A brief description of the Finite-Volume discretization of the total-load transport equation is provided here without any derivation or details. For a more comprehensive understanding, including information on advection schemes, gradient operators, and related aspects, please refer to the "HEC-RAS 2D Sediment Transport Technical Reference Manual" by Sánchez et al. (2019) (2D Sediment Manual). This reference is relevant because HEC-HMS shares the same 2D Sediment Transport engine as HEC-RAS. The 2D Transport Module in both applications employs explicit and implicit Finite-Volume methods to solve generic Advection-Diffusion equations.  The final form of the discretized total-load advection-diffusion equation is given by

                                                                               

                                                                                  where  Ω = cell volume

                                                                                              P = subscript indicating cell

                                                                                              f = subscript indicating face between cells P and N

                                                                                              N = subscript indicating neighboring cell to P and sharing face f

                                                                                              n = superscript indicating time step

                                                                                              Ctk = total-load sediment concentration of the kth grain class [M/L3]

                                                                                              Btk = total-load correction factor for the kth grain class

                                                                                              εtk = total-load diffusion coefficient corresponding to the kth grain class

                                                                                              Af = face vertical area [L2/T]

                                                                                              Ff = face-normal water flow [L3/T]

                                                                                              EtkHF= total-load erosion rate in hydraulic flow [M/T/L2]

                                                                                              DtkHF = total-load deposition rate in hydraulic flow [M/T/L2]

                                                                                              Stk = total-load source/sink term [M/T/L2]

                                                                                              ΔApW = cell wetted horizontal area [L2]

                                                                                              rpn = distance between cell points N and P [L]

                                                                                              θ = implicit weighting factor [-]

                                                                                              n + θ = superscript representing the temporal weighting  (Generalized Euler scheme)

When the implicit weighting factor is equal to 1, the scheme reduces to the first-order fully implicit Backward Euler scheme.  When the implicit weighting factor is equal to 0.5, the scheme is the second-order Crank-Nicholson scheme.  An implicit discretization is utilized for robustness.  However, future versions will have the option to use an explicit scheme.

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include the total load scaling factor, critical mobility scaling factor, sheet & splash erodibility coefficient, sediment total roughness factor, and adaptation coefficient.

A tutorial using the 2D Sediment Transport simulation can be found here: TBD.

A Note on Parameter Estimation

For comprehensive details regarding input parameters, kindly consult the "HEC-RAS 2D Sediment Transport Technical Reference Manual (2D Sediment Manual)" authored by Sánchez et al. in 2019.