A Preliminary Evaluation of 

Bank Storage Associated with 

Libby Reservoir in 

Northwestern Montana

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1899-L

Prepared in cooperation with the 

Montana Bureau of Mines and Geology, 

Butte, Montana
A Preliminary Evaluation of 

Bank Storage Associated with 

Libby Reservoir in 

Northwestern Montana

By DONALD L. COFFIN

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1899-L

Prepared in cooperation with the 

Montana Bureau of Mines and Geology, 

Butte, Montana

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1970
UNITED STATES DEPARTMENT OF THE INTERIOR 

WALTER J. HICKEL, Secretary

GEOLOGICAL SURVEY

William T. Pecora, Director

Library of Congress catalog-card No. 73 608591

For sale by the Superintendent of Documents, U.S. Goyernment Printing Office 

Washington, D.C. 20402 Price 25 cents (paper cover)
CONTENTS

Page

Abstract . ........ . .... ..... . ... .. .. . .... .. .. ................ ............... LI

Introduction .. .. . ..... . .. .... .. . .. .. ... .......... . ......... ......................... .. 1

Problem ................. ................. ......................... ..... ........... ...... .... . 1

Purpose ......... ..... . ...... .... ...... ............. ... ...... .. . ....... ...... 3

Geologic setting ..................... ................... .. . ........ ......... ... ............. .. ... ...... 4

Electric analog ... . . .......... . . ..... ........... . . . ............... ...... ............... 7

Construction ............. ... .. . .......................... .. ......................................... 7

Stimulation ............. .. . ................................................ .. ... ... .............. .. 10

Results ................................................. .... ..................... ............................. 12

Conclusions ................................................................. .......................... ... ... ..... 15

Parameters affecting bank storage ........ .. ...................... . ........................... 15

Limits of the area of intensive data collection.................... ..... .. ............ 18

Discussion ................................................................................................................ 20

Shortcomings of the analog.................... . ...... .......................................... 22

Plans for a new model.......... ........... ................................... ..................... . . 24

References cited ............................. .... .................................................................. 25

ILLUSTRATIONS

Page 

FIGURE 1. Index map of northwestern Montana and Eastern British

Columbia . . . .... .. .............. . ........ L2

2. Surficial geologic map of Tobacco Plains area in northwestern

Montana . . . . ........... . .. .. ....... 4

3. Sketches comparing a diagrammatic geologic section with the 

conditions assumed in the electric analog and in the mathematical model of Cooper and Rorabaugh ..... . ............. ....... . 8

4. Schematic sketch of the Kootenai River profile and the annual

pulse applied to subdivisions of the reservoir ..... . ......... 9

5. Photographs of the oscilloscope face showing cumulative bank

storage and water-level changes .... . .... . . ....... . 10

6. Graph showing cumulative bank storage for analog runs 1, 2,

and 3.. ...... . . . .... 14

7. Graph showing cumulative active bank storage above Rexford . 17

TABLES

Page 

TABLE 1. Hydraulic characteristics assumed for the geologic units ... L7

2. Active bank storage along Libby Reservoir... . ....... . . . .... 13

3. Summary of water-level fluctuations in various lithologic types

and at various distances from the reservoir . ..... ................. ..... 15

III
CONTRIBUTIONS TO THE HYDROLOGY OF 

THE UNITED STATES

A PRELIMINARY EVALUATION

OF BANK STORAGE ASSOCIATED

WITH LIBBY RESERVOIR IN

NORTHWESTERN MONTANA

By DONALD L. COFFIN

ABSTRACT

Permeable sand and gravel deposits beneath the floor of the Rocky Mountain 

Trench in northwestern Montana and southeastern British Columbia will become 

saturated and provide additional storage for Libby Reservoir, which is scheduled to 

begin filling in 1972. Because subsurface geologic data are insufficient to predict 

accurately the amount of usable bank storage, plans cannot be made to use this water 

for project purposes. An electric analog of the area is too crude to make final estimates 

of bank storage, but the model study points out that the distribution of active bank 

storage along the reservoir is mainly a function of the size and shape of the reservoir 

stage hydrograph and of the slope of the floor of the reservoir. The magnitude of 

active bank storage is controlled by transmissivity and storage coefficient. The model 

study indicates that geologic data necessary to evaluate bank storage accurately need 

only be collected over about one-fourth of the length of the reservoir and within 

about 2 miles of its edge. The study allowed the estimated cost of the data collection 

plan to be reduced by about half.

INTRODUCTION 

PROBLEM

The U.S. Army Corps of Engineers is building Libby Dam 

on the Kootenai River in northwestern Montana (fig. 1). 

The length of the reservoir will be about 90 miles, of which 

about 40 miles will be in Canada. About 50 miles of the reservoir will be in the Rocky Mountain Trench, which contains unconsolidated deposits of sand and gravel. Bank 

storage may be important in the operation of the reservoir 

because the sand and gravel deposits are permeable and beLl
L2 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

116°00' 45' 30' 15' 115-00'

15'

49°00'

45'

EXPLANATION

Approximate boundary of 

Rocky Mountain Trench

Approximate boundary of 

Libby Reservoir

I 

\ MONTANA

^ -j 

Upper limit ofv 

^Siss-. Libby Reservoir^

Base map from U.S. Corps of Engineers 

FIGURE 1. Index map of northwestern Montana and southeastern British Columbia.

cause the yearly change in stage of the reservoir can be as 

much as 172 feet under critical water conditions.
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L3

Bank storage is water absorbed into aquifers adjoining a 

reservoir when the stage of the reservoir rises above the water 

table in the aquifers. Some of the water may return to the 

reservoir when the reservoir stage falls below the water table 

in the aquifers. In some reservoirs, the amount of bank storage may be large enough to increase significantly the amount 

of water available from the reservoir. Capacity tables for 

most reservoirs do not include bank storage. An accurate 

determination of bank storage will allow more efficient operation of the reservoir for its various beneficial uses. For 

reservoirs used primarily for generating electricity, an accurate 

capacity table including usable bank storage allows optimum 

generation of firm power, which commands the highest price.

