 22 Sep 2022
 3 Minutes to read
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Flow Head Boundary
 Updated on 22 Sep 2022
 3 Minutes to read
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The FlowHead Boundary represents a flow against stage rating relationship, usually used as a downstream boundary condition. This boundary condition is in essence a rating curve.
Data
Field in Data Entry Form  Description  Name in Datafile 

Node Label  Node label at boundary  Label 
Data Interpolation  SPLINE if a cubic spline is to be fitted to the data, or LINEAR to use linear interpolation. (If the field is blank then linear interpolation is used.)  smooth 
Flow  Flow (m^{3}/s) corresponding to water level h_{i}  Q_{i} 
Stage  Water level (metres above datum)  h_{i} 
Theory and Guidance
The Flow Head Boundary represents a flow against stage rating relationship, usually used as a downstream boundary condition.
All end points on the network require a boundary condition. The Flow Head Boundary defines a set of data pairs specifying flows and water levels above datum.
This boundary condition is in essence a rating curve.
Equations
These is only one equation as follows:

The discrete form of the equation is:

At intermediate points either linearisation is used:

or a cubic spline is fitted. You can choose which form of interpolation to apply.
General
It is important that the maximum and minimum flows and levels specified are greater than those expected to be encountered in the computations, otherwise the simulation engine will fail partway through the model run.
The rating curve may be determined from field observations. Alternatively, the normal depth equations may be used as an approximation  care must be taken to ensure that an approximate boundary condition is located sufficiently far downstream so that inaccuracies do not affect the results in the area of interest. Sensitivity tests can be used to test this.
FlowHead boundary conditions can be extracted from previous unsteady model runs using the Tabular CSV tool (Results tab). However, a "looped rating curve" will usually result from an unsteady run and a best fit single valued curve would need to be estimated before importing back into a model.
Note that in many cases a singlevalued rating is an approximation and should be positioned sufficiently far downstream such that the approximation in the boundary condition does not affect the accuracy in the area of interest. This can also be checked through sensitivity tests.
Where Flood Modeller cannot determine the normal direction of flow (for example at Junctions), then outflows from the system are expressed as negative flows and inflows are expressed as positive. However, if the normal flow direction can be determined (for example there are River units immediately upstream of the Flow Head Boundary), then the Q in the Flow Head Boundary data should be set to be positive for flow out of the system.
The boundary condition can only be specified at an extreme point in the network.
There is a limit of 50 data pairs for the flowstage data.
Unsmoothed boundary data may give rise to step changes, spikes or oscillations in flow and/or stage results. Smoothing data prior to computation or use of the spline function is recommended.
If spline is specified as the interpolation method, then a cubic spline is fitted to the data. This will help smooth data where the curvature is high. However, if the data is noisy, or if there are sudden changes in gradient, splines may lead to oscillations and may not be suitable.
Datafile Format
Line 1  keyword QHBDY [comment]
Line 2  Label
Line 3  n_{1} [,z] [smooth]
Line 4 to Line 3+n_{1}  Q_{i}, h_{i}
where:
Label = Node label at boundary
n_{1} = Number of ensuing flow and water level data pairs
z = Elevation above datum (not used)
smooth = SPLINE if a cubic spline is to be fitted to the data, or LINEAR to use linear interpolation. (If the field is blank then linear interpolation is used.)
Q_{i} = Flow (m^{3}/s) corresponding to water level h_{i}
h_{i} = Water level (metres above datum)
Example
QHBDY
UNIT002
2 0.000 LINEAR
1.000 0.000
2.000 1.000