Storage routing is based on mass conservation and the assumption of monotonic relationships between storage and discharge in a link.
This is a simplification of the full momentum equation and assumes that diffusion and dynamic effects are negligible. The method uses index flow in flux, storage and mass balance equations. A weighting factor is used to adjust the bias between inflow and outflow rate, hence allowing for attenuation of flow. The storage routing equation is shown below and some of its terms are represented diagrammatically in Figure 1:
| Equation 1 |
|---|
Figure 1 shows the feature editor for storage link routing and Table 1 outlines the parameters required.
Figure 1. Storage routing link
Table 1. Parameters for link storage routing
| Parameter | Description | Units | Range | Default |
|---|---|---|---|---|
| General configuration | ||||
| Avg. Reg. Flow | Used to calculate travel time for orders in the ordering phase. It is not used in the flow distribution phase. | megalitres per day | real ≥ 0 | 0 ML/d |
| Elevation | Note that while it is usual to use zero storage as the reference point for the elevation of a link or node, there is no convention for a link as to whether that should be at the start or end of the reach, or some point in between. Source has no mechanism for indicating the fall across a reach. | |||
| Initial conditions | If necessary, one of these parameters may be used to seed a reach with either an initial flow or storage (see below) so that reach behaviour is fully defined from the first model time-step. | |||
| Initial flow | megalitres per day | real ≥ 0 | 0 ML/d | |
| Initial storage | The amount of water deemed to be in the link on the first time-step. For example, if there is a lag of two days, and there is 10ML in the link at the start of the run, then 5ML is deemed to be flowing out each day (total initial storage divided by lag). | megalitres | real ≥ 0 | 0 ML |
| Reach length | Not used in computations and is only for documentation purposes. | metres | real ≥ 0 | 0 m |
| Routing parameters | ||||
# Divisions | Number of reach divisions. Conceptually, this parameter describes the number of times that a reach is replicated. The effective length of a reach is determined from its behaviour, which is controlled by the combination of the storage exponent m, the inflow bias x and the storage constant K. Specifying multiple reach divisions implies applying the same set of behavioural parameters multiple times. In other words, if the effective length of a single-division reach is 500 metres (as derived from its behavioural parameters), changing the # Divisions parameter to 2 implies a combined effective length of 1000 metres. If you want to sub-divide a 500 metre reach into two 250 metre sections, you must also change the behavioural parameters to achieve this. | whole units | integer ≥ 1 | 1 |
| Inflow bias (attenuation factor, x) | The weighting factor x is used to adjust the bias between inflow and outflow rate and allows for flow attenuation. A recommended starting value is 0.5. | dimensionless | real 0 ≤ x ≤ 1 | 0 |
| Generic | ||||
| Storage constant (K) | When using linear routing (m=1), the units of the storage constant K are in seconds. For models using daily time-steps, the recommended starting value is 86400 (the number of seconds in one day). When using non-linear routing (m≠1), the recommended starting value should be calculated as shown in Equation 2. | K units | real ≥ 0 | 0 |
| Storage exponent (m) | If m=1, linear (Muskingum) routing is implied, otherwise non-linear routing is implied. | time-steps | real 0 < m ≤ 1 | 0 time-steps |
You can also specify a piecewise relationship (as shown in Figure 4) instead of a generic one.
Figure 2. Storage routing link, Piecewise
Rating curve
Rating curves (Figure 3) are used to describe the physical characteristics of the reach and convert a flow into a level, ie. they produce an output of level. They can be specified in one of two ways:
- Using the Cross Section Editor to specify a physical cross section, and then generating the rating curve; or
- Directly entering the rating curve - the piecewise linear editor allows you to define relationships with respect to water level, discharge rate, reach width and dead storage. You can define multiple rating curves for a reach, each scheduled to commence on a particular date.
To define a new rating curve directly:
- Right click Rating Curve and choose Add Rating Curve;
- Today’s date will automatically be entered for Start Date. To change this, click the calendar on the right side (see Working with date-pickers);
- Enter the water level, discharge rate, reach width and dead storage; and
- Enter an appropriate value for Overbank Flow Level.
Figure 3. Storage routing link, Rating curve
You can also use the Import button to import a rating curve from a .CSV file the format of which is shown in Table 3.
Table 2. Storage routing link, Rating curve (data file format)
| Row | Column (comma-separated) | |||
|---|---|---|---|---|
| 1 | 2 | 3 | 4 | |
| 1 | Level | Discharge (ML/d) | Surface width (m) | Dead storage (ML) |
| 2..n | level | rate | width | storage |
where:
level is the storage height in the reach in metres above dead storage
rate is the outflow from the reach in the corresponding level
width is the surface width of the reach at the corresponding level
storage is the dead storage in the reach at the corresponding level
There should be at least one row describing the maximum depth at which there is zero flow, and which quantifies the maximum amount of dead storage in the reach. Thereafter, the dead storage volume should remain constant. Table 3 shows an example of this. A depth of 0.5 metres defines the maximum amount of dead storage (100 megalitres), after which the dead storage remains constant. Note that if discharge is 0, then dead storage must be increasing, or it must be equal to the previous value of dead storage.
Table 3. Storage routing link, Rating curve (example)
| Level (m) | Discharge (ML/d) | Surface width (m) | Dead storage (ML) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0.1 | 0 | 5 | 50 |
| 0.5 | 0 | 10 | 100 |
| 1 | 10 | 11 | 100 |
| 5 | 500 | 15 | 100 |
To edit an exising rating curve, select the curve from the list of available curves under Rating Curve. Edit the data and click OK to close the editor. To delete a rating curve, right click the curve from the list and choose Delete.
You can also export rating curves to .CSV files by clicking the Export button.
Link losses and gains
Choose Loss/Gain to specify flux as a function of flow using a piecewise linear editor.
By convention, losses are described using positive numbers whereas gains are specified using negative numbers. In other words, a gain is a negative loss.
Note: In the Flow vs Loss/Gain table, flow cannot be negative. Additionally, the values for Loss/Gain Qloss must be increasing (as shown in Figure 4).
Figure 4. Storage routing, Loss/Gain
Link Evaporation
Choose Evaporation to specify the rate of evaporation per unit of surface area (Figure 5). Typically, this is done using a time series (loaded using Data Sources), the format of which is shown in Table 4. You can also specify the rate of evaporation as a single value, or as an expression using the Function Editor.
Figure 5. Storage routing, Evaporation
Table 4. Storage routing link, Evaporation (data file format)
| Row | Column (comma-separated) | |
|---|---|---|
| 1 | 2 | |
| 1..n | time | value |
where:
time is the time of obersvation in "dd/mm/yyyy hh:mm:ss" format
value is the evaporation rate in millimetres per time-step