The water resources of the Kootenai valley above Libby dam 

have been little developed, mainly because of sparse population 

and abundant water. As a result, very few hydrogeologic data 

are available, especially those data defining the ground-water 

system. Much of the area is heavily timbered and relatively 

inaccessible, especially during the winter; thus, data necessary 

to evaluate bank storage are difficult and expensive to collect. 

The aim of a study by the U.S. Geological Survey and the Montana Bureau of Mines and Geology was to estimate bank storage. 

Sufficient data were not available for an accurate estimate and 

funds are not currently available for an extensive data-collection 

program. Therefore, it seemed advisable to make a preliminary 

evaluation with a view toward defining the most important 

data to collect for a more accurate estimate. This preliminary 

evaluation also developed guidelines that could be used to relate 

the cost of collecting data to the benefits that would accrue from its 

use.

PURPOSE

This paper describes how a simple electric-analog model was used 

as an aid in designing a data-collection program. The analog was 

developed to help the hydrologist relate various physical parameters of the system to bank storage and to evaluate the relative 

importance of the parameters. A data-collection program can then 

be designed to measure these parameters in the areas where 

they most affect bank storage. A data-collection program developed 

from the relationships made clear by the model will result in a 

controlled collection of data and should minimize the collection of 

data that have little use in the final analysis. In addition to the 

above, the range of bank storage was estimated. This estimate is 

much too crude for use in managing the reservoir; however, it does
L4 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

115°12'30"

*?>( ^Edgeo, permeable ^^^^^^^^

 'X rocks ~J^i~Z2\>Qa°l ~^"x /

Base from U.S. Geological Survey 

Rexford and Eureka North 1 :24 000, 1963

FIGURE 2. Surficial geologic map of Tobacco

provide an order of magnitude of the amount of bank storage that 

might be available.

GEOLOGIC SETTING

The Kootenai River flows southward down the broad valley of the Rocky Mountain Trench into the United States and 

leaves the trench about 10 miles south of the international boundary (fig. 1). In the United States the trench seems to be a graben
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L5

EXPLANATION

Alluvium

Gravel along the Kootenai 

River; sand and gravel 

along tributaries

posited in the highenergy environment of glacial 

Lake Kootenai

Geology by D. L. Coffin

Plains a.ea in northwestern Montana.

Outwash

Sand, gravel, and clay deposited near the shore of 

glacial Lake Kootenai

Till

Stony clay deposited by the 

advancing Cordellerian 

ice gheet, relatively impermeable

Contact between deposits of different 

hydrologic characteristics

Boundary of Libby Reservoir

Location where hydrograph was taken from 

electric analog

X 

Test-hole location

APPROXIMATE SCALE

having a floor about 7 miles wide and a vertical displacement of 

several thousand feet. The walls are Precambrian sedimentary and 

low-grade metamorphic rocks. Since its formation during Tertiary 

time, the trench has been partly filled by debris from the adjacent 

mountains. Most of the debris forming the floor of the trench is 

Pleistocene and Holocene deposits of unconsolidated silt, sand, and 

gravel. The Kootenai River has cut a valley as much as a 

mile wide and 200-300 feet below the floor of the trench.
L6 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

Little evidence of geologic history prior to Pleistocene time 

can be seen from rocks exposed on the floor of the Rocky Mountain 

Trench. The last glacial advance filled the trench with more than 

5,000 feet of ice and modified the rocks so greatly that evidence of 

earlier events was almost completely removed or deeply buried. As 

the ice moved down the trench, it ground and compacted the underlying deposits into clay till. Till was mounded into drumlinlike 

hills on the floor of the trench and was plastered over the 

Precambrian rock walls. Eventually the ice began to melt and the 

front receded to the north. The ancestral Kootenai river became 

dammed by ice or by isostatic rebound downstream from the 

trench, whereupon the floor of the trench became covered by as 

much as 400 feet of water. Streams from the adjacent mountains 

deposited their loads along the foot of the steep walls of the 

trench. In most places this area of deposition was near or along the 

shore of the lake. These outwash deposits range in size from sand 

to boulders and contain less than 20 percent of clay.

The streams reworked the outwash and carried much of the 

material into the lake, where it was further reworked and resorted 

by lake currents. Coarser material formed deltas radiating from 

the mouths of tributaries. The deltaic deposits, which grade into 

and interfinger with the outwash, are well sorted and range from 

coarse sand to medium gravel. Interfingering lakeward with 

the deltaic deposits are the lake-bottom deposits of silt, clay, and 

fine to medium sand. The lake-bottom deposits resulted from the 

settling of sediment from the turbid lake water. Deposits associated 

with the glacial lake rest on till. Many of the drumlinlike 

hills of till were not completely covered by lake deposits and 

now form streamlined mounds projecting above the relatively 

level lake-floor surface.

After recession of glacial conditions, the glacial lake drained and 

the Kootenai River entrenched itself 200 to 300 feet into the lakebottom deposits. This inner valley is generally less than a mile 

wide, and its floor is underlain by about 50 feet of medium to very 

coarse gravel. The inner valley will contain the reservoir formed by 

Libby Dam (fig. 1).

