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Water Resource Associates |
HYDRAULICS
HYSIM uses kinematic routing of flows. This enables the hydraulics component to use channel dimensions and Manning's roughness coefficient. The only situations where the equations would not apply are in rivers artificially controlled by sluice gates, influenced by tides or with very flat gradients. In general if a stage/discharge relationship is possible then the kinematic approximation is acceptable.
Wave theory
Whilst flow in open channels can be described most accurately by the Saint Venant equations, these equations are not explicitly solvable. The methods of solution that are available are not suitable for a hydrologic model as they require an iterative solution for small time increments. Fortunately most of the terms in the Saint Venant equations have only minor effects and flow can be described adequately by the simplified form known as the kinematic method (Lighthill & Witham).
The velocity of a kinematic wave, Vw, is given by :
Vw = d Q .......................... 1
d A
where Q is the incremental change in flow and A the incremental change in area.
Manning's formula when applied to a triangular channel gives:
Q a A4/3
where Q is the discharge and A is the sectional area of flow.
For a broad rectangular channel the equivalent equation is :
Q a A5/3
Since most channels fall between these two extremes then it has been assumed that
Q = CA1.5 .............................. 2
For flow in bank, A, as a function of Q, is calculated by re-arranging equation 2.
For flow out-of-bank exponential relationships are developed at the start of the program. They are of the form :
A = a Qb ................................ 3
where a and b are constant. They are based on the geometry and roughness of the flood plain using Manning's equation. Two such relationships are used, one for when the flood plain is filling up and one for when it is full.
Kinematic waves
The way the kinematic theory is used in the model can best be visualized by reference to the following figure. The input hydrograph is shown as the solid line. Using equation 2 or 3 the sectional area for the input flow is calculated. From equation 1 the velocity of the wave and hence its travel time is calculated. The hydrograph is then displaced by this travel time for each time increment. The result of this stage is represented by the dotted line.
The time increments of the "dotted" hydrograph will not generally be the same as those of the model. This "dotted" hydrograph is therefore redistributed to produce the "dashed" hydrograph.
The situation sometimes arises where a later wave has a higher velocity than an earlier wave, and catches up with it within a section. The program checks whether any such events occur, and if they do it recalculates the time of travel of the resulting "coalesced" wave from the point at which it was formed. This approach is of particular importance when flows go out-of-bank and rapid changes in wave velocity occur.
Whilst the above approach involves a degree of compromise it is very stable and can be used with time steps much longer than the time of travel of a kinematic wave in the section being modelled, an advantage when using daily data but when travel times in a short river have to be simulated.
HYSIM Introduction, HYSIM Hydrology, Use of HYSIM, Papers on HYSIM