A MULTI-CRITERIA WATER QUALITY INDEX FOR OPTIMAL by John
A MULTI-CRITERIA WATER QUALITY INDEX FOR OPTIMAL
ALLOCATION OF RECLAIMED MUNICIPAL WASTEWATER by
Kuo -an Yu
A Dissertation Submitted to the Faculty of the
SCHOOL OF RENEWABLE NATURAL RESOURCES
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
WITH A MAJOR IN WATERSHED MANAGEMENT
In the Graduate College
THE UNIVERSITY OF ARIZONA
THE UNIVERSITY OF ARIZONA
I hereby recommend that this dissertation prepared under my direction by
John Kuo-an Yu
A Multi-Criteria Water Quality Index for Optimal
Allocation of Reclaimed Wastewater
be accepted as fulfilling the dissertation requirement for the degree of
Doctor of Philosophy
As members of the Final Examination Committee, we certify that we have read this dissertation and agree that it may be presented for final defense.
de t il
Final approval and acceptance of this dissertation is contingent on the candidate's adequate performance and defense thereof at the final oral examination.
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made avilable to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
I want to thank
Lucien Ducstein for initiating my interest in water quality indices.
I owe many thanks to
Martin M. Fogel, my major adviser and dissertation director, who spared no effort in his guidance and suggestions throughout this study.
I am particularly thankful to Drs. H. L. Bohn and G. S. Lehman for their valuable criticism and advice. I am grateful to the other members of my graduate committee,
J. L. Thames and Dr. W. H.
Fuller, for the assistance and time which they offered so generously.
Further, I would like to thank Dr.
D. A. King for the time he has taken to discuss the recreational demand for water and for providing guidance in this project.
I am particularly grateful to my wife Gloria and my son
Muhan for their patience, understanding, and assistance.
The author was supported in part by grants from the Office of
Water Research and Technology, Practical Use of Decision Theory to
Assess Uncertainties About Action Affecting the Environment, and the
Environmental Protection Agency, Environmental Monitoring and Assessment of Coal Strip Mining and Reclamation in the Four Corners Area.
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS
LIST OF TABLES
Literature Critique and Problem Presentation
Optimization of the
. . ,
The Multi,-Criteria Water Quality
Comment on Benefit and Cost Analysis
Risk Cost-Cost Function Analysis
3. THE STUDY AREA
Description of Tucson Region
Physiography, Biology, and Climate
Water-Based Recreational Areas
Description of Tucson Sewage Treatment
Quantities of Treated Sewage
Influent and Effluent
Historical Distribution of Sewage Plant
TABLE OF CONTENTS--Continued
COST FUNCTIONS FOR SEWAGE TREATMENT
The Determinants of Cost Functions
The Calculation of Unit Cost
BENEFITS TO BE DERIVED FROM SEWAGE RECLAMATION
Agricultural Statistics of the Tucson Area
Consideration of Pathogenic Organisms with
Acreage of Suggested Lake
Costs of Constructing a Lake
Total Benefits to the Tucson Area
RESULTS AND DISCUSSION
The Derived Multi-Criteria Water Quality Index
• • • •
Further Considerations on MCWQI
Comparability of WOIs
CONCLUSIONS AND RECOMMENDATIONS
APPENDIX A: HISTOGRAMS OF THE INFLUENT WATER QUALITIES
APPENDIX B: TABLE OF FECAL COLIFORMS
APPENDIX C: HISTOGRAMS OF THE EFFLUENT WATER QUALITIES
LIST OF ABBREVIATIONS
LIST OF REFERENCES 119
LIST OF ILLUSTRATIONS
The optimum end point for pollutant reduction
Costs of removing the pollutant residuals for a
A hypothetical demand curve for water-based recreation
The derivation of marginal benefit for an improved water quality stage
Conceptual diagrams indicating the desired removal rate for individual pollutants
Risk cost/cost function
Key map, Santa Cruz River Basin
Population growth of Pima County
Tucson regional wastewater flow through 2020
The plane layout of the Tucson wastewater treatment plant at Sweetwater Road
Cost of biochemical oxygen demand removal in
Cost of suspended solids removal in
Cost of detergent removal
Cost of nitrogen removal in
Cost of phosphorus removal in
Cost of coliform removal
The relationship between the soil nutrient content and plant yield
The farmed lands in the Tucson region
Risk of illness and the concentration of vi coliforms
LIST OF ILLUSTRATIONS—Continued
Benefit and cost curves for the removal of suspended solids
Benefit and cost curves for the removal of nitrogen . 93
22. Benefit and cost curves for the removal of phosphorus . 95
LIST OF TABLES
Employment trends in the Tucson metropolitan area
Market values of leading industries in Pima County,
Population growth of Tucson and Pima County
Expansion of the City of Tucson incorporated area
Wastewater detention periods in the Sweetwater Road treatment plant
Volumes of wastewater influent received at Tucson
Sweetwater Road treatment plant
Costs of treatment, Sweetwater Road Wastewater
Treatment Plant, Tucson, Arizona
Quality of influent and effluent sewage flows at City of Tucson treatment plant, 1974-1975
Sewage effluent distribution of the Tucson treatment plant at Sweetwater Road
Six-year (1969-1974) averaged acreage of the crops planted in Tucson region with each crop's unit water consumption and
1975 product values
Socio-economic evaluation of the beneficial uses of the nation's water resources
Consumptive use of water by crops in Arizona
• • •
Average pan and lake evaporation for Tucson region
Acreage of hypothetical lake surface
Crop yields associated with fertilizer applied and the costs of operation and material
Crop yield equations using nitrogen and phosphorus as independent variables viii
LIST OF TABLES--Continued
Benefits estimated from nitrogen by using Tucson
Sweetwater Road treatment plant effluent
Benefits estimated from phosphorus by using Tucson
Sweetwater Road treatment plant effluent
Benefits estimated from crops and recreation lake by using Tucson Sweetwater Road treatment plant effluent
Use-oriented benefits and treatment cost analysis have been incorporated into a water quality index to derive economically optimized pollutant concentrations for use in the development of waste water treatment programs. This multi-criteria water quality index can be used in decision-making at federal and local governmental levels.
Five major pollutants (coliforms, nitrogen, phosphorus, suspended solids, and detergent) were considered in the treatment of municipal wastewater. With each higher level of improvement, the treatment costs increase proportionally, but the benefits associated with the reuse of this treated wastewater also increase in all cases except that of nutrient removal for agricultural use. Listed in descending order of their general utility, possible uses of reclaimed water include water supply, recreation, irrigation, industrial use, waste disposal, transportation, and commercial fishery.
The optimal concentration of a pollutant was defined as that point at which the marginal costs of its removal equal the marginal benefits thereby obtained. The optimum net benefits associated with each kind of reclamation are derived simultaneously. The multicriteria water quality index is a combination of the maximum net benefits and the water quality index of the optimal individual concentrations. Walski and Parker's water quality index was used in rating water quality.
This methodology was applied to the Tucson region for the expediency of acquiring data. Possible uses considered for the reclaimed municipal wastewater included agricultural irrigation and recreational lakes in the Tucson metropolitan area. Results from this study indicate that the multi-criteria water quality index is zero dollars, or (NB
, WQI = 0). Similar evaluations for other cities, made in the same way, would permit ranking of this index.
This ranking would be useful for making decisions concerning the allocation of regional funds for treating municipal wastewater. This approach could also be used on a local level for determining optimal concentrations of pollutants and for optimal allocation of the treated water.
An index is a number, usually dimensionless, whose value expresses a measure or estimate of the relative magnitude of some condition. Indices are useful as shorthand expressions for complex combinations of multiple factors. Their usefulness depends upon their general acceptability--perhaps only as a reasonable compromise--based upon consistency and convenience rather than any rigorous scientific justification. Each index should be carefully defined as closely as is practicable, but it should be understood that no single number can contain all the information about a complex situation (Truett et al.
Another purpose of an index is to provide the public with simple understandable yet scientifically accurate guides for assessing quality. There is little doubt that our society needs an easily understood water quality index (WQI) for the judgment and decision-making concerning our water resources and for the dissemination of information to the general public. Herbert Inhaber (1976) in his book, Environmental Indices, clearly depicted the importance of such indices.
Literature Critique and Problem Presentation
Commonly published water quality data include so many parameters that the quality appraisement of a water body becomes a difficult task even with the aid of a computer (Newsome 1972). Sylvester
(1968) stated that the fifty-five quality parameters published for the State of Washington were too numerous for them all to be considered.
The Environmental Protection Agency (EPA) has developed three indices for water quality control (Truett et al.
Duration, and Intensity
Index, upon which the other two are built, gives consideration to spatial analysis in yearly examination rather than point analysis of one day. It is easy to understand and is applicable to any stream. However, it is not based on physical, chemical, and economic analysis. Personal judgment is the key issue in the application of this index.
Many publications (Horton 1965; Brown et al, 1973;
Tillman et al. 1973; Greeley et al. 1972) have dealt with the evaluation of water quality by developing a water quality index or WQI.
At present there are more than
100 water quality indices or indicators in use throughout the United States ("A Measure of Quality" 1976),
Like the setting of water quality standards, these WQIs also depend on their developers' experience and knowledge, i.e., the rating and weighting of a chosen parameter is totally at their own disposal. These indices cannot be compared with each other and do not indicate the level to which the water should be treated economically.
Deininger and Maciunas (1972) and
Landwehr et al. (1975) favor one general
(1974) emphasize users'
In addition to the delineation of water quality conditions, the economic and institutional constraints imposed by society must be considered. Water resources are for people and all other life forms.
Water quality has meaning only in terms of the people involved: those who are affected by water quality within or beyond the boundaries of the watershed in question, and those who own or use the watershed for any of the numerous goods and services it produces. They determine the value of water on a scale of possible alternatives to satisfy their needs, desires, or rights.
Hence, the definition of a
WQI should not be left entirely to the chemist, physicist, biologist, or engineer. It must also have public input. White
128) has stated that "criteria must be based on public health protection and not cost." However, some questions must be asked of his argument. Is there any trade-off between cost and criteria? Will the society be willing to pay for such a high standard? Lynn and Metzler
(1968,p. 1311) said, "The fact is that members of a society who have concerns that go beyond basic survival are unwilling to devote the largest part of their energies to protect their environmental health measures." Wright
(1968) also considered that the dynamics of our society are much more important than pollution abatement. The WQI might be improved by considering social welfare.
The frequency of a particular WQI should also be considered from time to time as the expressed water quality will vary.
Generally the problems can be summarized as follows:
Should there be one
WQI for all water or one for each class of water use?
How many parameters should be incorporated into the
How should the importance of the composing parameters be individually weighted? For example, is nitrogen more important than coliforms?
How should each parameter be rated? For example, does water quality go down linearly or exponentially with an increase in phosphorus concentration?
Can a monetary value be assigned to a
WQI? If so, does it have any particular advantage?
