Channel Routing Hydrograph - Modified Att-Kin Method

Channel routing is used to analyze the effects of a channel on a hydrograph's peak flow and travel time. You may choose from either the Convex or Modified Att-Kin methods to route a hydrograph downstream.

The Modified Att-Kin (attenuation-kinematic) method is used in the TR-20 and TR55 methodologies. It is a combination of the storage indication method and the kinematic wave method to reflect the reservoir and translation effects on natural flood waves. The hydrograph is first routed through a reservoir assuming that the outflow is proportional to the storage. The resulting outflow hydrograph is then translated using kinematic wave principles. The storage routing portion allows for attenuation and translation. Kinematic routing translates the outflow hydrograph but doesn't attenuate the peak.

The continuity equation is

    I_i - (O_i+1 - O_i) / 2 = (S_i+1 - S_i) / Δt

where:    I_i        = Inflow hydrograph discharge at (i)th time step
             O_i       = Outflow hydrograph discharge at (i)th time step
             O_i+1    = Outflow hydrograph discharge at (i+1)th time step
             S_i       = Storage at (i)th time step
             S_i+1    = Storage at (i+1)th time step
             Δt       = Routing time step

Substitution of S = KO leads to

    O_i+1 = C_mI_i + (1 - C_m)O_i

where:    C_m = 2Δt/(2K + Δt)
              K = L / (60mV)
              V = Q / A
              A = (Q / x)^1/m

              where:   L    = Channel length (ft or meter)
                          V    = Average velocity in the channel (ft/s or m/s)
                          Q    = Average channel flow, default value is the peak discharge of the inflow hydrograph (cfs or cms)
                          A    = Wet cross section area of the channel (sq. ft or sq. meter)
                          x     = Flow equation multiplier, > 0.0
                          m    = Flow equation exponent, default value is 5/3, usually is 1.0 <= m <= 2.8

The coefficient x can be estimated using Manning's Formula:

    x = S^1/2 / nP^2/3
         
where:   S   = Average slope of the channel
            n    = Manning's n value
            P    = Wetted perimeter of the flow (ft or m)       

Select Modified Att-Kin Method from Watershed > Hydrograph Routing > Channel Routing menu. Specify the inflow hydrograph and enter the channel length, the routing coefficient x and the time coefficient m. The routing interval is as same as the time increment of the inflow hydrograph. Button Estimate Coefficients x and m allows you to enter the parameters of the Channel to determine the x and m coefficients. Once the parameters are entered, click on the Calculate button to compute the coefficients. OK button accepts the values and proceeds to the previous dialog.

After entering all information, click Routed Hydrograph button to generate the routing hydrograph. A dialog is opened with the tabular and graphic hydrograph data, from there you can draw the hydrograph on screen and save it to a file.

Channel Routing Hydrograph - Modified Att-Kin Method

Channel Routing Hydrograph - Estimate Coefficients Dialog

Routed Hydrograph Dialog