the Week of Proper 28 / Ordinary 33
Click here to join the effort!
Bible Encyclopedias
Water Supply
1911 Encyclopedia Britannica
or This article is confined to the collection and storage of water for domestic and industrial uses and irrigation, and its purification on a large scale. The conveyance of water is dealt with in the article Aqueduct.
Collecting Areas Surface Waters. - Any area, large or small, of the earth's surface from any part of which, if the ground were impermeable, water would flow by gravitation past any point in a natural watercourse is commonly known in Europe as the " hydrographic basin " above that point. In English it has been called indifferently the " catchment basin," the " gathering ground," the " drainage area " and the " watershed." The latter term, though originally equivalent to the German Wasserscheide- " water-parting " - is perhaps least open to objection. The water-parting is the line bounding such an area and separating it from other watersheds. The banks of a watercourse or sides of a valley are distinguished as the right and left bank respectively, the spectator being understood to be looking down the valley.
The surface of the earth is rarely impermeable, and the structure of the rocks largely determines the direction of flow of so much of the rainfall as sinks into the ground and is not evaporated. Thus the figure and area of a surface watershed may not be coincident with that of the corresponding underground watershed; and the flow in any watercourse, especially from a small watershed, may, by reason of underground flow from or into other watersheds, be disproportionate to the area apparently drained by that watercourse.
When no reservoir exists, the volume of continuous supply from any watershed area Dry is evidently limited to the minimum, or, so-called, extreme dry weather flow of the stream draining it. This cannot be determined from the rainfall; it entirely depends upon the power of the soil and rock to store water in the particular area under consideration, and to yield it continuously to the stream by means of concentrated springs or diffused seepage. Mountain areas of io,000 acres and upwards, largely covered with moorland, upon nearly imper meable rocks with few water-bearing fissures, yield in temperate climates, towards the end of the driest seasons, and therefore solely from underground, between a fifth and .a quarter of a cubic foot per second per 1000 acres. Throughout the course of the river Severn, the head-waters of which are chiefly supplied from such formations, this rate does not materially change, even down to the city of Worcester, past which the discharge flows from 1,256,000 acres. But in smaller areas, which on the average are necessarily nearer to the waterparting, the limits are much wider. and the rate of minimum discharge is generally smaller.
Thus, for example, on woo acres or less, it commonly falls to onetenth of a cubic foot, and upon an upland Silurian area of 940 acres, giving no visible sign of any peculiarity, the discharge fell, on the 21st of September 1893, to one-thirty-fifth of a cubic foot per second per woo acres. In this case, however, some of the water probably passed through the beds and joints of rocks to an adjoining valley lying at a lower level, and had both streams been gauged the average would probably have been considerably greater. The Thames at Teddington, fed largely from cretaceous areas, fell during ten days in September 1898 (the artificial abstractions for the supply of London being added) to about one-sixth of a cubic foot, and since 1880 the discharge has occasionally fallen, in each of six other cases, to about one-fifth of a cubic foot per second per woo acres. Owing, however, to the very variable permeability of the strata, the tributaries of the Thames, when separately gauged in dry seasons, yield the most divergent results. It may be taken as an axiom that the variation of minimum discharges from their mean values increases as the separate areas diminish. In the eastern and south-eastern counties of England even greater variety of dry weather flow prevails than in the west, and upon the chalk formations there are generally no surface streams, except such as burst out after wet weather and form the so-called " bournes." On the other hand, some rocks in mountain districts, notably the granites, owing to the great quantity of water stored in their numerous fissures or joints, commonly yield a much higher proportion of so-called dry weather flow.
When, however, a reservoir is employed to equalize the flow during and before the period of dry weather, the minimum flow continuously available may be increased to a much higher figure, depending upon the capacity of that reservoir in relation to the mean flow of the stream supplying it. In such a case the first essential in determining the yield is to ascertain the rainfall. For this purpose, if there are no rain-gauges on the drainage area in question, an estimate may be formed from numerous gaugings throughout the country, most of which are published in British Rainfall, initiated by the late Mr G. J. Symons, F.R.S., and now carried on by Dr H. R. Mill. But except in the hands of those who have spent years in such investigations, this method may lead to most incorrect conclusions. If any observations exist upon the drainage area itself they are commonly only from a single gauge, and this gauge, unless the area is very level, may give results widely different from the mean fall on the whole area. Unqualified reliance upon single gauges in the past has been the cause of serious errors in the estimated relation between rainfall and flow off the ground.
