An Economic Analysis of Selected Strategies 

for Dissolved-Qxygen Management: 

Chattahoochee River, Georgia

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1140

An Economic Analysis of Selected Strategies 

for Dissolved-Oxygen Management: 

Chattahoochee River, Georgia

By JOHN E. SCHEFTER and ROBERT M. HIRSCH

GEOLOGICAL SURVEY PROFESSIONAL PAPER

A method for evaluating the cost effectiveness 

of alternative strategies for dissolvedoxygen management is demonstrated

1140

UNITED STATES GOVERNMENT PRINTING OFFICE, WASH INGTO N : 1980
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY

H. William Menard, Director

Library of Congress Catalog-card No. 80-600113

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

Washington, D.C. 20402
CONTENTS

Abstract __________________________________________

Introduction _______________________________________

Nature of the problem ____________________________

Buford Dam _______________________. 

Relationship of flow and dissolved oxygen ______. 

Managing the dissolved-oxygen concentration _____. 

The range of alternatives _______________. 

The alternatives considered _____________________

Study overview _______________________, 

The dissolved-oxygen model ___________________________

Results from the dissolved-oxygen model _________ 

The hydrologic simulation model ________________________

Operation of the Buford Dam hydroelectric generating

facility: assumptions and definitions ___________ 9 

Description of the hydrologic simulation model ______ IQ 

Results from the hydrologic simulation model _______ H

Page

1

1

1

1

3

3

4

4

5

5

6

7

Estimation of costs: benefits foregone and waste-treatment 

costs __________________________________________

Estimates of benefits, given 1954-56 drought conditions _ 

Recreation ____________________________________

Hydroelectric power and peak generating capacity ___ 

Estimation of average annual benefits _________________

Estimation of added waste-treatment costs _____________

The reregulation project _______________________________

Least-cost method of producing a given minimum dissolvedoxygen concentration _____________________________

Sensitivity of the least-cost solution to the cost of dependable peak-generating capacity ______________________

Institutional constraints and associated costs ______________

Concluding remarks ___________________________________

References cited ______________________________________

Appendix A-Analysis of the reregulation project ___________

Page

13

14

14

14

16

17

18

21

21

23

24

25

25

ILLUSTRATIONS

Page

FIGURE 1. Graph showing dissolved-oxygen concentrations at the Fairburn, Ga., station monitor and mean daily discharge at the

Atlanta, Ga., station during July 1977 ________________________________________—————— 2 

2. Schematic map of the study reach of the Chattahoochee River, Ga ___________________________—————— 3 

3, 4. Graphs showing:

3. Minimum dissolved-oxygen concentration as a function of minimum flow at the Atlanta, Ga., gage, given that 48

percent of the waste flow receives nitrification, for 1990 conditions ____________________————__ 6

4. Relationships of parameters of aQA + b=D to percentage of total waste flow receiving nitrification ________—__ 7 

5-7. Iso-dissolved-oxygen curves showing combinations of percentage of total waste flow receiving nitrification and minimum discharge at Atlanta, Ga., that are predicted to result in minimum dissolved-oxygen concentrations of 3, 4, and 5 mg/L:

5. For 1980 conditions __________________________________————————————————————— 8

6. For 1990 conditions ________________________________________________________ 8

7. For 2000 conditions __________________________________________————————————— 9 

8. Diagram showing simulated releases at Buford Dam, Ga., during weeks 33 and 40 of 1954, given a minimum flow at

Atlanta, Ga., of 1,290 and 1,600 ft3/S, For 1990 conditions ____________________________________ 13 

9-12. Graphs showing:

9. Pool elevations of Lake Sidney Lanier, Ga., over the period of simulation, given that the minimum flow at Atlanta,

Ga., is set at 1,290 and 1,600 ft3/s, for 1990 conditions ______________________________——___ 14

10. Benefits from recreation on Lake Sidney Lanier, Ga., given various pool elevations ———————————————————— 15

11. The relationship between average annual benefits foregone and minimum flow at Atlanta, Ga., for 1980, 1990, and

2000 _________________________________________________————————————— 18

12. The estimated annual cost of adding a nitrification process to secondary waste-treatment plants, as a function of the

percentage of the total waste flow receiving nitrification ___________________————————————— 19

in
IV CONTENTS

Page

Fici'KKs 13,14. Diagrams illustrating:

13. The method of determining the least-cost combination of the percentage of waste flow receiving nitrification 

and the minimum flow at Atlanta, Ga., required to produce a minimum dissolved-oxygen concentration 

of 4 mg/L, in 1990 ______________________________________________________ 19

14. The solution for least-cost combinations of percentage of wastes receiving nitrification and minimum flow 

at Atlanta, Ga., necessary to produce a minimum dissolved-oxygen concentration of 5 mg/L, 

for 1980, 1990, and 2000 _________________________________________________ 21

15. Graph showing the costs (benefits foregone plus added waste-treatment cost) of attaining various minimum dissolvedoxygen concentrations under different policies for 1990 _______________________________—___ 24

16. Diagram illustrating the relationship between estimated annual dependable-peaking-capacity benefits and minimum flow

at Atlanta, Ga., with and without reregulation, for 1980, 1990, and 2000 __________________________ 26

TABLES

Fagv

TAHLK 1. The expected average daily flow from waste-treatment plants discharging to the Chattahoochee River between Atlanta,

Ga., and Whitesburg, Ga., in 1980, 1990, and 2000 ________________________________________ 6 

2-4. Withdrawals from:

2. Lake Sidney Lanier, Ga ______________________________________________________ H

3. The Chattahoochee River, Ga., from Buford Dam to Morgan Falls Dam ___________________________ 11

4. The Chattahoochee River, Ga., from Morgan Falls Dam to the Atlanta gage ________________________ 12 

5-7. Hydrologic-simulation-model results:

5. Of water discharge and electric-power production of Buford Dam, Ga., for 1990 conditions ________________ 12

6. For years 1980, 1990, and 2000 _________________________________________________ 12

7. And estimated benefits for 1990, given certain minimum flows at Atlanta, Ga., under 1954-56 drought conditions __ ig

8. The average daily flow from waste-treatment plants discharging to the Chattahoochee River between Atlanta, Ga., and

Whitesburg, Ga., and the annualized cost of adding a nitrification process to the plants ____________________ 18

9. Combinations of percentage of wastes receiving nitrification and minimum flow at Atlanta, Ga., that will provide minimum

dissolved-oxygen concentrations of 3, 4, and 5 mg/L at least cost, for 1980, 1990, and 2000 __________________ 20

10. Costs of dependable peak generating capacity above which the indicated minimum dissolved-oxygen concentration can be

achieved at least cost by operating Buford Dam, Ga., so as not to forego benefits from dependable peak generating capacity_ 22 

11, 12. Economic-efficiency loss if least-cost combination of the percentage of wastes receiving nitrification and the minimum flow 

at Atlanta, Ga., is selected under the assumption that the cost of peak generating capacity:

11. Is $23.34/kW/yr but actual cost is $49.35/kW/yr _________________________________________ 23

12. Is $49.35/kW/yr but actual cost is $23.34/kW/yr ________________________________________ 23 

13. Percentage of wastes that must receive nitrification to provide minimum dissolved-oxygen concentration of 3, 4, and 5

mg/L at least cost, given that the minimum flow at Atlanta, Ga., is constrained to 860 ft3/s, for 1980,1990, and 2000 ___ 24
AN ECONOMIC ANALYSIS OF SELECTED STRATEGIES FOR DISSOLVEDOXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GEORGIA

By JOHN E. SCHEFTER and ROBERT M. HIRSCH

ABSTRACT

A method for evaluating the cost-effectiveness of alternative 

strategies for dissolved-oxygen (DO) management is demonstrated, using the Chattahoochee River, Ga., as an example. The conceptual 

framework for the analysis is suggested by the economic theory of production. The minimum flow of the river and the percentage of the total 

waste inflow receiving nitrification are considered to be two variable 

inputs to be used in the production of given minimum concentration of 

DO in the river. Each of the inputs has a cost: the loss of dependable 

peak hydroelectric generating capacity at Buf ord Dam associated with 

flow augmentation and the cost associated with nitrification of wastes. 

The least-cost combination of minimum flow and waste treatment 

necessary to achieve a prescribed minimum DO concentration is identified.

Results of the study indicate that, in some instances, the wasteassimilation capacity of the Chattahoochee River can be substituted 

for increased waste treatment; the associated savings in wastetreatment costs more than offset the benefits foregone because of the 

loss of peak generating capacity at Buford Dam. The sensitivity of the 

results to the estimates of the cost of replacing peak generating capacity is examined. It is also demonstrated that a flexible approach to the 

management of DO in the Chattahoochee River may be much more 

cost effective than a more rigid, institutional approach wherein constraints are placed on the flow of the river and (or) on waste-treatment 

practices.

INTRODUCTION

This study has two primary purposes: (1) to 

demonstrate a method of evaluating the cost effectiveness of alternative strategies for the management of 

the concentration of dissolved oxygen (DO) in a river; (2) 

to demonstrate how the results of a U.S. Geological 

Survey (U.S.G.S.) River Quality Assessment can be applied within the context of economic analysis to a DO 

management problem. Results of the U.S.G.S. Chattahoochee River Quality Assessment are utilized to 

estimate the costs associated with selected strategies 

for maintaining three different minimum DO concentrations in the Chattahoochee River between Atlanta, Ga., 

and West Point Lake, Ga.

NATURE OF THE PROBLEM

During 1977 the dissolved-oxygen (DO) concentration 

in the Chattahoochee River at Fairburn, Ga., 25 miles 

downstream of Atlanta, was less than 5.0 mg/L

(milligrams per liter), 10 percent of the time (Stamer 

and other, 1978). The periods of low DO concentrations 

occurred primarily in the summer and autumn. During 

October the DO concentration was less than 5.0 mg/L 31 

percent of the time-more often than in any other 

month.

The occurrences of low DO concentrations correspond 

closely with the occurrences of low discharge of the 

river. This relationship can be seen in figure 1, which 

shows (top) the average daily DO concentration at Fairburn and (bottom) the average daily discharge at Atlanta, which is about 1.5 days traveltime upstream of Fairburn.

BUFORD DAM

Both graphs in figure 1 display a 7-day periodicity. 

The periodicity of the Atlanta hydrograph is a consequence of the pattern of releases at Buford Dam.

Figure 2 is a schematic map of the Chattahoochee 

River. In this figure, the various impoundments, gages, 

water-supply withdrawal points and waste-water 

discharge points of interest to this study are identified 

and located by river mile.

The multipurpose Buford Dam impounds Lake Sidney 

Lanier, which has a storage capacity of 1.9 million acrefeet at normal pool elevation. In a study of the benefits 

of the Buford Dam-Lake Sidney Lanier project, the U.S. 

Army Corps of Engineers (1977) estimated that 74 percent of the average annual benefits come from recreation, 17 percent from hydroelectric power, and the remainder from flood control, navigation (in the 

Apalachicola waterway), water supply (for the Atlanta 

metropolitan area), and low-flow and water-quality 

maintenance (for the Chattahoochee River from Atlanta 

to West Point Lake).

Buford Dam has an installed hydroelectric generating 

capacity of 105 MW (megawatts), which is used primarily during periods of peak demand. Electricity is 

generated primarily about 6 hours per day on weekdays. 

During these peak hours water is released from Lake 

Sidney Lanier at a rate as high as 10,000 ft3/s, and at
ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

i i I i l 

FAIRBURN STATION

3500

O 

O

CO 3000 

cc.

UJ

a.

ti

UJ

2500

5 2000

D 

O

? 1500

UJ

CD 

cc

O 

CO

O

1000

500

1 I I I I I 

ATLANTA STATION

PEAK HYDROPOWER RELEASE

HYDROPOWER RELEASE

I I I I I I l I J__L

III!

1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

C C

3 0

w -ri w 'd £ c c w -d w -rf +- c c w "D w 'd S

|||-*3||||-*3*5l|-« CO CO CO

DAY IN JULY

FIGURE 1.-Dissolved-oxygen concentrations at the Fairburn, Ga., station monitor and mean daily discharge at the Atlanta, Ga., station

during July 1977.
INTRODUCTION

Water-supply ) 

withdrawals *

Lake Sidney Lanier 

Buford Dam

Waste-water 

discharges

Reach of 

minimum DO

Morgan Falls Dam

Atlanta gage 

Peachtree Creek

Fairburn gage

Shoals 

(>> Whitesburg gage

Shoals 

C 9 Franklin gage

River 

miles 

360

-340

-320

-300

-280

-260

- 240

- 220

L 200

West Point Lake

FIGURE 2.-Schematic map of the study reach of the Chattahoochee River, Ga. (DO, dissolved oxygen.)

other times (morning, lates night, and weekends) the 

rate of release is approximately 600 ft3/s.

The extreme fluctuation in the flow of the river due to 

these releases is somewhat dampened by Morgan Falls 

Dam, located 10 miles above Atlanta, and by the natural 

attenuation of the flood wave over the 46 miles between 

Buford Dam and Atlanta. There is some tributary inflow 

between Buford Dam and Atlanta, but there are also 

water-supply withdrawals in this reach. The effects of 

the low release rates at Buford Dam that occur from late 

Friday night through midday Monday are somewhat 

mitigated but are very evident in the Sunday and Monday flows at Atlanta.

