Water Quality: Stepped Labyrinth Weir Option for Aeration and Boat Passage

A new type of structure, called a stepped labyrinth weir, may increase downstream dissolved oxygen at dams and hydroelectric facilities while also providing safe passage for recreational boats.

By Garrett M. Monson and John S. Gulliver

A low level of dissolved oxygen (DO) is one of the most-cited water quality parameters at hydro installations. Frequently, low DO is caused by thermal stratification in the reservoir that does not allow oxygen transfer at the water surface to reach the depth of the turbine intakes. Some sort of aeration often is necessary, and often the technology chosen is site-specific. One option is aerating hydraulic structures, which add oxygen to the water through air entrainment and increased oxygen transfer across the entrained bubbles.

Recreation is a second challenge. Increasingly, operating licenses issued by the Federal Energy Regulatory Commission (FERC) contain requirements for sustaining or improving recreational activities. Today, these facilities are expected to meet a variety of needs for the surrounding area, including recreational water sports, in addition to supplying clean, sustainable energy. Aerating structures pose a physical danger to the practice of such recreational activities. Thus, one challenge of many aerating structures is to facilitate recreation while increasing DO levels.

To solve this conflict, a new aerating structure is explored that seeks to improve water quality downstream from the dam while also providing for the passage of small boats such as canoes and kayaks. The stepped labyrinth weir proposed for this purpose combines proven technologies to address the diverse needs of today’s hydroelectric facility owners and operators.

Development of concept

The concept behind a stepped labyrinth weir is the need to combine an aerating weir design with one suited for boat passage. Weirs designed specifically for the purpose of aeration include the Chatuge aerating infuser1,2 and South Holston River labyrinth weir,2 both developed by the Tennessee Valley Authority. Other work has focused on aeration over a roughened weir for use in the Platte River near Denver, Colo.,3 where cascading weirs roughened with cobblestones are used to increase oxygen transfer at a low-head weir.

Additional research involves studies of energy dissipation and safe boating conditions. Scientists have studied cascades and the occurrence of skimming flows,4 as well as canoe chutes and boating conditions.5 Combining these proven technologies points to an improved structure that provides efficient aeration and recreationally safe hydraulic conditions.

The concept proposed in this article adjusts an existing design procedure6 to optimize both aeration and boat passage, two often-conflicting objectives. The final design should be based on best fit, economic considerations and satisfactory hydraulic conditions, as determined from experiments and physical model studies.

Conceptual procedure

The conceptual procedure adjusts an existing labyrinth weir to meet the requirements of aeration and boating flows. The concept assumes that:

• Cobblestones act similar to a multiple notched weir for aeration;3
• Canoes and kayaks (herein referred to as boats) require a minimum depth of 6 inches over the weir crest;
• The weir operates similar to a broad-crested weir with critical depth over the weir crest equal to two-thirds the total head over the weir;7 and
• Cobblestones act similar to a quarter-round upstream edge.

The equations are best utilized in a spreadsheet format and are summarized in Table 1 on page 64. This iterative procedure allows the structure to fit site limitations. Figure 1 shows the plan and profile views of the structure.

The first block of Table 1 lists input data that would come from a hydrologic analysis of the site. This includes minimum boating flow, elevation change in the reach of the site, proposed crest height based on elevation available, corresponding channel elevation, crest elevation and total head over the weir.

The second block contains assumed data. Inlet contraction loss can be set at zero or estimated from preliminary calculations. The angle of the labyrinth weir side legs (α) affects the number of bays (N) based on the width available at the site. Values of α vary between 8 and 90 degrees and greatly impact the capacity and recreational effectiveness of the structure. Values of N and α are varied to determine the number of bays that results in a hydraulically and recreationally effective layout at minimal cost. The inside width of the upstream apex (A’) is set to allow passage of boats, typically a canoe or kayak with a beam width of 3 feet. As α increases, A’ can be decreased to reduce width of the structure.

The third block of data contains the detailed calculations identifying the geometry of the labyrinth and equations used for each calculation. Table 1 also contains two guides regarding the acceptable ranges of variables: H/P0 < 0.9, and 3 ≤ w/P0 ≤ 4. These limitations help keep the design in an economical and hydraulically efficient range.6 Skimming flow must be avoided at minimum boating flows due to dangerous hydraulic conditions and elimination of aeration potential. To determine if skimming flow occurs, find the slope of the structure and verify that hc/Hd ≥ 0.91 – 0.14tanβ for 25° ≤ β ≤ 55°.4

This concept calls for each weir crest to be capped with cobblestones to break up the nappe and cause the weir to act somewhat like a multiple notched weir. This increases aeration and rounds the sharp edges of the weir, making it safer for boating. Cobblestones with a diameter close to the value of t provide the most breakup. These cobbles are grouted to the top of the weir crest in a tightly packed formation.

The volume of concrete needed and placement costs can be approximated. If a low slope is available or the structure is to be used as a bypass around a high-head dam, multiple single-drop weirs with pools in-between may be preferred. These single drop weirs could work together as a stepped weir without the added cost of one continuous structure.

