Surface microtopography affects a series of complex and dynamic hydrologic and environmental processes that are associated with both surface and subsurface systems, such as overland flow generation, infiltration, soil erosion, and sediment transport. Due to the influence of surface depressions, overland flow essentially features a series of progressive puddle-to-puddle (P2P) filling, spilling, merging, and splitting processes; and hydrologic systems often exhibit threshold behaviors in hydrologic connectivity and the associated overland flow generation process. It is inherently difficult to realistically simulate the discontinuous overland flow on irregular topographic surfaces and quantify the spatio-temporal variations in dynamic behaviors of topography-dominated hydrologic systems. This dissertation research aims to develop a hydrologic model to simulate the discontinuous, dynamic P2P overland flow processes under the control of surface microtopography for various rainfall and soil conditions, and propose new approaches to quantify hydrologic connectivity. In the developed P2P overland flow model, the depressions of a topographic surface are explicitly incorporated into a well-delineated, cascaded P2P drainage system as individual objects to facilitate the simulation of their dynamic behaviors and interactions. Overland flow is simulated by using diffusion wave equations for a DEM-derived flow drainage network for each puddle-dominated area. In addition, a P2P hydrologic connectivity concept is proposed to characterize runoff generation processes and the related spatio-temporal dynamics. Two modified hydrologic connectivity indices, time-varying connectivity function and connectivity length of the connected areas and ponded areas, are proposed to quantitatively describe the intrinsic spatio-temporal variations in hydrologic connectivity associated with overland flow generation. In addition, the effects of DEM resolution, surface topography, rainfall distribution, and surface slope on hydrologic connectivity are also evaluated in this dissertation research. The developed model can be applied to examine the spatio-temporally varying P2P dynamics for hydrologic systems. This model provides a means to investigate the effects of the spatial organization/heterogeneity of surface microtopography, rainfall, and soil on overland flow generation and infiltration processes. In addition, the two proposed hydrologic connectivity indices are able to bridge the gap between the structural and functional hydrologic connectivity and effectively reveal the variability and the threshold behaviors of overland flow generation.