Description and rationale
Modelling of ownership on links is an essential component of modelling water ownership in Source, as it enables ownership to be tracked through links in Source models. The rationale for modelling water ownership, and the overall principles, are discussed in the Ownership Systems SRG entry.
Scale
The concept of spatial scale in the context of ownership on links relates to the fact that it applies to link divisions and these have length, width and depth dimensions (even if they are represented as points for modelling). 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 on links has been developed by eWater CRC for Source.
Scientific Provenance
Ownership on links 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
The requirement is that there should be at least two water users (as well as an ownership system) in the river system being modelled, in addition to at least one link.
Definitions
| Dead storage | The storage remaining in a division when the stream has ceased to flow. This storage is affected by fluxes which are independent of index flow in the division. See the Link Storage Routing SRG entry for more information. |
| Division | In Source, a routing link represents a river reach, which is divided into one or more divisions of equal length. Ownership modelling takes place at the level of a division. |
| Fixed flux | 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 expression. |
| Flow based flux | Lateral flux in a division whose rate is a function of the division’s index flow rate. |
| General purpose flow based flux | A modeller configured, piecewise monotonically increasing relationship between flux and index flow. See the Link Storage Routing SRG entry for more information. |
| Groundwater flux | A function of head/water level which, in turn, is a function of flow. The flux calculated via a linked groundwater model. See the Link Storage Routing SRG entry for more information. |
| Lateral flux | Flow into or from the division that is not from upstream or going downstream. In Source, this can consist of groundwater infiltration, evaporation, precipitation, time series flux (representing diversions etc.), or flow based flux (general purpose, could be used to represent overbank loss). See the Link Storage Routing SRG for more information. |
| Live Storage | That part of the total storage in a division that is a function of the index flow rate (see the Link Storage Routing SRG for more information). |
| Murray-style loss | Method of sharing the loss (or gain) from a division due to high flow. Losses caused by flows in excess of the regulated flow range are shared to owners in proportion to how far each of them is above their fixed share of the regulated flow range. In Source, the losses to be shared in this way are represented by the flow based flux. |
| Net evaporation | Evaporation less rainfall. |
| Owner | An entity such as a state, country or water user group that has a defined share of water in the river system, where this share is managed completely separately from any other share. |
| Ownership system | A component in Source used to track and manage the ownership of water in a defined section of a modelled river network. An ownership system has a set of owners that share water within the ownership system’s boundaries. Each of these owners may lend water surplus to their requirements to other owners with a deficit via the ownership system’s borrow and payback systems. Lending owners can be paid back some time later at any location within the ownership system boundary. |
| Proportional flux | Loss fluxes that are shared in proportion to the ownership of the water in the division. |
| Storage | Volume of water within a division at a defined point in time. |
| Time series flux | A modeller specified time series used to represent known losses or gains of particular owners from a division. See the Link Storage Routing SRG for more information. |
Other definitions can be found in the eWater River Systems glossary.
Assumptions and Limitations
Table 1. Assumptions and constraints applicable to modelling ownership on links
| 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 storage in a link equals the link’s total storage volume. |
| 3 | The sum of all owners’ shares of flow in a link equals the link’s total flow. |
Background
In Source, components that are physically or logically connected are joined using a link. If the connection is significant enough to have an effect on the time that water would take to pass along it then the link is modelled as a routing link. Each routing link is subdivided into one or more divisions.
Figure 1 below shows a single routing division, its storage compartments and fluxes. Each owner’s share of these storage compartments and fluxes must be determined for every division. The principles on which these calculations are based are discussed in the Theory section and the sequencing of the calculations is described in the Methodology section.
Figure 1. Division ownership conceptual model
Definition of terms used in equations
Table 2. Symbols used in equations
| Symbol | Description | Units |
|---|---|---|
| dt | Model time-step | time |
| Deficit(o) | Owner’s deficit to be made up using borrow and payback. | volume |
| FluxTS | Sequence of time series flux values for the link input by the modeller. | |
| FluxTS(o) | Sequence of time series flux values for the link for owner o, input by the modeller. | |
| Storage routing function used to determine the live storage volume in a link division. See the Link Storage Routing SRG for more information. | volume | |
| g | Linear function to translate between ratios: from change in storage/total storage into change in flow/total flow. | n/a |
| j | An owner whose current storage contributes to the high flow loss, i.e. is greater than their share of the high flow threshold. | n/a |
| I | Division inflow volume | volume |
| I(o) | Division inflow volume for owner o | volume |
| Loss | Total volume of loss from the division (negative if water is gained). | volume |
| Lossfixed | Total volume of loss that is shared in a predetermined way. It is assumed to have been adjusted to reflect any shortfall in volume to meet it during the flow phase (trying to pump a division dry for example). | volume |
| Lossfixed(o) | The (volume) share of fixed loss owned by owner o. | volume |
| LossfixedMAX(o) | Maximum fixed loss that owner o has the capacity to sustain. | volume |
| LossHF | Total high flow loss | volume |
| LossHF(o) | High flow loss for an owner | volume |
| Lossprop | Total volume of loss that should be shared in proportion to the ownership of the water in the division. This volume is assumed to have been adjusted to reflect any shortfall that occurred in the flow phase (such as a division with non-zero area at empty trying to evaporate water from an empty division). | |
