“…If velocity does not vary considerably, the fraction of nutrient removed by in-stream processes can be expressed as a function of reach length and flow rate. Different forms of decay functions can be found in the literature [41,29,28], and we implemented an exponential decay function as follows: where O t is the flux of material from the reach at time t, I t is the input of material at time t, k is the decay parameter, L is the reach length, and Q t is the flow rate (discharge) at time t. Material routing is estimated in two steps. For each stream reach, routing is performed with the convex method; then output from the routing procedure supplies the input to the decay function, i.e., I t in Eq.…”