An estimate of annual runoff from England and Wales, / Evaluation de l'écoulement annuel en Angleterre et aux Pays de Galles,

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1 Hydrlgical Sciences Bulletin ISSN: (Print) (Online) Jurnal hmepage: An estimate f annual runff frm England and Wales, / Evaluatin de l'éculement annuel en Angleterre et aux Pays de Galles, T. J. MARSH & I. G. LITTLEWOOD T cite this article: T. J. MARSH & I. G. LITTLEWOOD (1978) An estimate f annual runff frm England and Wales, / Evaluatin de l'éculement annuel en Angleterre et aux Pays de Galles, , Hydrlgical Sciences Bulletin, 23:1, , DOI: / T link t this article: Published nline: 25 Dec Submit yur article t this jurnal Article views: 46 View related articles Citing articles: 4 View citing articles Full Terms & Cnditins f access and use can be fund at Dwnlad by: [ ] Date: 10 January 2018, At: 06:22

2 Hydrlgical Sciences~Bulletin-des Sciences Hydrlgiques, 23,1, 3/1978 An estimate f annual runff frm England and Wales, T. J. MARSH and I. G. LITTLEWOOD Water Data Unit, Reading Bridge Huse, Reading, Berkshire RG1 8PS, UK Received 2 Nvember 1977, revised 23 Nvember 1977 Dwnladed by [ ] at 06:22 10 January 2018 Abstract. One cnsequence f the drught was a grwing cncern abut the distributin with respect t time f the available water resurces in England and Wales. Varius indices f drught have been derived based largely n recrds f rainfall, but in sme cases n studies f the discharge fr certain rivers. This paper presents estimates f annual runff frm England and Wales as a whle, frm 1728 t Evaluatin de l'éculement annuel en Angleterre et aux Pays de Galles, Résumé. Par suite de la sécheresse en n a épruvé une inquiétude crissante au sujet de la répartitin en ce qui cncerne le temps des ressurces en eaux dispnibles en Angleterre et au Pays de Galles. De diverses indices de sécheresse nt été dérivées qui se basent pur la plupart sur les enregistrements de précipitatin, mais il y a aussi des cas qui se basent sur des études d'éculement pur certaines rivières. Cette mémire présente des évaluatins de l'éculement annuel en Angleterre et au Pays de Galles en ttalité, de 1728 jusqu'à INTRODUCTION A cnsequence f the sustained drught f , when viewed against a backgrund f increasing water use, is the upsurge f attentin given t the security f water resurces in perids f lw rainfall. Water is required fr public water supply, industry, agriculture and t maintain eclgical and amenity standards. Althugh advances in the integratin f water resurces n a reginal level may have lessened the impact f lcal drughts, thse cncerned with water management will still wish t knw the likelihd f the 1976 situatin recurring. Mst recent examinatins f drught frequency have attempted t assess the prbability assciated with cumulative rainfall ttals ver a nminated perid (Wright, 1976; Perry, 1976). It is knwn, fr instance, that the 16-mnth rainfall ver England and Wales fr the perid cmmencing April 1975 was the lwest since recrds began in 1727 (Mrris & Ratcliffe, 1976). Cncentratin n the analysis f rainfall data is hardly surprising given the shrt recrds f runff. Nevertheless it is the rivers which prvide a majr part f the natin's water supply and the necessary dilutin f effluents and their transprt t the sea. Hence it is imprtant t assess the frequency f drught in terms f runff. Althugh Daltn (1802) made the first estimate f the /78/ Blackwell Scientific Publicatins 131