| Lossprop(o) | The (volume) share of proportional loss owned by owner o. | volume |
| m | Mass of the sample taken | mass |
| mi | Mass of the substance in the sample | mass |
| M | Total mass in a specified volume | mass |
| Mi | Mass of substance in a specified volume | mass |
| no | Number of owners | n/a |
| Net(o) | Net volume of water that owner o has in storage (in a “dead” division) | volume |
| O | Division outflow volume, including outflowing lateral fluxes | volume |
| O(o) | Division outflow volume for owner o | volume |
| o | Owner of water in the division | n/a |
| Division index flow rate, which is the index flow for the current time step. See the Link Storage Routing SRG for more information. | volume/time | |
| Owner’s share of division’s index flow rate for the current time step. | volume/time | |
| Threshold for high flow/upper limit to regulated flow (used to determine high flow losses). | volume/time | |
| r | Symbol used to simplify mass balance equations. | |
| Ratiods(o) | Owner o’s share/ratio of the dead storage volume. This value is specified by the modeller. | n/a |
| Ratiolive(o) | Owner o’s ratio of index flow rate to total index flow rate. Used to calculate their share of active storage and proportional losses. | n/a |
| Ratioloss(o) | Owner o’s share/ratio of losses. | |
| RatioHFT(o) | Owner o’s share/ratio of the high flow threshold. This value is specified by the modeller. | n/a |
| RatioTS(o) | Owner o’s share/ratio of time series flux. | |
| Storage | Current total volume of water stored in the division. | volume |
| Storage(o,t) | The total volume of water stored in the division at time step owned by owner o. | volume |
| Storage(o,t-1) | Total volume of water stored in the division at the previous time-step (t-1) owned by owner o. | |
| Storage(t) | Total volume of water stored in the division at time-step t. | volume |
| Storage(t-1) | Total volume of water stored in the division at the previous time-step t-1. | |
| Storageds | Current dead storage in the division. If the division is dead, this is the total division storage, Storage(t). If the division is live this is StoragedsMAX. | volume |
| Storageds(o) | Current dead storage in the division owned by owner o. | |
| StoragedsMAX | Maximum total dead storage in a division specified by the modeller. | volume |
| StoragedsMAX(o) | Owner o’s share of the maximum total dead storage in a division. | volume |
| Storageexclude | Total volume of water at current time step belonging to owners that are not contributing to the high flow loss. | volume |
| StorageHFT | Division storage threshold that corresponds to reach high flow rate threshold qHFT, i.e. . | volume |
| StorageHF | Total volume of current storage that contributes to high flow loss. | volume |
| Storagelive | Current live or active storage volume in a division. | volume |
| Storagelive(o) | Current live or active storage volume in a division owned by owner o. | volume |
| Surplus(o) | Owner’s surplus that can be shared using borrow and payback. | volume |
| t | Time-step index | n/a |
| t1 | Start time index | n/a |
| t2 | End time index | n/a |
| x | Muskingum parameter (see the Link Storage Routing SRG for more information) |
States of a division: live or dead
At any time-step a routing link division can be classed as being either:
- Live: A division is described as being live if a solution for the time step can be found that satisfies both the continuity and storage equations. The general form of the continuity equation is discussed in the Ownership Mass Balance section, below (see equations 15 and 16).
OR
- Dead: If the only solution that can be found satisfies the continuity equation but not the storage equation, then the division is described as being dead (i.e. it has ceased to flow).
A division is dead if x = 1 and or if x ≠ 1 and the following is true:
| Equation 1 |  |
|---|
Ownership of division storage
At the start of division ownership processing, the last time-step’s storage (Storage(t-1)) and each owner’s share of it (Storage(o,t-1)) are known from the flow phase routing calculations. The volume of water in a routing link division can be divided into:
- Live Storage: If the division is live then the live storage is the result of evaluating the storage equation for the current inflow and outflow.
- Dead Storage: If the division is dead then the dead storage is the total volume of water in the division. It is possible for the dead storage to be larger than the maximum specified by the modeller as the division may be, for example, in the process of transitioning from dead to live but there is not enough water in the division to satisfy both the continuity and storage equations. If the division is live then the dead storage is equal to the maximum volume (StoragedsMAX) specified by the modeller.
The live storage in a division is the storage above dead storage, as shown in Figure 1, and is obtained from:
| Equation 2 |  |
|---|
The total volume of water in a division is then:
| Equation 3 |  |
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Sharing dead storage
Ownership of the dead storage is shared by fixed ratio (Ratiods(o)) to all of the owners. Hence:
| Equation 4 |  |
|---|
Where the sum of all the ratios is equal to one. That is:
| Equation 5 |  |
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Also if the maximum total dead storage specified by the modeller is StoragedsMAX then each owner’s share of this is:
| Equation 6 |  |
|---|
Water is borrowed and lent between all of the owners so that the fixed ownership share given by equation (4) is always maintained.
Sharing live storage
Live storage is shared according to the owner’s share of the index flow rate (q‾(o)) (see the Proportional Routing section, below, for an explanation of this approach). The live storage calculation is done after each owner’s outflow has been determined.
| Equation 7 |  |
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| Equation 8 |  |
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Ownership of fluxes
Inflow flux
In the flow phase, the outflow flux from the division upstream becomes the inflow flux to the current division (or the outflow flux from the upstream node becomes the inflow to the division if the most upstream division in a link is being considered). The same is true for the inflow flux per owner (the ownership processing for the upstream division or node has already determined its outflow per owner).
| Equation 9 |
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| Equation 10 |
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