A reconnaissance geologic map was made of the surficial 

deposits on the floor of the Rocky Mountain Trench between 

Rexford and the upper limit of the reservoir. The areal distribution of the geologic units in the United States part of 

the trench is shown in figure 2. However, few subsurface 

data are available, and the thickness or configuration of the 

base of the surficial deposits cannot be mapped. Two test
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L7

holes were drilled in the Tobacco Plains during the study 

one through the alluvium along the Kootenai River and the 

other in the area where the deltaic deposits and lake-bottom 

deposits interfinger. The test holes confirmed the interpretation of the geology. The first test hole shows 44 feet of 

alluvium lying on lake-bottom sand and silt. The second shows 

158 feet of deltaic deposits interfingering with lake-bottom 

deposits and resting on till.

ELECTRIC ANALOG 

CONSTRUCTION

In order to construct an analog model of the reservoir and adjacent aquifers, the subsurface distribution of the geologic units was 

assumed to be the same as the surface configuration, and values 

of T (transmissivity) and 5 (storage coefficient) were assumed for 

each geologic unit. The assumed values are based on the lithologic 

characteristics of the rocks penetrated by the test holes and on 

known values for similar rock types in nearby areas. The values 

assumed for the three model runs are given in table 1. These asTABLE 1. Hydraulic characteristics assumed for the geologic units

Geologic 

unit

Alluvium

Lake-bottom

deposits.

Deltaic deposits

Outwash .

Till .

Precambrian

strata.

Lithology

Gravel ..... ... . .

Silt, clay, sand ... ..

. Sand, gravel

Sand, gravel, clay

.. Clay, sand, boulders

Dolomite, argillite,

quartzite

Transmissivity (ft2 day-1 )

67,000

1,300

13,000

9,300

0

0

Coefficient of storage

Run 1

0.20

.05

.15

.10

Run 2

0.10

.025

.075

.05

Run 3

0.40

.10

.30

..20

sumptions essentially convert the three-dimensional mental image 

developed by the geologist into a two-dimensional simple hydrologic model. The three-dimensional image can, for lack of a better 

word, be called a conceptual model. A diagrammatic cross section 

of the conceptual model is shown in figure 3. Included for comparison in figure 3 is a schematic sketch of the analog and of the analytic model developed by Cooper and Rorabaugh (1963). The relation of the geology to the hydraulic characteristics of the groundwater system can be visualized by viewing each geologic unit 

shown in figures 2 and 3 as an area of uniform ability to store and 

transmit water. Discussion of the assumptions and the validity of 

the conceptual model is reserved for later in the paper.
L8 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

West 

2900' -i

2800'- 

2700' - 

2600'- 

2500'- 

2400' - 

2300'-

2200'

Tobacc

Deltaic deposits *' Outwash deposits /

Relatively

- \-^ Impermeable 

deposits

VERTICAL SCALE GREATLY EXAGGERATED 

DATUM IS MEAN SEA LEVEL

Diagn-.rmatic geologic section across the Tobacco Plains

Reservoir stage Land surfaceImpermeable 

valley wall

11Y'

at rrl v

Reservoir stage/ 

at time t 0 SL ,TL

Initial water table^^

Aquifer

Sketch of aquifer across the Tobacco Plains 

as assumed for the electric analog

Reservoir stage

Reservoir stage' 

at time ta

Land surface-.

Initial water table^

Aquifer of transmissivity T, 

storage coefficient S

Impermeable

valley walk

-----I

Sketch of aquifer across the Tobacco Plains as assumed for the 

mathematical model of Cooper and Rorabaugh (1963)

FIGURE 3. Sketches comparing a diagrammatic geologic section with the conditions 

assumed in the electric analog and in the mathematical model of Cooper and 

Rorabaugh (1963). SL, Sn, and So are the storage capacities of the lake-bottom, 

deltaic, and outwash deposits, respectively; TL, TD, and To are the transmissivities 

of these deposits. The initial time is t0 ; some later time is tn. The difference between 

the reservoir stages at these times is h0 .

The area modeled is the floor of the Rocky Mountain Trench 

from 5 miles north of the head of the reservoir southward to Rex-
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L9

ford. The model includes the part of the reservoir between the 

maximum and minimum stages.

A network of resistors and capacitors was built at a scale of 1 

inch equals Viz mile. The shape and size of the aquifer boundaries 

is the same as those of the geologic units mapped in the field. 

Each unit's ability to store and transmit water is represented by 

an appropriate value of capacitance and resistance. The reservoir 

area, which is represented by a low-resistance wire connected directly to the aquifer network and to ground, is divided into subareas connected to each other by a diode. Subareas were determined 

by the depth of water at maximum stage of the reservoir. Each 

subarea represents an area of the reservoir where the valley floor 

slopes 10 feet.

Description of the model is summarized by the following list of 

assumptions:

1. Flow in the aquifer is two dimensional.

2. Bank storage is a linear function of reservoir stage and time.

3. The reservoir is in full hydraulic connection with the adjacent 

aquifer.

4. The reservoir fully penetrates the aquifer and has vertical 

banks.