What is the economically optimal level to which each pollutant should be treated?
How does this optimal concentration compare to that produced by the existing treatment plant capability?
Should the local government choose to add an advanced treatment plant?
The WQI ranges from zero to one, i.e., from the worst to the best condition. Based upon any of the methods mentioned by the previously discussed authors, the WQI of a secondarily treated effluent will be zero. This is because secondary treatment does not improve even slightly the levels of phosphorus, nitrogen, and salts, But a zero WQI does not necessarily mean that there is no monetary value if this water is used for agriculture or other purposes.
WQI is used not only to indicate the quality of the water but also to rank the priority for the pollution control actions
among different water sources, incorporating the monetary value associated with the WQI will aid the decision-making process.
The purpose of this study was to develop methods of approach to water quality management which might be applied as rapidly as
5 techniques and concepts permit, The major objective of the study was to develop a WQI-economic model or index by which the benefits and costs resulting from water pollution control measures might be interrelated.
The scope of the study was tentatively set for the analysis of municipal sewage. An attempt was made to discern economically optimal removal rates for pollutants and the uncertainties associated with these processes.
This chapter describes the development of the water quality index and the search for economically optimal treatment levels of the major sewage pollutants. The procedures involved in the derivation of a multi-criteria water quality index
(MCWQI) are presented step by step in this chapter.
There are many parameters promulgated for the indication of water quality. The WQI can be expressed as a vector
WQI= f(x 1 ,x 2 ,x 3 ,...xn )
(1) where x l
might be biochemical oxygen demand; x 2 , suspended solids; x
3' coliforms, and so on. Since n could be a number in the hundreds or even thousands (see McKee and Wolf
1963), it seems impossible to integrate every xn into the WQI.
It is possible to reduce n by using a computer program to calculate correlation coefficients. From the correlation coefficient matrix, those parameters not having significant correlation with others can be culled out. The intrinsic problem of this method is that different parameters may require different treatments, One parameter's existence in the
WQI may indicate the condition of other parameters but the appearance of this parameter in the
WQI may lead people to
believe that the other parameters do not need treatment. Another method for the reduction of n involves consultation of the published
7 literature. Based upon past experience combined with a knowledge of the source of pollutants and the designated water use, the number of parameters can be reduced. It is obvious that a
WQI for crops could exclude such parameters as coliform bacteria and color; the WQI for boilers need only be concerned with turbidity, certain chemicals, temperature, and dissolved oxygen of the water in order to avoid any scaling, corrosion, and waste of heat.
The prime constituents found in municipal sewage are:
1) suspended solids and dissolved organic matter;
2) surface active agents such as detergents;
3) coliform organisms which function as biological indicators of pathogenic organisms; and
4) nutrients such as nitrogen and phosphorus (Frankel
1965). The vector for municipal sewage (ASWQI) is
MSWQI = f(S.S., BOD, ABS, coliforms, N, P)
(2) where S.S. is the suspended solids,
BOD is the biochemical oxygen demend, ABS is a detergent surfactant,
N is nitrogen, and P is phosphorus.
Optimization of the
There are two ways by which to analyze the economic optimization of each parameter:
1) the benefit-cost analysis; and 2) the risk cost-cost function analysis. The objective function of benefit-cost analysis is given by
U(x,y) B(Y) - C(x)
8 where x and y are vectors of system inputs and outputs, respectively.
C(x) represents the costs associated with the inputs and
B(y) the benefits associated with the output. The criteria for efficiency would indicate that water quality should be improved to the point where marginal benefits are equal to marginal costs (Figure
1), that is, dU(x,y) dy dB(y) dy dB(y) dC(x) dy dy dC(x) dy
The cost function,
C(x), has been researched intensively in the past five years (Tihansky 1974).
There are many determinants within the cost function but these are generally categorized under two headings: capacity and efficiency. Frankel (1965) developed an empirical equation for the total annual cost for treating municipal waste:
+ 1] [165,000(0.71E - 0.75E
) 50,000E10 0 ] (6) where Q is the waste flow in millions of gallons per day (MGD) and
E is the fraction of
BOD removed. Based upon census and population conjecture,
Q can be assumed to be constant, while the costs and removal levels can be derived. The function in parentheses is calculated for an efficiency not exceeding
0.95. As the efficiency approaches unity, however, the function underestimates the exponential rise in
The optimum end point for pollutant reduction.
costs. The term E
00 is thus added to account for this case. The other bracketed expression reflects economics of scale, where effi-
1 0 ciency is held constant. Figure
2 demonstrates the economic impact of pollutant removal levels for a
2.5 MGD waste flow (Frankel 1965).
The capital, operation, and maintenance costs for a certain standard-sized treatment plant may generally be estimated and will not vary appreciably even though the cost functions are affected by many factors such as topography, pH, water temperature, and waste transport distance. Additional factors include the benefit functions which consider population trend, long and short term demand for goods and services, quality of the facility or service, spatial distribution of alternate resources, and climatology of the region, Details of the cost functions will be given in Chapter
Research on the benefit function is in a fledgling stage because of the difficulty of quantifying such intangible factors as aesthetic quality and a balanced ecology (Tihansky 1974).
The benefit of water quality improvement programs is directly related to water use (Thomann
Benefits may accrue, therefore, from the following;
Improved quality of municipal and industrial water supplies;
Increased recreational uses of water;
Improved commercial fishery and wildlife;
0 o 80
- 40 o c...)
20 40 60 80
Removal Efficiency, %
2. Costs of removing the pollutant residuals for a 2.5 MGD plant.
Ameliorated irrigation water;
Improved navigation and waste disposal water.
In determining the benefits to be derived from reclaimed water, the feasibility of these uses should be considered first. If a region has no industrial plant, for example, the reclaimed water cannot be assigned for industrial use. Also, navigation is generally
12 considered impossible in an inland desert region. The decision for the destined uses must be based on geography, demography, climate, socio-economic conditions, existing industries, etc.
The second point to be noted is the ranking of these feasible uses of the reclaimed water. There is no doubt that water should go to the highest revenue-generating uses, i.e., the highest demand first.
After the highest demand is fulfilled, the rest of the water goes to the next highest use and so on. Stone (1971) gave the following order: domestic water supply, recreation, land reclamation, industrial use, waste disposal, transportation, and commercial fishery, in descending order of economic use.
All of these benefits to be derived from the reclaimed sewage originate in the values of the various uses rather than the selling price of the water. This is because the final product, whether as a commodity or as a recreation pond, has more transferability and attractiveness than the raw water. The water is looked upon as a prerequisite for the production of goods and services. All of the other costs, such as fertilizer, insecticide, machinery, electricity, operation, maintenance, and other materials essential for the final production, are deducted from the final selling price of the products.
Only in rare cases is treated wastewater or sewage being considered for a domestic water supply. People have strong resentment against this water even when it is treated in compliance with the highest standards (Stone
In addition, it is very costly to bring sewage to drinking quality when compared to the cost of tapping a new source. Groundwater recharge (seeping rather than pressured injection) would probably be a preferred alternative for use of sewage as a domestic supply. In general, sewage effluent can be eliminated from consideration as a possible source of domestic water supply at the present time.
The next highest use is recreation. There are two ways by which the quantity of water to be allocated to recreation may be determined. The first is by using a standard method. For example, the National Recreation Association
(1952) has recommended that the
City of Tucson should have one acre of park land for each hundred people.
DeCook (1970) suggested that
5% of the total park land should be devoted to a recreation lake. If we assume a water depth of ten feet, the quantity of water needed can be determined by consideration of pond seepage, evaporation, and a complete annual recirculation. Then, a standard site can be selected to derive the per acre water-based recreation revenue. Assuming that the per acre value is perfectly elastic, the total revenue can be deduced for the entire region.
The second method involves the development of a demand curve for the water-based recreation (Figure
Taking a nondiscriminating monopolist method (Martin,
Smith 1974), the monopolistic owner
(e.g., the Park and Recreation Department) could set a charge for the resource that would maximize the total revenue from the resource, i.e., maximize the seller's surplus. The total water-based revenue is the sum of the consumer's surplus and the seller's surplus. The total quantity of water allocated from the sewage effluent can be estimated in the same way as previously discussed.
It is very possible that irrigation storage lakes can be incorporated with recreation lakes if the latter are smaller than the former. Since the planting seasons vary with the kinds of crops and the crop acreage also varies, the construction of a storage lake is probably necessary to detain the constant discharge of effluent.
The first step is to find the unit water used by crops. The acreage of cropped land can be increased township by township from the crop atlas to a point where the total consumptive use of water approximates the capacity of the sewage treatment plant . The total revenue is the product of the crop yield by the crop price. With knowledge of the planting schedule, the consumptive use of water, the potential evaporation, the seepage, and the lake depth, the size of this detention lake can be calculated.
Figure 3. A hypothetical demand curve for water-based recreation.
If there is still some water left after the irrigation requirements are met, the excess water can be directed to industrial use. The quantity of water will be determined by the consumption of that industry. For example, in the Tucson region, possible industrial uses are copper ore processing, and power plant boiler and cooling tower water.
The quantity of water needed by each of them can be estimated. The total revenue from the final product may be assigned to the water after deducting costs other than those of the water.
Waste Disposal, Transportation, and Commercial Fishery
If the reclaimed water cannot be assigned to the abovementioned uses, or if there is unused water, the water can be used for waste disposal, transportation, or commercial fishery, The quantity of water required to flush out garbage, thermal and other wastes or to float a barge or ship in a canal can be estimated. Probably the reclaimed water has its greatest value in the dry season when the water level in the river and canal is low.
The quantity of water for a fishing pond can be estimated in much the same way as that for a recreation pond. Its revenue is expressed as the amount of fish produced.
Benefits can be estimated for a given water quality state which may be defined as an ordered set of "significant ranges" of concentration of constituents describing the quality of a water resource with which a particular benefit function is associated (Newsome 1972).
17 treatment of wastewater brings water quality to a new state which is associated with an improved benefit, Figure
4 describes the procedure.
Generally, Bray's equation (Bray
1945, 1948, 1962) may be used for the estimation of the product and the associated water quality.
The value of a recreation pond is inversely proportional to the concentration of nutrients and coliforms.
Conversely, the value of irrigation water is directly proportional to the nutrients. If no crop-yield equation can be found in the local Land Grant University's
Agricultural Experiment Station, Bray's equation may be assumed. Some of the details of using Bray's equation will be revealed later in the case study.
Multi-Criteria Water Quality Index
The most economically feasible improvement of each constituent in Equation 2 can be found as shown in Figure 5. The net benefit (NB) vector corresponding to Equation 2 is
= (NB 1 ,NB 2 ,...NB 6 )
Assuming the highest net benefit of one of the components covers the revenue of all other determinants, the multi-criteria
WQI (MCWQI) will take the form
MCWQI= f(NB max
NB max is the maximum net benefit and r is the removal rate of the pollutants. It is possible that one net benefit will not cover all
original water quality state improved water quality state water uses at original state
_sl improved water quality uses
$ of uses
$ of uses
,A water quality
The derivation of marginal benefit for an improved water quality stage.
