 23 Oct 2022
 9 Minutes to read
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VPMC Cross Section
 Updated on 23 Oct 2022
 9 Minutes to read
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The VPMC Cross Section uses the same method as the VPMC Routing Unit, but with the added ability to derive wavespeed and attenuation curves from crosssection details.
Data
Field in Data Entry Form  Description  Name in Datafile  

Section Label  node label at discharge point  Label1 

First Lateral Inflow Node  first lateral inflow node label  Label2 

Second Lateral Inflow Node  second lateral inflow node label  Label3 

First Lateral Inflow  First lateral inflow label  Label4 

Second Lateral Inflow  Second lateral inflow label  Label5 

Third Lateral Inflow  Third lateral inflow label  Label6 

Fourth Lateral Inflow  Fourth lateral inflow label  Label7 

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 data will not be used).  dx 

Water Surface Slope  average water surface slope over reach (must be positive). If this is unavailable, an average bed slope should be used  slope 

Minimum Number of Subnodes  minimum number of subnodes allowed (default and minimum 2, ie just the upstream and downstream nodes)  minsub 

Maximum Number of Subnodes  maximum number of subnodes (default and maximum 100)  maxsub 

Low Flow Smoothing Factor  low flow smoothing factor such that the wavespeed at Q=0 (c0) is limited below by c0fact × cmax, where cmax is the maximum inbank wavespeed.  c0fact 

n/a  number of ensuing data lines (can be zero if this is the last section of the reach and section data are not needed for velocity calculation)  n_{1} 

Chainage  cross chainage [m]  x_{i} 

Bed Elevation  elevation of bed [m]  y_{i} 

Manning’s N  Manning's 'n' roughness coefficient  n_{i} 

Start of Panel  character '*' denoting the first data pair in a panel  * 

RPL  relative path length (only following a '*'  optional, to take account of differences between floodplain and channel reach lengths. See RIVER SECTION for details)  r_{i} 

Marker  The words 'LEFT', 'RIGHT', or 'BED' specifying the left bank top, right bank top and thalweg. Currently, only the lower of LEFT and RIGHT bank is used, to determine bankful elevation.  LRB 

Easting  Easting coordinate  not used in calculations  easting 

Northing  Northing coordinate  not used in calculations  northing 

Specify Velocity Using  For “VQ Section”, the velocityflow relationship is calculated using the section geometry; for “VQ Power Law”, enter the coefficients a, b, V_{0} and Q_{0} to define the flowvelocity relationship; otherwise (VQ Rating), enter the relationship at discrete points in the supplied table. 


Constant a  scaling parameter for velocity calculation (>0)  a  
Exponent b  power law parameter for velocity calculation (>0)  b  
Lowest Permitted Velocity  lowest permitted velocity (>0)  V_{o}  
Flow Below which Velocity is Set to Vo  flow below which velocity is set to Vo (>0)  Q_{o}  
Number of VQ Data Pairs  number of subsequent V Q data pairs  ndat  
Velocity and Flow Table  a table of velocity and flow values used to interpolate velocity values for subsequent Flood Modeller Quality simulations.  V,Q 
 these fields 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 1D Simulation window, must always be specified unless VQ SECTION is set.
Theory and Guidance
The VPMC Cross Section (MUSKXSEC) models the flow of water in natural and manmade open channels, using a Variable Parameter MuskingumCunge method to route the flow. Wavespeed and attenuation parameters are derived from section details supplied by the user, and the method is otherwise identical to the VPMC Routing (MUSKVPMC) unit. Lateral inflows can be distributed along a reach between adjacent units.
The VPMC Cross Section calculates 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 Cross Section is based on the diffusion equation, and uses a numerical scheme which is similar to the Muskingum equation with variable parameters k and x. The method requires a relationship between discharge, wavespeed and attenuation, which is derived from crosssection details.
In order to smooth out convergence problems at low flows, it is possible to impose a lower bound on the wavespeed as a proportion of the maximum inbank wavespeed. The default value is 0.0 (i.e. no lower bound); a maximum value of 0.5 is suggested, and is that specified in the literature for the RIBAMAN software package (HR Wallingford, 1989). Left and/or right bank markers may be specified to denote the bank extents for this purpose.
A minimum of two VPMC Cross Section or VPMC Routing nodes is required for each river or channel reach. The downstream section need not have any wavespeed/attenuation or section data, and such data are not used 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.
The program automatically selects a distance step based on the Courant condition at each timestep, but within userdefined constraints. The distance increment in any case cannot exceed the distance between adjacent MUSK sections. Intermediate nodes are generated internally, and so it is only necessary to provide a MUSKVPMC or VPMC Cross Section at each end of a reach. Flows at the internal nodes cannot be examined directly, but the user can control how many such nodes are generated.
Up to two boundary units can be connected as lateral inflows to each MUSKVPMC unit. These can be flow/time boundaries or hydrological boundaries. The generated flow is distributed evenly along the reach between a pair of MUSK nodes. It is not possible to split a lateral inflow into more than one MUSKVPMC or VPMC Cross Section,  one must attach the inflow boundary unit to a lateral inflow unit; the lateral inflow nodes (labels 47) within the VPMC Routing Section unit must then be crossreferenced in the lateral inflow unit.
REPLICATE units cannot be used with VPMC Cross Sections.
Equations
The equations used in the VPMC Cross Section are identical to those for the MUSKVPMC unit, and the user is referred to VPMC Routing for details.
For a VPMC Cross Section, the wavespeed c and attenuation parameter a are derived from section properties according to the equations:

and
where: a = attenuation parameter [1/m] B = flow surface width [m] h = stage [m] S_{0} = 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 unit file (extension .zzu) at the beginning of the run. They can then be modified and input as usersupplied data to a MUSKVPMC unit if desired.
For information on space increment determination, timestep considerations and attenuation parameter constraints, please refer to MUSKVPMC.
Water Quality Simulations
If the flood routing model is to be used to generate output for a future water quality simulation, an approximate method must be used to calculate the nodal velocities required. See Routing Velocity Calculation for more information.
General
Calculation of the wavespeed and attenuation curves involves derivation of a conveyance table as for RIVER sections, with the added requirement of an average reach slope.
The calculated curves are saved to the Unit Characteristics file (extension .zzu) if the model is run in Boundary mode.
The curves are calculated directly form the section data supplied by the use, and so may exhibit features resulting from sudden changes in crosssection shape. In particular, 'spikes' may appear on the wavespeed curve at around bankfull due to the rapid increase in conveyance and flow width. If this occurs then it is recommended to run the model in Boundary mode first, which writes the wavespeed and attenuation curves to the Unit Characteristics file (extension .zzu). These curves can then be smoothed manually to produce a more physically realistic shape, and used as the input data for a MUSKVPMC unit.
Automatic smoothing at low flows can be effected by specifying a lower bound on the wavespeed as a proportion of the maximum inbank wavespeed. A value of less than 0.5 is recommended. The sole use of left and/or right bank markers in this unit is to denote the bank extents for this purpose.
The wavespeed and attenuation curves are output as a VPMC Routing (MUSKVPMC) unit, which can be imported directly into VPMC unit, or alternatively, applied as an “Event Data” file to a simulation, as long as it comprises a complete reach or reaches. It may be necessary to remove some data points, however, as a maximum of 100 points are permitted in the wavespeed/attenuation curves for a MUSKVPMC unit.
If Flood Modeller is used then Muskingum units can be preceded or followed by normal Flood Modeller river reaches. 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). The three types of Muskingum unit (MUSKINGUM, MUSKVPMC and MUSKXSEC) can be mixed within a reach.
The normal connectivity rules apply for Muskingum units and therefore an appropriate downstream boundary (e.g. HeadTime Boundary or FlowHead Boundary is required at the downstream end of Muskingum routing reaches which are not connected to a structure, although this will not have any impact on the routing calculations.
A normal depth calculation is carried out using Manning's equation, to give an approximation to the water level in the section which would be achieved if normal depth conditions applied. This can be overridden by supplying a QRATING unit with the same node label as the MUSKXSEC unit. For the last MUSKXSEC section in a reach, the unit immediately downstream determines the level and the section data are not used.
REPLICATE units cannot be used to replicate MUSKVPMC or MUSKXSEC units. MUSKXSEC units also cannot be used in conjunction with INTERPOLATE units.
In very rare circumstances, it is possible in large models for the data storage space to become full. If an error message indicates that this has happened, then the storage required for each MUSKXSEC unit can be reduced by decreasing the value of maxsub and allowing fewer internal subnodes. This may also decrease run times.
The variation of the number of space increments may occasionally lead to the loss of resolution on the flood wave or poor volume conservation. This is because the space increment is based on the discharge at the upstream end of the reach, and so the number of calculation subnodes may drop dramatically while the floodwave is still within the reach. If this becomes a problem, the user should fix the parameters minsub and maxsub to give a suitable number of subnodes; the recommended number is that corresponding to the maximum inflow into the reach. This can be obtained by carrying out a full unsteady run and inspecting the resulting inflows and subnode numbers (which are stored in the unit state for the upstream section). The model can then be run again with the new fixed space increment.
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 'MUSKXSEC'
Line 3  Label1 [, Label2 [, Label3]] [, Label4, Label5, Label6, Label7]
Line 4  dx, z, slope, minsub, maxsub, qmax, c0fact
Line 5  keyword 'CROSS SECTION'
Line 6  n_{1}
Line 7 to Line 6+n_{1}  x_{i}, y_{i}, n_{i}, [, *, r_{i}, LRB, easting, northing]
Line 7+n_{1}  keyword 'VQ POWER LAW' or 'VQ RATING' or 'VQ SECTION'
The remaining data must not be supplied if VQ SECTION is specified.
Line 8+n_{1}  Vo, Qo, a, b, (if 'VQ POWER LAW') or ndat (if 'VQ RATING')
Line 9+n_{1} to Line 8+n_{1}+ndat  V, Q (if 'VQ RATING')