Topographic depressions are naturally occurring low land areas surrounded by areas of high elevations, also known as “pits” or “sinks”, on terrain surfaces. Traditional watershed modeling often neglects the potential effects of depressions by implementing removal (mostly filling) procedures on the digital elevation model (DEM) prior to the simulation of physical processes. The assumption is that all the depressions are either spurious in the DEM or of negligible importance for modeling results. However, studies suggested that naturally occurring depressions can change runoff response and connectivity in a watershed based on storage conditions and their spatial arrangement, e.g., shift active contributing areas and soil moisture distributions, and timing and magnitude of flow discharge at the watershed outlet. In addition, recent advances in remote sensing techniques, such as LiDAR, allow us to examine this modeling assumption because naturally occurring depressions can be represented using high-resolution DEM. This dissertation provides insights on the effects of depressions on overland flow processes at multiple spatial scales, from internal depression areas to the watershed scale, based on hydrologic connectivity metrics. Connectivity describes flow pathway connectedness and is assessed using geostatistical measures of heterogeneity in overland flow patterns, i.e., connectivity function and integral connectivity scale lengths. A new algorithm is introduced here to upscale connectivity metrics to large gridded patterns (i.e., with > 1,000,000 cells) using GPU-accelerated computing. This new algorithm is sensitive to changes of connectivity directions and magnitudes in spatial patterns and is robust for large DEM grids with depressions. Implementation of the connectivity metrics to overland flow patterns generated from original and depression filled DEMs for a study watershed indicates that depressions typically decrease overland flow connectivity. A series of macro connectivity stages based on spatial distances are identified, which represent changes in the interaction mechanisms between overland flow and depressions, i.e., the relative dominance of fill and spill, and the relative speed of fill and formation of connected pathways. In addition, to study the role of spatial resolutions on such interaction mechanisms at watershed scale, two revised functional connectivity metrics are also introduced, based on depressions that are hydraulically connected to the watershed outlet and runoff response to rainfall. These two functional connectivity metrics are sensitive to connectivity changes in overland flow patterns because of depression removal (filling) for DEMs at different grid resolutions. Results show that these two metrics indicate the spatial and statistical characteristics of depressions and their implications on overland flow connectivity, and may also relate to storage and infiltration conditions. In addition, grid resolutions have a more significant impact on overland flow connectivity than depression removal (filling).