The Gravel River Bankfull Discharge Estimator Gary Parker, 10/2004

1. http://cee.uiuc.edu/people/parkerg/course_notes.htm A tool from the NCED Stream Restoration Toolbox: The Gravel River Bankfull Discharge Estimator Gary Parker, 10/2004

2. CAVEAT • This tool is provided free of charge. • Use this tool at your own risk. • In offering this tool, none of the following accept responsibility or liability for its use by third parties: • the National Center for Earth-surface Dynamics; • any of the universities and institutions associated with the National Center for Earth-surface Dynamics; or • any of the authors of this tool.

3. The Gravel River Bankfull Discharge Estimator This tool consists of an equation to estimate bankfull discharge in an undisturbed (reference) reach of a single-thread, mobile-bed gravel-bed stream from measured channel characteristics. River bankfull discharge is a key parameter for estimating channel geometry. A knowledge of bankfull discharge is necessary for the evaluation and implementation of many river restoration projects. The best way to measure bankfull discharge is from a stage-discharge relation. Bankfull discharge is often estimated in terms of a flood of a given recurrence frequency (e.g. 2-year flood, or a flood with a peak flow that has a 50% probability of occurring in a given year; Williams, 1978). In some cases, however, the information necessary to estimate bankfull discharge from a stage-discharge relation or from flood hydrology may not be available. The tool presented here provides an alternative estimator.

4. RIVERS ARE THE AUTHORS OF THEIR OWN GEOMETRY • Given enough time, rivers construct their own channels. • A river channel is characterized in terms of its bankfull geometry. • Bankfull geometryis defined in terms of river width and average depth at bankfull discharge. • Bankfull discharge is the flow discharge when the river is just about to spill onto its floodplain. • A river restoration scheme is likely to become more successful in a shorter amount of time if it takes into account the natural bankfull geometry of a channel. • This tool allows estimation of bankfull discharge of a single- thread gravel-bed river with a definable floodplain that actively moves the gravel on its bed from time to time. Bankfull discharge is estimated from measured bankfull channel characteristics.

5. THIS TOOL IS FOR GRAVEL-BED STREAMS Little Wekiva River, Florida, USA: a sand-bed river. Raging River, Washington, USA: a gravel-bed river This tool addresses gravel-bed streams. Typical gravel-bed streams have bed surface median sizes Ds50 in the range from 8 to 256 mm. Boulder-bed streams have median sizes in excess of 256 mm. Sand-bed streams have median sizes between 0.062 and 2 mm.

6. THIS TOOL ADDRESSES SINGLE-THREAD RATHER THAN MULTIPLE-THREAD RIVERS Raging River, Washington, USA: a single-thread gravel-bed river Sunwapta River, Canada: a multiple-thread (braided) gravel-bed river This tool addresses single-thread streams. A single-thread stream has a single definable channel, although mid-channel bars may be present. A multiple-thread, or braided stream has several channels that intertwine back and forth.

7. THIS TOOL ADDRESSES MOBILE-BED RATHER THAN THRESHOLD CHANNELS Trinity Dam on the Trinity River, California, USA. A threshold channel forms immediately downstream. Raging River, Washington, USA: a mobile-bed river This tool addresses mobile-bed gravel streams. Such streams are competent to modify their beds because they mobilize all or nearly all gravel sizes on the bed from time to time during floods. Threshold channels are defined in the next slide.

8. THRESHOLD CHANNELS Threshold gravel-bed channels are channels which are barely not able to move the gravel on their beds, even during high flows. These channels form e.g. immediately downstream of dams, where their sediment supply is cut off. They also often form in urban settings, where paving and revetment have cut off the supply of sediment. Threshold channels are not the authors of their own geometry. The relations presented in this tool do not apply to them. Trinity Dam on the Trinity River, California, USA. A threshold channel forms immediately downstream.

9. PARAMETERS USED IN THIS TOOL • This tool uses the following parameters: • Bankfull discharge Qbf in cubic meters per second (m3/s) or cubic feet per second (ft3/s); • Bankfull channel width Bbf is meters (m) or feet (ft); • Bankfull cross-sectionally averaged channel depth Hbf in meters (m) or feet (ft); • Down-channel slope S (meters drop per meter distance or feet drop per feet distance). • Bed surface median grain size Ds50. This parameter is usually measured in millimeters (mm); the value must be converted to meters or feet in using the tool presented here. • These parameters are defined before the tool is introduced. If you are familiar with the parameters, click the hyperlink to jump to the tool.

