Initial Conditions and Low Flow

Initial Conditions. In order for the unsteady flow model to run, the user must establish the initial conditions in the entire system. This means that it must have a flow and a stage at every cross section, as well as a stage in every storage area/2D flow area (storage areas and 2D flow areas can start dry). The most common way to establish the initial conditions is for the user to enter a set of initial flows for all the reaches, and the software performs a steady flow backwater profile to get the corresponding stages. The initial condition flows entered by the user must be consistent with all of the boundary condition flows at time zero (the start of the unsteady flow run).

Initial reservoir elevations and gate settings must also be consistent with the initial condition flows, such that the flow computed out of the reservoir at the first time step is consistent with what the user entered to perform the initial conditions profile (see figure below). If the user enters a low flow for the initial conditions backwater profile, and then at the first unsteady flow time step the program calculates a much larger flow coming out of the reservoir (due to gate settings and initial reservoir stages), this can cause an instability in the area just below the dam.

Another possible source of initial conditions causing the model to go unstable right away, are the initial storage area elevations. It is up to the user to enter an initial storage area water surface elevation for all storage areas, even if it is to start out dry (water surface is set to the lowest elevation of the storage area). When a storage area is hydraulically connected to a river reach (this is normally done with a lateral structure), and the initial water surface in the river reach is at an elevation that will cause a flow interaction with a storage area (water surface is above the lateral structure weir profile, or culverts, or gates), then that storage area needs to have an initial water surface elevation set equal to the computed initial stage in the river. If the storage area is set much higher or lower than the elevation of the river section it is connected to, then a large discharge may be computed at the hydraulic structure that connects them. This large discharge across the lateral structure will either take a lot of flow from the river (if the river stage is higher than the storage area), or it will have a large inflow into the river (if the storage area stage is much higher than the connected river stage). Either of these two cases can cause the model to become unstable at the initial start of the unsteady flow computations. By setting the storage area elevations to the same as the initial water surface of the cross section to which it is connected, then the computed flow across the lateral structure will be close to zero. Shown in the figure below are two lateral structures, which are connected to storage areas. The initial condition water surface elevation is higher than the downstream lateral structure. Therefore, the storage area connected to this structure must be set to the initial condition water surface elevation in this area. Because the initial water surface is lower than the most upstream lateral structure, the water surface elevation for that connected storage area can be set to dry, or whatever elevation is appropriate below the minimum elevation of the lateral structure.

Low Flow Conditions. Low flows can often be very difficult to model with an unsteady flow model. Medium to steeper slope streams will often have a pool and riffle sequence at low flow, and the water surface will generally pass through critical depth at the upper end of the riffle (bottom of the pool). In addition to this, the depths of water are very shallow. Once the flood wave begins the water surface will change quickly, and there will be a large change in depth with respect to distance and time. The leading edge of a dam break flood wave will be very steep, and can often be a source of model instability as it propagates down the river system. The finite difference solution to the equations will generally have the most trouble balancing during the initial dramatic rise at the beginning of the flood wave. The fact that the initial conditions may be very low flows and depths can make it even more difficult to solve the equations through those shallow and steep riffle regions.

There are several things the modeler can do to allow the program to solve the equations in a stable manner in low flow situations. The easiest solution is to increase the base flow for the initial conditions. This will provide a higher initial depth of water in general, and it may also drowned out the pool and riffle sequence. A general "rule of thumb" is to start out by trying a base flow around 1% of the peak flow that will be routed. Increase the base flow if necessary, but never go above 10% of the peak flow. If you artificially use a base flow that is 10% or more of the peak, the computed peak flow and stage will be higher than it would have been otherwise.

If you have increased the base flow to a reasonable level, and are still having model stability problems at the leading edge of the flood wave, then try adding a pilot channel for the reach in which the model is having stability issues. A pilot channel is an option in which will add some depth without adding much flow area or conveyance. The pilot channel is an option in HEC-RAS, and it is only used during low flow, once the cross sections get to some appreciable depth, the program automatically removes it from the cross section. To learn more about the use of pilot channels, please review the section on Pilot channels in "Modeling Culverts" of the HEC-RAS User's Manual.

One other option that can help stabilize the model during the initial rise of the flood wave, is turning on the Mixed Flow Regime Option. This option drops the acceleration terms when the Froude number gets greater than a user defined threshold, which is often the case on the leading edge of the flood wave.