0% r1 KV% suspended solid removal
Conceptual diagrams indicating the desired removal rate for individual pollutants.
the other benefits. If other net benefits are independent of the maximum net benefits, the
MCWQI will be
MCWQI f[(NB max
NB.), r 1 ,r 2 ,...r 6 ]
MCWQI =-- f[(NB max +
r 1 ,r 2 ,...r 6 ]
(1 0) where NB. is the net benefit of the pollutants being treated that are not covered in the maximum net benefit.
The removal rate can be changed back to real units by timing the untreated raw sewage concentrations. Then, following
Parker's method (1974), a number can be derived for these determinants.
The reason for using their water pollution index is that the
WQI resembles Landwehr's (1974) multiplicative water quality index with a weight attached to each parameter in which the parameters chosen are also considered for this study. Landwehr et al.
(1975) said that the sensitivity functions' of WQI parameters are very similar to their rating curves.
Landwehr, Maciunas, and
Deininger (1976) also pointed out that the unweighted multiplicative index is the best after a comparison of five water quality indices. The equation for calculating
WQI --= a-j1/Eai
1 1 where C. is the concentration of the ith parameter; f.(C.) is the sensitivity function for the ith parameter; a i is the weight associated
with the ith parameter; and n is the total number of parameters. In
20 this study, all values of a i are assumed to be equal to one.
Walski and Parker
(1974) gave the following sensitivity functions:
Dissolved Oxygen f(N) = exp
(-0.16N) f(P) exp (-2.5P) f(SS) exp (-0.02 SS) f(C) = exp (-0.0002 C) f(DO) = exp [0.3(DO - 8)],
DO < 8
The multi-criteria water quality index
(MCWQI) for municipal sewage has the final form
MCWQI = f[(NB max
ENB i ), WQI] (12) which is a single-valued number with units in dollars.
This multi-criteria water quality index may be calculated for different regions or different cities. Federal or state agents can allocate water pollution control funds based upon this index to those areas that they think are most appropriate. This approach has some advantages over the old
WQIs. First, it eliminates the need to choose a general WQI or a user's WQI, The most important water quality parameters associated with the water source are selected and later are considered individually for each possible use. Second, taking the dimension in dollars makes the
MCWQI comparable among different regions even if they do not have the same number of parameters.
Comment on Benefit and Cost Analysis
Benefit and cost analysis has been used in the United States since the passage of the Flood Control Act of
1936 to evaluate the worth of a project by computing and examining the ratio of monetary benefits derived from the project to the monetary costs associated with the project.
Critics of this technique have raised a number of questions which challenge its validity as a tool for proper evaluation of competing alternative projects in the field of water resource management.
Prest and Turvey (1965), for instance, have noted the complete absence of a priori structure for handling a given problem in this approach. Sewell et al.
(1962) consider it a less useful guide for ranking those alternatives which differ in capital intensity and where production, maintenance, and other operating costs are more important.
As Marshall (1965, p. 294) puts it, "One of the principal uses of benefit-cost analysis is to clothe politically desirable projects in the fig leaf of economic respectability." Whatever its drawbacks, since the Second World War, most of the decisions taken in the developing countries have been based on this analysis and lately this technique has moved into the planning and decision-making processes of most of the developing countries. Economic efficiency is still the framework for evaluation of water resource development plans prepared under the guidance of the World Bank and other international agencies,
No doubt under those new Principles and Standards for Planning (passed on September
10, 1973, by the U.S. Water Resources Council), equal emphasis will be laid on the second objective, namely, environmental
quality, However, standards for quantitative and qualitative assess-
22 ment of environmental quality, social well-being, and regional development are presently evolving and have yet to prove their validity in real life.
Risk Cost-Cost Function Analysis
The other method by which optimum cost may be estimated is the risk cost to cost function analysis. The risk cost is inversely proportional to the degree of treatment. Figure
6 shows the principle of this method.
This is easy to perceive. For example, the number of coliforms present in sewage is about
If the sewage is treated to several levels, say, 10,000/100 ml and 100/100 ml, the probability of a hazardous condition arising is certainly the highest for untreated effluent and the lowest for the 100/100 ml; at the same time, the treatment cost for the 100/100 ml is the highest, This is assuming that no shock load occurred because of the population-based design for the plant capacity. If shock loads do occur, it is usually under conditions where the waste flow exceeds the handling capacity of the plant or is far below it; in such cases, the risk cost will be much higher. In this study, the risk cost to cost analysis is put aside for future study.
The Tucson region was chosen as a case study. This study shows only the methods and procedures that are applicable. Many assumptions have been made for the expediency of the calculations.
Risk cost/cost function.
THE STUDY AREA
For reasons of data accessibility, the Tucson metropolitan area was adopted for this study. Both socio-economic and physical conditions will be briefly discussed here. A portion of this chapter is devoted to the description of the Tucson sewage treatment plant in order to establish a background for further analysis.
Description of Tucson Region
Physiography, Biology, and Climate
As shown in the map (Figure 7),
Tucson is located in the northeast part of Pima County in southern Arizona. It belongs to the Desert
Lowland physiographic classification with an elevation about 2,200 feet above mean sea level. The city is surrounded by high mountains; to the north and northeast are the Santa Catalina Mountains, to the east are the
Rincon Mountains, to the south are the Santa Rita Mountains, and to the west are the Tucson Mountains. The highest peaks, rising above 8,000 feet, are to the north and east some
20 to 30 miles distant.
The City of Tucson spreads over the alluvial valley floor through which flow the
Creek and the Santa Cruz River. The valley floor slopes downward from south to north at an average rate of about
20 feet per mile.
Since the Tucson basin lies within the Desert Lowland, the vegetation is characterized by creosote bush, palo verde, mesquite,
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DISTRICT SANTA CRUZ CO.
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Figure 7. Key map, Santa Cruz River Basin.
26 cacti, and desert grasses. Salt cedar and cottonwood thrive along the stream banks. With an increase in elevation, the vegetation changes from desert species to chaparral to pinon-juniper to ponderosa pine and finally to Douglas fir and white pine forest.
Within the urban limits wildlife, many varieties of birds, reptiles, and amphibians can be found. The black-tailed jack rabbit, the roadrunner, the western meadow lark, and the loggerhead shrike occur throughout the valley. Some game species are found in Tucson and adjacent basins, including desert mule deer, javeline, cottontail rabbit, mourning dove, and Gambel quail. Occasionally mountain lions roam down into the residential areas. The urbanization and agricultural development of natural lands has tended to displace the populations of these and many other species, but the increase in available surface water from irrigation has favored those species which are tolerant of human activity.
The study area characteristically has a long, hot summer and a mild winter. Tucson experiences sunshine during nearly 86% of the daytime hours. The
73-year record shows the average monthly temperature to vary from a low of
56 ° F in January to a high of
86 ° F in July. Crops tolerant of temperatures as low as
28°F can be grown from mid-,February through late
The annual average monthly humidity is
30%, and except for a few days of summer thunderstorms the relative humidity seldom reaches an uncomfortable level. Approximately
50% of the rain occurs from
July to September
(5.57 inches), nearly equaling that of the rest of the year
(5,56 inches). The summer rains are more sporadic and
27 torrential with short duration as the advecting
Gulf air mass meets the unstable convective air of the desert. The winter precipitation is widespread and moderate caused by frontal confrontation. The
105year records show that the seasonal coefficients of variation are
38.02% for summer (April-September) and
52.71% for winter (October-March); that for the entire year is
The regional high temperature and low humidity result in high evaporation rates. The average annual pan evaporation is
90.84 inches which equals
61 inches of potential lake evaporation using a pan coefficient of 0.67.
This means that evaporation is approximately six times greater than the average precipitation in the Tucson Basin.
A consulting firm (Bechtel Incorporated 1974, p.
1-12) did a thorough investigation of Tucson's social and economic setting in 1974.
Their report said:
• • metropolitan Tucson has a civilian labor force of over
150,000 with an average of over 4,000 workers actually seeking/finding employment each month in manufacturing, tourism, farming, construction, mining, government, education, warehousing, finance, astronomy, and retail services. Approximately
43% of those seeking employment are recent immigrants.
1 shows the employment trends in the Tucson metropolitan area. This table indicates a total employment of nearly
140,000 persons in
1975, in which the government has the highest number followed by wholesale and retail trade, services, and miscellaneous, manufacturing, construction, mining, and finance, insurance and real estate. Agriculture provides the lowest amount of employment. Data
Employment trends in the Tucson metropolitan area.
Transportation and utilities
Wholesale and retail trade
Finance, insurance and real estate
Services and miscellaneous
112,900 127,600 137,100 141,500 138,500
29 from the Arizona Department of Economic Security indicates that
1,600 persons worked in agriculture both in June
1972 and June
1973, while non-agricultural employment had
134,200 and 146,200 persons, respectively. Statistics from the Valley National Bank show an employment of
1,600 for agriculture in
Hence, it is possible that agriculture has a zero or negative growth rate in recent years.
The desert climate, plentiful labor, ample industrial sites, extensive transportation facilities, superior educational and training opportunities, reasonable taxes, and the fact that Mexico is only
60 miles away, all serve to attract firms to the Tucson area.
In 1972 the median income in Tucson was
This figure is consistent with the U.S. median household income in
1972 of $9,698
(Bechtel Incorporated 1974),
Forty-eight percent of the metropolitan
Tucson area's households enjoyed an income of
$10,000 in 1972. Most of the highest income households are in the northern and eastern parts of the city.
Table 2 indicates the market value of leading industries in
Pima County for the year 1974.
Agriculture offers a potential use for reclaimed sewage. The total farmed land in Pima County is approximately 60,000 acres. More than
96% of the land is in the eastern part of the county, namely, the
Continental-Sahuarita, Tucson, Cortaro, and Marana irrigation districts.
The recent distribution of crop acreage in Pima County shows a reduction in land used for cotton and an increase in grain and vegetable cultivation. The latter crops require less water than cotton and are more salable.
2. Market values of leading industries in Pima County,
Arizona Statistical Review
The state of Arizona now ranks first in the rate of immigration
("Americans on the Move"
1976). This is the result of the previously mentioned favorable climatic and socio-economic environments, and of the migration of old firms from populated and tax-loaded eastern small states to the Tucson and Phoenix areas. Also, many retired people move to southern and central Arizona in order to avoid winter snow hazards and take advantage of the dry desert air.
4 provide census data for past years. The
1975 populations are
452,000 for Tucson and Pima County, respectively; the majority of the Pima County population is located in the eastern one-third of the county comprising the greater Tucson metropolitan area, which extends beyond the city limits.
8 shows a
1975 population prediction of between
415,800 for Pima County, whereas the actual population was
This difference of
36,200 suggests that the population is growing very rapidly.