RELATIONSHIP OF FLOW AND DISSOLVED OXYGEN

There are three mechanisms whereby increased river 

discharge may affect the minimum DO in the river. The 

first is dilution: higher discharge causes a lower waste 

concentration, which results in a higher DO concentration throughout the DO sag. The second is a change in 

re-aeration: higher discharges generally cause less exchange of oxygen from the air to the water per unit 

volume of water and result in a lower DO concentration 

throughout the sag. The third is the decrease in travel 

time to the shoals, which are located between 30 and 50 

miles below Atlanta. Shoals have a pronounced reaerating ability; the sooner the shoals are reached the 

less the wastes are able to exert their oxygen demand 

and, thus, the higher is the minimum on the DO sag. The 

net effect of these three mechanisms appears to be, both 

empirically and in model results (Stamer and others, 

1978), that higher river discharges lead to higher 

minimum DO concentrations in the sag below Atlanta.

MANAGING THE DISSOLVED-OXYGEN CONCENTRATION

Stamer and others (1978) reported that on June 1-2, 

1977, when the river flow at the Atlanta gage was 1,150 

ft3/s, the minimum DO in the river was 4.0 mg/L and the 

DO was less than 5.0 mg/L along approximately a 20 

mile reach. At that time, the flow of waste water into 

the river was 185.3 ft3/s. The average concentration of 

the ultimate biochemical oxygen demand (BODu) of the 

waste water was 44 mg/L, and the average ammonianitrogen concentration was 11 mg/L. A model developed 

by Stamer and others (1978) predicts that under conditions anticipated for the year 2000 and with secondary 

waste treatment (370 ft3/s of waste water, BODu concentrations of 45 mg/L, and an ammonia-nitrogen concentration of 15 mg/L) the minimum DO concentration 

given the same river flow would be 1.1 mg/L and the DO 

concentration would be less than 5.0 mg/L along a 50 

mile reach. This model also predicts the change in the 

minimum DO given a change in the flow at Atlanta. For
ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

example, if the flow were 1,800 ft3/s instead of 1,150 

ft3/s in 2,000, the minimum DO concentration would be 

2.6 mg/L, and a reach of 43 miles would have a DO concentration less than 5.0 mg/L.

The model developed by Stamer and others (1978) also 

predicted minimum DO concentrations given other 

degrees of waste treatment. For example, if the BODu 

concentration of the waste effluent were 15 mg/L rather 

than 45 mg/L and the ammonia-nitrogen concentration 

were 5 mg/L rather than 15 mg/L, the minimum DO concentration would be 5.1 mg/L rather than 2.6 mg/L, 

given a flow at Atlanta of 1,150 ft3/s.

These model results clearly indicate that both 

modification of the hydrograph at Atlanta and modification of waste inputs from treatment plants located just 

below Atlanta are possible approaches to manipulating 

the present and future DO concentrations in the Chattahoochee River.

THE RANGE OF ALTERNATIVES

A number of techniques can be conceived that might 

be used alone or in combination to manage the DO concentration in the Chattahoochee River. The techniques 

include:

1. Improved sewage treatment, so that less water is required in the Chattahoochee River for water-quality 

maintenance purposes.

2. Construction of a sewage storage facility to hold the 

sewage for release during peak flows of the river.

3. Construction of a water-supply storage facility so as 

to permit increased withdrawals from the river during peak flow periods for use during low flow 

periods; this would leave more water available for 

water-quality maintenance during low flow periods.

4. Developing sources of water supply outside of the 

Chattahoochee River basin, so that more water 

could be available for water-quality maintenance.

5. Reducing the rates of water use (and, thus, sewage 

discharge), especially during low flow periods; this 

reduction could be accomplished by a number of rationing and (or) water-pricing schemes.

6. Dredging Morgan Falls Reservoir so as to increase 

its capacity and thus permit a more steady flow of 

the Chattachoochee River at Atlanta without 

affecting the dependable peaking capacity of 

Buford Dam.

7. Construction of a reregulation structure (dam and 

reservoir) between Buford Dam and Morgan Falls 

Dam so as to permit a more steady flow at Atlanta.

8. Changing the operating procedure of Buford Dam so 

as to release less water (and generate less electricity) during periods of peak demand for electricity 

and release more water at other times.

The full range of these techniques, both separately and 

in various combinations, may warrant consideration in 

the selection of an efficient method of improving the 

water quality of the Chattahoochee River below Atlanta.

THE ALTERNATIVES CONSIDERED

To reduce this study to a manageable size, given the 

resources available, only the following techniques are 

considered (separately and in combination):

1. Add nitrification to the treatment process at some or 

all of the treatment plants discharging into the 

Chattahoochee River or its tributaries between 

Atlanta and Whitesburg. The effluent concentrations given that secondary treatment is used are 

assumed to be 45 mg/L BODu and 15 mg/L NH4-N. 

Adding nitrification is assumed to result in concentrations of 27 mg/L BODu and 3 mg/L NH4-N.

2. Dredge Morgan Falls Reservoir and construct a reregulation structure between Buford Dam and 

Morgan Falls Dam.

3. Change the operating procedure of Buford Dam so as 

to give explicit consideration to the release of water 

from Lake Sidney Lanier for water-quality 

maintenance purposes.

Monetary costs are of course associated with the first 

and second techniques. Also, a change in the operation 

of Buford Dam may entail changes in the benefits 

presently derived from that project. There may be 

changes in the pool elevation of Lake Sidney Lanier that 

would affect recreation benefits and the amount of electrical energy produced per unit volume of water released. The relative proportion of high-valued peak power 

and lower-valued nonpeak (or base) power may change. 

Most importantly, as more water is reserved for lowflow maintenance less water is dependably available for 

peak power generation and the dependable peak 

generating (peaking) capacity of the generators at 

Buford Dam may change. The loss of this dependable 

peaking capacity will, it is assumed, entail the construction of peaking facilities elsewhere. Any change in the 

sum of these benefits as a result of change in the operation of Buford Dam for purposes of maintaining water 

quality is considered to constitute a cost incurred for 

that purpose.

In this study, an attempt is made to identify the leastcost combination of the three techniques (nitrification, 

change in the operation of Buford Dam for water-quality 

maintenance, and improved reregulation) that will 

achieve a given level of water quality as measured by the 

DO concentration in the Chattahoochee River. The 

least-cost combination of the three techniques are identified for three DO-concentration standards, 3, 4, and 5 

mg/L, to obtain estimates of the cost (in terms of increased treatment costs and benefits foregone) of
THE DISSOLVED-OXYGEN MODEL

achieving different DO concentrations in the river below 

Atlanta.

Also, the quantity of waste discharged to the river will 

increase along with-the population of the Atlanta region 

over time. Thus, for any given level of waste treatment 

and DO standard, the water required for water-quality 

maintenance will increase with time. For this reason, 

separate estimates of the costs of the least-cost combination of the three techniques are presented for the 

years 1980, 1990, and 2000.

Estimates of the costs do not include any change in 

the flood-control, navigation, and downstream 

hydroelectric-power-generation benefits as a result of a 

change in the operation of Buford Dam. Because the 

changes in operation considered are relatively minor, involving no change in the volume of the flood pool, no 

change in flood-control benefits would be expected. 

Navigation and downstream hydroelectric-power 

benefits would change only as a result of a major change 

in the seasonal pattern of releases from Buford Dam. 

The changes in operation of Buford Dam contemplated 

herein are substantial at the time scale of hours and days 

but not at the time scale of seasons. The only costs considered are the change in the benefits associated with 

recreation of Lake Sidney Lanier and generation of electric power at Buford Dam, the cost of adding nitrification to secondary waste-treatment facilities, and the 

cost of constructing and dredging reregulating facilities.

Just as costs are incurred in achieving or maintaining 

a given level of water quality in the Chattahoochee 

River, benefits may also be gained from so doing. 

Economic-efficiency criteria state that the net benefits 

to be obtained from an increase in the DO concentration 

of a river will be a maximum at that level of concentration where the cost of providing the last increment of 

DO concentration (for example, to 4.6 mg/L from 4.5 

mg/L) is just equal to the benefits to be obtained by improving the DO concentration by that amount. Estimation of the benefits to be obtained by improving the DO 

concentration of the river is beyond the scope of this 

study, and no attempt is made to identify that level of 

DO concentration that will maximize net benefits.

STUDY OVERVIEW

The model used to relate the minimum flow of the 

Chattahoochee River at Atlanta, the proportion of the 

wastes discharged that receive nitrification, and the DO 

concentration in the Chattahoochee River below Atlanta 

is described in the next section. This model provides 

estimates of the combinations of minimum flow at 

Atlanta and nitrification that will provide a given 

minimum DO concentration in the river.

A hydrologic simulation model that relates the flow of 

the Chattahoochee River at Atlanta and the pool elevation of Lake Sidney Lanier to the operation and dependable hydroelectric peaking capacity of Buford Dam is 

described next. This model also provides estimates of 

the maximum sustainable minimum flow at Atlanta and 

thus delimits the combinations of minimum flow and 

nitrification that are potentially capable of producing a 

given minimum DO concentration in the river.

The methods used to obtain estimates of the change in 

hydroelectric power and recreation benefits and of the 

waste-treatment costs are next described. Following 

this, the method of identifying the least-cost combination of additional waste treatment (nitrification) and 

flow augmentation is described. Finally, the sensitivity 

of the least-cost combination to the estimate of the cost 

of replacing peak generating capacity is explored, and 

an analysis of the consequences of certain institutional 

constraints on the cost of attaining a given DO concentration is provided.

This study does not represent an attempt to prescribe 

either specific operating rules for Buford Dam or a 

specific waste-treatment plan for the Atlanta region. 

This study only provides an examination of the relationship (or trade off) between the use of the Lake Sidney 

Lanier and Chattahoochee River waters for enhancement of its DO concentration on the one hand and 

hydroelectric-power generation on the other. That is, we 

asked to what extent can the waste-assimilation capacity of the river be substituted for an increased waste 

treatment with what concomitant decrease in treatment 

costs and at what cost, if any, in terms of hydroelectricpower and recreation benefits foregone? This question is 

explicitly posed, and one scheme for exploring it is 

presented herein.

THE DISSOLVED-OXYGEN MODEL

Stamer and others (1978) describe a dissolved-oxygen 

model (DOM) of the Chattahoochee River from the 

Atlanta gage at river mile (rm) 302.97 to the Franklin 

gage at rm 235.46. This model is used herein to estimate 

the minimum DO concentration in this reach as a function of (1) the minimum flow at the Atlanta gage (QA) 

and (2) the percentage of total wastes receiving nitrification (P) in addition to secondary treatment at the 

sewage-treatment plants along the reach.

Model runs were conducted using three different rates 

of waste-water discharge corresponding to the rates expected for the years 1980, 1990, and 2000. In table 1 is 

given the name, location (by river mile), and expected 

flow rate for each of the sewage-treatment plants along 

the reach. The estimates of the waste water flow rates 

were based on information published by the Atlanta 

Regional Commission (Atlanta Regional Commission,
ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

TABLE I.-The expected average daily flow in cubic feet per second, 

from waste-treatment plants discharging to the Chattahoochee River 

between Atlanta, Ga., and Whitesburg, Ga., 1980, 1990, and 2000

Expected average daily flow

1980 2000

Cobb-Chattahoochee

R. M. Clayton

South Cobb

Utoy Creek

Sweetwater Creek

Camp Creek

Annewakee Creek

Bear Creek

Total

300.56

300.24

294.78

291.60

288.57

283.78

281.46

281.45

274.48

24

131

38

42

15

250

29

150

51

46

3

22

6

7

314

31

161

48

44

3

27

6

42

8

370

1977). All waste waters are assumed to have a DO concentration of 6 mg/L when discharged from the treatment plants.

In the model, the Chattahoochee River at the Atlanta 

gage is assumed to have a BODU concentration of 4.0 

mg/L, an ammonia-nitrogen concentration of 0.02 

mg/L, and DO at its saturation concentration of 9.3 

mg/L. The tributary BODu concentrations range from 

3.0 mg/L to 7.0 mg/L; ammonia-nitrogen concentrations, from 0.01 mg/L to 0.12 mg/L; and DO concentrations are assumed to be at or near saturation. River 

water temperatures range from 20.8° C to 27.1° C. All 

these temperature, BODu, ammonia, and DO values are 

based on those observed in June 1977.

The model assumes steady flow conditions. Stamer 

and others (1978) verified that, even though the flows in 

this reach are often quite unsteady (see fig. 1), their 

model provides a satisfactory representation of the DO 

system in a given "parcel" of water as it moves 

downstream.

For 1990, as an example, 14 different runs of the DOM 

were conducted so as to provide a basis for the development of a general expression of the relationship between 

QA, P, and minimum DO concentration in the Chattahoochee River.

