Flood estimation from channel size: guidelines for using the channel-geometry method

Applied Geography (1992), 12,339-359

Flood estimation from channel size: guidelines for using the channel-geometry method Geraldene Wharton Department of Geography, Queen Mary and Westfield College, University of London, Mile End Road, London El 4NS, UK Abstract A fundamental requirement of hydrology is the estimation of flood discharges at ungauged river sites. Although a catchment-based approach has often been used, channel dimensions have been shown to be valid indicators of flood flow characteristics. The channel-geometry method of indirect flood estimation was first developed and applied in the US by the US Geological Survey, but success has also been reported for rivers in New Zealand, northwestern Italy, Britain, Java and Burundi. Channel-geometry equations are developed by relating flood discharges, measured at gauging stations, and channel dimensions, measured from natural river reaches in the vicinity of the gauge. Flood discharges can then be estimated at ungauged locations on natural streams from measurements of channel size. This paper gives guidelines for applying the channel-geometry method and describes the development of channel-geometry equations for British rivers. Since 1970, the need to proceed towards applications of physical geography has been widely advocated (see, for example, Chandler 1970; Douglas 1972; Jones 1983 and Gregory 1985: 188). Progress toward more relevant research has focused particularly upon strategic or ‘applicable’ topics. However, it is increasingly necessary that research yields specific results that can be used directly for applied purposes, that potential clients are identified and that research is communicated in a meaningful way (Roepke 1977). Guidelines are presented in this paper for estimating flood discharges from river channel dimensions and are the outcome of research developed to be in an explicitly applied form. Flood estimates are required for the scientific study of flooding and the design and appraisal of a variety of engineering works, including dam spillways, bridges and flood protection schemes. The installation of a gauge to measure streamflow is very costly and time consuming, with the result that data relate to only a small proportion of channel reaches. In Britain, the network of continuous gauging stations is particularly inadequate for low-discharge streams and an improvement in this situation seems improbable since the number of gauging stations is now stabilizing. Elsewhere the lack of instrumented stations is more acute. In the absence of a gauging station it may also be impossible to measure flood discharges directly because of the lack of access to the site, shortage of manpower, or inadequate advance notice of the flood. Therefore, considerable research effort has been devoted to the development of reliable indirect techniques of flood discharge estimation. Traditional indirect methods include: the extrapolation of streamflow records from the nearest gauged catchment; regression-based techniques, employing climatic and drainage basin explanatory variables; slope-area methods; and 0143-6228/92/0310339-210

1992 Butterworth-Heinemann

Ltd

340

Flood estimation from channel size

physically based hydrological models. Extrapolation of streamflow records is often impossible simply because no gauged catchments are available in a sufficiently proximate suitable location, while differences in the size or character of nearby catchments may preclude extrapolation even when records exist. The regressionbased ‘catchment approaches’ represent a progression from the rational formula (an empirical relation between a flood discharge characteristic, drainage basin area and a measure of precipitation intensity) but the precision of the estimates is improved by the inclusion of carefully selected catchment and climatic characteristics. The approach culminated in the UK with the production of the Flood studies report (Natural Environment Research Council 1975; see also Newson 1978 and Archer 1981), although many similar methods have been devised (for example, Thomas and Benson 1969). More recently, Beven and Wood (1983) have used measures of runoff-contributing areas and controls upon runoff production to predict flood frequency characteristics, but such drainage basin parameters are more time consuming to derive. Slope-area methods have been widely used and are based on hydraulic equations that relate discharge to the water-surface profile, channel geometry and channel roughness. To estimate flood discharges, surveys of flood peak profiles along a uniform channel reach are required, as well as cross-sectional surveys and estimates of the Manning roughness coefficient (Riggs 1985: 39). A major difficulty is the need to select the roughness coefficient subjectively. Field experience is desirable, though guidance can be obtained from Barnes (1967). Further difficulties may result from inaccuracies in measuring other variables in the Manning equation, leading to inconsistencies in the verified roughness coefficients. A simplified slope-area method has been developed by Riggs (1976) to overcome these problems. Discharge is related to cross-sectional area and to water-surface slope, but a roughness coefficient is not used because, in natural channels, roughness and slope are related. Physically based hydrological models of varying complexity have been combined with flow-routing procedures to provide detailed estimates of the full range of flows for ungauged sites. The models are based on theories for routing hillslope runoff through a channel network based on the geomorphology of a catchment (Rodriguez-Iturbe and Valdes 1979; Gupta et al. 1980; Wang et al. 1981; RodriguezIturbe et al. 1982). The resulting geomorphological unit hydrographs can be combined with a model of runoff production to derive a distribution of flood peaks. More recently, Beven (1987) has developed a topography-based model of catchment hydrology (TOPMODEL). One of the obstacles to the widespread use of such physically based hydrological models is their huge data requirements and, in some cases, it may prove a lengthy and costly procedure to obtain flood estimates. The hydrological modelling approach is unnecessary if the hydrograph is not required. An alternative approach, the channel-geometry method, employs river channel dimensions alone to estimate flood discharges at ungauged sites. Research on the interrelationship of stream channel geometry and river discharge, particularly studies which have employed channel dimensions as independent variables to estimate parameters of the discharge regime, provided the basis for the channel-geometry method (Wharton et al. 1989): Progress in the estimation of flood discharges from channel size has been largely achieved in the US by the Geological Survey (USGS) (for example, Hedman 1970; Hedman et al. 1972, 1974; Scott and Kunkler 1976; Riggs 1978; Osterkamp and Hedman 1979, 1982; Webber and Roberts 1981; Hedman and Osterkamp 1982; Omang et al. 1983a, 1983b and

