Geomorphology 28 Ž1999. 281–297
Estimating mean flow velocity in channel and floodplain areas and its use for explaining the pattern of overbank deposition and floodplain retention Bartłomiej Wyzga ˙
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Institute of Nature ConserÕation, Polish Academy of Sciences, ul. Lubicz 46, 31-512 Krakow, ´ Poland Received 2 April 1998; received in revised form 18 October 1998; accepted 31 October 1998
Abstract Stage-discharge curves for out-of-bank flows are derived from direct discharge measurements and theoretical calculations of channel and floodplain conveyance at a station, and comparisons of volumes of flood waves at successive stations. A method was developed which permits estimation of the mean flow velocity in the channel and floodplain zones at a given total discharge taken from a rating curve. Out-of-bank channel flows are estimated under the assumption that the interface planes between the channel zone and the floodplain are included in the wetted perimeter for the channel subarea. The floodplain flows are then calculated as the residual values after subtracting the flow in the channel zone from the total discharge. Results obtained using the method are presented for three cross-sections located on mountain, foothill and piedmont rivers within the upper Vistula drainage basin, southern Poland, and are considered in relation with the pattern of floodplain sedimentation caused by a major flood of July 1997. High rates of lateral thinning and fining of overbank deposits were observed for the piedmont Vistula River which is characterized by a marked contrast in mean velocity between the channel and floodplain flows. On the mountain Skawa River and the foothill Skawinka River mean velocity of the floodplain flow was high, both in absolute values and when compared with that of the channel flow; overbank deposits were generally thin there and showed minor changes in thickness, mean size and sorting across the floodplains. This study shows that the proposed method of estimating mean flow velocity in channel and floodplain areas may yield valuable information about hydraulics of out-of-bank flows, which may be used for explaining the observed pattern of floodplain deposition. The results also demonstrate that the floodplain of the Vistula acts mainly as a storage reservoir at low out-of-bank flows but its efficiency in carrying flood water grows when flow exceeds that of 12-year frequency. On the other hand, retention potential of the Skawa floodplain is very low but flow becomes increasingly stored after water starts to spread rapidly onto the higher terrace at a discharge of 14-year recurrence interval. q 1999 Elsevier Science B.V. All rights reserved. Keywords: mean flow velocity; overbank flow; flood flow hydraulics; overbank deposits; floodplain retention
1. Introduction Existing knowledge concerning the hydraulics of overbank flows is relatively limited. Current under)
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standing of water transfer in floodplain areas is based largely on experimental studies ŽKnight and Shiono, 1996. rather than on field measurements. This situation results from the infrequent and unpredictable occurrence of floods, especially high magnitude events, the short duration of overbank flows and
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the hazards associated with undertaking measurements during flood discharges. The unsteady nature of flood flows, particularly those in mountain rivers, means that flow conditions may change before a survey across the whole width of a floodplain is completed. As a result of these constraints, velocity measurements on rivers in out-of-bank conditions are rare and limited mostly to individual cross-sections under bridges, the geometry of which may differ markedly from that of natural cross-sections. Still more infrequent are surveys of successive cross-sections along a given river in flood or on a number of rivers in a larger drainage basin during the same flood event. Although determining the hydraulics of flood flows on a real river is very difficult, it is crucial for such practical reasons as establishing the conveyance capacity of a channel and floodplain or flood routing. It also enables sediment transfer into and over a floodplain area to be predicted or the depositional pattern observed after an event to be explained. As a given style of deposition may recur over the longer term, it determines the geomorphic evolution of a floodplain. It has been widely established by means of field, theoretical and laboratory investigations that overbank deposits tend to become finer and thinner with increased distance from the channel ŽKesel et al., 1974; Hughes and Lewin, 1982; James, 1985; Pizzuto, 1987; Guccione, 1993; Marriott, 1996.. However, the rate of fining and thinning of overbank deposits across the width of a floodplain may differ markedly between rivers with varying channel and floodplain geometry, and thus with varying hydraulic characteristics of flood flows. Therefore, the author has developed a method which enables the mean velocity of flow in the channel and floodplain zones at a given stage to be estimated from a rating curve determined by a hydrometric survey for a given gauging section. A major flood in July 1997 in southern Poland provided an opportunity to compare the results obtained from this analytical procedure with the pattern of floodplain sedimentation resulting from the event. The purpose of this paper is to present the rationale underlying the method, and to demonstrate its utility for explaining the depositional action of flood flow and the role of a floodplain in the transfer and
retention of flood water. This is achieved by considering three cross-sections located on mountain, foothill and piedmont rivers within the upper Vistula drainage basin.
