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Travel time in the reach is computed as follows: 

Equation 1	Image Added

A link configured for lagged flow routing is treated as a series of sub-reaches of equal length, with the travel time in each sub-division equal to one time-step. Water moves through the link progressively, without attenuation. You cannot configure fluxes, constituents or ownership on a lagged flow routing link. If lateral flows are significant and/or there is dead storage in the reach, you can approximate lagged flow routing using generalised non-linear Storage flow routing, as follows:

• Compute the number of divisions, n, by dividing the average wave passage time by the model time-step and round the result to a whole number. The result must be at least one (ie n ≥ 1).
• 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.

Storage flow routing

This type of link is represented in the Schematic Editor as a solid black line. Storage routing is based on mass conservation and the assumption of monotonic relationships between storage and discharge in a link. Refer to the Source Scientific Reference Guide for more details.

Figure 5 shows the parameters required to configure storage routing on a link.

You can also specify a piecewise relationship (as shown in Figure 6) instead of a generic one.

Figure 6. Link (Storage routing), Piecewise

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About 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; or
• The reach is above dead storage but fluxes during the time-step would lower the level in the reach to 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 up to 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 storage estimate is above dead storage then outflows are computed, otherwise the initial storage estimate is used and outflows are set to zero.

The next section provides an overview of the parameters shown in Figure 5.

If necessary, one of these parameters may be used to seed a reach with either an initial flow or storage so that reach behaviour is fully defined from the first model time-step.

Reach length

The Reach Length is not used in computations and is only for documentation purposes.

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This parameter is used to calculate travel time for orders in the ordering phase. It is not used in the flow distribution phase.

Number of 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.

Inflow bias

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.

Storage exponent

If m=1, linear (Muskingum) routing is implied, otherwise non-linear routing is implied. A recommended starting value for non-linear routing is m=0.8. Laurenson routing is obtained when m≠1 and x=0, in which case the storage routing equation simplifies to:

Storage constant

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:

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For example, if the reach length is 1000 metres, the time-step is one day, and m=0.8:

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The parameters for storage flow routing are summarised in Table 26.

Piecewise storage function

Link travel time can also 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 27. 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 subdivided into sufficient divisions such that the highest value of K for each division is less than half the time-step.

Wetland Link

This link used to connect storages in a wetland, or a wetland to a river. These links use a hydraulic model. There are different types of wetland link to reflect differences in hydraulic properties - eg. conveyances, weirs, pumps and culverts. Once a wetland link has been specified, double click it to configure it using the wetland link feature editor (Feature Editor 55).

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Link rating curve

Rating curves are used to describe the physical characteristics of the reach and convert a flow into a level, ie. they produce an output of level. 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:

• 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.

You can also use the Import button to import a rating curve from a .CSV file the format of which is shown in Table 28.

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 29 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.

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. Table 28 shows the file format.

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 that in the Flow vs Loss/Gain table, flow cannot be negative. Additionally, the values for Loss/Gain Qloss must be increasing.

You can enter the relationship manually, or import the data from a .CSV file, the format of which is shown in Table 31. This table shows the data file format for both evaporation and rainfall.

Link evaporation

Choose Evaporation to specify the rate of evaporation per unit of surface area. Typically, this is done using a time series, the format of which is shown in Table 31. You can also specify the rate of evaporation using an expression, or by reference to the output of another scenario. By default, expressions return units in millimetres per day but you can change this in the Expression Editor if required.

Rainfall on link surfaces

To specify the rate of precipitation per unit of surface area, choose Rainfall. This can be done using either a time series (format shown in Table 31) or an expression. A time series can have multiple columns containing rainfall data.

Timeseries Flux

This functionality is yet to be documented. If you would like assistance, please call 1300-5-WATER (1300-592-837).

Constituents

Before you can configure constituents for a link, you must define them first for the scenario using Edit > Constituents > Configure.... Refer to Links.

Ordering at links

Refer to Feature Editor 75 for details.

Ownership at links

Refer to G for details.Feature Editor 73 in chapter on Ownership.