Geraldine Wharton

341

Wahl 1983, 1984) and is considered an operational technique by the Water Resources Division of the USGS (Riggs 1978). However, success has also been reported for New Zealand (Mosley 1979), northwest Italy (Caroni 1982), Britain (Wharton et al. 1989), Java (Tomlinson 1990) and Burundi (Tomlinson 1991). As a reconnaissance method for indirect flood estimation, a greater degree of confidence can be placed in the channel-geometry method than the more traditional climatic and catchment-based approaches (Osterkamp and Hedman 1979). This is because the channel cross-section is sensitive to the combined effect of a range of catchment characteristics and its size at a specific location reflects the way in which the drainage basin characteristics translate the storm inputs into a range of channel-controlling discharges experienced at the channel cross-section (Wharton et al. 1989; see also Pickup 1976; Pickup and Warner 1976; Pickup and Rieger 1979). This adjustment of cross-sectional dimensions to accommodate the discharge and sediment load supplied from the drainage basin takes place within the additional and more local constraints of the boundary (Knighton 1987). Unlike the more traditional and relatively sophisticated approaches, therefore, the channel-geometry method is not hampered by the need for numerous input data, some of which are highly variable with time. Also, because the method is based on channel rather than basin characteristics, it provides discharge estimates more closely related to the measured variables (Osterkamp and Hedman 1982). The channel-geometry method also represents an improvement over slope-area methods because it avoids the need for slope and roughness estimates. The accuracy of the channel-geometry method depends upon the consistent measurement of river channel dimensions and the use of appropriate equations. The purpose of the following guidelines is to describe how channel-geometry relations are defined and to present equations developed for British rivers, to give standardized procedures for obtaining the necessary channel-geometry data, and to discuss the selection of appropriate equations for the computation of specific flood discharges.

Guidelines

for using the channel-geometry

method

Preliminary guidelines (Wharton 1989a, 1989b) were drafted to attract suggestions, either about the general approach or the detailed procedures of the channelgeometry method, and were circulated to the National River Authority regions in England and Wales; the River Purification Boards in Scotland; the Drainage Division, Department of Agriculture, Belfast; and to water engineers and scientists and fluvial geomorphologists in Britain, the US, Canada, Italy, New Zealand and Australia. The following revised guidelines were then prepared. Developing channel-geometry

equations

The channel-geometry method is based upon the assumption that channel dimensions and a measure of discharge are related by a power function (Osterkamp 1978). Although the technique has its origins in the downstream hydraulic geometry concept (Leopold and Maddock 1953), in channel-geometry studies discharge characteristics are related to channel dimensions measured at a standard geomorphic reference level recognizable at all sites, such as bankfull, rather than at the highly variable water surface. This requires the accumulation of streamflow

342

Flood estimation from channel size

data from gauging stations and channel dimensions, measured from natural reaches in the vicinity of the gauge, to develop equations of the form: Q = aWb

and

river

Q = cAd

Q is some measure of streamflow, such as the mean annual flood; and Wand the channel width and cross-sectional area, respectively, measured at a specified geomorphic or channel-geometry reference level. The coefficients (a and c) and the exponents (b and d) are estimated numerically from the data. Velocity cannot be measured when using the level of a geomorphic feature to evaluate flow characteristics and, although mean channel depth can be measured and related to discharge, the variability of channel profiles and the capacity for measurement error commonly lead to unreliable results. Thus, most channel-geometry equations are limited to relations between discharge and channel width or channel cross-sectional area. Flood discharges can then be estimated at ungauged locations from these measurements of channel size. Before channel-geometry equations are developed and applied consideration must be given to the type of stream being measured, the discharge parameter being estimated, and the regional conditions of climate, geology and topography (Hedman and Osterkamp 1982), because these factors influence the accuracy of the flood discharge estimates. The method is most suited to perennial streams with stable banks that are not easily widened by peak discharges, such as upland streams with coarse armour or lowland streams with well-vegetated banks formed largely of cohesive silt and clay. Conversely, channel geometry is less likely to provide accurate flood estimates for flashy streams, including ephemeral streams, that have non-cohesive banks and lack a well-developed growth of riparian vegetation. Osterkamp and Hedman (1979) anticipated that, for many streams, estimates of the five- or ten-year flood from the channel-geometry method are often as reliable as those based upon five to ten years of streamflow records. However, the method seems to be less accurate when estimating highly infrequent peak flows, but this cannot be completely substantiated because the recurrence interval of rare flood events cannot be estimated accurately from most gauging station records. Evidence suggests that rivers with a wide range of peak flood discharges are susceptible to changes in form and should exhibit transient features (Stevens et al. 197.5). A non-equilibrium channel geometry could also be the result of an extreme flood (Burkham 1972), the effects of which may last for a long time, in comparison to those of lesser events. Measurements taken from ‘non-equilibrium channels’, whose dimensions are not adjusted to present flow conditions (water and sediment discharge), will therefore provide inaccurate discharge estimates. The accuracy of channel-geometry equations (as indicated by the standard errors of estimate) is determined by the quality of the streamflow and the channelgeometry measurements. The experience of the person collecting the channel dimension data is thus crucially important and Wahl(l976, 1977) reported on a test undertaken in northern Wyoming to determine how consistently untrained individuals could measure channel geometry. Guidance on the selection of reaches and cross-sections and the measurement of channel dimensions aims to minimize such error. To achieve reliable measurements of channel size, the channelgeometry reference level must be chosen consistently. Three reference levels are commonly used by workers in the US: the bankfull level, the active-channel level and the depositional-bar level (Fig. la). The depositional-bar and active-channel reference levels are ‘in-channel’ reference levels suggested by W.B. Langbein in 1966 (Osterkamp and Hedman 1982: 2). where

A are

Geraldine

Wharton

343

active floodplain

Bankfull

(C - C’)

Active

channel

(8 - B’)

DepositIonal

bar (A - A’)

a

lower limit of

--_-

Bankfull

level (X - X’)

------

OvertoppIng

level (Y -Y’)

b Figure 1. Channel-geometry reference levels: (a) reference levels commonly used by the United States Geological Survey Water Resources Division (after Hedman and Osterkamp 1982); (b) reference levels used to develop channel-geometry equations for British rivers

