Using a 1D steady flow model to compare field determination methods of bank-full stage O. Navratil, M.-B. Albert, C. Boudard & J.-M. Grésillon Cemagref, Lyon, France
ABSTRACT: Existing methods to determine bank-full stage and then bank-full discharge from field measurements give very diverging results. With the aim of clarifying this question, we use a 1D steady flow hydraulic model as reference in order to compare the main existing methods, applied on height case studies. We present here our methodology for one of these cases, the Ardour River at Folles, in the Loire river basin, France. Consistency of bank-full definitions is tested with the help of the hydraulic model. Thus, the evolution of flooded area with discharge at river reach scale allows us to define the hydraulic significance of the different elevations and discuss the validity of each method on the basis of hydraulic definition. 1 INTRODUCTION Bank-full discharge is an interesting parameter to summarize channel morphology at reach scale and to study morphology - hydrology relationships. But identifying bank-full flow conditions for natural rivers is a heavy challenge. The in depth comparative analysis published by Williams (1978) evidenced that existing methods generally used lead to very diverging results. He wrote that “ideally, the various methods should all be compared with the ’true’ bank-full discharge for each station. However, the chances of being present to measure a flow just at bank-full, however defined, are extremely small, and the true bank-full discharges are unknown for the stations of this study. So the different methods are simply compared with one another”. Other works aimed to compare different estimations of bank-full discharge (e.g. Radecki-Pawlik 2002). Therefore, we try to follow up these studies, using hydraulic model results, in order to define the hydraulic significance of each stage definition.
long, i.e., about 25 times the mean bank-full channel width (Wb=9m), with a mean slope of about 0.0047.
Figure 1: Upstream view of the Ardour river reach with main channel and floodplain.
The channel has low sinuosity (1.03) with a well developed floodplain. It is a C3 channel type, according to Rosgen classification (Rosgen 1994). The reach includes a gauging station with 30 years of records and a well-known stage-discharge relationship available from the Regional Environmental Department. A bridge situated at the middle of the river reach does not constrain the main channel flow. Water surface profile starts to be disturbed only for discharge greatly above bank-full conditions (discharge exceeding 20m3/s).
2 STUDIED RIVER REACH Ardour River at Folles is situated in the Loire river basin, France. The stream reach surveyed is an alluvial river with perennial flow (figure 1). No significant upstream regulation or diversion occurs. Its associated river basin is a 131 km² drainage area underlying by a granitic bed rock. The studied reach is 230 meters
3 TOPOGRAPHIC MEASUREMENTS Topographic measurements were practiced in the stream channel and adjacent floodplain (figure 2) and linked to staff gage elevation using an electronic, digital, total-station theodolite. Nineteen cross-sections were surveyed to describe the main
morphological variations and water surface profile at the reach scale.
fields indicators (Leopold et al. 1994, Osterkamp & Hedman 1982). 2 Geometric criteria requiring measured crosssections (Wolman 1955, Riley 1972, Pickup 1976, Williams 1978, Harrelson et al. 1994). 4.1 Geomorphic definitions
Figure 2: Topographic measurement in the main channel of Ardour River at Folles.
Elevation (in mete
Along the river reach, eleven morphological features were systematically surveyed at each crosssection to describe the main breaks in the cross section geometry (figure 2): five features on each side of the channel in addition to the thalweg elevation.
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Figure 3: Used reference levels at a channel cross-section (not to scale).
The intersection between water surface and channel banks on the left and right sides are also surveyed, to characterize the hydraulic conditions at the time of survey. These measurements have been led at two different flow conditions. Topographic measurements will be used 1/ to define bank-full elevation all along the river reach on the basis of different definitions and 2/ to build an hydraulic model. 4 BANK-FULL STAGE DEFINITIONS Two different ways exist to define bank-full stage based on morphological criteria (Williams 1978): 1 On site estimations of the elevation of incipient flooding at different cross-sections, all along the stream survey, using morphological breaks as
Topographic measurements provide two geomorphic indicators at cross-section scale to characterize the transitional area between main channel and floodplain surface: the Bank Inflection and Top of Bank elevations (figure 3). The Bank Inflection feature corresponds to the upper limit of the main channel. It is the end of the near vertical channel bank. Many authors used to detect this feature on field. Leopold and Wolman define this break as the active floodplain elevation for near straight channel or river reaches that have a low sinuosity (Leopold et al. 1994). It also corresponds to the limit of the active channel (Osterkamp & Hedman 1982). The Top of Bank feature corresponds to the elevation of the Valley Flat (Williams 1978; Leopold et al., 1994), the flood stage (Emmett 1972) or the predominant bench (Kilpatrick & Barnes 1964). It can be defined as the end of the transitional area between main channel and floodplain, and in this way, the beginning of a near flat surface (figure 3). This morphological feature has been already used for an other study on this river reach (Navratil 2002). Right and left banks show different bank-full elevations most of time. At each cross-section, we retain the lowest elevation, corresponding to the lowest limit of incipient flooding. These geomorphic definitions of bank-full stage are therefore highly dependent on operator expertise and channel difficulties to detect such features (Wahl 1976). However, these measurements provide, rather than a single elevation, a range of bank-full elevation all along the river reach. 4.2 Geometric definitions Using topographic measurements available at crosssections, we applied three classical methods analyzed by Williams (1978). Wolman’s definition is the elevation corresponding to the minimum in the width to mean depth ratio function of the elevation. It was first introduced by Wolman (Wolman 1955) and used by many authors (Harvey 1969, Pickup & Warner 1976, Richards 1982, Carling 1988, Radecki-Pawlik 2002). Figure 4 shows an example of such a relationship at one cross-section.
