Overview
A new option called 'Use Airspace' has been added to the 'Ownership' in storages in Source. As a result, some modifications are done to the 'Ownership in Storages - SRG' page. Only the additions/modifications made to the original storage ownership SRG are explained here and hence for the unchanged sections, one should refer to the original page of previous releases. For example, only the changed and new equations are mentioned here. The modifications are done to explain the calculation method behind the 'Use Airspace' option.
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The new method makes the proportional loss calculation fixed at the start of the timestep and thus allows for the calculation of spills required for the airspace owner logic. And it also happens to simplify the other calculations meaning that there's no iterations and the logic for positive and negative losses are exactly the same. The fundamental difference is that the losses are calculated based on the owners' maximum release for the timestep rather than based on the owners' storage at the end of the timestep. In this method, instead of sharing the losses based on the proportion of capacity share of each owner, the losses are shared based on each owner's share of working volume. Therefore, for an owner i, the working volume is calculated as:
Equation 1 |
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where:
Wi - Working volume of owner i.
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The total working volume for all owners is:
Equation 2 |
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where:
Ti - Total working volume.
The proportional loss attributed to owner i is Pi and is given by:
Equation 3 |
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where:
P is the total proportional loss, negative if a gain (rainfall).
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Based on the working volume, release, borrow, internal spill, external spill and proportional loss, an owner's final storage volume is calculated as:
Equation 4 |
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where:
Vi2 - Owner ’s volume of water in the reservoir at the end of time step.
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The final storage volume is updated after calculating the internal and external spills. The changes in the spill calculations are illustrated in the later sections.
Maximum release
If the storage working volume is less than or equal to ownership tolerance level (0.0001 m3), the maximum release for an owner is:
Equation 5 |
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where:
ri - Owner i’s ratio share of the reservoir’s storage capacity.
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Before each owner’s share of spills can be determined, it is necessary to determine which owners will spill. Where the spill calculation returns a negative value, owners can receive internal spill, while a positive value indicates that the owner is spilling (has filled their storage share).Based on the working volume calculation method, Equation (4) is rearranged to give an expression for the volume of water that can spill (internally and externally) from an owner’s capacity share:
Equation 6 |
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where:
Vimax - Owner i’s maximum allowed volume of water in the reservoir this time step.
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The total external spill by all owners is known and is given by total outflow minus the total release of all owners as in:
Equation 7 |
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If there is an owner which uses the 'Use Airspace' option and its spill is greater than zero, the spill is given by:
Equation 8 |
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It is to be noted that the spill by the 'Use Airspace' owner Spilla is included in Spilli
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The calculations in the previous sections established which owners are spillers when working volume based proportional losses are taken into account. The next step is to determine the internal (between owners) and external (leaving the reservoir) components of the spill by the owners excluding the owner which uses 'Use Airspace' option. This is done as the 'Use Airspace' owner does not spill internally. Based on the calculations in the previous sections, the total spill is:
Equation 9 |
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Then the external spills by the owners who do not use 'Use Airspace' option is calculated and it is given by:
Equation 10 |
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Case where internal spills are disabled
If internal spill is disabled the internal spill volume is zero (ISi = 0). The ownership of the external spills is set based on how much each owner would spill in total if internal spill was operating:
Equation 11 |
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Case where internal spills are enabled
When internal spills are enabled, the equations 33 to 43 are followed as in the previous version of SRG with no changes. These equations are based on the equations 9 and 10, which are in turn based on owners who do not use 'Use Airspace' option.
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