Blunt Extension and Dynamic Generation of Multifractal Cascade Fields Tree for Rainfall Drop Trajectories Simulations

Precipitation variability at small space-time scales significantly influences hydrological processes, particularly in heterogeneous environments such as urban areas. Building on established methodologies for generating universal multifractal cascade fields, we propose an alternative approach that optimizes memory efficiency while maintaining the fidelity and flexibility of high-resolution simulations. Our method generates cascade fields dynamically, we call it Cascade Tree, which reduces memory usage by over 100 times compared to precomputing and storing full datasets. This improvement complements existing techniques by offering a scalable option for real-time applications.

 

To further enhance the realism of the simulated fields, we integrate the blunt extension of universal multifractals, which smooths transitions between far branches in Cascade Tree and addresses non-conservativeness in a computationally efficient manner. By leveraging GPU acceleration, we achieve rapid computation of cascade fields, enabling their use in simulating complex phenomena such as rainfall dynamics in turbulent wind fields.

 

The method is applied to simulate 3D trajectories and velocities of raindrops in a high-resolution multifractal turbulent wind field, using real wind field data to improve the applicability of the results. Our simulations capture the spatial and temporal variability of rainfall and demonstrate the dispersion of over 100,000 raindrops across scales relevant to radar pixels and urban catchment hydrology.

 

This work provides new tools for exploring rainfall-driven processes, with applications ranging from downscaling radar precipitation data to refining hydrological response models. By complementing established methods with a memory-efficient and GPU-accelerated framework, our approach bridges the gap between drop-scale dynamics and catchment-scale impacts.