A typical run may be described as follows: The flow at 

the Atlanta gage (rm 302.97) is 1,800 ft3/s. The Atlanta 

Water Works (rm 300.62) withdraws 109 ft3/s, leaving a 

flow of 1,691 ft3/s to the confluence of the Chattahoochee River and Peachtree Creek (rm 300.52). Over 

the next 26.14 miles from this point, eight waste water 

treatment plants discharge effluent at the rates 

specified in table 1. The total flow from these plants is 

314 ft3/s. In addition, a total of 93 ft3/s of tributary flow 

(the 7-day 10-year low flow of each tributary) enters the 

mainstem over the 65 miles between Peachtree Creek 

and the Franklin gage. Thus, the flow along the entire 

reach varies from 1,800 ft3/s down to 1,691 ft3/s and 

back up to 2,098 ft3/s at the downstream end.

In the particular model run being considered here, 

seven of the eight treatment plants are assumed to 

employ only secondary treatment, whereas the R. M. 

Clayton plant (rm 300.24) employs nitrification in addition to secondary treatment. The flow from the R. M. 

Clayton plant is predicted to be 150 ft3/s in 1990, 

whereas the total flow from all eight plants is predicted 

to be 314 ft3/s. Thus, 48 percent of the wastes receive 

nitrification (P = 48). Given that QA is set at 1 800 ft3/s 

and that P = 48, the model results show a minimum DO 

concentration of 5.0 mg/L in the study reach.

Another run of the DOM was conducted, identical with 

the run just described, except that the flow at the Atlanta gage was 850 ft3/s (resulting in a flow at Peachtree 

Creek of 741 ft3/s and a flow at the Franklin gage of 

1,148 ft3/s). Given a QA of 850 ft3/s and a P set at 48, the 

model estimated a minimum DO concentration of 2.8 

mg/L.

According to Stamer and others (1978), the relationship between minimum DO and flow at Atlanta is very 

nearly linear (see fig. 3). Thus the results of the two 

model runs just described may be summarized by an 

equation of the form

o,QA + 6 = D,

where QA is the minimum flow at the Atlanta gage, in. 

cubic feet per second, andZ) is the minimum DO over the 

reach, in milligrams per liter. The equation may be considered valid only for QA values in or near the range of 

850 ft3/s to 1,800 ft3/s. Inserting the appropriate values 

for the slope (a) and the intercept (6) results, for the example described, in

0.0023QA + 0.89 = D.

RESULTS FROM THE DISSOLVED-OXYGEN MODEL

Pairs of runs (one for QA = 1,800 ft3/s; the other for QA 

= 850 ft3/s) similar to the two just described were conducted for a total of seven different cases. In each of 

these cases, the combination of treatment plants providing only secondary treatment and those providing

^ Bi-li———I——————I——————I——————I——————I————

co BE

3§ 2

800 1000 1200 1400 

QA, IN CUBIC FEET PER SECOND

1600 1800

FIGURE 3.-Minimum dissolved-oxygen concentration (D) as a 

function of minimum flow at the Atlanta, Ga., gage (QA), 

given that 48 percent of the waste flow receives nitrification, 

for 1990 conditions.
THE HYDROLOGIC SIMULATION MODEL

secondary treatment plus nitrification (that is, the value 

of F) was varied. The results of these 14 runs are 

presented in the two graphs in figure 4. In figure 4a, the 

slope parameter (a) is plotted against the percentage of 

the total waste flow receiving nitrification (P). In figure 

4b, the intercept parameter (6) is plotted against P. 

These figures suggest that both a and b are strongly 

related to P. The relationship between a and P was expressed by a linear regression (R2 = 0.99) and that between 6 andP, by apiecewise linear regression. (Each of 

the two regressions of 6 on P had an R2 = 0.99.) The implication of these good fits (high R2) is that P is a very 

good predictor of the relationship between QA and D as 

provided by the DOM and that the locations of those 

sewage-treatment plants chosen to provide nitrification 

is only minor importance. Thus, in the context of this 

study, the location of the plants providing nitrification 

may be ignored, and the treatment levels can be 

characterized by P-the percentage of the wastes receiving nitrification. The regression lines in figure 4 thus 

describe the relationship between QA,D, and P.

0.004

0.003

0.002

0.001

. '' 

Relationship between a and P

Relationship between b and P

0 20 40 60 80 100

PERCENTAGE OF TOTAL WASTE FLOW

RECEIVING NITRIFICATION (P)

FIGURE 4. - Relationship of parameters of aQA+ b=D to percentage of 

total waste flow receiving nitrification (P).

Figure 6 provides a useful graphical description of this 

relationship. It shows the combination of treatment (P) 

and minimum flow (QA) necessary to achieve a minimum 

DO concentration (D) of either 3, 4, or 5 mg/L. These 

curves are denoted "iso-DO" (iso-dissolved-oxygen) 

curves.

The same procedure as that just described was used to 

approximate the relationship between D, P, and QA for 

the years 1980 and 2000. The results are depicted in 

figures 5 and 7.

Note that P refers to the percentage of the total waste 

flow receiving nitrification and that this total increases 

with time. The consequences of the expected increase in 

waste water flow can be seen by comparing the required 

amount of nitrification in 1980, 1990, and 2000 given, 

for example, QA = 1,500 ft3/s and D = 4 mg/L. It is 

estimated that, given these conditions, the percentage 

of the total waste effluent that must receive nitrification 

would increase from 22 in 1980, to 36 in 1990, and to 48 

in 2000. Since the total waste flow is increasing (see 

table 1), this means that the flow receiving nitrification 

would have to be 55 ft3/s (0.22 x 250) in 1980, 113 ft3/s 

(0.36 x 314) in 1990, and 178 ft3/s (0.48 x 370) in 2000.

Given any minimum DO standard (D*), the combination of P and QA selected must lie on or above the iso-DO 

curve representing D* milligrams per liter. But, not all 

combinations of P and QA along these iso-DO curves are 

technically feasible. For example, from figure 6, setting 

QA equal to 1,800 ft3/s and P equal to 50 will provide a 

minimum DO concentration of 5 mg/L in 1990. As will be 

seen, it is not possible to sustain this minimum flow at 

Atlanta under all hydrologic conditions. In addition, it is 

necessary to associate a cost with each combination of P 

and QA so as to permit identification of the least-cost 

combination. This cost is related in part to the minimum 

flow at Atlanta, which in turn is related to the operation 

of Buford Dam. The hydrologic simulation model (HSM) 

used both to identify the feasible values of QAand to provide a basis for estimating the costs (benefits foregone) 

associated with these values is presented in the next section.

THE HYDROLOGIC SIMULATION MODEL

The hydrologic simulation model (HSM) was 

developed to determine, under a set of assumptions that 

shall be specified, the pattern of releases from Lake 

Sidney Lanier that are necessary to achieve a given 

dependable minimum flow at the Atlanta gage (QA>. The 

pattern of release has effects on the benefits associated 

with each of the project purposes, and the HSM is 

designed to provide a basis for estimating the change in 

the project benefits as a result of a change in the pattern 

of release.
ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

1800

10 20 30 40 50 60 70 80 

PERCENTAGE OF TOTAL WASTE FLOW RECEIVING NITRIFICATION (P)

90 100

FIGURE 5. - Iso-dissolved-oxygen curves showing combinations of the percentage of total waste flow receiving nitrification (P) and minimum discharge at Atlanta, Ga., (QA) that are predicted to result in minimum dissolved-oxygen concentrations (D) of 3,4, and 5 mg/L, for 1980 conditions.

900 -

10 20 30 40 50 60 70 80 

PERCENTAGE OF TOTAL WASTE FLOW RECEIVING NITRIFICATION (P)

100

FIGURE 6. -Iso-dissolved-oxygen curves showing combinations of the percentage of total waste flow receiving nitrification (P) and minimum discharge at Atlanta, Ga., (QA) that are predicted to result in minimum dissolved-oxygen concentrations (D) of 3, 4, and 5 mg/L, for 1990 conditions.
THE HYDROLOGIC SIMULATION MODEL

The key relationship that the HSM describes is that 

between the dependable minimum flow at Atlanta and 

the dependable hydroelectric peak generating (peaking) 

capacity of Buford Dam. The "amount" of each of these 

"products" that can be dependably provided by the 

Buford Dam project is a function of the inflows to Lake 

Sidney Lanier and tributary flows to the Chattahoochee 

River above Atlanta over an extended (at least twoyear) drought.

The meaning of the word "dependable" is of paramount importance to an understanding of the HSM. 

Dependable minimum flow is defined as that rate of 

flow that can be provided at all times throughout a 

period in which the flows (for example, both into Lake 

Sidney Lanier and tributary flow between Buford Dam 

and Atlanta) are those that occurred in the most severe 

extended drought in the historic record. Similarly, 

dependable peaking capacity is defined as that peaking 

capacity that can be provided at all times throughout a 

period in which the flows are those that occurred in the 

most severe extended drought in the historic record. 

The most severe extended drought occuring in the study 

area during the 49-year historic record was a 132 week 

period comprising June 1954 through December 1956. 

As there is no reason to believe that a more severe 

drought will not occur in the future, that which is 

defined as "dependable" herein may not be "dependable" 

in the future. Rather than attempt to estimate the probability of more severe droughts or to justify this definition of "dependable" on some economic grounds, it is accepted simply on the basis that previous studies of the 

Buford Dam project and of the Chattahoochee River 

(U.S. Army Corps of Engineers, 1977; Atlanta Regional 

Commission, 1977) have relied on the same convention.

OPERATION OF THE BUFORD DAM HYDROELECTRIC 

GENERATING FACILITY: ASSUMPTIONS AND DEFINITIONS

Though Buford Dam has an installed hydroelectric 

generating capacity of 105 MW, the rate of production 

of electrical energy varies with the pool elevation of the 

reservoir and with the rate of flow of the water past the 

turbines; that is, it varies with the pattern of releases 

from Lake Sidney Lanier. The calculation of 

hydroelectric-power production is based on the following formula (Joe DeWitt, U.S. Army Corps of 

Engineers, Savannah District, oral commun. 1978):

Pe= 82.645(0.12390 + 0.000925 (£-1,055)) Q, 

where

Pe = power, in kilowatts,

E =pool elevation, in feet above sea level, and

Q =flow through the powerplant, in cubic feet 

per second.

It is assumed that all water released from Lake Sidney 

Lanier is used for the production of electric energy.

The HSM is designed to first pattern the release of 

water from Lake Sidney Lanier so as to maximize the 

dependable summer-peak generating capacity of Buford

10 20 30 40 50 60 70 80 

PERCENTAGE OF TOTAL WASTE FLOW RECEIVING NITRIFICATION (P)

90

FIGURE 7. -Iso-dissolved-oxygen curves showing combinations of the percentage of total waste flow receiving nitrification (P) and minimum discharge at Atlanta, Ga., (QA) that are predicted to result in minimum dissolved-oxygen concentrations (D) of 3, 4, and 5 mg/L, for 2000 conditions.
10 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

Dam. Given that this has been accomplished, the model 

allocates the release of water within any given week so 

as to maximize the peak energy production. Both of 

these maximizations are conducted subject to the constraints that the given downstream water-supply needs 

and minimum flow at Atlanta (QA) are satisfied. 

Definitions used for the HSM are as follows:

Peak energy. All electric energy generated between 2 p.m. and 8 p.m.

on weekdays.

Nonpeak base energy. All electric energy other than peak energy. 

Dependable peak generating (peaking) capacity. The minimum rate

of electric-energy production during the peak hours of the summer

periods of the 132 week simulation period. 

Summer. Early June (week 22) through late September (week 33).

To understand the design and assumptions of the 

HSM, it is helpful first to understand the intertemporal 

distribution of the demand for electric energy. The 

quantity of electric energy demanded generally reaches 

a peak during the afternoon and early evening on 

weekdays and falls to a low during the early morning 

hours and on weekends. Though the "height" of these 

peaks varies throughout the year, the peak demand for 

electric energy is typically the greatest during the summer months. The electric-utility companies attempt to 

maintain sufficient generating capacity to meet the 

maximum peak demand, which will occur typically during the afternoon or evening of a summer weekday.

Hydroelectric turbines are especially useful for peak- ' 

ing purposes as they require very little startup time and 

can be brought online quickly. Because of this capability, j 

the limited water available is not generally used to pro- \ 

duce base power, except when water must be released to j 

meet downstream needs or to vacate the flood pool. j

The release of water from Lake Sidney Lanier is j 

therefore assumed to be patterned so as to maximize the j 

dependable summer peaking capacity of Buford Dam, 

for it is during the summer that the electric-utility company (the Georgia Power Co.) that purchases power 

from the dam is most likely to require maximum 

generating capacity. If no releases are necessary (for example, when tributary flows are high and the pool elevation of Lake Sidney Lanier is below 1,070 feet above sea 

level), it is assumed that no base electric energy is produced. Consequently, it is assumed that Buford Dam 

provides no dependable base generating capacity.

DESCRIPTION OF THE HYDROLOGIC SIMULATION MODEL

The HSM is designed to answer the following questions:

1. What is the range of minimum flows at the Atlanta 

gage (QA) that could have been achieved under the j 

1954-56 drought hydrology? j

2. Given a minimum flow at Atlanta (QA), what plan of 

operation of Buford Dam will maximize the dependable peaking capacity of the dam?

3. What is the dependable peaking capacity of Buford 

Dam, given this plan and QA?

