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Water quality considerations in the design of water resource systems
~aler Rewarth ~¢ol. ~,. p p ~09 tO q ' 5 Per[lamon Pr~:~,, 1~74 P r l n l c d ~n ~.ircal I'lrl|aln
W A T E R Q U A L I T Y C O N S . I D E R A T I O N S IN THE D E S I G N O F WATER R E S O U R C E S Y S T E M S C. PAGr and A. E. WAR~ Water Resources Board. Reading. England (Receired 11 Noremher 1973)
I. INTRODUCTION
in the water resource system If the predicted levels of
The u~ of simulationmodelsfor the evaluationof pro- quality exceed any limits imposed on grounds such as p o s e d water resource systems has recently been investigated [I]. In this work, long periods of synthetic river flow data are generated possessing the same statistical characteristics as the historic flow records. These data are used as input to the simulation model together with such physical constraints as reservoir storage. pumping capacities and minimum flow constraints on river abstraction. The simulation model is then run for the projected water demands for the region, and the water resource system evaluated in terms of failure to meet demands. In the past. the application of mathematical techniques to the evaluation of water resource systems has concentrated on the quantitative aspect. However, with the growing need to abstract water from the lower reaches of rivers, and the increasing volumes of discharges of waste water to rivers, it has become important to investigate the effect of water-quality considerations on the yields of water resource systems. A potential method of evaluating such effects is to extend water-quantity simulation models to include waterquality parameters. Unfortunately, data on water quality are often less complete than those for river flows. Moreover, the natural processes which occur in rivers and stored water, and which affect some aspects of water quality, are not well understood. Nevertheless, it is possible to model adequately some water quality characteristics, and. if due regard is given to the sensitivity of the results of the simulation model to uncertainties which surround the input data, such a model may be used to predict the fluctuations of water quality at key points
public health, then the effects of improvements to the standards of effluents entering the system ma~ be simulated. Alternatively, it may be possible to obtain an improvement in the quality of water taken into supply by abstracting or storing river water o n h at times when the water quality is good. However, an.~ such improvemerit would be at the expense of the reliable yield of the system as calculated solely on the basis of water quantity, This report describes a research project aimed at introducing water quality parameters into a quantityonly simulation model of the resources of the Welland" and Nene River Authority.* Initially. two v,ater quality characteristics were c~nsidered. The first, chloride, was expected to. exhibit conservative behaviour throdghout the water resource system, and to occur in the rivers mainly as a result of discharges from well defined sources. The modelling of chloride was regarded as a tesi of the proposition that a water quantity model could be extended to include water qualit3 despite the fact that it is of only limited significance to water supply undertakings. The second characteristic, nitrate, which was expected to be more dil'ficuh to model, was to be considered only after the successful simulation of the behaviour of chloride. Nitrate was adopted as an example of a pollutant expected to have increasing significance to the operation of water resource systems as the rivers receive increasing volumes of waste water. 2. THE WATER QI. ALITY MODEL (a) Generalfi, atures
This paper was received for the Paris Conference. but together with several more was accepted for Water Rese,~rch as there was no place for it on the Conference Programme. * The area of the Welland and Nene River Authority is in eastern England. After March 1974. the region will become part of the new Anglian Water Authority. w.a. 8 '! I~H
Figure I shows the principal resources of the Welland and Nene River-Authority area. The two major rivers, the Welland and the Nene are to be used to fill a pumped-stor.age reservoir. Empingham, which is under construction. The water stored in Emphingham will supply Northampton and Leicester, and regulate the 969
970
C. Pa6t and A, E W xk',, Within the model, decisions are made on a dall~ basis on the quantity of water to pump from an? ri~cr to any other river, reservoir or centre of demand. Similarly, decisions are made on the quantit? of v, ater to be taken from storage for direct supply to centres of demand or for river regulation. These decisions are based on the values of the demands, the amount of water in the reservoirs, the river flows and pumping capacities. The decisions may depend also on the levels of x~ater quality parameters in the river or stored
Welland to support abstractions for Peterborough. Such regulation could also be achieved by the direct transfer of Nene water to the Welland. South Lincolnshire (excluding Peterborough)will be supplied both from the Lincolnshire Limestone aquifer and by direct abstraction from the Welland. A s e c o n d , much smaller pumped-storage reservoir, Pitsford. is filled from the Nene and supplies part of the demand of Northampton. Waste water from Northampton is discharged to the Nene upstream of the intake for Empingham. and will thereby introduce a degree of rec3cling through the reservoir.
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{c) Water ql~alit)" =ktta (b) Structure of the modt'l "
Two historic records were used to provide most of the water quality data for the model. These were for the river Nene at Wansford and the river Welland at Tinwell (the locations of the intake pumping stations for filling Empinglmm reservoir). Both records, which include 32 water quality characteristics, covered a period of 5 years throughout which an averaged daily sample had been taken every 2 weeks. The historic records were analysed with two objectives: firstly to isolate the contributions to the levels of chloride and nitrate attributable to discharges of waste water. This was done because, in the future, the pollution load from effluents will tend to rise whereas other contributions (or background sources) might be expected to remain much the same. The second objective was to de~ribe mathematically the fluctuations in the levels of river water-,quality arising from background sources, and hence to generate synthetic ~ater-quality records for input to the model. Whereas the Nene at Wansford contains a significant proportion of waste water, the Welland at Tinwell
The model is a simple accounting procedure with built-in lags and attenuations. Natural (i.e. effluent free) average daily flows for the rivers Welland. Nene. Gwash and Glen are taken from a synthetic flow sequence, and their progress through the resource system is traced, adding in flows from effluent treatment works and tributaries, and subtracting quantities pumped to stoi'age reservoirs or directl~~to centres of demand. Similarly, background average daily inputs for the two water quality characteristics are traced through the system, additions being made where effluents are discharged to the rivers, and allowances introduced where necessary to account for degradation due to natural processes occurring in the rivers and reservoirs. The quality of river water downstream of any tributary or effluent discharge is calculated assuming complete and instantaneous mixing of the two sources. Any input to a r~servoir is assumed to mix in the same way with the body of water already in storage.
