Overview
Description and rationale
Modelling of ownership at nodes is an essential component of modelling water ownership in Source, as it enables ownership to be tracked at nodes in Source models. The rationale for modelling water ownership, and the overall principles, are discussed in Ownership - SRG. This SRG entry deals with those aspects of ownership that apply to water entering, leaving and residing in a reservoir (storage nodes). Requirements are summarised in Table 1. Rules-Based Ordering - SRG describes how owner orders are created, adjusted and released at storage nodes. More information on the storage node is available in Piecewise Linear approach to Reservoir Routing - SRG.
Table 1. Partner user requirements
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In every model component, ownership is conserved when it is not explicitly transferred or exchanged, i.e. the following volume equation holds for each owner o:
ΔStorageo = Inflowo - Outflowo - Diversiono - Losso + Gaino + Borrowedo - Lento
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The equation governing ownership in storages is for an owner o:
ΔStorageo = Inflowo - RegulatedReleaseo - Cededo - FixedLosso - ProportionalLosso - InternalSpillo - ExternalSpillo + Borrowedo - Lento
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Scale
The concept of spatial scale in the context of Ownership relates to the fact that it can apply to all or part of the length of a river system. Ownership status can be updated as often as at every model time step, or less often if required.
Principal developer
This version of modelling ownership at storage nodes has been developed by eWater CRC for Source.
Scientific Provenance
Ownership has been modelled in predecessors to Source, such as IQQM and MSM, for many years. The concepts in these models have been updated and enhanced to suit the needs of Source.
Version
Source v3.8.8.
Dependencies
In addition to the dependencies applicable to storage nodes, the minimum requirement is that there should be at least two water users and an Ownership system in the river system being modelled.
Availability/conditions
Automatically included with Source.
Structure & processes
Assumptions
Table 2. Assumptions and Constraints
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Definitions
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The difference between the current storage capacity and the volume of water in storage.
For an owner: The difference between an owner’s current storage capacity and their volume of water in storage.
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Spiller
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Volume in storage when the reservoir is at the full supply level.
For an owner: The owner’s share of the volume in storage when the reservoir is at the full supply level.
Ownership continuity equation
Ownership in reservoirs is governed by the continuity equation, in which each owner’s share of water is conserved. Ownership of water is changed only in the following set of cases:
- Water is ceded to other owners according to rules configured by the modeller.
- An owner does not have sufficient storage capacity to hold its water, so it is internally spilled to other owners. (The modeller may opt to disable this process where it is not required).
- Water is borrowed or lent to other owners so that demand can be met. Borrow accounts are used to track this lending, so that water is later paid back either at the nominated payback storage, or via the resource assessment process (as described in Borrow and Payback - SRG).
Ownership can also be temporarily suspended. When this occurs, all water in the reservoir is assigned to a single owner, and the borrow and payback processes are turned off.
An owner’s volume of water in storage is adjusted for their share of inflows, regulated releases, external and internal spills, lateral losses and gains, and flows along wetland links. Inflows may be from upstream or via wetland links. Regulated release ownership is determined by each owner’s downstream order.
Lateral losses and gains include rainfall, evaporation and groundwater infiltration. These fluxes are categorised into those that are shared in proportion to the share of water stored, or according to fixed ratio. The user configures which of the lateral fluxes fall into each category (fixed/proportional). Wetland link flows are treated as fixed losses (see Ownership in Wetlands - SRG for more information).
Therefore, for an owner, i, the continuity equation gives for a time step:
...
where:
Vi2 - Owner ’s volume of water in the reservoir this time step.
Vi1 - Owner ’s volume of water in the reservoir last time step.
Ii - Volume of inflow this time step belonging to owner i.
Ci - Net volume of water ceded by owner i this time step to all other owners, negative if this owner has ceded less water to other owners than received.
Pi - Proportional loss attributed to owner i, negative if a gain.
Fi - Fixed loss attributed to owner i, negative if a gain.
ISi - Net internal spill of owner i, negative if spill into owner’s share.
ESi - External spill for owner i.