The uncertainties are illustrated by the following actual example: A battery of fourteen rain-gauges, in the same vertical plane, on ground having the natural profile shown by the section (fig. I), gave during three consecutive years the respective falls shown by the height of the dotted lines above the datum line. Thus on the average, gauge C recorded 20% more than gauge D only ft. distant; while at C, in 1897, the rainfall was actually 30% greater than at J only 560 ft. away. The greatly varying distribution of rainfall over that length of 1600 ft. is shown by the dotted lines measured upwards from the datum to have been remarkably consistent in the three years; and its cause - the path necessarily taken in a vertical plane by the prevailing winds blowing from A towards N - after passing the steep bank at C D - may be readily understood. Such examples show the importance of placing any rain-gauge, so far as possible, upon a plane surface of the earth - horizontal, or so inclined that, if produced, especially in the direction of prevailing winds, it will cut the mean levels of the area whose mean rainfall is intended to be represented by that gauge. It has been commonly stated that rainfall increases with the altitude. This is broadly true. A rain-cloud raised vertically upwards expands, cools and tends to precipitate; but in the actual passage of rain-clouds over the surface of the earth other influences are at work. In fig. 2 the thick line A C D E F CH I fs F' G. FIG. 2.
| i | !0 1. | p H | p E f | 'S ? /,, i // ?/ ,/ /?// / / |
represents the profile of a vertical section crossing two ranges of hills and one valley. The arrows indicate the directions of the prevailing winds. At the extreme left the rain-clouds are thrown up, and if this were all, they would precipitate a larger proportion of the moisture Since the above was written, this work has been taken over by the " British Rainfall Organization." FIG. I. they contained as the altitude increased. But until the clouds rise above the hill there is an obvious countervailing tendency to compression, and in steep slopes this may reduce or entirely prevent precipitation until the summit is reached, when a fall of pressure with commotion must occur. Very high mountain ranges usually consist of many ridges, among which rain-clouds are entangled in their ascent, and in such cases precipitation towards the windward side of the main range, though on the leeward sides of the minor ridges of which it is formed, may occur to so large an extent that before the summit is reached the clouds are exhausted or nearly so, and in this case the total precipitation is less on the leeward than on the windward side of the main range; but in the moderate heights of the United Kingdom it more commonly happens from the causes explained that precipitation is prevented or greatly retarded until the summit of the ridge is reached. The following cause also contributes to the latter effect. Imagine eleven raindrops A to K to fall simultaneously and equi-distantly from the horizontal plane A M. A strong wind is urging the drops from left to right. The drops A and K may be readily conceived to be equally diverted by the wind, and to fall near the tops of the two hills respectively. Not so drop C, for directly the summit is passed the wind necessarily widens out vertically and, having a greater space to fill, loses forward velocity. It may even eddy backwards, as indicated by the curved arrows, and it is no uncommon thing, in walking up a steep hill in the contrary direction to the flight of the clouds, to find that the rain is coming from behind. Much the same tendency exists with respect to all drops between B and E, but at F the wind has begun to accommodate itself to the new regime and to assume more regular forward motion, and as J is approached, where vertical contraction of the passage through which the wind must pass takes place, there is an increasing tendency to lift the raindrops beyond their proper limits. The general effect is that the rain falling from between G and K is spread over a greater area of the earth G'K' than that falling from the equal space between B and F, which reaches the ground within the smaller area B'F'. From this cause also, therefore, the leeward side of the valley receives more rain than the windward side. In the United Kingdom the prevailing winds are from the south-west. and some misapprehension has been caused by the bare, but perfectly correct, statement that the general slope towards the western coast is wetter than that towards the eastern. Over the whole width of the country from coast to coast, or of the Welsh mountain ranges only, this is so; but it is nevertheless true that the leeward side of an individual valley or range of hills generally receives more rain than the windward side. Successive abstraction of raindrops as the rain-clouds pass over ridge after ridge causes a gradually diminishing precipitation, but this is generally insufficient to reverse the local conditions, which tend to the contrary effect in individual ranges. The neglect of these facts has led to many errors in estimating the mean rainfall on watershed areas from the fall observed at gauges in particular parts of those areas. In the simplest case of a single mountain valley to be used for the supply of an impounding reservoir, the rainfall should be known at five points, three being in the axis of the valley, of which one is near the point of intersection of that axis with the boundary of the watershed. Then, in