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Fig. I. Diagram of the Welland and Nene water resource system.
Water qualiD considerations Table I. Data u~cd in the model of the Welland and Nene water resource system CapaciD of Empingham Reservoir CapaciD of Lincolnshire Limestone Aquifer Capacity of Pitsford Reservoir CapaeiD of Nenc to Empingham pipeline Capacity of Wclland to Empingham pipeline Minimum prc~cribcd tlo~von Ncnc Minimum prescribed tlo~,, on "¢,'elland Projected 21M~1~,tter demand for Northampton Projected 21~1 ~atcr demand for Leicester ffrom Empinghaml Projected 21~11~atcr demand lot Pcterborough ProJected 2~1 water demand for S. Lincolnshire
is relativcl~ free from effluent and therefore its record was assumed to provide a reasonable representation of natural water qualit). In the absence of a detailed record of water qualit.~ for the effluent free part of the Nene. this was also applied to the Nene. This assumption was rea~nablc because of the similar environment and proximit) of lhc t',xo rivers, and was borne out by such records as ~Vel'Cavailable for the upper Nene [3"]. An attempt has been made to determine the most suitable methods of representing in the model both the background and effluent inflows of levels of water quality characteristics. So far, most attention has been given to the inputs of chloride. For the present. detailed de~riptions of tl,,c daily fluctuations in the quality olscwage cltlucnts ha'~e not been included. The daily chloride load in the effluent has been split into t~o parts,-thc contributions from domestic and industrial sources. The current contributions from these sources have been determined from a mass-balance model of the average situation in the region. For future conditions it has been assumed that It) the chloride load from domestic sources depends directl~ on the population served and'that the current per capita loads will apply and lit) the chloride from industrial sources will have the same concentration as at present. For the natural inflows, constant daily mean values of concentration of pollutants were used initially. This meant that fluctuations in water quality predicted by the model were due entirely to natural variations in river flows, which provided different levels of dilution of efl:luents from day to day. To enable a better representation of background leve~s to be made. an approach was attempted similar to that used for the analysis of flow records for the generation of synthetic daily flow data. The record for a given water-quality characteristic was investigated to determine the extent to which fluctuations could be correlated with variations in other factors. The most obvious factors to consider were: (i] time of year: lit) river flow:
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124 million m~ 350 million m3 17.5(10 m3 520.000 m3 day- t 360,000 m3 day136.~D0 m"~da~36.(~) m3 da~- t 306.tk"~Om3 day18.0~0 m~ day74.000 m~ day137.f¢)0 m3 day -
(iii) autoregressive effects, i.e. correlation between successive daily values; (iv) other water quality characteristics. Although there may not always be obvious physical reasons for such relationships, if there is evidence from the past records that the3 do exist, it is desirable to retain them in the model in order to make valid projections of future conditions. Since the available records contained readings at intervals not less than two weeks, it was not possible to identi~ the daily autoregressive component. Inspection of the records indicated no obvious correlation between successive fortnightly readings. This aspect of the records was therefore neglected. Similarly. correlation between different water qualiD constituents has received limited attention. Variation of the levels of chloride and nitrate with time of year was investigated by obtaining the best fit Fourier series. For chloride, the amount of variation in the record which could be accounted for was only It) per cent of the total v~.riance: for nitrate nitrogen the figure was 45 per cent. Ala illustration of the chloride record with the best fit annual cycle is shown in Fig. 2. The record contains too many peaks for a large proportion of the variance to be explained. Linear regression analysis was used to investigate the relation between water quality and flow. No correlation was found between nitrate nitrogen and flo~ and for chloride, only 12 per cent of the total variance in the quality records could be explained. Inspection of the plot of chloride concentration against flow suggested that a non-linear relationship might produce a better fit. Consequently. regression analyses were performed of chloride with the reciprocal and with the logarithm of flow; the amounts of variance accounted for being 15 and 24 psr cent respectively. After considering the correlation of river water quality with time of year and river flow. there remained a large unexplained proportion of the total variance. However. in the derivation of a synthetic water quality
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C. P XGEand A. E. WA~',
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SAMPLING OATE5 (YEARS)
Fig. 2. Calculated annual cycle and the historic chloride record for the River WelMnd.
record, further progress may be made by identifying the mathematical distribution of the residuals remaining after removing tbe deterministic components from the quality record, and by g e t , rating a random sample from this distribution. These generated residuals may then be used with the quality record derived from the deterministic equations to provide a synthetic quality record for input to the model. Thus.there are a number of possible levels of complexity which may be employed in the generation of a synthetic record of river water qualit3: (it constant mean values independent of season or river flow: (ii) seasonally dependent values generated from the bestfit Fourier series: t'iii) values generated as a function of river flow: (iv) as (iii) or (ii) with random residuals superimposed. For certain water quality parameters, some of these methods are not suitable. For example, for chloride. variation with season is sufficiently small to not merit further investigation. For nitrate nitrogen, as discussed abo~e, 45 per cent of the variance is explained by correlation with time of year. but variation with flow is negligible. The sensitivity of the model to the following three different forms of synthetic chloride record was tested: d) constant mean values: (ii) values generated from the logarithm of river-flow; (iii) as (ii) with random residuals superimposed. It was found that the chloride levels predicted by the model were very similar for all three forms of input data. Compared with method (it. method (ii) produced
a 40,~ decrease in the predicted mean chloride level for Empingham reservoir, but there was no further change when method (iii) was used. The predicted maximum levels were identical for all three methods. The small decrease from method (i) to method (ii) could be attributed to (at the background chloride levels in the rivers being lower when flows were higher and (b) more water being pumped to the reservoir from the rivers in these high flow periods. The decrease was not larger than 4"° because of the low level of correlation between chloride concentration and the logarithm of flow. The negligible difference between methods lii) and (iii) was du~" to the fact that the fluctuations introduced into the b a c k ~ o u n d levels of chloride for the rivers in method (iii) were too small to influence the large body of water stored in the reservoir. As a result of these tests, it was thought that there was some justifi~tion for preferring method fii) to method (it. but that no further benefit was to be gained by using method (iii). It should be recognized that the conclusions reached concerning the best form of synthetic chloride data do not necessarily apply to other water quality characteristics. Better correlation of a water quality characteristic with flow or time of year might well lead to a greater difference between methods/it and (ii). Additionatl.~. when the day-to-day decisions to pump a reser~oir depend on the daily levels in the rivers of a given poilutant. it is important that infrequent peaks in the historic water quality record are reproduced in the synthetic data. This can only be achieved by incorporating the random residuals in the synthetic data.
