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S is the storage in the reach,
k is the storage routing constant
m is the storage routing exponent, and
q~ is the index flow, which is given by
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- The reach is at or below dead storage and the fluxes during the time-step are insufficient to raise the level above above the dead storage;
- The reach is above dead storage but fluxes during the time-step would lower the level in the reach below dead storage; or
- The reach is above dead storage and remains above dead storage during the time-step.
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- Computes an initial storage estimate by using inflows to fill the reach upto 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 sotrage storage estimate is above dead storage, then outflows are computed. Otherwise, otherwise the initial storage estimate is used and outflows are set to zero.
Storage constant (k)- storage routing constant
When using linear routing (m = 1), the units of the storage routing 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 When 0 < m < 1 (non-linear routing (m ≠ 1), the recommended starting value ) k should be calculated as follows:
| Equation 3 |
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| Equation 4 |
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| 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.
| 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 23. | 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 | |||||
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