EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 9, 175-180 (1984)

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RIVER CHANNEL CHANGE: PROBLEMS OF INTERPRETATION ILLUSTRATED BY THE RIVER DERWENT, NORTH YORKSHIRE

K. RICHARDS AND C. GREENHALGH Deparimeni of Geography, Universiiy of Hull, Hull HU6 7RX, U.K.

Received 25 October 1981 Revised 16 June 1983

ABSTRACT

Some inherent limitations of the spatial interpolation method of identifying and interpreting channel adjustment are illustrated by a study of the River Derwent in Yorkshire. Here, cross-sections downstream from a river diversion appear to have contracted in size when compared with predictions based on upstream relationships between channel form variables and basin area. However, these sections are slightly larger than expected for their diminished discharge, suggesting that they have not fully adjusted to altered environmental conditions and are still in a transient state.

KEY WORDS River cross-sections Channel changes Hydraulic geometry

INTRODUCTION

Changes in channel geometry caused by human interference with fluvial processes have received considerable attention (e.g. Gregory, 1977; Rhodes and Williams, 1979). Although data from calibrated river reaches measured before and after a disturbance provide the best insight into the mechanisms of adjustment (Leopold, 1973), two indirect approaches have often been adopted in the absence of the necessary prior calibration period. Control catchment data may be used, with comparisons being made between disturbed channels in altered basins, and equilibrium channels in adjacent, otherwise similar natural catchments (e.g. Hammer, 1970). Alternatively, spatial interpolation within the experimental catchment is attempted. The variation of channel geometry downstream through undisturbed reaches is used to define trends, established with respect to basin area or channel length. These are projected downstream from the disturbance so that the ‘expected’ channel form can be compared with the observed adjusted morphology (Park, 1977).

These indirect approaches are often the only possible methods if initial calibration data are unavailable. However, several major limitations are evident. First, they provide basic data on the magnitude of change in specific morphometric variables such as channel with (w), depth (d) or capacity (C), but no evidence of the process of change-that is, the physical mechanisms and the temporal patterns of change. Second, the channel form variables are measured relative to scale factors such as basin area or channel length. These are essentially surrogates for discharge, which increases downstream systematically in perennial rivers. The equilibrium channel geometry is, however, controlled by an interaction between hydrological and sedimentological catchment properties which cannot readily be interpreted using these surrogate indices. Third, comparison with spatially-separated undisturbed river reaches assumes constancy of potential environmental controls between reaches, and underestimates the complex multivariate control of channel form. For example, a natural

0197-9337/84/020 175-06$01 .OO 0 1984 by John Wiley & Sons, Ltd.

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change of valley form and stream gradient often occurs at a reservoir site, thereby complicating interpretation of the effect of the reservoir on the river channel. An additional problem is that the same disturbance may have different effects in different catchments: demonstration of significant channel adjustment in one basin does not readily permit extrapolation to a general model of channel change. Finally, channel adjustment to climatic change may be a continual, progressive process best defined as a dynamic equilibrium, but a sudden enforced step-function change in discharge and sediment yield resulting from human interference causes a lagged, delayed response in which the channel passes through a series of transient states before achieving the new equilibrium. These indirect methods cannot readily identify the existence of such a transient phase in the adjustment process.

The River Derwent in North Yorkshire has experienced some localized adjustment to discharge diversion for flood control purposes, and is here used to illustrate some of the limitations of an indirect assessment of channel change.

THE RIVER DERWENT: A CASE STUDY

The North York Moors form an upland area of about 1200 km2 underlain by Jurassic sandstones, limestones and shales folded into a broad anticlinal structure with an east-west major axis. Maximum heightsare just over 425 m on the lower Jurassic Estuarine Sandstone in the core of the region. A prominent north-facing escarpment in middle Jurassic Corallian Limestone, dissected by south-flowing streams, forms the Tabular Hills on the southern dip-slope of the anticline (Figure 1). Tertiary drainage of the region is thought to have been dominated by eastward-flowing rivers (Cowper Reid, 1901), of which the strike valley at the foot of the Corallian scarp near Scarborough may be a remnant. If this alignment did exist, it has been comprehensively disrupted by the effects of the anticlinal uplift, and especially by extensive Quaternary fluvio-glacial drainage diversion (Gregory, 1965).

