Lateral Structure Coefficients

Written by Chris Goodell, P.E., D.WRE  |  WEST Consultants

Copyright © RASModel.com.  2013.  All rights reserved.

Lateral structures can be used in HEC-RAS to transfer flow from a river/reach to a storage area, or to another river/reach.  With the coming release of HEC-RAS with 2D capabilities (estimated beta release January/February 2014), you’ll be able to hook a river/reach to a 2-D area using a lateral structure. 
Although its primary function in HEC-RAS is to transfer flow out of one river/reach into another component (river/reach, storage area, 2D area), a lateral structure can physically represent a wide range of geometric features, including a levee, a flow diversion structure, a morning glory spillway, or even a natural ground or bathymetric profile.  Including a lateral structure in your model to represent a levee is important if the levee is ever overtopped or breached during the simulation.  Flow diversion structures can have multiple outlet features, including culverts, gates, and spillways.  These features are all available in the lateral structure editor in HEC-RAS. 
Another common use of lateral structures is to simulate flow transfer from the river to a tributary during a flood event.  This is especially convenient if you don’t want to model the tributary as an individual reach, but still want to account for it’s available storage, for a proper accounting of flood wave attenuation in the main stem river/reach.  As an example, the following figure shows a storage area representing a tributary to the main stem river.  This storage area is connected to the main stem by a lateral structure (highlighted in red). 

Because a lateral structure can represent a variety of different flow transferring structures (or non-structures), the hydraulics in and around the lateral structure can be quite different, depending upon the case.  Every lateral structure in HEC-RAS requires a lateral weir coefficient, and different hydraulics mean different lateral weir coefficients.  Any hydraulics textbook will have a multitude of weir coefficients for “inline” conditions, but it’s rare to find something similar for lateral flows, or diversion flows.  But it is generally agreed that lateral structure weir coefficients should be much lower than a similar inline configuration.  For example, an inline, hydraulically efficient broad-crested weir might have a weir coefficient around 3.0 (US units) or 1.7 (SI Units).  Turn that structure sideways (a lateral structure), and it will have a coefficient closer to 2.0 (US Units) or 1.1 (SI Units).  The difference is due to the energy/momentum loss associated with turning flow lines from their downstream orientation to a lateral direction out of the river/reach.    Unfortunately, there has simply not been a lot of research done on quantifying this energy/momentum loss and what that does to lateral weir coefficients.
The research that is available could be useful and might be worth checking out.  Hagar’s equation is one reference and is actually built into the HEC-RAS lateral structure editor, under Lateral Weir Embankment…Weir Computations.  It will compute an equivalent lateral weir coefficient based on an inline value (the Default Weir Coefficient) and some physical and hydraulic properties of the weir and  the adjacent river/reach. 

You can read more about Hagar’s equation in the HEC-RAS Hydraulic Reference Manual on page 8-17. 
Useful references for lateral structure weir coefficients (including Hager’s):

• Hager, W.H. (1987). “Lateral Outflow over Side Weirs.” Journal of Hydraulic Engineering, ASCE, 113(4).
• Borghei, S.M.; Malili, M.R.; Ghodsian, M. (1999). “Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow.” Journal of Hydraulic Engineering, ASCE, October, 1999.
• Ranga Raju, K.G.; Prasad, B.; Gupta, S.K. (1979). “Side Weir in Rectangular Channel.” Journal of Hydraulic Engineering, ASCE, 105(5).
• Subramanya, K.; Awasthy, S.C. (1972). “Spatially Varied Flow over Side Weirs.” J. Hydr. Div., ASCE, 98(1).
• Singh, R.; Manivannan, D.; Satyanarayana T. (1994). “Discharge Coefficient of Rectangular Side Weirs.” Journal of Irrigation and Drainage Engineering, ASCE, 120(4).

However, none of these references discuss lateral weir coefficients for lateral flow transfers over natural ground, or surface flow (i.e. non-elevation overbank terrain).  HEC has a reference table for lateral structure coefficients that I like to use-it’s also included in the new “Combined 1D and 2D Modeling with HEC-RAS” document that was released in August 2013, in anticipation of the new 2D feature in HEC-RAS expected to be released as a beta version in the January/February 2014 time frame.   Note how low the suggested range of coefficients is for “non-elevated overbank terrain.”  Because they are not dimensionless, be aware that weir coefficients in SI Units are different from US units by a factor of the square root of the ratio of the SI gravitational constant to the US gravitational constant,