2. Field setting The study focuses on the Wadowice gauging station on the Skawa River, the Radziszow ´ station on the Skawinka River, and the Smolice station on the Vistula ŽFig. 1.. These stations relate to catchments with different geological and morphological characteristics, which are clearly reflected in the diverse hydrological regime of the rivers and morphology of their channels ŽTable 1.. The Skawa River drains the Beskidy Mts which are underlain by flysch with a high proportion of sandstone and range up to 1725 m asl. in elevation ŽFig. 1.. Its channel has a relatively steep slope and a pebble-cobble bed. Owing to its high energy and high variability of discharge ŽTable 1., the river is likely to have been characterized by a wandering gravel-bed river pattern in its natural state Žcf. Nanson and Croke, 1992.. However, repeated channelization of the river during the 20th century has resulted in the formation of a nearly straight Žsinuosity of 1.04., single-thread channel. It has incised by 2.3 m since the beginning of the century, with 1 m of the downcutting being achieved in the last dozen or so years. As a result, the floodplain which was active several decades ago has been transformed into a terrace, while narrow floodplain bands have developed on parts of the former channel bed. These bands have different elevations on either side of the channel Žsee Fig. 5A below., reflecting two main stages of channel regulation and the resulting episodes of bed degradation Žcf. Wyzga, ˙ 1993, 1996.. The gauge cross-section at Wadowice is situated half-way between two bridges in a straight reach of the Skawa River. The Skawinka is a small river draining an area of the Carpathian Foothills with hilly relief and elevations up to 545 m asl. ŽFig. 1.. Its basin is underlain by flysch bedrock with a high proportion of shales and having a cover of loess or residual loam. At the beginning of the 20th century the river was straightened in its lower course, and afterwards, to prevent
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Fig. 1. Location of the investigated gauging stations within the upper Vistula River drainage basin. Ž1. mountains of intermediate and low height; Ž2. foothills; Ž3. intramontane and submontane depressions; Ž4. uplands; Ž5. gauging stations investigated; Ž6. boundaries of the catchments of the Vistula, Skawa and Skawinka Rivers to the stations investigated.
bed degradation, several concrete drop structures were built. One of them is located about 400 m downstream of the gauging station at Radziszow ´ and this maintains the channel slope and energy of the river at relatively low values ŽTable 1.. The channel bed is formed from sand and gravel material here. As the river is characterized by a great variability of discharges, flood protection dikes have been constructed along the channel, thus considerably reduc-
ing the former floodplain width and increasing the depth of inundation of overbank flows. The Skawinka exhibits gentle bends at Radziszow ´ Žsinuosity of 1.10., and the dikes that run parallel to its channel allow water on the floodplain to flow parallel to river banks in a manner typical of quasi-straight compound channels Žcf. Sellin and Willetts, 1996.. The extent of the inter-dike zone in the study reach is 2.3 times greater than the bankfull width of the river.
Table 1 Hydrological and morphological characteristics of the Skawa River at the Wadowice station, of the Skawinka River at the Radziszow ´ station, and of the Vistula River at the Smolice station River Gauging station
Skawa Wadowice
Skawinka Radziszow ´
Vistula Smolice
Drainage area Žkm2 . Mean annual discharge Ž1961–1997.Žm3 sy1 . Mean annual flood Ž1961–1997.Žm3 sy1 . Channel slope Bankfull width Žm. Bankfull discharge Žm3 sy1 . Specific stream power at bankfull flow ŽW my2 .
835 12.7 242 0.0031 66.3 211 96.8
317 2.95 70 0.00042 20.3 48.4 9.75
6796 80.0 580 0.00016 82.8 372 6.96
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The Smolice station is located on the upper Vistula River just downstream of the junction with its tributary the Skawa ŽFig. 1.. Apart from the Carpathians, the catchment of the Vistula comprises a large percentage of lowland, and thus the discharges are much more subdued here than for its mountain and foothill tributaries ŽTable 1.. In this reach the Vistula flows parallel to the mountains through the Oswie ´ ¸cim Basin, a morphological expression of the Carpathian Foredeep. Owing to this setting, channel slope and river energy are low ŽTable 1., despite considerable shortening and narrowing of the river as a result of channelization works carried on since the second half of the 19th century ŽŁajczak, 1995.. The bed material consists of sandy gravel to pebble gravel. At the beginning of the 20th century, flood protection dikes were constructed on the floodplain with a spacing 4.5 times broader than the present-day bankfull width of the river. At the end of the 1980s a meander loop just downstream of Smolice was cutoff, the dikes relocated and the floodplain smoothed by bulldozer; as a result, this newly formed floodplain slopes toward the channel and almost lacks natural levees. The Vistula in the vicinity of Smolice now flows in gentle bends Žsinuosity of 1.10. across two-thirds of the inter-dike zone width, thus forming a typical quasi-natural compound channel Žcf. Sellin and Willetts, 1996.. The three gauging stations considered are located in unconstrained cross-sections, the geometries of which are typical of the neighbouring reaches of the rivers. At the same time, there are bridges in the vicinity of the Wadowice and Radziszow ´ stations and this allows direct flow measurements on the Skawa and Skawinka Rivers to be performed during out-of-bank conditions. The Vistula is impounded 12 km downstream of the Smolice station and the inflow to the reservoir may easily be calculated using simple hydraulic principles. Since there is no significant lateral inflow between the station and the dam, these data provide a valuable control upon the stage-discharge relationship for the Smolice station.
