• 22 Sep 2022

Article summary

The Flow-Head 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 (m3/s) corresponding to water level hi

Qi

Stage

Water level (metres above datum)

hi

## 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:

 Q = Q(h) (1)

The discrete form of the equation is:

 Q =[Q1, Q2, ... ,Qn] (2)

At intermediate points either linearisation is used:

 Qint =Qi + (h - hi) (Qi+1 - Qi) / (hi+1 - h1) (3)

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 part-way 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.

Flow-Head 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 single-valued 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 flow-stage 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 - n1 [,z] [smooth]

Line 4 to Line 3+n1 - Qi, hi

where:

Label = Node label at boundary

n1 = 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.)

Qi = Flow (m3/s) corresponding to water level hi

hi = Water level (metres above datum)

### Example

``````QHBDY
UNIT002
2     0.000    LINEAR
1.000     0.000
2.000     1.000``````