Page Comparison

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1. Fixed loss fluxes whose ownership is known a priori (because they are shared by fixed ratio or by some other means such as time-series or expressionfunction), and
2. Proportional loss fluxes that are shared in proportion to the ownership of the water in the division.

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The total fixed loss, Loss_fixed, is distributed to owners based on the specified ratios, expressionfunction, or time series such that:

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1. Initialise temporary parameters.

2. Set each owner’s upstream inflow I(o) to equal that owner’s share of the upstream component’s outflow using equation (10). (The upstream component is the next division upstream, or if it is the first division in the link, the upstream node).

3. Determine the volume of the total flow based flux, fFlow_LG(), for this time step to be shared according to fixed ratio, expression function or time series specified by the modeller.  Where relevant, also determine the volume, Loss_HF, that is to be shared using high flow rules (i.e. Murray-style losses), which is the volume that is in excess of the value of fFlow_LG().
   • If the ownership system uses Murray-style losses:

     1. The flux based on flow up to the high flow threshold is shared according to fixed ratio. This volume is:

        Equation 57

     2. The flux based on flow above the high flow threshold is shared according to high-flow rules. This volume is:

        Equation 58

   • Otherwise, all the flux is shared using fixed shares, expression function or time series specified by the modeller:

     Equation 59

4. Determine every owner’s fixed flux total for this time step (Loss_fixed(o)), where the modeller has specified which of the link’s lateral fluxes (time series, general purpose flow based, groundwater and net evaporation) are fixed at the ownership system level (noting these must satisfy equation (11)).
   1. Time series flux:
      1. Determine the owner’s share of input time series flux(es) Flux_TS(o):

         • If the time series flux for the current link is not input per owner, and for the ownership system time series flux sharing is by fixed ratio, apply the specified owner’s ratio to the total time series flux, Flux_TS, that was calculated prior to ownership processing (Flux_TS has been adjusted to ensure total loss does not exceed the amount of water in the division).

           Equation 60

         • If the time series flux for the current link is input per owner, get the owner’s flux for this time step from the input time series:
           If LossGain_TS < 0 the flux is a gain, this needs no adjustment:

           Equation 61

           Otherwise, the flux is a loss that may need to be scaled down (This is to allow for the case where the time series has pumped the division dry. The overall time series loss Flux_TS has already been adjusted by link processing to ensure losses do not exceed water in the link. Input owner time series losses are scaled down so their sum does not exceed the total  adjusted for any owner time series gains.).

           Equation 62

      2. Set the following

         Equation 63

   2. Determine the owner’s fixed share of the flow based flux when the ownership system uses Murray-style lossesor it uses fixed ratio to share other lateral fluxes:

      Equation 64

      Equation 65

   3. If the ownership system uses fixed ratio to share other lateral fluxes: Apply the owner’s configured Ratio_loss(o) to the remaining lateral fluxes and add their share of these to their fixed flux total:

      • Owner’s net evaporation flux: 

        Equation 66

      • Owner’s groundwater flux: 

        Equation 67

        Equation 68

5. Determine the total proportional flux, Loss_prop.
   1. Initially Loss_prop = 0

   2. If time series flux sharing is ‘Proportional’, a total time series was input, so:

      Equation 69

   3. If Murray-style losses are not being modelled and other lateral flux sharing is ‘Proportional’:

      Equation 70

   4. If other lateral flux sharing is ‘Proportional’:

      Equation 71

6. Determine the division’s state (‘dead’ or ‘live’).
   • If Muskingum weighting factor  and there is no inflow (I = 0), it is ‘dead’:
     State = Dead

   • Otherwise, compare the result of the storage function to the mass balance equation to determine division state (if they are within maxError, the division is ‘live’): 
     
     

     Equation 72

     Equation 73

      then State = Live

     Otherwise State = Dead

7. Find the division’s storage using a method appropriate to the state of the division (i.e. whether ‘dead’ or ‘live’).  These methods are summarised in the two following sections.

8. Calculate each owner’s outflow, O(o), using equations (15) or (16), as appropriate, rearranged so the term O(o) is on the left hand side of the equation. 

   Equation 74

9. Adjust owner shares of outflow as necessary to ensure that none are negative.  The principles are discussed in Ownership Adjustments, above.  In summary, if O(o) < 0, the owner concerned borrows from other owners to ensure O(o)=0.
   • If any owner’s outflow is negative then:

     1. Calculate surplus/deficit for each owner.

        Equation 75

        Equation 76

     2. Pass owner surpluses and deficits to the Borrow method. This will return how much owners borrowed or lent (OwnerBorrowed(o), OwnerLent(o)).

     3. Adjust the outflows to account for borrowing:

        Equation 77

        Equation 78

10.  Calculate owner mass balances to report, based on equation (15) or (16), as appropriate, using adjusted values of O(o)=0.

    Equation 79

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