...
S is the storage in the reach,
K k is the storage constant
m is the storahe exponent, and
...
- Configure a storage flow routing reach where:
- n = number of divisions;
- x = 1;
- m = 1; and
- k = model time-step.
- If you need to account for lateral flows where n = 1 and the average travel time is a fraction of the model time-step (eg. a reach with a one day lag in a model with a monthly time-step), you can adjust k to a smaller value without affecting the shape of the hydrograph.
Dead storage
Dead storage refers to the capacity of a storage that is below the minimum operating level. At this water level, there is no outflow. The level of the reach with respect to dead storage at the beginning of the time-step affects its level in subsequent time-steps as follows:
- The reach is at or below dead storage and the fluxes during the time-step are insufficient to raise the level above dead storage;
- The reach is above dead storage but fluxes during the time-step would lower the level in the reach below dead storage; or
- The reach is above dead storage and remains above dead storage during the time-step.
To determine if the reach is at or below the dead storage level, Source:
- Computes an initial storage estimate by using inflows to fill the reach upto but not exceeding the dead storage level;
- Computes a revised storage estimate based on any remaining inflows and fluxes, but ignoring outflows; or
- If the revised sotrage estimate is above dead storage, then outflows are computed, otherwise the initial storage estimate is used and outflows are set to zero.
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 follows:
| Equation 4 |
|---|
For example, if the reach length is 1000 metres, the time-step is one day, and m = 0.8:
| Equation 5 |
|---|
Configuring storage routing
Figure 2 shows the feature editor for storage link routing and Table 1 outlines the parameters required.
Figure
...
2. 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 |
...
Piecewise storage function
Link travel time can also specify a piecewise relationship (as shown in Figure 4) instead of a generic one.
...
be set using a piecewise linear editor. This describes a series of relationships between reach index flow rate q¯ versus travel time. The slope of the curve is the same as that for index flow rate versus storage so the rating curve can be derived using dead storage (zero flow) as the starting point. The data points can be entered manually or imported from a .CSV file, the format of which is shown in Table 2. Quadratic interpolation is used to find points in each defined segment on the curve (as in BigMod where x = 1).
Piecewise routing allows you to specify how k varies with flow. If x = 1, then k must always be less than or equal to the time-step. In BigMod routing, the highest value of k is found in the travel time relationship, and the reach should be sub-divided into sufficient divisions such that the highest value of k for each division is less than the half the time-step.
Figure 3. Storage routing link, Piecewise
...
Table 2. Storage routing link, Travel time (data file format)
| Row | Column (comma-separated) | |
|---|---|---|
| 1 | 2 | |
| 1 | Index flow | Travel time |
| 2..n | flow | day |
Link rating curve
Rating curves (Figure 34) 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:
...
- 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
...
4. 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
...
3. 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 |
...
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 34 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
...
4. 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 |
...
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 By convention, losses are described using positive numbers whereas gains are specified using negative numbers. In other words, a gain is a negative loss.
| Info | ||
|---|---|---|
| ||
| 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 |
...
| 5). |
Figure
...
5. Storage routing, Loss/Gain
Link Evaporation
Choose Evaporation to specify the rate of evaporation per unit of surface area (Figure 56). Typically, this is done using a time series (loaded using Data Sources), the format of which is shown in Table 45. You can also specify the rate of evaporation as a single value , or as an expression using the Function Editor.
Figure
...
6. Storage routing, Evaporation
Table
...
5. Storage routing link, Evaporation (data file format)
| Row | Column (comma-separated) | |
|---|---|---|
| 1 | 2 | |
| 1..n | time | value |
...
| Info | ||
|---|---|---|
| ||
| Note: The file format shown in Table 45, as well as the screen shown in Figure 5 can be replicated for Rainfall and Timeseries Flux. The former allows you to specify the rate of precipitation; the latter allows the input of a time series of total water lost or gained on a link. Values can be positive or negative. A negative value denotes water returned to the link (a gain). See also Link losses and gains. |