Flood area modelling from an elementary data base

Journal o f Hydrology, 53 ( 1 9 8 1 ) 85--94

85

Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m -- Printed in T h e Netherlands

[1] FLOOD A R E A MODELLING FROM AN ELEMENTARY D A T A BASE

A D R I A N M c D O N A L D and D A V I D L E D G E R

School of Geography, University of Leeds, Leeds LS2 9JT (Great Britain) Department of Forestry and Natural Resources, Edinburgh University, Edinburgh EH9 3JU (Great Britain) (Received April 1, 1980; accepted for publication October 16, 1980)

ABSTRACT McDonald, A. and Ledger, D., 1981. Flood area modelling from an elementary data base. J. Hydrol., 53: 85--94. A m o d e l is developed which treats the floodplain as a storage area for flows in excess of the channel capacity. T h e volume of overspill is distributed over the floodplain restricted only by the major division of the floodplain and the topography. An example of the application of the model is gL,en for a section of the floodplain of the River Nith in SW Scotland. Flood area prediction for a 50-yr. return interval flood is shown to be 85% accurate. It is argued t h a t storage models are more appropriate and potentially m o r e useful than channel extension models.

INTRODUCTION

The choice of a rational response to flood hazard depends upon an appreciation of the long-term losses that are incurred due to flooding and the reduction in loss that results from the application of various management strategies. The calculation of loss depends upon an accurate estimate of the value of the areas at risk, the damage levels resulting from floods of different characteristics, the frequency of flooding and the area inundated by a flood of a given magnitude. This paper considers the final factor -- that of determining the area flooded.

THE E L E M E N T S OF T H E M O D E L

The model treats the floodplain as a storage area and calculates the extent of the flood from information on overspill volume and from details of the floodplain topography. The path of the flood is considered to follow a sequence of field inundations determined almost entirely by the difference in height of adjacent fields. This sequence of inundation is called the flood series. The flood series

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© 1981 Elsevier Scientific Publishing C o m p a n y

86 is constrained by the division of the floodplain into large sections called flood units. Within a flood unit, the flood sequence is determined by relative field height alone. The flood series starts from breaches in the levee, the locations of which are determined from past floods, from measurements of channel capacity, or are allocated randomly. The e x t e n t to which a flood will inufldate the area depends on the volume of overspill. The overspill volume is moved along the flood series field by field. For a given overspill volume, the water level diminishes as the area flooded increases. Eventually, the height of floodwater in a field is n o t sufficient to flood the next field in the series and the flood area has been determined. In those cases where the n e x t field is flooded, a new flood depth is calculated by equating the volume of water required to fill the next field to the new flood depth with the volume of water generated by the drop in flood stage in all the fields thus far flooded. The volume of overspill is calculated from the flood hydrographs having peaks in excess ~f bankfull discharge. The general relationship between overspill volume and peak discharge is given in Fig. l a . This is applicable

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Fig. 1. The general relationship (a) between total overspill volume and peak discharge for a simple hydtograph which is illustrated in (b). In (c) and (d) the influence of varying assumptions concerning the form of levee collapse on total overspill volume are illustrated.

87

only to simple hydrographs. It is assumed that no significant return flow (flow from the floodplain to the fiver channel) will take place between the c o m m e n c e m e n t of overbank/over levee flow and the flood peak and that in practice little return flow will occur on the recession limb until the fiver discharge is at least equal to, or less than, that at the onset of flooding. Nonetheless, the range of values of overspill volume still depends upon whether overflow (along some length of the bank or levee) or breach flow (through some failed bank or levee section) dominates, and upon the significance of the breach and the rapidity of its formation. Fig. l b , c and d shows changes in overspill volume assessment dependent upon on intact levee (b), a steady (c) or catastrophic (d) collapse of the bank/levee. Clearly the relative significance of the differences in calculated overspill volume caused by the varying assumptions of levee collapse illustrated in Fig. 1 are greatest at low flood levels but at high flood levels in a situation of variable channel capacity or breach flow some of the flood waters m a y well pass the overspill site. In order to assess their significance, the difference in flow volume above and below the modelled section of floodplain would be needed but in practice this will frequently be unavailable. The flood is routed along the flood series, which is the field-by-field sequence of flooding. The next field in the flood series is always adjacent to a flooded field (or in a few cases a breach location) and if lower in elevation than the flooded field, is that field with the greatest elevation difference. If higher than the flooded field it is that field having the minimum elevation difference with the flooded field. Each field is assumed to be flat. The field was used because it is both the smallest management unit and the unit upon which much elementary data are based. The free spread of water along the flood series is constrained by the subdivision of the floodplain into flood units caused by major intrusions of natural and physical features such as land promentories and railway embankments into the field elevation dominated floodplain topography. It is assumed that floodwater volume would have to flU an entire flood unit before it could continue through the flood series into an adjacent flood unit. The use of flood units means that in practice the exact location of breaches (discussed above) is unnecessary since flooding of any significance at a point within a unit will soon start to follow a c o m m o n flood pattern. The routing of the floodwater through the flood series is continued for as long as the inequality given in eq. 1 below is satisfied. When these conditions are not satisfied, the routing is terminated and applied versions of such models would continue to damage and loss calculation phases. Yn + Zn + a ~ Yn +1