Water quality considerations 3. APPLICATIONS OF TitE SIMISLATION MODEL OF THE V~,ELLAND AND NEXE ~ATER RESOURCE SYSTEM In this section, some examples are given of the use of the model to examine the effect on chloride concentrations of altering the constraints and operating rules of the water resource system. In each case the model was used to simulate 100 yr of operation of the system for the projected demands of 2(.)01. The time period of lO0 yr was selected as providing a reasonable number of extreme events for moderate costs of computation. (a}. The cffect of recirculation
9":3
of 136.()00 m a d a y - ~be left in the river Nene bclo~v the intake pumping station at Wansford. It has been suggested that the recycling of effluent from Northampton through the reservoir would cause a build up of poilutams, and that this effect might be ameliorated by an increase in the minimum flow constraint lbr ri~er abstraction stipulated for the Nene at Wansford. The simulation model was used to investigate the effect on the water resource system of increasing the minimum flow constraint at Wansford b) 25 per cent to 170,000 m 3 d a y - ~. This increase.was found to cause a reduction of only 5 per cent in the predicted levels of chloride in Empingham reservoir: the mean concentration being reduced from 57 to .~4 mg I- ~. This small improvement in water qu:dit.x occurred because under the higher minimum flow constraint :t smaller quantity of the river water containing the highest proportion of effluent was pumped to. the reservoir. However. the improvement was achieved at the expen~ of exposing the system to a greater risk of failure for a given demand. For the lower minimum flow constraint. only three..quartersofthe reservoir storage was e vet used. For the increased flow constraint, the whole storage was required and the system came close to failure. To summarize, it was shown that a sacrifice of approximately 25 per cent of the available storage in Empingham. (i.e. 27,000 m a) would have to be made to achieve a 5 per cent improvement in the average chloride concentration of the stored water. These percentages cannot be applied directly to other conservative water quality characteristics because of the considerable contribution of background levels of chloride to those pumped to storage. In the general case. the proportion of the concentration of a conservative pollutant in an effluent which is pumped to the reservoir has been calculated in (a), above, to be 30 per cent. Following the increase to the minimum flow constraint this proportion is reduced to 25 per cent. Thus for a conservative
For some water quality characteristics the effluent quality depends on the quality of water supplied to the demand centre. In Fig. 1, it ma) be seen that the effluent from Northampton is discharged to the Nene uPStream of the intake pumps for Empingham reservoir. Since Empingham is to be used to supply Northampton there may be a tendency for the concentrations of certain pollutants to build up in the system due to the re-use of a proportion of the water. The simulation model was used to investi~te the magnitude of this recycling effect by examining the response of the system to the removal of the effect of recycling o n the quality of the effluent from Northampton. It showed that the effect of recycling on the levels of chloride is small, producing an increase from only 52 to 57 mg 1- J in the predicted mean concentrations in the reservoir and 6~71 mg 1- t in the predicted max•imum concentrations. Chloride is of limited interest to water undertakings. Nevertheless. the results obtained indicate the average pror, ortion of the concentration of a conservative water quality characteristic discharged in waste water which will appear in Empingham reservoir. Assuming an average background chloride concentration of 35 mg I- t and a net addition of 75 mg I- t after use, this proportion is: (avera[e concentration in reservoir--avera[e back[round concentrationl (average net concentration added on use) i.e. 30 per cent. = 157- 35)75 Without recycling the comparable figure is 23 per cent. These proportions may be used to assess the influence on the quality of the stored water of any conservative pollutant discharged in the effluent. Similarly. for degradable pollutants and characteristics whose concentrations cannot at present be measured, the figures provide an indication of the likely maximum effects of recirculation on the quality of water in the reservoir. (b)
Increase o./'rninintumflow constraint
In the Act authorizing the construction of Empingham Reservoir, it was stipulated that a residual flow
pollutant originating only in effluents, the average reduction in concentration brot!ght about by increasing the minimum flow constraint by 25 per cent would be 530 x 100 i.e. 17 per cent. (c) Alternatire methods o.1 supplying Peterhorough Both the main rivers of the area. the Nene and the Welland. are possible sources of supply for Peterborough (see Fig. I). Although the Nene flows through Peterborough and is the larger river, it has been suggested that the increasing proportion of effluent entering the Nene from Northampton area might render it
974
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Fig. 3. Predicted chloride concentrations in Empingham Reservoir resulting from different strategies for meeting the future demand of Peterborough.
