Fig. 4
Sequence calculations implemented to perform turbidity simulations. Darker shading indicates VCDM aspects leading to downstream (ds) node observed turbidity (T). Lighter shading indicates inputs and calculations that are standard in 1D network modelling software. ks: pipe roughness; S0: hydraulic gradient; τa: shear stress; t: time; f: Darcy Weisbach friction factor; Re: Reynolds number; Q: flow; D: internal pipe diameter; ρ: fluid density; βe, βr and α: VCDM parameters; ϕ (τ, t): relative amount of material on the pipe wall with strength τ at time t; ϕ (τ, t0): relative amount of material on the pipe wall with strength τ at time t0; dN (t) /dt: rate of material release per unit area of pipe wall; L: pipe length; Tus: turbidity at the upstream node; Tds_pred: predicted turbidity at the downstream node. 
indicates a model input. 
indicates a model process. Light shading indicates hydraulic model inputs and processes, while dark shading indicates VCDM specific ones