3. The July 1997 flood Floods on the rivers under investigation typically occur during the summer. In the first 10 days of July
1997, after a number of moderately rainy days, very heavy rain fell in the mountains of southern Poland ŽIMGW, 1997.. The greatest precipitation occurred in the upper part of the Oder River drainage basin, resulting in a catastrophic flood there. In the western mountainous part of the upper Vistula River basin, more than 200 mm of rain fell between 3 and 10 July, and in the uppermost course of the Vistula 333 mm of rain were recorded. Discharge records on the Skawinka River started in 1961, and so a common period, 1961–1997, has been chosen for evaluating the recurrence interval of the July 1997 flood for the gauging stations considered. At Smolice on the Vistula, the flood had a maximum discharge of 1440 m3 sy1 with a recurrence interval of 14 years; the river was in out-ofbank condition for 7.5 days. The peak flow of 378 m3 sy1 attained at Radziszow ´ on the Skawinka River had a recurrence interval of 18.7 years, and the floodplain was inundated there for 2.5 days. At Wadowice, the Skawa River peaked at a discharge of 725 m3 sy1 which has a 29-year recurrence interval, while bankfull stage was exceeded for slightly more than 2 days at this site. In September 1996 another major flood had occurred in the study area with a magnitude exceeding that of the July 1997 flood on the Skawinka but lower than the 1997 flood on the Skawa and Vistula Rivers. This situation is important since during the 1997 flood the rivers were already adjusted to convey high flows and no significant modification to their channels occurred.
4. The method for estimating mean flow velocity in channel and floodplain areas from a rating curve Stage-discharge curves for out-of-bank flows at gauging stations are constructed and verified using three sources of information: 1. direct flow measurements although, as mentioned in the introductory part of this paper, they may be rare or even lacking; 2. theoretical assessment of flows being conveyed in channel and floodplain zones at a given stage, based on known or predetermined values of friction slope, boundary roughness and hydraulic ra-
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dius and the assumed interaction between channel and floodplain flows; and 3. comparison of volumes of a flood wave calculated for successive stations on a river or stations located on stem and tributary streams. The third point is of special importance since, when repeated for flood waves of different magnitude, the comparison enables considerable improvement over existing rating curves. It is so because in rivers of the temperate zone, for which water infiltration into the alluvium plays a minor role, flood wave volumes should increase downstream at a rate which is in reasonable agreement with the respective increase in mean annual discharge or with the amounts of precipitation recorded in successive subcatchments. Being derived from the different, but mutually consistent data mentioned above, the resulting rating curves may yield valuable information on the hydraulics of overbank flows, providing that the
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cross-sectional geometry at a station is representative of the river reach. Flow on a floodplain is generally slower than in the channel zone. Differences in flow velocity between the floodplain and the channel zone cause interaction between the two zones and lateral transfer of momentum by which flow is accelerated over the floodplain and slowed-down in the channel zone ŽRajaratnam and Ahmadi, 1981; Knight and Shiono, 1996.. This interaction is centered over the top of the river bank where the lateral shear between the flows is at its maximum and where a line of vertical vortices develops ŽKnight and Shiono, 1996.. To approximate the effect of flow retardation in a channel zone, the channel banks with their boundary roughness are assumed to extend vertically up to the water surface. Then the relationship between mean velocity and discharge, characteristic of the uppermost part of in-bank flows, may be extrapolated for
Fig. 2. Relationship between the mean flow velocity in total cross-section Ž1., in channel zone Ž2. and in floodplain zone Ž3. of the cross-section, and discharge for the Smolice gauging station on the Vistula River during a rising phase of the July 1997 flood. Values of the mean flow velocity in channel zone are determined by linear extrapolation of the relationship characteristic of the uppermost in-bank flows, and values of the mean flow velocity in floodplain zone are calculated by the Eq. Ž1.. Q bf denotes bankfull discharge. Points represent conditions for stage changing at 10 cm intervals for the Smolice station ŽFigs. 2 and 3B. and at 5 cm intervals for the Radziszow ´ ŽFig. 4B. and Wadowice ŽFig. 5B. stations.
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the portion of the out-of-bank flows conveyed in the channel zone. With the help of a basic rule of hydraulic geometry that velocity increases exponentially with discharge ŽLeopold and Maddock, 1953.,
this can be best achieved by converting discharge to logarithmic values and simple extrapolation of a linear relationship between velocity and the logarithm of discharge for out-of-bank discharges Žsee
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illustration of this procedure for the Smolice station in Fig. 2.. Having an estimate of mean flow velocity in the channel zone, one can obtain mean velocity of flow in the floodplain, Vf , by the equation: Vf s
Q y A c Vc Af
Table 2 Mean velocity in the floodplain area as a percentage of mean velocity for the total cross-section Ž Vf r V . and of mean velocity in the channel zone Ž Vf r Vc . at the Smolice, Radziszow ´ and Wadowice gauging stations Smolice
Ž 1.
where Q is total discharge, A c and A f are cross-sectional areas of flow in channel and floodplain zones, respectively, and Vc is the mean flow velocity in the channel zone. The outlined procedure takes account of empirical observations that the conveyance capacity of a channel zone is lower, and that of a floodplain higher, than they would be in the absence of the transfer of momentum between the zones ŽWormleaton et al., 1982.. Out-of-bank channel flows are estimated here under the assumption that the interface planes between the channel zone and the floodplain are included in the wetted perimeter for the channel subarea. On the other hand, the floodplain flows are calculated as the residual values after subtracting the flow in the channel zone from the total discharge taken from the rating curve.
5. Mean velocity of total, channel and floodplain flows in the investigated cross-sections Results of applying the method are presented for the stage-discharge curves valid for the rising phase of the July 1997 flood. At the Smolice station on the Vistula River the banks differ in height by about 0.7 m, and the right-hand floodplain is divided into two levels ŽFig. 3A.. The floodplain is under grass, except for the top edge of both banks where they are overgrown with osiers. Mean flow velocity ŽFig. 3B. increased here from about 0.4 m sy1 at the lowest discharges to 1.28 m sy1 at bankfull discharge, and then remained at the same value until the right-hand
287
Q3 Q5 Q10 Q15 Q20
Radziszow ´
Wadowice
Vf r V
Vf r Vc
Vf r V
Vf r Vc
Vf r V
Vf r Vc
8.6 16.4 28.2 35.5 40.4
6.4 10.4 16.0 19.7 22.3
24.0 41.6 65.7 73.8 77.0
20.2 31.9 52.8 61.2 64.6
7.7 28.5 47.5 53.7 55.5
7.5 27.3 45.2 50.9 52.3
floodplain started to be inundated at a discharge of 480 m3 sy1 . Then, velocity fell gradually to a minimum of 1.01 m sy1 , attained when the whole interdike zone became submerged at a discharge of 1060 m3 sy1 , and afterwards increased very slowly with increasing depth of inundation. Mean velocity in the channel zone ŽFig. 3B. attained values of 1.39 m sy1 with the stage level at the right bank top, 1.75 m sy1 when water reached the toes of the dikes, and 1.87 m sy1 at the maximum discharge of the July 1997 flood. Mean velocity on the floodplain ŽFig. 3B. increased slowly with increasing out-of-bank discharges, reaching 0.35 m sy1 at the flood peak. However, intervals of slower or faster increase in velocity of the floodplain flow may be identified, the former linked with inundation of the two levels on the right-hand floodplain and the latter occurring when the submerged zone was constrained. Mean velocity in the floodplain zone was generally low at Smolice, both when considered in absolute values ŽFig. 3B., and when compared with the mean for the total cross-section and for the flow in the channel zone ŽTable 2.. At the Radziszow ´ station on the Skawinka River, the left-hand floodplain has an extent of 17 m to the toe of the dike ŽFig. 4A., and is under grass and
Fig. 3. ŽA. Pre-flood morphology of the Vistula River cross-section at the Smolice gauging station. Arrows indicate location of sediment samples, and numbers following sample symbols refer to mean grain size of the sediments in millimetres. Morphological zones of the cross-sections shown in Figs. 3A, 4A and 5A: Ž CH . channel; Ž FP . floodplain; ŽTR . terrace. ŽB. Relationship between the mean flow velocity in total cross-section, in channel zone and in floodplain zone of the cross-section, and discharge for the Smolice gauging station during a rising phase of the July 1997 flood. Symbols as in Fig. 2. Discharges are referred to their recurrence interval determined by the annual maximum series method from the years 1961–1997. An interpretation of the rating curve was continued beyond the flood peak to recognize the pattern of flow velocities for the flows of at least 20-year recurrence.
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Fig. 4. ŽA. Pre-flood morphology of the Skawinka River cross-section at the Radziszow ´ gauging station. ŽB. Relationship between the mean flow velocity in total cross-section, in channel zone and in floodplain zone of the cross-section, and discharge for the Radziszow ´ gauging station during a rising phase of the July 1997 flood. Symbols as in Fig. 2.
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289
Fig. 5. ŽA. Pre-flood morphology of the Skawa River cross-section at the Wadowice gauging station. ŽB. Relationship between the mean flow velocity in total cross-section, in channel zone and in floodplain zone of the cross-section, and discharge for the Wadowice gauging station during a rising phase of the July 1997 flood. Symbols as in Fig. 2.
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butterbur Ž Petasites .. The right-hand floodplain is 11 m in width, being overgrown with osiers. Mean flow velocity ŽFig. 4B. increased here from 0.15 m sy1 at the lowest discharges to 1.40 m sy1 at bankfull stage and to 1.48 m sy1 at the stage level with the right bank. It remained at about the same value until the left part of the floodplain became fully submerged at a discharge of 85 m sy1 . Subsequently velocity increased, slowly at first, until the whole inter-dike zone had become inundated at a discharge of 165 m sy1 , and then more rapidly, attaining 2.11 m sy1 at the peak flow of the July 1997 flood. Mean velocity in the channel zone ŽFig. 4B. attained 1.71 m sy1 when the left-hand part of the floodplain became submerged, 2.07 m sy1 with the flow covering the whole of the inter-dike zone, and 2.51 m sy1 at the flood peak. At the same time, mean velocity on the floodplain ŽFig. 4B. increased at quite a high rate to a value of 1.61 m sy1 when the 1997 flood was at its maximum. This rate was apparently increasing after water had reached the toe of both dikes. At the Radziszow ´ station the mean velocity of the floodplain flow attained high values in relation to the mean for the total cross-section and for the flow in the channel zone ŽTable 2.. At the Wadowice station on the Skawa River the floodplain on the left side has a width of 12 m and that on the right side is a strip only a few metres wide ŽFig. 5A.. The left-hand floodplain is overgrown with grass and butterbur while a thicket of osiers and Japanese knotweed Ž Reynoutria japonica. occurs along a bounding slope of the terrace. Here mean flow velocity ŽFig. 5B. increased rapidly with increasing in-bank flows up to 2.06 m sy1 at bankfull discharge, and then at a slower rate, attaining 2.38 m sy1 at a discharge of 525 m3 sy1 just before water started to cover the terrace. Afterwards, it grew very slowly, reaching a maximum of 2.46 m sy1 at a discharge of 685 m3 sy1 . Finally, with water spreading more rapidly across the terrace, it diminished slightly to 2.45 m sy1 at the maximum discharge of the July 1997 flood. Mean velocity in the channel zone ŽFig. 5B. was only marginally greater than the mean for the total cross-section, reflecting the limited proportion of the flow conveyed on the floodplain ŽFig. 5A.. It amounted to 2.50 m sy1 at the onset of the inundation of the terrace and to 2.65 m sy1 at the flood
peak. Flow on the floodplain was initially slow, but after its width became constrained by the terrace slope at a discharge of 270 m3 sy1 , mean velocity on the floodplain ŽFig. 5B. increased rapidly up to 1.12 m sy1 at the start of submergence of the terrace. Afterwards, mean velocity in the extra-channel area grew at a much slower rate, attaining a maximum value of 1.37 m sy1 at a discharge of 685 m3 sy1 and finally decreasing to 1.31 m sy1 at the peak flow of the 1997 flood. At Wadowice the mean velocity of the floodplain flow was relatively high when viewed in absolute values, but somewhat lower than that on the Skawinka River when compared to the mean for the total cross-section and for the flow in channel zone ŽTable 2.. 6. Depositional patterns and changes to floodplain vegetation resulting from the July 1997 flood The analysis presented in the previous section indicates that considerable differences exist between the individual gauging sections with regard to the velocity of floodplain flow ŽFigs. 3B, 4B and 5B. and to the relationship between mean flow velocity in the channel and on the floodplain ŽTable 2.. To verify whether these theoretically predicted patterns of flow velocity are consistent with the depositional patterns and the changes to vegetation in the floodplain resulting from the July 1997 flood, field observations were undertaken at these cross-sections a few days after the event. Sediment samples were collected across one side of the floodplain at each station and the grain size distributions were determined using sieving or hydrometer analyses. One type of analysis Žhydrometer. has been employed for all samples from the Radziszow ´ and Wadowice stations but both types had to be applied to samples from Smolice where considerable variation in sediment grain size across the floodplain was evident. On the basis of the analysis described above, a marked contrast in mean velocity of flow occurred between the channel and floodplain areas at the Smolice station on the Vistula River, the flow on floodplain being slow even at the flood peak ŽFig. 3B.. This suggests a strong velocity gradient across the floodplain width, that should have resulted in rapid deposition near the bank of the majority of the sediment carried in suspension into the floodplain
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Fig. 6. Natural levee deposits on the left-hand floodplain of the Vistula River at Smolice. A sand ridge, formed from the coalescing sediment shadows developed behind the clumps of osiers, is visible proximally to the river bank.
area, and in considerable differences in thickness and grain size between proximal and distal overbank deposits. In fact, exactly such a pattern was found in the field, when six sediment samples were taken from the left-hand side of the floodplain ŽFig. 3A.. Near to the river bank a zone of levee deposition, about 25 m wide, occurred ŽFigs. 6 and 7.. Near the bank a sand ridge developed, 4 m wide and concordant with an older form. The flood deposits were up to 30 cm in thickness there and showed large-scale, chevron-like cross lamination. They formed sediment shadows developed behind clumps of osiers ŽFig. 6., typical of natural levees overgrown with trees or bushes ŽTeisseyre, 1989.. Further away from the bank the levee deposits were 15–20 cm thick and showed either megaripples, 10 cm high, or ripples on the surface ŽFig. 7.. On the lee side of the ripples there were accumulations of grains of Carboniferous coal ŽFig. 7. which form an admixture of anthropogenic origin in the bed material of the upper Vistula River
ŽRutkowski, 1986.. Laterally the levee deposits terminated sharply at low avalanche slopes ŽFig. 7.. The levee deposits Žsamples A–C. were mediumgrained, well sorted sands with a narrow range of mean size Ž Mz s 1.89–1.60 f Ž0.27–0.33 mm.. and standard deviation Ž s I s 0.39–0.44 f . values. These features resulted apparently from transport in traction before final deposition of the sediments. At a distance of 40 m from the river bank silty sands were found Ž Mz s 3.85 f Ž0.069 mm., sample D., giving way to muds Ž Mz s 5.72 f Ž0.019 mm., sample E. 20 m further away, and to clayey muds Ž Mz s 6.64 f Ž0.01 mm., sample F. 90 m from the bank. Simultaneously, these deposits were rapidly thinning laterally from about 5 cm at the location of sample D to merely 0.5 cm near sample F. Close to the dike toe only a film of sediment on grass blades could be observed. The deposits formed outside the levee Žsamples D–F. were characterized by a very poor sorting Ž s I s 2.30–2.68 f ., typical of the sediment falling out from suspension.
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Fig. 7. Natural levee deposits on the left-hand floodplain of the Vistula River at Smolice. Ripples are seen on the sediment surface in the foreground while megaripples in the background. Black spots on the lee side of some ripples are accumulations of clasts of Carboniferous coal. Note the sharp boundary between the zone of levee deposits and the remaining part of the floodplain where standing grass is visible.
Grass blades and stems of herbaceous plants were bent down to the ground within the zone of levee deposits and at a distance of a few metres from it, but further within the floodplain they were standing without any evidence of mechanical damage from the current ŽFig. 7., thus testifying to the low velocity of the floodplain flow at Smolice. At the Radziszow ´ station on the Skawinka River five sediment samples were collected across the left-hand side of the floodplain ŽFig. 4A.. The width of the floodplain is equal to about one channel width, similar to the distance between the extreme samples on the Vistula River floodplain at the Smolice station. At both these sites the floodplain is confined by flood protection dikes, its surface slopes similarly towards the channel, and the river gradient and the calibre of bed material are also comparable. However, the manner in which overbank deposits on the Skawinka River floodplain vary laterally is different from that on the floodplain of the Vistula River. Overbank deposits at Radziszow ´ were represented by muds, the mean size decreasing by only a factor
of two across the whole floodplain width from 5.21 f Ž0.027 mm. at the bank top Žsample A. to 6.06 f Ž0.015 mm. at the toe of the flood protection dike Žsample E.. Sediment thickness diminished from about 6 cm near the bank to 0.5 cm at the most distal position. All the floodplain sediments were very poorly sorted Ž s I s 2.18–2.60 f ., however, no trend in this parameter was visible here. Thus, overbank deposits at Radziszow ´ were generally thin and showed minor changes in thickness, mean size and sorting with increasing distance from the channel. Such a pattern accords with the high velocity of floodplain flow postulated by the theoretical calculations ŽFig. 4B. and proven by the grass and butterbur being bent down to the ground here. This high velocity resulted apparently from the close spacing of the dikes that considerably confine the floodplain width. With little difference in velocity of flow between the channel and floodplain ŽTable 2., no suitable conditions occurred for rapid deposition of suspended sediment near the bank and for pronounced levee formation. In fact, at the flood crest
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Fig. 8. Downstream view of the Skawa River and its left-hand floodplain at Wadowice. The location of the gauging section on the floodplain is indicated by white arrows marking the bank top and the toe of a terrace. Note osiers bent down to the ground on the floodplain immediately upstream of the gauging section.
the flow was too fast over the whole floodplain to allow deposition of any grains in the size range found in the overbank deposits Žcf. Sundborg, 1967.. Four sediment samples were taken across the left-hand side of the floodplain of the Skawa River at Wadowice ŽFig. 5A.. The sediments ranged from silty sands on the bank top Ž Mz s 3.68 f Ž0.078 mm., sample A. to silts 4 m from the bank Ž Mz s 4.68 f Ž0.039 mm., sample B., and to muds at two distal locations Ž Mz s 5.80 f Ž0.018 mm. for sample D.. They were poorly sorted with standard deviation values, s I , increasing from 1.53 f near the bank to 2.00 f near the slope of the terrace. Although the spatial changes in grain size and sorting were relatively minor at Wadowice, the narrowness of the Skawa River floodplain and the considerable changes in vegetation density across its width make it difficult to compare this reach with those on the other rivers investigated. Importantly, the thickness of overbank deposition was relatively low, amounting from 6–7 cm near the
bank to about 1.5 cm near the slope of the terrace. Also here the flow must have been too fast at the flood crest to allow deposition on the floodplain. This high flow velocity is confirmed by the considerable damage to floodplain vegetation, not only herbaceous plants but also osiers growing upstream from the gauging section, which were bent down and aligned parallel with the current ŽFig. 8.. 7. Evaluating the role of the floodplain in conveyance and retention of flood water With the distribution of flow between the channel and floodplain areas established, the role of the floodplain in conveyance and retention of flood water at given discharge levels can be evaluated. This is undertaken here using a diagram developed by Bhowmik and Demissie Ž1982. in which the ratio of flow area on the floodplain to the total flow area is plotted against the ratio of discharge on the floodplain to the total discharge ŽFig. 9..
