Selecting an Appropriate Network Topology¶
Selection of the network topology is without doubt the most important task in the modelling process. A carefully selected network topology will avoid many problems during the calibration and application phase. It is, however, not possible to give detailed guidelines on how to design the network for all cases. The design should be based on a thorough insight into the hydraulics of the area to be modelled and an understanding of how the model works. Experience is, therefore, a key factor in the selection of the network topology. Some general guidelines for the less experienced user are given below.
Selecting the area to be modelled¶
When selecting the extent of the area to be modelled the following should be taken into consideration:
- Topographical/bathymetric data should be available for the entire area.
- At the model boundaries, time series of water level or discharge or a rating curve should be available, see Chapter 5.
- The boundary should be located at a sufficient distance from the area of interest to ensure that changes in the area of interest being investigated do not affect the boundary. This is of particular importance when the effects of major modifications to the flow are being investigated, for example, embankment and channelisation schemes.
Selecting which reaches to include¶
Reaches in 1D network represent flow paths, therefore in many cases it is quite clear where reaches should be included in the model.
It is important to note that the selection of reaches should be based on a compromise between computational time and the level of detail. The 1D engine is designed in such a way that it is relatively easy to include new reaches in existing setups. Thus, in general, it is advisable to limit the number of reaches in the initial setup and only include more reaches if required.
The following should be considered:
- River tributaries can be included in a model setup either as reaches or as lateral inflows. A lateral inflow will cause almost no increase in computational time and will be sufficiently accurate for most minor tributaries. A tributary included as a reach will give the correct routing (delay and attenuation) of the water flow, but will increase data requirements and computational time.
- Reaches are used in the schematisation of quasi 2D flow between flood cells, see Section 4.8.
Selecting the grid spacing¶
Given a hydraulic event to be modelled, the user has to determine the grid spacing; the distance between grid points in the model. The inexperienced user should base this selection of grid spacing on trial and error. Ideally, the model should be run first with a fairly large grid spacing, followed by runs with smaller and smaller grid spacings. The grid spacing to choose in the simulation is the largest grid spacing for which a smaller grid spacing does not significantly change the result of the simulation. Then the simulation result will be independent of the grid spacing parameter.
The stability conditions of the model depend mainly on the ratio between the time step and the grid spacing, see Section 4.4; i.e. when the space step is reduced it is also necessary to decrease the time step. The implication is that the computational time increases by a factor of 4 every time the space step is reduced by a factor of 2. Thus the number of grid points should be kept as low as possible.
From a simplified analysis of the numerical scheme it is possible to find some theoretical guidelines for the selection of the grid spacing. For instance, a certain number of grid points (about 30 to 50) per wave length is required to obtain a reasonable accuracy for the overall solution. In general the wave length(s) of a flow event can be expressed by
Equation: The wave length (s) of a flow event
where,
\(L\) wave length
\(T\) duration of event (wave period)
\(y\) water depth
In smaller rivers which experience flash floods a representative “wave period” may be a few hours. Thus a relatively small grid spacing will be required in order to resolve the flow events. In tidal flow with a period of more than 12 hours the wave length will mostly be very large, implying that a very large (20-30 km) grid spacing may be applied. In practice, however, variability of the cross sectional shape of the river, junctions with tributaries, etc. will require smaller grid spacing.
A relevant length scale for backwater effects is L = y/Ib, where Ib is the bottom slope. In models, where it is important to resolve backwater effects accurately, the grid spacing should be selected in such a way that the grid spacing is at least 4-6 times smaller than this length scale.