10. BANKFULL PARAMETERS: THE RIVER AND ITS FLOODPLAIN floodplain A river constructs its own channel and floodplain. channel At bankfull flow the river is on the verge of spilling out onto its floodplain.

11. THE DEFINITION OF BANKFULL DISCHARGE Qbf Let  denote river stage (water surface elevation in meters or feet relative to an arbitrary datum) and Q denote volume water discharge (cubic meters or feet per second). In the case of rivers with floodplains,  tends to increase rapidly with increasing Q when all the flow is confined to the channel, but much less rapidly when the flow spills significantly onto the floodplain. The rollover in the curve defines bankfull discharge Qbf. The floodplain is often somewhat poorly-developed in mountain gravel-bed streams. Bankfull stage, however, can often still be determined by direct field inspection. Minnesota River and flooded floodplain, USA, during the record flood of 1965

12. CHARACTERIZING BANKFULL DISCHARGE Qbf • Bankfull discharge Qbf is used as a shorthand for the characteristic flow discharge that forms the channel. • One way to determine it is by means of direct measurement of the flow in a river. Since bankfull flow is not frequent, this method may be impractical in a river restoration scheme. • Another way to estimate it is from a stage-discharge curve, as described in the previous slide. In order to implement this, the river must be gaged near the reach of interest. • Another way is to estimate it using stream hydrology. It has been found that in gravel-bed streams bankfull flow is often reasonably estimated in terms of a peak flood discharge with a recurrence of 2 years (e.g. Williams, 1978 ). This corresponds to a flow discharge that has a 50% probability of occurring in any given year. • When none of the above methods can be implemented, Qbf can be estimated from bankfull channel characteristics, as described in this tool.

13. CHARACTERIZING BANKFULL CHANNEL GEOMETRY: BANKFULL WIDTH Bbf AND BANKFULL DEPTH Hbf Bankfull geometry is here defined in terms of the average characteristics of a channel cross-section at bankfull stage, i.e. when the flow is at bankfull discharge. Here the key parameters are: bankfull width Bbf and cross-sectionally averagedbankfull depthHbf. These parameters should be determined from averages of values determined at several cross-sections along the river reach of interest.

14. CAVEAT: NOT ALL RIVERS HAVE A DEFINABLE BANKFULL GEOMETRY! Rivers in bedrock often have no active floodplain, and thus no definable bankfull geometry. Wilson Creek, Kentucky: a bedrock stream. Image courtesy A. Parola. Highly disturbed alluvial rivers are often undergoing rapid downcutting. What used to be the floodplain becomes a terrace that is almost never flooded. Time is required for the river to construct a new equilibrium channel and floodplain. Reach of the East Prairie Creek, Alberta, Canada undergoing rapid downcutting due to stream straightening. Image courtesy D. Andres. The tool presented here cannot be used to estimate bankfull discharge from bankfull channel characteristics if a) there is no floodplain or b) the channel is so disturbed that it is no longer interacting morphologically with its floodplain.

15. FIELD MEASUREMENT OF BANKFULL CHANNEL GEOMETRY Not all field channels have definable bankfull geometries. Even when a channel does have a definable bankfull geometry, some experience and judgement is required to measure it. In the future a worked example complete with photographs and data files will be added to the toolbox. Until this is done, the user is urged to spend some time to determine how bankfull geometry should be determined.

16. CHARACTERIZING BED SEDIMENT IN GRAVEL-BED STREAMS: MEDIAN SURFACE SIZE Ds50 Armored surface Gravel-bed streams usually show a surface armor. That is, the surface layer is coarser than the substrate below. substrate Bed sediment of the River Wharfe, U.K., showing a pronounced surface armor. Photo courtesy D. Powell.

17. SURFACE AND SUBSTRATE MEDIAN SIZES Here the surface median size is denoted as Ds50 and the substrate median size is denoted as Dsub50. The surface is said to be armored when Ds50/Dsub50 > 1. This ratio also provides a rough estimate of ability of the stream to move its own gravel. Low values of Ds50/Dsub50 (e.g. < 1.3, i.e. relatively weak armoring) are generally indicative of relatively high mean annual sediment transport rates, whereas high values of Ds50/Dsub50 (e.g. > 4, relatively strong armor) are generally indicative of relatively low mean annual sediment transport rates (Dietrich et al., 1989). Notes on bed sampling, grain size distributions and the determination of median sediment size are given in and Appendix (slides 21-27) toward the end of this presentation. To jump to them click the hyperlink bed sampling.