unsuitable for supplying Peterborough. The Welland, although some distance from Peterborough, might be more suitable from the standpoint of water quality. However, the Welland will be required also to supply the South Lincolnshire demand since the predicted value for the year L"~01cannot be met completely from the Lincolnshire Limestone aquifer. This commitment means that the Welland will not be able to meet the full Pcterborough demand. Two possibilities exist for regulating the Welland to provide the additional water: (i) transfer of Nene water to the WeUand using part of the pumping scheme otherwise used to fill Empingham. In this way, the poorer quality Nerte water is diluted with Welland water prior to abstraction for Peterborough; (iil release of water from Empingham to the Welland via the river Gwash {Fig. I). The Nene water is thereby mixed with Welland water in the storage reservoir which provides 'also a buffer between the river Nene and Peterborough. Three alternative methods of supplying Peterborough were evaluated using the simulation model The three methods are summarized below: Method I. (i) Provide as much water as possible from the Weiland without violating the minimum flow constraints for river abstraction (Table I ). (ii) Transfer water from the Nene to the Welland provided the flow of the Nene is above its minimum flow constraint for river abstraction. (iii) Release water from Empingham reservoir to the Welland (via the Gwash). Method 2. (i) As (i) above. (ii) As (iii) above. In this method the direct transfer of Nene water to the Welland is not considered. Method 3. (i) Supply the whole demand directly from the Nene. In methods I and 9_ the Peterborough demand will fail to be met only when Empingham reservoir fails. In method 3, there will always be sufficient water in the Nene so long as the demand for Northampton is being
met and the resulting effluent is discharged to the Nene
[t]. It was found that no one method provided a greater degree of reliability than the others in terms of I~ailure to meet all the demands of the system. The major differences between the methods arose in the predicted levels of water quality and the amounts of water pumped through different links of the system. Graphs showing the predicted frequency of occurrence of different chloride levels in Empingham reservoir and in the supply to Peterborough are given in Figs. 3 and 4. The levels of chloride in the supply to Peterborough were found to be lowest for method 2 {mean level: 46 mg l- i. maximum level: 90 mg l- 1). This was not surprising because this method featured no direct transfer of Nene water to Peterborough or to the Welland. The figures for Empingham reservoir for method 2 were correspondingly higher because less Welland water was available for storage, and the deficit was made up by taking more from the poorer quality Nene. Of the other two methods, although the predicted mean level of chloride in the supply to Peterborough w~s considerably less for method I than for method 3 (59 mg I-1 against 76 mg l" ~). the predicted maximum concentration was only slightly lower t 133 mg l- 1 against 143 mg l- 1). The maximum levels occurred at times of low river flows during which times most of the supply to Peterborough in method l came via the dir.Jct transfer of Nene water to the Welland. The resulting quality of the supply to Peterborough was at these times only marginally better than the quality of the Ne'ne itself, i.e. the supply for method 3. The relatively low levels of chloride in the supply to Peterborough achieved using method 2, were obtained only with greatly increased pumping costs. Compared with method I. an extra quantity averaging 44.000 m 3 day-* had to be pumped from the Welland to Empingham. Compared with method 3. an extra 50.000 m 3 day- * had to be pumped from the Nene to the Wel-
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Fig..4. Predicted chloride concentrations in the supply to Pelerborough re~ultmg from d~ltL'rent stra~,:g~es Ior meeting the future demand.
land a n d a n extra 43.O(1~) m ~ da', - ~ from tile Welland to Empinghana. M e t h o d 3. invol~ing no a b s t r a c t i o n s from the Welland to P e t e r b o r o u g h ,.~as the most ect-momic m e t h o d of supply in terms of costs of pumping. •~. ( O ' ~ C ' L t slO~,S Simulation ha,; been shovcn to be a u.~lul m e t h o d of investigating the general quatit) of water supplied from a resource system. A means of evalu;|ting the effect of quality c o n s t r a i n t s on the yield of the resource s~ stem is provided, a n d the relative effectiveness of diflk:rent m e t h o d s of reducing lhc c o n c e n t r a t i o n s entcrin~ suppl', ma.~ be as:,cssed. The potential exists for the inclusion of cost information in the simul:~tion m o d e l ~ h i c h ~ i l l p,:rmit a n e¢ono,'nic c o m p a r i s o n of the options. W o r k is c o n t i n u i n g on water qualit~ characteristics of more spc¢itic interest to ~ u t e r u n d e r t a k i n g s than chloride a l t h o u g h the study of this characteristic does provide a n indic:|tion of the maximtua~ lexels attain-
able by degradable pollut:lnt,; \ ,;lad\ tfl l~i!r:tl¢ hds indicated the m l p o r t a n c c o~ the ~a~,onal cllk:ct o n the b a c k g r o u n d quality levels, on the quality of elt'lt|ents. a n d on the effect of storage on qualit). Currentl.~ these effects arc being analysed in more detail. ..Ickm~u'iedqt, m e u t s - - T h c author, ~.i,,l~ It', th:ir;k \ I t R E Field and Mr. N. Lo~ of tile Fisheries ;aid I),,lltlt;on Pro~cntion Dcp:|rtment of the ~,~,.'clland 'rod %¢1~' Rl~,.'r \utllorit) for helptid discussion.,, and fi~r suppi.~in~ \~:ttcr quaht3 records. The authors also wish to thank the I)trect,,: ,~f the Water Re~urcc~, Board for permission to ptINi,,h Ihl,. xsork Tile views expressed tire tho.~ of tile atll!h',r~. ;tnd llot ileccssaril.~ those of the Board. REF[~RE\(E~ [ l ] Jamieson D G.. Radl~.,rd P J and Scx~o~,, J I~ ~lq-4~
Tl'c H:'dr,,to~/ic D:'.~i~p~ ~l It'~ttcv l'~c,,,tlr(~ SI ,r,.'m.~. Water Rc~ourc¢~ Board Report. In pr,:,, [2] Bloomer R J. G. and .~\ton J. R. 7i~, (,,.,,.,,,!~,,~: oJ Svulhc'..,t F h m D,~t,. Public:ltion \ o ~5 \\~ltcr Resources Board. England. [3] Welland and Nene Ri~.cr .~ttthorilx...%nnu.fl Reports 1967-19~.',. 196X-19fi9. 1960 19"(L 19"~b I'~'1. I9"1. 1972. 19"2- 1973.