4. What is the peak and nonpeak electric-energy production, given this plan and QA?

5. What is the history of pool elevations of Lake Sidney

Lanier, given this plan and QA? 

The HSM is designed to find a plan of releases from 

Buford Dam and Morgan Falls for the 132-week period 

that maximizes the dependable peaking capacity of 

Buford Dam subject to the following flow and storage 

constraints:

dSi/dt=Ti-Vfi-Qi, (1)

Qi< 10,000, (2)

Si(to)= 8.35 xlO10, (3)

Si(£/) = 4.69xl010 , (4)

S!<8.35xl010, (5)

Ql + T2 >W2 , (6) 

ds2ldt= Qi + T9~- W2 -Q2 , (7)

S2(*0)=0, (8)

S2(*/)>0, (9)

S2 < 1.09 xlO8 , and (10)

Qa + r8 -W8 *QA. (11)

The decision variables are all time varying, defined for 

values > 0 and are as follows:

51 = storage in Lake Sidney Lanier, in cubic feet;

52 = storage in Morgan Falls Reservoir, in cubic

feet; 

Q! = release from Buford Dam (Lake Sidney

Lanier), in cubic feet per second; and 

Q2 = release and spill from Morgan Falls Dam, in

cubic feet per second.

The initial storage conditions, beginning of week 22, 

1954, are

Si(t0) = initial storage in Lake Sidney Lanier, in

cubic feet, and 

S2(to) = initial storage in Morgan Falls Reservoir, in

cubic feet.

The final storage conditions, end of week 49, 1956, are 

S^tf) = final storage in Lake Sidney Lanier, in cubic

feet, and 

S2(tf) = final storage in Morgan Falls Reservoir, in

cubic feet. 

The time-varying model parameters are

TI = inflows to Lake Sidney Lanier, in cubic feet 

per second (constant over a week; values 

are those used in U.S. Army Corps of 

Engineers, 1977);

T2 = tributary inflows between Buford Dam and 

Morgan Falls Dam, in cubic feet per second, (constant over the week; values equal 

one half of the tributary flow values 

reported in U.S. Army Corps of 

Engineers, 1977);
THE HYDROLOGIC SIMULATION MODEL 11

Ts = tributary inflows Morgan Falls.to the Atlantic Gage, in cubic feet per second (constant 

over the week, values equal one half of the 

tributary flow values reported in U.S. Army Corps of Engineers, 1977);.

Wi = withdrawals from Lake Sidney Lanier, in 

cubic feet per second (constant over week; 

varies with time of year and year of 

analysis; see table 2);

W2 = withdrawals from the Chattahoochee River, 

Buford Dam to Morgan Falls Dam, in cubic 

feet per second (constant over week; varies 

with time of year and year of analysis; see j 

table 3), and

Ws = withdrawals from the Chattahoochee River, 

Morgan Falls Dam to the Atlanta gage, in 

cubic feet per second (constant over week, 

varies with time of and year of analysis; 

see table 4).

The time constant model parameter is

QA = Minimum flow at the Atlanta gage, in cubic

feet per second. 

The model constraints are as follows:

1. the continuity equation for Lake Sidney Lanier;

2. limitation on release from Buford Dam, 10,000 

ft3/s, the channel capacity below the dam;

3. initial storage conditions for Lake Sidney Lanier, 

equal to initial storage for the same period in the 

U.S. Army Corps of Engineers base plan of 

operations;

4. final storage conditions for Lake Sidney Lanier, 

equal to final storage for the same period in the 

U.S. Army Corps of Engineers base plan of 

operation.

5. capacity constraint for Lake Sidney Lanier, 

8.35xl010 ft3 , corresponds to pool elevation of 

1,070 ft. above sea level (normal pool elevation);

6. flows in the Buford Dam to Morgan Falls Dam 

reach, must be greater than or equal to the 

withdrawals in the reach at all times;

7. the continuity equation for Morgan Falls Dam; 

8, 9. initial and final storage in Morgan Falls Res-1 

ervoir (arbitrary);

10. capacity constraint on Morgan Falls Reservoir 

storage, and

11. flows at Atlanta gage, must be greater than or 

equal to the specified minimum flow QA, at all 

times.

RESULTS FROM THE HYDROLOGIC SIMULATION MODEL

The results of any run of the HSM, where a run is 

specified by a choice of years (1980,1990, or 2000) and a 

choice of QA values, are the values of the following 

variables:

1. end-of-week pool elevation for each week;

2. release rate and power production for the 30 peak 

hours in each week;

3. release rate and power production for the 72 nonpeak 

weekday hours in each week; and

4. release rate and power production for the 66

weekend (nonpeak) hours in each week. 

These results are summarized as total nonpeak energy, 

total peak energy, and dependable peaking capacity.

To illustrate the results of the HSM, two examples are 

described. Both are based on water-supply withdrawals 

estimated for the year 1990 (tables 2, 3, and 4). In the 

first case, the required minimum flow at Atlanta (QA) is 

set at 1,290 ft3/s. Values for two different weeks of 

operation are considered in detail in this comparison: 

those of week 33 (mid-August), 1954, and week 40 (early 

October), 1954. In both weeks, the tributary flows (Tz 

and Ts) were equal to zero. The releases and 

hydroelectric-power production under each run are 

given in table 5. The release patterns for these weeks 

are shown in figure 8.

Comparison of the two cases brings out two important 

points about the consequences of increasing the required 

minimum flow at Atlanta. The first is that the releases 

from Buford Dam are redistributed with respect to the

TABLE 2. - Withdrawals, in cubic feet per second, 

from Lake Sidney Lanier, Ga.

1-13

14-17

18-22

23-26

27-35

36-39

40-44

45-52

Average

1980

12.6

13.3

14.0

14 7

15.5

14.0

13.3

12.6

13.6

Year

1990

23.6

24.9

26.2

27.5

29.0

26.2

24.9

23.6

25.5

2000

77.3

81.9

86.0

90 9

95.3

86.0

81.9

77.3

83.7

TABLE 3. -Withdrawals, in cubic feet per second, from Chattahoochee 

River, Ga., Buford Dam to Morgan Falls Dam

Weeks

Year

1980 1990 2000

1-13

14-17

18-22

23-26

27-35

36-39

40-44

45-52

Average

114.9

121.6

127.7

134.0

141.5

127.7

121.6

114.9

124.3

160.4

169.8

178.3

187.1

197.6

178.3

169.8

160.4

173.6

375.7

397.7

417.6

439.3

462.7

417.6

397.7

375.7

406.6
12 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

TABLE 4. -Withdrawals, in cubic feet per second, from Chattahoochee 

River, Ga., Morgan Falls Dam to the Atlanta gage

Yeardrawdown during the summer-recreation season than 

will a high QA. From the standpoint of recreation, a plan 

of operation with QA= 1,600 ft3/s has a more desirable 

result than does a plan with QA= 1,290 ft3/s.

After running the HSM for a range of different QA 110 qq q A A A 107 8

14-17 IIIIIIIIIIIIIIIIIII 35^2 46^9 H4!i values for any given year, two values of QA emerge as 

18-22 —————————— 37.0 49.3 119.9 having special significance. The first of these is the max27-1::::::::::::::::::: 4?:o ll'l ill imum sustainable QA value (i,eoo ft3/s for 1990). it is, of

36-39 —————————— 37.0 49.3 119.9 course, the maximum sustainable QA only under the

40-44 ______________ 35.2 46.9 114.1 .-. . ,, , TTCni/r T _..• i -j. • 45_52 __________ 33.3 44.4 107.8 specific assumption of the HSM. In particular, it is re- 

————————~rr———7777— quired that all water-supply requirements be met and

Average __________ 36.0 48.0 116.7 /. 1,1 -, m-* i-/» j _. __ j i -t.

________________________________ that, under the 1954-56 drought hydrology, the

! minimum storage in Lake Sidney Lanier is not allowed

TABLE 5.-Hydrologic-simulation-model results of water discharge j to fay bejow IQ7 m[\\[OIl acre-feet (pool elevation 

and electric-power production at Buford Dam, Ga., for 1990 I ., „.„ _ „.,. ,.,._„ , /• ,1 , - i

conditions \ l»043-9 ft), which is 56 percent of the storage at normal 

________________________________ I pool elevation (1,070 ft).

————————————-————————————————— 

Minimum flow at the Atlanta gage (QA)______________ 1,290 ft3/s 1,600 ft3/s . ml ,, , ,, ~ ,, , . ,, . , , . ,, , ,

j The other value of QA that is of interest is that value

_____________ee ' 5_____________ below which no additional dependable peaking capacity

Discharge, in cubic feet per second: can be gained by further decreasing QA. For example,

Average ———————————————— 2,290 1,780 this value is 1,290 ft3/s for 1990. Given this minimum

UrpJak hours _____________ 10,000 6,480 i fl°w requirement, it is possible to fully utilize the

Nonpeak hours ———————————— ' 198 'i98 generating turbines with a release of 10,000 ft3/s during

Electric-enlrgy p^odilclior^rrn megawatf-hoursr' ' ' all summer peaking hours. The dependable peaking

Total —————————————————— 4,270 3,500 capacity in this case is equal to the generating capacity

Peak ____ _____ q qqn o 320 Nonpe^7"weekdays~III~~~~I~II~~ 'i60 'i60 f°r a fl°w °f 10,000 ft3/s and a pool elevation of 1,043.9

Nonpeak', weekends——————————— 780 1,020 ft (the minimum pool elevation for the three summers of —————————————————————————————— the simulation period). These two values of QA and the

____________Week 40.1954____________ associated values for dependable peaking capacity are

TV , . , . f . , given for each of the three years in table 6. Discharge, in cubic teet per second: ° J 

Average _____________________ 1,510 1,820

During: c „„„ ,. 0 ,« The HSM, then, was used to delimit the feasible range Peak hours _________________ 5,760 6,810 . ~ . '., ,!.. , ,, . , . U1 ~ y, Nonpeak hours ___________ 170 170 of QA as it identified the maximum sustainable QA. It 

Weekends __—_———————— 1,030 1,340 aiso provided estimates of dependable peak generating

Electric-energy production, in megawatt-hours: ., , , , , , , ,. Total __________1_________ 2,720 3,360 capacity, weekly peak and nonpeak power production,

Peak _—— ————————————— 1J860 2^250 and the weekly pool elevation of Lake Sidney Lanier

Nonpeak, weekdays ______________ 130 130 , . , , •> .. . /. ,1 •> • •, /?•< Nonpeak, weekends ___________ 730 980 upon which to base estimates ot the change in benefits

———————————————————————————————— given a change in Q^i.

time of the week: weekend flows increase and peak 

flows either decrease (if summer) or increase (if nonsummer). The second point is that releases are redistributed 

with respect to time of year: weekly average flows during the summer season decrease, and flows during the 

remainder of the year increase.

In figure 9 is depicted the 132-week record of 

simulated pool elevations for these two cases. Given that 

QA is set equal to 1,600 ft3/s, the pool elevation varies 

less throughout each year and tends to be higher during 

the summer months. When QA is low, less water need be 

saved for flow maintenance in the autumn, and thus 

more may be used for summer-peak power production. 

Consequently, a low QA will result in more reservoir

TAHLK G.-Hydrologic-simulation-model results, 

for 1980, 1990, and 2000

Year 1980 1990 2000

Maximum sustainable value of QAJ ____

Dependable peaking capacity at maximum sustainable QA 2 _____________

Value of Q A associated with maximum 

dependable peaking capacity1 ______

1670

66

1380

Maximum value of dependable peaking 

capacity2 _______________________

1600

66

1290

98

1230

58

870

97

1 In culm- feet per- second. 

- In megawatts.
ESTIMATION OF COST: BENEFITS FOREGONE AND WASTE-TREATMENT COSTS 13

ESTIMATION OF COSTS: BENEFITS FOREGONE 

AND WASTE-TREATMENT COSTS

In this section, the method used to obtain estimates of 

the recreation and hydroelectric benefits associated 

with a given QA under (here, 1954-56) drought conditions is described first. Then, it is argued that these 

drought condition benefits are not representative of the 

benefits associated with any given QA under more nearly i 

average hydrologic conditions, and the method used to 

approximate average annual benefits is described. 

These estimates of the benefits associated with a given 

QA permit estimation of the costs, in terms of benefits 

foregone, associated with a change in QA and, thus, with 

a change in the operation of Buford Dam.

Also described is the method used to obtain estimates

of the cost of adding a nitrification process to secondary 

waste-treatment facilities and, thus, of increasing the 

percentage of the total waste flow receiving nitrification 

(P\

It was necessary to select an interest, or discount, rate 

with which to amortize both the benefits of the 

hydroelectric peak generating capacity of Buford Dam 

and the capital cost of adding a nitrification process to 

the waste-treatment facilities. If the peak generating 

capacity of Buford Dam is diminished by operating rules 

requiring releases from Lake Sidney Lanier for waterquality maintenance purposes, this lost capacity will 

have to be replaced (it is assumed) by an electric utility 

company in the private sector of the economy. The 

Georgia Power Co. is currently constructing a 

hydroelectric pump-storage peaking facility (its "Rocky

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FIGURE 8. - Simulated releases at Buford Dam, Ga., during weeks 33 and 40 of 1954, given a minimum flow at Atlanta (QA) of 1,290 ft3/s and

1,600 ft3/s, for 1990 conditions.
14 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

Mountain Project") and is amortizing the capital cost of 

this facility using a discount rate of 11.24 percent (C.R. 