3 132 T. J. Marsh and I. G. Littlewd ttal runff frm England and Wales in 1802, mdern assessments have been hampered by a lack f basic data. The regular recrding f river flw dates back t the middle f the nineteenth century but there are very few statins n majr basins with cntinuus recrds f flw f mre than 50 years duratin. Hwever, the impetus t gauging statin cnstructin fllwing the creatin f the Surface Water Survey and later the Water Resurces Bard, ensured the cmpletin f a cmprehensive netwrk which nw mnitrs runff frm 70 per cent f England and Wales and permits the realistic assessment f ttal runff. Dwnladed by [ ] at 06:22 10 January 2018 Estimatin f cntemprary runff frm England and Wales T estimate the annual runff frm England and Wales ( km 2 ) an examinatin was made f thse basins which were tgether cnsidered t be mst representative f the entire area. The water-year (Octber-September) was chsen as the time base t minimize net strage effects. The criteria fr the selectin f drainage basins were: (i) the cmbined area f the basins selected shuld cver as much f England and Wales as pssible cnsistent with criteria (ii) t (v); (ii) each basin shuld have available a cmplete recrd f mnthly natural flws (gauged flw adjusted fr net abstractin r augmentatin) fr an extended perid; (iii) the average rainfalls f the chsen basins shuld cver the range t be expected fr large basins; (iv) the average areal rainfall fr the selected basins cnsidered tgether shuld be clse t that f England and Wales; and (v) their gegraphical distributin shuld ensure that all but the lcalized drughts, during the calibratin perid, wuld be represented. Althugh there was sme cnflict between these criteria, inspectin f flw data held n the Water Data Unit archive revealed nine basins suitable fr selectin, and their gegraphical distributin is shwn in Fig. 1. The basins chsen are listed in Table 1 with their areas and averages f rainfall and runff; the cmmn perid f their flw recrds being Tgether the index basins cver 21 per cent f England and Wales and their cllective average rainfall is 885 mm r 98 per cent f the average general rainfall fr England and Wales (904 mm). A mre elegant apprach t the selectin f index basins wuld have invlved the identificatin, by a methd such as multiple regressin, f thse basins which in cmbinatin behave mst sympathetically with the ttal runff frm England and Wales, but the length f available flw recrds tgether with their lack f cntinuity dictated that a subjective chice be made. Water-year runffs frm these nine basins, cnsidered as ne area, were derived fr and taken as an estimate f the 17-year time series f runff frm England and Wales. The precisin with which ttal runff has been estimated depends n hw representative the index basins are f England and Wales. In this respect it is encuraging that the difference between the mean runff ( ) frm the nine basins (428 mm) and the crrespnding rainfall fr England and Wales (897 mm), amunts t 469 mm, which is in clse agreement with the estimated average actual evapratin frm England and Wales (472 mm) (Rdda et al, 1976) fr apprximately the same perid. Detailed assessment f ttal runff fr England and Wales in recent years, emplying basins cvering 50 per cent f the area, indicated that an accuracy f better than ± 10 per cent may be ascribed t the estimated runff values fr The mean water-year runff ver the perid crrespnds t a mean discharge frm England and Wales f sme 2036 m 3 s _1 ; by cntrast the equivalent figure fr Octber 1975 t September 1976 is 960 m 3 s" 1.

4 Annual runff frm England and Wales 133 Dwnladed by [ ] at 06:22 10 January 2018 FIG. 1. Basins used t derive cntemprary runff. T investigate the frequency assciated with water-year runff f a given magnitude, a mdel was required which wuld relate the runff t existing lng time series f hydrlgical variables and thereby permit the hindcasting f annual runff ver a cnsiderable time perid. Develpment f a rainfall/runff mdel Octber-September rainfall, by itself, is nt the best identifier f water-year runff because it des nt allw fr actual evapratin nr fr strage changes in the sil and in the aquifers. Bth actual evapratin and strage are difficult t assess and attempts t derive a multiple regressin mdel incrprating lcalized measures f these variables prved unsuccessful. The individual crrelatin cefficients (r) assciated with the linear regressin f bserved annual runff against a number f annual series were as fllws: Grundwater levels at Chilgrve (Chalk), 0.78; field drainage-rthamsted (50 cm

5 134 T. J. Marsh and I. G. Littlewd TABLE 1. Index basins selected fr runff estimatin Basin annual Av. runff Gauging area areal rainfall River statin (km 2 ) (mm) (mm) Dwnladed by [ ] at 06:22 10 January 2018 Tyne Nidd Trent Thames Exe Severn Wye Dee Lune Bywell Hunsingre Clwick Teddingtn Thrvertn Bewdley Cadra (Redbrk frm 1972) Erbistck (Manley Hall frm 1972) Haltn f sil), 0.76; England and Wales mean rainfall minus actual evapratin at Kew Observatry, 0.70; hydrlgically effective rainfall at Kew Observatry, Whilst the crrelatin cefficients (r) are all significant at the 1.0 per cent level, the residuals are large and the abve results serve mainly t emphasize the unrepresentative nature f available lng-time series f single pint measures f evapratin and strage. Antecedent rainfall is clearly an imprtant factr in determining water-year runff, hence in searching fr a simple mdel, the estimates f ttal runff derived frm the nine selected basins (RUNOFF (bs)) were regressed n RAIN 12, RAIN 13, RAIN 23, RAIN 24 where RAIN 12 = the general rainfall in a given water-year, RAIN 13 = RAIN 12 + the general rainfall fr the preceding September (N.B. general rainfall is the average rainfall fr England and Wales) RAIN 23 = RAIN 22 + the general rainfall fr the preceding Nvember RAIN 24 = RAIN 23 + the general rainfall fr the preceding Octber The results f this exercise are shwn in Fig. 2. The cmbinatin f rainfall in a given water-year plus the rainfall in the preceding mnths f June t September (t give RAIN 16) may be seen t be best crrelated with the runff in that water-year. This indicates a cntrl n water-year runff f the rainfall amunt in the previus summer and early autumn. The way in which the curve jining the crrelatin cefficients in Fig. 2 increases t a maximum and then slwly decreases shws the relative cntributin f this cntrl as the antecedent perid cnsidered is lengthened. Similar crrelatins can be btained fr individual basins t reveal ptimum rainfall perids but RAIN 16 is apprpriate fr England and Wales as a whle.