W A T E R Q U A L I T Y C O N S . I D E R A T I O N S IN THE D E S I G N O F WATER R E S O U R C E S Y S T E M S C. PAGr and A. E. WAR~ Water Resources Board. Reading. England (Receired 11 Noremher 1973)
I. INTRODUCTION
in the water resource system If the predicted levels of
The u~ of simulationmodelsfor the evaluationof pro- quality exceed any limits imposed on grounds such as p o s e d water resource systems has recently been investigated [I]. In this work, long periods of synthetic river flow data are generated possessing the same statistical characteristics as the historic flow records. These data are used as input to the simulation model together with such physical constraints as reservoir storage. pumping capacities and minimum flow constraints on river abstraction. The simulation model is then run for the projected water demands for the region, and the water resource system evaluated in terms of failure to meet demands. In the past. the application of mathematical techniques to the evaluation of water resource systems has concentrated on the quantitative aspect. However, with the growing need to abstract water from the lower reaches of rivers, and the increasing volumes of discharges of waste water to rivers, it has become important to investigate the effect of water-quality considerations on the yields of water resource systems. A potential method of evaluating such effects is to extend water-quantity simulation models to include waterquality parameters. Unfortunately, data on water quality are often less complete than those for river flows. Moreover, the natural processes which occur in rivers and stored water, and which affect some aspects of water quality, are not well understood. Nevertheless, it is possible to model adequately some water quality characteristics, and. if due regard is given to the sensitivity of the results of the simulation model to uncertainties which surround the input data, such a model may be used to predict the fluctuations of water quality at key points
public health, then the effects of improvements to the standards of effluents entering the system ma~ be simulated. Alternatively, it may be possible to obtain an improvement in the quality of water taken into supply by abstracting or storing river water o n h at times when the water quality is good. However, an.~ such improvemerit would be at the expense of the reliable yield of the system as calculated solely on the basis of water quantity, This report describes a research project aimed at introducing water quality parameters into a quantityonly simulation model of the resources of the Welland" and Nene River Authority.* Initially. two v,ater quality characteristics were c~nsidered. The first, chloride, was expected to. exhibit conservative behaviour throdghout the water resource system, and to occur in the rivers mainly as a result of discharges from well defined sources. The modelling of chloride was regarded as a tesi of the proposition that a water quantity model could be extended to include water qualit3 despite the fact that it is of only limited significance to water supply undertakings. The second characteristic, nitrate, which was expected to be more dil'ficuh to model, was to be considered only after the successful simulation of the behaviour of chloride. Nitrate was adopted as an example of a pollutant expected to have increasing significance to the operation of water resource systems as the rivers receive increasing volumes of waste water. 2. THE WATER QI. ALITY MODEL (a) Generalfi, atures
This paper was received for the Paris Conference. but together with several more was accepted for Water Rese,~rch as there was no place for it on the Conference Programme. * The area of the Welland and Nene River Authority is in eastern England. After March 1974. the region will become part of the new Anglian Water Authority. w.a. 8 '! I~H
Figure I shows the principal resources of the Welland and Nene River-Authority area. The two major rivers, the Welland and the Nene are to be used to fill a pumped-stor.age reservoir. Empingham, which is under construction. The water stored in Emphingham will supply Northampton and Leicester, and regulate the 969
970
C. Pa6t and A, E W xk',, Within the model, decisions are made on a dall~ basis on the quantity of water to pump from an? ri~cr to any other river, reservoir or centre of demand. Similarly, decisions are made on the quantit? of v, ater to be taken from storage for direct supply to centres of demand or for river regulation. These decisions are based on the values of the demands, the amount of water in the reservoirs, the river flows and pumping capacities. The decisions may depend also on the levels of x~ater quality parameters in the river or stored
Welland to support abstractions for Peterborough. Such regulation could also be achieved by the direct transfer of Nene water to the Welland. South Lincolnshire (excluding Peterborough)will be supplied both from the Lincolnshire Limestone aquifer and by direct abstraction from the Welland. A s e c o n d , much smaller pumped-storage reservoir, Pitsford. is filled from the Nene and supplies part of the demand of Northampton. Waste water from Northampton is discharged to the Nene upstream of the intake for Empingham. and will thereby introduce a degree of rec3cling through the reservoir.
watdr,
{c) Water ql~alit)" =ktta (b) Structure of the modt'l "
Two historic records were used to provide most of the water quality data for the model. These were for the river Nene at Wansford and the river Welland at Tinwell (the locations of the intake pumping stations for filling Empinglmm reservoir). Both records, which include 32 water quality characteristics, covered a period of 5 years throughout which an averaged daily sample had been taken every 2 weeks. The historic records were analysed with two objectives: firstly to isolate the contributions to the levels of chloride and nitrate attributable to discharges of waste water. This was done because, in the future, the pollution load from effluents will tend to rise whereas other contributions (or background sources) might be expected to remain much the same. The second objective was to de~ribe mathematically the fluctuations in the levels of river water-,quality arising from background sources, and hence to generate synthetic ~ater-quality records for input to the model. Whereas the Nene at Wansford contains a significant proportion of waste water, the Welland at Tinwell
The model is a simple accounting procedure with built-in lags and attenuations. Natural (i.e. effluent free) average daily flows for the rivers Welland. Nene. Gwash and Glen are taken from a synthetic flow sequence, and their progress through the resource system is traced, adding in flows from effluent treatment works and tributaries, and subtracting quantities pumped to stoi'age reservoirs or directl~~to centres of demand. Similarly, background average daily inputs for the two water quality characteristics are traced through the system, additions being made where effluents are discharged to the rivers, and allowances introduced where necessary to account for degradation due to natural processes occurring in the rivers and reservoirs. The quality of river water downstream of any tributary or effluent discharge is calculated assuming complete and instantaneous mixing of the two sources. Any input to a r~servoir is assumed to mix in the same way with the body of water already in storage.
