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1. If the division is transitioning from dead to live (i.e. State_t-1 = Dead) and Storage(t - 1) < Storage_dsMAX, Storage(t - 1), and the fixed lateral flux for each owner, Loss_fixed(o), are adjusted as described in the Division transitioning from dead to live section under Ownership adjustments (equations (47), (48), (49) and (50) above).  The steps are:

   1. Adjust each owner’s fixed lateral flux to include the volume to fill dead storage

      Equation 88

   2. Set the apparent storage for last time step to the maximum dead storage.

      Equation 89

   3. Set the apparent storage for each owner at the last time step to their share of the maximum dead storage.

      Equation 90

2. Calculate the total ‘live’ storage for reporting (and use in further calculations), where Storage_live = Storage(t) - Storage_dsMAX as per equation (20).
3. Calculate trial storage volumes for each owner (that assume no high flow loss):

   1. If Muskingum  x = 1, outflow and storage are not interdependent, so the proportional routing model can be applied directly:  

      Equation 91

   2. Otherwise outflow and storage interact, so a more complex method is needed:

      1. Adjust owner fixed lateral fluxes to ensure no owner has a negative outflow:

         1. To determine the ratio r, use equation (21)

            Equation 92

            (Note that Storage_live = Storage(t) - Storage_dsMAX)

         2. Adjust owner fixed lateral fluxes to ensure no owner has a negative outflow. This involves finding the maximum fixed loss that each owner can sustain with non-negative outflow and the resultant surplus/deficit using equations (51), (52) and (53). 

            Equation 93

            Equation 94

            Equation 95

         3. Pass owner surpluses and deficits to the Borrow method (Refer to Borrow and Payback - SRG for more information). This will return how much owners borrowed or lent (OwnerBorrowed(o), OwnerLent(o)).

         4. For each owner: Add amount lent and subtract amount borrowed from the fixed loss - refer to equations 84 and 85.

      2. Use the proportional routing model equation (37) to determine trial volumes for each owner (assuming no high flow losses at this stage): 

         Equation 96

         Equation 97

4. If there is a high flow loss (Loss_HF > 0):

   1. If Muskingum x ≠ 1 high flow losses will impact storage volumes. The approach described  in the section on High flow loss formula (Murray-style), under Live division model, assumptions and equations above, is used to determine the final storage volume for each owner.

   2. Calculate owner shares of the high flow loss using equation (26): 

      Equation 98	Image Added

5. Calculate each owner’s share of each proportional lateral flux for reporting using equation (20), after rearranging so the term Loss_prop is on the right hand side (i.e. by rearranging to match the form of equation (13)):

   1. If the time series flux is configured to be shared proportionally 

      Equation 99	Image Added

   2. If other lateral fluxes are configured to be shared proportionally:

   3. For each of

   each proportional lateral flux for reporting using equation (20), after rearranging so the term Loss_prop is on the right hand side (i.e. by rearranging to match the form of equation (13)):
   1. If the time series flux is configured to be shared proportionally 

   2. If other lateral fluxes are configured to be shared proportionally:

   1. groundwater, net evaporation fluxes and, if Murray-style losses are not being modelled, flow based flux (Flux_GW, Flux_NE, Flux_flow): 

      Equation 100	Image Added

Adjust Owner Storage Volumes For High Flow Loss

In a live division when there is a high flow loss (Loss_HF > 0) and the Muskingum x ≠ 1 (meaning that outflow and storage interact), owner storage volumes need to be adjusted for the high flow loss.  The steps are as follows:

1. Create a list of HighFlowOwners whose trial storage exceeds their share of the high flow threshold volume (Storage(o, t) > Storage_HFT(o) + Storage_dsMAX(o)), and another list of the remaining ExcludedOwners (that have Storage(o, t) ≤ Storage_HFT(o) + Storage_dsMAX(o)).

2. Find the modified high flow storage threshold that applies to HighFlowOwners:

   Equation 101	Image Added

3. Find the total storage and the total proportional flux volumes owned by the   (whose storage volume does not contribute to the high flow loss):

   Equation 102	Image Added

   Equation 103	Image Added

4. Find the total division storage volume contributing to high flow losses this time step: 

   Equation 104	Image Added

5. Calculate for each owner in HighFlowOwners their final storage for this time step using equation (39) with Storage_live substituted for Storage(t) - Storage_dsMAX:

   Equation 105	Image Added

Data

Input data

Details on data requirements are provided in the Source User Guide.

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References

Border Rivers Commission (xxxx) Border Rivers Bulk Water Sharing Plan

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