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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 5:

Equation 2	Image Added

where:

S is the storage in the reach,

K is the storage constant,

m is the storage exponent, and

q‾ is the index flow, which is given by 

Equation 3	Image Added

where:

I is inflow to the reach during the time-step,

O is outflow from the reach during the time-step, and

x is the inflow bias or attenuation factor.

Figure 5. Prism and wedge storage

Image Added

Refer to the Source Scientific Reference Guide for more details.

Figure 6 shows the parameters required to configure storage routing on a link.

You can also specify a piecewise relationship (as shown in Figure 7) instead of a generic one.

Figure 7. Link (Storage routing), Piecewise

Image Added

About 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; or
• The reach is above dead storage but fluxes during the time-step would lower the level in the reach to 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 up to 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 storage estimate is above dead storage then outflows are computed, otherwise the initial storage estimate is used and outflows are set to zero.

The next section provides an overview of the parameters shown in Figure 5.

If necessary, one of these parameters may be used to seed a reach with either an initial flow or storage so that reach behaviour is fully defined from the first model time-step.

Reach length

The Reach Length is not used in computations and is only for documentation purposes.

Anchor
Average regulated flow Average regulated flow

Average regulated flow

This parameter is used to calculate travel time for orders in the ordering phase. It is not used in the flow distribution phase.

Number of 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.

Inflow bias

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.

Storage exponent

If m=1, linear (Muskingum) routing is implied, otherwise non-linear routing is implied. A recommended starting value for non-linear routing is m=0.8. Laurenson routing is obtained when m≠1 and x=0, in which case the storage routing equation simplifies to:

Equation 4	Image Added

Storage constant

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 5	Image Added

For example, if the reach length is 1000 metres, the time-step is one day, and m=0.8:

Equation 6	Image Added

The parameters for storage flow routing are summarised in Table 1.

Table 1. Link (Storage routing parameters)

Piecewise storage function

Link travel time can also 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).

Table 2. Link (Storage routing travel time, data file format)

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 subdivided into sufficient divisions such that the highest value of K for each division is less than half the time-step.

Wetland Link

This link is used to connect storages in a wetland, or a wetland to a river. These links use a hydraulic model. There are different types of wetland link to reflect differences in hydraulic properties - eg. conveyances, weirs, pumps and culverts. Once a wetland link has been specified, double click it to configure it using the wetland link feature editor (Figure 8).

Image Added

Link rating curve

Rating curves are used to describe the physical characteristics of the reach and convert a flow into a level, ie. they produce an output of level. 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:

• 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.

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. Link (Storage routing, Rating curve, data file format)

Where:    level is the storage height in the reach in metres above dead storage

rate is the outflow from the reach in megalitres per day in the corresponding level

width is the surface width of the reach in metres at the corresponding level

storage is the dead storage in the reach in megalitres 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 4 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. Link (Storage routing, Rating curve, example)

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. Table 3 shows the file format.

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 that 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 9).

Figure 9. Link (Storage routing, Loss/Gain)

Image Added

You can enter the relationship manually, or import the data from a .CSV file, the format of which is shown in Table 5. This table shows the data file format for both evaporation and rainfall.

Table 5. Link (Evaporation.Rainfall, data file format)

Where     time is the time of observation in "dd/mm/yyyy hh:mm:ss" format

value is the evaporation rate/rainfall in millimetres per time-step

Link evaporation

Choose Evaporation to specify the rate of evaporation per unit of surface area. Typically, this is done using a time series, the format of which is shown in Table 5. You can also specify the rate of evaporation using an expression, or by reference to the output of another scenario. By default, expressions return units in millimetres per day but you can change this in the Expression Editor if required.

Figure 10. Link (Evaporation)

Image Added

Rainfall on link surfaces

To specify the rate of precipitation per unit of surface area, choose Rainfall. This can be done using either a time series (format shown in Table 5) or an expression. A time series can have multiple columns containing rainfall data.

Figure 11. Link (Rainfall)

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Timeseries Flux

This 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.

Figure 12. Link (Timeseries flux)

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Constituents

Before you can configure constituents for a link, you must define them first for the scenario using Edit » Constituents. Refer to Links.

Ordering at links

Refer to Figure number for details.

Ownership at links

The intention of ownership in links is to define which owner is responsible for fluxes that occur on links. Refer to Figure number for details.