What is being modeled with the Lateral Structure	Description	Range of Weir Coefficients
Levee/Roadway – 3 ft (1 meter) or higher above natural ground	Broad crested weir shape, flow over Levee/road acts like weir flow	US Units: 1.5 to 2.2 (2.0 default) SI Units:  0.83 to 1.2 (1.1 default)
Levee/Roadway – 1 to 3 ft (0.3 to 1.0 meter) elevated above ground	Broad crested weir shape, flow over levee/road acts like weir flow, but becomes submerged easily.	US Units:  1.0 to 2.0 SI Units:  0.55 to 1.1
Natural high ground barrier – 1 to 3 ft (0.3 to 1.0 meter) high.	Does not really act like a weir, but must flow over high ground to get into 2D (or storage) area.	US Units: 0.5 to 1.0 SI Units: 0.28 to 0.55
Non-elevated overbank terrain. Lateral Structure not elevated above ground	Overland flow escaping the main river.	US Units: 0.1 to 0.5 SI Units:  0.06 to 0.28

*Hydrologic Engineering Center, August 2013.  “Combined 1D and 2D Modeling with HEC-RAS”

Although this table is presented within the context of 1-D to 2-D flow transfers, these values will work with river/reach to storage area or river/reach to river/reach flow transfers as well.  As noted in the referenced document (HEC 2013), “In general, Lateral Structure weir coefficients should be lower than typical values used for inline weirs.  Additionally, when a lateral structure (i.e. weir equation) is being used to transfer flow from the river (1D region) to the floodplain (2D Flow Area), and then [sic] the weir coefficients that are used need to be very low, or too much flow will be transferred.”  Also, “The number 1 problem people have been having with interfacing 1D river reaches with 2D areas, is user’s [sic] have been using way to [sic] high of weir coefficients for the situation being modeled.  If the lateral structure is really just an overland flow interface between the 1D river and the 2D floodplain, then weir coefficients in the range of 0.1 to 0.5 must be used to get the right flow transfer and keep the model stable.” 

The HEC 2013 document ("Combined 1D and 2D Modeling with HEC-RAS") with the Table of lateral weir coefficients can be downloaded from my Google Drive site here:  https://drive.google.com/file/d/0B_s8OLJOgOi0Nm5sdHFhSzFUYkk/edit?usp=sharing.  The lateral weir coefficient table is on page 35.

Extending your Cross Sections to High Ground?

Copyright © RASModel.com. 2013.  All rights reserved.

What are the implications of having a cross section that is too short and doesn't extend all the way out to the highest computed water surface elevation?  Does it affect the results?  Take this cross section for example. It is missing much of the left overbank (presumably).

Image courtesy of Adam Bohnoff

First of all, when RAS encounters this situation, it will automatically extend the last station elevation point vertically to the height of the computed water surface.  This adds a so-called "vertical wall" to the end of the cross section.  Additional wetted perimeter will be included for water that comes into contact with the "vertical wall". 

So what does this mean?  Well, you will be missing out on wetted area-possibly a LOT of wetted area.  Maybe it's negligible.  It's up to you to decide.  For typical rivers, the added wetted perimeter associated with the "vertical wall" will not make much of a difference in the results.  If you plan on mapping the computed flood plain in RAS Mapper, or in GIS using the GeoRAS extension, you'll miss out on some areas that should be shown as inundated. 

I see a few possible scenarios that you would need to consider.  Your course of action will depend on whether your model is steady or unsteady, and how much error you're willing to accept at this location:

1.  The missing wetted area is actually very small.  Either the maximum water surface elevation just exceeds the end point or perhaps there is a bluff just to the left of the first station elevation point that would contain all of the water.  In this case, you probably don't waste time getting additional survey data and leave the cross section as is, or you manually approximate in a station elevation point to capture the bluff. 

2.  There is considerable flow area that is missing, but it is so far out in the overbank or it's in a flow separation area and it can all be considered ineffective.  In a steady flow model, you can probably leave this as is.  Ineffective flow area is ignored in steady flow computations.  The answer will be slightly different if you extended the cross section and put in an ineffective flow trigger.  This is strictly due to the difference in quantified wetted perimeter.  For typical rivers, where the width is much greater than the depth, this will make little difference in your results.  For unsteady flow, there could potentially be a huge error in the results if you leave the cross section as is.  In unsteady flow modeling, ineffective flow areas are accounted for as hydraulic storage in HEC-RAS.  Hydraulic storage will attenuate the flood wave as it progresses through a system.  Omitting available storage can significantly affect both the propagation and attenuation of your flood wave.  I strongly recommend extending the cross section to high ground in this case. 


For steady flow, the differences in RAS will be very slight between these two options, limited to the wetted perimeter computed added at the vertical wall (ineffective flow assumes a frictionless boundary). In unsteady flow, these two options could produce VERY different results. 

3.  There is considerable flow area that is missing, and it is actively conveying flow.  In this case, steady, or unsteady, you'll want to extend the cross section to high ground.  Omitting this portion of your cross section will have a direct impact on the computed water surface elevation.  The degree to which depends on how much of the cross section area you are omitting, but it could be quite significant. 

