GEOLOGICAL SURVEY CIRCULAR 409 

WATER YIELD AND RESERVOIR 

STORAGE IN THE 

UNITED STATES 

,. UNITED STATES DEPARTMENT OF THE INTERIOR 

Fred A. Seaton, Secretary 

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director 

GEOLOGICAL SURVEY CIRCULAR 409 

WATER YIELD AND RESERVOIR STORAGE IN THE UNITED STATES 

By Walter B. Langbein 

Washington, D. C., 1959 

Free on application to the Geological Survey, Washington 25, D. C. 

CONTENTS 

Page Page 

Introduction................................................. 1 Future capacity........................................... 4 

Relation between storage capacity Conclusions................................................ 5 

and regulation........................................... 1 References.................................................. 5 

Existing capacity.......................................... 3 

lLLUSTRA TIONS 

Page 

Figure 1. Regulation-capacity ratio in relation to usable capacity............................................................ 2 

2. Regulation-flow ratio in relation to usable capacity.................................................................. 3 

3. Estimated future development of storage in the United States.................................................... 5 

TABLE 

Page 

Table 1. Capacity and regulation of some representative reservoirs....................................................... 1 

Ill 

.. 

WATER YIELD AND RESERVOIR STORAGE IN THE UNITED STATES 

By Walter B. Langbein 

INTRODUCTION 

The capture and storage of water during high-water 

periods for use during low-water periods represents 

salvage of water which otherwise would be wasted and 

possibly would cause flood damage. The aggregate capacity of regulatory storage reservoirs in the United 

States (excluding those with capacities of less than 5,000 

acre-feet) has increased from 33 million acre-feet in 

1920 to 273 million acre-feet in 1953 (Thomas and Harbeck, 1956). The trend in reservoir construction for all 

purposes i~ still steeply upward. The amount of water 

that is now made available for use by reservoir storage and the amount that can be made available by additional storage are estimated in this paper. 

RELATION BETWEEN STORAGE CAPACITY AND 

REGULATION 

A reservoir regulates streamflow for beneficial use 

by storing water for later release. Changes in storage 

are the measure of the work done by a reservoir. The 

term "regulation" is here defined as the amount of 

water that is stored or released from storage in a 

period of time, generally a year. For calculation purposes, regulation is the sum of all gains in reservoir 

contents. Because any gain in storage eventually is offset by a loss, the sum of the gains tends to equal the 

~urn of the losses; therefore, regulation could also be 

defined as the sum of all the drafts on storage. 

The ability of a reservoir to regulate river flow depends on the ratio of its capacity to the volume of river 

flow. The ratio of the capacity in acre-feet to the mean 

annual flowin acre-feetper yearisthe detention period 

of the reservoir and has the dimension of years. 

The total of the gains in storage during a period of 

years, divided by the number of years, gives the mean 

annual regulation. Dividing the mean annual regulation 

by the usable capacity of the reservoir gives the ratio 

of the regulation to the capacity (the regulation-capacity 

ratio), and dividing it by the mean annual flow gives the 

ratio to the mean annual flow (the regulation-flow ratio). 

The regulation provided by existing storage facilities 

can be determined by studying the records of typical reservoirs. A representative group of reservoirs is listed 

in table 1 with the usable capacity, detention period, and 

annual regulation of each. Reservoirs were selected to 

cover detention periods ranging from about 0.01 year 

to 20 years. 

The relation between the ratios of mean annual regulation to capacity and of capacity to annual flow for the 

reservoirs in table 1 is plotted on figure 1. This figure 

shows that reservoirs with capacities of about 0.17 of a 

Table !.-Capacity and regulation of some representative reservoirs 

Usable capacity Mean annual regulationl 

Reservoir and State ! 

Detention Acre-feet ,Ratio to Ratio to 

Acre-feet 2 period per year capacity mean annual 

(years) a flow 

Piney, Pa .•••..•....•..•..•......•....••..••...••.. 13,000 0.011 70,000 5.4 0,06 

Great Falls, Tenn .••.......••........•.•.••..••. 49,400 .021 204,000 4: ... 1 .089 