(1)

where Yn is the height of the nth field in the series; Z , is the floodwater depth in field n; and a is an edge factor. a is an edge effect factor by which the assumption of flat fields is made more realistic by accepting that field boundaries are usually higher than the

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mean field height due to such factors as plough turns, non-cropping, fencing, hedging and debris trapping. The depth of floodwater at different times during the flood series is calculated on the following basis. The volume of water used to fill the next field in the series is equal to the volume of water that is required from all previously flooded fields such that a uniform flood depth is maintained. The new flood depth determined in this manner is entered into eq. 1 to determine whether the next field in the flood series will flood. The use of a singlestep system in which fields are flooded progressively is clearly a simplification of the flood situation in nature. One would expect that the fields would flood in a progressive series in relation to their level and proximity to the floodwater, but that field flood events would overlap and would not be single-step events. It is to be expected that some flood extension due to preferential routing along tracks would also take place. The principles on which the routing of floodwater is calculated are illusl,rated in Fig. 2 which shows the situation in fields n and n + 1. Field n + 1 is being flooded and it is of interest to determine the depth of floodwater following the inundation. It .will be remembered that fields 1 to n are already flooded. Let the area of the field n be X . , its height and the present depth of floodwater in it, Z . . Let be the depth of floodwater in field n, following the flooding of field n + 1. T h e :

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The left-hand term represents the volume of floodwater in fields 1 to n involved in the decrease in flood height from Z , to D n . The term (Y, + D~ -- Yn+~ ) is a reformulation of the flood depth in field n + 1, i.e. Z(n+l), in terms of the known values Yn and Yn÷l, and the desired unknown D~, thus: Zn+ l

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Examination of the terms in eq. 6 shows that data concerning flood depth and field heights are required for only fields n and n + 1. The only item that needs to be derived from values for each field in the entire flood series is area. This formulation means that a considerable reduction in complexity is achieved. Flood depth in field n + 1 is calculated from eq. 4. The model routes the flood along the flood series using eq. 1, and eq. 4, using terms derived from eq. 6, calcuhtes the new inputs for eq. 1. When eq. 1 is no longer satisfied the routing of the flood is terminated and summary statistics for the flood may be calculated. These statistics would include the total area of the flood, the number of fields flooded and their location; and the final floodwater depth in each field. Since the model is based upon the field unit, information on crop type and value at risk {related to time) could be readily incorporated to provide information on monetary loss.

AN EXAMPLE

The River Nith in SW Scotland has a history of severe flooding. From Friars Carse to the confluence of the River Nith with Cluden Water the bulk of its floodplain lies to the east of the river. There are no major inputs between these points (Fig. 3). The floodplain has a number of artificial and natural barriers to the advance of floodwater and Fig. 4 shows the subdivision into flood units on the basis of these barriers. The area and height of each field in the floodplain has been determined by field survey and by abstraction from published records. The hydrograph record has been taken from the stage recording station at Friars Carse. Discharge capacity of the river at bank and levee overflow stages has been determined from measurements of cross-section and hydraulic characteristics at seven points in the floodplain (Fig. 4), augmented by information on the stage heights at which

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flooding commenced in the past. Flood areas have been calculated for all floods on record up to 1975. For the purpose of this paper the calculated area of the January 1962 flood can be compared with observed values. This flood is the largest on record at Friars Carse and indeed is one of the largest in the historic record for the Nith, having a return interval of "~ 50 yr. (Fig. 5). The calculated and actual .flood outlines are given in Fig. 6. The apparently fair coincidence of the outlines can be more rigorously tested by allocating each field to one of three categories: (1) correct; (2) unpredicted flood; and (3) incorrect prediction of flood. Using the maximum area covered by amalgamating the actual and predicted flood areas the category numbers were 133, 10 and 13, respectively, representing a rate of accurate flood location prediction of 85%. The predicted flood area total exceeds 95% of the actual flood area total. Failures of the model which are all located in the same area suggest that some further factors come i.nto play. The consistent unpredicted flooding in ~he Bankfoot unit cannot be corrected by the input of larger overspill volumes into the most northerly reported breach in the Kessicks unit. No levee collapse was reported f o r the Bankfoot unit. The most likely explanation is that some levee overflow took place d~rectly into the Bankfoot unit.