6 Annual runff frm England and Wales 135 Dwnladed by [ ] at 06:22 10 January 2018 RAIN 12 RAIN 13 RAIN 14 RAIN 15 RAIN 16 RAIN 17 RAIN 18 RAIN 19 RAIN 20 RAIN 21 RAIN 22 RAIN 23 RAIN 24 FIG. 2. The variatin f crrelatin cefficient, r, frm the regressin f runff n RAIN 12, RAIN 13...RAIN 24. A summary f the regressin f RUNOFF (bs) against RAIN 16 is tabulated belw: RUNOFF = RAIN withr = and a RUNOFF = 93.2 mm The standard errr f the estimate (RUNOFF), S = a RUNOFF sf(l-r 2 ) = 93.2\/(l-~0-953) = 20.3 mm RUNOFF ACTUAL RUNOFF PREDICTED (1) 59/60 64/65 69/70 75/76 WATER YEARS FIG. 3. Runff bserved frm the nine basins and estimated by the regressin mdel.

7 136 T. J. Marsh and I. G. Littlewd TABLE 2. England and Wales RAIN 16 and runff (mm) Year RAIN 16 Runff Year RAIN 16 Runff Year RAIN 16 Runff * 1043* * September 1752 had 19 days. Dwnladed by [ ] at 06:22 10 January 2018

8 Annual runff frm England and Wales 137 TABLE 2 (cntd). England and Wales RAIN 16 and runff (mm) Year RAIN 16 Runff Year RAIN 16 Runff Year RAIN 16 Runff Dwnladed by [ ] at 06:22 10 January

9 138 T. J. Marsh and I. G. Littlewd and represents the 68 per cent cnfidence limits crrespnding t the predicted runff. The 95 per cent cnfidence limits, given by 2S, aie ± 40.6 mm. By cmparisn the crrespnding limits fr runff estimated using RAIN 12, in a linear regressin equatin, are ± 93.6 mm. Figure 3 illustrates the gdness f fit ver the perid Included in this time interval are 3 f the 35 driest water-years in the perid ; it is cnsidered that the clse agreement between the bserved and estimated values ver the calibratin perid makes this mdel particularly suitable fr estimating runff in dry water-years. Dwnladed by [ ] at 06:22 10 January 2018 Generatin f the runff time series The mdel described by Equatin (1) was emplyed t hindcast water-year runff t 1728 using RAIN 16 values derived frm the mnthly general rainfall series, cmmencing in January 1727, supplied by the Meterlgical Office (Nichlas & Glassple, 1931; Wales-Smith, 1971). Thrughut the eighteenth century the sparse raingauge netwrk did nt lend itself t the definitive assessment f areal rainfalls; the earliest cmputed runffs shuld therefre be treated with cautin. A listing f RAIN 16 and estimated runff frm 1728 t 1976 is given in Table 2. Frequency analysis The runff time series was ranked frm smallest (m return perid fr a given event cmputed where % PROBABILITY T = n + 1 m 1) t largest (m = n) and the AT RUNOFF IN ANY SINGLE WATER YEAR WILL r GREATER THAN STATED AMOUNT J [ BE J I I I I 1 I I I I 1_ -300 % PROBABILITY THAT RUNOFF IN ANY SINGLE WATER YEAR WILL IE EQUAL TO OR LESS THAN STATED AMOUNT FIG. 4. Water-year runff against prbability

