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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 this range. Hence, if q‾(o) is owner o’s current flow rate, RatioHFT(o) is their share of the high flow threshold, q‾HFT is the high flow threshold, the total flow rate, and LossHF the total high flow loss, then owner o’s share of the high flow loss is:
| Equation 24 | |
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Substituting equation (19) into equation (24) enables it to be re-written in terms of the division’s storages, as follows:
| Equation 25 | |
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High flow losses are worn only by owners where Storage(o,t)-StoragedsMAX(o) is greater than their share of the high flow threshold (StorageHFTRatioHFT(o)). Owners that will not be required to contribute the high flow loss are identified by calculating Storage(o,t) for each owner assuming that LossHF=0 and finding those that fall short of their share of the high flow threshold.
From equation (25), for those owners that exceed their share of the threshold:
| Equation 26 |
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The denominator of equation (26) is the total volume above the high flow threshold of owners contributing to the high flow loss. The equations that follow are used to determine values required to find this.
Firstly, a modified high flow threshold is defined that applies to the owners, j (where j is defined in Table 2, and the relevant owners are those that have, with LossHF=0, a trial value of Storage(o,t) such that Storage(o,t) > StoragedsMAX(o) + StorageHFTRatioHFT(o)):
| Equation 27 |
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where:
j Owners: LossHF(j) ≠ 0 is set-builder notation to indicate that the modified high flow threshold is the sum of all the owners’ shares of the threshold where the high flow loss is not going to be zero.