18. CHARACTERIZING DOWN-CHANNEL SLOPE S Down-channel bed slope should be determined from a survey of the long profile of the channel centerline. The reach chosen to determine bed slope should be long enough to average over any bars and bends in the channel, which are associated with local elevation highs and lows.

19. DATA BASE FOR THE TOOL • The bankfull discharge predictor presented here was developed by Parker (2004) from the following data base for gravel-bed streams. • 16 stream reaches flowing from the Rocky Mountains in Alberta, Canada (Kellerhals et al., 1972); • 23 mountain stream reaches in Idaho (Parker et al., 2003); • 23 upland stream reaches in Britain (mostly Wales) (Charlton et al.1978); • 10 reaches along the upper Colorado River, Colorado (Pitlick and Cress, 2002) (Each reach represents an average of several subreaches.) • The original data for Qbf, Bbf, Hbf, S and Ds50 for each reach can be found in the companion Excel file, ToolboxGravelBankfullData.xls. • The predictor was further tested with a set of 11 reaches in Maryland/ Pennsylvania, USA (McCandless, 2003) and 62 reaches of British streams (Hey and Thorne, 1986).

20. RANGE OF PARAMETERS USED TO DEVELOP THE TOOL Among all four sets of data, the range of parameters is as given below: Bankfull discharge Qbf (in meters3/sec) 2.7 ~ 5440 Bankfull width Bbf (in meters) 5.24 ~ 280 Bankfull depth Hbf (in meters) 0.25 ~ 6.95 Channel slope S 0.00034 ~ 0.031 Surface median size Ds50 (in mm) 27 ~ 167 These ranges define the range of applicability of the tool.

21. THE TOOL The tool consists of the following relation. Where g = the acceleration of gravity (9.81 meters/second2 or 32.2 feet/second2), That is, if Bbf, Hbf, S and Ds50 can be determined from field measurements, Qbf can be estimated from the above relation. The tool is implemented as an Excel spreadsheet in the next slide. Caution: use the relation subject to the caveats of Slides 5, 6, 7, 8 and 14!

22. IMPLEMENTATION OF THE TOOL Stop the slide show and double-click the Excel spreadsheet to activate it. If you type in the indicated input parameters in the indicated units, Qbfis computed as output. Caution: use the relation subject to the caveats of Slides 5, 6, 7, 8 and 14!

23. ACCURACY OF THE TOOL The plot shows the values of Qbf predicted by the tool versus the reported (observed) values for the data set used to develop the tool. In 93% of all reaches the predicted value is between half and twice the reported value.

24. APPENDIX: SEDIMENT SIZE DISTRIBUTIONS IN GRAVEL-BED STREAMS Armored surface Implementation of the regression relations requires a knowledge of the median size of the surface armor Ds50. This value must be determined by sampling the bed. In order to characterize the bed sediment of the stream the surface and substrate should be sampled separately. The results of sampling are plotted in terms of percent finer versus grain size (mm) as illustrated below. substrate Bed sediment of the River Wharfe, U.K., showing a pronounced surface armor. Photo courtesy D. Powell.

25. WOLMAN COUNT OF SURFACE SEDIMENT The simplest way to sample a gravel bed surface is by means of a Wolman count (Wolman, 1954). The gravel surface is paced, and at set intervals a particle next to the toe of one’s foot is sampled. The sampling should be chosen so as to capture the spatial variation in bed texture. Grain size is characterized in terms of the b-axis of a grain (middle axis as measured with a caliper) or the size of the smallest square through which the grain will fit. A series grain size ranges is set for estimating the grain size distribution. In analyzing a Wolman sample, it is necessary to determine the number of grains in each range. These numbers are used to determine the grain size distribution. A sample calculation is given in the live spreadsheet of the next slide. Wolman sampling is not practical for sand-sized or smaller grains. More specifically, grains finer than about 4 mm should not be included in a sample. It should be understood that this method misses the finer grains in the surface.

26. GRAIN SIZE DISTRIBUTION FROM WOLMAN COUNT The live spreadsheet to the right shows a worked example for a Wolman count. Stop the slide show and double-click to activate it. It is customary to plot grain size on a logarithmic scale when presenting grain size distributions.