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Fig. 9. ŽA. Relationship between the ratio of floodplain-flow area to total cross-sectional area and the ratio of discharge over the floodplain to total discharge for the Smolice station on the Vistula, the Radziszow ´ station on the Skawinka River, and the Wadowice station on the Skawa River. The relationship for each station is determined up to the highest flow from the period 1961–1997. ŽB. Expanded view of the relationship for the Wadowice station. Flows of given recurrence interval are indicated.
In this diagram the 458 line depicts conditions in a river cross-section with uniform resistance and an ideal flow distribution, where discharge increases proportionally to the cross-sectional area of the stream. The cross-sectional area of flow in a floodplain zone may be subdivided into two imaginary components: one in which water would flow with the same mean velocity as in the channel zone, and the second in which water would remain motionless and thus be temporarily retained in the floodplain. The former would take the same percentage of the total cross-sectional area as is the percentage of the total flow conveyed in the floodplain zone. The latter, determining the retention potential of the floodplain in the cross-section, is thus read on the diagram as a vertical distance between a given point and its projection on the 458 line. When flow spreads onto the floodplain surface, water is stored dominantly in the overbank section, this being represented by points increasingly deviating from the line of proportionality on the diagram. With growing depth of inundation, flow becomes faster in the overbank section. Then the role of the floodplain in carrying flood water increases, and both the floodplain and the channel tend towards conditions of a single conveyance channel with uniform characteristics; this being shown by points approaching the 458 line on the diagram. It is apparent that the floodplain of the Vistula at Smolice acts mainly as a storage reservoir at low out-of-bank flows ŽFig. 9A.. Its retention potential rapidly increases up to the flow with a 6.5-year return period and then remains at the same, high level. Only when flow exceeds that of the 12-year return period, does the floodplain start to slowly approach the conditions of a conveyance channel. The floodplain of the Skawinka River at Radziszow ´ is more efficient in conveying flood water than the Vistula floodplain ŽFig. 9A.. Its retention potential increases up to the discharge with a 5-year recurrence interval, but subsequently diminishes at a rather rapid rate with an increase in the return period. In contrast, very little flood water is carried outside the channel zone of the Skawa River, and the retention potential of its floodplain at Wadowice is very low ŽFig. 9A.. The latter increases until the narrow floodplain bands on both channel sides become inundated at the flow of 7-year frequency, and
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after then remains at about the same level ŽFig. 9B.. The retention potential of the extra-channel zone increases again after water starts to spread rapidly onto the terrace, at a discharge corresponding to the 14-year return period.
8. Discussion The characteristics of the spatial patterns of overbank deposition and of the changes to floodplain vegetation resulting from the July 1997 flood has confirmed, in a qualitative sense, the predicted patterns of flow velocity in the channel and floodplain zones in the sections considered. This confirms the method as a useful tool in determining hydraulics of out-of-bank flows; however, some points concerning its application need to be discussed. Most importantly, the method is not the simple reverse of a theoretical calculation, using flow formulae such as the Manning equation, of the discharge conveyed in channel and floodplain areas at a given stage. Although such a calculation may be performed for any river cross-section with unknown accuracy, stage-discharge curves for gauging stations offer a relatively high degree of confidence which derives from direct flow measurements Žoccasional. and comparison of flood wave volumes at successive stations Žroutine.. However, even with a correctly established rating curve the conveyance of both zones will differ from that calculated by the Manning equation owing to the momentum exchange, and a successful determination of the flows Žand thus of their mean velocity. will depend on the proper recognition of the degree of interaction between channel and floodplain flows ŽKnight and Shiono, 1996.. The theoretically predicted values of flow velocities which have been confirmed by the patterns of floodplain sedimentation and vegetation damage tests are the velocities at the flood crest. Laboratory tests have shown that using vertical divisions between channel and floodplain areas, and including the vertical interface planes in the wetted perimeter for the channel subarea, provides predictions close to the actual values of discharge at relatively high depths of floodplain inundation, but underestimates floodplain flows at low depths ŽWormleaton et al., 1982.. This
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would cast doubt on the reliability of the method proposed at shallow floodplain flows in compound channel morphologies where water rapidly expands over a flat, wide floodplain after exceeding the bankfull stage, as was the case in the experiments of Wormleaton et al. Ž1982.. Finally, it needs to be emphasized that relating the pattern of overbank deposition to the reconstructed pattern of flow velocity may be successful only for such floodplain morphologies where sediment particles settle from water which can flow freely in the downvalley direction. In contrast, all particles present in the water column become deposited where water is ponded in closed depressions on a floodplain, and this distorts the link between the hydraulics of floodplain flows and the spatial pattern and rates of overbank sedimentation in these localities.
