This is an extension of the original Muskingum method. It essentially incorporates sound hydraulic principles using the kinematic wave approach to estimate Muskingum method:
C1, C2, C3, and C4 are the Muskingum Parameters
= flow at time x and position y
q1 =lateral inflow per unit length
Dt = routing interval
Lm = sub length of channel
k and x are storage constant and weighting factor for the Muskingum method.
The basic difference between the Muskingum method and Muskingum-Cunge method is in the evaluation of k and x.
For the Muskingum method, the parameters k and x are derived from recorded floods.
For the Muskingum-Cunge, method k and x are calculated from hydraulic principle. Flood data is still required for verification of results.
In the situation has been modified slightly to suit the urban situations where gauged data are not available.
The following equations are used for the evaluation of k and x:
= curvature of hydrograph peak
= flow either side of peak
= peak discharge at head of channel
= routing interval
= Attenuation parameter
Wc = average width of channel at peak
L = total length of channel
Lm = channel sub length
Sm = slope of channel sub length
n = number of space nodes along channel
=First approximation of the attenuation of the peak
=recorded or approximated wave speed
=average peak discharge along the reach
w= convection parameter
L, and as above,
Since the above equations are based on recorded flood data it was necessary to replace the wave speed term with an alternative for ungauged urban catchments
In these cases the wave speed (L/T) was replaced by the equation derived assuming a monoclinal flood wave.
= approximate wave speed
=channel waterway area
y= depth of flow in channel
R= hydraulic radius
Wc= water surface width
Qp= peak discharge at head of channel
Equation B is derived from the Kleitz-Seddon Law (Seddon 1900) and Manning’s formula.
Once the parameter k and x have evaluated the routing of the flood is carried out using Equation A
The figure below shows the diagrammatic representation of a typical link cross-section as presently defined in the MCCR module.