Bi - Total borrowed from other owners by owner i, negative if the owner is lending to other owners.
Ri - Volume of regulated water released this time step for owner i.
This methodology uses an implicit (backward) Eulerian numerical scheme which implies that fluxes that are a function of the state of the reservoir are a function of the end of time step value (V2).
The modeller may disable internal spills, so this element may be left out of the equation.
Each owner’s inflow and last time step storage is known at the start of the reservoir ownership calculations. Shares or functions configured by the modeller determine owner fixed losses and volumes ceded or received (noting that owners cannot cede more than the current storage volume). The remaining parts of the equation to be calculated are the owner’s borrow, internal spill (where relevant), external spill and proportional loss.
Borrow and payback
Owners with insufficient water in the reservoir to meet their release requirements can borrow it from other owners with surplus water. Payback occurs in a reservoir only when it has been configured as a ‘payback storage’, i.e. it:
- has a local borrow and payback system that tracks borrow in the reservoir
or
- is the ‘reconciliation’ storage for the ‘global’ borrow and payback system used to track borrow within the ownership system governing the river/section of river the reservoir forms part of.
When the reservoir is a ‘payback storage’, owners with water surplus to their release requirements will pay back any water they borrowed earlier by reassigning part or all of the surplus to their creditor(s).
| Info | ||
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| Note: Borrow and payback calculations do not occur when ownership is suspended. |
Borrow calculations
Knowing that when an owner draws its share of the storage down to zero, its share of the proportional losses will also be zero, for each owner, i, the maximum volume of water it can release this time step without relying on borrowing (by setting Bi = 0) can be calculated:
| Equation 2 |
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If the reservoir is empty, this equation is modified to account for proportional gains (such as rainfall) that could be released, or that have dried up the reservoir over the period considered:
| Equation 3 |
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where:
ri - Owner i’s ratio share of the reservoir’s storage capacity.
P - Total proportional loss, negative if a gain.
From this, surplus and deficit release capacities can be calculated for each owner:
| Equation 4 |
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| Equation 5 |
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Using the borrow method described in Borrow and Payback - SRG Bi for each owner can be calculated. Any owner that had to borrow will have Vi2 = 0.
Bi = Borrowedi - Lenti
| Info | ||
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| Note: Borrow account balances are updated for borrowing in storages, except when ownership is suspended (see section on Suspension of Ownership). |
Payback calculations
If this reservoir is a payback storage, shares of storage are adjusted as owners with the capacity to do it, pay back water that they borrowed earlier. The surplus release capacities are re-evaluated but this time water already lent is considered:
| Equation 6 |
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Equation (6) returns a value of zero for owners that had to borrow water. It is only necessary to calculate the repayment for owners with a positive surplus that have previously borrowed from other owners (Surplusi > 0, |BPSystem.NetBorrow(i, OtherOwner)| > 0 ). Borrow and Payback - SRG describes distribution systems and priority levels.
Payback is done at each priority level in order from highest to lowest:
At a given priority level, pl, for each owner, i, that has a Surplusi > 0, the steps are:
Accumulate amount the owner owes other owners at the priority level:
Equation 7 - If the owner has borrowed from any other at the priority level ( (CanPayback(pl, i) > 0):
Calculate the ratio to limit the owner’s payback to their current ability to repay:
Equation 8 - For every other owner OtherOwner that shares with owner i at the priority level:
Calculate the payback to the other owner using the ratio above
Equation 9 Update the borrow record for the payback to the other owner
Equation 10 Equation 11 Adjust current time step borrow totals for the payback:
Equation 12 Equation 13 Update the surplus remaining to be shared at the next priority level down:
Equation 14
Forfeiture of credit
If a reservoir is a payback storage, a check is made to ensure that no owner’s credit owing to them exceeds their capacity to store it. If any owner has more water owed to them than they have remaining airspace, the excess is forfeited back to the debtors in order of priority. This methodology is similar to that used for calculating payback, but in this case the forfeits run in the opposite direction to the repayments.
