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Note: If the routing division is using an attenuation factor x=0 (i.e. Image Modified), equation (23) can be rearranged to the continuous stirred reactor equation (equation (46)). This means that for fully forward weighted routing schemes, proportional routing is the same as fully-mixed.

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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 Loss_HF=0, a trial value of Storage(o,t) such that Storage(o,t) > Storage_dsMAX(o) + Storage_HFTRatio_HFT(o)):

Equation 27	Image Added

where:

j  Owners: Loss_HF(j) ≠ 0Image Added 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.

Next, it is necessary to determine the total volume of water this time step belonging to owners that are not contributing to the high flow loss, i.e. Storage_exclude:

Equation 28	Image Added

The denominator of equation (26) (current live volume contributing to high flow loss) is then:

Equation (26) can now be recast in terms of the total volume in the division:

Rearranged:

High flow loss solutions over a time-step

Case of Muskingum weighting x = 1 (Index flow rate = Inflow)

In this case, the index flow rate is the same as the inflow rate, and an owner’s share of inflow will determine their share of active storage.  The proportional routing formula (equation (19)) can be rewritten and applied to inflow as shown in equation (32), below and then rearranged to determine the owner’s share of storage.