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| Note: The stability criteria must also be satisfied for a model to run correctly. If this is not the case, the following error appears during runtime: Routing parameters have caused instability in storage routing. Refer to the Stability Criteria for more information. |
This is a simplification of the full momentum equation and assumes that diffusion and dynamic effects are negligible. The method uses index flow in flux, storage, and mass balance equations. A weighting factor is used to adjust the bias between the inflow and outflow rate, hence allowing for attenuation of flow. The storage routing equation is shown below, and some of its terms are represented diagrammatically in the Figure below.
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To determine if the reach is at or below the dead storage level, SourceMUSICX:
- Computes an initial storage estimate by using inflows to fill the reach up to but not exceeding the dead storage level;
- Computes a revised storage estimate based on any remaining inflows and fluxes, but ignoring outflows; or
- If the revised storage estimate is above dead storage, then outflows are computed. Otherwise, the initial storage estimate is used and outflows are set to zero.
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| Routing Parameter | Description | Units | Range | Default |
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# Divisions | Number of reach divisions. Conceptually, this parameter describes the number of times that a reach is replicated. The effective length of a reach is determined from its behaviour, which is controlled by the combination of the storage exponent m, the inflow bias x and the storage constant K. Specifying multiple reach divisions implies applying the same set of behavioural parameters multiple times. In other words, if the effective length of a single-division reach is 500 metres (as derived from its behavioural parameters), changing the # Divisions parameter to 2 implies a combined effective length of 1000 metres. If you want to sub-divide a 500 metre reach into two 250 metre sections, you must also change the behavioural parameters to achieve this. | whole units | integer ≥ 1 | 1 |
| Inflow bias (attenuation factor, x) | The weighting factor x is used to adjust the bias between inflow and outflow rate and allows for flow attenuation. The weighting factor is usually in the range 0 ≤ x ≤ 0.5 (Davis and Sorensen, 1969). A recommended starting value is 0.2. | dimensionless | real 0 ≤ x ≤ 1 | 0 |
| Storage constant (k) | When using linear routing (m = 1), the units of the storage constant k are in seconds and the wave travel time is equal to k times the number of divisions. When using non-linear routing (m ≠ 1), a starting value could be calculated using Equation XX Equation 20 in the Appendix -B. | k units | real ≥ 0 | 0 |
| Storage exponent (m) | If m=1, linear (Muskingum) routing is implied, otherwise non-linear routing is implied. m=0.74 is a good starting value for a natural channel. | time-steps | real 0 < m ≤ 1 | 0 time-steps |
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