The River Derwent drains the south-eastern dip slope of the Moors, collecting the headwaters of several minor streams which probably originally drained east to the North Sea. It then flows south to break through the limestone escarpment in the Forge Valley, a probable fluvio-glacial meltwater channel. Its catchment area at this point is 122 km’. South of the Forge Valley the Derwent enters the Vale of Pickering where a coastal plug of glacial till prevents it entering the sea and causes it to flow west to leave the vale via the Kirkham Abbey gorge, supposed by Kendall(l902) to have formed as a glacial lake overflow channel. The Vale of Pickering is underlain by upper Jurassic Kimmeridge Clay with a superficial veneer of alluvial, possible lacustrine and glacial deposits, and is poorly drained, having a maximum height of c. 30 m. In order to minimize flooding in the Vale, an artificial by-pass channel, the Sea Cut, was dug between 1800 and 1810 to follow the east-west strike valley from a point just north of the Forge Valley to the North Sea at Scalby (Figure 1). Winter flow in the Derwent is almost entirely diverted along this channel. As a result the channel in the Forge Valley has adjusted its morphology to the reduced flood magnitudes and sediment loads carried following diversion of both water and sediment down the Sea Cut. From a gravel-bed upland stream above the Sea Cut, it becomes a sluggish stream with heavy summer weed growth in the Forge Valley, where it transports sand over a paved bed.

EVIDENCE OF CHANNEL ADJUSTMENT

Channel cross-sections were levelled at eleven sites on the Derwent mainstream headwards of the Sea Cut diversion, and at three sites in the Forge Valley (Figure 1). Sites were chosen randomly, but sections were identified at rifles in straight reaches in order to eliminate systematic within-reach variability. Cross-sections were plotted and bankfull width, mean depth and cross-section area (channel capacity) were measured. Identification of a true bankfull level was usually straightforward, since the cohesive banks were steep and well- defined in straight reaches. These channel cross-section dimensions were related to the catchment areas upstream from the measured sections, these being obtained by planimetering the basins defined on 1:25,000 maps.

Figure 2A illustrates the systematic increases of width, depth and capacity downstream with increasing

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Figure 1. The River Derwent; location map

catchment area above the Sea Cut diversion, the regression relationships defined for the eleven upstream sites all being statistically significant at p = 0.01. The Forge Valley data are plotted using a different symbol and indicate a marked reduction of channel size. Defining the observed value of channel property as a percentage of that predicted by projection of the upstream trend, the channel capacity is on average 31 per cent of that expected for the three Forge Valley sites. This reduction is compounded of a 61 per cent ‘reduction ratio’ for width, and a 47 per cent reduction ratio for depth (capacity being the product of width and mean depth). These changes reflect the inability of the Derwent to transport a relatively fine sediment load through the Forge Valley reach with its now reduced flood discharges. Bed material sizes decline gradually from Dg4 values of approximately 30 cm at the headward site to about 3 cm just above the Sea Cut, but this gravel bed is replaced within the Forge Valley by sand over an inherited paved gravel surface. The sand and silt carried by the reduced stream have accumulated to form lateral berms within the original channel, with an upper surface just below the prior floodplain level. Reduction of width and depth has been fostered by sedimentation on the river banks, where weed growth is particularly extensive in summer in shallow, stagnant water. The evidence of Figure 2A,

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, 0

!