So...how do we extend the cross sections?  In a perfect world, you'd have your survey crew go out and get you more points.  Unfortunately this cost money and takes time, frequently both of which you don't have an excess of when doing a hydraulic model study.  If your RAS geometry is already set up in GIS and your terrain model extends far enough laterally, you could simply extend the cross section cut line to the high ground and reimport into RAS.  Easy! 

However, if you do not have a georeferenced model and you can't get your survey crew out to the field in a timely (and cost-effective) manner, you can always approximate the extension of your cross sections using a USGS topo map. 

These "Quad" maps can be found for free on-line for any location in the US.  In fact, there are similar topography data sets for just about the entire world-available on-line for free.  The downside is that their resolution is quite inadequte for typical river modeling, and they don't include bathymetry (underwater topography).  However, for the purposes of extending your cross section to high ground, this can be an acceptable alternative to a physical survey. 

Simply find and download a terrain map that covers your area of concern.  Locate your existing cross section line on that map.  Then extend it to high ground, marking the locations where your cross section line crosses contour lines. Note the elevations, and the relative distances between contours, then manually enter that data as new station elevation points. 

Q & A: Flow Attenuation

Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © RASModel.com. 2012. All rights reserved.

Question: 
When running an unsteady flow model with a single inflow hydrograph, why does my discharge decrease in the downstream direction for a given output profile? 

Answer: 
This is called flow attenuation.  You see this to varying degrees in all unsteady flow models and it is a real phenomenon.  The shallower the reach, or the wider the floodplain, the more pronounced this effect will be.  In very steep streams, you may not notice flow attenuation at all. 
The physical process is as follows:  As the flood level rises, water moving downstream fills in available volume.  This volume is called storage.  Water going into storage is taken away from the flow going downstream and that is why you see a decrease in discharge as you move in the downstream direction.  Wider floodplains and shallower reaches have more available storage volume, which is why flow attenuation is pronounced under these situations.  Once the flood wave passes, and you are on the receding limb of the flood hydrograph, the water that had gone into storage now returns to the active discharge.  In this case you’ll see an increase in flow as you move in the downstream direction.  Notice in the figure below that the discharge at time 0042 (before the peak of the flood wave) decreases in the downstream direction, while the flow at time 0124 (after the peak of the flood wave) increases in the downstream direction.

You can also see this effect when viewing hydrographs in the figure below from two cross sections, one upstream (River Station 2500) and one downstream (River Station 2400).  The attenuation of flow is the difference in peak discharge between these two hydrographs-in this case, about 2.3 cms.  The area between these two curves represents a volume of water.  The area to the left, where the upstream discharge is greater than that downstream discharge, represents water going into storage.  The area to the right, where the upstream discharge is less than the downstream discharge, represents water leaving storage.

Attenuation is included in the conservation of mass equation, which is one of the two equations (the St. Venant equations) used to define the movement of water through a reach in HEC-RAS-the other being conservation of momentum.    From the HEC-RAS Hydraulic Reference Manual (Page 2-22), “Conservation of mass for a control volume states that the net rate of flow into the volume be equal to the rate of change of storage inside the volume.”    In other words, Inflow minus outflow equals the change in storage over time.  The equation is:

where A = flow area, Q equals discharge, t = time, and x = length. 
The discretized form of this is more practical to use and may be more familiar: 

Where I = Inflow to a discrete control volume, O = Outflow, DS = Change in Storage, Dt = time duration (i.e. time step).

Steady versus Unsteady Flow

Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © RASModel.com. 2010. All rights reserved.
I was recently emailed this question regarding steady flow versus unsteady flow results:

“My question is fairly basic. I have heard from a couple of other engineers that when flood levels are generated with usteady flows that it is typical to then run a steady simulation with the routed flows from the unsteady run as unsteady results may be considered less accurate? Is this standard or conventional practice to your knowledge? “

While it is common to have a companion steady flow version, I would disagree that this is done because unsteady results are considered less accurate. Two equally well constructed models, one steady, one unsteady could certainly produce different results, but the unsteady will be more accurate. The unsteady flow St. Venant equations are more physically correct than the energy equation which is used to compute steady flow. From a numerical standpoint, the energy equation has an advantage in that it can be analytically solved, yielding an exact solution. The unsteady flow equations must be reduced to a discrete form (finite difference approximation) to solve, so there is some built-in error. However, if done correctly, this error is inconsequential for river models. RAS does a good job of this. The biggest difference is that steady flow models do not take into account the effects of in-channel and off-line storage in the attenuation of the flood wave. This can be quite significant. Some modelers take the tact of constructing a steady flow model with the computed routed flows from the unsteady flow model. While this is a “forced” way of accounting for the storage effect, it is no more accurate than its unsteady counterpart. And it would be a significant effort to set up a steady flow model with a flow change at every cross section. I don’t recommend it.

In short, given two equally well constructed models, one steady and one unsteady, of the same reach, I would take the results from the unsteady flow model every time.

Any other thoughts out there on this subject?