Thrasher, Georgia Power Co., written commun., June 5, 

1978). Though the choice of a discount rate is somewhat 

subjective and requires a value judgment, a rate of 10 

percent was chosen as being indicative of the opportunity cost of capital in the private sector of the economy.

All estimates of benefits and costs are presented in 

terms of first-quarter 1976 dollars.

ESTIMATES OF BENEFITS GIVEN 1954-56 

DROUGHT CONDITIONS

RECREATION

Estimates of the benefits from recreation at Lake 

Sidney Lanier are based on data obtained from a U.S. 

Army Corps of Engineer publication (1977). According 

to the Corps of Engineers, the recreation benefits obtained from Lake Sidney Lanier vary with both the pool 

elevation of the reservoir and the season of the year. 

They have published (1977) estimates of both the peakand the offpeak-season recreation associated with pool 

elevations ranging from 1,055 to 1,080 feet above sea 

level. For example, the Corps of Engineers estimated 

that a pool elevation of 1,070 feet has associated peakseason benefits of $17,820,900 and offpeak season 

benefits of $13,011,100. For purposes of this study, it 

was assumed that the peak-season benefits were 

distributed uniformly over the 22 weeks from May 1

through September 30 and that the offpeak-season 

benefits were uniformly distributed over the 30 weeks 

from October 1 through April 30. Thus, a pool elevation 

of 1,070 feet would have associated with it recreation 

benefits of $810,041 per week during the peak season 

and $433,703 per week during the offpeak season. The 

weekly recreation benefits associated with each pool 

elevation are graphed in figure 10.

The HSM provided the weekly pool elevation of Lake 

Sidney Lanier given that Buford Dam was to be 

operated so as to achieve a specified minimum flow at 

Atlanta. The weekly recreation benefits associated with 

each of the weekly pool elevations were summed over 

the 132 weeks of the simulation period and averaged to 

obtain an estimate of the average annual recreation 

benefits from Lake Sidney Lanier (under 1954-56 

drought conditions) given a specified minimum flow at 

Atlanta.

HYDROELECTRIC POWER AND PEAK 

GENERATING CAPACITY

To place a dollar value on the generating capacity of, 

and electric energy produced at, Buford Dam, it is 

necessary to ask: what is the least-cost method of producing an equivalent amount of electric energy by an 

alternative technique and what is the cost? A detailed investigation of alternative techniques and their 

associated costs is beyond the scope of this study, but it 

is necessary to briefly discuss some of the details 

involved in such an investigation.

1075

1070

LU 

LU

LU

iu 1065 

O

CO

LU 

LU

•z.

O

LU 

LU

_

O 

O 

a.

1060

0^=1600 cubic feet per second

Z 1055

1050

1045

1040

QA= 1290 cubic feet per second^ \\

1954 1955 1956

YEAR

FIGURE 9.-Pool elevation of Lake Sidney Lanier over the period of simulation, given that the minimum flow at Atlanta, Ga., (QA) is

set at 1,290 ft3 /s and 1,600 ft3 /s, for 1990 conditions.
ESTIMATION OF COSTS: BENEFITS FOREGONE AND WASTE-TREATMENT COSTS 15

For purposes of analysis, it is useful to separate the 

cost of producing electric energy into two components: 

the capacity cost and the energy cost of production. The 

energy cost consists of the fuel (for example, coal) cost 

of producing a unit (for example, a kilowatt-hour) of 

electric energy. The capacity cost stems primarily from 

the capital investment in the generating facility. If an 

electric-utility company is to invest in a generating 

facility, it must receive a rate of return on its investment 

at least equivalent to that which could have been earned 

if the money had been invested elsewhere; this is the socalled opportunity cost of capital and is determined by 

the interest or discount rate. The initial capital cost and 

useful life of a generating facility, along with the discount rate, are the main determinates of the capacity 

cost of producing electric energy at that facility.

As it is currently operated, Buford Dam is used 

primarily for the generation of electric energy during 

periods of peak demand. Though it has been assumed 

herein that the dam provides no dependable base 

generating capacity, it does produce some energy during nonpeak hours because water is sometimes released

DO

Z

o

900,

800

700'1

600

500

400

300

>] 200 

^

100

Off-peak season 

(Weeks 1-17 and 40-52)

0 1055 1060 1065 1070 1075 1080 

POOL ELEVATION OF LAKE SIDNEY LANIER, IN FEET

FIGURE 10.-Benefits from recreation on Lake Sidney Lanier, given 

various pool elevations.

during these hours to satisfy downstream flow requirements. Any nonpeak energy produced at Buford 

Dam has an energy value equivalent to the cost of producing it by some least-cost alternative method. Similarly, the electric energy produced during peak periods has 

an energy value equivalent to the energy cost of producing it by some least-cost alternative.

To assign a capacity value to the generating capacity 

of Buford Dam and an energy value to the electric 

energy produced there, it is necessary to make an 

assumption as to the least-cost alternative source of 

capacity and energy. It was assumed that any peaking 

capacity lost at Buford Dam because of a change in its 

operating rules could be replaced by a facility similar in 

cost to the Georgia Power Co.'s 675-MW "Rocky Mountain" facility, which is scheduled to come online in 1983. 

Using data obtained from the Georgia Power Co. (C.R. 

Trasher, Georgia Power Co., written commun., June 5, 

1978) and assuming a 10-percent discount rate, it is 

estimated that the capacity cost of electric energy produced by this pump-storage facility will be $23.34/kW/yr 

(in first-quarter 1976 dollars). The dependable peaking 

capacity of Buford Dam was assigned this value.

Electric energy produced at Buford Dam was assigned 

different values depending upon whether it was produced in a period of peak demand or in a period of base 

demand. According to estimates provided by the Atlanta Regional Office of the Federal Power Commisison to 

the U.S. Army Corps of Engineers (1977), the energy 

cost of electricity produced by coal-fired thermal electric 

powerplants in the Atlanta area was 7.75 mills/kWh during the first quarter of 1976. Because any electricity produced at Buford Dam during periods of base demand 

could be substituted for electricity produced by coalfired thermal electric plants, the base electricity produced at the dam was assigned an energy value of 7.75 

mills/kWh. However, if peak electricity produced at 

Buford Dam is to be replaced by electricity generated at 

a facility similar in cost to the Georgia Power Co.'s 

"Rocky Mountain" facility, such electricity must be 

assigned a higher energy value. The Georgia Power Co. 

estimates that 1.4 kWh of electricity must be expended 

in pumping for storage (in offpeak periods) to generate 

1.0 kWh of electricity in peak periods (Georgia Power 

Co., 1972). Given that base-period electricity has an 

energy cost of 7.75 mills/kWh, then peak-period electricity furnished by the "Rocky Mountain" pump-storage 

facility will have an energy cost of 10.85 mill/kWh 

( =7.75 mills/kWh x 1.4). Accordingly, peak-period 

electricity produced at Buford Dam was assigned an 

energy value of 10.85 mills/kWh.

It should be noted that the U.S. Army Corps of 

Engineers has assumed that the alternative to producing peak energy at Buford Dam is to produce it by a coal-
16 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

TABLE 7. -Hydrologic simulation-model results and estimated benefits 

for 1990, given certain minimum flows at Atlanta, Ga., under 1954- 

• 56 drought conditions.

Minimum Hows, in cubic feet per second

Creek

________________________________

nl Oiattahoochee River and 1 'each tree

1,290

1,180

l.tiOO 

1,490

Annual _______

Annual nonpeak 

Annual peak ___

Average energy output, in 

megawatt-hours per year

132,500 134,400

34,500 45,800

98,000 88,600

Dependable peaking capacity, 

in megawatts

(See minimum flows given for Atlanta) _ 98.1 65.9

Nonpeak energy ___________

PeaK energy ______________

Dependable peaking capacity 

Recreation _______________

Total

Benefits, in millions of dollars 

per year

.27 .35

1.06 .96

2.29 1.54

24.38_____25.00

28.00 27.85

fired thermal electric powerplant. Using estimates provided by the Atlanta Regional Office of the Federal 

Power Commission, the Corps of Engineers valued the 

dependable generating capacity of Buford Dam at 

$49.35/kW/yr. They assigned an energy value of 7.75 

mills/kWh to electric energy produced at the Dam (U.S. 

Army Corps of Engineers, 1977). The sensitivity of the 

results of this study to the value assigned to dependable 

peak generating capacity is examined in a following section.

Given results of any run of the HSM, it is possible to 

compute the estimated annual energy benefits and 

dependable-peaking-capacity benefits (under the 

assumed drought conditions) associated with a particular QA. Energy benefits were calculated as the sum 

of average annual peak energy production multiplied by 

its value (10.85 mills/kWh) plus average annual nonpeak 

energy production multiplied by its value (7.75 

mills/kWh). Dependable peaking-capacity benefits are 

equal to the dependable peaking capacity times its value 

($23.34/kW/yr).

In table 7 is summarized the results of the HSM runs 

and the benefit calculations for the two cases (QA=1,290 

ft3/s and QA = 1,600 ft3/s) described in the previous section. Given 1990 water-supply requirements and the 

drought conditions, the effects on annual benefits as a 

result of changing QA to 1,600 ft3/s from 1,290 ft3/s are 

nonpeak-energy benefits increase by 30 percent, peakenergy benefits decrease by 9 percent, dependablepeaking-capacity benefits decrease by 33 percent, and 

recreation benefits increase by 3 percent. Total benefits

are decreased by one-half of one percent. In terms of 

benefits foregone, the cost of increasing QA to 1,600 ft3/s 

from 1,290 ft3/s in 1990 is estimated to be $150,000/per 

year.

ESTIMATION OF AVERAGE ANNUAL BENEFITS

The method of estimating the benefits derived from 

Buford Dam under different operating rules given 

1954-56 drought conditions is described in the 

preceding section. It is necessary to specify drought conditions to obtain an estimate of the maximum sustainable QA and of the dependable peaking capacity 

associated with each QA. It is not appropriate, however, 

to base an estimate of average annual benefits on worstcase (drought) conditions.

The estimates of the average annual benefits to be obtained under different minimum flows at Atlanta would 

be more appropriately based on a simulation of dam 

operations over the entire available hydrologic record, 

including the worst-case drought. Such a simulation, 

however, would be an extended task. Also, only the 

change in average annual benefits (that is, benefits 

foregone) as a result of a change in QA is of interest here. 

Thus, the estimates of the benefits foregone associated 

with a change in QA are based on the simplifying 

assumption that the change in average annual benefits 

due to a change in QA is solely the result of the 

associated change in the dependable peaking capacity of 

Buford Dam.

From table 7, note that the sum of peak-energy, 

nonpeak-energy, and recreation benefits increases with 

QA. Conversely, dependable-peaking-capacity benefits 

decrease with an increase in QA. This offsetting relationship does not hold for years of more nearly average or 

above average flows.

In any year, base- and peak-energy benefits and 

recreation benefits are a function both of the flows in 

that year and of QA. But, dependable-peaking-capacity 

benefits are a function only of QA since they are determined only on the basis of the limiting (1954-56) 

hydrologic conditions. When water is more plentiful, 

setting QA at a high value (1,600 ft3/s) rather than a low 

value (1,290 ft3/s) does not have much effect on reservoir 

operations or on benefits. With plentiful water, it 

becomes possible to simultaneously satisfy the objectives of maximizing peak-energy production, holding 

lake levels stable (near 1,070 ft) for recreation, and providing high minimum flows at Atlanta.

As an example, consider the period from June 1959 

through May 1960. During this period the average flow 

to Lake Sidney Lanier was 2,229 ft3/s, whereas during 

June 1954 through May 1955, the average flow was 

1,311 ft3/s. After adjusting for storage, the reported 

(35-year) average flow at the U.S. Geological Survey
ESTIMATION OF COSTS: BENEFITS FOREGONE AND WASTE-TREATMENT COSTS 17

gage below Buford Dam is 2,168 ft3/s. Clearly, the 

period from June 1959 through May 1960 had more 

nearly average flows than did the years 1954-56.

The HSM was run using this 1959-60 record and the 

following constraints:

1. All water-supply requirements (1990 levels) are satisfied.

2. The release through the turbines during all peakpower periods (52 weeks, 30 hours per week) is 

10,000 ft3/s; and

3. Reservoir storage is not to exceed 1.917 million acreft (at 1,070 ft pool-elevation.)

The simulation was conducted for QA values of 1,290 

ft3/sandl,600ft3/s.

The annual recreation benefits associated with the 

two minimum flows differ by less than $1,000. The 

results of the simulation associate a minimum pool 

elevation of 1,065.6 ft with a QA of 1,290 ft3/s and a 

minimum elevation of 1,064.6 with a QA of 1,600 ft3/s. As 

can be seen by referring to figure 10, recreation benefits 

are nearly the same for all elevations between 1,064 and 

1,071 ft.

