About storage routing

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

where:

S is the storage in the reach,

K is the storage constant

m is the storahe exponent, and

q~ is the index flow, which is given by

Equation 2

where:

I is the 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.

Figure 1. Prism and wedge storage

Travel time

Travel time in the reach is computed as follows:

Equation 3

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

1. Configure a storage flow routing reach where:
   • n = number of divisions;
   • x = 1;
   • m = 1; and
   • k = model time-step.
2. 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.

Figure 2 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

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)

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)

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 Q_loss 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)

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