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The main goal of this dissertation research is to investigate catchment hydrological processes including infiltration and saturation excess runoff generation with consideration of groundwater table. For the infiltration process, an infiltration Péclet number was proposed to quantify the relative effects of gravity and capillary force on the evolution of infiltration capacity in the special case of the presence of a shallow water table, and a power law functional form of Time Compression Approximation was developed whose exponent was found to vary with the Péclet number. For the saturation excess runoff process, a new probability distribution model based on the SCS distribution function was developed. This new daily hydrologic model provided a framework for unifying water balance models from daily to mean annual timescales, and was applied to quantify the relative effects of climate variabilities on streamflow across different timescales for the U.S. Based on the new water balance model, a new analytical expression for mean annual baseflow was developed which was successfully used for disentangling the impacts of mean annual climate and landscape properties on baseflow generation in the U.S. and U.K. Inspired by the different statistical distributions of water storage at catchments, this dissertation further demonstrated that different functional forms of Budyko equation in the literature could be considered as emergent outcomes of the spatial variability of available water for evaporation. Considering the importance of water storage capacity and its spatial variability on hydrological processes, numerical simulations were conducted to explore the control of climate humidity on the spatial distribution of water storage at the catchment scale, and a new framework for unifying different saturation excess runoff models was obtained. The studies in this dissertation advance our understanding of hydrological processes with the presence of a groundwater table.