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## Flood Routing definitions

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**lag**Peak flow attenuation Recession limb Rising limb Outflow at x+Dx c Dt time t time t+Dt x Flood Routing definitions Q(t) Inflow at x tp time**Flood Routing methods**• Hydraulic • 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**t+ t**t A Q Q+Q x Kinematic Wave Equation Continuity with no lateral inflow yields: 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 4 8 5 6 Nucleus Dt b Dt 7 1 2 Dx Distance x**3**8 4 5 6 7 2 1 Continuity Around the Nucleus bdt adx**Generalized Muskingum equation**Let and get Q4=f(Q1 , Q2 , Q3) Collecting terms, Setting b = 0.5 yields where**or**Convert the Wave equation to a Diffusion equation Diffusion coefficient is related to channel conveyance Deriving the Diffusion equation Non-centered finite difference scheme creates a numerical error**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. Determine weighting coefficients**Numerical Stability Criteria**Condition for numerical stability is Unstable**From parts 1 & 2**or Limits for Dx and Dt For b = 0.5 and For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N = 2,3,4...**From parts 1 & 2**or or From parts 2 & 3 Limits for Dx and Dt For b = 0.5 and For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N=2,3,4... For very short channels, use routing time-step equal to sub-multiple of hydrology time step, dt=Dt/N, N=2,3,4...**Estimated values of weighting coefficients**Details of last conduit design are displayed Changes to Dx or Dt reported for information User can change computed X or K values MIDUSS 98 Route Command