Master equation model for solute transport in river basins: part I channel fluvial scale

Normal and anomalous diffusion are ubiquitous in many physical complex systems. Here we define a system of diffusion equations generalized in time and space, using the conservation principles of mass and momentum at channel scale by a master equation. A numerical model for describing the steady one-dimensional advection-dispersion equation for solute transport in streams and channels imposed with point-loading is presented. We find the numerical model parameter as the solution of this system by estimating the transition probability that characterizes the physical phenomenon in the diffusion regime. The results presented (Part I) refer to the channel scale and represent the first part of a research project that has been extended to the basin scale.