Regional models operate within limited ranges of spatial and temporal scales. The upper limit of the spatial spectrum is determined by the size of the model domain; the lower limit is determined by its spatial resolution. Phenomena that take place at smaller scales, the so-called sub-grid scale processes, are typically described via physical parameterizations at the model resolution. Conceptually, this implies an assumption of scale separation between the resolved and the parameterized processes, therefore breaking the breath of dynamical interactions among complex (multiphase) physics across scales. To minimize this effect, various approaches have been proposed based on the idea of refining model resolution including spectral, multi-grid and nested formulations. The nested approach, which relies on the use of an interactive hierarchy of increasingly smaller model domains of increasingly finer resolution over a geographic region of interest, is the most widely used. Scale-bridging capacity refers to the model's ability to reproduce observed multi-scale physical effects. The objective of this research is to develop a methodology to assess the scale-bridging capacity of nested models, and how that affects their predictive reliability (i.e., their long-term function). For this purpose, we rely on a multi-fractal framework to describe quantitatively the space-time variability of moist processes in models and in satellite imagery. To illustrate our approach, we rely on multiple simulations of monsoon onset over the Himalayas and Northern India using a cloud resolving model and MM5. One important result of this work is to show that the models lack scale-bridging capacity in the case of cloud and precipitation processes. We propose an explanation of the differences between the scaling behavior of simulated fields and observations that is rooted on the representation of the governing physics in the models.