VPMC Routing Section
    • 23 Oct 2022
    • 7 Minutes to read
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    VPMC Routing Section

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    Article summary

    The VPMC Routing Section models the flow of water in open channels using a Variable Parameter Muskingum-Cunge method to route the flow.


    Field in Data Entry Form
    Name in Datafile

    Section Label

    node label at discharge point



    First Lateral Inflow Node

    first lateral inflow node label



    Second Lateral Inflow Node

    second lateral inflow node label



    First Lateral Inflow

    First lateral inflow label



    Second Lateral Inflow

    Second lateral inflow label



    Third Lateral Inflow

    Third lateral inflow label



    Fourth Lateral Inflow

    Fourth lateral inflow label



    Distance to Next Section

    distance to next discharge point or cross section in metres (a zero specifies the end of the reach and for this last node the section geometry data will not be used)



    Bed Elevation

    optional bed elevation (mAD) - not used in routing calculation, but will be added to water depth when calculating water level



    Roughness Type

    roughness type - keyword 'MANNING' or 'COLEBROOK-WHITE'



    Channel Roughness

    channel roughness (Manning or Colebrook-White)



    Floodplain Roughness

    floodplain roughness (Manning or Colebrook-White)



    Channel Slope

    channel longitudinal slope (m vertical/m horizontal)



    Floodplain Slope

    floodplain longitudinal slope (m vertical/m horizontal) - usually less than or equal to channel slope due to channel meanders



    Channel Bed Width

    channel bed width (m)



    Channel Top Width

    channel top width (m)



    Floodplain Width

    total floodplain width, including both left and right banks and channel (m)



    Flooded Width

    average width of flooding on floodplain at bankfull (m)



    Channel Depth

    total channel depth (m)



    Depth Above Bankful – Full Floodplain Innundation

    depth above bankfull for full inundation of floodplain (m)



    Depth Above Bankful – Full Floodplain Depth

    depth above bankfull for full width flow on floodplain (m)



    Depth Below Bankful – Isolated Flooding Begins

    depth below bankfull at which isolated flooding begins (m)



    Valley Side Slope

    valley side slope (m vertical/m horizontal)



    Subintervals from...

    Choose whether to calculate the internal distance spacing from a specified maximum discharge (Specify Discharge) or proportion of bankful flow (Calculated)



    Maximum Discharge – Upstream Reach

    maximum event discharge at upstream end of reach, for use in calculating number of subintervals. Set to (default of) zero to relate to bankfull flow instead



    Proportion of Bankful Flow In Calculating Subintervals

    Proportion of bankfull flow to be used in calculating number of subintervals, in the absence of maxQ. Default to 1.0, which is appropriate for a flood model. For an in-bank water quality model, the advised setting is 0.75



    Specify Velocity Using

    For “VQ Power Law”, enter the coefficients a, b, V0 and Q0 to define the flow-velocity relationship; otherwise (VQ Rating), enter the relationship at discrete points in the supplied table.



    Constant a

    scaling parameter for velocity calculation (>0)


    Exponent b

    power law parameter for velocity calculation (>0)


    Lowest Permitted Velocity

    lowest permitted velocity (>0)


    Flow Threshold

    flow below which velocity is set to Vo (>0)



    number of subsequent V Q data pairs


    Velocity and Flow Table

    a table of velocity and flow values used to interpolate velocity values for subsequent Flood Modeller Quality simulations


    - The remaining data are only used when the results of the simulation are to be used for a subsequent water quality simulation. However dummy data values, or the defaults in the Editor, must always be specified.

    Theory and Guidance

    The VPMC Routing Section (MUSK-RSEC) models the flow of water in natural and man-made open channels, using a Variable Parameter Muskingum-Cunge method to route the flow. Wavespeed and attenuation parameters are derived from user-defined geometric and roughness factors, and the method is otherwise identical to the VPMC Routing node. Lateral inflows can be distributed along a reach between adjacent nodes. The VPMC Routing Section is based on the routing method in the software package RIBAMAN (HR Wallingford, 1989).

    The VPMC Routing Section is used to calculate the discharge within a river or channel reach given the inflow hydrograph at the upstream end, up to two flow boundaries as lateral inflows and up to four lateral inflow units.

    The VPMC Routing Section routes a flood wave down the river reach using a relationship between discharge, wavespeed and attenuation, which is derived from the geometric and roughness properties of the reach.

    A minimum of two VPMC Routing Section nodes is required for each river or channel reach. The downstream section need not have any geometric data, and such data are not used in the routing calculation even if they are supplied. In general, it is only necessary to supply two nodes for any one reach, even if the distance between them is considerable.

    Flood Modeller automatically selects a distance step based on the Courant condition. The distance increment cannot exceed the distance between adjacent VPMC Routing Sections. Intermediate nodes are generated internally, and so it is only necessary to provide a VPMC Routing Section at each end of a reach. Flows at the internal nodes cannot be examined directly, but you can control how many such nodes are generated.

