Hydraulic model schematisation

Once decisions have been made about the channel network schematisation and its various model elements, choices have to be made about equations and their associated data. In most cases, channel flow will be based upon the description of the full De Saint Venant equations, although also mixed models may be constructed. It could make sense, for example, to describe the flow in upstream, steep river branches with hydrologic models or artificial neural networks (ANNs), whereas in the principal rivers the full De Saint Venant equations are applied. In all cases, however, the models must include representative values for channel storage and conveyance, whether these are specified directly or hidden in the parameters of a hydrologic model. In principle, the model must compensate for conveyance or storage which has been neglected in the topological schematisation.

One important decision is the choice of distance step x, which should be based upon a good representation of the hydraulic processes. The choice is based upon: · The wave length modelled. A rule of thumb is to model waves with at least 50 to

100 grid point along important wave components;

· The representation of the local variations in hydraulic parameters, such as sudden contractions and expansions;

· Placement of grid points closely around hydraulic structures or other discontinuites in the system.

Channel conveyance is described at cross-sections. Under all circumstances these cross-sections must be lines perpendicular to the direction of mean velocities. In the case of meandering rivers these cross-section alignments have to be defined on the basis of sound engineering judgement. A complicating factor is the change of velocity vector directions with changing stage.

For man-made channels the specification of cross-section parameters is rather straight forward. As the dimensions are usually quite accurately known, the most sensitive input parameter is the roughness coefficient. For simple channel geometries, the use of the hydraulic radius as an approximation of a representative depth is quite acceptable. The hydraulic radius is defined as the surface of the conveying cross-section divided by the wet perimeter (Equation (5.11) or (5.12)) and assumes a uniform distribution of the shear force along this wet perimeter. For cross-sections with varying depths this assumption is incorrect. The local shear force in the cross-section is a linear function of the local depth. For this reason, the conveyance of compound channels has to be based upon a summation of the conveyances of individual sub-sections where for each of them this shear force is more or less uniform (Equation (5.9)).

An advantage of such integration is that each sub section can be given its own roughness value. Another advantage is that by keeping track of the individual contribution of the sub sections to the overall conveyance of the channel, computed discharges can be redistributed across the section to provide water velocities for each sub section. This ability may be important in simulating water quality or morphological processes in flood plains where the use of local velocities is required. In the integration, contributions of sub sections with small conveyance are without any loss of accuracy added to those of the other sub sections. There is no need to neglect the conveyance of shallow and highly resistant parts of the cross-sections as these may still give substantial contributions during floods or may be important in the overall assessment of the morphologic or water quality behaviour.

One of the basic assumptions in a one-dimensional schematisation is the use of a constant water level slope all along the cross-section. In meandering channels, however, the slope may be quite different for different sub sections. One way to include this effect in the derivation of the conveyance is by giving each sub section a weight in the integration, as a function of the distance to its equivalent part in the next cross-section. Equation (5.11) will then be modified as follows

( )

( )

_{( )}( )

å

(

)

å

where x is the distance for which the cross-section parameters are representative along the x-axis and xja similar value for sub section j.

Storage parameters usually are given as a function of stage and linked to cross- sections. For uniform channels, as often designed in irrigation and drainage systems, the storage width is equivalent to the flow width. Storage width data are simply extracted from cross-section information. In natural rivers, however, meandering and irregular flood plain topography requires more complex procedures. § 5.2 gives an extensive discussion of the correct definition of the storage width parameter bs. It follows that storage parameters have to be extracted from information provided by topographic maps, currently mostly available in the form of digital elevation models (DEMs) in GIS. For successive compartments along the river axis, approximate water level slopes have to be assumed to extract from these maps storage area as a function of stage. Division of these areas by the length of the compartment along the x-axis, provides the parameter values for bs. For models of lesser economic value, procedures may be simplified, if needed.

Storage connected to channels which have been neglected in the topological schematisation must be added to the model as additional storage. In the cross-sections the compensation can be made in the form of additional storage width. It can also be introduced in the schematisation in the form of additional storage areas at nodes. It is recommended to keep track of the changes that this correction phase has given in parameter values derived during the primary phase of schematisation. It is always advised to keep good records of all the steps taken in the development of a model and the way the model parameters have been defined. Without such records it is practically impossible to introduce future improvements or modifications correctly. This is even more so when various persons are involved in the model development and/or the development takes place over a considerable length of time.

Hydraulic structures may be described by their empirical relationships, by the application of an energy conservation principle upstream and a momentum conservation principle downstream or by specifying the discharge water level relationships in matrix form. In case of empirical relationships, care must be taken that the parameters describing free flow and submerged flow, successively, give a consistent computed discharge at the moment of transition from one flow state to the other. If applicable, additional entrance energy losses must be specified. Composite cross-sections of the structure require an adaptation of the topological schematisation by defining parallel structures. Similar to the definition of conveyance, the total discharge through the composite structure is defined by adding up the contributions of the individual structure components.