10 Annual runff frm England and Wales 139 Crrespnding values f prbability (P = 1/7) were cmputed; Fig, 4 shws a plt f magnitude against prbability. It shuld be nted that fr the perid the bserved ttal runff values, frm the nine index statins, have been used. DISCUSSION Dwnladed by [ ] at 06:22 10 January 2018 When dealing statistically with events as rare as the recent drught, their frequency cannt be accurately assessed with the limited histrical data available, but Fig. 4 demnstrates that water-year runff similar t that experienced in 1976 (202 mm) is exceptinal indeed; a prbability f 0.5 per cent t 0.8 per cent is assciated with runff f this magnitude. It can be estimated, with mre cnfidence, that a 300 mm ttal runff can be expected, n average, nce every 20 years. Gegraphically, drughts are nt unifrm in their effect; the intensity varies frm regin t regin. Lcal strage capacities als influence the perids ver which extended lw flws becme critical. The prbability f cntinued lw rainfall als varies spatially with a greater risk in the lw rainfall areas f the suth and suth east f England (Rdda, 1965; CWPU, 1976). Examinatin f the rainfall distributin f histrical drughts clearly demnstrates, hwever, that the spatial variatins are nt capricius. The extended perids f rainfall deficiency f 1887, 1921, 1933/34 and 1959 were assciated with general rainfalls f less than 80 per cent f the mean cmbined with large areas experiencing nly per cent f the average fr perids f 9-15 mnths. Taking England and Wales as a single gegraphical regin, it is t be expected that ttal runff will display similar characteristics with lcal intense drughts superimpsed n a natinal deficiency. If the frequencies f runff events illustrated by Fig. 4 are t be valid fr strategic planning purpses, it shuld be demnstrated that statistically the time series f runff exhibits neither verall trend nr predictable fluctuatins. Fig. 5 shws a plt f the 11-year mving average f runff, RAIN 12 and RAIN 16. N verall trend is discernible but a number f interesting fluctuatins are apparent. The significance f these departures frm average cnditins shuld be cnsidered alngside Fig. 6 which illustrates 11 'year' mving averages derived frm a series f cmputer-generated randm numbers frm a nrmal distributin having a mean and standard deviatin identical t that fr RAIN 16 ver the perid The tw plts display similar fluctuatins indicating that, n the evidence presented, the variability f water-year runff is essentially f a randm nature. CONCLUSIONS Ttals f 16 mnth rainfall (RAIN 16 June t September) fr England and Wales have been shwn t be highly crrelated with water-year runff (r = 0.976) enabling a time series f annual runff t be hindcast t 1728 emplying the available rainfall recrd. It is thught that the methd by which RAIN 16 was identified as the best independent variable fr England and Wales culd be successfully applied n a reginal r, in sme instances, a basin scale t reveal the best length f rainfall fr estimating annual runff frm rainfall alne. Simple prbability analysis has shwn that annual runff frm England and Wales

11 140 T. J. Marsh and I. G. Littlewd Dwnladed by [ ] at 06:22 10 January 2018 CO 00 t

12 Annual runff frm England and Wales 141 Dwnladed by [ ] at 06:22 10 January 2018 en,_ CO t 3-

13 142 T. J. Marsh and I. G. Littlewd f the rder f 300 mm can be expected, n average, nce every 20 years and runff f 200 mm n average, nce every years. Tempral variatins f water-year runff frm England and Wales must still be cnsidered randm due t the lack f statistical evidence t suggest therwise. ACKNOWLEDGEMENTS The Authrs wish t express their gratitude t clleagues fr cmments during the preparatin f this paper. We als thank the staff f the Central Water Planning Unit, Reading, Berkshire, and the Directr-General and staff f the Meterlgical Office, Bracknell, Berkshire, fr prviding sme f the necessary data. This Paper is published with the permissin f the Directr f the Water Data Unit. Dwnladed by [ ] at 06:22 10 January 2018 REFERENCES Central Water Planning Unit (1976) The Drught: A Hydrlgical Review: Technical Nte N. 17. Daltn, J. (1802) Experiments and bservatins t determine whether the quantity f rain and dew is equal t the quantity f water carried ff by rivers and raised by evapratin; with an enquiry int the rigin f springs. Mem. Lit. Phil. Sc. Manchester, 5,Pt II, Mrris, R.M. & Ratcliffe, R.A.S. (1976) Under the weather. Nature, 264, 4-5. Nichlas, FJ. & Glassple, J. (1931) General mnthly rainfall ver England and Wales 1727 t British Rainfall: HMSO, Perry, A.H. (1976) The lng drught f Weather, 31, Rdda, J.C. (1965) A drught study in suth-east England. Wat. Eng., August, Rdda, J.C, Dwning, R.A. & Law, F.M. (1976) Systematic Hydrlgy: Newnes-Butterwrths, pp. Ill and 120. Wales-Smith, B.G. (1971) Mnthly and annual ttals f rainfall representative f Kew, Surrey, frm Met. Mag. 100, Wright, CE. (1976) Once in 1,000 years? Water, Nvember, 2-6.