Each owner’s current airspace can be calculated as:
| Equation 15 |
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The total credit owed to an owner i is:
| Equation 16 |
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The maximum volume each owner will be required to forfeit:
| Equation 17 |
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If any owner’s value of MaxForfeiti is greater than zero, there is credit that must be forfeited.
The process to forfeit credit is done at each priority level, in order from highest to lowest:
At a priority level, for each ‘creditor’ owner i that has a MaxForfeiti > 0, the steps are:
Accumulate the amount owed to the creditor by other owners sharing at the priority level:
Equation 18 - If the creditor has an amount owing at this priority level (Owedi > 0):
Calculate the amount of credit forfeited to each other owner at the priority level - this is proportional to the other owner’s share of the total owed to this owner at the priority level:
Equation 19 Adjust the borrow record for the creditor and their debtors for the amount forgone:
Equation 20 Equation 21 Update the amount left to forfeit at the next priority level down:
Equation 22
Spill calculations
Each owner is entitled to use a fixed proportion** of the storage capacity of a reservoir (ri) which means that at any time its storage cannot exceed:
| Info | ||
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| ** Owners that have a share of the reservoir which floats on top of the other owners will have to be dealt with later. If an owner doesn’t have any storage capacity (ri = 0) then its water will internally spill to those owners that do. |
| Equation 23 |
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where:
Vimax - Owner i’s maximum allowed volume of water in the reservoir this time step.
ri - Owner i’s ratio share of reservoir storage capacity.
Vmax - Storage capacity of reservoir.
V2 - Storage volume of reservoir this time step.
The maximum function in equation (23) is used to cover the cases where the reservoir is surcharged. If the reservoir is currently subject to a pre-release (A pre-release can be releases made for flood mitigation or in the case of Dartmouth Dam, for example, those made through the power station when the storage is above a defined target level.) then the storage capacity is considered to be the current storage volume and equation (23) becomes:
| Equation 24 |
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For any owner, i, to be spilling Vi2 = Vimax otherwise the owner would still possess airspace and would not be spilling, and also the current storage volume cannot be greater than the maximum by definition.
Identifying spilling owners
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).
Case when there is net proportional loss (P ≥ 0)
This case applies if there is a net proportional loss from a non-empty reservoir, or on the unusual case of an empty reservoir that spills over the time step due to net proportional gain. Equation (1) is rearranged to give an expression for the volume of water that can spill (internally and externally) from an owner’s capacity share:
| Equation 25 |
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Case when there is net proportional gain (P < 0)
Where there is a net gain of fluxes that are proportionally shared, allowance is made for the fact that some owners may have their share of the storage filled and the excess has to be given to the other owners. Firstly, where each owner’s storage would be without the gain is estimated, making sure that this estimate does not exceed its current storage capacity:
| Equation 26 |
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where:
The superscript j denotes owners with capacity to receive spills.
Proportional gain P is distributed in an iterative process. Initially the proportional gain remaining to be distributed (Prem) equals the total P, and every owner’s spill Spilli is zero. Prem is distributed until there are no more owners that will spill. This process is outlined below:
A total of the estimated unassisted storage volumes is calculated:
Info icon false Note: This is using the notation suggested by Knuth (1992 [http://arxiv.org/abs/math/9205211v1]). Essentially it’s saying that the summation is for all of the terms where the conditions in the square brackets are true. So [Spillj ≤ 0] indicates that we want the summation of Vjest for all j where Spilli is less than or equal to zero. For each owner not already identified as spilling (Spillj ≤ 0) we calculate an initial estimate of their spill volume totals:
Equation 27 If an owner is discovered to be spilling (Spillj > 0), the remaining proportional gain is updated:
Equation 28 And a final estimate of total spill calculated:
Equation 29 - If during this pass any owners are discovered to be spilling then it is necessary to return to equation (27) and keep repeating the process until no more spilling owners are discovered.
When the process is finished equation (30) is evaluated for those owners found to be not spilling.
Calculating internal and external spill shares
The calculations in previous sections established which owners are spillers when proportional gains and losses are taken into account. The next step is to determine the internal (between owners) and external (leaving the reservoir) components of the spill. Based on the calculations in the previous sections the total spill is:
| Equation 30 |
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The total external spill is the total outflow O minus the total release for all owners:
| Equation 31 |
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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 32 |
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Case where internal spills are enabled
When internal spill is active, the total internal spill is the difference between the total and external spills:
| Equation 33 |
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The ratio of external to total spill is:
| Equation 34 |
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So, for an owner i, the external spill is:
| Equation 35 |
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For spilling owners, internal spill is the difference between their total and external spills. Internal spill is zero if the owner is not spilling:
| Equation 36 |
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Water spills to those owners with airspace in proportion to their share of the storage capacity, r. Only owners, j, with capacity to receive spills are considered, so the fraction of internal spills an owner is entitled to is:
| Equation 37 |
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The calculation is complicated by the fact some of the receiving owners may fill their share before the entire internal spill is transferred. To handle this we use an iterative approach where the spill is shared until one of the receiving owners is full and the weights from equation (37) are recalculated and the process repeated until there is no unaccounted for internal spill. Firstly a capacity limit is calculated for each owner that can receive internal spill.
| Equation 38 |
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Finding the smallest value of capi (Mincap) making sure that it is no more than 1,
| Equation 39 |
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The incremental internal spill for every owner, i, is calculated as:
| Equation 40 |
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The total internal spill is then updated to represent the amount remaining:
| Equation 41 |
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and each owner’s share of internal spills is also updated to:
| Equation 42 |
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The values of Spilli are updated:
| Equation 43 |
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The process from equation (37) to equation (43) is repeated until InternalSpill approaches zero. Once this occurs the values of Esi and ISi will also be known for all owners where Spillj ≥ 0 the value of Vi2 will be Vimax.
Proportional Loss Sharing
If internal spill is active, each spilling owner, k, is required to meet a fixed part of the proportionally shared lateral flows:
| Equation 44 |
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The proportional loss remaining to be shared by non-spilling owners is then:
| Equation 45 |
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This remaining proportional loss is shared between each non-spilling owner according to their share of non-spilling owner storage:
First, each non-spilling owner j’s storage is estimated using the ownership continuity equation, without proportional loss:
Equation 46 The estimated total storage of non-spilling owners (without proportional loss considered) is:
Equation 47 Hence, the proportional loss for each non-spilling owner j is then:
Equation 48
A revised (final) storage volume is then calculated for all owners from:
| Equation 49 |
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To determine the evaporation, rainfall and groundwater infiltration components of proportional losses for each owner, the owner share of proportional loss is applied to totals for each proportional flux type:
| Equation 50 |
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Suspension of Ownership
Ownership in a reservoir may be temporarily suspended. This occurs when a storage override function configured by the modeller returns a value of “true”. At this point, the owners’ storage shares are saved, and borrow account balance updating is turned off.
When the override function returns a value of “false” following on from one of “true”, the ownership system is restored to the state it was in before ownership was suspended. This means that the owners’ storage shares are restored to the values saved before ownership was suspended, and borrow account balance updating is turned back on.
The current share of water in storage for each owner is saved when the result of the override function transitions from “false” to “true”, which is when the suspension is activated (If the reservoir is empty then V = 0 and Sharei = ri.):
| Equation 51 |
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where:
ri - Owner i’s ratio share of the reservoir’s storage capacity.
Vi - Owner i’s volume of water in the reservoir.
V - Total volume stored in the reservoir.
When ownership is suspended, all water is temporarily reassigned to a single owner s. The storages are reset:
| Equation 52 |
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The owners’ shares of the storage capacity are overridden:
| Equation 53 |
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While the suspension is in place the normal calculations are followed, and borrowing can still occur, but any borrowing is not recorded and it is not paid back.
When the result of the override function transitions from “true” to “false”, that is the suspension is deactivated, each owner’s share of water in storage is reset to represent what it was before the suspension started:
Vi = Sharei × V
The owners’ shares of the storage capacity (ri) are restored to the values they were before the suspension started.
Outlet Path Ownership
Determining capacity
Outlet capacity is described by a modeller configured minimum and maximum possible release at each storage level in a piecewise relationship. The capacities of outlets on the same outlet path are combined to determine the minimum and maximum release for an outlet path at each storage volume in the relationship. The slopes and intervals of these outlet path relationships are used to calculate the release range for any storage volume, which are adjusted to take into account spill (the minimum release) at the storage level on all other outlet paths. There may be multiple outlet paths for the same storage, with differing priorities. Hence outlet path release ranges are adjusted in each time step for releases on higher priority outlet paths. Further information on outlet path minimum and maximum release calculations is available in Piecewise Linear approach to Reservoir Routing - SRG.
Sharing release capacity
Shares of outlet path capacity are input by the modeller. Outlet path capacity is shared either in proportion to the owner’s share of last time step’s storage volume (V1i/V1), or as a fixed ratio.
As ownership is calculated after the physical reservoir model has been run the volume of water that was released from the reservoir in the current model time step is known:
| Equation 54 |
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where:
R - The total volume released from the reservoir this time step.
Rp - The total volume released from the reservoir this time step down outlet path p.
The total order on each outlet path is the sum of orders on that path for all owners:
| Equation 55 |
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Case where outlet path release ≥ total order
Where any path’s outflow equals or exceeds the total orders on that path (Rp > 0) then the regulated releases do not have to be restricted and each owner’s release can be set equal to their order:
| Equation 56 |
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Case where outlet path release < total order
If the outflow down a path is less than the orders on that path then there is a restriction and the water considered to have been released for each owner has to be scaled back. For each owner, their share of the release capacity is calculated as follows:
| Equation 57 |
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From this, surplus and deficit release capacities can be calculated for each owner:
| Equation 58 |
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| Equation 59 |
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If any owner possesses a surplus, the borrow method described in Borrow and Payback - SRG is used to calculate Bi for each owner with a deficit. The records of borrowing and payback are not updated for these transactions
| Equation 60 |
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The regulated flow going down this path can then be set as:
| Equation 61 |
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Once this is done for all the outlet paths, the total regulated release for each owner is:
| Equation 62 |
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| Note: When ownership is suspended, the ‘override owner’ is assigned 100% share of outlet path capacity. If there are any orders for other owners at this time, the other owners may still borrow capacity in order to make a release. This situation is unlikely though, as the ordering system should detect that the other owners have no storage share and send their orders elsewhere (where possible). |
Data
Input data
Details on input data requirements are provided in the Source User Guide.
Parameters or settings
Input parameters and setting are summarised in Tables 3 and 4, below.
Table 3. Storage Ownership Parameters
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Storage sharing table: Capacity
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Ceding table: Ceding function
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Function that determines the volume of water the ‘from’ owner will cede to the ‘to’ owner each time step.
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Indicates how groundwater infiltration is shared.
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Must return true or false value.
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Table 4 — Storage Outlet Path Ownership Parameters
| Parameter Name | Parameter Description | Unit type | No. of values | Allowable values & validation rules | Default Value(s) |
|---|---|---|---|---|---|
| Outlet path | Name of a storage outlet path | n/a | 1 per outlet path | Read only | Name of configured outlet path |
Outlet path: Capacity sharing method | Indicates whether the outlet path’s capacity will be shared in fixed ratio or in proportion to each owner’s storage. | n/a | 1 per outlet path | ‘Fixed Ratio’ or ‘Proportional’ | 'Proportional’ |
| Outlet path capacity sharing table: Owner | An owner in the storage’s ownership system | n/a | 1 per owner in o.s. * | Read only | Each owner in the storage’s o.s. * |
Outlet path capacity sharing table: Share | Owner’s percentage share of outlet path capacity. | % | 1 per owner & outlet path | Owner percentages for each outlet must add up to 100% | Equal share of 100 per owner. |
* Note: The initials o.s. refer to the current storage’s ownership system.
Output data
Recorded variables are summarised in Tables 5 and 6, below.
Table 5. Recorded variables: Storage ownership
| Model element | Parameter | Units | Variable/calculation | Freq. | Display format |
|---|---|---|---|---|---|
| Storage + owner | Upstream inflow rate | Volume/time | Ii/dt | Time step | Displayed as: Graph, Table, Statistics (min, max, average over the modelled time period) |
| Upstream inflow volume | volume | Ii | |||
| Storage volume | volume | Vi2 | |||
| Ownership overridden | 0 or >0 | No variable. Any value >0 indicates override. | |||
| Evaporation volume | volume | Pi/P or fixed owner% × Storage evaporation volume | |||
| Rainfall volume | volume | Pi/P or fixed owner% × Storage rainfall volume | |||
Infiltration volume | volume | Pi/P or fixed owner% × Storage infiltration volume | |||
| Wetland flow volume | volume | See Wetlands SRG | |||
| Wetland flow rate | volume/time | See Wetlands SRG | |||
| Ceded volume | volume | No variable | |||
| Internal spill volume | volume | ISi | |||
| External spill rate | volume/time | ESi/dt | |||
| External spill volume | volume | Esi | |||
| Release rate | volume/time | Ri/dt | |||
| Release volume | volume | Ri |
Table 6. Recorded variables: Storage outlet path ownership
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Displayed as:
Graph,
Table,
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Further changes to 'Use Airspace' option
In addition to the new calculation method, there are two additional changes to the 'Use Airspace' option:
- The 'Use Airspace' option may be used when Internal Spilling is disabled (set to "None"). In this case the owner specified to 'Use Airspace' will externally spill first, down to the owner's specified capacity share, before the remainder of the spill is shared amongst all owners proportionally as normal. Although disabling Internal Spilling already allows owners to exceed their capacity share, this option now allows specifying which owner will spill first.
- An owner with the 'Use Airspace' option set can receive water internally spilled from other owners if it is below its specified capacity share. Previously the owner would not receive spills which either lead to other owners being able to exceed their capacity share or incorrect spill values being calculated.
Changes to Ownership in Storages - SRG
The calculations used in the Owner Working Volume Proportion method are outlined below, specifying the additions / modifications to the methodology described in the Owner Capacity Share Proportion Method. Only the additions / modifications made to the methodology are explained here and hence the original methodology should be referred to for the unchanged sections.
Table 1. Additional partner user requirements
No | Requirement |
|---|---|
8.3 | An owner can exceed it's share of storage capacity temporarily by enabling the 'Use Airspace' option. The owner which uses the use airspace option does not internally spill to other owners and if there is external spill, the airspace owner spills first. |
Assumptions
Table 2. Assumptions and Constraints
No | Assumption/Constraint |
|---|---|
5 | The owner which uses 'Use Airspace' option can have 0% or more capacity share. |
6 | Only one owner can enable the 'Use Airspace' option at a time. |
Definitions
Use Airspace | Functionality used by an owner to exceed its share of storage capacity without internally spilling to other owners |
Airspace sharing and working volume proportional loss calculation method
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. By having the proportional losses fixed also happens to simplify other calculations, meaning that some iterations for estimating and solving the losses are no longer needed and the logic for positive and negative losses become exactly the same. The fundamental difference is how the losses are calculated. In the original method, sharing the proportional losses was calculated based on each owner's proportion share of the storage volume at the end of the timestep (which is capped at each owners capacity share when internal spilling is enabled). Both spills and losses were back calculated so that the attributed share of the loss was the same share of the final storage. The new method instead shares losses according to the owner's maximum release volume for the timestep, referred to as the Working Volume.
For an owner i, the working volume is calculated as:
Equation 1 |
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where:
Wi - Working volume of owner i.
Vi1 - Owner ’s volume of water in the reservoir last time step.
Ii - Volume of inflow this time step belonging to owner i.
Ci - Net volume of water ceded by owner i this time step to all other owners, negative if this owner has ceded less water to other owners than received.
Fi - Fixed loss attributed to owner i, negative if a gain.
The total working volume for all owners is:
Equation 2 |
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where:
W - 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).
If the total working volume is less than or equal to ownership tolerance level (0.0001 m3), then proportional loss Pi becomes:
| Equation 4 |
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where:
ri - Owner i’s ratio share of the reservoir’s storage capacity.