The city population increases partly because the City of Tucson expands its boundaries each year as shown in Table
The fast urbanization makes
Tucsonans more dependent on automobiles. Population density per square mile was
1960, 3,300 in
Water-Based Recreational Areas
The City of Tucson has a well-designed urbanization plan. As discussed previously, the National Recreation Association
(1952) proposed a
100 persons/acre standard for Tucson municipal parks with each
Population growth of Tucson and
4. Expansion of the City of Tucson incorporated area.
0 400 o o
/ • /
1960 1970 1980
Population growth of Pima County.
Source: Arizona Planning Division, Office of Economic
Planning and Development (1974).
35 park having at least one-fourth of the area available for playground or active sports.
Among the parks, only Randolph Park and Kennedy Park have recreational lakes, each containing approximately 15 to
20 surface acres.
Another recreational area is being developed in the northwest area of
Tucson near the city treatment plant. This park will also have a
20 acre lake. Lakeside Lake (11 acres) was opened for fishing after
16, 1976. This lake is situated on the east side of the city, and its facilities are still in the developmental stage.
DeCook (1970, p.
100) thought that a partially unfilled demand presently exists for the water-based urban recreational facility.
The other non-urban water-based local recreational areas in the Tucson region reported by Cox
(1969) are Rose Canyon Lake, Parker
Canyon Lake, Pena Blanca Lake, Riggs Lake, and Rucker Lake, Only the first three are within approximately a one hour driving radius of the city. Many
Tucsonans use them for picnicking and fishing. There are other more distant lakes in central, northern, and eastern Arizona.
For these lakes, the recreational activities include sightseeing, boating, swimming, camping, hiking, as well as picnicking and fishing
The "Tucson Trend Survey" (Tucson Daily Citizen
showed the average Tucson household spent
$515 on a vacation with an annual range from
$838. More than half of vacationing
Tucsonans traveled outside of Arizona, and nearly one-fourth vacationed in foreign countries. Almost two-thirds of the households took weekend trips outside
Pima County. The most popular vacation areas for
Tucsonans within the
state were the White Mountains
(7%), and Nogales
Description of Tucson Sewage
The Tucson treatment plant on Sweetwater Road is situated in the northwest corner of metropolitan Tucson, west of Highway I-10 and east of the Santa Cruz River. Further north the county treatment plant
(Ina Road) treated
0.4 MGD in 1970, but this capacity was increased to
25 MGD in
1976 (Ehrich, Kluesener, and Harper 1973).
The Ina Road plant was built to accept some of the overload wastewater from the
City of Tucson (Figure 9).
The Sweetwater Road plant now has a capacity of
36.9 MGD and may be enlarged to
45-50 MGD. All the data analyzed in this study is concentrated on the Sweetwater Road plant.
Methods of Treatment
The city plant is a secondary treatment plant with the final effluent being released after chlorination. It consists of three
Plant #1 is a conventional activated sludge plant with
"plug" flow and tapered aeration. This plant was completed in
1951, and has a handling capacity of 12 MGD. Plant #2 is a high-rate trickling filter process. This plant was completed in 1960 with a capacity of
Plant #3 was designed for the activated sludge process with step aeration. This plant was activated in
1968 and it can treat
10 depicts the plan layout of Tucson's wastewater treatment plant. The sewage influent is first screened to remove coarse
(County) 60 mgd
(Assumes 36 mgd)
Tucson regional wastewater flow through
Source: Bechtel Inc. (1974).
impurities. Then the sewage goes to the grit chamber for the removal
39 of heavy objects. Lighter suspended solids settle out in primary sedimentation tanks and are pumped to the sludge thickener.
Effluent from settling tanks flows to aeration tanks and trickling filters. The secondary treatment is also a biological treatment using bacteria and other micro-organisms to consume organic waste. Biologically treated effluent goes to secondary sedimentation tanks for the removal of suspended solids. After chlorination, the final effluent is released to the Santa Cruz River or used as irrigation water.
Sludge from the sedimentation tanks is pumped into thickener tanks and digesters. The concentrated sludge is broken down by bacterial action and methane gas is produced as a by-product. Finally the digested sludge is drawn to open beds for drying and Eventual use.
Table 5 shows the detention periods in the treatment plant.
On the average the wastewater requires between
7 and 9 hours to flow through the grit chamber to the final chlorination point.
Quantities of Treated Sewage
The sewage influent received at the treatment plant for the
1974-1975 period was
(31.1 MGD), The average Tucsonan returns
89 gallons per day
(GPD) to the sewage plant, which is slightly higher than the U.S. average of 75 GPD. In addition to the higher evaporation rate in arid Tucson, some additional factors also affect the quantities of water used. The per capita water use has declined since the city began charging sewerage fees based on the water meter
Wastewater detention periods in the Sweetwater Road treatment plant.
Source: City of Tucson (1975).
Stages common to Plants
#2, and #3
Primary sedimentation tanks
Secondary sedimentation tanks
Primary sedimentation tanks
Secondary sedimentation tanks
Primary sedimentation tanks
Secondary sedimentation tanks
41 reading. The still increasing water bill is having a significant impact on water consumption.
6 shows that the average amount of water received by the treatment plant was
85 GPD per person in the first half of the
This quantity increased to
102 gallons in
This increase was possibly induced by the gradually widespread acceptance of large-water-use appliances such as dishwashers and washing machines.
1971-1972 per capita water consumption began to drop, but due to the simultaneous population growth, the total sewage at the treatment plant did not drop at the same time, but instead lagged by two years.
The annual sewage flow was
It dropped to
During the same period, the population served by the facility increased from
349,520, or nearly
24,200 more people. This indicates that the economic externalities have a significant influence on water consumption. It is possible that future per capita consumption of water will steadily decrease if the scarcity of this commodity becomes severe.
The difference between the maximum and minimum daily rates of flow is rather small, and these rates are relatively consistent throughout the year. Although the summer:winter ratio of water production and distribution by the city water utility ranges from
3:1, consumptive use is much higher in the summer season, with the net result that the rate of influent flow to the treatment plant varies only slightly.
Sewage losses at the plant are very small, and these are compensated for by a well at the treatment plant. The gains and losses at the plant are considered to be balanced and the city records show that
Volumes of wastewater influent received at Tucson Sweetwater
Road treatment plant.
Source: City of Tucson
effluent flows have approximately equalled influent flows for recent
43 years (DeCook 1970).
Costs of Treatment
The unit treatment cost is the least for the active sludge system with step aeration and is highest for the standard active sludge, being $51.64/MG and $74.27/MG respectively for the 1973-1974 fiscal year. The unit cost for the trickling filter is
All of these are gross costs, i.e., capital outlay and operation and maintenance costs. The average cost for the whole treatment plant is
Table 7 presents the history of treatment cost at the Sweetwater Road treatment plant in Tucson. The gross unit costs were relatively stable until
In the year 1974-1975 the unit cost jumped by about twenty dollars over that of the previous year.
There was no capital outlay for the 1974-1975 fiscal year. All of these increases were derived from operation and maintenance costs.
The above costs do not include the cost of transporting sewage, as this cost is assumed to be balanced by revenue from sewage fees.
Qualities of Sewage Influent and Effluent
The sewage quality generally does not vary very much from year to year, but some of the pollutants do change. The quality characteristics are listed in Table
8. The sewage influent has an average concentration of
250 parts per million (ppm) for suspended solids,
33 ppm for total nitrogen, 21 ppm for phosphate, and a total
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Quality of influent and effluent sewage flows at City of
Tucson treatment plant,
All units are mg/1 except pH or as noted. Plants land
3 are activated sludge units. Plant
2 is a trickling filter unit. Source: City of Tucson
Total solids, evaporation
(105 ° C)
Total alkalinity (CaCO
Aluminum ana Iron
& Potassium (Na)
of 117 ppm for both sodium and potassium. The major differences be-
46 tween influent and effluent are in the content of suspended solids,
BOD, chemical oxygen demand, and volatile residue. Secondary treatment has less influence on other water quality constituents.
The frequency distributions of the major influent and effluent pollutants are shown in Appendices A and C. The sampling frequency was about four times per month. Twenty-four hour composite samples were analyzed. The time-span covered by this data is seven years
(1966-1967 to 1970-1971, 1972-1973, and
Since the plants have nearly identical capacities, the final effluent for the Sweetwater Road plant is assumed to be an equal mixture of all three of them. The statistical distribution is generally consistent between Plants 1 and
2 has a different treatment capability and its peak will shift to the right in the distribution figures. The average data will sometimes generate a second peak which is lower than the first with regard to the distribution of some of the pollutants. Most of the data is skewed to the right.
It is difficult to model the influent wastewater quality by any of the known probability distributions; the binomial, geometric, exponential, Poisson, normal, log-normal, gamma, and Gumbel were tried, but none of them gave satisfactory fits to the data.
Historical Distribution of Sewage Plant Effluent
Grain crops in this area were irrigated with raw sewage from
1928, when a primary treatment plant was constructed, treated effluent has supplied irrigation water for various
crops. The historical distribution of treated effluent since
1964 is shown in Table
Tucson Gas and Electric Company contracted for an amount of
1,200 acre feet per year at a price of
However, the company did not use the water covered by the contract.
On March 1, 1953, the City Sewer Farm requested a minimum of
2,310 acre feet up to a maximum of
3,200 acre feet of effluent per year for the irrigationof a farm of approximately
640 acres. The water was to be delivered at the rate of
$4.00/acre foot, at city expense, to the highest point of the land.
1, 1955, the Oshrin
Farms signed a twenty year contract covering all excess effluent under the above agreement. The purchaser agreed to pay $1.00/acre foot and to transport it to their
2,100 acre farm. The purchaser would also construct a regulating pond or detention basin for storage and control of any effluent water delivered but not immediately used.
1963, the Pima County Sanitary District
47 the conveyance and storage work and agreed to make the requisite allocation. The District acquired the right to purchase and resell any effluent water in excess of 13 MGD. Even though most of the effluent water was purchased by users, some of the water was dumped into the Santa Cruz River. Since 1973-1974, most of the treated effluent has been shifted to the Santa Cruz River due to a blockage in the transporting conduit,
Sewage effluent distribution of the Tucson treatment plant at Sweetwater Road.
Source: City of Tucson (1963
T & W
COST FUNCTIONS FOR SEWAGE TREATMENT
With technological advancement, the treatment of wastewater has shown great improvement in developing more economical and efficient equipment, to the point that it is now possible to bring such water up to drinking standards.
Primary treatment removes sedimentary solids and reduces
BOD by as much as 35%.
Secondary treatment consists of biological oxidation and settlement of the residual organic material, with a cumulative reduction in BOD of up to
In Tucson, for examples, Plants
3 are capable of removing up to
90% or more of suspended solids while Plant
2 can remove an average of
78% of the suspended matter.