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Fig. I. Diagram of the Welland and Nene water resource system.
Water qualiD considerations Table I. Data u~cd in the model of the Welland and Nene water resource system CapaciD of Empingham Reservoir CapaciD of Lincolnshire Limestone Aquifer Capacity of Pitsford Reservoir CapaeiD of Nenc to Empingham pipeline Capacity of Wclland to Empingham pipeline Minimum prc~cribcd tlo~von Ncnc Minimum prescribed tlo~,, on "¢,'elland Projected 21M~1~,tter demand for Northampton Projected 21~1 ~atcr demand for Leicester ffrom Empinghaml Projected 21~11~atcr demand lot Pcterborough ProJected 2~1 water demand for S. Lincolnshire
is relativcl~ free from effluent and therefore its record was assumed to provide a reasonable representation of natural water qualit). In the absence of a detailed record of water qualit.~ for the effluent free part of the Nene. this was also applied to the Nene. This assumption was rea~nablc because of the similar environment and proximit) of lhc t',xo rivers, and was borne out by such records as ~Vel'Cavailable for the upper Nene [3"]. An attempt has been made to determine the most suitable methods of representing in the model both the background and effluent inflows of levels of water quality characteristics. So far, most attention has been given to the inputs of chloride. For the present. detailed de~riptions of tl,,c daily fluctuations in the quality olscwage cltlucnts ha'~e not been included. The daily chloride load in the effluent has been split into t~o parts,-thc contributions from domestic and industrial sources. The current contributions from these sources have been determined from a mass-balance model of the average situation in the region. For future conditions it has been assumed that It) the chloride load from domestic sources depends directl~ on the population served and'that the current per capita loads will apply and lit) the chloride from industrial sources will have the same concentration as at present. For the natural inflows, constant daily mean values of concentration of pollutants were used initially. This meant that fluctuations in water quality predicted by the model were due entirely to natural variations in river flows, which provided different levels of dilution of efl:luents from day to day. To enable a better representation of background leve~s to be made. an approach was attempted similar to that used for the analysis of flow records for the generation of synthetic daily flow data. The record for a given water-quality characteristic was investigated to determine the extent to which fluctuations could be correlated with variations in other factors. The most obvious factors to consider were: (i] time of year: lit) river flow:
b
j
124 million m~ 350 million m3 17.5(10 m3 520.000 m3 day- t 360,000 m3 day136.~D0 m"~da~36.(~) m3 da~- t 306.tk"~Om3 day18.0~0 m~ day74.000 m~ day137.f¢)0 m3 day -
(iii) autoregressive effects, i.e. correlation between successive daily values; (iv) other water quality characteristics. Although there may not always be obvious physical reasons for such relationships, if there is evidence from the past records that the3 do exist, it is desirable to retain them in the model in order to make valid projections of future conditions. Since the available records contained readings at intervals not less than two weeks, it was not possible to identi~ the daily autoregressive component. Inspection of the records indicated no obvious correlation between successive fortnightly readings. This aspect of the records was therefore neglected. Similarly. correlation between different water qualiD constituents has received limited attention. Variation of the levels of chloride and nitrate with time of year was investigated by obtaining the best fit Fourier series. For chloride, the amount of variation in the record which could be accounted for was only It) per cent of the total v~.riance: for nitrate nitrogen the figure was 45 per cent. Ala illustration of the chloride record with the best fit annual cycle is shown in Fig. 2. The record contains too many peaks for a large proportion of the variance to be explained. Linear regression analysis was used to investigate the relation between water quality and flow. No correlation was found between nitrate nitrogen and flo~ and for chloride, only 12 per cent of the total variance in the quality records could be explained. Inspection of the plot of chloride concentration against flow suggested that a non-linear relationship might produce a better fit. Consequently. regression analyses were performed of chloride with the reciprocal and with the logarithm of flow; the amounts of variance accounted for being 15 and 24 psr cent respectively. After considering the correlation of river water quality with time of year and river flow. there remained a large unexplained proportion of the total variance. However. in the derivation of a synthetic water quality
9",
C. P XGEand A. E. WA~',
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1969
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Fig. 2. Calculated annual cycle and the historic chloride record for the River WelMnd.
record, further progress may be made by identifying the mathematical distribution of the residuals remaining after removing tbe deterministic components from the quality record, and by g e t , rating a random sample from this distribution. These generated residuals may then be used with the quality record derived from the deterministic equations to provide a synthetic quality record for input to the model. Thus.there are a number of possible levels of complexity which may be employed in the generation of a synthetic record of river water qualit3: (it constant mean values independent of season or river flow: (ii) seasonally dependent values generated from the bestfit Fourier series: t'iii) values generated as a function of river flow: (iv) as (iii) or (ii) with random residuals superimposed. For certain water quality parameters, some of these methods are not suitable. For example, for chloride. variation with season is sufficiently small to not merit further investigation. For nitrate nitrogen, as discussed abo~e, 45 per cent of the variance is explained by correlation with time of year. but variation with flow is negligible. The sensitivity of the model to the following three different forms of synthetic chloride record was tested: d) constant mean values: (ii) values generated from the logarithm of river-flow; (iii) as (ii) with random residuals superimposed. It was found that the chloride levels predicted by the model were very similar for all three forms of input data. Compared with method (it. method (ii) produced
a 40,~ decrease in the predicted mean chloride level for Empingham reservoir, but there was no further change when method (iii) was used. The predicted maximum levels were identical for all three methods. The small decrease from method (i) to method (ii) could be attributed to (at the background chloride levels in the rivers being lower when flows were higher and (b) more water being pumped to the reservoir from the rivers in these high flow periods. The decrease was not larger than 4"° because of the low level of correlation between chloride concentration and the logarithm of flow. The negligible difference between methods lii) and (iii) was du~" to the fact that the fluctuations introduced into the b a c k ~ o u n d levels of chloride for the rivers in method (iii) were too small to influence the large body of water stored in the reservoir. As a result of these tests, it was thought that there was some justifi~tion for preferring method fii) to method (it. but that no further benefit was to be gained by using method (iii). It should be recognized that the conclusions reached concerning the best form of synthetic chloride data do not necessarily apply to other water quality characteristics. Better correlation of a water quality characteristic with flow or time of year might well lead to a greater difference between methods/it and (ii). Additionatl.~. when the day-to-day decisions to pump a reser~oir depend on the daily levels in the rivers of a given poilutant. it is important that infrequent peaks in the historic water quality record are reproduced in the synthetic data. This can only be achieved by incorporating the random residuals in the synthetic data.