344

Flood estimation from channel size

The depositional-bar level (A-A’ in Fig. la) is useful for channels with well-graded sediment and well-developed depositional bars. However, it was not used in developing channel-geometry equations for British rivers because it is not applicable to the full range of natural river types in Britain and the average elevation of the highest surfaces of the channel bars has been employed by some workers to define bankfull (Wolman and Leopold 1957; Hickin 1968; Lewis and McDonald 1973). The active-channel level (B-B’ in Fig. la) was used by Hedman et al. (1974) to determine flood frequency discharge and later described by Osterkamp and Hedman (1977: 256). However, for many channels in humid areas, and rivers whose flow regime is baseflow dominated, the active-channel level and bankfull level may coincide. To avoid inconsistencies in reported channel dimension values this level was also not used to develop British equations. Bankfull (C-C’ in Fig. la) has been employed by many workers (for example, Wolman and Miller 1960; Woodyer 1968; Andrews 1980), while others have taken measurements at the top of the ‘main channel’ (Riggs 1974) or ‘whole channel’ (Riggs and Harenberg 1976). Williams (1978) has discussed 11 possible definitions of bankfull used by various investigators (see also Riley 1972) and Gregory (1976a, b, c) has employed lichenometry in bankfull determination along compound and bedrock channels. Field identification of bankfull should be based upon a combination of definitions. However, the level of the active floodplain is probably the most meaningful for the recognition of the bankfull channel-geometry reference level. An active floodplain is an overflow surface that is periodically constructed and possibly eroded by the river but is undergoing net growth during the ‘present time’ (past 10 years or so). In some areas the active floodplain may be the valley flat, whereas in others it may be a narrow (1 to 3 m wide), rather inconspicuous overflow surface some metres lower than the valley flat and contained within the banks of the latter. (Williams 1978: 1141) A primary concern in developing British channel-geometry equations was that the selected reference levels should be recognizable along the full range of natural river types. Two channel-geometry reference levels were finally employed and recommended for future use: the bankfull level, defined as the level of the active floodplain; and the level of overtopping, defined as the level of incipient flooding or the top overflow surface (Fig. lb). These two reference levels coincide for many rivers. However, in incised channels the level of the active floodplain will be at a lower elevation than the stage at which overbank flooding occurs. Along such rivers the discharge which just fills the channel to the tops of the banks, and hence marks the condition of incipient flooding, is termed the overtopping discharge rather than the bankfull flow. The use of these two reference levels was also proposed to facilitate the use of archive channel dimensions to calculate flood discharges. Cross-sections from archive sources rarely depict the channel morphology in sufficient detail to permit the recognition of the active floodplain where this is not also the main overtopping surface. Thus, channel dimensions from archive cross-sections may be measured consistently using the level of overtopping. British equations

Channel-geometry equations were developed from sites throughout Britain, yielding a representative sample of the range of natural river types. As many sites as possible were used to extend the range of hydrologic, geologic, topographic and climatic conditions sampled. The locations were selected according to criteria relating to both the flood flow characteristics and the channel morphology.

Geraldine Wharton

345

Gauging stations were selected only from those 643 UK stations possessing annual maximum flood peak data, held in the Surface Water Archive, and the highest stage-discharge rating curves (graded A or B as defined in the Flood studies report (Natural Environment Research Council 1975). All the selected stations possessed at least five years of flood peak data, and most stations at least 15 years, when the preliminary analysis commenced in 1987. They also had no artificial modification of the flow regime so that flood peaks are unaffected and, most importantly, the river channel was not modified by channelization (see Brookes 1985,1988: 5; Brookes et al. 1983). River reaches were excluded from consideration if they had undergone resectioning, realignment, embanking, bank protection, or clearing of vegetation and debris to such an extent that channel dimensions were affected. The feasibility of establishing channel-geometry equations for flood discharge estimation in Britain was investigated using channel cross-section and river flow data retrieved from records held by the Surface Water Archive at the Institute of Hydrology. This preliminary analysis (Wharton et al. 1989), which demonstrated the potential of the channel-geometry method in Britain, was followed by an extensive field survey programme and further retrieval of channel dimension data from archive sources (water authorities and river purification boards). This resulted in 75 sites possessing field-surveyed data and 109 sites possessing data from archive sources finally being available. For each channel cross-section, extracted from archive sources or surveyed in the field, the following channel dimensions were calculated at the selected channel-geometry reference level (bankfull or overtopping): channel width (W), channel cross-sectional area (A) and mean channel depth (D). Where more than one channel cross-section was available per river gauging station site, the channel dimensions were determined for each cross-section and arithmetic mean values computed. The flood characteristics which were calculated from annual maximum flood peaks were selected as the mean annual flood (Q,,) and the floods with return periods of 1.5 and 5 years (Q,.s and Qs respectively). The mean annual flood was calculated as the arithmetic mean of the annual floods and Qi.s and Q, were estimated by fitting an Extreme Value Type 1 (EVl) distribution to the annual maxima by probability-weighted moments following the recommendation of the Flood studies report (Natural Environment Research Council 1975) and Landwehr et al. (1979). However, the choice of probability model and fitting procedure is not critical at such low return periods (Wharton 1989a: 78-80). The compatibility of archive and field survey data was assessed prior to developing the channel-geometry equations for British rivers (Wharton 1989a: 158-202). Differences were revealed in the channel dimensions calculated from the two sources which could be explained by the use of different channel-geometry reference levels. Thus, two sets of channel-geometry equations were developed: the first set employed channel dimensions calculated at the level interpreted as bankfull according to detailed field survey and the identification of the active floodplain, while the second set used channel dimensions calculated for the level of overtopping according to the cross-sectional survey data contained in the archive. Figure 2 shows the location of these ‘bankfull’ and ‘overtopping’ sites. Regression equations, relating the flood characteristics as the dependent variables to the channel dimensions as the independent variables, were derived by applying linear least squares to base-10 logarithm-transformed values of the variables. Logarithmically transformed values of morphological and hydrologic data were used following the inspection of graphical plots and the need to equalize

346

Flood estimation from channel size

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Figure 2(a). Location

of sites employed

in the development ‘bankfull sites’

of channel-geometry

equations:

Note: Site numbers refer to the gauging station numbers employed in the Surface Water Archice (Institute of Hydrology) and the Flood .sfudies report (Natural Environment Research Council 1975). Gauging stations are formally archived and indexed by use of a six-digit number, such as 055010. The first three digits identify the hydrometric area in which the station is located (55); and the second three digits identify the number of the individual station (IO). This gauging station number is then expressed in

Geraldine Wharton

_. i

Figure 2(b)) Location

of sites employed in the development ‘overtopping sites’

’

of channel-geometry

equations:

the form S/10 on the location maps. It should be noted that five stations have additional information coded in the fourth digit (046806, 048902, 072804, 072807 and 084806). The digit 8 indicates an independently numbered series without continuous flow data; the digit 9 indicates that measurements have been discontinued.