1 and 3 reduce the
BOD of the effluent by
91% respectively, while Plant 2 averages 70%.
At the advanced or tertiary treatment stage, the general classes of critical parameters and the corresponding treatment procedures which effectively act upon them are:
Suspended solids removal--lime or alum coagulation, sedimentation (chemical clarification), sand or mixed media filtration, and microstraining;
Inorganic removal--electrodialysis, distillation, freezing, ion exchange, reverse osmosis, and demineralization;
Organic removal--activated carbon adsorption, advanced oxidation, foam fractionation, and filtration;
Nutrient removal--precipitation of phosphate, biological denitrification, air stripping of NH
, and sand filtration;
Removal of turbidity, color, odor, and toxic substances-activated carbon adsorption;
Removal of pathogenic micro-organisms--chlorination, activated carbon adsorption, and filtration.
The cost function for treating municipal wastewater can be described as follows:
,x 2 „..x
) (13) where C is the pollution control cost and xx
n are the levels of waste removal efficiency.
Capital costs and operation and maintenance costs are the two major costs for water pollution control. Capital costs are required for constructing the physical works, i.e., the plant and equipment.
These costs are amortized over the life of the structure. Generally these costs are fixed at a point of time, and are called point costs.
The capital costs consist of: cost of equipment or structure, design and engineering, contracting fees and supervision, land purchasing or site improvement, installation or placement of equipment, receiving, shipping, and transport expenses, start-up, and structure modification. Costs, such as initial engineering and design,
51 purchasing general overhead, and accounting, are usually assumed to be 10% of the capital costs. The indirect costs are depreciation, real estate texas, insurance, interest, and general overhead.
Operation and maintenance costs represent the day-to-day usage and upkeep of treatment facilities. Costs in this category include maintenance, plant supplies, labor and supervision, utilities, chemicals, and disposal of waste.
Most of the pollution control cost may be estimated by the design capacity and removal efficiency, In reality, the majority of cost-predicting equations are based on design capacity, probably because the chemical composition of the influent will be altered during treatment. This makes the calculation of efficiency impossible.
Municipal wastewater composition, however, is not significantly changed by treatment.
One thing that must be noted is that oftentimes cost functions cannot be explained only by design capacity and removal efficiency.
Other factors, such as water temperature, labor wages, pH level, topography, type of tubing and auxiliary equipment, and waste transport distance, can influence the total cost.
The Calculation of Unit Cost
The derivation of unit cost for wastewater treatment comprises the amortization of the capital costs and the calculation of operation and maintenance costs. These costs can be found in Table
B1 of the EPA Technical Report
430/9-75-002 (Van Note et al.
52 or in Table IV of
A Comparison of
Alternatives (Council on Environmental Quality
[CEQ] and Environmental
Protection Agency [EPA]
337) gives the amortization equation as a V o i(1 + i) n /[(1 + i) n
(14) where a =-- amount of equal annual or period payment i interest rate which varies from
5% to 10% n =. number of years of interest-bearing period; here the life expectancy of the treatment plant is usually set at
=-- value of sum of money when placed at interest; this value includes base capital costs and land costs.
In order to arrive at the annual capital cost (in cents per
1,000 gallons), the results from Equation
14 are divided by 3,650 Q where Q is the quantity of wastewater being treated in
The daily operation and maintenance cost, which consists of daily labor, electricity, fuel, solid and effluent transportation, and chemical costs, is divided by 10 Q in order to derive a unit cost expressed in cents/1,000 gallons. The final unit cost is the sum of the capital cost and the operation and maintenance cost,
Frankelts data (1965) are tentatively used for the cost functions (Figure
11 to Figure
The estimates for the 36 MGD
Tucson treatment plant are obtained from these curves. In order to account for the inflation that has continued since the energy crisis in the
201 u! 'ClOW ed .poo ionuuo
I o o o
o re) n
! o re)
N o sJoi lop
J ed 4
o o o
smi lop L
0 a) sJoi lop
201 u! 'COW
ied .poo ionuuo 10401
01 u! `Govi
.poo ionuuo 1E401
1 o 5
104 io 3
30 40 50
Annual cost of treatment/MGD, in 6 3 dollars
Figure 16. Cost of coliform removal.
Curves are after Frankel (1965, Figure 8).
59 winter of
1973-1974, the present value of Frankel's data is estimated by
PV = B(1 + i) n
(15) where B is the initial investment; i is the inflation rate; and n is the difference in years from the present to the year the cost data was collected. Generally, i is set around 5% to
6% per year.
(ENR) is frequently published and updates the ENR
Cost Index. Cost estimates can be updated by multiplying the base cost by the ratio of the current
ENR Index to the index which prevailed at the time that the base cost was formulated.
The EPA also publishes a Sewage Treatment Plant Construction Cost Index
(STP) which can be used in the same way as the
It is obvious that the marginal cost corresponding to removal efficiency will increase abruptly after utilizing the secondary process. For some of the pollutants, the cost of removing 90% of their concentration would be relatively small, but removal of an additional
2% would cost twice as much or more than the removal of the first 90%.
CEQ and EPA
(1974) indicated that if the plant size changes by a factor of x, the cost will change by a factor of x n
where n varies from
0 to 1.
For a treatment plant of a size smaller than
100 MGD, n is equal to about
0.6, and for plants with capacities greater than
100 MGD, n will approach unity. Assuming a value of n equal to 0.6, a plant of size A MGD will cost x dollars, while a plant of size
B MGD will cost $x(B/A)
The unit cost for a plant
60 of size B will be $x(B/A)
/B or $x
)/MGD. If a size A
MGD plant is represented by a unit cost of x/A dollars/MGD, a size
B MGD plant will have a unit cost of
Therefore, based upon Frankel's
1965 data for a
MGD plant, the unit cost for a
36 MGD plant is
(1 + 0.06)
0,69 times that of the
2.5 MGD plant.
It is assumed in these calculations that the reduction of each individual pollutant has the same factor as the whole plant has with the increase of treated volume.
BENEFITS TO BE DERIVED FROM SEWAGE RECLAMATION
Considering the five reclamation measures mentioned previously, the most practical uses of treatment plant effluent for the Tucson region are irrigation and recreation lakes. A psychological barrier still exists against the use of treatment plant effluent as a domestic water source (Schmidt,
Kugelman, and Clements 1975; Stone 1976).
Perhaps recharging groundwater along the sandy river bed with effluent represents an alternative which the public might accept for the conversion of wastewater into drinking water. First, this will reduce the degree of psychological unacceptability, and second, a few feet of soil profile does improve water quality as has been indicated by the
Narrow Project in Los Angeles (Frankel
1967) and by the Flushing Meadows Project in Phoenix (Gilbert et al. 1976).
The possibility of industrial use has not been ruled out, but up until now, it seems that no industry has adopted sewage plant effluent in the Tucson area. Tucson Gas and Electric Company had contracted for some of this water but did not use it. Most of the copper mines around Tucson are at higher elevations than the city, and the costs of pumping against gravity may make their reuse of sewage plant effluent unfeasible, at least for the present.
Commercial fishery may be possible for warm water species such as
and channel catfish.
Hallock and Ziebell (1970)
62 did fishery research in Tucson using tertiary treated wastewater.
The total produce reached
697 pounds per acre per year with the addition of extra fertilizer. Cold water fish such as trout will not survive in the warm water temperatures that accrue during the Tucson summers.
The impact of reclaimed wastewater upon wildlife needs to be investigated.
Szot (1975) did wildlife perception research in urban
Tucson. His conclusion was that
Tucsonans like wildlife, birds, and small animals, but not snakes. Because these values are intangible, no monetary estimate was given. A possible benefit of effluent lakes would be their potential as water bird habitats. The chances for game animals are less since most of the disposed water bodies are within densely populated areas.
When a soil-plant scientist considers the growth of a certain crop, he most generally assumes that a sufficient supply of water is available. He is concerned only with the adequacy of macro-nutrients, i.e.,
N, P, K, C, H, 0, Ca, Mg, S, and micro-nutrients such as B,
Zn, Cu, Fe,
Cl, and Co. Among these the most important for a semiarid region are
P since the soil usually contains enough Ca, Mg, and
Water and atmosphere supply
H, and O. This corresponds to domestic sewage which also emphasizes the importance of
N and P.
(1936) makes four assumptions: 1) nutrient uptake is proportional to and dependent upon the amount of nutrients in the soil; 2) plants absorb nutrients in excess of their metabolic
63 requirements as long as a supply in the soil exists;
3) there is a minimum level of nutrients required by plants to sustain life; and
4) the percentage sufficiency of nutrient is a function of its percent composition in the plant. Figure
17 depicts the relationship between plant yield and amount of soil nutrient as envisioned by Macy.
In Zone I of Figure
17, an increase in a given nutrient will result in increased plant yield but not an increase in the nutrient content of the plant tissue. In Zone II, both plant yield and plant nutrient content will increase with an increase of that nutrient in the soil. In Zone III, the plant absorbs more nutrient than it needs, concentrating that nutrient in its tissues, but not increasing its yield. This is the region of luxury consumption. Probably there exists a fourth zone for which additional nutrient above Zone III will cause physiological drought and drastically decrease the yield. This is usually referred to as "fertilizer burning."
In another relationship, Bray (1945, 1948, 1962) has modified
Mitscherlich's equation to result in log (k - y) log A
- c i b cx
(16) where A is the yield possibility when the supply of a nutrient is adequate, y is the yield obtained, c l is the proportional constant, b is the amount of nutrient in the soil as measured by a soil test, c is the efficiency factor for the method of applying the fertilizer, and x is the amount of fertilizer needed to attain a certain yield of y. Mitscherlich defined the value A as the ultimate plant yield when all growth factors are optimum. Bray defined A as the yield possible
pia!,k % cU ts0
65 when all nutrients are present in adequate quantities but not in harmful excess. Many other factors govern the yield possible in addition to the soil fertility and the amount of fertilizer (Bray
If the soil fertility is assumed to be constant for a certain series of soils, the yield can then be correlated with the application of fertilizer. Kelso, Martin, and Mack
204) studied desert irrigated farms; they found that no major geographic pattern of different soil productivity levels exists, and that the data from the farm survey, based upon soil conditions, provide no evidence indicating differences in productivity levels between different farm-sized groups. Hence, the equation for the Tucson region may be simplified as log (A - y) log A
(17) where A, y, c and x have been previously described. If this expression is found to be inadequate, a computer program could be written to handle the fertility differences among sub-areas.
Agricultural Statistics of the Tucson Area
In a free market such as the United States it is very difficult to regulate the farm regime by any agency. Farmers make their own decisions regarding what to plant, how to plant, and where to plant on their farm lands.
Linear programming, which gives optimum returns from management under given constraints such as acreage of available land, quantities of available water, value of products, and the fixed and
66 variable costs used for production, seems less successful if it is applied to many individual farmers. It is possible for one farmer to optimize his own operation by linear programming. The six-year
(1969-1974) averaged acreage for each crop type is listed in Table
10 for the Tucson region. This average is assumed for the general usage of land since the total acreage of certain crops changes from year to year.