/ 0.1 J /

/ /

A I 1 I l l I I I 1 2 5 10 20 50 100 300

drainage area ( km2) - A

B I 1 I l l 1 1 1

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Figure 2. (A)The relationships between channel properties and catchment area. (B)The relationships between channel properties and the discharge equalled or exceeded 5 per cent of the time

which provides a typical example of the spatial interpolation approach to the identification of channel adjustment, would seem to suggest that the channel in the Forge Valley has contracted in size as a result of the reduced streamflow occasioned by upstream flow regulation. While essentially a reasonable conclusion, this is revealed to be an oversimplification by further analysis.

EVIDENCE OF ‘TRANSIENCE IN CHANNEL ADJUSTMENT

Using data from gauging stations on other rivers in the North York Moors, it is possible to establish a regional relationship between a convenient discharge index and basin area. The 5 per cent duration flow was initially selected as a compromise between the rarer, more extreme events thought to be geomorphologically dominant (the bankfull flows) and less extreme flows which are more reliably estimated from the available data. It is also a compromise between flows which dominate the transport of suspended sediment (Benson and Thomas, 1966) and bedload (Pickup and Warner, 1976). The relationship thus obtained was

Q5 = 0.12 A’’’’ (1)

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with discharge Q, in m3 s - l and area A in km2. This may be used to estimate the 5 per cent discharge at ungauged sections of known basin area within the same hydrological region. Assuming similar general runoff conditions, it allows estimation of this discharge index at the eleven upstream sites sampled along the River Derwent.

The resulting downstream hydraulic geometry relationships for the upstream sites on the Derwent are (channel dimensions in metres)

and

w = 7.36 Qs0‘46 d = 0.68 Q50‘56

C = 4.98 Q5”02

all of which are significant at p = 001. Since there is a gauging station at West Ayton (Figure 1) at the downstream end of the Forge Valley, the true, measured 5 per cent flow passing through this reach is known, and in Figure 2B the cross-section data for the Forge Valley sections are plotted in relation to this known discharge. It can be seen that these sections are not too small for the discharge they carry. In fact, their data points plot as positive residuals from the general trend, indicating that the sections are slightly larger than expected, being deeper and, particularly, wider than the averages for this discharge. The implication of this may be that the channel in the Forge Valley is still in a transient state and has not yet created the equilibrium morphology appropriate to its altered discharge and sediment supply. However, a further test of this hypothesis is desirable, since the above analysis is inconclusive in itself. Confidence limits have not been plotted on Figure 2B because technically they should incorporate the errors in estimating discharge from basin area, and channel dimensions from discharge. Furthermore, the theoretical justification for selecting the discharge equalled or exceeded 5 per cent of the time as an appropriate flow index is weak.

The 5 per cent discharge of the Forge Valley sections (average depth 0.83 m, cross-section area 7.89 m2) is closest to that of the slightly smaller sections 5 and 6 upstream, where the mean depth is 0.68 m and the cross- section area is 6.34 m2. Using a relative roughness relationship based on that of Limerinos (1969),

the friction factor (f) can be estimated for the gravel-bed sections 5 and 6. Mean bankfull velocity is then calculated from the bankfull depth, slope and friction factor, and bankfull discharge is the product of velocity and cross-section area. For sections 5 and 6 this ranges from 11.5 to 14.2 m3 s- In the Forge Valley, bankfull discharge estimation is more difficult, because the control of flow resistance at peak discharge is less obvious. If the underlying gravel and pebbles are dominant roughness elements, predicted bankfull discharges are 7.2 to 9.6 m3 s - l (based on the same technique). If sand controls the skin resistance and also creates form resistance, an alternative estimation technique is required. The method developed by Alam and Kennedy (1969) for estimating composite skin and form roughness was used, and the bankfull discharge thus calculated is 8.3 m3 s - l . These results all indicate that the larger Forge Valley sections have a significantly lower bankfull discharge than the upstream sections 5 and 6, which adds support to the conclusion that they remain in disequilibrium.

