Development of space-time rainfall intensity duration frequency curves based on a multifractal approach

Changing climate signals and urban populations' growth requires proper hydrologic risk analysis to create and operate water resource infrastructures in a sustainable way. Although modernized computational facilities are becoming popular to understand different complex systems, the scientific community is still behind in proper analysis of extreme rainfall events as they are erratic in time and space. To fill the existing knowledge gap, it becomes obvious to incorporate spatiotemporal rainfall variability in designing rainfall Intensity Duration Frequency (IDF) curves.  Many statistical approaches have been suggested to describe the space-time structure of rainfall; nevertheless, none of them is enough to represent, for all observational scales, the geometrical structure observed in either rainfall time series or rainfall-derived spatial fields. This research presents a more holistic approach to derive the IDF curves without losing information and (or) statistical assumptions.  This study uses such a promising notion to understand the rainfall field's space-time geometrical structure via codimension functions. The results show us the space-time structure of rainfall exhibits a dynamical scaling, and it suggests the idea of a double multifractal spectrum for representing time and space. Based on the idea of a double multifractal spectrum, IDF curves can be shifted to Intensity – Area – Frequency – Duration (IADF) curves to get a better approach for engineering and scientific purposes. Furthermore, this research suggests that changes of parameters for this approach could reflect climate-change signals and would be useful to generate non-stationary IADF curves and improve engineering design practices.