order to connect with these the effect of the rightand left-hand slopes, there should be at least one gauge on each side about the middle height, and approximatel y in a line perpendicular to the axis of the valley passing through the central gauge. The relative depths recorded in the several gauges depend mainly upon the direction of the valley and steepness of the bounding hills. The gauge in the bottom of the valley farthest from the source will in a wide valley generally record the least rainfall, and one of those on the south-west side, the highest. Much will depend upon the judicious placing of the gauges. Each gauge should have for io or 15 yds. around it an uninterrupted plane fairly representing the general level or inclination, as the case may be, of the ground for a much larger distance around it. The earliest records of such gauges should be carefully examined, and if any apparently anomalous result is obtained, the cause should be traced, and when not found in the gauge itself, or in its treatment, other gauges should be used to check it. The central gauge is useful for correcting and checking the others, but in such a perfectly simple case as the straight valley above assumed it may be omitted in calculating the results, and if the other four gauges are properly placed, the arithmetical mean of their results will probably not differ widely from the true mean for the valley. But such records carried on for a year or many years would afford no knowledge of the worst conditions that could arise in longer periods, were it not for the existence of much older gauges not far distant and subject to somewhat similar conditions. The nearer such long-period gauges are to the local gauges the more likely are their records to rise and fall in the same proportion. The work of the late Mr James Glaisher,F.R.S., of the late Mr G.J. Symons, F.R.S., of the Meteorological Office and of the Royal Meteorological Society, has resulted in the establishment of a vast number of raingauges in different parts of the United Kingdom, and it is generally, though not always, found that the mean rainfall over a long period can be determined, for an area upon which the actual fall is known only for a short period, by assigning to the missing years of the shortperiod gauges, rainfalls bearing the same proportion to those of corresponding years in the long-period gauges that the rainfalls of the known years in the short-period gauges bear to those of corresponding years in the long-period gauges. In making such comparisons, it is always desirable, if possible, to select as standards longperiod gauges which are so situated that the short-period district lies. between them. Where suitably placed long-period gauges exist, and where care has been exercised in ascertaining the authenticity of their, records and in making the comparisons, the short records of the local gauges may be thus carried back into the long periods with nearly correct results. Rainfall is proverbially uncertain; but it would appear from the most trustworthy records that at any given place the total rainfall during any period of 50 years will be within i or 2% of the total rainfall at the same place during any other period of 50 years, while the records of any period of 25 years will generally be found to fall within 32% of the mean of 50 years. It is equally satisfactory to know that there is a nearly constant ratio on any given area (exceeding perhaps 1000 acres) between the true mean annual rainfall, the rainfall of the driest year, the two driest consecutive years and any other groups of driest consecutive years. Thus in any period of 50 years the driest year (not at an individual gauge but upon such an area) will be about 63% of the mean for the 50 years. That in the two driest consecutive years will be about 75 °A of the mean for the 50 years. That in the three driest consecutive years will be about 80% of the mean for the 50 years. That in the four driest consecutive years will be about 83% of themean for the 50 years. That in the five driest consecutive years will be about 85% of the mean for the 50 years. That in the six driest consecutive years will be about 862% of the mean for the 50 years. Apart altogether from the variations of actual rainfall produced by irregular surface levels, the very small area of a single rain-gauge is subject to much greater variations in short periods than can possibly occur over larger areas. If, therefore, instead of regarding only the mean rainfall of several gauges over a series of years, we compare the relative falls in short intervals of time among gauges yielding the same general averages, the discrepancies prove to be very great, and it follows that the maximum possible intensity of discharge from different areas rapidly increases as the size of the watershed decreases. Extreme cases of local discharge are due to the phenomena known in America as " cloud-bursts," which occasionally occur in Great Britain and result in discharges, the intensities of which have rarely been recorded by rain-gauges. The periods of such discharges are so short, their positions so isolated and the areas affected so small, that we have little or no exact knowledge concerning them, though their disastrous results are well known. They do not directly affect. the question of supply, but may very seriously affect the works from which that supply is given. Where in this article the term " evaporation " is used alone, it is to be understood to include absorption by vegetation. Of the