Evaluating oxygen transfer

The aeration performance of the stepped labyrinth can be evaluated by determining the oxygen transfer efficiency (E):

Equation 1


• C is DO concentration upstream (u) and downstream (d) of the structure respectively; and
• s is saturated concentration of DO in the stream.

A transfer efficiency of 1 means DO has reached saturation with the atmosphere, and a value of E = 0 represents no oxygen transfer.

The fourth block in Table 1 shows how the aeration efficiency of the stepped labyrinth weir can be estimated at each site based on the number of drops, height of each drop and flow. The downstream concentration of DO of the stream can be calculated:8

Equation 2

Cn = Cs (E) + Cn-1 (1 – E)

• Cn is DO concentration downstream of the nth drop;
• Cs is the saturated concentration of DO in the stream; and
• Cn-1 is the DO concentration upstream of the nth drop.

The value of the oxygen transfer efficiency of the structure at 20 degrees Celsius also can be estimated:8

Equation 3

E20 = 1 – 1/[1 + 1.186 x Hd x Q ((0.195 cos (2a) + 0.335) x Hd -0.522)]

• Hd is the height of each drop in meters; and
• Q is the volumetric discharge (m3/sec).

Then, the value of E can be estimated at the river temperature, T:9

Equation 4

ET = 1 – (1 – E20)f


f = 1.0 + 0.02103 (T – 20) + 8.261 x 10-5 (T – 20)2

Example application of procedure

Consider a reach below a dam with a DO concentration of 3.0 mg/L that has a width (W) of 20 meters and a boating flow (Qmin) of 5 m3/sec (177 cfs) at 10 C. The saturation concentration is 8 mg/L and required DO is 5 mg/L. The proposed site for a stepped labyrinth weir has an elevation change (Δelev) of 1 meter. The crest height (P0) is selected at 1 meter above approach channel bed elevation to take advantage of the available change in elevation. A total head over the weir (H) of 0.23 meter is assigned to allow boat passage.

Frictional losses across the weir are assumed to be 0 for the initial design. N is assumed at five with α of 30 degrees. A’ is set at 1 meter to allow the passage of the beam of a canoe or kayak.

Wall thickness (t) is calculated at 0.17 meter. The inside width of the downstream apex is set at 0.17 meter. The outside width of the downstream apex (D) and upstream apex (D’) are calculated to be 0.36 meter and 1.19 meters respectively. Total head over the crest is divided by crest height (H/P0) to be used as a check on computations. From Table 1, the crest coefficient (Cd) can be set at 0.61. From the information above, the effective crest length (L) is calculated to be 15.1 meters. The length of the weir from upstream apex to downstream apex (B) is determined to be 2.39 meters. The actual (L1), effective (L2), and total length (L3) of the walls are calculated to be 2.57 meters, 2.47 meters, and 32.5 meters, respectively. The distance between cycles (w) is determined to be 3.93 meters. This value is divided by crest height to provide the parameter w/P0 at 3.93, which is in the preferred range of 3 to 4.

The total drop height (Ht = 1 m) corresponds to the upstream-to-downstream water surface elevation change. Based on the total height, the height of a single drop (Hd) at 0.5 meter and the number of drops (n) at 2 are selected to keep Hd between 0.33 and 0.5 for safe boating. The depth of the pool (dp) is set at two-thirds of the drop height; in this example dp is 0.33 meter. The length of pool (lp) needed to accommodate the jet for this design is 0.78 meter. The step crest height for subsequent steps (p) is calculated at 0.16 meter. The slope of the structure (β) is calculated to check for unwanted skimming flow, and in this case β is 33.3 degrees and skimming flow does not occur.

Throughout the design process, it is important to check parameters such as H/P0, w/P0 and β to ensure they are within recommended boundaries. If any of these parameters are not, N and α should be altered to bring these parameters within the recommended ranges.

Oxygen concentration downstream of the weir is computed from the oxygen transfer efficiency, which is calculated using Equation 3 to be 0.35. This value is adjusted to the temperature of the river, T = 10 C, using Equations 4 and 5, giving (E10) equal to 0.29. With an aeration efficiency of 0.29 and two steps of height 0.5 meter, the estimated DO concentration downstream of the structure calculated using Equation 2 is 5.5 mg/L.

In the above calculations, it has been assumed, out of necessity, that the flow of the upper weir has minimal influence on the flow or the oxygen transfer efficiency of the lower weir. Some influence, however, is expected, especially with regard to the transfer efficiency.

Meeting licensing or relicensing requirements

Today’s FERC relicensing requirements for hydro projects often call for improvement in recreation in addition to water quality. In the recent case of a project in South Carolina, the license requires the establishment of canoe/kayak landings and portages to enhance recreational opportunities.10 Part of the license includes monitoring DO and remediation of any deficiencies. The tailrace of the lower dam of the project travels 990 feet before joining the river. This may be an area where a stepped labyrinth weir can be considered to allow recreational boaters who launch near or above the dam to reach the whitewater area downstream. A bypass structure layout may also be considered to limit the need for landings and portages. The weir could provide aeration to remediate low DO and safe passage of canoes and kayaks.