The farm land proposed for the use of reclaimed sewage water is on the down slope side of the treatment plant, i.e., Cortaro and
Marana irrigation districts. This will save the cost of pumping against gravity and will also lessen construction costs as an existing water delivery system can be used.
Most of the farming operations in the Tucson region are of the winter type, starting in October and continuing until June. Some corn, lettuce, and sorghum are planted as summer crops, but the acreage is much less than for the winter crops. This means a fixed cost for a storage pond is necessary. A possible means of compromise would be to develop a large recreational pond in the northwest part of the city and to cooperatively use this pond for storage.
The value of crops varies each year, but generally these values show an upward trend
The 1975 Arizona Agricultural Statistics (Mayers
1976) are used here. Costs for producing these crops are from Arizona
Field Crops Budget, Pima County (Hathorn and Armstrong 1976) and others.
The net value accrued by treatment plant effluent is the difference between total revenue and costs.
The proposed crop acreage and amount of irrigated land are shown in Figure
18 and Table
Consideration of Pathogenic Organisms with Irrigation
One topic which should be discussed is the possibility of contamination by pathogenic organisms from the use of reclaimed water.
Bell (1976) conducted a study in a semi-arid prairie region and concluded the fecal coliforms were completely destroyed by exposure to
10 hours bright sunlight. Larkin, Tierney, and Sullivan
(1976) said that polio virus could survive for
14 days in lettuce and
36 days in radishes. During this experiment, however, there were many cloudy and rainy days.
The Tucson region has at least
86% cloudless days throughout the year. By Bell's inference, the supposition that no enteropathogenic contamination will occur may be justified if we assume that all irrigation is stopped two days before harvesting.
Next to water supply, the social value of recreation is ranked second among the many beneficial uses of sewage effluent; the economic value of recreational use is also ranked second after water supply. As indicated in Table
11, a survey by Stone (1971) pointed out that sanitary engineers do not recognize the fact that the economic value of recreation use is as great as the social value. Hence, it would appear that sanitary engineers should become more cognizant of the fact that social and economic values are very closely related. Therefore, the
The farmed lands in the Tucson region.
Blackened area is the assumed land for irrigation with reclaimed wastewater.
(1969-1974) averaged acreage of the crops planted in Tucson region with each crop's unit water consumption and
1975 product values,
Matlock (n.d.). Marana includes Townships
Cortaro includes Townships
1212, 1213, and 1313.
Hathorn and Armstrong
Socio-economic evaluation of the beneficial uses of the nation's water resources,a
Recreation (unlimited boating)
Recreation (limited boating)
Transportation (waterways, harbor)
b Weighted average is the possible range of 1
(lowest value) to 10
Rank is ranked in order of
(highest value) to 9 (lowest value).
71 reclamation of municipal sewage should be heavily weighted on the recreational side.
The most prominent example of the recreational value of reclaimed effluent water in the United States is the Santee Project in
San Diego County, California (Merrell and
That project uses
0.4 MGD effluent to furnish water for a 30-acre lake. More than
50,000 people visit there each year. The most popular activities are boating, picnicking, and fishing. No health hazard has been found for these recreational uses on this lake. The fish product is
400 pounds per acre per year. This example suggests that the recreational use of
Tucson sewage treatment effluent would also be feasible.
Recreational lakes probably should have the maximum priority in the development of Tucson urbanization as discussed in Chapter
This is based upon the rate of urban spreading and the lack of available surface water bodies in the Tucson vicinity. The northwest side of Tucson and the area towards
Valley havethe shallowest groundwater table in the entire region. This shallow water table makes pumping more economically profitable. Hence, using treatment plant effluent for recreational lakes and leaving groundwater for domestic use might be the most prudent management of the water resources.
Using a direct method,
DeCook (1970, p.
103) estimated that the net returns from a recreational pond in the City of Tucson would be
$502.83 per acre foot per year for a 20-acre, conceptual Randolph Park lake. This means
$15,085 per surface acre per year without considering the construction costs. Using an indirect method, Martin, Gum and
Smith (1974) estimated the
1970 monopolistic value of warm water fishing to be $364 per acre per year and that of general outdoor recreation to be
$2.33 per acre for Game Region
(Pima County). The
$366.33 per surface acre per year is much less than
Since DeCook's research was in a heavily populated area, it would possibly represent the maximum net benefit for a good, urban recrea-
72 tional lake. Any deterioration in water quality such as algae blooming, high turbidity, low fish survival rate due to surfactant, low dissolved oxygen, and high concentration of coliforms would decrease the value of
$15,085 per surface acre per year.
Algae blooms will kill fish, forbid water contact activities, and discourage people from access to the lake due to the unpleasant odor. The most important factors governing algae blooms are phosphate and nitrate (Hudson 1969, p.
Generally, phosphate is much more important than nitrate since some blue green algae can fix nitrogen.
Borchardt and Azard (1968) indicated that the critical level for algae growth is 1.5 mg/1 of PO 4
1/5 to 4/5 mg/1 is the luxury uptake region; above 4.5 mg/1 the solution will have phosphate residue.
Nesbit (1969) showed that nuisance growth could be controlled when the phosphate concentration in the water was less than
0.5 mg/1 and that algae growth would be stopped when phosphate was less than
0.005 mg/l. The rate of algae growth is exponential (Maloney 1966).
Hence, Bray's modified yield equation could be applied by assuming
0% of the growth possibility when phosphate is
0.5 mg/1 and 98% when phosphate is 4.5 mg/l. The equation, therefore, is
(100 - y) = 2.23 - 0.46 PO
4 (18) where y is algae yield and
100 means 100% of the algae growth possibility. The recreational value of warm water is assumed to be maximum at
0.5 mg/1 of PO
4 when no algal growth is present, and zero when the growth rate reaches
The relationship between
NH 3 -N and algae growth indicates that the highest growth occurs when the level of
NH 3 -N ranges from
20 mg/1, and the lowest when the concentration is below
5 mg/1 or above
40 to 45 mg/1 (Golueke,
Oswald, and Gee
1967). The growth equation is given as log
(100 - y) = 2.532 - 0.135 N (19) where y is the percentage of algae growth possibility. Algae bloom is assumed when y reaches
Y ranges from
The presence of surfactant in the water counteracts its recreational value in two ways:
1) it inhibits algae growth by increasing oxidation (Maloney 1966); and 2) it kills aquatic animals by damaging their respiratory organs (Truelle
Associated foaming will also reduce the appeal of the water for recreation uses. Laws recently enacted in the United States require that all surfactants be changed from alkyl benzene sulfonate (ABS) to linear alkylate sulfonate
(LAS). Therefore, surfactant was no longer tested for in the Tucson sewage treatment plant (Trueblood
The removal rate of LAS is much higher than that of ABS: about
95% of the LAS is removed from standard activated sludge and 97% from
septic tank drainage (Klein and
The surfactant impact, therefore, did not merit further consideration in this study.
The effect of coliforms on recreational water has been studied by Mechalas et al.
Figure 19 is taken from Figures 11 and 16 in Mechalas et al.'s report. It indicates that the total risk of illness for virus and Salmonella is
12 per 100,000 when fecal coliform is around 5.8.10
MPN/100 ml, where MPN stands for the most possible number. Extrapolation of the data indicates that when fecal coliform is around 200 MPN/100 ml, the risk of illness would be
1.5 per 10 million people and would be due only to Salmonella. In this study, the FWPCA criteria (ORSANCO
Water Users' Committee 1971) are used.
Thus, the maximum recreational value is assigned to water that contains up to 200 MPN/100 ml fecal coliforms.
If the fecal coliform count is less than
2,000 MPN/100 ml, the water may be allocated to general recreational uses but with its value reduced to half of the maximum potential. It is very difficult to assign a zero value to water highly contaminated with fecal coliforms since other activities such as walking and picnicking can substitute for water contact activities.
The relationship between the degree of coliform contamination and recreational use is assumed to be exponential.
Tucson sewage plants do not routinely monitor the concentration of coliforms. The only data sampled in mid-March
1976 showed a wide range from
1,355 MPN/100 ml fecal coliforms for the treated effluents. Zero and
100 MPN/100 ml had the most frequent appearance
B). If the results of Santee Project can be transposed to
1 iforrns, MPN /100 ml
• total risk
• virus risk
forms, MPN /100m1
19. Risk of illness and the concentration of coliforms.
After Mechalas et al. (1972, Figures 11 and
Tucson, the assumption that no health hazard is posed by pathogenic organisms could be established.
Biochemical oxygen demand is the measure of the strength of
expressed by the amount of oxygen needed for bacteria to decompose energy generating compounds. The most important role of
BOD is its effect upon fish. If
BOD drives down the dissolved oxygen content of the water below
3 mg/1, few fish can survive. Hence, no fishing value can be assigned to such water. An anaerobic condition will generate foul odors which will in turn repel people from the recreational area. On the other hand, BOD is also a measure of water fertility. Oswald and
Golueke (1966) showed that the algae growth potential was linearly proportional to BOD. Therefore, BOD also affects the degree of algae blooming. The economic impact of
BOD is not considered in this study because it can be related to fertility, i.e., nitrogen and phosphorus.
Suspended solids (SS) can choke fish and reduce the aesthetic value of a lake. The British Standard sets suspended solids at
McGaukey (1971) took 20 and 100 mg/1 for values of the noticeable and limiting thresholds, respectively, in the evaluation of recreational water. The resulting equation is log
(100 - y)
= 2.7156 - 0.0241 SS (20) where y is a measure of the water condition; it is obtained by assuming a
98% reduction in recreational value if the concentration of suspended solids is
100 mg/1 and by 2% if it is
Acreage of Suggested Lake
If the plant reaches its maximum treatment capacity
(36 MGD), the effluent could create a
1,378 acre (2.15 square miles) lake. This assumption is based upon the local climate and the projected seepage rate. Assuming a
10-foot deep lake and total replacement of the water once every year, the water volume will be the equivalent of a lake with a 20-foot depth. DeCook (1970,
103) estimated 0.035 foot/day for a long-term seepage loss or
12.8 feet per year. Adding loss due to evaporation, the total loss will be
18.6 feet which may be rounded to
20 feet per year.
If the recreational lake also served as a storage reservoir for the assumed farmed land previously discussed, the lake surface area would be 999 acres. This lake would be filled in late March but would shrink to 25 acres by early October. The calculations required for determining the acreage of lake surface take the following steps;
Calculate total crop consumption of water for each half month (Table
12 times Table 10).
Calculate total effluent for each half month (assuming 36
Check which half month is the end of a series of negative supply of the sewage effluent by subtracting Step
Step 2 (September
16 in this study).
Choose the following month as the starting period (October
1 in this study).
