Modeling Rainfall Hyetographs from Cloud Droplet Size Distribution: A Similarity-Based Approach for Flood Nowcasting

Rainfall hyetographs are essential for hydrologic modeling and flood forecasting, yet they are unavailable in real time for nowcasting—limiting the effectiveness of early warning systems. To address this challenge, we present a novel mechanistic model that generates rainfall hyetographs directly from cloud droplet size distributions (DSDs) using a similarity-based framework grounded in the principle of scale invariance. By conceptualizing clouds as chaotic, scale-free systems with fractal structure, we derive a general power-law distribution to characterize DSDs, achieving strong agreement with classic field data (r2=0.9939; Nash–Sutcliffe efficiency coefficient=0.9937; and root mean squared error=0.0136). This model significantly advances beyond conventional statistical techniques, which rely on sparse empirical data and suffer from delayed responsiveness. It integrates cloud macrostructure, microphysical properties, and droplet descent dynamics to simulate rainfall from instantaneous thin clouds and is further extended to thick and persistent cloud scenarios. Unlike empirical or machine learning models, this physics-based framework enables real-time rainfall-runoff simulations before precipitation reaches the ground. The methodology is illustrated through representative case studies and is particularly well-suited for radar and satellite hydrology. Its practical relevance is demonstrated through recent flood events in Central Texas and Beijing, where the absence of predictive rainfall data contributed to substantial loss of life and overwhelmed emergency response systems. When integrated with radar and satellite observations, the general infiltration law, and the general unit hydrograph model, this similarity-based approach offers a robust and proactive alternative for flood nowcasting and emergency preparedness.