348

Flood estimation from channel size Table 1. Channel-geometry

equations for British rivers

(A) Bankfull equations (75 stations) Estimating

the mean annual flood (Q,,,)

from river channel

R’ = 0.73

Q fT,<,= 0.30 W,=’ ( wfJDh)yx = 0.2YA,,“” (WhlDh)“h7 Q 17111 Estimating

dimensions:

R’ = 0.78

QrnCz= 0.20 W,,“y7 = 1.164,“” Q fV,
fsee fsee

= I.86 = 2U)

R7 = 0.80

fsee

= 1.81

R’ = @80

fsee

=

= 1.86

the I .S-year flood (8, _5)from river channel

1.81

dimensions:

Q,.,

= 0.13 Wh’.“’

R’ = 0.78

fsee

Q,+

= 0.87Ah’.-”

R’ = 0.72

fsee

= 2.04

K2 = 0.79

fsee fsee

= 1.X4 = 1.84

R’ = 0.76 R’ = 0.72

fsee fsee

= 1.86 = 1.05

R’ = 0.79 Iv = 0.79

fsee fsee

= 1.82 = 1.82

R’ = 0.83 R’ = 0.86

fsee fsee fsee

= 1.66 = 1.66 = 1 .SY

R’ = 0.85

fsee

=

Q1.5 = O.lY Wh1’3’ (W,,/D,) Q,.,

= O.lY/$,

Estimating

O’J.i

I.lh(Wh/~h)ll.7i

the 5-year flood ( QS) from river channel

Q.5 = 0.28 W,,‘-” Qs = l.ShA,+’ “’ Qs = 0.43 W~>“‘y( WhlDh)-0’52 Qq = @43A,,“”

(W,,/Dh)0.“3

R2

=

0.80

dimensions:

(B) Overtopping equations (109 stations) Estimating

the mean annual flood (Q,,,,) from river channel

12,tzti = 0.34 W<,[‘-fiX

Q ,,I,, = 1.2()&f .(u “-“l Q ,?,N= 0.56 WC,,“” ( W,,,/D,,,) Q ,,,
dimensions:

R’ = 0.83

the 1 .S-year flood (Q, .5) f.ram river channel

1.61

dimensions:

Q, _? = (1.27 W,,,““’

R’ = 0.82

fsee

= 1.66

Q,_5 = O.Y3A,,,’ “’ Q, ,s = 0.45 W 01L.U’(W 0,/D 01)-0-h7

R’ = 0.84

fsee fsee fsee

= = =

fsee fsee fsee fsee

= 1.66 = 1.68 = I.61 = 1.63

Q,.,

= 0.4YA,,‘.”

Estimating

( W<,,lD,,r)‘1-3h

the S-year flood (Q,) from river channel

Qs = 0.44 W,,,““’ Qs = l.S7A,,‘.“” l.‘)X(W,,,D,,)0.37 Q5 = 0.71 W,, Qs = O~79A,,“‘yX ( W<,,/D,,,)‘1’34 NOW: See Table 2 for list of symbols

R’ = 0.86 R’ = 0.85

I.66 1.5’) 1.61

dimensions: R’ = (I.82 R’ = Cl.82 R’ = 0.85 R’ = 0.84

Geraldine Wharton

349

the variance in the data for different values of the independent variable. Least-squares regression analysis was undertaken using the Genstut package (Alvey et al. 1982) and was performed in preference to structural analysis (Mark and Church 1977; Osterkamp et al. 1978; Williams 1983) for two main reasons: first, to achieve consistency with the catchment-based regression equations published in the Flood studies report (Natural Environment Research Council 1975); secondly, because of the problem of estimating the error associated with the independent variables which, in the case of the archive data employed in the present study, comprise channel-geometry measurements taken by many different workers over many years. (A measure of the relative errors of the dependent and independent variables is required to convert a simple regression relation to a structural relation.) In the proper use of least-squares regression analysis, all the error is assumed to be in the dependent variable and this seems a more satisfactory situation when developing a set of predictive equations for estimating flood discharges since it does not give a false impression of the predictive power of the channel-geometry relations. Table 1 gives ‘bankfull’ and ‘overtopping’ channel-geometry equations developed for natural British rivers for estimating the mean annual flood and floods with return periods of 1.5 and 5 years. Relationships between the mean annual flood and river channel dimensions calculated at the bankfull and overtopping reference levels are shown in Figs 3 and 4, respectively. The close similarity between the exponents of the equations predicting Q,,, Q1_s and Q, implies that the ratios between these floods are very consistent between sites. The equations are applicable only within the range of natural rivers for which they were developed (Table 2) because regression analyses do not define actual physical relations. The inclusion of a width-depth ratio, proposed as an index of channel character and a correction factor for boundary materials (Osterkamp and Hedman 1982), was the most profitable means of improving the predictive power of the channelgeometry equations (Wharton 1989a: 262). Sediment properties were not incorporated directly in the channel-geometry equations because this would require channel-geometry equations to be developed for various channel material subgroups and the additional measurement of sediment properties. Measurement of river channel dimensions

Once channel-geometry equations have been defined, measurements of channel size are required at the ungauged sites to estimate flood discharge characteristics. Field survey of river channel geometry is recommended. Guidelines on the selection of reaches and cross-sections and the survey of cross-sectional profiles are presented to ensure consistent measurement of the channel geometry. However, when a field visit cannot be made or when the flow conditions preclude the measurement of channel geometry, it may be necessary to utilize channel dimensions retrieved from archive sources. Advice is also given on the use of archive data. Criteria for the selection of reaches

1. Selected reaches should be natural, at least 4-5 channel widths in length, and be relatively straight or stabilized reaches of meandering channels. 2. The following reaches should be avoided (see Hedman et al. 1974; Hedman and Kastner 1977; Hedman and Osterkamp 1982):

3.50

Flood estimation from channel size Table 2. Limits of definition of the channel-geometry Parameters wh

Ah (m-1 h) W,, A,, Cm
equations

Minimum

Mean

Maximum

3.7 1.7 7.0 7.3

16.3 18.2 36.8 100.9

54.8 62.5 109.2 458.6

List of Symbols = mean annual flood (m’ SC’) flood (m’ SC’) ii; 1 1.5year return-period S-year return-period flood (m’s_‘) channel width at bankfull level (m) channel cross-sectional area at bankfull (m’) mean channel depth at bankfull, calculated as Ah/Wh (m) width-depth ratio for the bankfull level channel width at the overtopping level (m) channel cross-sectional area at the overtopping level (m’) mean channel depth at the overtopping level, calculated as A,,IW,, (m) width-depth ratio for the overtopping level coefficient of determination factorial standard error of the estimate (antilogarithm of see). (The standard error of the estimate, see. is calculated as the square root of residual sum of squares divided by the degrees of freedom.)

w:= A/, Q, WblD,, WO, A,,, D,,,

= = = = = =

R’ = fsec

=

reaches that have been widened, deepened and realigned by construction work; narrow widths; (ii) r-caches lined with riprap or concrete that have abnormally such as debris dams; (iii) reaches altered by natural linings or obstructions (iv) reaches with bedrock banks; braided reaches and reaches where active bank cutting or bar (v) excessively deposition is in the process of changing the channel width; (vi) reaches with large pools or local steep inclines. or inlets should not enter the river within the measuring 3. In addition, tributaries reach because this could cause a significant increase in discharge over the reach and a change in bankand bed-material characteristics (Schumm 1960; Knighton 1980), and because adjustments to cross-sectional form may occur abruptly at tributary junctions (Thornes 1974; Richards 1980).

6)

Criteria for the selection

of cross-sections

1. Select at least three rectangular to trapezoidal cross-sections whenever possible; cross-sections of unusual shape should not be used. 2. Selected cross-sections should be spaced at least one channel width apart and provide meaningful reach averages.

Geraldine Wharton

351

a

1000 600 400

100 z E’

60 40

E”20 0 10 6 4 .

.

2

.

0

. 0

2

4

6

10

20

40 wb

60

100

200

400 600

100

200

400 600

1000

(m)

b

1000 600 400 200 100 L? 40 60 E z 20 0 IO 6 4 2-

.

0

. 0

2

4

6

10

20

40

60

1000

An (m*) Figure 3. Relationships between mean annual flood and bankfull channel dimensions for data from the 75 sites shown in Fig. 2a (the regression equations are detailed in Table la): (a) relationship between mean annual flood (Q,,) and bankfull channel width (W,); (b) relationship between mean annual flood (Q,,) and bankfull cross-sectional area (Ah)

3.52

Flood estimation from channel size

a

1000 600 400 200 100 g 40 60 E. 2 20 a 10 6 4 2 0 0

2

4

6

10

20

40

60

100

200

400 600

l(

100

200

400 600

1000

WOt (m)

b

1000

600 400 200

5; 60

31

40

E”20 u IO 6 4 2 0 0

2

4

6

10

20

40

60

&t (m2) Figure 4. Relationships between mean annual flood and overtopping channel dimensions for data from the 109 sites shown in Fig. 2b (the regression equations are detailed in Table lb): channel width (IV,,); (b) (a) relationship between mean annual flood (Q,,) an d overtopping relationship between mean annual flood (QmR) and overtopping cross-sectional area (A,,)

Geraldine Wharton

353

3. Do not choose sections upstream

4. 5. 6.

7.

or downstream from tributaries that would change the drainage area by more than 10 per cent (Osterkamp 1988; see also Hedman and Osterkamp 1982). Select cross-sections where the channel-geometry reference level is about the same elevation on both banks and along the reach (Hedman et al. 1974). Flow velocities should be relatively symmetrical across the sections because non-uniform velocities indicate unstable channel conditions and processes such as local scour or deposition. For stabilized reaches of meandering channels, cross-sections should be located at or near points of inflexion to reduce variations in the measurement of cross-sectional geometry (see Omang et al. 1983a: 7). For reaches which exhibit weak to moderate riffle-pool sequences, se1 :ct cross-sections in the straighter intermediate sections where flow velocities do not differ greatly across the width (Osterkamp 1978). However, when the channel exhibits a well-developed riffle-pool sequence (see Richards 1976a, 1978a, 1978b), and there is no intermediate straight section in the sequence, average channel size measurements may be obtained either by selecting at least two pool and two riffle sections or by choosing cross-sections on the leading edge of the riffles. The latter is recommended when pools are very deep and are likely to provide exaggerated channel size measurements.

Field survey procedures. To achieve and refine channel-geometry relations with transfer value, these suggested instructions (or alternatives leading to exactly equivalent measures) must be followed by all field personnel collecting the channel dimension data.

1. Identify the channel-geometry reference levels by careful consideration of both channel banks over the entire length of the survey reach and with reference to Fig. lb. Bankfull is defined as the elevation of the active floodplain. The height of the lower limit of perennial vegetation, usually trees, should be used to aid bankfull determination. The overtopping reference level is the level of incipient flooding or the top overflow surface. All available evidence should be used to define the bankfull and overtopping limits of the channel. When bankfull and overtopping levels do not coincide, cross-sections should be surveyed at both reference levels to allow both sets of equations to be used for flood discharge estimation. 2. Survey the channel cross-sections with an electronic distance measurer, an automatic level or a Quickset level (see Pugh 1975). The survey line should adopt a simple shortest cross-channel distance and should be marked by a tape measure stretched from the lowest bankfull or overtopping level to the opposite bank. When channel banks are of different heights the tape should not be stretched from bank top to bank top as this results in exaggerated channel dimension measurements. 3. Take level readings several metres beyond the bankfull and overtopping limits of the channel where possible. Record the levels of the right-hand and left-hand bank edges and bank bases; the channel elevations across the channel at l-m intervals; the bank or bed elevations at points where morphological changes occur; and the water level, noting the date and time of survey. If the channel width exceeds 30 m, and the bed elevations are relatively uniform, levels may be recorded at 2-m intervals across the channel. Record all measurements in metres and to two decimal places.

