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In a live division, the maximum fixed loss an owner could meet is that which would occur when their outflow is equal to zero (i.e. when O(o) = 0).  The value of Loss_fixed(o) that will result in O(o) = 0 can be found from equation (23), re-expressed as follows:

Equation 51	Image Added

For each owner, the values of surplus and deficit for borrow and payback are therefore:

Equation 52	Image Added

Equation 53	Image Added

Live Division – Outflow Borrow and Payback

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In a dead division, determining whether each owner has a surplus or a deficit, and the magnitude, is based on the mass balance equation (equation (15)), re-expressed as follows:

Equation 54	Image Added

A positive net volume is a surplus, and a negative net volume is a deficit.  Hence the values for borrow and payback are:

Equation 55	Image Added

Equation 56	Image Added

Methodology

Model Phase: Configuration

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• • Owner percentages of dead storage: Ratio_ds(o)
  • Owner percentages of time series fluxes (for the fixed ratio option): Ratio_TS(o)
  • Owner percentages of other lateral fluxes (for the fixed ratio option): Ratio_loss(o)
  • Owner percentages of the high flow threshold (if applicable): Ratio_HFT(o)
• For each individual link, the following are input:
  • Initial owner shares of flow or active storage
  • Whether the time series flux is to be input per owner (if so, this overrides the ownership system method of sharing time series flux), or not.
  • If the time series flux is to be modelled by owner, Flux_TS(o), otherwise Flux_TS
  • If Murray style losses are to be modelled, the high flow threshold Image Added above which high flow conditions apply.

Model Phase: Initialisation

When the model is initialised at the start of the scenario run, for a given link the ownership processing is initialised using the same values for all divisions in the link.  Each owner’s share of the initial storage volume is calculated.  In addition, if Murray-style losses are being modelled, the threshold storage volume and each owner’s initial share of this are determined, and the initial value of the volume of flow based flux caused by flow at the high flow threshold is also determined.

Model Phase: Ordering

No ownership calculations are involved in the ordering phase.

Model Phase: Flow distribution

In this phase, ownership processing for a link is performed after other link processing is completed.  Computational steps are summarised in Figure 2.

Figure 2. Flowchart- of main steps in ownership processing for a division in a time step

Image Added

For every division, to determine owner volumes of inflow, lateral flux, outflow, storage and mass balance, the steps for each model time step are as follows:

1. Initialise temporary parameters.

2. Set each owner’s upstream inflow I(o) to equal that owner’s share of the upstream component’s outflow using equation (10). (The upstream component is the next division upstream, or if it is the first division in the link, the upstream node).

3. Determine the volume of the total flow based flux, fFlow_LG(Image Added), for this time step to be shared according to fixed ratio, expression or time series specified by the modeller.  Where relevant, also determine the volume, Loss_HF, that is to be shared using high flow rules (i.e. Murray-style losses), which is the volume that is in excess of the value of fFlow_LG(Image Added).

• • If the ownership system uses Murray-style losses:

1. 1. 1. The flux based on flow up to the high flow threshold is shared according to fixed ratio. This volume is: