## 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 describes how the ownership of inflows and outflows at inflow and confluence nodes in the flow distribution phase of Source is determined and tracked. Rules-Based Ordering - SRG describes how owner orders are adjusted for future inflows at inflow nodes. More information on the inflow node and confluence node is available in Inflow node - SRG and Confluence node - SRG, respectively.

### 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 inflow and confluence 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 inflow and confluence 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

Automatically included with Source.

## Structure & processes

### Assumptions

**Table 1. Assumptions and Constraints**

No | Assumption/Constraint |
---|---|

1 | Owners cannot have a negative share of water in storage or in transit |

2 | The sum of all owners’ shares of flow in a node at each model time step equals the node’s total flow volume. |

3 | In the flow phase, the volume of each owner’s total downstream orders due to have arrived is known at every node and link. |

### Theory

Inflows are modelled in Source by the inflow node and the confluence node is used to represent locations where two rivers (or a tributary and river) join to form a single river downstream. The ownership of water at inflow locations and confluences must be considered in Source when ownership is being modelled.

A key rule of ownership modelling in Source is that within an ownership system, ownership is conserved unless it is explicitly transferred (see Ownership - SRG*)*. In unregulated systems, ownership of inflow to a location is conserved in that location’s downstream outflow. In regulated systems, ownership of water at a particular location can be exchanged. Source allows owners to share water within an ownership system’s boundaries, and so lend water to each other as required to meet downstream orders (see Borrow and Payback - SRG). Owner borrowing to meet orders downstream of an inflow or confluence node can therefore result in shares of outflow changing. However, to conserve ownership overall within the system, where water is lent, an account is kept in order for it to be paid back later.

Inflow and confluence nodes have no storage, or lateral loss/gain, hence the ownership conservation/ mass balance equation considers only inflow and outflow. At a confluence node, both inlet links must fall within in the same ownership system, so no rules are required to transfer flow between owners. However, at an inflow node, the additional inflow entering the river at the node has no ownership, so rules must be defined to determine how to share this between owners.

This SRG entry describes how sharing rules are configured at inflow nodes, and how, in the flow distribution phase, owner shares of outflow from inflow nodes and confluences are determined. Owner shares of inflow also need to be considered during the order phase of Source. At both inflow and confluence nodes, future inflows can be used as a supplementary source for each owner’s orders, and hence reduce the storage release required. Rules-Based Ordering - SRG describes how inflow is forecast and used in this way. The information for inflow nodes provided here is also summarised in Inflow node - SRG.

**Variables used**

Highlighting is used to distinguish between variables and procedures/functions/methods in the table below:

Yellow indicates the item is a method (function or procedure), items with no highlighting are variables.

Symbol | Purpose/Description | Units | Usage phase |
---|---|---|---|

conservedO(i) | Inflow/confluence node outflow for owner i when there are no downstream orders to consider. | volume | Flow |

Deficit(i) | The additional outflow volume owner i requires at this timestep to meet their total downstream orders. | volume | Flow |

DSOrder(i, t) | Total downstream order for owner i due to have arrived at the current node in time step t (for the order to be delivered on time). | volume | Flow |

DSTarget(i, t) | If there are any downstream orders due, this is the current node’s target outflow for owner i in time step t, which is DSOrder(i, t) limited by the owner’s share of any overall shortfall in outflow. | volume | Flow |

I_{1}(i) | For owner -Confluence node: The first inlet branch. | volume | Flow |

I_{2}(i) | For owner -Confluence node: The second inlet branch. | volume | Flow |

MassBalance(i) | Inflow or confluence node mass balance for owner i | volume | Flow |

O | Total outflow from a node in the current time step | volume | Flow |

O(i) | For owner i, their share of outflow from a node. | volume | Flow |

OwnerBorrowed(i) | The flow that owner i borrowed from other owners in order to meet its downstream orders. | volume | Flow |

OwnerLent(i) | The surplus flow that owner i lent to other owners. | volume | Flow |

owner% | Inflow node: Configured percentage of additional inflow to be assigned to an owner. | percentage | Configuration, Flow |

Surplus(i) | The outflow volume owner i has at this time-step in addition to that required to meet their total downstream orders. | volume | Flow |

TotalDSOrder | Total downstream order due to have arrived at the current node in the current time step. | volume | Flow |

fFlow(t) | Function that returns total additional inflow volume at an inflow node configured by time series or function | volume | Flow |

fInflow(t) | Function to return the additional inflow volume at an inflow node for owner in time step - Fixed ratio:
*fInflow(i, t) = owner% × fFlow(t)* - Time series, function: Directly configured
| volume | Flow |

**Inflow node**

At an inflow node, the modeller configures a ‘source’ of flow for each owner, that returns an additional volume of inflow to enter the river downstream of the node. There are three options:

- Fixed ratio: Each owner
*i*receives a specified percentage of the additional inflow volume (as determined by the configured time series or function*fFlow(t)*in the current time step*t*):*fInflow(i, t) = owner% × fFlow(t)* - Time series: The modeller specifies for every owner a time series of inflow (
*fInflow(t)*). - function: The modeller specifies a function to calculate inflow for every owner
*o*for each time step (*fInflow(i, t)*).

There are two categories of inflow node in Source:

*Headwater inflow node*: This type of inflow node has no model components connected to its inlet, so the only flow leaving the node is that from the configured inflow source. Ownership is conserved, so at any time step,*t*, the outflow for owner*i*is:Equation 1 *Tributary inflow node*: This type of inflow node has a link representing a river reach connected to its inlet, so the flow leaving the node is the total of the upstream inflow and that from the configured inflow source (additional inflow). Ownership of this total is conserved, so at any time step,*t*, the outflow for owner*i*is:Equation 2

In an unregulated system, the owner’s final outflow from the node is always *conservedO(i)*. In a regulated system, however, the ownership system attempts to assign each owner enough water to meet their total order downstream. If there is insufficient total outflow to meet total downstream orders due at the node, *TotalDSOrder*, the shortfall is shared between each owner to determine their ‘target’ flow *DSTarget(i, t)*:

Equation 3 |
---|

The owner’s ‘conserved’ outflow (*conservedO(i)*) is compared to their ‘target’ volume, *DSOrder(i, t)*, to determine whether they have a surplus or a deficit; i.e.:

Equation 4 |
---|

Equation 5 |
---|

Owner’s with a surplus lend water to those with a deficit, and the difference is recorded in a borrow and payback account. More detail on how this is done is given in Borrow and Payback - SRG. The volume of flow borrowed to meet owner requirements *OwnerBorrowed(i)* is added to their ‘conserved’ outflow, and the volume lent is subtracted:

Equation 6 |
---|

**Confluence node**

The confluence node behaves the same way as an inflow node in terms of ownership. The only (minor) difference is in the calculation of the ‘conserved’ outflow. For each owner *i*, this is simply the sum of their inflows on both inlet branches (*b1, b2*) :

Equation 7 |
---|

If there are downstream orders to consider (as in a regulated system), shortfall sharing and borrow and payback are applied in the same way as for an inflow node to determine the final outflow volume for each owner.

### Process

**Flow phase**

The following steps are used to calculate the outflow for each owner at an inflow or confluence node:

- Get each owner’s inflow to the node:
- Inflow node
*I*(or zero if the node represents a headwater)_{b1}(i) = upstream inlet link 1 O(i)*I*_{b2}(i) =*fInflow(i, t)* - Confluence node
*I*_{b1}(i) = upstream inlet link 1 O(i)*I*_{b1}(i) = upstream inlet link 2 O(i)

- Inflow node
Determine the conserved outflow per owner, which is the sum of all inflows:

Equation 8 Get from the ordering system each owner’s total ordered volume that due at this node in this time step

*DSOrder(i, t)*, and the total for all owners*TotalDSOrder*:Equation 9 - Calculate the node’s outflow:
- If
*TotalDSOrder > 0*, owners share the flow in order to best meet orders:Calculate the ‘target’ owner outflow (to best meet downstream orders) as their total ordered volume due, limited by their share of any shortfall in outflow

*O*:Equation 10 Determine the volume of each owner’s outflow that is surplus or deficit to the target:

Equation 11 Equation 12 Use the ‘borrow and payback’ method to share outflow from owners with a surplus to those with a deficit (See Borrow and Payback - SRG).

Calculate each owner’s outflow as their conserved outflow plus borrow minus lending:

Equation 13

Otherwise, set each owner’s outflow to their conserved outflow:

Equation 14

- If
Calculate the node’s mass balance for each owner:

Equation 15

## Data

### Input data

Details on data are provided in the Source User Guide.

### Parameters or settings

Parameters are listed in Tables 2 and 3 below for inflow nodes and confluence nodes, respectively.

**Table 2. Inflow Node: Ownership Parameters**

Parameter name | Parameter description | Unit type | No. of values | Allowable values & validation rules | Default Value(s) |
---|---|---|---|---|---|

Ownership system | Name of the ownership system the inflow node belongs to. | n/a | 1 | Any ownership system for the scenario. | Default ownership system. |

Sharing Method | Indicates how owner shares of flow are to be specified. | n/a | 1 | ‘Fixed percentage’ or ‘Owner flow function’ | ‘Fixed percentage’ |

Owner | Name of an owner in the node’s ownership system. | n/a | One per owner | Read only | n/a |

Owner Percentage, | Percentage of the total ‘additional inflow’ to assign to the corresponding owner. | % | One per owner | Integer: 0-100. Sum for all owners = 100% | Equal for each owner |

Source Details (for | One set of parameters. |

**Table 3. Confluence Node: Ownership Parameters**

Parameter name | Parameter description | Unit type | No. of values | Allowable values & validation rules | Default Value(s) |
---|---|---|---|---|---|

Ownership system | Name of the ownership system the inflow node belongs to. | n/a | 1 | Any ownership system for the scenario. | Default ownership system. |

Owner | Name of an owner in the node’s ownership system. | n/a | One per owner | Read only | n/a |

### Output data

Outputs of the model that can be viewed in the Recording Manager are summarised in Table 4, below.

**Table 4. Recorded variables for Inflow and Confluence Nodes (reported by owner)**

Model Element | Parameter | Units | Methodology variable | Frequency | Display format |
---|---|---|---|---|---|

Inflow Node - Owner | Upstream flow | Volume/time | I_{b1}(i)/dt | Time step | Displayed as: Graph, Table, Statistics (min, max, average over the modelled time period) |

Upstream flow volume | volume | I_{b1}(i) | |||

Inflow | Volume/time | I_{b2}(i)/dt | |||

Inflow volume | volume | I_{b2}(i) | |||

Downstream flow | Volume/time | O(i)/dt | |||

Downstream flow volume | volume | O(i) | |||

Downstream order due | volume | DSOrder(i, t) | |||

Mass balance | volume | MassBalance(i) | |||

Borrow and payback | volume | See Borrow and Payback - SRG | |||

Forecast volume | volume | See Rules-Based Ordering - SRG | |||

Confluence Node – each Owner | Upstream flow | Volume/time | Time step | Displayed as: Graph, Table, Statistics (min, max, average over the modelled time period) | |

Upstream flow volume | volume | I_{b1}(i) + I_{b2}(i) | |||

Downstream flow | Volume/time | O(i)/dt | |||

Downstream flow volume | volume | O(i) | |||

Downstream order due | volume | DSOrder(i, t) | |||

Mass balance | volume | MassBalance(i) | |||

Borrow and payback | volume | See Borrow and Payback - SRG | |||

Forecast volume | volume | See Rules-Based Ordering - SRG |