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Wolman’s definition corresponds to the limit of the main channel. Riley’s definition corresponds to a higher level.
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Figure 4: Minimum in the width to mean depth ratio.
Riley’s definition is the stage corresponding to the first maximum of the bench index (Riley 1972). This index characterizes the evolution of bank slope versus elevation (from upper to lower elevation). Figure 5 shows such relationship and the bank-full stage defined at a cross section. Different maxima appear, corresponding to other break in bank slope (Radecki-Pawlik 2002).
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Figure 7: Different bank-full elevations at a cross-section for each definition.
We obtain three sets of elevation values estimated at each cross-section along the reach and corresponding to three different ways for determining bank-full elevation (example of William’s definition at figure 8). For the five definitions, bridge sections are omitted in order to keep cross-sections that are free to adjust their form to actual flow regime.
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Figure 5: Riley's Bench Index versus elevation.
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Williams’s definition (Williams 1978) is the elevation corresponding to a change in the relation between wetted area to top width (figure 6).
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Figure 8: Williams’s definition elevations all along the studied reach.
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5 HYDRAULIC MODEL 10
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Figure 6: Evolution of the wetted area versus elevation.
As evidence in figure 7, the three methods lead to different bank-full elevation values. Williams and
The hydraulic model can be used as a standard of comparison under the condition it provides an accurate estimation of water level at each cross-section for in-bank and over-bank discharges. Other hydraulic parameters as width, wetted perimeter, mean water depth, wetted area and maximum water depth can be derived from this computed elevation. A one dimensional code of simulation for steady and sub-critical flow is used (Baume & Poirson 1984). The water surface profile is calculated with good accuracy with the equations used into this code
(Nicollet & Uan 1979). But, basics hypothesis have first to be verified. The sinuosity of the station being low (see study area), the one dimensional hypothesis is admitted. As we characterize the morphology of the main channel in term of capacity, the steady flow is then justified. As the mean slope is very small for all the station studied, the flow is subcritical. Afterwards, the good accuracy of the river modeling depends on quality of the topographical model, calibration data and method used. In addition to longitudinal variability of the current cross sections, the topographic measurements included the description of possible hydraulic controls (bridges, weirs). A relationship between water level and discharge at the downstream cross-section was developed using a uniform flow model, in accordance with on field measurements at two different flows. To calibrate our model, we used water surface profiles measured for two different discharges, one at low flow (Q=2.26 m3/s), the other one at near bank-full flow (Q= 7.43 m3/s). A rating curve is also available by the Regional Environmental Department, with its range of validity. We fitted a single roughness coefficient for the entire reach. A single Manning's ‘n’ value for the entire reach is accepted with a mean error of 5 cm. Figure 9 shows an example of calibration for Q= 7.43 m3/s. Then, it allows us to calibrate our model for other discharges with the rating curve available at one cross-section and extrapolate the result for the entire reach using the single channel method to calibrate the model for over-bank flow conditions. Such a calibration provides a good estimation of water profile for in-bank and over-bank flows within the range of validity of the rating curve.
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consider that bank-full flow occurs at a break in slope, above which small increases in depth are accompanied by disproportionately large increases in width. To characterize the hydraulic meaning of bankfull definition, we use the hydraulic model to estimate the evolution of flooded area for a large range of flows, at the reach scale. Figures 10a, 10b, 10c shows the flooded area, calculated by the hydraulic model at three different discharges: (a) in-bank flow (Q=3.5 m3/s), (b) intermediate flow (Q=7 m3/s) and (c) over-bank flow (Q=14 m3/s). (a)
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Figure 9: Hydraulic model calibration with a single Manning’s ‘n’ value for the entire reach.
Figure 10a, 10b, 10c: Over view of the flooded area at the reach scale for tree discharges from upstream (right side) to downstream (left side): Q=3.5 m3/s; Q=7 m3/s; Q=14 m3/s.