Representative annual pulse applied to reservoir nodes

20 30 40 

DISTANCE UPSTREAM FROM REXFORD, IN MILES

FIGURE 4. Schematic sketch of Kootenai River profile and the annual pulse applied 

to subdivisions of the reservoir. The sections represent areas of the reservoir where 

bank storage was measured on the analog. The maximum rise of reservoir stage, in 

feet, is ho.
L10 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

........... mmm

TIME, IN YEARS 

A

1

TIME, IN YEARS 

B

FIGURE 5. Photographs of the oscilloscope face showing cumulative bank storage and water-level changes. A, Total volume 

of cumulative bank storage at any instant; the cyclic changes 

between a and b represent the yearly change in cumulative 

bank-storage volume; run 2. B, Water-level changes at an 

expanded time scale and at a location 2 miles east of the 

reservoir; run 1, hydrograph at location 34. C, Water-level 

changes for 40 years at the same location as B; run 2, hydrograph at location 34. D, Water-level changes at a location 

half a mile from the reservoir; run 2, hydrograph at location 

2.

5. The initial potentiometric surface is in equilibrium and the only 

cause of fluctuation is the reservoir.

6. The subsurface distribution of the geologic units is the same as 

the surface configuration and each geologic unit has a uniform 

ability to store and transmit water.

STIMULATION

The model is stimulated by applying to it an electric pulse that 

represents the annual fluctuation in stage proposed for the reser-
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR Lll

20

TIME, IN YEARS 

C

40

TIME, IN YEARS 

D

voir (fig. 4). Stimulation is the process of exciting the passive 

elements of the model to simulate the operation of the reservoiraquifer system. Each subarea is stimulated by a pulse of different 

magnitude at a slightly different time (fig. 4) to account for the 

reservoir's variance of depth and fluctuation in space as well as 

time. The pulse from the wave generator is divided by a diode network so that each upstream subarea receives a smaller pulse than 

the adjacent downstream subarea (fig. 4).

The model was stimulated by applying to it a pulse representing 

40 years of equal stage fluctuations. Current from the reservoir 

(rate) was integrated with time to measure the volume of bank 

storage (fig. 5A). To find the areal distribution of bank storage, 

current was measured from sections of the reservoir (fig. 4). 

Each section consisted of four or more subareas. Each subarea, in 

turn, represented a reach of the Kootenai River profile having a 

difference of 10 feet in elevation.

Though not a direct measure of bank storage, water-level (voltage) changes were measured at 34 random points throughout the 

floor of the Rocky Mountain Trench. These measurements show
L12 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

the effect of the reservoir at various places in the aquifer. Oscilloscope hydrographs of two points are shown in figure 5; their locations are shown in figure 2.

Bank storage and water-level changes were measured at the 

same locations during three model runs. The coefficient of storage 

was changed proportionally everywhere on the model before the 

second and third runs. During the second run, S was one-half of 

initial S; and during the third run, S was twice initial S. Because 

the volume of bank storage depends upon the product of S and T 

and upon the ratio of T to S, varying the magnitude of S causes 

the model to represent bank storage for a set of different aquifer 

parameters, which are TS and T/S (See section on "Parameters 

affecting bank storage.")

RESULTS

The model analysis helps to understand how the fluctuating reservoir stage could affect the aquifer. Figure 5B shows an oscilloscope picture at an expanded scale of a well hydrograph about 2 

miles east of the reservoir. The yearly stage fluctuation of the reservoir (160 ft on the reservoir directly west of the well) has been 

damped to about 12 feet and delayed by about 40 days. At the 

end of the first reservoir cycle, not all the water has drained that 

entered the aquifer during the rising reservoir stage. Thus, after 

each cycle, more water is in the aquifer than before the cycle. Theoretically, given enough time and equal cycles of the reservoir, the 

fluctuation would approach simple harmonic motion and cause the 

water-level fluctuation in the aquifer to be damped harmonic motion. When the reservoir-aquifer system reaches this condition, it 

has achieved a periodic steady state, and equal amounts of water 

are gained and lost each year. Under these conditions, in a semiinfinite aquifer fully penetrated by a reservoir with a level floor, 

the water levels in the aquifer would annually fluctuate about a net 

rise equal to half the reservoir fluctuation opposite the point 

(Jacob, 1950, p. 365). Also, the amplitude of the annual waterlevel fluctuations would decrease exponentially with distance from 

the reservoir. At Libby Reservoir the yearly fluctuation is not 

everywhere constant because the reservoir floor slopes and the 

aquifer is not infinite. These two facts would cause the annual 

water levels to fluctuate about a net rise of less than one-half of the 

reservoir fluctuation opposite the point in the aquifer. The time for 

the aquifer to reach the periodic steady state varies from a few 

years near the reservoir to more than 40 years at places far from 

the reservoir (fig. 5 C and D}. In a semi-infinite aquifer under 

periodic steady-state conditions, simple calculations using heat-
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L13

flow equations can be made to find the head distribution, volume 

of bank storage, and time lags (Ferris, 1950). Such calculations 

illustrate the entire reservoir-aquifers system only after many 

years of equal reservoir cycles. In the real reservoir-aquifer system unequal annual reservoir cycles might prevent the system 

from reaching a periodic steady state during the life of the reservoir.

It is convenient, at this point, to simplify the oscilloscope 

photographs showing the accumulated volume of bank storage 

(fig. 5A). The distance below a line drawn to connect the 

points of least annual volume of bank storage represents the 

minimum volume of bank storage that will go into inactive storage 

in the aquifer. This water will not return to the reservoir under 

presumed operating conditions and is called inactive bank storage. 

If, however, the reservoir did not always fill, the inactive bank storage would be released to the reservoir until all the inactive storage 

was returned or until the stage of the reservoir rose. The distance 

above the lower line and below the line connecting the points of 

highest annual volume of bank storage represents the volume of 

water that will return to the reservoir each year. This water 

is called active bank storage. Shortly after the first few cycles 

of reservoir fluctuation, active bank storage approaches a constant value. Curves showing the total active and inactive 

bank storage for runs 1, 2, and 3 are shown in figure 6. The 

amounts of active bank storage are tabulated for sections 

(fig. 4) of the reservoir in table 2.