Ownership continuity equation
Based on the working volume, release, borrow, internal spill, external spill and proportional loss, an owner's final storage volume is calculated as:
Equation 5 |
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where:
Vi2 - Owner ’s volume of water in the reservoir at the end of time step.
Bi - Total borrowed from other owners by owner i, negative if the owner is lending to other owners.
Ri - Volume of regulated water released this time step for owner i.
ISi - Net internal spill of owner i, negative if spill into owner’s share.
ESi - External spill for owner i.
The final storage volume is updated after calculating the borrowed, internal and external spill values.
Borrow and payback
As an owner's proportional losses are now known, they can now be included in the borrow and payback calculations.
Borrow calculations
Equations (2) and (3) from the original (default) method, for calculating the maximum release for an owner, are replaced by:
Equation 6 |
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where:
Pi - Owner's proportional loss (as specified in Equation 3 and 4)
In the original method, losses would not affect borrowing as the losses were based on end of timestep storage volumes. This allowed for cases where an owner would borrow water and then receive internal spills (and potentially then rain) which would increase the owner's storage volume above zero.
Spill calculations
The spill calculations are modified to allow the use airspace owner option and simplified due to the owner's proportional losses being known. There is no longer different logic for when total proportional losses (P) are positive and negative.
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:
Equation 7 |
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Identifying spilling owners
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). Equation (5) is rearranged to give an expression for the volume of water that can spill (internally and externally) from an owner’s capacity share:
Equation 8 |
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where:
Vimax - Owner i’s maximum allowed volume of water in the reservoir this time step.
The equations 26 to 29 in the SRG of original method are made redundant due to the inclusion of proportional loss based on storage working volumes.
Spill by the 'Use Airspace' owner
If there is an owner which uses the 'Use Airspace' option, the spill calculated for that owner, in equation 8, is capped at the total external spill:
Equation 9 |
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Please note that Spilli refers to each individual owner's spill (including the the 'Use Airspace' owner) whereas Spilla is only the spill for the single 'Use Airspace' owner.
The 'Use Airspace' owner does not internally spill to other owners but can receive internal spills from other owners if it is under its capacity share. In this case the calculated spill may be negative. Therefore, the spill amount is the minimum of it's calculated spill and the total external spill of the storage.
Case where internal spills are disabled
When internal spills are disabled, each owner's spill (including the 'Use Airspace' owner's) will be modified so it is greater or equal to zero:
| Equation 10 |
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Calculating internal and external spill shares
The calculations in the previous sections established which owners are spillers when 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. This is determined by following the steps outlined below.
1. Firstly, the total of all spills greater than zero is calculated as:
| Equation 11 |
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2. If the spill by 'Use Airspace' owner is greater than zero, then it is calculated first before other steps:
a) The external spill of the 'Use Airspace' owner is:
| Equation 12 |
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b) The total spill for the remaining owners is adjusted by the amount externally spilled by the 'Use Airspace' owner:
Equation 13 |
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c) The external spill for the remaining owners is adjusted by the amount externally spilled by the 'Use Airspace' owner:
Equation 14 |
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3. Calculate the internal and external spill for each owner. If the 'Use Airspace' owner's spill is greater than zero then the TotalSpill and ExternalSpill values will have been modified above. Otherwise they will be unchanged.
a) Case when internal spills are disabled
The internal spill is:
| Equation 15 |
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The external spill is:
| Equation 16 |
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This has been modified so that the max calculation is calculated earlier, in equation (10), for all owners.
b) Case where internal spills are enabled
When internal spills are enabled, equations (33) to (43) as in 'Owner Capacity Share Proportion Method' SRG are followed without any changes (other than using the possibly modified TotalSpill and ExternalSpill values above).
Proportional Loss Sharing
In this method, the equations (44) to (50) as in 'Owner Capacity Share Proportion Method' SRG are made redundant due to the adoption of the new proportional loss calculation method, as in equations (3) and (4) above. The final storage for each owner is thus calculated according to equation (5), above, as all values have now been calculated.