27. KLINGEMAN SAMPLE OF SURFACE SEDIMENT The methodology for a Klingeman sample of the surface sediment is outlined in Klingeman et al. (1979). A circular patch of sediment is specified on the bed. The largest grain that shows any exposure on the bed surface is located and removed. All of the bed material (including sand) is then sampled down to the level of the bottom of the hole created by removing the largest grain. The resulting sample is analyzed by mass (weight) rather than number. A Klingeman sample captures the sand as well as the gravel in the surface layer. Sampling is, however, more laborious than that required for a Wolman sample. In addition, several Klingeman samples at different locations may be needed to characterize the spatial variability of the surface sediment. A sample calculation is given in the live spreadsheet of the next page.

28. KLINGEMAN SAMPLE OF SURFACE SEDIMENT contd. The live spreadsheet to the right shows a worked example for a Klingeman sample. Stop the slide show and double-click to activate it.

29. BULK SAMPLE OF SUBSTRATE The substrate may be sampled in bulk. The surface layer is first carefully stripped off down to the depth of the bottom of the largest particle exposed on the surface. A bulk sample (e.g. cubical) volume of substrate is then excavated. According to the guidelines of Church et al. (1987), the mass (weight) of the sample should be at least 100 times the mass (weight) of the largest grain contained in the sample. Several such samples may be needed to characterize the spatial variability of the substrate. The sample is analyzed in terms of mass (weight) rather than number.

30. MEDIAN SIZE It is useful to characterize a sample in terms of its median size D50, i.e. the size for which 50% of the material is finer. To do this, find the grain sizes D1 and D2 such that the percentage content F1 is the highest value below 50% and the percentage content F2 is the lowest percentage above 50%. The median size D50 is then estimated by log-linear interpolation as: For example, in the Klingeman sample of slide 13: D1 = 32 mm, F1 = 45.24%, D2 = 64 mm and F2 = 59.52%. The calculation of D50 is illustrated in terms of the live spreadsheet below. Stop the slide show and double-click to activate it.

31. REFERENCES Charlton, F. G., Brown, P. M. and R. W. Benson 1978 The hydraulic geometry of some gravel rivers in Britain. Report INT 180, Hydraulics Research Station, Wallingford, England, 48 p. Church, M. A., D. G. McLean and J. F. Wolcott 1987 River bed gravels: sampling and analysis. In Sediment Transport in Gravel-bed Rivers, Thorne, C. R., J. C. Bathurst, and R. D. Hey, eds., John Wiley & Sons, 43-79. Dietrich, W. E., J. W. Kirchner, H. Ikeda and F. Iseya 1989 Sediment supply and the development of the coarse surface layer in gravel-bedded rivers. Nature, 340, 215-217. Ferguson, R. I. 1987 Hydraulic and sedimentary controls of channel pattern. In Rivers: Environment and Process, K. Richards. ed., Blackwell, Oxford, 129-158. Hey, R. D. and Thorne, C. R. 1986 Stable channel with mobile gravel bed. Journal of Hydraulic Engineering, 112(8), 671-689. Kellerhals, R., Neill, C. R. and D. I. Bray 1972 Hydraulic and geomorphic characteristics of rivers in Alberta. River Engineering and Surface Hydrology Report, Research Council of Alberta, Canada, No. 72-1.

32. REFERENCES contd. Klingeman, P. C., C. J. Chaquette, and S. B. Hammond 1979 Bed Material Characteristics near Oak Creek Sediment Transport Research Facilities, 1978-1979. Oak Creek Sediment Transport Report No. BM3, Water Resources Research Institute, Oregon State University, Corvallis, Oregon, June. McCandless, T. L., 2003, Maryland Stream Survey: Bankfull Discharge and Channel Characteristics of Streams in the Allegheny Plateau and the Valley and Ridge Hydrologic Regions. Report CBFO-S03-01, U.S. Fish and Wildlife Service, Chesapeake Bay Field Office, May, 33 p. Parker, G., Toro-Escobar, C. M., Ramey, M. and S. Beck 2003 The effect of floodwater extraction on the morphology of mountain streams. Journal of Hydraulic Engineering, 129(11). Parker, G. 2004 Quasi-universal relations for bankfull hydraulic geometry of single-thread gravel-bed rivers . In preparation. Pitlick, J. and R. Cress 2002 Downstream changes in the channel of a large gravel bed river. Water Resources Research38(10), 1216, doi:10.1029/2001WR000898, 2002.

33. REFERENCES contd. Williams, G. P. 1978 Bankfull discharge of rivers. Water Resources Research, 14, 1141-1154. Wolman, M.G. 1954. A method of sampling coarse river bed material. Trans. Am. Geophys. Union, 35, 951–956.