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Fig. 4. Location of the flood units and cross-section sites for the determination of channel capacity. DISCUSSION The modelling of flood events in which the floodplain becomes an extension of the channel has been attempted on a theoretical basis by Porter {1972}. Porter made the assumption that the floodplain would have a constant slope, both downstream and normal to the river; that there were no limiting macrostructures in the floodplain and that the roughness coefficient remained constant. Channel extension floods, for example that of the Ettrick reported by Ledger et al. (1978), appear to occur in upland areas where climate and topography limit the value of the land at risk. In contrast the floodplain, acting as a store as discussed in McDonald and Brookes (1978) or as a system having a low conductivity with the channel at times of flood as expressed by Lewin and Hughes (1980), appears much more likely to occur downstream where the floodplain has become extensive and in these areas the value of the land and its cover is greatly increased. Whether a point exists where floodplain characteristics change markedly and where modelling strategies must also change may yet be a matter for further debate, but Klein (1976) has demonstrated that tile relationship between c a ~ h m e n t area and hydraulic regime appears to experience a break point at a catchment area of 250 km 2 .

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It is clear that models of the form discussed here cannot be applied to upland catchments and that without subdivision of the water input and without incorporating a time element into the model they fail to develop the understanding of floodplain geomorphology. Nonetheless, such criticisms do not detract from the use of the model as a management tool or as a potential tool in floodplain geomorphology. Whether the data requirements specified in McDonald and Brookes { 1978} for the use of such a model are too great and will inhibit its application in many cases is not clear but if data on floods can be determined by aerial survey (Currey, 1977) then evaluation of flood-

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Fig. 6. The actual and modelled areas flooded by the ~ 5 0 y r . return interval flood of January 1962.

plain topography can clearly be obtained in a similar manner (subject to the scale of resolution being satisfactory) despite the inherent complexity of floodplains as outlined by Schmudde (1963), Kellerhals {1976} and Lewin and Weir (1977).

CONCLUSION'

In the larger, more complex and economically more significant floodplains "channel extension" modelling proposed by Porter (1972} seems inapplicable, both because of the physical structure of the floodplain and because

94

of the management structure which will modify roughness coefficients in time and space. Apparently, sound flood area predictions can be made on the basis of field units which are of particular management significance. The most significant gaps still appear to be in the calculation of overspill volumes since the topographic data are becoming more readily determined from aerial photographs and are available from existing sources in many situations. Improvements in the understanding of return flows are necessary before the model discussed here could be expanded to examine such factors as the dura*~ion of standing water or the distribution of floodwater over time following the passage of a hydrograph peak.

ACKNOWLEDGEMENTS

We wish to thank the Solway River Purification Board and The Department of Agriculture and Fisheries for Scotland for their help. Pamela Naden made helpful comment on an e~.~rlydraft of this paper. This work was funded by a grant from the Natural Environment Research Council and was made possible by ~he help of the farl_ners of Nithsdale and other floodplain occupants in the U.K.

REFERENCES Currey, D.T., 1977. Identifying floodwater movement. Remote Sensing Environ., 6: 51--61. Kellerhals, R., Church, M. and Bray, D.I., 1971q. Classification and analysis of river processes. Proc. Am. Soc. Civ. Eng., J. Hydraul. Div., 102: 813--829. Klein, M., 1976. Hydrograph peakedness and basin area. Earth Surf. Processes, 1 : 27--30. Ledger, D.C., McDonald, A.T. and Fleming, R., 1978. The Ettrick floods: physical, economic and political appraisal. Pap. to Flood Patrol Gr., Inst. Hydrol., Plynlimon, Sept. 22, 1978. Lewin, J. and Hughes, D.A., 1980. Welsh floodplain studies, II. Application of a qualitative inundation model. J. Hydrol., 46: 35--49. Lewin J. and Weir, M.J.C., 1977. Morphology and recent history of the Lower Spey. Scott. Geogr. Mag., 93: 45--51. McDonald, A.T. and Brookes, S.M., 1978. A manual for using flood and FLOODN; device~ for caiculating fl~cd areas and flood damage,~ in agricultural floodplains. School Geogr., Univ. Leeds, Leeds, Comput. Manual No. 8. Porter, E.A., 1972. Assessment of flood risk for land use planning and property insurance. Ph.D. Thesis, Cambridge University, Cambridge (unpublished). Schmudde, T.H., 1963. Some aspects of the landforms of the lower Missouri River floodplain, Ann. Assoc. Am. Geogr., 53: 60--73.