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In the flow phase, the outflow flux from the division upstream becomes the inflow flux to the current division (or the outflow flux from the upstream node becomes the inflow to the division if the most upstream division in a link is being considered). The same is true for the inflow flux per owner (the ownership processing for the upstream division or node has already determined its outflow per owner).
| Equation 9 | |
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| Equation 10 |
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Outflow flux
The total outflow volume is also known after the reach’s flow routing is complete. Ownership processing determines each owner’s share of this outflow flux. The owner’s share of this flux is calculated based on mass balance and proportional routing. The resultant equation (equation (23)) and its derivation are explained in the section on Owner’s outflow formula (excludes high flow losses) below.
Lateral loss fluxes
The volume of lateral loss fluxes from every link division is known from the routing calculations for each time step after the flow phase. These fluxes may be divided into two categories:
- Fixed loss fluxes whose ownership is known a priori (because they are shared by fixed ratio or by some other means such as time-series or expression), and
- Proportional loss fluxes that are shared in proportion to the ownership of the water in the division.
Proportional fluxes may be further categorised into those based on total water in the division, and those above a specified threshold, as in the Murray-style losses. These Murray-style losses are also referred to as high flow losses.
Fixed loss sharing
The total fixed loss, Lossfixed, is distributed to owners based on the specified ratios, expression, or time series such that:
| Equation 11 |
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An owner’s share of fixed losses is adjusted if that owner does not have sufficient water in the division to cater for the loss. In a live division, an owner’s highest possible fixed loss occurs when their outflow is zero. In a dead division, the owner’s fixed loss cannot be larger than their share of dead storage. The Borrow and Payback mechanism is used to adjust owner shares of fixed loss for these situations. See the section on Ownership Adjustments for more information.
Proportional loss sharing
If the division is live, owner shares of proportional losses are based on each owner’s index flow rate (see the Proportional Routing section for an explanation of this approach).
| Equation 12 |
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| Equation 13 |
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If the division is dead, proportional losses are shared according to the owner’s fixed share of dead storage:
| Equation 14 |
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Murray-style High Flow Loss Sharing
In the Murray, losses caused by flows in excess of the regulated flow range are shared to owners in proportion to how far each of them is above their fixed share of the regulated flow range. When the modeller specifies Murray-style losses for an ownership system in Source, this method of sharing is applied only to the general purpose flux, which is a function of flow, when specified on links that fall within the ownership system. The calculation of each owner’s share of the high flow loss is explained in the section on High flow loss formula (Murray-style), below.
Fill dead storage flux
The division’s dead storage is shared according to fixed ratios. As this rule dictates each owner’s share of part of the total storage, it necessitates changing other parameters of the ownership conservation (mass balance) equation when a dead division is transitioning to the live state. The volume required to fill the dead storage compartment is treated as an additional loss that is shared according to fixed ratios.
Ownership mass balance
It is assumed that ownership is conserved in every division of a reach. This is reflected in the ownership mass balance equation below. This shows that the difference between an owner’s share of storage at the beginning and end of a time step should be the sum of their share of all the division’s fluxes.