Ocoee No. 1, Tenn ......•••.........••..•....... 33,100 .035 204,000 3.6 .13 

Claytor, Va ...•..•.••.......••.•.........•••.•... 100,000 .04 150,000 1.5 .06 

Mas coma Lake, N. H ........................... 7,744 .05 22,000 2.8 .14 

Franklin D. Roosevelt Lake, Wash ......... 5,072,000 .07 4,800,000 .95 .07 

West Fork Bitterroot, Mont .................. 31,700 .14 26,000 .82 .12 

Hiwassee, N. C ..........•.............•......•.. 1,376,000 .265 330,000 .90 .24 

Green Mountain, Colo ...........•.............. 146,900 .34 111,000 . 75 .26 

Gibraltar, .Calif .................................. 7, 731 .39 4,300 .55 . 21 

Stillwater, N. ¥ ................................. ~ 106,000 .40 91,000 .86 .34 

Sacandaga, N. Y ................................. 762,300 .51 560,000 . 75 .38 

First and Second Connecticut 

Lakes, N.H .................................... 88,106 .60 62,000 .70 .42 

Norris, Tenn ................................. ~ ... 2,281,000 .72 1,070,000 .47 .34 

Shasta Lake, Calif .............................. 4,377,000 .80 1,530,000 .35 .28 

Lake Alamanor, Calif .......................... 649,800 1.0 250,000 .38 .38 

Salmon River Canal Co., Idaho .............. 182,650 1.6 57,500 .31 .54 

Henrys Lake, Idaho ............................. 79,351 2.1 20,600 .26 .54 

Lake Mead, Ariz.-Nev ......................... 27,207,000 2.1 4 5, 750,000 .21 .44 
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2 WATER YIELD AND RESERVOIR STORAGE IN THE UNITED STATES 

Table 1.--Capacity and regulation of some representative reservoirs--Continued 

Usable capacity Mean annual regulationl 

Reservoir and State Detention Acre-feet Ratio to Ratio to 

Acre-feet2 period capacity mean annual 

(years)3 per year flow 

Lake Mead and Lake Mohave, 

Ariz.-Nev •..••.•••••.•••••.•••••.•••••••••••••• 29,000,000 2.3 4 6,500,000 ,.._D.22 ;10.51 

Fort Phantom Hill, Tex •••••••••••.•.••••••••• 69,500 2.3 11,900 .175 .40 

Lake Kickapoo, Tex ••••••••••••••.•••••••.••••• 106,000 2.6 20,200 .19 .49 

Elephant Butte, N. Mex ••.••••.•••••••••••••••• 2,185,000 2.6 4 3-75,000 .17 .45 

Elephant Butte and Caballo, 

N.Mex ••..•...•..••.••..•••••••.••.••••••••••••• 2,526,000 3.0 4 470_,000 .185 .55 

Quabbin, Mass ................................... 1,279,000 6.0 119,000 .09 ,56 

San Carlos, Ariz ................................ 1,205,000 6.7 4 117,000 .097 .65 

Lake Henshaw, Calif .......................... 194,320 21.8 8,170 .042 .91 

1 For reservoirs with detention periods greater than 0.1 year, regulation was computed from monthly changes in 

reservoir contents. For reservoirs with shorter detention periods, daily data were used. 

2Thomas and Harbeck (1956). 

3Ratio of usable capacity_, in acre-feet, to mean annual flow, in acre-feet per year. 

4 Including evaporation losses. 

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USABLE CAPACITY IN RELATION TO MEAN ANNUAL FLOW 

(DETENTION PERIOD, IN YEARS) 

Figure !.-Regulation-capacity ratio in relation to usable capacity. 

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EXISTING CAPACITY 3 

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USABLE CAPACITY IN RELATION TO MEAN ANNUAL FLOW 

(DETENTION PERIOD, IN YEARS) 

Figure 2.-Regulation-flow ratio in relation to usable capacity. 

year's flow have their full capacity utilized once each 

year. The total of the changes in contents of reservoirs 

with capacities of less than 0.17 of a year's flow exceeds 

the capacity; in other words# their capacity is used more 

than once each year. Reservoirs with usable capacities 

equal to a year's mean flow have an average annual 

utilization of about 37 percent of their capacity. 

Figure 2 shows how reservoir capacity influences 

regulation expressed as a ratio to mean annual flow. 

The regulation increases with the detention period, 

approaching 80 percent of the annual flow for largeholdover reservoirs. The annual regulation cannot, 

of course~ exceed ·the annual runoff. The graph on 

figure 2 is defined by the following equation: 

Q = 2.5 ~R ( 

R ;·6 

Q 1- g_ 

in which R is the mean annual regulation, Q is the 

mean annual river flow, and C is usable capacity. The 

form of this equatiQn parallelS that of the equations 

for storage, based on analogy with queues (Langbein, 

1958). The equation indicates that usable capacity 

would go to infinity if regulation, JY Q• we.re to approach unity. The equation may alsoserve as a guide 

for determining the capacity needed to obtain a specific amount of regulation.l 

lThe regulation, f3J.Q• can be computed from a comparison of the duratfO'ii' curve of the inflows into the 

proposed reservoir with the duration curve of the 

desired outflow from reservoir. 