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4. Take photographs of the survey reach and cross-sections. These should also show the bank vegetation, especially when vegetation limits have been used to identify bankfull. 5. If it is not possible to completely survey the channel cross-sections, take channel width measurements instead. Channel width should be measured at both the bankfull and overtopping reference levels, where these are different. Measurements may be taken using a tape measure or by optical tacheometry for larger channels. Again care should be taken to measure from the lowest bankfull or overtopping reference level to the opposite bank. 6. Plot channel cross-sections from the survey data and calculate the following channel dimensions for each profile: width (IV), cross-sectional area (A), mean depth (D = A/W) and width-depth ratio (W/D). Compute reach values as the arithmetic means of the channel dimensions calculated for each of the cross-sectional profiles. If the bankfull and overtopping levels do not coincide, calculate mean channel dimensions for both reference levels. Archive data sources. Archive information either consists of cross-sectional profiles or reported values of channel size and its use is problematic: surveys may have been undertaken by many different operators and therefore the data are likely to be inconsistent; the extent to which reported archive values reflect current channel dimensions is not known; and there is the increased difficulty of identifying the channel-geometry reference levels, Channel morphology is rarely portrayed in sufficient detail on archive sections to enable the recognition of an active floodplain (bankfull), where this is not depicted by a major break of slope and where this differs from the top overflow surface (overtopping level). Nor is archive information likely to give vegetation limits which may be used to identify the active floodplain. However, a field visit is not always possible and it is sometimes necessary to utilize channel dimension data from archive sources. In such cases, site maps or longitudinal profiles should be used to select appropriate reaches and cross-sections, as specified above, and all channel dimensions should be measured from the level of overtopping because of the problems of bankfull determination. Computation offlood discharges The following recommendations relate to the selection of appropriate channelgeometry equations and the estimation of different return period floods from river channel dimensions. Overtopping equations should be employed when channel dimensions have been retrieved from archive data or when field survey has revealed coincident bankfull and overtopping and overtopping levels at a site. The use of both bankfull equations is recommended when channel geometry has been surveyed in the field at the two reference levels to allow the comparison of flood estimates. Estimates from the bankfull and overtopping equations should closely agree, although the slightly higher value should be selected as the ‘final’ flood discharge estimate. Discrepancies in the flood estimates computed from different channel-geometry equations may result if highly irregular and unrepresentative cross-sections have been used; reselection of sites may be necessary. Equations based on channel cross-sectional area are superior to those based on channel width because a cross-sectional area value is more reliable and representative of the channel size than a single width value. For channels which exhibit a riffle-pool sequence this is particularly important: channel width may

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vary markedly from pool to riffle sections (Richards 1976b), whereas the cross-sectional area of the channel tends to remain relatively constant over a survey reach. Thus, channel width equations should only be employed when crosssectional profiles are not available. The use of channel-geometry equations which incorporate the influence of boundary materials, through an index such as the width-depth ratio (see Table l), are also recommended. Although it is possible to derive channel-geometry equations to estimate any flood discharge, the estimation of different return-period floods may be achieved by combining an estimate of the mean annual flood, derived from channelgeometry equations, with the appropriate region curve. Along British rivers the use of region curves is recommended when estimating floods with return periods greater than five years because the extent to which channel dimensions are indicative of less frequent floods is not known. Each river will have a different ‘memory’ for extreme events, determined by the fluvial history of the river and its characteristics (Wolman and Miller 1960; Schumm and Lichty 1963; Burkham 1972; Stevens et al. 1975; Wolman and Gerson 1978; Andrews 1980; Gupta 1983). In Britain, channel geometry is more indicative of the mean annual flood than it is of more unusual floods, such as the lo-year flood. Thus, Table 1 presents channel-geometry equations for estimating the mean annual flood and floods with return periods of 1.5 and 5 years. To estimate different return-period floods an estimate of the mean annual flood is combined with the appropriate region curve, presented in the Flood studies report (Natural Environment Research Council 1975, Vol. I: 172-4). The region curves are presented both graphically and numerically. A region curve has been derived for each of ten regions (hydrometric areas) in Great Britain (Natural Environment Research Council 1975, Vol. I: 122 and 334) and each of the curves makes use of any historical data which can be regarded as reliably expressed in terms of discharge. Conclusions

A variety of methods exist for the estimation of flood discharges at ungauged sites. The channel-geometry method can be particularly useful for reconnaissance purposes or in situations when traditional methods cannot be applied because, where estimating relations have been defined, channel width or cross-sectional area are the only measurements required. The equations given in Table 1 are specifically for use in Great Britain but the method is capable of development elsewhere. To date, channel-geometry equations have also been developed for many regions of the US; South Island, New Zealand; Piedmont, northwest Italy; Java; and Burundi, East Africa; and the approach is currently being tested in Ghana. The guidelines presented in this paper, for the correct application of the channel-geometry method, are the outcome of research on the channel-geometry method in Britain and the US, with the Water Resources Division of the US Geological Survey, and comments received from appropriate workers. The guidelines aim to promote wide and consistent use of the channel-geometry method for flood discharge estimation. If interregional consistency is achieved it will be possible to compare channel-geometry equations developed for the estimates of flooding in different climatic regions. Such an indirect technique of flood discharge estimation is of great applied value in view of the real constraints of cost, manpower and time involved in obtaining flood estimates from alternative methods.

3.56

Flood estimation from channel size

Acknowledgments I am indebted to everyone who helped with the production particular thanks go to Ken Gregory, Waite Osterkamp, Arnell and Paul West. I also wish to acknowledge the of Hydrology and studentship, CASE with the Institute drawing the diagrams.

of these guidelines. My Angela Gurnell, Nigel provision of a NERC to thank Ed Oliver for

References N. G., Galway, N. and Lane, P. (1982) An introduction to Genstat. New York: Academic Press. Andrews, E. D. (1980) Effective and bankfull discharges of streams in the Yampa River Alvey,