6 A SYNTHETIC REPRESENTATION OF OVERFLOWING DEVELOPMENT
For Q=3.5 m3/s, the flow is contained in the main channel. For Q=7 m3/s, local area are flooded, due to vegetation interact with bank morphology and local sedimentation. For Q=14 m3/s, the flow is well de-
For the purpose of this study, bank-full stage was defined according to morphological indicators. We
Flooded area at the reach scale
veloped in the floodplain. For this flow conditions, the flooded area is relatively homogeneous, excepted a local area corresponding to bridge’s embanked cross-sections at the middle of the reach and a downstream morphological singularity. With the aim to study overflowing increase at reach scale and to compare different definitions of bank-full elevations, we use the relationship between the mean flooded area versus discharge (figure 11).
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Figure 11: Evolution of the mean flooded area versus discharge (solid line) and the 95% confidence interval (dashed lines).
In spite of taking into account variability of flooded area, the 95% confidence interval is also computed. From low flow to about 15 m3/s, the mean flooded area is significant at the reach scale. For upper flow, variability increases largely. At low flow, flooded area increases rapidly for a little rise of discharge (flows of about 0 to 1.5 m3/s). Next, different ranges of discharge can be characterized when studying the relative increase of flooded area with a constant step of discharge (figure 11): 1 A smooth evolution of the flooded area with a constant rise of discharge: flows from 1.5 to 5 m3/s. 2 The intermediate range of discharge where local over-bank areas occur, can be associated to the transition between main channel and floodplain flows: flows from 5 to 7.5 m3/s. Its low bound is characterized by a sudden rise in flooded area. 3 The third range of discharge called the over-bank flow describes the floodplain evolution flow: from 7.5 to about 15-20 m3/s. Its low bound corresponds to the beginning of a relatively constant increase of flooded area and ended at the limit of the floodplain. At upper discharge, a smooth evolution of the flooded area versus discharge can be detected, corresponding to valley margin (flows upper than 15-20 m3/s). Such a relationship will help us to find the hydraulic significance of each of the five bank-full definitions (see bank-full stage definitions).
7 CONSISTENCY OF BANK-FULL DEFINITIONS AT RIVER REACH SCALE Bank-full stage has been computed at each crosssection all along the site survey, for each definition (table 1). The range of bank-full discharge can be up to a factor 4, showing the great variability for each definition. Bank-full discharge can’t be considered at a single cross-section, but rather at a reach scale. These results demonstrate and complete further analysis that concept of bank-full discharge has no significance at a single cross-section (Riley 1972, Williams 1978). Assumption that bank-full discharge concept is significant at a larger scale, i.e., that water surface profiles corresponds, on the average, to morphological features all along a stream reach, for characteristic discharges is now tested. Water surface profiles are computed for different discharges. The least square method is used to determine the discharge that minimizes, at the reach scale, the mean absolute difference between water surface levels modeled and morphological levels previously defined. For example, figure 12 shows the Williams’s bank-full elevation and the adjusted water surface profile for Q=7.2 m3/s (table 1). Table 1 gives the main results of this test for other bank-full definitions. It allows us to appreciate the consistency, at reach scale, of these different bank-full elevations.
Bank-full Definitions
At the crosssection scale Range of discharge (m3/s) 4-14 1.9-8.4
At the reach scale Discharge Mean absolute (m3/s) difference (m) 7.1 0.15 4.1 0.13
Top of Bank Bank Inflection Wolman’s 3.8-13 6.8 0.15 definition Williams’s 4.8-13 7.2 0.18 definition Riley’s 8-25 15 0.26 definition Table 1: Bank-full discharge computed (1) at each cross section and (2) at the reach scale with its mean absolute difference.
For all definitions retained, bank-full elevations are normally distributed around water surface profiles with a 95% confidence interval. The mean difference is less than 0.002 m for each definition. All definitions are then consistent at river reach scale. Characteristic discharges corresponding to morphological features have physical significant at this scale (table 1).
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Figure 12: Example of adjustment of water surface profile (Q=7.2 m3/s) with William’s definition of bank-full stage.