5. The difference between Step 2 and Step 1 is divided by the sum of the assumed lake depth and loss which is the addition
E o o
SE o o ga, o o o
0 rn en en
0 an en a,
0 cn an
N an an eL4
an an an
-E ar n4
01 0 en
0 07 ul
N lan Q
9 an n4 CO
n g ,,, W .
,.. 0 o +...
<50 a +.,
C c0 c., a;
79 of potential lake evaporation (Table
13) and seepage.
The quotient is the lake surface area (Table
Time the lake surface area with the assumed ten feet depth of water in order to derive the amount of water stored from last period. Add this storage to the difference of Step
1 and Step
2 of the coming half month.
Divide this volume of water by the sum of lake depth
(10 feet) and the water loss of the succeeding half month. The quotient represents the surface area of the next half month (Table
Repeat Step 6.
Costs of Constructing a Lake
For a surface reservoir in which seepage losses are minimized,
Cluff (1968) gives the following estimate:
/acre foot, 10 feet depth @ $0.40/ yd 3
including short haul and light compaction.
The cost is
Sealing (material and labor): natural clay and Wyoming bentonite,
, $2,400/acre, polyethylene film liner
@ $0.014/ft 2
of $1,800/ acre, PVC 10-mil black plastic liner
Bank trimming and landscape: $500/acre.
Total, using the highest figure:
Average pan and lake evaporation for Tucson region,
Lake Evaporation (in.) b
80 aUniversity of Arizona Station,
0.67 of pan evaporation.
Acreage of hypothetical lake surface .
Accommodated to the volume of Sweetwater Road treatment plant effluent and the consumptive uses of crops in Cortaro and Marana irrigation districts, Tucson region,
Arizona. Based on the following assumptions: seepage rate
= 0.035 feet/day lake depth effluent rate
---- 10 feet
36 MGD irrigation on 1st and 16th of each month
$1,000/acre foot for
10 feet reservoir depth.
5% for 20 years, this will be
The total cost is
$83.25 per acre foot per year, or
$832.50/surface acre. Inflated to the prevailing
1970 cost at
5% rate to match
DeCook's data, the cost is
Total Benefits to the Tucson Area
The total benefit generated by each parameter is the sum of the agricultural and the recreational revenues.
15 gives the crop yield equations using phosphorus and nitrogen as independent variables. Since published yield equations were not available, Bray's equation was assumed to be valid. Table
16 gives the basic data used in Bray's equation. It is assumed that the yield in Table
16 is 98% of the maximum yield.
The number of pounds of fertilizer required can be changed into ppm by dividing by the weight of water consumed. Wheat, for example, needs
105 pounds nitrogen for a 5,000 pound production.
12 gives 2.1 feet of water for the growth of wheat. Assuming that the effluent has a weight of
62.4 pounds per cubic foot, calculations indicate that in order to produce
5,000 pounds of wheat, the required water must contain 18.39 ppm nitrogen.
Crop yield equations using nitrogen and phosphorus as independent variables.
Nitrogen and phosphorus given in ppm.
Log (6.12 - y) --- 0.787 - 0.741 P
Log (2433.67 - y) = 3.386 - 0.217
Log (2433.67 - y) = 3.386 - 0.9232 P y = 3436.2 + 38.3358 N - 0.0874 N
Log (7755 - 7) =--- 3.889 - 0.228 P
(4081.63 - y) = 3.61 - 0.0624 N
Log (4081.63 - y)
--- 3.61 - 0.569 P
(165.82 - y) = 2.22 - 0.0134 N
Log (165.82 - y)
= 2.22 - 0.0396 P y = 2535.65 + 11.507 N - 0.031 N
Log (3637.47 - y) = 3.565 - 0.1546 P tons/acre lbs/acre lbs/acre lbs/acre cwt/acre lbs/acre
No data available, assume a constant yield at $362.81/acre
Log (4.35 - y) ---- 0.6384 - 0.333 N
Log (4.35 - y) = 0.6384 - 4.679 P tons/acre
Log (2244.9 - y) = 3.35 - 0.3215 N y
= 16.5479 + 0.0974 N
- 0.00012 N
' lbs/acre c tons/acre
Log (38.8 - y) = 1.589 - 0.409 P
No data available, assume a constant yield at
Denotes fertilizer applied in lbs/acre.
Thompson, Jackson, and
Huszar, Skold, and Danielson
Nelson, Jackson, and
Crop yields associated with fertilizer applied and the costs of operation and material.
6.00 tons lint 900 lbs seed
4.26 tons h
200.0 16-20-0, 41 N
200.0 16-20-0, 73 N
200.0 16-20-0, 125 N
31 P, 200 N
175 N e
, 77.7 P f
205 C0(NH 2 ) 2
400 N, 40 P i a
Hathorn and Armstrong (1976).
b Wright and Stubblefield
Starkebaum, Skold, and
d Mayers (1976).
Huszer, Skold, and Danielson
MacGillivry, Sims, and
gRaguse, Berry, and Street
Assume the yield of All Hay in Mayers
Hathorn (1976). Assume pecan is 13 years old.
Jackson, and Gebert (1976).
For orchards, no yield data could be established. It is assumed that a
$361.81/acre yield may be obtained based upon data for navel and sweet oranges. Both are assumed to give constant yields with the increased fertilization from the effluent water. This estimate may be in error, but there seems to be no better alternative.
Several points should be observed concerning the use of
All of the assumptions made by Bray are assumed to be valid.
The yield is assumed to be zero when the calculated yield is less than zero, and the costs shown are only the operation costs.
The yield will increase continuously with an increase of phosphorus. This is one of the limitations of Bray's equation because it assumes an exponential growth curve.
The total yield calculated from nitrogen equations initially increases with an increase of nitrogen, and then decreases as more fertilizer is added. This is the result of using a second order polynomial equation for wheat, corn, and sugar beets.
The maximum yield of cotton is the sum of
900 pounds of lint and 1,485 pounds of seeds. The price for lint is
$0.50/pound and for seed, $100.00/ton. Using the weighting method, the price for each pound of cotton generated from the yield equation is
All of the operation costs are converted to
1976 values by a
6% inflation rate.
The yield equation for corn is taken from a Colorado experiment. Its constant, therefore, is adjusted to the yield of Pima County as published in
Arizona Agricultural Statistics (Mayers
On an annual basis, a 566-acre lake can be assumed to be the optimal area for generation of revenue. These
566 acres are the average of the half-monthly lake sizes listed in Table
100 people/acre standard for Tucson park land and a conjectured population of about
392,000 for the
36 MGD effluent capacity, the total park land area for Tucson would be
3,920 acres. Assuming that
5% of this land is allocated to a recreational lake, the lake surface area would be
As seen in Table
14, the maximum lake storage volume required would be
1,000 acres and would occur on March
The lake is divided into two parts: one for recreation and the other for irrigation storage. If water is clean, the total revenue generated by this effluent lake wouldbe (15,085 - 917.84)-196, a net of
18, 19, and
20 are used to calculate the effects of phosphorus, nitrogen, and suspended solids on the recreational revenue.
The inherent problem here is in the extrapolation of results from a 20-acre lake to a much larger lake. In other words, a perfectly elastic demand is assumed.
18 give the benefits estimated from the effects of nitrogen and phosphorus. Table 19 gives the total benefits generated from the reuse of the wastewater.
Benefits estimated from nitrogen by using Tucson Sweetwater
Road treatment plant effluent .
Benefits estimated from phosphorus by using Tucson Sweetwater Road treatment plant effluent.
Benefits estimated from crops and recreation lake by using
Tucson Sweetwater Road treatment plant effluent.
Due to Nitrogen
Net Revenue (Dollars)
Due to Phosphorus
Due to Suspended
RESULTS AND DISCUSSION
In this chapter the results of the Tucson case study are presented, and the merits and defects of using this multi-criteria water quality index are discussed in detail.
The Derived Multi-Criteria Water Quality
For each parameter, an optimum benefit for a given treatment can be derived. It is assumed that the parameter which has the highest net benefit covers the other benefits derived from the concentration reduction of the rest of the parameters. If not, these other discrete benefits should be added to this highest one.
Figure 20 shows the maximum net benefit to be 1.83.10
6 dollars when the suspended solids are removed to
87% of the influent mean, or
30 ppm. This is generated by recreation alone since the suspended solids are considered neither detrimental nor beneficial to the crops.
21 shows the optimum net benefit to be 9.77.10
5 dollars for recreation when nitrogen is removed to
90% of the influent mean, or 3.8 ppm. The fixed cost of constructing a storage lake, plus the operation and material costs of farming, render the value of crop yield less than these costs when the concentration of nitrogen is less than
20 ppm. The recreational revenue drops quickly with the increase of nitrogen concentration so that it adds little to the total revenue.
I t t I I I
0 10 20 30 40 50 60 70 80 90 100
Benefit and cost curves for the removal of suspended solids.
10 20 30 40 50 60 70 80 90 100
Benefit and cost curves for the removal of nitrogen.
The maximum net benefits for the total and for agriculture are the same,
5 dollars at zero removal rate, i.e.,
22 shows the maximum net benefit to be
5 dollars for recreation when phosphorus is removed to
98.6% of the influent mean, or
The total and the agricultural benefits are
5 dollars at a zero removal rate, or
The Multi-Criteria Water Quality Index, therefore, is
, WQI= 0) for the Tucson region. Appendix
C shows that the Tucson Sweetwater Road treatment plant can reduce its suspended solids to a level of
30 ppm approximately
50% of the time.
Most of the time, however, it cannot reduce nitrogen and phosphorus to their optimum concentrations for recreational uses. However, the treatment plant exceeds the optimum agricultural requirements for nitrogen and phosphorus
100% of the time.
Further Considerations on
A possible bias, if this method is applied, is that the economist tends to maximize his regional benefits to make the
MCWQI more appealing for getting funds. This problem is difficult to solve.
If calculations are made along the lines described herein and use is made of historical data, the real world situation will differ little with the one deduced from the calculations.
MCWQI is the result of two items: the WQI and the net economic value. A region which has relatively good water quality and potentially high net benefits should gain pollution control funds first since this allows for the best use of the public money. The
Phosphorus Removal, %
22. Benefit and cost curves for the removal of phosphorus.
factors of good water quality and poor economic conditions will mask
96 the purpose of water pollution control. In this situation, the
MCWQI will indicate a need for taking action in this region when the underlying problem is not water quality at all. Limited water pollution control funds should not bear the responsibility for boosting the economy of a region. Other measures should be taken to solve purely socioeconomic problems. Probably most rural areas fall into this category.
One must remember the derivation of this
The MCWQI represents the most profitable point to which polluted water should be corrected. If the original water is physically, chemically, and biologically clean, the maximum net benefits will probably occur around the zero removal rate. Any further installations at the treatment plant will reduce the net benefit to the region having good water quality.