Basin, Colorado and Wyoming. Journal of Hydrology, 46, 311-330. Archer, D. R (1981) A catchment approach to flood estimation. Journal of the Institution of Water Engineers and Scientists, 35, 275-289. Barnes, H. H. (Jr) (1967) Roughness characteristics of natural channels. Washington, DC: United States Geological Survey. Water Supply Paper 1849. Beven, K. (1987) Towards the use of catchment geomorphology in flood frequency predictions. Earth Surface Processes and Landforms, 12. 69-82. Beven, K. and Wood, E. F. (1983) Catchment geomorphology and the dynamics of runoff contributing areas. Journal of Hydrology, 65, 139-158. Brookes. A. (1985) River channelization: traditional engineering methods, physical consequences and alternative practices. Progress in Physical Geography, 9, 44-73. Brookes. A. (1988) Channelized rivers: perspectives for environmental management. New York: Wiley. Brookes, A., Gregory, K. J. and Dawson, F. H. (1983) An assessment of river channelization in England and Wales. The Science of the Total Environment, 27. 97-111. Burkham, D. E. (1972) Channel changes of the Gila River in Safford Valley, Arizona, 1846-1970. Washington. DC: United States Geological Survey, Professional Paper 655-G. Caroni, E. (1982) I metodi empirici per la valutazione della portate. In Valutazione defle Piene (E. Marchi, ed.). Rome: Consiglio Nationale dell Ricerche, Conservazione del sulo, Dinamica Fluvial, Pubicazione 165. Chandler, T. J. (1970) The management of climatic resources. Unpublished inaugural lecture, University College, London. Douglas, I. (1972) The environment game. Unpublished inaugural lecture, University of New England, Armidale, New South Wales. Gregory, K. J. (1976a) Lichens and the determination of river channel capacity. Earth Surface Processes, 1, 273-285. Gregory, K. J. (1976b) Bankfull identification and lichenometry. Search 7(3), 99-100. Gregory, K. J. (1976~) The determination of river channel capacity. Armidale, NSW: Armidale New England Research Series in Applied Geography. Gregory, K. J. (1985) The nature of physical geography. London: Edward Arnold. Gupta, A. (1983) High-magnitude floods and stream channel response. In Modern and ancient @vial systems (J. D. Collinson and J. Lewin, eds), pp. 219-227. Oxford: Blackwell, International Association of Sedimentologists, Special Publication 6. Gupta, V., Waymire, E. and Wang, C. (1980) A representation of an instantaneous unit hydrograph from geomorphology. Water Resources Research, 16(5), 855-862. Hedman, E. R. (1970) Mean annual runoff as related to channel geometry of selected streams in California. Washington, DC: United States Geological Survey, Water Supply Paper 199-E. Hedman, E. R. and Kastner, W. M. (1977) Streamflow characteristics related to channel geometry in the Missouri River Basin. United States Geological Survey Journal of Research, S(3), 285-300.

Geraldine Wharton

357

Hedman, E. R. and Osterkamp, W. R. (1982) StreamfZow characteristics related to channel geometry of streams in western United States. Washington, DC: United States Geological Survey, Water Supply Paper 2193. Hedman, E. R., Kastner, W. M. and Hejl, H. R. (1974) Selected streamflow characteristics as related to active channel geometry of streams in Kansas. Kansas: State of Kansas Water Resources Board Technical Report, No. 10. Hedman, E. R., Moore, P. 0. and Livingston, R. K. (1972) Selected stream,flow characteristics as related to channel geometry of perennial streams in Colorado. Washington, DC: United States Geological Survey, Open-File Report (200), H358s. Hickin, E. J. (1968) Channel morphology, bankfull stage, and bankfull discharge of streams near Sydney. Australian Journal of Science, 30(7), 274-275. Jones, D. K. C. (1983) Environments of concern. Transactions of the Znstitute of British Geographers, NS 8, 429-457. Knighton, A. D. (1980) Longitudinal changes in size and sorting of stream bed material in four English rivers. Geological Society of American Bulletin, 91, 55-62. Knighton, A. D. (1987) River channel adjustment: the downstream dimension. In River channels: environment and process (K. S. Richards, ed.), pp. 95-128. Oxford: Blackwell. Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979) Probability-weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research, 15, 1055-1064. Leopold, L. B. and Maddock, T. (Jr) (1953) The hydraulic geometry of streams and some physiographic implications. Washington, DC: United States Geological Survey Professional Paper 252. Lewis, C. P. and McDonald, B. C. (1973) Rivers of the Yukon north slope. In Fluvial processes and sedimentation, pp. 251-271. Alberta, Canada: National Research Council of Canada. Mark, D. M. and Church, M. (1977) On the misuse of regression in earth science. Mathematical Geology, 9, 63-75. Mosley, M. P. (1979) Prediction of hydrologic variables from channel morphology, South Island rivers. Journal of Hydrology (NZ), 18(2), 109-120. Natural Environment Research Council (1975) Flood studies report. London: HMSO. Newson, M. D. (1978) Drainage basin characteristics, their selection, derivation and analysis for a flood study of the British Isles. Earth Surface Processes, 3, 277-293. Omang, R. J., Parrett, C. and Hull, J. A. (1983a) Mean annual runoff and peak f7ow estimates based on channel geometry of streams in Southeastern Montana. Washington, DC: United States Geological Survey, Water Resources Investigations, 82-4092. Omang, R. J., Parrett, C. and Hull, J. A. (1983b) Flood estimates for ungauged streams in Glacier and Yellowstone National Parks, Montana. Washington, DC: United States Geological Survey, Water Resources Investigations, 83-4147. Osterkamp, W. R. (1978) Bed- and bank-material sampling procedures at channel-geometry sites. Paper presented at the National Conference on Quality Assurance of Environmental Measurements, Denver, Colorado. Osterkamp, W. R. (1988) Personal communication. Osterkamp, W. R. and Hedman, E. R. (1977) Variation of width and discharge for natural high-gradient stream channels. Water Resources Research, 13(2), 256-258. Osterkamp, W. R. and Hedman, E. R. (1979) Discharge estimates in surface-mine areas using channel-geometry techniques. Paper presented at the Symposium on Surface Mining Hydrology, Sedimentology and Reclamation, University of Kentucky, Lexington, Kentucky. Osterkamp, W. R. and Hedman, E. R. (1982) Perennial-streamflow characteristics related to channel geometry in Missouri River Basin. Washington, DC: United States Geological Survey, Professional Paper 1242. Osterkamp, W. R., McNellis, J. M. and Jordan, P. R. (1978) Guidelines for the use of structural versus regression analysis in geomorphic studies. Washington, DC: United States Geological Survey, Water Resources Investigations 78-135.