Channel-in-channel sections have developed in the Forge Valley reach by bankside sedimentation creating a new, lower bankfull surface and converting the old floodplain into a terrace in terms of its inundation frequency. However, prolongation of the ‘transient’ disequilibrium state is possible in such a contracting channel because the depositional process is relatively slow. This is accentuated in the Forge Valley by diversion of some of the sediment load required to effect the channel change along the Sea Cut with the water discharge. The above calculations suggest that Forge Valley sections would plot as positive residuals above a channel capacity-bankfull discharge relationship for the Upper Derwent. To base interpretation entirely on such a relationship would be questionable because of the circularity implicit in calculating bankfull discharge from channel section data. Nevertheless, this example indicates that spatial interpolation, with its reliance on basin area data, cannot distinguish clearly between an equilibrium, fully-adjusted channel, and a channel still in disequilibrium. In the Forge Valley, disequilibrium reflects the facts that the cross-section areas are still too

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large because sedimentation is incomplete, and the bankfull discharges calculated for those oversized sections are also larger than the true values for discharges of the order of 1-2 year return period experienced in this reach.

DISCUSSION

If the channel is still in disequilibrium, it becomes difficult to evaluate the significance of the other problems of interpretation discussed above. For example, the multivariate nature of channel geometry involves mutual adjustment of cross-section, plan geometry and channel gradient to the imposed water discharge, sediment yield and calibre, and valley surface gradient. The channel capacity might be smaller than average for a given discharge if valley slope is low, because the stream power, and therefore the capacity for bank erosion, is less. In the Forge Valley, the inherited valley slope is markedly reduced, to about half the value just upstream from the Sea Cut. Thus the final equilibrium capacity might be expected to be less than that predicted by the regression relationship of Figure 2B, implying that the existing departure from equilibrium is rather greater than is apparent from this diagram. However, the interaction between discharge (or basin size) and slope which helps determine channel capacity upstream may not be the same as that which occurs in the Forge Valley, where the narrowness of the valley floor inhibits the development of meanding, which is the main process by which the channel slope is reduced below the valley slope. We may hypothesize, on the basis of data from equilibrium, undisturbed sections, what the final equilibrium in the disturbed reach should be; however, such hypotheses must remain untested until independent process data permit an unequivocal decision to be made that the disturbed reach has achieved an equilibrium state.

REFERENCES

Alam, A. M. Z. and Kennedy, J. F. 1969. ‘Friction factors for flows in sand-bed channels’, Journ. Hydr. Div., Proc. Am. Sor. Ciu. Eng., 95,

Benson, M. A. and Thomas, D. M. 1966. ‘A definition of dominant discharge’, Bull. In t . Ass. Sci. Hydro/. , 9, 76-80. Cowper Reid, F. R. 1901. The geological history ofthe rivers ofeas t Yorkshire, Clay 8~ Sons, London. 103 pp. Gregory, K. J. 1965. ‘Proglacial Lake Eskdale after sixty years’, Trans. Inst. Brit. Geogr., 36, 149--162. Gregory, K. J. (Ed.) 1977. River Channel Changes, Wiley, London. 448 pp. Hammer, T. R. 1970. ‘Stream channel enlargement due to urbanization’, Water Res. Res., 8, 153C1540. Kendall, P. F. 1902. ‘A system of glacier lakes in the Cleveland Hills’, Quart. Journ. Geol. Soc. London., 58, 471-571. Leopold, L. B. 1973. ‘River channel change with time: an example’, Geol. Soc. America Bull., 84, 1845-1860. Lirnerinos, J. T. 1969. ‘Relation of the Manning coefficient to measured bed roughness in stable natural channels’, U.S. Geol. Survey. Pro$

Park, C. C. 1977. ‘Man-induced changes in stream channel capacity’, in Gregory,,K. J. 1977, op. rit., 121-144. Pickup, G. and Warner, R. F. 1976. ‘Effects of hydrologic regime on magnitude and frequency of dominant discharge’, Journ. Hydro/. , 29,

Rhodes, D. D. and Williams, G. P. (Eds). 1979. Adjustments of the Fluvial System, Kendall Hunt, Dubuque, Iowa. 372 pp.

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