The relations illustrated by figures 1 and 2 seem to 

be well defined despite the substantial differences in 

stream regimen and in manner of operation. 

EXISTING CAPACITY 

Taking the reservoirs in the United States reported 

by Thomas and Harbeck (1956) (excluding those built 

solely for flood control) and classifying them by capacity (in terms Qf detention periods}, results in the 

following: 

Aggregate Total 

Detention Number usable Regula- regulaperiod of capacity tion- tion 

(years) reser- (million capacity (million 

voirs acre-feet) ratiol acrefeet) 

less than 0.05 415 19.0 2.00 38 

0.05-0.19 ••••• 343 55.0 1.20 66 

0.20-0.49 •.•.. 210 61.0 .70 43 

0.50-0.99 ••.•• 167 45.7 .45 21 

1 .. 0-1.49 •••••• 68 43.5 .31 13 

1.5 and over •• 64 49.0 .20 10 

Total or 

average ·•••' 1,267 273.2 0.70 191 

lFrom figure 1. 

Thus, the computed annual water supply made 

available by existing reservoirs is about 190 million 

acre-feet. This quantity, reduced by an estimated 
4 WATER YIELD AND RESERVOIR STORAGE IN THE UNITED STATES 

net-evaporation loss of 10 million acre-feet (mostly 

in the Western States), is 13 percent of the total flow 

of the rivers of the United States (1,400 million acrefeet). The percentage of regulation varies in different 

river basins. The figures for some typical major 

drainage basins are: 

Drainage basin 

Regulation, 

in percent, 

of total flowl 

Ohio River (excluding the Tennessee 

and Cumberland River!~)····:· ............ . 

Tennessee and Cumberland R1vers ....... . 

Colorado River2 ................................ -

lExcluding flood-control reservoirs. 

17 

50 

2Not including Glen Canyon Reservoir, now under 

construction. 

Water control by storage t"oUows a law of diminishing 

returns. Each successive increment of control requires a larger amount of reservoir storage space than 

the preceding-increment. The net effect is iilustrated 

by figure 2. Storage capacity equal to a year's flow 

can regulate almost 40 percent of the flow, but doubling 

the capacity increases regulation only by about onethird. There is, therefore, a limit to the amount of 

storage that it is feasible to build with prospect of 

useful return. 

Although in the East a considerable increase in 

usable water supply can be obtained by additional reservoir storage, some drainage basins in the West may 

already be approaching the limit. 

For example, the capacity of existing reservoirs in 

the Colorado River basin is nearly 35 million acrefeet. Most of this capacity, which is in Lake Mead, is 

used to regulate the flow of the main stem. The regulatory capacity soon will be nearly doubled by the 

construction of Glen Canyon Reservoir, which will have 

a usable capacity of about 20 million acre-feet. But 

evaporation imposes a ceiling on potential river regulation in an arid climate. If, as in Lake Mead and as 

computed for the Glen Canyon Reservoir (U. S. Bureau 

of Reclamation, 1954). annual evaporation averages 

about 27,000 acre-feet per million acre-feet of usable 

capacity, one can construct from figure 2 the following 

relation between storage capacity and net regulation 

for the Colorado River system: 

Capacity Annual -Net 

of reser- Annual evaporaattrtual 

Detention voirs in regulation tion regulaperiod system (million (million tion 

(years) (mill~ on acre-feet) acre- (million 

acre- feet) acrefeet)l feet) 

1.0 .............. 13 4.7 0.4 4.3 

2.2 .............. 2 29 6.3 .8 5.5 

3.0 .............. 39 6.8 1.1 5.7 

4.0 .............. 52 7.2 1.4 5.8 

5.0 .............. 65 7.6 1.8 5.8 

6.0 .............. 78 7.9 2.1 5.8 

lBased on annual flow of 13 million acre-feet. 

2Approximate present main-stem development. 

Selected detention periods are listed in the first 

column. The capacity was obtained by multiplying the 

detention period by the mean annual flow of the 

Colorado River. The annual regulation was obtained 

from figure 1, as shown in the following example: The 

regulation-capacity ratio for a detention period of 1 

year is 0.37. Thus, 0.37 multiplied-by the capacity 

required for a detention period of 1 year, 13 million 

acre-feet, equals 4. 7 million acre-feet. The annual 

evaporation is based on the evaporation rate of 27,000 

acre-feet per million acre-feet of capacity. The net 

annual regulation is the annual regulation minus the 

annual evaporation. 

