Introduction to special section on Stochastic Transport and Emergent Scaling on Earth's Surface: Rethinking geomorphic transport-Stochastic theories, broad scales of motion and nonlocality

In many geomorphic transport systems, the time and length scales of motion vary widely: particles can be trapped for both short and long periods of time and they can travel large or small distances in very short intervals of time. To model such systems we need fresh conceptual and mathematical formalisms. The goal of this collection of papers is to challenge existing thinking in geomorphic transport by putting forward new ideas and theories for environmental fluxes, from particle transport in a single stream, to landslide debris mobilization, sediment and water transport on hillslopes, dynamic transport on river networks, and interpretation of sedimentary deposits over geologic time. Advanced stochastic theories of transport are proposed, the notion of nonlocal flux is introduced, and fractional advection-diffusion equations are explored as possible models of geomorphic transport.