About storage routing
Storage routing is based on mass conservation and the assumption of monotonic relationships between storage and discharge in a link.
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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 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 Figure 1.
| Equation 1 |
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where:
S is the storage in the reach,
K is the storage constant
m is the storahe exponent, and
q~ is the index flow, which is given by
| Equation 2 |
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where:
I is the inflow to the reach during the time-step,
O is outflow from the reach during the time-step and
x is the inflow bias or attenuation.
Figure 1. Prism and wedge storage
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Travel time
Travel time in the reach is computed as follows:
| Equation 3 |
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A link configured for lagged flow routing is treated as a series of sub-reaches of equal length, with the travel time in each sub-division equal to one time-step. Water moves through the link progressively, without attenuation. You cannot configure fluxes, constituents or ownership on a lagged flow routing link. If lateral flows are significant and/or there is dead storage in the reach, you can approximate lagged flow routing using generalised non-linear storage flow routing, as follows:
Compute the number of division, n, by dividing the average wave passage time by model time-step and round the result to a whole number. The result must be at least one (ie. n ≥ 1);
- Configure a storage flow routing reach where:
- n = number of divisions;
- x = 1;
- m = 1; and
- k = model time-step.
- If you need to account for lateral flows where n = 1 and the average travel time is a fraction of the model time-step (eg. a reach with a one day lag in a model with a monthly time-step), you can adjust k to a smaller value without affecting the shape of the hydrograph.
Figure 2 shows the feature editor for storage link routing and Table 1 outlines the parameters required.
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