The net regulation indicates, insofar as main-stem 

regulation of the Colorado River is concerned, that the 

capacity of existing reservoirs and of those under 

construction (total nearly 50 million acre-feet) is near 

a theoretical optimum-the minimum capacity necessary to provide the maximum obtainable regulation-and 

that any increase in capacity will not increase the 

supply. Furthermore, this optimum is insensitive. 

There is no significant gain in net regulation between 

29 and 78 million acre-feet of capacity. The gain in 

regulation to be achieved by increasing the present 29 

million acre-feet to nearly 50 million acre-feet of 

capacity appears to be largely offset by a corresponding 

increase in evaporation. 

These conclusions, based on figure 2 and reservoir 

evaporation as reported under operating conditions, reflect practical gains or losses in regulation of water by 

reservoirs. The present analysis deals only with the 

problem of water supply and is intended only to convey 

a principle. Appraisal of the benefits of such operations 

in power or irrigation is a separate problem. 

FUTURE CAPACITY 

Woodward (1957) estimated that an annual increment 

of 9 to 10 million acre-feet of storage will be needed to 

meet anticipated increases in water use. This rate of 

increase will about double the present storage over the 

next 25 to 30 years, a rate that about parallels the rate 

of increase in the use of surface water. The estimated 

future development of storage in the United States is 

shown in figure 3. The actual increase will depend on 

how strategically the reservoirs are installed. 

The present reservoir capacity of 273 million acrefeet is equal to 0.195 of the annual flow of the rivers 

of the country. The total regulation is 190 million acrefeet. These data correspond to point A on figure 3. If, 

as indicated by the present rate of increase in use of 

surface water for all purposes, the need for regulated 

supply of water will double in the next 25 years, the 

regulated annual supply a quarter of a century hence 

will be 380 million acre-feet. If the storage facilities 

to effect this development are located most strategically, that is so as not to duplicate present or future 

installations, the capacity needed would correspond to 

point B on figure 3. This capacity would be twice the 

present capacity. However, if the new installations are 

in basins which already are intensively developed, the 

total capacity needed would be that corresponding to 

point C on figure 3, the line A~ being parallel to the 

curveon figure 2. This cap~ity-would be 1,200 million 

acre-feet, or about 4.5 times the present capacity. 
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USABLE CAPACITY, IN MILLIONS OF ACRE-F'tET 

Figure 3.-Estimated future development of storage in the United States. 

Thus, there is a wide range to challenge ingenuity in 

achieving efficient location of reservoirs. 

CONCLUSIONS 

Reservoir-storage development in the United States 

has made available for use about 190 million acre-feet 

of water or about 13 percent of the total river flow. 

The degree of storage development is highly variable. 

It is relatively greatest in the sparsely populated 

Colorado River basin and least in the populous Ohio 

River basin. The trend in construction of reservoirs 

in the United States is still steeply upward, but, as observed in Engineering News-Record (1958), the point 

of ultimate development for hydroelectric power, 

irrigation, flood control, and navigation may be seen 

on the horizon. Water supply and pollution control may 

become the dominant objectives of water storage. 

Although in the United States as a whole, substantial increase in water supply can be obtained by 

additional storage development, water control by 

storage follows a law of diminishing returns. There 

is a limit to the amount of storage that can be useful. 

The Colorado River basin is an example of a river 

basin where storage development may be approaching, 

if not exceeding, the useful limit. The prospect of a 

shift in emphasis toward water supply for towns and 

factories sharpens the need for added development of 

storage in the populated· regions of the country. Future 

needs for storage capacity to meet anticipated demands 

for water challenge ingenuity in achieving efficient 

location of the added storage. 

REFERENCES 

Engineering News-Record, 1958, Toward unity among 

developers, v. 160, no. 7, Feb. 13, p. 205. 

Langbein, W. B., 1958, Queuing theory and water storage: Am. Soc. Civil Engeers Proc. Paper 1811. 

Thomas, N. 0., and Harbeck, G. E., 1956, Reservoirs 

in the United States: U. S. Geol. Survey WaterSupply Paper 1360 -A. 99 p. 

U .. S. Bureau of Reclamation, 1954, Colorado River 

storage project: 83d Cong., 2d sess., House Doc. 364. 

Woodward, D. R., 1957, Availability of water in the 

United States with special reference to industrial 

needs by 1980: Industrial College of the Armed 

Forces, Thesis 143, 74 p. 

IIIT.-DUP. SEC .• WASH., D.C. lo81o09