐Runoff Models for Ungauged Basins—Application to the Peruvian Coastal Basins

Rainfall–runoff modelling in data‐scarce regions remains a major challenge in climatology due to limited hydrometric records and the heterogeneity of watershed responses. To address this problem, we introduce a new class of parsimonious nonlinear rainfall–runoff models that rely solely on two geometric descriptors of the basin: surface area and elongation ratio. The models are derived using the global modelling technique, insensitive to the initial conditions. Models are built and validated across 49 basins distributed over ~223 000 km 2 in the Peruvian Pacific slope and coast. Two generalized formulations were obtained: Model G I , based on the four northernmost basins, and Model G II , derived from a larger set. Both reproduce key hydrological features, including annual maxima, minima, and the geometry of phase‐space orbits. Model G II , although less parsimonious, consistently outperforms G I in terms of error metrics, while retaining physical interpretability. Simulations reveal that elongation exerts a stronger influence on runoff dynamics than area, particularly under extreme rainfall (e.g., El Niño events). Stability analysis further shows that basins with intermediate elongation (~0.45–0.60) are the most robust, whereas very rounded or highly elongated basins approach instability or divergence. Importantly, the proposed framework is transferable to ungauged basins, offering predictive capability with minimal parameterisation. These findings highlight the structural similarity of watershed responses across diverse climatic and geomorphic settings in coastal Peru, suggesting broader applicability to other semi‐arid regions with episodic extreme events.