Water quality considerations 3. APPLICATIONS OF TitE SIMISLATION MODEL OF THE V~,ELLAND AND NEXE ~ATER RESOURCE SYSTEM In this section, some examples are given of the use of the model to examine the effect on chloride concentrations of altering the constraints and operating rules of the water resource system. In each case the model was used to simulate 100 yr of operation of the system for the projected demands of 2(.)01. The time period of lO0 yr was selected as providing a reasonable number of extreme events for moderate costs of computation. (a}. The cffect of recirculation
9":3
of 136.()00 m a d a y - ~be left in the river Nene bclo~v the intake pumping station at Wansford. It has been suggested that the recycling of effluent from Northampton through the reservoir would cause a build up of poilutams, and that this effect might be ameliorated by an increase in the minimum flow constraint lbr ri~er abstraction stipulated for the Nene at Wansford. The simulation model was used to investigate the effect on the water resource system of increasing the minimum flow constraint at Wansford b) 25 per cent to 170,000 m 3 d a y - ~. This increase.was found to cause a reduction of only 5 per cent in the predicted levels of chloride in Empingham reservoir: the mean concentration being reduced from 57 to .~4 mg I- ~. This small improvement in water qu:dit.x occurred because under the higher minimum flow constraint :t smaller quantity of the river water containing the highest proportion of effluent was pumped to. the reservoir. However. the improvement was achieved at the expen~ of exposing the system to a greater risk of failure for a given demand. For the lower minimum flow constraint. only three..quartersofthe reservoir storage was e vet used. For the increased flow constraint, the whole storage was required and the system came close to failure. To summarize, it was shown that a sacrifice of approximately 25 per cent of the available storage in Empingham. (i.e. 27,000 m a) would have to be made to achieve a 5 per cent improvement in the average chloride concentration of the stored water. These percentages cannot be applied directly to other conservative water quality characteristics because of the considerable contribution of background levels of chloride to those pumped to storage. In the general case. the proportion of the concentration of a conservative pollutant in an effluent which is pumped to the reservoir has been calculated in (a), above, to be 30 per cent. Following the increase to the minimum flow constraint this proportion is reduced to 25 per cent. Thus for a conservative
For some water quality characteristics the effluent quality depends on the quality of water supplied to the demand centre. In Fig. 1, it ma) be seen that the effluent from Northampton is discharged to the Nene uPStream of the intake pumps for Empingham reservoir. Since Empingham is to be used to supply Northampton there may be a tendency for the concentrations of certain pollutants to build up in the system due to the re-use of a proportion of the water. The simulation model was used to investi~te the magnitude of this recycling effect by examining the response of the system to the removal of the effect of recycling o n the quality of the effluent from Northampton. It showed that the effect of recycling on the levels of chloride is small, producing an increase from only 52 to 57 mg 1- J in the predicted mean concentrations in the reservoir and 6~71 mg 1- t in the predicted max•imum concentrations. Chloride is of limited interest to water undertakings. Nevertheless. the results obtained indicate the average pror, ortion of the concentration of a conservative water quality characteristic discharged in waste water which will appear in Empingham reservoir. Assuming an average background chloride concentration of 35 mg I- t and a net addition of 75 mg I- t after use, this proportion is: (avera[e concentration in reservoir--avera[e back[round concentrationl (average net concentration added on use) i.e. 30 per cent. = 157- 35)75 Without recycling the comparable figure is 23 per cent. These proportions may be used to assess the influence on the quality of the stored water of any conservative pollutant discharged in the effluent. Similarly. for degradable pollutants and characteristics whose concentrations cannot at present be measured, the figures provide an indication of the likely maximum effects of recirculation on the quality of water in the reservoir. (b)
Increase o./'rninintumflow constraint
In the Act authorizing the construction of Empingham Reservoir, it was stipulated that a residual flow
pollutant originating only in effluents, the average reduction in concentration brot!ght about by increasing the minimum flow constraint by 25 per cent would be 530 x 100 i.e. 17 per cent. (c) Alternatire methods o.1 supplying Peterhorough Both the main rivers of the area. the Nene and the Welland. are possible sources of supply for Peterborough (see Fig. I). Although the Nene flows through Peterborough and is the larger river, it has been suggested that the increasing proportion of effluent entering the Nene from Northampton area might render it
974
C. PAGEand A. E. Warn ~8 F
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Fig. 3. Predicted chloride concentrations in Empingham Reservoir resulting from different strategies for meeting the future demand of Peterborough.