If the economic analysis shows a net gain at a point where the water quality is not improved to a good standard, the
MCWQI will be higher and will mask the needs of water treatment. A possible example is that of industrial ore processing water. Since the WQI accounts for the presence of coliforms which are not considered to reduce the quality and quantity of the product, the poor water quality will not be revealed by
MCWQI. The fishery ponds in the Far East use night soil to fertilize phytoplankton. While such water is of poorer quality
, in terms of bacterial contamination, it may be ranked higher than less contaminated water by the
MCWQI due to the fact that the purer water has a lower economic value in terms of its potential for use as a plant growth supplement.
The worst water condition occurs when both the economic revenue is low and the corresponding water quality is bad. The regional
MCWQI will be the lowest. This region should be the last one for the allocation of water pollution control funds because no monetary benefit will be generated by treatment measures. This argument can go to the other side. Since the original water quality is so bad, some pollution control actions are urgently needed by society and nations because environmental correction has no national boundary for the sake of human posterity. But this argument still goes back to the original question that, if the law requries water pollution control, where should limited funds be used first? Water pollution control measures' are very costly. If a region can generate some compensation for this expenditure, actions surely should be taken in that area. Gradually water pollution control will shift to the lower economic benefit areas. The MCWQI does account for these characteristics.
Nationally speaking, secondary benefits add nothing to the income if full employment is a matter of public policy. But the transferability of secondary benefits from one region to another does emphasize their importance from a regional standpoint (Gregory
The water quality index used in this
MCWQI will cause regional incomparability if the composing parameters are different in different regions. This problem can be solved by fixing the number and kind of parameters for a national scale since most municipal wastewater in different localities generally has similar characteristics. These
98 are pH, nitrate, phosphate, coliforms, suspended solids,
BOD, temperature, turbidity, and DO. Some differences rarely occur but inimical constituents, such as trace elements, pesticides, and phenol, should automatically shift the
WQI to zero when they exceed a certain level.
Since they are not routinely measured, except when a dangerous situation is suspected, they are only weighted as one or zero in the
On the other hand, even when the
WQIs have different constituent parameters
, the final MCWQIs are still comparable.
Maciunas and Deininger (1976) argued that the comparison of different
WQIs is just like the comparison of an apple and an orange. The
MCWQI changes both apple and orange into monetary values which render them comparable.
The potential value of the water can only be realized when there is demand. This means that when we consider possible revenue sources, we consider which parameter is important to each source since consumers will not allow any one parameter to endanger their lives and properties. The MCWQI makes double checks on the composing parameters:
1) considered in terms of the water's sources; and 2) considered in terms of the water's uses.
The calucaltion of
MCWQI takes more time and labor than
Most of the work will be spent in the appraisement of intangible values . It is very possible that different economists will derive different economic values as a result of differing points of view.
435) added that the difficulty posed by including
99 these intangibles does not introduce a serious error in the benefitcost ratio (although this has certainly been the case in some past instances), but rather that the inclusion of non-market values tends to throw a cloud of suspicion on the otherwise careful analysis.
Compared with agriculturally generated revenues, recreational lakes will generate the highest net profit for each acre of laud in the Tucson region. It would seem that all the reclaimed water should be reserved for recreation lakes instead of being partially shared with agriculture. The agricultural reuse of the treatment plant effluent will cause partially emptied lakes, not only reducing the total recreational revenue but also impairing the aesthetic value of the whole recreation area.
It is also very possible that the formation of such a large recreational lake will lower the per acre revenue in the Tucson Basin.
Skeat (1969, p.
150) stated that the "completion of a navigation project, the price for the rail haulage of freight falls and thus the charge applied to water haulage in the original benefit-cost analysis do not show the anticipated money saving in practice." Thus, the probable value will not reach
$15,085 per surface acre per year as estimated by
DeCook (1970) after the completion of an approximately
The other thing worthy of mention is the complicated situation added by other pollutant sources, if they exist, downstream.
Pollution has far-reaching effects not only in the generating watershed, but also in the watershed that the pollutant passes through.
The socio-economic considerations should include all of these transit
watersheds. How do we attribute the socio-economic damage of water
100 pollution to the headwater point source or to the downstream point sources? This is a problem. Perhaps we should use such models as those advocated by Beck and Yong (1976) and Bishop and Gremey (1976) to predict the concentration of pollutant downstream from the residual discharge point and incorporatively weight this into the concentration generated downstream. Fortunately this situation dOes not occur in the Tucson region since most of the water will quickly sink into channel beds, and also because of the assumption that a reservoir would be provided with a sufficient volume to hold the treated effluent.
CONCLUSIONS AND RECOMMENDATIONS
The water quality index
(WQI) has been used as a tool for the management of water resources. The Multi-Criteria Water Quality Index
(4CWQI) developed in this study is a supplement to
WQI for lending more versatility, not only in water quality but also in economic feasibility.
The MCWQI consists of two components: the
WQI and the maximum net benefit generated from the possible uses of the water.
Following a review of the literature,
Walski and Parker's WQI (1974) has been adopted. As indicated earlier (Equation
11), the multiplicative
WQI has the form:
[iiri[fi(Ci)] where C. is the concentration of the ith parameter; f.(C.) is the
11 rating curve for the ith parameter; a i is the weight associated with the ith parameter; and n is the total number of parameters. Considering municipal wastewater, the parameters include nitrogen, phosphorus, suspended solids, coliforms, and dissolved oxygen. The rating curves for these parameters are exponential.
Landwehr, Maciunas and Deininger
(1976) said that the best result will occur when each one of the a.
102 equals one. This
WQI will range from zero to one, i.e., from the worst to the best water quality.
When determining the value derived from the utilization of a water resource, one should consider water supply, recreation, irrigation, industrial use, waste disposal, transportation, and commercial fishery. The allocation of water is based upon the society's demand for each of the possible uses. Generally, the one which has the higher demand will offer higher revenue.
Within each kind of use, the benefit increases with the improvement of water quality and the cost of improvement goes up accordingly. This is generally true except in the case of nutrient removal from water for agricultural uses. Here, benefit-cost analysis is employed to determine the optimal net benefit and associated concentrations. The MCWQI is the product of the maximum net benefit resulting from treating one of the pollutants for specific uses and the
WQI of the optimum concentrations for each important pollutant.
Following are the major findings drawn from the study.
Walski and Parker's (1974) WQI is sufficient for indicating chemical and biological water quality. The Multi-Criteria Water Quality
Index is sufficient to express not only the chemical and biological conditions but also the economic conditions.
The MCWQI allows ranking among different regional water sources, as it has dimension in dollars. The incomparability of WQIs due to different constituent parameters in different regions is eliminated since the
MCWQI expresses water quality in terms of monetary value.
The ranking of
MCWQI allows a regulatory agency to arrange the priority for distribution of water pollution control funds. In the process of calculating
MCWQI, it also determines the optimal concentrations to which each pollutant should be removed in that locality.
WQI is zero for most secondarily treated effluent.
Thus, water pollution control prioritieS are unobtainable for zero
WQI regions. A zero
WQI does not mean that there is no monetary value if the water is used far agricultural and other purposes. The
MCWQI has the additional advantage over the
WQI of allowing for the monetary component.
The index is zero dollars for the Tucson case study.
This zero dollars
MCWQI is caused by the zero value of
This means that the economically optimized water quality is poor by
Walski and Parker's standards. This water, however, will generate
6 dollars in benefits based upon the relationship between the content of suspended solids and recreation. The derived optimum concentration is 30 ppm for suspended solids,
37.96 ppm for nitrogen, and 11.74 ppm for phosphorus.
Almost half of the time, the existing Tucson facility on
Sweetwater Road can treat suspended solids to a concentration of 30 ppm.
Most of the time the plant fails to produce the economically optimal concentrations of nitrogen and phosphorus for recreational use. As for agriculture, the treatment plant exceeds the optimum concentrations of nitrogen and phosphorus
100% of the time.
The costs used in this analysis need a thorough study for a general, nationwide application.
For other deteriorated water sources, either point or nonpoint, the procedure developed here can also be utilized.
A wildlife ecological study is needed. The influence of a large urban recreational lake on fauna and the metropolitan residents attitudes toward urban-accustomed animals require a thorough investigation.
The estimated lake acreage is
196 surface acres by the standard method. The demand for surface acreage by urban water-based recreation should be investigated for the Tucson region.
The amount of water needed for irrigation is dependent upon the kind of crops and the acreage of crops. Both of them vary from year to year. If the six-year average of crops acreage is chosen, the detention lake would have a surface area of
(1.56 square miles) for a
36 MGD treatment plant in Tucson.
Ranking for different regions should be performed according to
(MB,WQI) within the same
MCWQI rank. That is, if Region A and
B have the same zero
MCWQI, probably Region A should be ranked higher if it has a higher net benefit than Region B.
MCWQI determinations are needed for the verification and validation of this index's capability and feasibility.
The author feels that this
MCWQI should serve only as a reference in decision-making, not as a target value to be aimed at.
In other words, poor water sources should be improved whenever possible,
105 and good quality water should not be downgraded only because the index permits lesser quality. For example, if a secondary treatment plant is in existence, and the
MCWQI indicates that a primary plant would be sufficient, the results of the
MCWQI analysis should not justify the removal of the secondary plant and the resulting sacrifice of water quality.
HISTOGRAMS OF THE INFLUENT WATER QUALITIES
s = 40.56
n = 118
/ o.o 85
20 230 250 270 190 310 330 350 370 390 410
s = 4.95
n = 131
24.4) 245 31.0
n = 126
0 . /
44 45 do ZS AP
s = 24.14
n = 132
Suspended Solids, mg/1
s =-,- 4.06
n -=-- 125
8 o. o o
9 /2 /5 a
TABLE OF FECAL COLIFORMS
Effluent fecal coliforms, MPN/100 ml
Plant 1 Plant 3
HISTOGRAMS OF THE EFFLUENT WATER QUALITIES
s = 24.46
n = 327
5 /5 25 35 45 55 65 75 95 95 /05 "5 /-
3 5 /3 5
6 l6 25 35
46 55 66 75 .95' gs
Suspended Solids, mg/1
n =-- 333
0 ocq z4 28
NO 3 -N, mg/1
n = 192
o 43 04 46
ai 18 40 42
s =-- 3.91
n -= 355
0 0 o 2 4 ,4
/2 /4 /6
24 22 24
NH 3 -N, mg/1
Amount of equal annual payment
Alkyl benzene sulfonate, a foaming agent used in detergents
Biochemical oxygen demand; usually takes
5 day value
Per hundred weight,
Engineering News Record, a cost index
Gallons per day
Interest or inflation rate
Linear alkylate sulfonate, a surfactant substitute fpr ABS
Methylene blue active substance
Multi-Criteria Water Quality
Milligrams per liter
Million gallons per day, or 1,120 AF/year
Most possible number
Water quality index for municipal sewage
Number of years of interest bearing period
Parts per million
Sewage Treatment Plant Construction
Value of sum of money when placed at interest
Water quality index
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