Flood Routing definitions lag Q(t) Peak flow attenuation Inflow at x Outflow at x+Dx Recession limb Rising limb tp time c Dt x time t time t+Dt

Flood Routing methods Hydraulic Hydrologic Uses both dynamic and continuity equations Allows backwater effects to be modelled Solution advanced by timestep Dt Hydrologic Uses only continuity equation Cannot model backwater effects Solution advanced downstream by Dx

Kinematic Wave Equation Continuity with no lateral inflow yields: Q Q+Q x t+ t t A For quasi-uniform flow: Substitute and separate variables to get wave eq. or where c = dQ/dA is wave celerity

Space-Time Coordinates Time t a Dx Flow Q4 unknown 3 8 4 5 6 Nucleus Dt b Dt 1 7 2 Dx Distance x

Continuity Around the Nucleus 8 7 6 5 4 3 2 1 bdt adx

Generalized Muskingum equation Let and get Q4=f(Q1 , Q2 , Q3) Collecting terms, Setting b = 0.5 yields where

Deriving the Diffusion equation Non-centered finite difference scheme creates a numerical error or Convert the Wave equation to a Diffusion equation Diffusion coefficient is related to channel conveyance

Determine weighting coefficients Compare the two equations for the diffusion coeff. D f(a,b,D)=0 leads to multiple sets of (a,b) coordinates for any value of D.

Numerical Stability Criteria Condition for numerical stability is Unstable

Limits for Dx and Dt For b = 0.5 and From parts 1 & 2 or For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N = 2,3,4...

Limits for Dx and Dt For b = 0.5 and From parts 1 & 2 or For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N=2,3,4... From parts 2 & 3 or For very short channels, use routing time-step equal to sub-multiple of hydrology time step, dt=Dt/N, N=2,3,4...

MIDUSS 98 Route Command

MIDUSS 98 Route Command Details of last conduit design are displayed Estimated values of weighting coefficients User can change computed X or K values Changes to Dx or Dt reported for information

Results of Route command

Calculating celerity