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| 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 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 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 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 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 storage routing - SRG for more information. |
Other definitions can be found in the eWater River Systems glossary.
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| 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 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 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 storage routing - SRG for more information) |
States of a division: live or dead
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Live storage is shared according to the owner’s share of the index flow rate () (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.
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An owner’s share of fixed losses is adjusted if that owner does not have sufficient water in the division to cater for the loss. In a live division, an owner’s highest possible fixed loss occurs when their outflow is zero. In a dead division, the owner’s fixed loss cannot be larger than their share of dead storage. The Borrow and Payback mechanism is used to adjust owner shares of fixed loss for these situations. See the section on Ownership Adjustments for Ownership adjustments for more information.
Proportional loss sharing
If the division is live, owner shares of proportional losses are based on each owner’s index flow rate (see the Proportional Proportional Routing section for an explanation of this approach).
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The owner’s index flow rate () is determined from the inflow volume I(o), outflow volume O(0) and the Muskingum parameter x (see the Link Storage Routing storage routing - SRG for details):
| Equation 17 |
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| Anchor | ||||
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Proportional routing is used to share the division’s active (live) storage between owners. This is based on the idea that ownership travels at the rate that each owners’ flow influences the flow in the division. If we consider a division and divide each owners’ inflow into a very large number of small pieces, that each time one more of these slices is passed through, the increment in division storage (Storage) can be approximated as a linear function g of the increment in the index flow rate :
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This can be rearranged to solve for an owner’s storage volume, Storage(o,t), as follows:
| Equation 46 |
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| Anchor | ||||
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In some situations, adjustments need to be made to owners’ shares of a division’s mass balance equation so that the shares all add up to the correct total. An imbalance can occur when:
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If an owner’s share of fixed losses is greater than their available capacity to meet a lateral outflow flux requirement, then an adjustment is made which entails borrowing from other owners that have surplus capacity available, with later payback. Different methods are used to determine whether each owner has a capacity deficit or has surplus capacity, depending on whether the division is live or dead (see the following sub-sections below). The borrow and payback options available are:
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| Model element | Parameter | Units | Freq. | Display format |
|---|---|---|---|---|
| Division + owner | Upstream flow | Volume/time | Time-step | Displayed as: Graph, Table, Statistics (min, max average over the modelled time period. |
| Upstream flow volume | Volume | |||
| Downstream flow | Volume/time | |||
| Downstream flow volume | Volume | |||
| Storage volume | Volume | |||
| Live storage volume | ||||
| Dead storage volume | ||||
| Lateral flow volume | ||||
| Lateral flow | Volume/time | |||
| Groundwater flux | ||||
| Net evaporation | ||||
| Flow based flux | ||||
| Time series flux | ||||
| High flow loss(if applicable) | ||||
| Mass balance | Volume | |||
| Borrow balance | Volume | See Borrow and Payback - SRG | ||
| Net borrow | ||||
| Link + owner | Same as above. Link upstream inflow = first division's upstream inflow, link downstream outflow = last division's downstream outflow. Storage is total for all link divisions. | |||
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