Representing the form and formation of Earth’s topography under natural and anthropogenic drivers

While the Earth's topography may appear static at a casual glance, it is continuously shaped by diverse geomorphic processes operating across various spatial and temporal scales. These processes leave distinctive spatial patterns of ridges and valleys on natural terrains, influencing the flow and availability of water, energy, and nutrients across the surface and subsurface, thereby impacting overall ecosystem functionality. Given the pivotal role of Earth's dynamic topography, a key question emerges: How do different surface processes transform the land surface, and how can we effectively quantify these changes? In pursuit of this question, this dissertation utilizes a minimal process-based modeling approach, with the use of analytical and numerical methods, dimensional analysis, and model output comparisons with observational data to elucidate the interplay of these geomorphic processes and landform changes. We analyze the effects of hillslope processes of soil creep and landslide erosion in creating smooth, convex to planar hillslope profiles, in contrast to surface runoff, which generates intricate branching patterns of ridges and valleys as it intensifies. In the final section of this thesis, we transition from a geomorphic perspective to a practical examination of soil erosion within human timescales. We evaluate existing experimental methodologies for estimating erosion rates and analyze empirical soil erosion models from a physics-based perspective of sediment transport