9. Concluding remarks The method presented permits the mean flow velocity in the channel and floodplain to be estimated for a given total discharge taken from a stage-discharge curve. This method benefits from the information concerning discharges carried in the total cross-section which is contained in the rating curve. Out-of-bank channel flows are estimated under the assumption that the interface planes between the channel zone and the floodplain are included in the wetted perimeter for the channel subarea, and thus the relationship between velocity and discharge, characteristic of the uppermost in-bank flows, is extrapolated for out-of-bank flows conveyed in the channel zone. The floodplain flows are then calculated as the residual values after subtracting the flow in the channel zone from the total discharge. To test the reliability of the method, patterns of flow velocity during a major flood of July 1997 have been determined for three river cross-sections in different settings within the upper Vistula drainage basin and compared with the patterns of floodplain sedimentation resulting from the event. High rates of thinning and fining of overbank deposits across the floodplain have been observed for the piedmont Vistula River characterized by a marked contrast in mean velocity between the channel and floodplain
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flows. On the mountain Skawa River and the foothill Skawinka River mean velocity of the floodplain flow was high, both in absolute values and when compared with that of the channel flow; overbank deposits at these sites were generally thin and showed minor changes in thickness, mean size and sorting with increasing distance from the channel. As the theoretically predicted patterns of flow velocity conform with the hydraulic conditions required to produce the described depositional patterns, the method proves useful for determining the hydraulics of outof-bank flows. Recently two-dimensional finite element and finite difference techniques have been proposed to model the spatial pattern of floodplain flows ŽBates et al., 1992. and of overbank sedimentation on floodplains ŽNicholas and Walling, 1995.. Although such techniques can successfully predict these phenomena, both require a detailed knowledge of the surface morphology of the floodplain before an event, and thus their usefulness seems limited to well documented, small floodplains. On the contrary, the present method is based on data available from a hydrometric survey and seems useful for rapid assessment of hydraulic conditions for numerous gauging sections during a flood. Thus, the method could be employed for predicting or explaining the patterns of sedimentation on floodplains, provided that crosssectional geometry at a station is representative of the river reach. The results obtained by the method can also be used to evaluate the role of the floodplain in conveyance and retention of flood water. It has been shown that the floodplain of the Vistula acts mainly as a storage reservoir at low out-of-bank flows but its efficiency in carrying flood water increases when flow exceeds that with a 12-year return period. On the other hand, the retention potential of the Skawa floodplain is very low but storage increases after water starts to spread rapidly onto the higher terrace at a discharge of 14-year recurrence interval. A lesson about the interdependence of the crosssectional geometry of a stream and the hydraulic characteristics of flood flows can be drawn from the cases considered in this paper. It is well known that the velocity of flow through a cross-section depends on the cross-sectional geometry. The inter-dike zone at Radziszow ´ is considerably narrower than that at
Smolice when compared with the channel width at these stations; as a result, the velocities of floodplain flow are much higher at Radziszow ´ and the retention potential of the Skawinka floodplain is lower than that of the Vistula floodplain. However, it is less commonly appreciated that the hydraulics of flood flows determine the cross-sectional geometry of a river in its channel and floodplain areas. This relationship manifests itself in the influence exerted on the geomorphic evolution of a floodplain by a given character of overbank deposition. It has been shown above that the considerable difference in mean velocity between channel and floodplain flows at the Smolice station resulted in the deposition of a thick layer of natural levee sediments. A persistence of such a depositional style should lead to rapid aggradation in the area of the natural levee and to a formation of floodplain surface sloping towards marginal flood basins. Indeed, high rates of aggradation of the natural levees of the Vistula in the 20th century have been documented in the Oswie ´ ¸cim Basin ŽMacklin and Klimek, 1992. as well as in the other reaches of the upper course of this river ŽŁajczak, 1995.. On the other hand, investigations carried out by the present author in the Raba valley identified a considerable increase in mean velocity at a given discharge ŽWyzga, ˙ 1993. and a concomitant marked reduction in the rate of overbank sediment accretion ŽWyzga, ˙ 1991. that resulted from channelization and the subsequent incision of this river. The analysis of the pattern of flow velocity at the Wadowice station presented above shows that velocities are high not only in the channel zone but also over the narrow floodplains formed as a result of the incision of the Skawa River. In such a river reach sediment transported in suspension is carried downstream and even many floods may have a negligible depositional effect on the floodplain there.
Acknowledgements Free access to data of the Hydrologic Survey is kindly acknowledged, and I thank all of the staff of the Survey who helped me in gathering information on the course of the 1997 flood in the investigated cross-sections. Thanks are also due to Victor R.
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