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| Note: The stability criteria must also be satisfied for a model to run correctly. If this is not the case, the following error appears during runtime: Routing parameters have caused instability in storage routing. Refer to Stability criteria for more information. |
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.
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q~ is the index flow, which is given by
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where:
I is the inflow to the reach during the time-step,
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x is the inflow bias or attenuation.
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Figure 1. Prism and wedge storage
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- For linear routing (ie m=1) k is equal to the wave travel time divided by the number of divisions. The wave travel time is how long the wave takes to move through the reach
- For non-linear routing, (m≠1) k can be calculated using the known wave travel time per division for the reach and the chosen value of m for a representative flow rate
| Equation |
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where:
Tw is the known travel time for the reach in seconds
n is the number of divisions
Qw is the flow rate at which you want the travel time to be Tw in m3/s.
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Figure 2. Storage routing link
Table 1. Parameters for link storage routing
| Parameter | Description | Units | Range | Default | |||||
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| General configuration | |||||||||
| Avg. Reg. Flow | Average regulated flow is 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 | Source simulates evaporation and rainfall using the user defined reach length and a reach width (based on simulated flow and a user defined rating curve) to calculate surface area. | 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. The weighting factor is usually in the range 0 ≤ x ≤ 0.5 (Davis and Sorensen, 1969). A recommended starting value is 0.52. | 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 and the wave travel time is equal to k times the number of divisions. When using non-linear routing (m ≠ 1), a starting value could be calculated using Equation XX in the scientific reference guide. | k units | real ≥ 0 | 0 | |||||
| Storage exponent (m) | If m=1, linear (Muskingum) routing is implied, otherwise non-linear routing is implied. m=0.74 is a good starting value for a natural channel. | time-steps | real 0 < m ≤ 1 | 0 time-steps | |||||
Piecewise storage function
Link Flow travel time can also be set using a piecewise linear editorfunction. 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 pointrate versus travel time. 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.. See the SRG for details: Link storage routing - SRG.
To get hydraulically valid results, the maximum travel time can not be more than the timestep divided by the inflow bias ( x ) per division. For example in a daily model, if you have three divisions and x = 1, the maximum travel time can be no more than 3 days. If x = 0.5 the maximum travel time could not be any more than 6 days
Figure 3. Storage routing link, Piecewise
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Rating curves (Figure 4) 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.
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- 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.
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Figure 4. Storage routing link, Rating curve
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Choose Evaporation to specify the rate of evaporation per unit of surface area (Figure 6). Typically, this is done using a time series (loaded using Data Sources), the format of which is shown in Table 5. You can also specify the rate of evaporation as a single value or as an expressiona function.
Figure 6. Storage routing, Evaporation
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Choose Timeseries Flux to configure flux as a value, data source or function.
The Timeseries flux can be a loss or a gain, adjustments to orders can be enabled under ordering.
Ordering at links
Choose Ordering and configure the parameters as shown in Figure 7.
Figure 7. Link (Ordering)
Ownership at links
Ownership must be enabled at the scenario-level (using Edit » Ownership) prior to configuring ownership at storage routing links. Refer to Ownership for details.
References
Davis, C.V., and K.E. Sorensen (1969) Handbook of Applied Hydraulics, 3rd Edition, C.V. Davis and K.E. Sorensen (eds). McGraw-Hill.