Reservior Routing
Three techniques for pond routing is provided in StormShed3G™. The answers will be identical
for the most part, mainly due to the way StormShed3G™ creates the storage characteristic curve.
The program uses a small interval, 0.1 ft in most cases in creating the curve.
In cases where there is not much data, or the detention pond is rather large, as in reservoir
size, then the different methods would make a difference and the Runge-Kutta or Numeric Routing
techniques would give more accurate results. The ability of the two more advanced methods is
generally lost when the interval between stage-storage data points is small. In cases where
volumes are estimated from topographic information and where contours are not uniformly separated,
these two methods would be a better choice than Puls routing.
Level Pool (Puls)
Level pool routing is also knows as the Storage-Indication Method as well as Puls routing.
Generally, it relies on what is known as a storage characteristic curve. The details of
how to create storage characteristic will not be discussed here, only the format of the table itself.
Generally the storage characteristic table consists of eight columns:
| Column> | Description |
|---|
| Column 1 | Elevation in feet. |
| Column 2 | Stage in feet. This is just the difference between values in column 1. |
| Column 3 | Area in acres. This column may or may not be required depending on the storage
structure that is selected. |
| Column 4 | Incremental Volume (acre-feet). Generally based on the storage structure
that is selected. |
| Column 5 | Storage (acre-feet). This column is just the accumulated values from
the previous column. |
| Column 6 | Flow (cfs). This is the discharge that can be expected from the stage
in column 2. Based on the control structure that is selected. |
| Column 7 | S-Odt/2. This is an important column. It is the storage minus the
outflow times half the time interval. In acre-feet. |
| Column 8 | S+Odt/2. This is the opposite of the previous column. It is the
storage plus the outflow times half the time interval. In acre-feet. |
Once the storage characteristics table is completed, it will be used in the actual routing of the
flows through a detention pond. Routing is based on the continuity equation:
The formula is rearranged to the following form:
It is now clear that the rearranged form of the continuity equation is directly related
to the format of the storage characteristic table. Namely the S-Odt/2 and S+Odt/2 columns.
The procedure is now straightforward. Given the time increments I1 and I2, it is easy
to compute the
portion of the above equation.
The second part of the above equation is based
on the computed stage of the previous time step. Using the previous stage, look up the
value
from the storage characteristics table. With the right side of the above equation completely
solved, all one needs to do is to look up the stage and flow that corresponds to the S+Odt/2 value
that was just computed.
Runge-Kutta
A more accurate method of solving the continuity and storage equations is the Runge-Kutta
method (Chapra and Canale, 1985). The Runge-Kutta method is a method for solving ordinary
differential equations with various orders of accuracy. The implementation in StormShed3G™
extends to the fourth order of accuracy following the technique outlined in Example 4.6 of
Hydrology and Floodplain Analysis, Philip B. Bedient and Wayne Huber, Addison-Wesley Publishing
Company, copyright 1988.
A full discussion of the steps and theory behind the method is outside the scope of this manual.
Numerical
In addition to the Level Pool and Runge-Kutta techniques, StormShed3G™ also provides a
classic Numerical Routing technique. The numerical technique solves the continuity equation
for the unknowns S2 and O2. Since both S and O are functions of the stage, they are functionally
related and can be used to solve for O2. Solving for O2 requires an iterative solution.
The solution procedure is as follows:
- Assume O2 = O1
- Calculate delta S from the continuity equation
- Calculate S2 = S1 + delta S
- Determine Y2 for S2 and the stage-storage curve.
- Determine O2 for Y2 from the stage-discharge curve.
- Repeat steps 2-5 until O2 remains unchanged.
The technique is demonstrated in example 6.7 of Design Hydrology and Sedimentology for
Small Catchments, Haan, Barfield, Hayes, Academic Press, 1981.