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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,
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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,
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When using linear routing (m = 1), the units of the storage constant k are in seconds. For models using daily time-steps, the recommended starting value is 86400 (the number of seconds in one day). When using non-linear routing (m ≠ 1), the recommended starting value should be calculated as follows:
| Equation 3 |
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For example, if the reach length is 1000 metres, the time-step is one day, and m = 0.8:
| Equation 4 |
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| Anchor | ||||
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Table 1. Parameters for link storage routing
| Parameter | Description | Units | Range | Default |
|---|---|---|---|---|
| General configuration | ||||
| Avg. Reg. Flow | ||||
Average regulated flow is used to calculate travel time for orders in the ordering phase. It is not used in the flow distribution phase.
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| megalitres per day | real ≥ 0 | 0 ML/d | |
| Elevation | Note that while it is usual to use zero storage as the reference point for the elevation of a link or node, there is no convention for a link as to whether that should be at the start or end of the reach, or some point in between. Source has no mechanism for indicating the fall across a reach. | |||
| Initial conditions | If necessary, one of these parameters may be used to seed a reach with either an initial flow or storage (see below) so that reach behaviour is fully defined from the first model time-step. | |||
| Initial flow | megalitres per day | real ≥ 0 | 0 ML/d | |
| Initial storage | The amount of water deemed to be in the link on the first time-step. For example, if there is a lag of two days, and there is 10ML in the link at the start of the run, then 5ML is deemed to be flowing out each day (total initial storage divided by lag). | megalitres | real ≥ 0 | 0 ML |
| Reach length | Source simulates evaporation and rainfall using the user defined reach length and a reach width (based on simulated flow and a user defined rating curve) to calculate surface area. | metres | real ≥ 0 | 0 m |
| Routing parameters | ||||
# 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. A recommended starting value is 0.5. | dimensionless | real 0 ≤ x ≤ 1 | 0 |
| Generic | ||||
| Storage constant (k) | When using linear routing (m = 1), the units of the storage constant k are in seconds. For models using daily time-steps, the recommended starting value is 86400 (the number of seconds in one day). When using non-linear routing (m ≠ 1), the recommended starting value should be calculated as shown in Equation 2. | k units | real ≥ 0 | 0 |
| Storage exponent (m) | If m=1, linear (Muskingum) routing is implied, otherwise non-linear routing is implied. | time-steps | real 0 < m ≤ 1 | 0 time-steps |
Piecewise storage function
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Table 2. Storage routing link, Travel time (data file format)
| Row | Column (comma-separated) | |
|---|---|---|
| 1 | 2 | |
| 1 | Index flow | Travel time |
| 2 … n | flow | day |
| Anchor | ||||
|---|---|---|---|---|
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Table 3. Storage routing link, Rating curve (data file format)
| Row | Column (comma-separated) | |||
|---|---|---|---|---|
| 1 | 2 | 3 | 4 | |
| 1 | Level | Discharge (ML/d) | Surface width (m) | Dead storage (ML) |
| 2 … n | level | rate | width | storage |
where:
level is the storage height in the reach in metres above a datum
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Table 4. Storage routing link, Rating curve (example)
| Level (m) | Discharge (ML/d) | Surface width (m) | Dead storage (ML) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0.1 | 0 | 5 | 50 |
| 0.5 | 0 | 10 | 100 |
| 1 | 10 | 11 | 100 |
| 5 | 500 | 15 | 100 |
To edit an exising rating curve, select the curve from the list of available curves under Rating Curve. Edit the data and click OK to close the editor. To delete a rating curve, right click the curve from the list and choose Delete.
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Table 5. Storage routing link, Evaporation (data file format)
| Row | Column (comma-separated) | |
|---|---|---|
| 1 | 2 | |
| 1..n | time | value |
where:
time is the time of obersvation in "dd/mm/yyyy hh:mm:ss" format
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