Non-local Theories of Geomorphic Transport: From Hillslopes to Rivers to Deltas to the Stratigraphic Record

Landscapes are shaped by the interplay between tectonics and climate. The mass fluxes associated with the physical and chemical processes acting across the landscape involve the production and transport of sediment and solutes from the uplands to the lowlands. The processes operating on the Earth's surface dictate the selective long-term preservation of the history of these processes in the geological record. Acknowledging the stochastic nature of the processes that drive the evolution of the landscapes at various time scales involved is essential for building predictive models of sediment transport on the Earth's surface. However, traditional models often do not acknowledge the high variability of the driving forces, broad scales of motion involved and the heavy-tailed nature of events that shape the landscapes. This thesis research challenges existing thinking and puts forth a new class of macroscopic sediment transport models which take into account the probabilistic structure of the processes that shape the landscapes. A new class of macroscopic sediment flux models that are based on non-local theories, where sediment flux is not only a function of local hydro-geomorphic quantities but is a linear function of the space-time history of the system, are introduced. The unifying goal underlying this work is to develop sediment transport models that capture the extreme heterogeneity of the involved processes over a large range of scales, consider the presence of extreme fluctuations that arise due to the climatic forcing, and the spatial heterogeneity of landscapes that affects sediment production, storage, movement and delivery and to study how these surface dynamics are preserved in the Earth's geological record.