358

Flood estimation from channelsize

Pickup, G. (1976) Adjustment of stream channel shape to altered hydrologic regime. Journal of Hydrology, 30, 365-373. Pickup, G. and Rieger, W. A. (1979) A conceptual model of the relationship between channel characteristics and discharge. Earth Surface Processes, 4. 37-42. Pickup, G. and Warner, R. F. (1976) Effects of hydrologic regime on magnitude and frequency of dominant discharge. Journal of Hydrology, 29, 51-75. Pugh, J. C. (1975) Surveying for field scientists. London: Methuen. Richards, K. S. (1976a) The morphology of riffle-pool sequences, Earth Surface Processes. 1, 71-88. Richards, K. S. (1976b) Channel width and the riffle-pool sequence. Bulletin of the Geological Society of America, 87, 883-890. Richards, K. S. (1978a) Simulation of flow geometry in a riffle-pool stream. Earth Surface Processes. 3, 345354. Richards. K. S. (1978b) Channel geometry in the riffle-pool sequence. Geografiska Annaler, 6OA, 23-27. Richards, K. S. (1980) A note on changes in channel geometry at tributary junctions. Water Resources Research, 16, 241-244. Riggs, H. C. (1974) Flash flood potential from channel measurements. In Flash Floods Symposium, pp. 52-56. International Association of Hydrological Sciences, Publication No. 112. Riggs, H. C. (1976) A simplified slope-area method for estimating flood discharges in natural channels. United States Geological Survey Journal of Research. 4(3), 285-291. Riggs, H. C. (1978) Streamflow characteristics from channel size. Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers, 104 (HYl), 87-96. Riggs, H. C. (1985) Streamflow characteristics. Amsterdam: Elsevier, Developments in Water Science 22. Riggs, H. C. and Harenberg, W. A. (lY76) Flood characteristics of streams in Owyhee County, Idaho, Washington, DC: United States Geological Survey, Water Resources Investigations, Open-File Report 76-88. Riley, S. J. (1972) A comparison of morphometric measures of bankfull. Journal of Hydrology. 17, 23-31. Rodriguez-Iturbe. I. and Valdes, J. (1979) The geomorphic structure of hydrologic response. Water Resources Research, 15(6), 1409-1420. Rodriguez-Iturbe, I., Gonzalez, M. and Bras, R. L. (1982) A geomorphoclimatic theory of the instantaneous unit hydrograph. Water Resources Research, 18(4), 877-886. Roepke, H. G. (1977) Applied geography: should we, must we, can we? Geographical Review, 67, 481-482. Schumm, S. A. (1960) The shape of alluvial channels in relation to sediment type. United States Geological Survey Professional Paper, 352B, 17-30. Schumm, S. A. and Lichty, R. W. (1963) Channel widening and flood-plain construction along Cimarron River in south-western Kansas, Washington, DC: United States Geological Survey, Professional Paper 352D. Scott. A. G. and Kunkler. J. L. (1976) Flood discharges of streams in New Mexico as related to channel geometry. Washington, DC: United States Geological Survey, Open-File Report 76-414. Stevens, M. A., Simons, D. B. and Richardson, E. V. (1975) Non-equilibrium river form. Journal of Hydrology, Proceedings of the American Society of Civil Engineers, 101 (HY5), 557-566. Thomas, D. M. and Benson, M. A. (1969) Generalization of streamfZow characteristics from drainage basin characteristics. Washington, DC: United States Geological Survey. Open-File Report. Thornes, J. B. (1974) Speculations on the behaviour of stream channel width. London: London School of Economics Graduate School of Geography, Discussion Paper No. 49. Tomlinson, J. (1990) Personal communication. Tomlinson, J. (1991) Personal communication.

Geraldine Wharton

359

Wahl, K. L. (1976) Accuracy of channel measurements and the implications in estimating streamflow characteristics. In Modern developments in hydrometry, Vol. 2, pp. 311-319. Padua, Italy: World Meteorological Organization. Wahl, K. L. (1977) Accuracy of channel measurements and the implications in estimating streamflow characteristics. United States Geological Survey Journal of Research, 1.5(6), 811-814. Wahl, K. L. (1983) Determining streamflow characteristics based on channel cross section properties. In Improving estimates from f?ood studies, pp. l-10. Washington DC: Transportation Research Board, Transportation Research Record 922. Wahl, K. L. (1984) Evolution of the use of channel cross-section characteristics for estimating streamflow characteristics. United States Geological Survey Water Supply Paper, 2262, 53-66. Wang, C. T., Gupta, V. K. and Waymire, E. (1981) A geomorphologic synthesis of non-linearity in surface runoff. Water Resources Research, 17, 545-554. Webber, E. E. and Roberts, J. W (1981) Flood flow characteristics related to channel geometry in Ohio. Washington, DC: United States Geological Survey, Open-File Report 81-1105. Wharton, G. (1989a) River discharge estimated from river channel dimensions in Britain. Unpublished PhD thesis, University of Southampton, UK. Wharton, G. (1989b) Guidelines for estimating flood discharges in Britain from river channel dimensions. Southampton: University of Southampton, Department of Geography, Discussion Paper No. 33. Wharton, G., Arnell, N. W., Gregory, K. J. and Gurnell, A. M. (1989) River discharge estimated from river channel dimensions. Journal of Hydrology, 106, 365-376. Williams, G. P. (1978) Bank-full discharge of rivers. Water Resources Research, 14, 1141-1154. Williams, G. P. (1983) Improper use of regression equations in earth sciences. Geology, 11, 195-197. Wolman, M. G. and Gerson, R. (1978) Relative scales of time and effectiveness of climate in watershed geomorphology. Earth Surface Processes, 3, 189-208. Wolman, M. G. and Leopold, L. B. (1957) River flood plains: some observations on their formation. Washington, DC: United States Geological Survey, Professional Paper, 282-C. Wolman, M. G. and Miller, G. P. (1960) Magnitude and frequency of forces in geomorphic processes. Journal of Geology, 68, 54-74. Woodyer, K. D. (1968) Bankfull frequency in rivers. Journal of Hydrology, 6, 114-142. (Revised manuscript received 19 February 1992)