unsuitable for supplying Peterborough. The Welland, although some distance from Peterborough, might be more suitable from the standpoint of water quality. However, the Welland will be required also to supply the South Lincolnshire demand since the predicted value for the year L"~01cannot be met completely from the Lincolnshire Limestone aquifer. This commitment means that the Welland will not be able to meet the full Pcterborough demand. Two possibilities exist for regulating the Welland to provide the additional water: (i) transfer of Nene water to the WeUand using part of the pumping scheme otherwise used to fill Empingham. In this way, the poorer quality Nerte water is diluted with Welland water prior to abstraction for Peterborough; (iil release of water from Empingham to the Welland via the river Gwash {Fig. I). The Nene water is thereby mixed with Welland water in the storage reservoir which provides 'also a buffer between the river Nene and Peterborough. Three alternative methods of supplying Peterborough were evaluated using the simulation model The three methods are summarized below: Method I. (i) Provide as much water as possible from the Weiland without violating the minimum flow constraints for river abstraction (Table I ). (ii) Transfer water from the Nene to the Welland provided the flow of the Nene is above its minimum flow constraint for river abstraction. (iii) Release water from Empingham reservoir to the Welland (via the Gwash). Method 2. (i) As (i) above. (ii) As (iii) above. In this method the direct transfer of Nene water to the Welland is not considered. Method 3. (i) Supply the whole demand directly from the Nene. In methods I and 9_ the Peterborough demand will fail to be met only when Empingham reservoir fails. In method 3, there will always be sufficient water in the Nene so long as the demand for Northampton is being
met and the resulting effluent is discharged to the Nene
[t]. It was found that no one method provided a greater degree of reliability than the others in terms of I~ailure to meet all the demands of the system. The major differences between the methods arose in the predicted levels of water quality and the amounts of water pumped through different links of the system. Graphs showing the predicted frequency of occurrence of different chloride levels in Empingham reservoir and in the supply to Peterborough are given in Figs. 3 and 4. The levels of chloride in the supply to Peterborough were found to be lowest for method 2 {mean level: 46 mg l- i. maximum level: 90 mg l- 1). This was not surprising because this method featured no direct transfer of Nene water to Peterborough or to the Welland. The figures for Empingham reservoir for method 2 were correspondingly higher because less Welland water was available for storage, and the deficit was made up by taking more from the poorer quality Nene. Of the other two methods, although the predicted mean level of chloride in the supply to Peterborough w~s considerably less for method I than for method 3 (59 mg I-1 against 76 mg l" ~). the predicted maximum concentration was only slightly lower t 133 mg l- 1 against 143 mg l- 1). The maximum levels occurred at times of low river flows during which times most of the supply to Peterborough in method l came via the dir.Jct transfer of Nene water to the Welland. The resulting quality of the supply to Peterborough was at these times only marginally better than the quality of the Ne'ne itself, i.e. the supply for method 3. The relatively low levels of chloride in the supply to Peterborough achieved using method 2, were obtained only with greatly increased pumping costs. Compared with method I. an extra quantity averaging 44.000 m 3 day-* had to be pumped from the Welland to Empingham. Compared with method 3. an extra 50.000 m 3 day- * had to be pumped from the Nene to the Wel-
\I. ,~ICI qtl,tlll.'. ¢ O l l ~ . i d e r a t l o n s
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Fig..4. Predicted chloride concentrations in the supply to Pelerborough re~ultmg from d~ltL'rent stra~,:g~es Ior meeting the future demand.
land a n d a n extra 43.O(1~) m ~ da', - ~ from tile Welland to Empinghana. M e t h o d 3. invol~ing no a b s t r a c t i o n s from the Welland to P e t e r b o r o u g h ,.~as the most ect-momic m e t h o d of supply in terms of costs of pumping. •~. ( O ' ~ C ' L t slO~,S Simulation ha,; been shovcn to be a u.~lul m e t h o d of investigating the general quatit) of water supplied from a resource system. A means of evalu;|ting the effect of quality c o n s t r a i n t s on the yield of the resource s~ stem is provided, a n d the relative effectiveness of diflk:rent m e t h o d s of reducing lhc c o n c e n t r a t i o n s entcrin~ suppl', ma.~ be as:,cssed. The potential exists for the inclusion of cost information in the simul:~tion m o d e l ~ h i c h ~ i l l p,:rmit a n e¢ono,'nic c o m p a r i s o n of the options. W o r k is c o n t i n u i n g on water qualit~ characteristics of more spc¢itic interest to ~ u t e r u n d e r t a k i n g s than chloride a l t h o u g h the study of this characteristic does provide a n indic:|tion of the maximtua~ lexels attain-
able by degradable pollut:lnt,; \ ,;lad\ tfl l~i!r:tl¢ hds indicated the m l p o r t a n c c o~ the ~a~,onal cllk:ct o n the b a c k g r o u n d quality levels, on the quality of elt'lt|ents. a n d on the effect of storage on qualit). Currentl.~ these effects arc being analysed in more detail. ..Ickm~u'iedqt, m e u t s - - T h c author, ~.i,,l~ It', th:ir;k \ I t R E Field and Mr. N. Lo~ of tile Fisheries ;aid I),,lltlt;on Pro~cntion Dcp:|rtment of the ~,~,.'clland 'rod %¢1~' Rl~,.'r \utllorit) for helptid discussion.,, and fi~r suppi.~in~ \~:ttcr quaht3 records. The authors also wish to thank the I)trect,,: ,~f the Water Re~urcc~, Board for permission to ptINi,,h Ihl,. xsork Tile views expressed tire tho.~ of tile atll!h',r~. ;tnd llot ileccssaril.~ those of the Board. REF[~RE\(E~ [ l ] Jamieson D G.. Radl~.,rd P J and Scx~o~,, J I~ ~lq-4~
Tl'c H:'dr,,to~/ic D:'.~i~p~ ~l It'~ttcv l'~c,,,tlr(~ SI ,r,.'m.~. Water Rc~ourc¢~ Board Report. In pr,:,, [2] Bloomer R J. G. and .~\ton J. R. 7i~, (,,.,,.,,,!~,,~: oJ Svulhc'..,t F h m D,~t,. Public:ltion \ o ~5 \\~ltcr Resources Board. England. [3] Welland and Nene Ri~.cr .~ttthorilx...%nnu.fl Reports 1967-19~.',. 196X-19fi9. 1960 19"(L 19"~b I'~'1. I9"1. 1972. 19"2- 1973.