• 15 Aug 2022
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Article Summary

The Head Time Boundary allows the input of a stage hydrograph (specifying water level versus time) as a boundary condition. This is usually applied at the downstream end(s) of the network.

## Data

Field in Data Entry Form

Description

Name in Datafile

Boundary Unit Label

Node label at boundary

Label

Units of Time

optional keyword or value for units of time in the following data set. Can be any numerical multiplier or one of the following: seconds (the default), minutes, hours, days, weeks, fortnight, lunar (month), months (of 30 days), quarter, years or decades.

tm

Data Extending Method

policy for extending data if the run finishes after the end of the boundary data. Options are:

• REPEAT - if the data are to be repeated from the beginning
• EXTEND - if the stage is to be fixed at the last given value
• NOEXTEND - no extension

If NOEXTEND is used (or the field is left blank) then the program will stop with an error message if there are insufficient boundary data.

repeat

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

Stage

water level at time ti (mAD)

hi

Time

time (in units of tm - default of seconds)

ti

## Theory and Guidance

The Head Time Boundary allows the input of a stage hydrograph as a boundary condition.

This boundary condition is usually applied at the downstream end(s) of the network. All extreme points on the network require a boundary condition.

The Head Time Boundary specifies a set of pairs of data comprising water levels above datum and time.

The data can be checked prior to a computational run using a Flood Modeller boundary mode simulation.

### Equations

The discrete form of the continuous equation h = h(t) used in a Head Time Boundary is:

 h = [h1, h2 , ... , hn] (1)

At intermediate points either linearisation is used:

 hint = hi + (t - ti)(hi+1 - hi) / (ti+1 - ti) (2)

or a cubic spline is used. You can choose which interpolation method to apply.

The following figure illustrates these equations: ### General

The boundary condition can only be applied to a node at an extreme point in the network. Typically the node will be a cross section node, a junction node or the downstream node of a structure.

The head-time boundary condition must be correct for the event to be simulated. This is straightforward for modelling a historic event if head-time observations at that location are available. For design runs of the model it may be necessary to switch to a rating-curve (Flow Head Boundary condition). The downstream boundary condition, if approximate, must be moved to a location sufficiently far downstream such that the approximation does not affect the solution in the area of interest. This can be checked through sensitivity tests.

Head-time boundary conditions are easy to specify if the model terminates downstream of a weir and the weir is known not to drown out during the event being considered.

The data pairs specified need not coincide with computational time steps. However, when digitising the data to capture the shape of the hydrograph, it is important to note that when linear interpolation is used between data points more points may be needed where curvature is high.

If Spline interpolation is specified, 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.

If Extend and Spline are both specified, then the gradient of the hydrograph is clamped to zero at the last point.

If Repeat and Spline are both specified, then the gradients at the first and last point and the second derivative are assumed to be equal. Note that this is true even if the run is short enough that the hydrograph does not actually need to be repeated. In all other cases a natural spline (ie zero second derivative at each end) is used.

The suitability of the fit can be checked prior to a full unsteady run by using boundary mode.

Note that the head used is the water level above datum and not the total head.

Head-time boundary conditions can be extracted from previous model runs using the Tabular CSV output processor in the Flood Modeller (Results Tab). These can then be re-imported if a sub-model is to be set up from the larger model, for example.

Unsmoothed boundary data may give rise to step changes, spikes or oscillations in flow and/or stage results. You are recommended to consider smoothing data prior to computation.

## Datafile Format

Line 1 - Keyword `HTBDY' [comment]

Line 2 - Label

Line 3 - n1 [,z], [tm] [repeat] [smooth]

Line 4 to Line 3+n1 - hi, ti

where:

Label = Node label at boundary

n1 = Number of ensuing water level and time data pairs

z = Elevation above datum (not used in computations)

tm = optional keyword or value for units of time in the following data set. Can be any numerical multiplier or one of the following: seconds (the default), minutes, hours, days, weeks, fortnight, lunar (month), months (of 30 days), quarter, years or decades.

repeat = policy for extending data if the run finishes after the end of the boundary data.

Options are:

REPEAT - if the data are to be repeated from the beginning

EXTEND - if the stage is to be fixed at the last given value

NOEXTEND - no extension

If NOEXTEND is used (or the field is left blank) then the program will stop with an error message if there are insufficient boundary data.
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.)

h= water level at time ti (mAD)

t= time (in units of tm - default of seconds) 