total quantity of rainfall a very variable proportion is rapidly absorbed or re-evaporated. Thus in the western mountain districts of Great Britain, largely composed of nearly impermeable rocks more Lion. or less covered with pasture and moorland, the water evaporated and absorbed by vegetation is from 13 to 15 in. out of a rainfall of 80 in., or from 16 to 19%, and is nearly constant down to about 60 in., where the proportion of loss is therefore from 22 to 25%. The Severn down to Worcester, draining 1,256,000 acres of generally flatter land largely of the same lithological character, gave in the dry season from the 1st of July 1887 to the 30th of June 1888 a loss of 17.93 in. upon a rainfall of 27.34 in. or about 66%; while in the wet season, ist of July 1882 to the 30th of June 1883, the loss was 21 09 in. upon a rainfall of 43.26 in., or only 49%. Upon the Thames basin down to Teddington, having an area of 2,353,000 acres, the loss in the dry season from the ist of July 1890 to the 30th of June 1891 was 17.22 in. out of a rainfall of 21.62 in., or 79%; while in. the wet season, 1st of July 1888 to the 30th of June 1889, it was. 18.96 out of 29.22 in., or only 65%. In the eastern counties the rainfall is lower and the evaporation approximately the same as upon the Thames area, so that the percentage of loss. is greater. But these are merely broad examples and averages. of many still greater variations over smaller areas. They show generally that, as the rainfall increases on any given area evaporation increases, but not in the same proportion. Again, the loss from a given rainfall depends greatly upon the previous season. An inch falling in a single day on a saturated mountain area will nearly all reach the rivers, but if it falls during a drought seven-eighths may be lost so far as the period of the drought is concerned. In such a case most of the water is absorbed by the few upper inches of soil, only to be re-evaporated during the next few days, and the small proportion which sinks into the ground probably issues in springs many months later. Thus the actual yield of rainfall to the streams depends largely upon the mode of its time-distribution, and without a knowledge of this it is impossible to anticipate the yield of a particular rainfall. In estimating the evaporation to be deducted from the rainfall for the purpose of determining the flow into a reservoir, it is important to bear in mind that the loss from a constant water surface is nearly one and a half times as great as from the intermittently saturated land surface. Even neglecting the isolated and local discharges due to excessive and generally unrecorded rainfall, the variation in the discharge of all streams, and especially of mountain streams, is very great. We have seen that the average flow from mountain areas in Great Britain towards the end of a dry season does not exceed one-fifth of a cubic foot per second per 1000 acres. Adopting this general minimum as the unit, we find that the flow from such areas up to about 5000 acres, whose mean annual rainfall exceeds 50 in., may be expected occasionally to reach 300 cub. ft., or 1500 such units; while from similar areas of 20,000 or 30,000 acres with the same mean rainfall the discharge sometimes reaches 1200 or 1300 such units. It is well to compare these results with those obtained from much larger areas but with lower mean rainfall. The Thames at Teddington has been continuously gauged by the Thames Conservators since 1883, and the Severn at Worcester by the writer, on behalf of the corporation of Liverpool, during the io years 1881 to 1890 inclusive. The highest flood, common to the two periods, was that which occurred in the middle of February 1883. On that occasion the Thames records gave a discharge of 7.6 cub. ft. per second per moo acres, and the Severn records a discharge of 8.6 cub. ft. per second per moo acres, or 38 and 43 respectively of the above units; while in February 1881, before the Thames gaugings were commenced, the Severn had risen to 47 of such units, and subsequently in May 1886 rose to 50 such units, though the Thames about the same time only rose to 13. But in November 1894 the Thames rose to about 80 such units, and old records on the Severn bridges show that that river must on many occasions have risen to considerably over 100 units. In both these cases the natural maximum discharge is somewhat diminished by the storage produced by artificial canalization of the rivers. These illustrations of the enormous variability of discharge serve to explain what is popularly so little understood, namely, the advantage which riparian owners, or other persons Comperei nterested in a given stream, may derive from works cation water. constructed primarily for the purpose of diverting the water of that stream - it may be to a totally different watershed - for the purposes of a town supply. Under modern legislation no such abstraction of water is usually allowed, even if limited to times of flood, except on condition of an augmentation of the natural dry-weather flow, and this condition at once involves the construction of a reservoir. The water supplied to the stream from such a reservoir is known as " compensation water," and is generally a first charge upon the works. This water is usually given as a continuous and uniform flow, but in special cases, for the convenience of millowners, as an intermittent one.' In the manufacturing districts of Lancashire and Yorkshire it generally amounts to one-third of the whole so-called " available supply." In Wales it is usually about one-fourth, and elsewhere still less; but in any case it amounts to many times the above unit of one-fifth of a cubic foot per second per 1000 acres. Thus the benefit to the fisheries and to the riparian owners generally is beyond all question; but the cost to the water authority of conferring that benefit is also very great - commonly (according to the proportion of the natural flow intended to be rendered uniform) 20 to 35% of ' The volume of compensation water is usually fixed as a given fraction of the so-called " available supply " (which by a convention that has served its purpose well, is understood to be the average flow of the stream during the three consecutive driest years). the whole expenditure upon the reservoir works. Down to the middle of the 19th century, the proportioning of the size of a reservoir to its work was a very rough operation. Yield of There were few rainfall statistics, little was known stream of the total loss by evaporation, and still less of its with distribution over the different periods of dry and reservoir. wet weather. Certain general principles have since been laid down, and within the proper limits of their application have proved excellent guides. In conformity with the above-mentioned convention (by which compensation water is determined as a certain fraction of the average flow during the three driest consecutive years) the available supply or flow from a given area is still understood to be the average annual rainfall during those years, less the corresponding evaporation and absorption by vegetation. But this is evidently only the case when the reservoir impounding the water from such an area is of just sufficient capacity to equalize that flow without possible exhaustion in any one of the three summers. If the reservoir were larger it might equalize the flow of the four or more driest consecutive years, which would be somewhat greater than that of the three; if smaller, we might only be able to count upon the average of the flow of the two driest consecutive years, and there are many reservoirs which will not yield continuously the average flow of the stream even in the single driest year. With further experience it has become obvious that very few reservoirs are capable of equalizing the full flow of the three consecutive driest years, and each engineer, in estimating the yield of such reservoirs, has deducted from the quantity ascertained on the assumption that they do so, a certain quantity representing, according to his judgment, the overflow which in one or more of such years might be lost from the reservoir. The actual size of the reservoir which would certainly yield the assumed supply throughout the driest periods has therefore been largely a matter of judgment. Empirical rules have grown up assigning to each district, according to its average rainfall, a particular number of days' supply, independently of any inflow, as the contents of the reservoir necessary to secure a given yield throughout the driest seasons. But any such generalizations are dangerous and have frequently led to disappointment and sometimes to needless expenditure. The exercise of sound judgment in such matters will always be necessary, but it is nevertheless important to formulate, so far as possible, the conditions upon which that judgment should be based. Thus in order to determine truly the continuously available discharge of any stream, it is necessary to know not only the mean flow of the stream, as represented by the rainfall less the evaporation, but also the least favourable distribution of that flow throughout any year. The most trying time-distribution of which the author has had experience in the United Kingdom, or which he has been able to discover from a comparison of rainfalls upon nearly impermeable areas exceeding woo acres, is graphically represented by the thick irregular line in the left-hand half of fig. 3, where the total flow for the driest year measures too on the vertical percentage scale; the horizontal time scale being divided into calendar months. The diagram applies to ordinary areas suitable for reservoir construction and in which the minimum flow of the stream reaches about one-fifth of a cubic foot per second per moo acres. Correspondingly, the straight line a a represents uniformly distributed supply, also cumulatively recorded, of the same quantity of water over the same period. But, apart from the diurnal fluctuations of consumption which may be equalized by local " service reservoirs," uniform distribution of supply throughout twelve months is rarely what we require; and to represent the demand in most towns correctly, we should increase the angle of this line to the horizontal during the summer and diminish it during the winter months, as indicated by the dotted lines b b. The most notable features of this particular diagram are as follows: Up to the end of 59 days (to the 28th February) the rate of flow is shown, by the greater steepness of the thick line, to be greater than the mean for the year, and the surplus water - about i i % of the flow during the year - must be stored; but during the 184 days between this and the end of the 243rd day (31st August) the rate of flow is generally below the mean, while from that day to the end of the year it is again for the most part above the mean. Now, in order that a reservoir may enable the varying flow, represented cumulatively by the irregular line, to be discharged in a continuous and uniform