However, each definition of bank-full is more or less consistent all along the site. Mean differences between Top of Bank or the Bank Inflection elevations with water profiles are respectively 0.15 and 0.13 m. Wolman's and Williams's definitions are consistent too but with a mean error a little bit greater than geomorphic definitions (0.15 and 0.18 m). Riley's definition seems to be less consistent than others, with a mean difference of about 0.26 meter. The calibration uncertainty of water level modeled can explain about 20% of variability between water level and morphological features (calibration uncertainties are about 0.05 m). Then we can assess that Wolman and Williams’s definition, Top of Bank and Bank Inflection are consistent all along the reach. The Riley’s Bench Index seems to be a poor definition of bank-full condition for this site survey. Bank-full discharge expressed at a cross-section has no significance, but, on the opposite, this metric well describes the main channel morphology averaged at the reach scale. A test of robustness of bankfull discharge value with the length of the survey shows that this length must be about 20 times bankfull width to converge to bank-full discharge estimated using the all studied reach (test lead with the Bank Inflection elevation with an accepted error less than 5%). This test is in accordance with literature recommendations (Harrelson et al. 1994, Leopold et al. 1994). 8 HYDRAULIC SIGNIFICANCE OF BANKFULL DEFINITIONS AND CONCLUSIONS Bank-full discharge estimated with the hydraulic model for each definition (table 1) are now associated with its corresponding flooded area (figure 11). We can locate these values on the flooding evolution curve to determine their hydraulic significance (figure 13). It allows us to compare objectively results provided by the three different studied methods, the
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geomorphic methods and the incipient flooding at river reach scale. Wolman’s definition corresponds to incipient flooding (figure 13). William’s definition corresponds to the same range of flow, i.e., when flood begins to occur at particular cross-section along the reach. Riley’s Bench index definition does not correspond to a bank-full elevation. It corresponds to a greater flow in the floodplain. It is certainly due to the first index criteria (Riley 1972) that is inaccurate when considering the all section (Radecki-Pawlik 2002). Top of Bank definition corresponds to the beginning of flow into the floodplain usually called the flood stage. Bank Inflection definition is located at the upper limit of the “in-bank flow” range of discharge. It can be defined as the end of the main channel, just before over-bank flow occurs. Flooded area at the reach scale
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Figure 13: Evolution of the flooded area at the reach scale and bank-full discharges corresponding to different definitions: geomorphic and geometric definitions.
9 PERSPECTIVES The methodology described above will be applied to seven other river reaches. Expected results of this study are to give objective judgment on the different ways for determining bank-full stage and bank-full discharge and also possibility to gather together sets of bank-full discharge data estimated with different methods, when verified they lead to the same parameter definition. In this way, useful recommendations to improve operational procedures for determining bank-full stage on the field and then bankfull discharge will be provided. REFERENCES Baume, J. & Poirson M. 1984. Modélisation numérique d'un écoulement permanent dans un réseau hydraulique maillé à surface libre, en régime fluvial. La Houille Blanche 1/2: 95100. Carling, P. 1988. The concept of dominant discharge applied to two gravel-bed streams in relation to channel stability thresholds. Earth surface processes and landforms 13: 355367.
Emmett, W. W. 1972. The hydraulic geometry of some Alaskan streams south of the Yukon River, open file report. US Geological Survey: 102 p. Harrelson, C. C. & Rawlins, C. L. et al. 1994. Stream channel reference sites: en illustrated guide to field technique. G. T. R. R.-F. Collins, US Fish and Wildlife Service: 61. Harvey, A. M. 1969. Channel capacity and adjustment of streams to hydrologic regime. J. of Hydrology 9: 82-98. Kilpatrick, F. A. & Barnes H. H. 1964. Channel geometry of Piedmont streams as related to frequency of floods. US Geological Survey, Professional Paper 422 E: 10 p. Leopold, L. B et al. (ed.) 1994. Fluvial processes in geomorphology. New York: Dover Publication. Nicollet, G. & Uan M. 1979. Continuous free surface flow over composite beds. La Houille Blanche 1: 21-30. Navratil, O. & M. B. Albert et al. 2002. Water level time series analysis for bank-full flow studies in river. River Flow. Proc. Intern. Conf. On Alluvial Hydaulics., Louvain-laNeuve, Belgium, 4-6 September 2002. Rotterdam: Balkema.
Osterkamp, W. R. & Hedman E. R. 1982. Perennialstreamflow characteristics related to channel geometry and sediment in Missouri river basin. US Geological Survey 1242: 37. Pickup, G. & Warner R. F. 1976. Effects of hydrologic regime on magnitude and frequency of dominant discharge. J. of Hydrology 29: 51-75. Radecki-Pawlik, A. 2002. Bankfull discharge in mountain streams: Theory and practice. Earth Surface Processes and Landforms 27(2): 115-123. Richards, K. S. (ed.) 1982. Rivers. Form and process in alluvial channels. New York: Methuen and Co. Riley, S. J. 1972. Comparison of morphometric measures of bank-full. J. of Hydrol. 17(1-2): 23-31. Wahl, K. L. 1976. Accuracy of channel measurements and the implications in estimating streamflow characteristics. Modern development in hydrometry: 311-319. Williams, G. P. 1978. Bank-full discharge of rivers. Water Resources Research 14(6): 1141-1154. Wolman, M. G. 1955. The natural channel of Brandywine Creek, Pennsylvania. U.S. Geol. Surv. Prof. Pap. 271: 56 pp.
