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       P is the total proportional loss, negative if a gain (rainfall). 

If the storage working volume is less than or equal to ownership tolerance level (0.0001 m³), then proportional loss P_i becomes:

where:       

         r_i - Owner i’s ratio share of the reservoir’s storage capacity.

Based on the working volume, release, borrow, internal spill, external spill and proportional loss, an owner's final storage volume is calculated as: 

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 releaseBorrow calculations

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

6

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where: 

               r_i - Owner i’s ratio share of the reservoir’s storage capacity. P_i is as in Equation 4 as the proportional loss volume is already known. 

Previously, losses would not affect borrowing as the losses were based on end of timestep storages. 

Identifying spilling owners

Total External Spill

The total external spill by all owners is known and is given by total outflow minus the total release of all owners as in:

Spill by individual owner

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 (45) is rearranged to give an expression for the volume of water that can spill (internally and externally) from an owner’s capacity share:

where:       

         Vⁱ_max - Owner i’s maximum allowed volume of water in the reservoir this time step.

The equations 26 to 29 in the previous version of SRG are made redundant due to the inclusion  of proportional loss based on storage working volumes.

 Total External Spill The total external spill by all owners is known and is given by total outflow minus the total release of all owners as in:

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Equation 7

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the 'Use Airspace' owner 

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

9

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It is to be noted that the spill by the 'Use Airspace' owner Spill_a is included in Spill_iCalculating internal and external spill shares for the owners who do not use the 'Use Airspace' option.

The internal spill by 'Use Airspace' owner can be negative when there are internal spills to it. The airspace owner does not internally spill to other owners but can receive internal spills from other owners if it is under its capacity share.  Therefore, the spill amount is the minimum of it's calculated spill and the total external spill of the storage. 

The external spill of the 'Use Airspace' owner when its spill is greater than zero is given by:

The internal spill of the 'Use Airspace' owner when its spill is greater than zero is given by:

Calculating internal and external spill shares for the owners 

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:

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. The steps included are explained below.

Then the external spills by the owners who do not use 'Use Airspace' option is calculated and it is given by:

Case where internal spills are disabled

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