TABLE 2. Active bank storage along Libby Reservoir

Section

1 ...

2 .

3

4 ..

5 ...

6 .

Distance

upstream

from

Rexford

(miles)

.. . 5.5

... 10.0

-. 16.0

.... 26.2

..- 45.2

.... 51.2

Total ........

Run

Average

active

bank

storage

(acre-ft)

95,000

44,000

27,000

26,000

16,000

16,000

224,000

1

Percent

of

total

42

20

12

12

7

7

100

Run 2

Average

active

bank

storage

(acre-ft)

48,000

19,000

14,000

12,000

9,000

8,000

110,000

Percent

of

total

44

17

13

11

8

7

100

Accumulated 

average 

Kun 6 Bcrccnt of

Average

active

bank

storage

(acre-ft)

176,000

64,000

34,000

34,000

28,000

24,000

360,000

Percent

of

total

49

18

9

9

8

7

100

average 

active

bank

storage

for all

runs

45

63

74

85

93

100

Note. Active bank storage, in acre-ft, in the alluvium along the Kootenai River as estimated 

by the U.S. Corps of Engineers as follows:

Dam to Rexford ............. ...._........................... ... ....... ......................_ ...... ............. .... 32,000

Rexford to international boundary ......... .................._.... ..... .............. ...... 19,000

Boundary to Elk River ........................................................... ....... ................ ...... ......... 27,000

North of Elk River .............................................................................................................. 10,000

Total ............................... ................... ...... ... ........................ . ............................. 88,000
L14 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

24 32 40 0 8 16 

TIME SINCE RESERVOIR BEGAN TO FILL, IN YEARS

FIGURE 6. Cumulative bank storage for analog runs 1, 2 and 3. Aquifer characteristics for each run are shown in table 1.

Because the analog assumes a completely penetrating reservoir, the estimates of active bank storage do not include 

storage in the Kootenai River alluvium that is exposed at low stage 

of the reservoir but is covered by water at high stage of the reservoir. The U.S. Army Corps of Engineers has estimated the volume 

of alluvium along the Kootenai valley and the active bank storage in 

this alluvium as part of an independent and unpublished study 

(table 2). This part of the estimate by the Corps assumes a "water 

exchange" of 2 to 12 percent based on the lithology and permeability of the deposits. The estimate includes a relatively small volume 

of alluvium that will not be covered at high stage of the reser-
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L15

voir, but the estimate by the Corps can be used to help evaluate the amount of active bank storage not included in the 

analog.

Water-level fluctuations measured at various nodes in the 

aquifer model provide a comparative index that relates the amount 

of bank storage to the various lithologic rock types at various distances from the reservoir. A summary of the average yearly waterlevel fluctuations of 34 random nodes is shown in table 3. It is 

difficult to generalize from table 3 because each node point is

TABLE 3. Summary of water-level fluctuations in various lithologic types and at 

various distances from the reservoir

Average yearly range

in fluctuation

(feet)

Average lithologic type

Silt and sand ..... ..

Gravel .......

Silt and sand .... ------ .

Sand and gravel 

Sand, gravel and clay

Distance from reservoir 

(miles)

0.1-0.2

.1- .2

.4-1.0

1.1-1.8 

2.1-5.5

Run 1

41

15

20 <io

<10

Run 2

23

8

14

<10 

<10

Run 3

56

18

30

<10 

<10

affected differently by the shape and distance to impermeable 

boundaries and because the reservoir fluctuation is different opposite different nodes. Moreover, conclusions drawn from averages of 

such widely varying data could be misleading. About all that can 

be ascertained is that, at distances greater than 2 miles from the 

reservoir, the average yearly fluctuation may be less than 10 

feet. The rise over a period of years due to inactive bank 

storage may be as much as 80 feet.

CONCLUSIONS 

PARAMETERS AFFECTING BANK STORAGE

A data-collection program that acquires data in the areas 

where it will do the most good should be designed with a 

view toward the parameters that affect bank storage. The 

results of the analog provide the cumulative volume of bank 

storage but do not give much direct information about the 

parameters. Mathematical models show the effect of parameters on bank storage, but usually these models cannot account for the complex geometry of the system, so that the 

results may not be as accurate as the analog. It is desirable, 

therefore, to use the mathematical model to see the effect of 

various parameters on bank storage and to use the analog to 

calculate the volume of bank'storage.
L16 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

Cooper and Rorabaugh (1963) found the mathematical solution 

for the volume of bank storage, caused by a single flood-wave 

stage oscillation, to be of the form

v =

\ co 

where V = volume of bank storage,

h0 = maximum rise of reservoir,

T = transmissivity,

S = storage coefficient,

a) = frequency of stage oscillation,

t = time, and

I = distance to ground-water divide.

The term in brackets is a complex function of the ratio T:S, co, 

t, and I.

A plot from the analog of cumulative active bank storage 

versus distance upstream from Rexford is shown in figure 7. 

Changing the storage coefficients between runs causes the 

magnitude of the curves to vary. The shape of the curves, 

however, remains generally the same.

The analog shows that the accumulated volume of bank storage 

increases most rapidly between Rexford and the mouth of the Elk 

River. Cooper's and Rorabaugh's equation substantiates this, 

because it shows that the volume of bank storage increases proportionally to the maximum rise of reservoir stage (h0 ) . The 

maximum stage fluctuation will be about 170 feet near Rexford 

and will decrease upstream to 70 feet at the mouth of the Elk River. 