flow to satisfy a demand represented cumulatively by the straight line a a, its capacity must be such that it will hold not only the II % surplus of the same year, but that, on June loth, when this surplus has been used to satisfy the demand, it will still contain the water c d-19%stored from a previous year; otherwise between June 10th and August 31st the reservoir will be empty and only the dry weather flow of the stream will be available for supply. In short, if the reservoir is to equalize the whole flow of this year, it must have a capacity equal to the greatest deficiency c d of the cumulative flow below the cumulative demand, plus the greatest excess e f of the cumulative flow over the cumulative demand. This capacity is represented by the height of the line a'a' (drawn parallel to a a from the point of maximum surplus f ) vertically above the point of greatest deficiency c, and equal, on the vertical scale, to the difference between the height c = 48% and g= 78% or 30% of the stream-flow during the driest year. A reservoir so proportioned to the stream-flow with a proper addition to avoid drawing off the bottom water, would probably be safe in Great Britain in any year FIG. 3. for a uniform demand equal to the cumulative stream-flow; or, if it failed, that failure would be of very short duration, and would probably only occur once in 50 years. It may be at first sight objected that a case is assumed in which there is no overflow before the reservoir begins to fall, and therefore no such loss as generally occurs from that cause. This is true, but it is only so because we have made our reservoir large enough to contain in addition to its stock of 19%, at the beginning of the year, all the surplus water that passes during the earlier months in this driest year with its least favourable time-distribution of flow. Experience shows, in fact, that if a different distribution of the assumed rainfall occurs, that distribution will not try the reservoir more severely while the hitherto assumed uniform rate of demand is maintained. But, as above stated, the time-distribution of demand is never quite uniform. The particular drought shown on the diagram is the result of an exceptionally early deficiency of rainfall which, in conjunction with the variation of demand shown by the dotted line b b, is the most trying condition. The reservoir begins to fall at the end of February, and continues to do so with few and short exceptions until the end of August, and it so happens that about the end of August this dotted line, b b representing actual cumulative demand, crosses the straight line a a of uniform demand, so that the excess of demand, represented by the slope from June to September, is balanced by the deficiency of demand, represented by the flatter slope in the first five months, except as regards the small quantity b e near the end of February, which, not having been drawn off during January and February, must overflow before the end of February. To avoid this loss the II % is in this case to be increased by the small quantity b e determined by examination of the variation of the actual from a constant demand. After the reservoir begins to fall - in this case at the end of February - no ordinary change in the variation of demand can affect the question, subject of course to the cumulative demand not exceeding the reservoir yield for the assumed year of minimum rainfall. In assuming a demand at the beginning of the year below the mean, resulting in an overflow equal in this case to b e at the end of February and increasing our reservoir to meet it, we assume also that some additional supply to that reservoir beyond the 11 % of the streamflow from the driest year can be obtained from the previous year. In relation to this supply from the previous year the most trying assumption is that the rainfall of that year, together with that of the driest year, will be the rainfall of the two driest consecutive years. We have already seen that while the rainfall of the driest of 50 years is about 63% of the mean, that of the driest two consecutive years is about 15% of the mean. It follows, therefore, that the year immediately preceding the driest cannot have a rainfall less than about 87% of the mean. As the loss by evaporation is a deduction lying between a constant figure and a direct proportional to the rainfall, we should err on the safe side in assuming the flow in the second driest year to be increased proportionally to the rainfall, or by the difference between 63 and 87 equal to 24% of the mean of 50 years. This 24% of the 50 years' mean flow is 38% of the driest year's flow in fig. 3, and is therefore much more than sufficient to ensure the reservoir beginning the driest year with a stock equal to the greatest deficiency-19% - of the cumulative flow of that year beyond the cumulative demand. But in determining the capacity of reservoirs intended to yield a supply of water equal to the mean flow of two, three or more years, the error, though on the safe side, caused by assuming the evaporation to be proportional to the rainfall, is too great to be neglected. The evaporation slightly increases as the rainfall increases, but at nothing like so high a rate. Having determined this evaporation for the second driest consecutive year and deducted it from the rainfall - which, as above stated, cannot be less than 87% of the mean of 50 years - we may, as shown on fig. 3, extend our cumulative diagram of demand and flow into the reservoir from one to two years.
|
|---|