Peak-energy production is nearly the same given a QA 

of either 1,290 ft3/s or 1,600 ft3/s. In both cases, there is 

a 10,000 ft3/s flow through the power plant for 30 hrs 

per week during the full year at heads that differ by no 

more than 1 foot. As a result, the peak-energy benefits 

associated with the two different values of QA differ by 

less than $2,000.

Base-energy production is also virtually the same for 

both values of QA. Whether QA is set at 1,290 ft3/s or at 

1,600 ft3/s, the same total amount of water must be 

released during base-power periods over the course of 

the year to keep the reservoir level from rising above 

1,070 ft. The heads being nearly the same, the difference 

in base-energy benefits is very small.

Given the 1959-1960 flows, the only benefits 

significantly affected by the choice of QA are the dependable-peaking-capacity benefits. Given the 1959-60 

hydrologic conditions, an increase in QA to 1,600 ft3/s 

from 1,290 ft3/s decreases the dependable-peakingcapacity benefits by $0.75 million per yr (a 32,300 kW 

loss in capacity multiplied by the estimated capacity 

value of $23.34/kW/yr), as happens under 1954-56 

drought conditions.

The sum of the changes in all three other types of 

benefits is a function of both QA and the hydrology of 

that particular year. As a result of an increase in QA to 

1,600 ft3/s from 1,290 ft3/s the increase in the peak- and 

nonpeak-energy benefits and the recreation benefits 

ranges from a total of $0.56 million per year under the 

most adverse hydrologic conditions to zero for average 

or above-average years.

Thus, the assumption that all benefits other than the

dependable-peaking-capacity benefits are invariant with 

QA results in a slightly high estimate of the benefits 

foregone given an increase in QA; but, for simplicity, this 

assumption was adopted, and the relationship between 

QA and average annual benefits foregone, as graphed in 

figure 11, was computed on this basis.

ESTIMATION OF ADDED WASTE-TREATMENT COSTS

The location and flows of the waste-treatment plants 

discharging wastes into the Chattahoochee River between Atlanta and Whitesburg were specified in table 1. 

These configurations, for each of the three years, are 

based on data obtained from the Atlanta Regional Commission (1977).

In this study, the location and flows of the treatment 

plants are not considered to be decision variables; they 

are taken as given. Rather, the percentage of the total 

waste flow receiving nitrification (P) is considered to be 

the decision variable.

Data on waste-treatment costs (Giffels/Black and 

Veatch, 1977) were used to develop estimates of the 

capital, operation, and maintenance costs of adding a 

nitrification process to secondary waste-treatment 

plants. The capital costs were annualized using a 

10-percent discount rate and then added to the annual 

operation and maintenance costs to obtain the estimated 

annual cost of adding the nitrification process to each 

treatment plant. These costs are presented in table 8. 

The costs of nitrification were estimated under the 

assumption that the required equipment would be 

operated year-round, though nitrification may not be 

required to maintain a given DO standard under some 

water-temperature conditions. Thus, the cost estimates 

presented in table 8 may be biased upwards.

The data presented in table 8 were then used to 

develop estimates of the minimum annual cost of submitting any given percentage of the total waste flow to 

nitrification. This was accomplished by identifying the 

plant or combination of plants that could provide 

nitrificaton for a given percentage of the total waste 

flow at a minimum cost. The total annual nitrification 

cost of this plant or combination of plants was then plotted against the percentage of the wastes receiving 

nitrification in 1980, 1990, and 2000 to obtain the cost 

curves depicted in figure 12. These cost curves are, of 

course, predicated on the particular treatment plants 

listed in tables 1 and 8.

At this point, it seems desirable to summarize what 

has been so far accomplished herein. A dissolved-oxygen 

model was used to derive iso-DO curves, which delineate 

the combinations of P and QA potentially capable of producing a given level of DO. A hydrologic simulation 

model was used to delimit the feasible values of QA and 

to provide a basis for estimating the costs (benefits
18 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

foregone) associated with any given QA. Estimates of 

the benefits foregone as a result of an increase in QA and 

of the costs of increasing P have been developed. Given 

this information, it is now possible to identify the leastcost combination of P and QA capable of producing a 

given level of DO.

THE REREGULATION PROJECT

The U.S. Army Corps of Engineers has considered a 

project involving the construction of a reregulation 

structure on the Chattahoochee River just below Buford 

Dam and the dredging of the reservoir behind Morgan 

Falls Dam. This project would permit a more steady 

(and higher minimum) flow at Atlanta for any given 

level of peak generating capacity at Buford Dam. Conversely, an increase in QA would result in less 

dependable-peaking-capacity benefits foregone if the 

reregulation structure were built.

A version of the HSM in which it is assumed that this 

project is completed is described in appendix A. The 

estimated costs of the project were obtained from a U.S.

Army Corps of Engineers publication (1977). As is illustrated in the appendix (fig. 16), these costs exceed the 

project benefits, whether peak generating capacity is 

assigned a value of $23.34/kW/yr or of $49.35/kW/yr, 

Thus, the reregulation project would not be included in a 

least-cost scheme for providing a given level of DO, and 

it received no further consideration here.

LEAST-COST METHOD OF PRODUCING A GIVEN

MINIMUM DISSOLVED-OXYGEN

CONCENTRATION

The problem at hand can be usefully considered as one 

of finding the least-cost method of producing some given 

minimum DO concentration using two variable inputs: 

(1) some minimum flow rate at Atlanta (QA) and (2) some 

percentage of the total waste load receiving nitrification 

(P) in addition to secondary treatment. The curves 

labeled Z) = 3, D = 4, and D = 5 in figure 6, for example, 

give the various combinations of P and QA that are 

potentially capable of producing the indicated minimum 

DO concentration in 1990. If it is desired to "produce" a

TABLE 8.-The average daily flow from waste-treatment plants discharging to the Chattahoochee River between Atlanta, Ga., and Whitesburg, 

Ga., and the annualized cost of adding a nitrification process to the plants (in First-quarter 1976 dollars)

1980

Plant name

Cobb-Chattahoochee

R. M. Clayton

South Cobb

River 

mile

300.56

300.24

294.78

291.60

288.57

283.78

281.46

281.45

274.48

Average 

flow 

(ft3/s)

24

131

38 

42

15

Annual 

cost 

($1,000)

458.40

1704.19 

694.43 

722.43

359.82

1990

Average 

flow 

(ft3/s)

29 

150 

51 

46 

3 

22 

6

7

Annual 

cost 

($1,000)

518.27 

1932.45 

851.60 

771.07 

147.69 

444.02 

193.84

207.34

2000

Average 

flow 

(ft3/s)

31

161

48 

44 

3 

27 

6 

- 42 

8

Annual 

cost 

($1,000)

538.85 

2069.03 

819.79 

746.75 

143.95 

507.63 

193.84 

726.14 

216.69

LU O

2.0

DC

" i £

< 2 °-

D - W

1^1 ^§i

rn UJ Q

1.0

0.5

UL O

0

800

2000

1990 1980

1000 1200 1400 1600 1800

QA, IN CUBIC FEET PER SECOND

FIGURE 11.-The relationship between average annual benefits foregone and minimum flow at Atlanta (QA) for 1980,

1990, and 2000.
LEAST-COST METHOD OF PRODUCING A GIVEN MINIMUM DISSOLVED-OXYGEN CONCENTRATION 19

20 40 60 80

PERCENTAGE OF TOTAL WASTE FLOW

RECEIVING NITRIFICATION (p)

100

FIGURE 12. -The estimated annual cost of adding a nitrification 

process to secondary waste-treatment plants, as a function of 

the percentage of the total waste flow receiving nitrification 

(P), for 1980, 1990, and 2000.

minimum DO concentration of, say 4 mg/L in 1990, it 

only remains to find that feasible point (combination of P 

and QA) on the iso-DO curve labeled D = 4 in figure 6 that 

has associated with it a lower total cost in terms of 

benefits foregone and treatment costs than does any 

other feasible point of the curve.

Given the assumptions embedded in the HSM, the upper limit on the minimum flow that it is feasible to sustain at Atlanta is 1,670 ft3/s, 1,600 ft3/s, and 1,230 ft3/s 

in 1980, 1990, and 2000, respectively. Note that, from 

figure 6, it is feasible to attain a minimum DO concentration of 3 mg/L in 1990 without nitrification (P=0), given 

a limit of 1,600 ft3/s on QA, because the maximum 

necessary QA is only 1,430 ft3/s. However, a minimum 

DO concentration of 4 mg/L requires, if P=0, a 

minimum flow of about 1,750 ft3/s, whereas the maximum sustainable QA is only 1,600 ft3/s in 1990. If the 

minimum flow is set at the maximum sustainable in 

1990, the upper end of the feasible range of the iso-DO 

curve for 4 mg/L requires that 24 percent of the total 

waste load receive nitrification (P=24). The upper limit 

of the feasible range of an iso-DO curve is set by the 

lesser of either (1) the maximum necessary QA or (2) the 

maximum sustainable QA.

Every point on an iso-DO curve represents some combination of P and QA; thus each such point has an 

associated total cost. That cost can be determined using 

the- output of the HSM and the estimated cost of

40 50 60 70 

PERCENTAGE OF TOTAL WASTE FLOW RECEIVING NITRIFICATION (P)

80 90 100

FIGURE 13. - An illustration of the method of determining the least-cost combination of the percentage of waste flow receiving nitrification (P) and 

the minimum flow at Atlanta, Ga., (QA), required to produce a minimum dissolved-oxygen concentration of 4 mg/L, for 1990. Costs are in 

million dollars per year.
20 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

nitrification and of dependable peak generating capacity. Consider, for example, point A in figure 6; here 

P = 53 and QA = 1,290 ft3/s. From figure 11, it can be seen 

that, given this QA, no benefits are foregone in 1990. 

From figure 12, it can be seen that the additional wastetreatment costs associated with this P are equal to about 

2.13 million dollars per year. Thus, point A (P=53, 

QA = 1,290 ft3/s) has associated with it a total cost of 2.13 

million dollars per year. Next consider point B in figure 

6: here, P= 24 and QA = 1,600 ft3/s. From figure 11, it can 

be seen that at a QA of 1,600 ft3/s the benefits foregone 

equal 0.75 million dollars in 1990. The additional wastetreatment costs incurred, given that 24 percent of the 

total wastes are to receive nitrifiction, equal 1.08 million 

dollars per year. Thus, the total cost associated with 

point B is 1.83 million dollars per year.

By calculating the total cost associated with each 

point on the iso-DO curves depicted in figure 6, the combination of P and QA that will "produce" a given 

minimum DO concentration at least cost can be found. 

For 1990, the least-cost method of attaining a minimum 

DO concentration of 4 mg/L was determined to be 

associated with point B in figure 6.

It can be more readily seen that point B does represent a (1990) least-cost combination of P and QA by inspecting figure 13. The curve labeled D = 4 in figure 13 

corresponds to the similarly labeled iso-DO curve in 

figure 6.

The "kinked" curves in figure 13 connect combinations 

of P and QA that are associated with equal total costs; 

these curves are known as iso-cost curves. It has already 

been determined that point B in figure 13 (and the same 

point in fig. 6) has an associated total cost of 1.83 million 

dollars per year. Every combination of P and QA along 

the iso-cost curve that passes through point B has an 

associated total cost of 1.83 million dollars per year. For 

example, at point C (P = 40, QA = 1,360 ft3/s) on this isocost curve, the peak-generating-capacity benefits 

foregone, given a QA of 1,360 ft3/s, are (from fig. 11) 0.16 

million dollars per year; the additional treatment cost, 

given that 40 percent of the wastes are to receive 

nitrification, is (from fig. 12) equal to 1.67 million dollars 

per year. The total cost of the combination of P and QA 

at point C is, then, 1.83 million dollars per year. Iso-cost 

curves can be derived for any given level of cost, and 

eight such curves are depicted in figure 13.

Note that for any given level of QA, total cost will increase as P is increased, because of increased treatment 

costs. Note also that for any given level of P, total costs 

will increase with QA owing to increased benefits 

foregone, but such increases will occur only for those QA 

greater than 1,290 ft3/s (in 1990). For those QA less than 

1,290 ft3/s, there are no foregone benefits-that is, there 

is no decrease in the dependable peak generating capacity of Buf ord Dam associated with an increase in QA (see 

table 6). Thus, for a given level of P, the iso-cost curve is 

vertical below a QA of 1,290 ft3/s (in 1990) and represents 

only the nitrification costs associated with that level of 

P. Finally, note that as both P and QA are increased, 

total cost increases, and thus the iso-cost curves passing 

through those points associated with more of both P and 

QA represent higher levels of cost. That is, the iso-eost 

curves lying farther to the northeast of the origin in 

figure 13 represent higher levels of cost.

The least-cost combination of P and QA capable of producing a given minimum DO concentration is 

represented by that point where the lowest possible isocost curve just touches the iso-DO curve for that 

minimum DO concentration; in figure 13, this occurs at 

point B (P=24, QA = 1,600 ft3/s). All other combinations 

of P and QA capable of producing a minimum DO concentration of 4 mg/L in 1990 are associated with higher 

total costs.

The same procedure as that depicted in figure 13 was 

used to determine the least-cost method of producing a 

minimum DO concentration of both 3 mg/L and 5 mg/L 

in 1990. The results are presented in table 9 along with 

the least-cost combinations for producing the three 

minimum DO concentrations in 1980 and 2000. In table 

9 are also presented the separate components of total 

cost which are benefits foregone and the cost of adding 

the nitrification process to the waste-treatment plants.