Active bank storage also decreases upstream because the reservoir 

contains water for less time at the upper end. Thus, if there are 

no great changes in T or S along the length of the reservoir, the 

distribution in space of active bank storage is largely a function 

of ho and co.

Considering only the first term of Cooper's and Rorabaugh's 

equation: if h0 and co are constant, the volume of active bank storage will vary as V^>- In anv cross section of Libby Reservoir the 

maximum ho is determined by the height of the dam and by the 

slope of the streambed, and o> is determined by the operation of 

the reservoir. If the most efficient operation of the reservoir 

requires nearly a maximum fluctuation each year and a similar 

stage hydrograph each year, then the total volume of active bank 

storage is largely controlled by T and S of the aquifer.

Cooper and Rorabaugh show how the reservoirs stage fluctuation affects both the magnitude and the time distribution of bank 

storage. Also, the analog shows that the total volume of bank 

storage at any time depends on antecedent reservoir fluctuations.

L18 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

Various reservoir hydrographs or series of unequal reservoir 

hydrographs could easily be programmed into the model. Because 

the reservoir does not yet contain water, any combination of 

stage hydrographs would be speculative, and a complicated series 

of reservoir hydrographs might tend only to mask the effect of 

other parameters. A more sophisticated model should be programmed by a stage hydrograph computed from historic inflows 

and output from models developed by the U.S. Army Corps of 

Engineers and Bonneville Power Administration to test reservoir 

operation.

LIMITS OF THE AREA OF INTENSIVE DATA COLLECTION

To develop a plan to collect data necessary to estimate bank 

storage, it is desirable to define the accuracy needed for the estimate. Active reservoir storage is about 5 million acre-feet, and it 

seems illogical to try to estimate bank storage closer than about 

1 percent of active reservoir storage because of possible errors in 

measuring active reservoir storage. Active bank storage could 

probably be estimated closer than plus or minus 50,000 acre-feet, 

but relative to active reservoir storage, further refinement of the 

bank storage estimate would seem unnecessary. The data-collection 

program should not be designed to collect data intensively in 

areas that supply marginal amounts of bank storage.

The largest area along the reservoir where data should be collected intensively to estimate bank storage is between Rexford 

and the mouth of the Elk River, 28 miles upstream from Rexford, 

because this is the area of greatest potential bank storage. The 

area of intensive investigation might be reduced further by considering the limiting value of 50,000 acre-feet. Because the limiting value is a volume of water which depends on T and S, T and 

S must be known to define conclusively the area of intensive data 

collection. For planning purposes, however, T and S can probably 

be estimated close enough to define the limits of the area of intensive data collection. To illustrate the use of the limiting value, 

suppose that preliminary data were available (laboratory permeabilities or a pump test) to give an idea of T and -S. If the data 

suggest that values assumed for T and S in run 1 are reasonable, 

then active bank storage is estimated as 224,000 acre-feet. The 

accuracy desired for the final estimate is 50,000 acre-feet, so that 

subtracting this amount for the estimate leaves 174,000 acre-feet, 

which could be used in planning reservoir management. This 

amount of bank storage is distributed within the 20 miles upstream from Rexford (fig. 7). Thus, the area of intensive data 

collection should be limited to this 20-mile reach. Of course, the
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L19

final estimate of bank storage would be based on a model of the 

entire reservoir area. The point is that most of the water in bank 

storage will be from this 20-mile reach, where the most time and 

money should therefore be spent in data collection. Less sophisticated data over the rest of the area will not introduce a serious 

error in the final estimate. If preliminary data showed S and T 

values assumed during run 1 to be greatly in error, another proposed area would be defined by analyzing curves from another run.

Defining the limits of the area of intensive data collection east 

and west of the reservoir is less exact than defining the limit 

along the length of the reservoir. Obviously, hydrologic data 

should be collected only from the permeable deposits on the floor 

of the Rocky Mountain Trench, which is 5-10 miles wide. As annual water-level fluctuations more than 2 miles from the reservoir are estimated as less than 10 feet and appear to be 1-2 feet, 

the intensive area could probably be limited to about 2 miles 

from the reservoir without causing serious errors. If, however, 

inactive bank storage is of interest, almost the entire width of 

the trench would require data collection because the reservoir 

will eventually cause a net rise at some places of as much as 80 

feet.

The Corps of Engineers' estimate of active bank storage (table 

2) in the alluvium that will be covered by the reservoir indicates 

that 10,000 acre-feet would be above the mouth of the Elk River. 

Regardless of where data are intensively collected on the floor of 

the trench, the alluvium should be studied intensively to the Elk 

River because each unit volume of alluvium stores and transmits 

relatively large volumes of water. Upstream from the Elk River, 

data could be collected less intensively but still in sufficient 

quantity to detect major changes in T and S.

Conclusions summarized below regarding the size of the area 

of intensive data collection assume the conceptual model and T 

and S values for run 1 to be correct. Other values of T and S 

would define a different area for intensive data collection if the 

values for run 1 are found to be in error.

1. The area of intensive data collection is determined by the accuracy of measuring active reservoir storage, the magnitude 

and frequency of the reservoir fluctuation, the slope of the 

floor of the reservoir, and T and S of the aquifer.

2. The area should extend 20 miles upstream from Rexford.

3. The area should be confined to the floor of the Rocky Mountain Trench within 2 miles of the reservoir.

4. The alluvium along the Kootenai River should be studied most
L20 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

intensively between Rexford and the Elk River and in less 

detail to the head of the reservoir.

