- 15 Aug 2022
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# Flow Time Boundary

- Updated on 15 Aug 2022
- 5 Minutes to read

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The Flow Time Boundary models a discharge hydrograph (specifying flow versus time) as a boundary condition.This boundary condition is usually applied at the upstream end(s) of the network, at the top of tributaries for example.

## Data

Field in Data Entry Form | Description | Name in Datafile |
---|---|---|

Boundary Unit Label | Node label at boundary | Label |

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 flow is to be fixed at the last given value NOEXTEND - for 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 |

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. | t |

Flow Multiplier | Flow multiplier. User input multiplier for flow, e.g. if set to 2 then all flow values in the Flow,Time table will be multiplied by 2 before being used. Default is 1. | q |

Minimum flow | Minimum allowable flow (m If absent or zero, this value is ignored and no minimum flow is applied. | q |

Time Datum Adjustment | Optional. This value can be used to reduce all time values by the given value. For example, if the Time-Datum adjustment is set to 2.2 and the units of time are hours then all time values will be reduced by 2.2 hours (the hydrograph is moved 2.2 hours earlier). Default value is 0. | t |

Flow | Flow corresponding to t | Q |

Time | time (in units of t | t |

## Theory and Guidance

The Flow Time Boundary models a discharge hydrograph specified as a boundary condition.

This boundary condition is usually applied at the upstream end(s) of the network, at the top of tributaries for example. All extreme points on the network require a boundary condition. The Flow Time Boundary specifies a set of data pairs comprising flows and times.

Flows into the middle of a river reach must be input by including a junction or via a lateral inflow unit.

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

### Equations

The discrete form of the continuous equation Q = Q(t) used in the Flow Time Boundary is:

Q = [Q | (1) |

At intermediate points either linearisation is used:

Qint = Qi + (t - ti) (Qt+1 - Qt) / (ti+1 - ti) | (2) |

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

### General

Flow hydrographs may not be available from observations at a location exactly corresponding to the upstream end of a model and may therefore need to be estimated. Flood Modeller contains subcatchment hydrological units which can be used to estimate flow-time boundaries (flow hydrographs), although calibration is usually necessary to obtain a high level of accuracy. Alternatively flow-time boundaries can be estimated externally using other hydrological models and methods.

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

If Spline is specified, then a cubic spline is fitted to the data. This will help smooth data where the curvature is high. However, if the hydrograph 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.

Flow time boundary conditions can be extracted from previous model runs using the Tabular CSV results processing tool (Results Tab). These can then be re-imported if a sub-model is to be created from a larger model, for example.

It is also important to note that the Flow Time Boundary will force the flow at the node where it is located to the flow specified in the boundary data. For open channels, for example, the flow specified could be well out-of-bank and may have been attenuated or lost to the system further upstream. It could be necessary to extend the model further upstream in these circumstances or to make an adjustment to the estimated flows.

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 Rivers immediately downstream of the Flow Time Boundary), then the Q in the Flow Time Boundary data should be set to be positive for flow into the system.

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

A minimum flow can be specified, which enables data to be input without the need to screen for values low enough to cause potential stability problems. Note: this functionality applies the condition of strictly less than the minimum flow, therefore this should be borne in mind if negative flows are entered or expected.

## Datafile Format

Line 1 - keyword QTBDY [comment]

Line 2 - Label

Line 3 - n_{1} [t_{lag}] [z] [t_{m} ] [repeat] [smooth][q_{mult}][q_{min}]

Line 4 to Line 3+n_{1} - Q_{i }, t_{i}