Note that in a comparison of the least-cost combinations of a given DO standard across years, the DO standard of 5 mg/L provides the only case examined where

TABLE 9. -Combinations of percentage of wastes receiving nitrification 

and minimum flow at Atlanta, Ga., that will provide minimum 

dissolved-oxygen concentrations of 3, It, and 5 mg/L at least-cost, for 

1980, 1990, and 2000

Minimum 

dissolvedoxygen 

concentration 

(mg/L)

Percentage of 

wastes receiving nitrification (P)

Minimum

Atlanta

«A>

(ft3/s)

Costs, in million dollars per year

Nitrification

Benefits 

foregone Total

1980

3

4

5

0 

0 

62

1380 

1670 

1380

0.00 

0.00 

2.03

0.00 

0.71 

0.00

0.00 

0.71 

2.03

1990

3

4

5

0 

24 

63

1430 

1600 

1600

0.00 

1.08

2.72

0.34 

0.75

0.75

0.34 

1.83

3.47

2000

3

4

5

52 

70 

90

870 

870 

870

2.58 

3.76 

5.10

0.00 

0.00 

0.00

2.58 

3.76 

5.10
LEAST-COST METHOD OF PRODUCING A GIVEN MINIMUM DISSOLVED-OXYGEN CONCENTRATION 21

1700

PERCENTAGE OF TOTAL WASTE FLOW RECEIVING NITRIFICATION (P)

FIGURE 14. - Illustration of the solution for least-cost combinations of percentages of wastes receiving nitrification (P) and minimum flow at 

Atlanta, Ga., (QA) necessary to produce a minimum dissolved-oxygen concentration of 5 mg/L, for 1980,1990, and 2000. Costs, in millions of 

dollars.

the combination switches from no dependable-peakgenerating-capacity benefits foregone in 1980 to maximum sustainable flow in 1990 and then back to no 

benefits foregone in 2000. Comparing the least-cost 

combinations for all other DO standards across time 

reveals that they require the minimum flow at Atlanta 

be set at either the maximum necessary or the maximum 

sustainable in 1980 and 1990 and then be reduced to 870 

ft3/s in 2000.

The solutions for the least-cost combinations required 

to achieve a minimum DO concentration of 5 mg/L in 

1980,1990, and 2000 are depicted in figure 14. Note that 

the least-cost solution for 1990 would occur at that combination of P and QA represented by the point at the 

"kink" in the iso-cost curve if the slope of the upper portion of the iso-cost curve were only slightly "flatter." 

This is, the least-cost combination of P and QA, given a 

DO standard of 5 mg/L, nearly requires that Buford 

Dam be operated so as to forego no benefits from 

dependable peak generating capacity in 1990, just as it 

does require that it be operated in 1980 and 2000.

This suggests two related questions: First, how sensitive is the least-cost solution to the value of the 

parameters that determine the slope of the iso-cost 

curves? Second, how much difference would it make, in 

terms of added cost, if the least-cost solution were not 

chosen? It is to these questions that we now turn.

SENSITIVITY OF THE LEAST-COST SOLUTION TO THE 

COST OF DEPENDABLE PEAK GENERATING CAPACITY

Given the shapes of the iso-cost and iso-DO curves 

derived in this study, the least-cost combination of P and 

QA is found either at the upper end of the feasible range 

of the iso-DO curve or where the "kink" in an iso-cost 

curve just touches the iso-DO Curve. That is, the leastcost combination will require either that Buford Dam be 

operated so as to maintain the minimum flow at Atlanta 

at the maximum (necessary or sustainable) or that it be 

operated so as to forego no benefits from dependable 

peak generating capacity.

An increase in the cost of dependable peak generating 

capacity relative to that of nitrification would be sufficient to decrease the slope of the iso-cost curves. Any 

given level of total cost will be attained at a lower QA 

after an increase in the cost of peak generating capacity 

because the benefits foregone as a result of the loss of 

such capacity will be greater at each QA that would cause 

such a loss. However, given some positive cost for 

dependable peak generating capacity, that QA below 

which no capacity benefits are foregone will remain the 

same. Thus, the iso-cost curves associated with higher 

costs of peak generating capacity will lie beneath and 

have a lesser slope than will such curves associated with 

lower capacity costs.
22 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

Given a sufficient increase in the cost of peak 

generating capacity relative to that of nitrification, the 

least-cost combinations of attaining any given minimum 

DO concentration will switch from those requiring a 

maximum (necessary or sustainable) minimum flow at 

Atlanta to those that require that no dependable-peakgenerating-capacity benefits be foregone at Buford 

Dam. The dependable-peak-generating-capacity costs 

that cause such a switch in the least-cost combination of 

P and QA are presented in table 10.

TABLE 10. -Costs, in first-quarter 1976 dollars per kilowatt-hour per 

year, of dependable peak generating capacity above which the indicated minimum dissolved-oxygen (DO) concentration can be achieved 

at least cost by operating Buford Dam, Ga., so as not to forego benefits 

from dependable peak generating capacity

Minimum dissolved-oxygen con

3

4

5

Year

1980

f1 )

34

17

1990

69 

33 

25

2000

21 

22 

16

1 It is not necessary to forego peak generating capacity even if Q^ is set at the maximum 

necessary (1,380 ft3/s) to achieve a minimum DO concentration of 3 mg/L.

We have assumed that the replacement cost of 

dependable peak generating capacity at Buford Dam is 

equal to the $23.34/kW/yr estimated cost of the "Rocky 

Mountain" hydroelectric-power pump-storage facility. 

Consequently, the least-cost combination requires that 

no dependable peak generating capacity be foregone in 

order to provide a minimum DO concentration of either 

3, 4, or 5 mg/L in 2000 and to provide a minimum DO 

concentration of 5 mg/L in 1980. But, note that our 

estimate of $23.34/kW/yr is close to those costs that 

would require no peak generating capacity be foregone 

to provide a minimum DO concentration of either 3 or 4 

mg/L in 2000 and to provide a minimum DO concentration of 5 mg/L in 1990. For these DO standards in these 

years, the least-cost combination of P and QA is quite 

sensitive to the estimate of the cost of dependable peak 

generating capacity.

As was previously noted, the U.S. Army Corps of 

Engineers (1977) has assumed that any loss of dependable peak generating capacity at Buford Dam would be 

replaced using thermal electric generating facilities at a 

cost of $49.35/kW/yr. Using such a replacement cost, 

the least-cost combination of P and QA requires that 

Buford Dam be operated so as to forego no benefits from 

dependable peak generating capacity in providing a 

minimum DO concentration of either 4 or 5 mg/L. The 

least-coast combination would require that the dam be 

operated so as to maintain the maximum necessary QA 

in 1980 and the maximum sustainable QA in 1990 if the 

DO standard were set at 3 mg/L. But, no peak 

generating capacity would be foregone in 1980 given

that the maximum QA necessary to maintain a minimum 

DO concentration of 3 mg/L is only 1,380 ft3/s.

Suppose that the replacement cost of the dependable 

j peak generating capacity of Buford Dam is 

$49.35/kW/yr but that the choice of the least-cost combination of P and QA is based on an estimated cost of 

$23.34/kW/yr. Conversely, suppose that the replacement cost is really $23.34/kW/yr but that the least-cost 

combination is chosen under the assumption that the 

replacement cost is $49.35/kW/yr. In each case, the 

actual total cost will be greater than the calculated total 

cost of that which is (mistakenly) thought to be the leastcost combination of P and QA. The difference between 

the actual and calculated total costs is a measure of the 

loss in economic efficiency that would result from the 

use of an erroneous estimate of the cost of peak 

generating capacity.

The economic-efficiency losses that would result if the 

cost of peak generating capacity were actually 

$49.35/kW/yr but the least-cost combination were 

calculated and selected using an estimated cost of 

$23.34/kW/yr are listed in table 11; also presented is the 

correct least-cost combination of P and QA if the cost is 

actually $49.35/kW/yr. If the minimum DO concentration were set at 5 mg/L in 1990, for example, the 

calculated least-cost combination would require that 63 

percent of the total wastes receive nitrification and that 

the minimum flow at Atlanta be set at 1,600 ft3/s. But, 

the correct least-cost combination would require that 78 

percent of the waste receive nitrification and the 

minimum flow at Atlanta be set at 1,290 ft3/s. If we have 

underestimated the cost of peak generating capacity by 

$26.01/kW/yr ( = $49.35-$23.34), our (erroneous) leastcost combination of P and QA results in a $800,000 per 

year efficiency loss given a 5 mg/L-DO standard in 1990. 

This efficiency loss would result from too little nitrification and too much peak generating capacity lost relative 

to the "correct" least-cost combination.

The economic-efficiency losses that would result if the 

cost of peak generating capacity were actually 

$23.34/kW/yr but the least-cost combination were 

calculated and selected using an estimated cost of 

$49.35/kW/yr are listed in table 12. In this case, if the 

minimum DO concentration were set at 5 mg/L for 1990, 

the calculated least-cost combination would require that 

78 percent of the wastes receive nitrification and that 

the minimum flow at Atlanta be set at 1,290 ft3/s. But, 

the correct least-cost combination would require that 

only 63 percent of the waste receive nitrification and 

that the minimum flow at Atlanta be set at 1,600 ft3/s. If 

the cost of peak generating capacity is overestimated by 

$26.01, the (erroneous) least-cost combination of P and 

QA results in a $40,000/yr efficiency loss in 1990, given a 

5 mg/L DO standard.
INSTITUTIONAL CONSTRAINTS AND ASSOCIATED COSTS 23

TABLE 11. — Economic-efficiency loss, in million dollars per year, if the 

least-cost combination of the percentage of wastes receiving nitrification (P) and the minimum flow at Atlanta, Go,., fQ^, in cubic feet per 

second, is selected under the assumption that the cost of peak 

generating capacity is $23.34/kW/yr but the actual cost is 

$49.35/kW/yr,for 1980, 1990, and 2(900

Minimum

oxygen

(mg/L>

Least-cost combination

Calculated

P QA

Correct

P QA

Economic 

efficiency 

loss

1980

3

4

5

0 

0 

62

1,380 

1,670 

1,380

0 

31 

62

1,380 

1,380 

1,380

0.00 

.37 

.00

1990

3

4

5

0 

24 

63

1,430 

1,600 

1,600

0 

52

78

1,430 

1,290 

1,290

0.00 

.54 

.80

2000

3

4

5

52 

70 

90

870 

870 

870

52 

70 

90

870 

870 

870

0.00 

.00 

.00

TABLE 12. -Economic-efficiency loss, in million dollars per year, if the 

least-cost combination of the percentage of wastes receiving nitrification (P) and the minimum flow at Atlanta, Ga., (Q^), in cubic feet per 

second, is selected under the assumption that the cost of peak 

generating capacity is $49.35/kW/yr but the actual cost is 

$23.34/kW/yr, for 1980, 1990, and 2000

Minimum

oxygen

(mg/L)

-.east-cost combination

Calculated

P QA

Correct

P QA

Economic 

efficiency

loss

1980

3

4

5

0 

31 

62

1,380 

1,380 

1,380

0 

0 

62

1,380 

1,670 

1,380

0.00 

.42 

.00

1990

3

4

5

0

52 

78

1,430 

1,290 

1,290

0 

24 

63

1,430 

1,600 

1,600

0.00 

.30 

.04

2000

3

4

5

52 

70 

90

870 

870 

870

52 

70 

90

870 

870 

870

0.00 

.00 

.00

Note that, given the two estimates of peak generating 

capacity cost, only three cases have an economicefficiency loss associated with the choice of one estimate 

of the cost over the other-for a DO standard of 4 mg/L 

in 1980 and 1990 and for a standard of 5 mg/L in 1990. 

Note also that the "switching costs" presented in table 

10 fall between $23.34/kW/yr and $49.35/kW/yr in only 

these three cases. For all other cases, the least-cost combination of P and QA is the same, given a peakgenerating-capacity cost of either $23.34/kW/yr or 

$49.35/kW/yr.

If a decision maker is uncertain as to the cost of peak 

generating capacity and is risk adverse he might prefer 

to minimize the maximum possible economic-efficiency 

loss by choosing to base the selection of the least-cost 

combination on an estimated capacity cost of 

$49.35/kW/yr. However, we believe that it is inappropriate to assume that any peak generating capacity 

lost at Buford Dam would be replaced by thermal electric 

facilities. We prefer to base our calculations on the 

assumption that the peak generating capacity would be 

replaced by a facility similar in cost to the "Rocky Mountain" hydroelectric-power pump-storage facility. The 

Georgia Power Co. apparently found hydroelectricpower pump-storage to be the least-cost method of obtaining additional peak generating capacity.

INSTITUTIONAL CONSTRAINTS AND 

ASSOCIATED COSTS

The least-cost combinations of P and QA that are 

presented in table 9 are based on the assumption that 

there is complete flexibility in the choice of P and QA. In 

reality, constraints may exist in the form of laws or 

regulations that restrict the range of choice of P and (or) 

QA. The questions then become what is the least-cost 

plan, given these constraints, and what is the cost of 

that plan?