Similarly, a project in Jackson County, N.C., has been relicensed with a requirement that the project maintain the existing recreational boat landings and provide minimum flows for whitewater activities downstream on the East Fork of the Tuckasegee River. The operational standards also require that DO levels be kept above the 5 mg/L benchmark. The two tailraces below the dams in this project are sufficiently long, 1.85 miles and 1.46 miles, to provide sites for considering a stepped labyrinth weir with aeration capabilities.11

With the increased focus on recreation and water quality in the licensing or relicensing process and problems with low DO in many regions of the U.S., a stepped labyrinth weir is one option that can meet all needs.


This concept was created as a possible solution to the need for recreationally safe structures that simultaneously improve DO concentration. Research has shown the potential for aeration at hydraulic structures, specifically at labyrinth weirs, roughened weirs and stepped cascades. These structures were combined with guidelines for safe boating conditions and energy dissipation to inspire the stepped labyrinth weir for aeration and boat passage.

The stepped labyrinth weir has the potential to enhance the environmental, economical and social impacts of sustainability at or near dam sites. The structure’s purpose is to provide inexpensive aeration of streams, safe passage of recreational boats and in some instances additional recreation. In the case of Man Maq Dam in Jones County, Iowa, for example, a stepped labyrinth weir can work in harmony with the existing structure to allow kayaks and canoes to pass safely down the scenic and historic Maquoketa River.12

A stepped labyrinth weir may replace a low-head dam as an in-stream structure, or it may be used as a bypass structure at hydro plants, similar to canoe chutes5 or recent projects on Beaver Creek in Ohio.13 In these cases, the stepped labyrinth is broken into several single drops with pools in-between. This setup allows boaters to take the large descent of a dam in several smaller steps. A structure like this can also promote water quality and fish passage while mediating low flows.

An ideal situation for implementing a stepped labyrinth weir is during the hydropower relicensing process. The multiple benefits of a stepped labyrinth weir may help address increasing standards for water quality and recreational needs that are often part of the relicensing process.

The stepped labyrinth weir for aeration and boat passage may be one option for remediation of low DO, but it is not a universal solution. It is important to evaluate feasibility of the structure for each site. The features may be applicable to a site, and they may stimulate discussion and provide the basis for future study that would evaluate the practicality of this concept. Further research is necessary, however, before this concept can be adapted for design.


The Hydro Research Foundation provided funding and guidance for Garrett Monson through an HRF Fellowship. HRF mentor and advisor Dr. John Gulliver provided guidance and research materials. The Federal Energy Regulatory Commission provided li-censing information.


1Rizk, T.A., and G.E. Hauser, Chatuge Aerating Infuser Physical Model Study, WR28-1-17-101, Tennessee Valley Authority Engineering Laboratory, Norris, Tenn., 1993.

2Hauser, G.E., and Doug I. Morris, “High Performance Aerating Weirs for Dissolved Oxygen Improvement,” Proceedings of WaterPower 1995, HCI Publications, Kansas City, Mo., 1995.

3Watson C.C., R.W. Walters, and S.A. Hogan, “Aeration Performance of Low Drop Weirs,” Journal of Hydraulic Engineering, Volume 124, No. 1, pages 65-71.

4Boes R.M., and W.H. Hager, “Hydraulic Design of Stepped Spillways,” Journal of Hydraulic Engineering, Volume 129, No. 9, September 2003, pages 671-679.

5Caisley M.E., F.A. Bombardelli, and M.H. Garcia, Hydraulic Model Study of a Canoe Chute for Low-Head Dams in Illinois, IDNR WR009820 S98-284, Illinois Department of Natural Resources Office of Water Resources, Chicago, 1999.

6Tullis J.P., N. Amanian, and D. Waldron, “Design of Labyrinth Spillways,” Journal of Hydraulic Engineering, Volume 121, No. 3, March 1995, pages 247-255.

7Gupta R.S., Hydrology and Hydraulic Systems, Third Edition, Waveland Press Inc., Long Grove, Ill., 2008, page 547.

8Wormleaton P.R., and E. Soufiani, “Aeration Performance of Triangular Planform Labyrinth Weirs,” Journal of Environmental Engineering, Volume 124, No. 8, 1998, pages 709-718.

9Gulliver J.S., Thene J.R., and Rindels A.J., “Indexing gas transfer in self-aerated flows,” Journal of Environmental Engineering, Volume 116, No. 3, pages 503-523.

10Lockhart Power Company Project No. 2621-009 Order Issuing Subsequent Major License, Federal Energy Regulatory Commission, Washington, D.C., 2011, www.ferc.gov/industries/hydropower/gen-info/licensing/issued-licenses.asp.

11Duke Energy Carolinas, LLC, Project No. 2601-007 Order Issuing Subsequent License, Federal Energy Regulatory Commission, Washington, D.C., 2011, www.ferc.gov/industries/hydropower/gen-info/licensing/issued-licenses.asp.


13Hochanadel, D., “Dams Out, Kayaks In,” Stormwater, July/August 2011, pages 48-50.

Garrett Monson is a Hydro Research Foundation Fellow and John Gulliver, PhD, is a professor at the University of Minnesota.

This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.


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