DISCUSSION

This paper is essentially an effort to develop the most economical plan for collecting data to solve, with reasonable accuracy, a 

specific problem. The principle advantage of the exercise is that 

known facts are organized and areas where more information 

will be the most useful are pointed out. Studying the analog results and the mathematical model of Cooper and Rorabaugh helps 

to relate to one another the physical parameters that affect bank 

storage. Such an insight helps to evaluate the shortcomings of 

various approaches and to see the relative importance of various 

parameters; it is the beginning of a logical data-collection program. The approach also provides people in management with 

data that allows them to compare this project with other projects 

with respect to the possible return from allocated funds.

The principal disadvantage of building an electric analog from 

scanty field data is that the conceptual model generated by the 

hydrologist may require modification. The analog is essentially 

an electrical copy of the conceptual model. Without adequate 

data for checking the analog results, it is difficult to check the 

concepts used to build it.

At Libby Reservoir, where the conceptual model is based on 

the surface geology, the question is how deep surface geological 

concepts can be extended into the subsurface. The surface and 

subsurface are surely dissimilar, but it is not known to what degree or whether the degree of dissimilarity will cause significant 

hydrologic differences. Test drilling is necessary to determine the 

degree of dissimilarity. The problem of checking the validity of 

the geologic and hydrologic concepts would exist regardless of 

the type of model used to'estimate bank storage. It might be 

easier to change other models, but without additional field data 

changes would be meaningless.

The results of the analog allow consideration of several alternatives for studies to estimate better the ground-water gains and 

losses to the reservoir. The first alternative is simply no further 

study of the reservoir-aquifer system. Water contributed to the 

reservoir from the aquifers will be of benefit regardless of 

whether it is studied or not. Optimum reservoir management, 

however, requires that the amount of water available to the reservoir be known in advance so that power can be sold on a firm 

basis and flood-control benefits can be fully realized. For proper 

management of the reservoir, the amount of water available and
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L21

its worth need to be known. This study points out that a significant amount of water may be associated with bank storage and 

that it may be worth studying.

A second alternative is to study ground water associated with 

the reservoir by an approach similar to the one used for estimates made during1 this study. The cost of a hydrologic study to 

estimate accurately ground-water storage changes associated 

with the reservoir would probably be about $120,000, based on 

1969 costs, and it might cost $50,000 per year for 5-10 years to 

collect and analyze hydrologic data to substantiate and refine the 

estimate. The total cost for the program would probably be 

about $600,000, based on 1969 costs. If the average yearly bankstorage contribution to the reservoir is 224,000 acre-feet predicted by the analog during run 1 plus 66,000 acre-feet estimated 

to be stored in the alluvium that will be covered by the reservoir, 

the total (290,000 acre-ft) is about 5.8 percent of active reservoir 

storage.

This analog approach also indicates that inactive bank storage 

will remove some water permanently from the Columbia River 

System; such a removal would be a liability to the powergenerating capacity of the system. Much of the water that goes into 

inactive bank storage, however, will do so during the spring runoff period and will benefit the flood-control aspects of the Columbia 

River projects.

A third alternative would be to wait until the reservoir fills 

and to study bank storage by a water-budget approach. This 

would involve accurate measurements of inflow and outflow and, 

if continued for 5 or 10 years, might cost more than the second 

alternative. The results by this procedure have an undefined but 

large area of uncertainty because of inability to measure within 

close limits. For periods much less than a year, it is difficult to 

close the water budget for a reservoir imposed on a natural flow 

system, because the natural system causes delays between the 

measurement of aquifer recharge and flow of the recharge into 

the reservoir.

It is interesting, although academic, to compare the cost of 

two approaches toward the problem of collecting the geohydrologic data necessary to evaluate bank storage with reasonable 

confidence. The first approach was made after a brief reconnaissance of the area above Rexford and simply requires test drilling 

on an arbitrarily selected grid. The second approach was to construct the analog model and to use the results of the model to 

develop a plan to collect the data in the most critical areas.
L22 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

The first approach would cost about $250,000 or nearly twice 

as much as the second, which considers the natural flow system 

and its contributions to the reservoir in more detail. If the second approach is used, the savings would not be real because it is 

unlikely that the first would have been completely funded. The 

second approach may not be completely funded; however, reductions in funding will cause a minimum loss of estimate accuracy 

because the results of the analog may be used to plan further 

reductions in collecting data.

The analog approach shows some promise as a technique to 

estimate bank storage. The approach tends to minimize data 

collection as well as provide a working model of the reservoiraquifer system. The final working model, whether it is an electric 

analog or some other kind, would be modified, and predictions 

would improve as data from a monitoring program became available to check predictions and make corrections. The monitoring 

program would consist mainly of measurements of streamflow 

and ground-water levels.

For proper management of the reservoir, the amount of water 

available from bank storage and from the natural flow system 

needs to be known in advance. Insofar as reservoir operation and 

precipitation can be predicted, the model could rapidly calculate 

the amount of water available from the aquifers. New calculations could be made as unexpected events occur, and thus the 

model calculations should be dependable for a few months in advance, but less dependable for periods of 6 months or a year. 

With the aid of a sophisticated model, it may become possible to 

regulate the reservoir so as to take maximum advantage of 

water available from the aquifers.

SHORTCOMINGS OF THE ANALOG

Assumptions used in constructing the electric analog are discussed below to show how they affect the estimate of bank storage. The first sentence in each of the following six sections states 

the assumption, and the following sentences describe the effect of 

the assumption on the estimate of bank storage.