Currently, the Georgia Department of Natural 

Resources requires that a minimum flow of 750 ft3/s be 

maintained in the Chattahoochee River immediately 

upstream of the confluence of Peachtree Creek (U.S. Army Corps of Engineers, 1977). This translates to a 

minimum-flow requirement of 860 ft3/s at the Atlanta 

gage.

If this requirement sets the QA at 860 ft3/s and no 

higher, then the problem of finding the "least-cost" 

method of producing a given minimum DO concentration is reduced to simply finding the minimum level of 

nitrification (that is, the minimum P) that will provide 

that DO concentration given this constraint on QA. For 

example, given a DO standard of 4 mg/L in 1990 and a 

QA of 860 ft3/s, the least-cost combination is indicated by 

point D in figure 13. Given the constraint on QA, 72 percent of the total waste must receive nitrification if a 

minimum DO of 4 mg/L is to be attained. The cost 

associated with this (constrained) least-cost combination 

is given by the iso-cost curve that passes through point 

D in figure 13-3.2 million dollars per year. The same 

procedure was used to find the least-cost method of providing a minimum DO concentration of both 3 mg/L and 

5 mg/L in 1990, given a QA of 860 ft3/s. The results are 

presented in table 13 and graphically in figure 15. 

(Points D and B in figure 15 correspond to the similarly
24 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

TABLE 13. -Percentages of wastes that must receive nitrification to 

provide minimum dissolved-oxygen concentration of 3, 4, and 5 mg/L 

at least-cost, given that the minimum flow at Atlanta, Ga., is constrained to 860 ft? is for 1980, 1990, and 2000

Minimum Percentage of 

dissolved- wastes reoxygen ceiving nitriconcentration fication (P) 

(mg/L)

Minimum Costs, in million dollars per year

Atlanta Nitri- Benefits 

(Q\) fication foregone 

(fWs)

Total

1980

3 39

4 59

5 ^ 84

860 1.35 0.00 

860 1.91 0.00 

860 3.12 0.00

1.35 

1.91 

3.12

1990

52

72

92

860

860

860

2.10

3.20

4.30

0.00

0.00

0.00

2.10

3.20

4.30

2000

52

70

90

860

860

860

2.58

3.76

5.10

0.00

0.00

0.00

2.58

3.76

5.10

labeled points in figure 13.) The least-cost methods of 

producing minimum DO concentrations of 3 and 5 mg/L 

in 1980 and 2000, given that QA is constrained to 860 

ft3/s, are also described in table 13.

As another example of a constraint and its associated 

cost, suppose that a requirement existed that QA be set at 

860 ft3/s and that all wastes receive nitrification 

(P=100). Because no dependable-peak-generatingcapacity benefits are foregone under this plan, the total 

costs are those of adding a nitrification process to all 

secondary treatment plants; these annualized costs total 

3.95 million dollars in 1980, 5.05 million dollars in 1990, 

and 5.95 million dollars in 2000. The total costs under 

this plan in 1990 are also depicted in figure 15. Note 

that, from figures 5 through 7, the constraint that 

P= 100 and QA = 860 ft3/s will result in a minimum DO 

concentration that is greater than 5 mg/L in each of the 

three years considered.

In each of these two examples, the difference between 

the lower costs of the "unconstrained" least-cost plan 

and the higher costs of the corresponding "constrained" 

least-cost plan is due solely to the imposition of the constraint. This additional cost provides an estimate of the 

cost of obtaining any benefits (monetary or nonmonetary, tangible or intangible) that might result from 

the constraint.

CONCLUDING REMARKS

This study has placed a DO management problem in a 

conceptual framework suggested by the economic 

theory of production. The minimum flow of the Chattahoochee River and the percentage of the waste inflow

6r//-

cc

<

CO

DC

O

a

LJ_ 

O

CO•z.

O

CO 

O 

O

1 -

100 percent nitrification

/

/

3456 

MINIMUM DO, IN MILLIGRAMS PER LITER 

FIGURE 15.-Costs (benefits foregone plus added wastetreatment cost) of attaining various minimum dissolvedoxygen (DO) concentrations under different policies, in 

1990. Note that cost is independent of the dissolved-oxygen 

standard, given a constraint of 100 percent nitrification.

receiving nitrification are considered to be two variable 

inputs that can be used to produce a given concentration 

of dissolved oxygen in the river. Results of the U.S.G.S. 

Chattahoochee River Quality Assessment project were 

used to establish the production relationship between 

minimum flow, waste treatment, and DO concentration. 

Each of the inputs has a cost: the loss of dependablepeaking-capacity benefits associated with flow augmentation and the cost associated with nitrification of 

wastes. An attempt was made to find the least-cost combination of minimum flow and waste treatment 

necessary to achieve a prescribed minimum DO concentration.

No attempt was made to identify the benefits 

associated with various concentrations of DO in the
APPENDIX A-ANALYSIS OF THE REREGULATION PROJECT 25

river. Thus, no attempt was made to provide an estimate 

of the minimum DO concentration that would maximize 

the net benefits from producing dissolved oxygen in the 

river.

It was not an objective of this study to prescribe a 

specific set of operating rules for Buford Dam and a 

waste-treatment plan for the Atlanta region. An objective was to demonstrate a method for evaluating the 

cost effectiveness of alternative strategies for DO 

management; the method is the primary message. The 

Chattahoochee River was used as an example because of 

the availability of U.S.G.S. data and models that could 

be used to derive the DO production relationship. 

Another objective was to demonstrate how the results of 

a U.S.G.S. Intensive River Quality Assessment could be 

applied to a water-quality management problem.

The DO curves presented in figures 5-7 were derived 

using the DO model of the Chattahoochee River 

developed by Stamer and others (1978). These curves 

describe the physical relationships between flow 

augmentation, nitrification, and DO and are useful in 

themselves. When cast with an economic framework, 

they provide a basis for decisionmaking.

In regard to the Chattahoochee River, the results indicate that for certain DO standards and between now 

and 2000 the waste-assimilation capacity of increased 

flows in the Chattahoochee River can be substituted for 

increased waste treatment. It is estimated that the savings in waste-treatment costs experienced by so doing 

will more than offset the benefits foregone because of 

the loss of peak generating capacity at Buford Dam. 

However, these results were demonstrated to be, in 

some cases, sensitive to the value assigned to peak 

generating capacity and may also be sensitive to (among 

other things) estimates of the discount rate and the costs 

of nitrification.

There is a strong indication that a flexible approach to 

the management of DO in the Chattahoochee River may 

be much more cost effective than a more rigid, institutional approach. Examples of such rigid approaches are 

prohibitions of flow augmentation for water-quality 

management or blanket requirements for high levels of 

waste treatment without regard to concomitant costs 

and resulting water-quality levels. An institutional constraint on flow augmentation or waste-treatment practices will not in general be consistent with the attainment of a prescribed DO standard at least cost; that is to 

say, such constraints will usually have an associated cost 

(or economic-efficiency loss).

Finally, note that our criterion for evaluating different DO-management strategies has been solely one of 

economic efficiency: What is the minimum-cost method 

of meeting a given DO standard? Equity, or distributional, considerations have been completely ignored.

For example, to attain a minimum DO concentration of 

5 mg/L in the Chattahoochee River in 1980 and 1990, 

the least-cost strategy requires that a little over 60 percent of the total waste flow receive nitrification and 

that, consequently, about 40 percent of the flow receive 

only secondary treatment. If the additional cost of 

nitrification is borne only by the taxpayers in the service 

area of those plants required to add the nitrification process, the taxpayer serviced by those plants at which 

nitrification is not required do not bear any of the additional waste-treatment cost incurred in meeting the DO 

standard. As another example, consider that in choosing 

between combinations of P and QA that will produce a 

given level of DO, some combinations require that more 

dependable peaking capacity be foregone and less additional waste-treatment costs be incurred than do others. 

Those individuals that bear the costs of replacing the 

peaking capacity and those that experience the savings 

in treatment costs because the peaking capacity has 

been foregone are not necessarily the same individuals. 

The choice of a least-cost method for attaining a given 

minimum DO concentration has distributional or equity 

implications that have not been considered in this study.

REFERENCES CITED

Atlanta Regional Commission, 1977, Atlanta region areawide wastewater management plan [revised]: Atlanta Regional Commission 

in cooperation with U.S. Army Corps of Engineers, Savannah 

District; Georgia Department of Natural Resources, Environmental Protection Division; and the U.S. Environmental Protection 

Agency, 28 p.

Georgia Power Co., 1972, Application to the Federal Power Commission for a license for the Rocky Mountain project: October 

1972, Exhibit W, pages 44 and 45 of 47 pages.

Giffels/Black and Veatch, 1977, Overview plan with environmental 

assessment, Detroit Water and Sewerage Department [revised], 

vol. 1 o/Comparative waste-water collection and treatment costs: 

Detroit, Giffels/Black and Veatch, 118 p., 2 sections, rept. code PF 

101.

Stamer, J. K., and others, 1978, Magnitudes, nature, and effects of 

point-nonpoint discharges in the Chattahoochee River basin, 

Atlanta to West Point Dam, Georgia: U.S. Geological Survey 

Open-File Report 78-577, 130 p.

U.S. Army Corps of Engineers, 1977, Lake Lanier restudyPreliminary base plan of operations: Savannah, Ga., U.S. Corps of 

Engineers, Savannah District, lip. 2 figs., exhibits A-E.

APPENDIX A—ANALYSIS OF THE 

REREGULATION PROJECT

If the proposed reregulation structure were built just 

below Buford Dam (capacity 8,400 acre-feet) and if the 

Morgan Falls reservoir were dredged to a capacity of 

3,500 acre-feet, then more peak hydroelectric power 

could be produced given any required minimum flow at 

the Atlanta gage. By storing more of the water released 

from Buford Dam during peaking hours, most or all the
26 ECONOMICS OF DISSOLVED-OXYGEN MANAGEMENT: CHATTAHOOCHEE RIVER, GA.

water-supply and minimum-flow needs throughout the 

entire week can be met.

The HSM was modified to simulate this situation, and 

two variables were added to account for the addition of 

the reregulating structure: SR (storage in ft3) and QR 

(discharge from the reregulating structure in ft3/s). The 

additional flow and storage constraints of the HSM are

(12)

(13)

(14)

SR<3.66xl08 . (15) 

Some other constraints in the original HSM are 

changed, as follows:

(6a)

dS2/dt = QR + T2 -W2 -Q2 , and (7a) 

S2 <1.52xl08 . (lOa) 

Added and changed constraints are

12. continuity equation for the reregulating reservoir;

13. and 14. initial and final storage in reregulating

reservoir (arbitrary); 

15. capacity constraint for reregulating reservoir,

3.66 x 108 ft3 = 8,400 acre feet;

6a. the withdrawals below Buford Dam but above 

Morgan Falls Dam, must be satisfied by the 

release from the reregulating reservoir plus 

tributary flows;

7a. continuity equation for Morgan Falls reservoir,

the inflow being the release from the reregulating

reservoir plus tributary flow minus withdrawals;

and

lOa. the capacity of Morgan Falls reservoir, increased

by dredging to 1.52x 108 ft3 = 3,500 acre feet. 

This modified HSM was run to determine the relationship between dependable peaking capacity and QA for 

each of the three years.

Figure 16 shows the dependable-peaking-capacity 

benefits as a function of QA with and without the 

reregulating structure and Morgan Falls reservoir 

dredging. Also these benefits minus the cost of these improvements are shown in this figure.

According to the U.S. Army Corps of Engineers' Lake 

Sidney Lanier restudy (1977), the capital cost of the 

reregulating structure is $11.50 million and the operation and maintenance costs are $65,800 per year. 

Based on a discount rate of 10 percent and a life of 100 

years, the annualized cost of the facility is $1.22 million 

per year. The Corps reports the initial cost of the 

Morgan Falls reservoir dredging is $1.65 million and annual maintenance-dredging costs are $15,000/per year. 

Based on a 10 percent discount rate and a 100 year life, 

the annualized cost of the Morgan Falls reservoir dredging is $0.18 million per year. Thus, the annual cost of 

both projects is $1.40 million per year.

The figures show that the costs of these improvements 

exceeds the gain in dependable-peaking-capacity 

benefits. These calculations were made under the 

assumption that the cost of dependable peaking capacity 

is $23.34/kW/yr. Even if this cost were assumed to be 

$49.35/kW/yr, the costs of the improvements would exceed the gain in dependable-peaking-capacity benefits. 

There may, however, be other benefits from the project, 

such as enhancement of the river for recreational use or 

the mitigation of channel erosion.

CO 

QC

1980

eo

1990

CO

1 2

2000

800 1000 1200 1400 1600 

QA, IN CUBIC FEET PER SECOND

1800

FIGURE 16.-The relationship between estimated annual dependable-peaking-capacity benefits and minimum flow at Atlanta, 

Ga., (QA), with and without reregulation, for 1980,1990, and 

2000. Solid line is without reregulation; dashed line is with 

reregulation; dotted line is benefits with reregulation minus 

the annualized cost of reregulation.

•ft U.S. GOVERNMENT PRINTING OFFICE: 1980 O 311-344/126