    Up to two Boundary Conditions can be connected as lateral inflows to each VPMC Routing Section. These can be flow/time boundaries or hydrological boundaries. The generated flow is distributed evenly along the reach between a pair of VPMC Routing Section nodes. To split a lateral inflow into more than one VPMC Routing Section, one must attach the inflow boundary unit to a lateral inflow unit; the lateral inflow nodes (labels 4-7) within the VPMC Routing Section unit must then be cross-referenced in the lateral inflow unit.

    Replicated Sections cannot be used with VPMC Routing Sections.


    The equations used in the VPMC Routing Section are identical to those for the VPMC Routing node. See the VPMC Routing topic for details.

    For a VPMC Routing Section, the wavespeed c and attenuation parameter a are derived from section geometry according to the equations:






    a = attenuation parameter [1/m]

    B = flow surface width [m]

    h = stage [m]

    S0 = average reach slope [m/m].

    The derived curves can be inspected prior to a full unsteady run by using boundary mode. They are written to the routing results file (extension .zzu) at the beginning of the run. They can then be modified and input as user-supplied data to a MUSK-VPMC unit if desired. The wave speed curve should exhibit the properties shown in the following graph:

    Space Increment

    Flood Modeller determines the space increment for the duration of the simulation so that the equation




    is satisfied as nearly as possible, ie giving a Courant number as near as possible to unity. Here Dx is the space step, Dt is the initial timestep set by the user and c is a representative value of the wavespeed. The space step cannot exceed the distance between adjacent sections, and an integer number of space steps is required between each section.

    The representative wavespeed used in the equation above is defined as the wavespeed corresponding to a reference discharge. This reference discharge can be specified directly by the user, or can be set as a fixed proportion of bankfull flow. For a flood model, it is recommended that a factor of 1.0 times bankfull flow is used. For an in-bank water quality model, a factor of 0.75 times bankfull flow is more appropriate.

    The number of subnodes used is stored in the unit state array for the upstream MUSK-RSEC unit and can be inspected graphically or tabulated in the usual way.

    The MUSK-RSEC unit differs from the MUSK-VPMC and the MUSK-XSEC in that here the space increment does not vary through the simulation.

    Velocity Calculation

    If the flood routing model is to be used with the Water Quality model then an approximate formula may be used to calculate nodal velocities in the same way as for Muskingum Routing and VPMC Routing nodes.


    The calculated wavespeed and attenuation curves are saved to the routing results file (extension .zzu) if the model is run in Boundary mode.

    Muskingum units can be preceded or followed by normal river reaches. The MUSK-RSEC unit will generate an estimated water level based on Manning's equation and the bed elevation zval. If this is not appropriate, then a rating curve (QRATING) can be defined at the upstream end of the routing reach if it joins a hydraulic river reach. Muskingum and river sections cannot be mixed within a reach; reaches of the two types can be joined by JUNCTION units (with only two nodes if necessary).

    If a MUSK-RSEC is downstream of a structure, then the water level calculated from the section geometry in the MUSK-RSEC unit will be used as the downstream water level in the structure calculation and may therefore influence drowning of the structure. If this is not appropriate, for example because the datum level for the section is not known, then a QRATING unit containing a rating curve for the river should be attached to the MUSK-RSEC unit.

    The water level in the last section in a MUSK-RSEC reach is always set by the next unit downstream and not by the section details in the MUSK-RSEC unit itself.

    The normal connectivity rules apply for MUSK-RSEC units and therefore a HTBDY or QHBDY is required at the downstream end of MUSK-RSEC routing reaches which are not connected to a structure. The boundary unit will set the water level for the last MUSK-RSEC node.

    REPLICATE units cannot be used to replicate MUSK-RSEC units.

    RIVER units should not be directly connected to Conduit units. Users can connect CONDUIT and RIVER reaches using a Junction if no head loss occurs at the join. Alternatively, the specialised Culvert Inlet and Culvert Outlet units can be used to model the losses associated with transitions from open channel to culverts and vice versa. Bernoulli Loss units are also available to model more generalised losses.

    Datafile Format

    Line 1 - keyword 'RIVER' [comment]

    Line 2 - keyword 'MUSK-RSEC'

    Line 3 - Label1 [, Label2 [, Label3]] [, Label4, Label5, Label6, Label7]

    Line 4 - dx, [zval]

    Line 5 - keyword 'RIBAMAN'

    Line 6 - Rtype

    Line 7 - Crough, Frough

    Line 8 - Cslope, Fslope

    Line 9 - B1, B2, B3, B4

    Line 10 - D1, D2, D3, D4

    Line 11 - VS

    Line 12 - maxQ, [BFprop]

    Line 13 - keyword VQ POWER LAW or VQ RATING

    Line 14 - Vo, Qo, a, b, if 'VQ POWER LAW' or ndat if 'VQ RATING'

    Line 15 to Line 15+ndat - V, Q if 'VQ RATING'

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