1. The reservoir is in full hydraulic connection with the aquifer. 

Shortly after the reservoir begins to fill, an accumulating clay 

and silt layer as well as entrapped air will tend to decrease the 

hydraulic connection. The connection will become worse as clay 

and silt accumulate and cause bank storage to be less than predicted; the prediction will be come more in error with time.

2. Transmissivity and the storage coefficient do not change with 

time. As the reservoir fluctuates, the saturated thickness of the
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L23

banks will change from zero to as much as 172 feet. The assumed values of T consider that the banks are always saturated 

to the maximum flow line of the reservoir. Actually, this would 

be true during only about 2 or 3 months during an average year. 

The assumption will cause bank storage to be less than 

predicted.

3. There is no bank storage in the aquifer beneath the reservoir. 

The alluvium along the Kootenai River is mostly gravel and 

appears capable of storing and transmitting large quantities of 

water per unit volume. The water stored by the alluvium is not 

considered in the analog, but this water may be accounted for 

by adding the active bank storage estimated from the volume 

of alluvium.

4. The reservoir fluctuates 170 feet each year, and the stage hydrograph is identical for 40 years. The maximum fluctuation 

planned for the reservoir is 172 feet during critical water conditions. The average operating fluctuation probably will be less 

than 170 feet and will depend on inflow to the reservoir and on 

reservoir operation. Firm operating rules are being developed 

for the reservoir but are not yet (1969) completed. Because 

bank storage is directly dependent upon the annual reservoir 

fluctuation, assuming a maximum fluctuation will tend to make 

bank storage a maximum.

5. There is no evaporation or transpiration from the aquifer. This 

assumption is probably nearly correct. Assuming a maximum 

80-foot rise of water level in the aquifer, the depth to water beneath the floor of the trench will be generally greater than 20 

feet. The bank slope above reservoir level is steep, and only in a 

narrow zone along the edges of the reservoir will the water table 

be near land surface; thus, the area of relatively high evapotranspiration will be small. During the winter and spring when 

the reservoir is lowest, snow will cover the exposed floor and 

retard evaporation.

6. The aquifer receives no recharge from precipitation. This 

assumption is necessary because field data are insufficient to 

define the natural flow system into which Libby Reservoir will 

be introduced. A more sophisticated analysis would require consideration of recharge, which considerably complicates the 

problem. Bank storage is defined as water entering the aquifer 

from the reservoir; however, storage increases in the aquifer result from both bank storage and additions by the natural flow 

system, which receives its water from recharge. As the reservoir 

stage lowers, water flowing into the reservoir from the aquifer
L24 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

may originate from both bank storage and the natural flow system. The total contribution of water to the reservoir from the 

aquifer is not considered in the electric analog because the analog considers only the bank-storage component. The natural flow 

system could affect the amount of bank storage, because if 

water levels in the aquifer near the reservoir are higher than 

the reservoir during rising stages, bank storage would be small; 

yet, if the stage of the reservoir lowers faster than groundwater levels, ground water will flow into the reservoir and contribute to its available storage as does bank storage. 

Limited field data from the Tobacco Plains indicate that 

ground-water levels near the east edge of the proposed reservoir 

rise rapidly in the last part of July or first part of August and 

slowly decline during the rest of the year. Superimposing the assumed reservoir-stage hydrograph on hydrographs from the natural flow system suggests that water would flow into the aquifers 

during rising reservoir stages; such a flow would delay the natural 

ground-water discharge to the Kootenai River until the reservoir 

stage began to decline in September or October. Thus, the natural 

flow system may cause bank storage to be smaller than that predicted by the electric analog, but the total ground-water contribution to the reservoir from the aquifer may be larger than predicted 

bank storage.

PLANS FOR A NEW MODEL

Construction and manipulation of the analog and discussion of 

its assumptions help to define plans for a new model to estimate 

bank storage more accurately. Criteria for a new model determine 

what field data need to be collected. The analog has helped to define the area necessary for intensive data collection as a function 

of transmissivity and storage coefficient. Discussion of the results 

points out that recharge is important and must be considered in 

the next model. Test drilling and hydrologic testing in the area of 

intensive data collection, as well as better definition of the natural 

flow system, would justify construction of a new model. Because 

the time distribution of bank storage will be important to reservoir 

operation, the new model would have a much expanded time scale, 

so that seasonal bank storage could be predicted. The model would 

include the following modifications of the first model:

1. The hydraulic diffusivity would be based on observed values of 

T and S for individual areas.

2. Hydraulic connection between the reservoir and aquifer would 

be modeled as less than 100 percent and as a function of time.
BANK STORAGE ASSOCIATED WITH LIBBY RESERVOIR L25

3. Transmissivity close to the reservoir would be allowed to vary 

as a function of the reservoir stage.

4. Recharge would be programmed into the model.

5. The alluvium beneath the reservoir would be modeled.

6. The reservoir fluctuation would be based on streamflow record 

and on reservoir operating-rule curves.

REFERENCES CITED

Cooper, H. H., Jr., and Rorabaugh, M. I., 1963, Ground-water movements and bank

storage due to flood stages in surface streams: U.S. Geol. Survey Water-Supply

Paper 1536-J, p. 343-366. 

Ferris, J. G., 1950, A quantitative method for determining ground-water characteristics

for drainage design: Agr. Eng., v. 31, no. 6, p. 285-291. 

Jacob, C. E., 1950, Flow of ground water, Chap. 5 in Rouse, Hunter, ed., Engineering

hydraulics: New York, John Wiley & Sons, p. 321-386.

.S. GOVERNMENT PRINTING OFFICE: I97O