SO 1 09/71
        Systems Analysis for Water Quality
        Management-Survey and Abstracts
           Office of Water Programs
       U.S.  Environmental Protection Agency
September 1971

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        SYSTEMS ANALYSIS FOR WATER
QUALITY MANAGEMENT - SURVEY AND ABSTRACTS
                by
       Enviro Control, Inc.
       1250 Conn. Ave., N.W.
        Wash., B.C.  20036
            for the

      WATER QUALITY OFFICE

ENVIRONMENTAL PROTECTION AGENCY
      Contract #68-01-0096
         September 1971

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             EPA  Review Notice
  This  report has  been reviewed by the Water
  Quality Office,  EPA, and  approved  for publi-
  cation.  Approval does not signify that the
  contents necessarily reflect the views and
  policies of the  Environmental Protection
  Agency.
                      11
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $1.75

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                    ABSTRACT
A survey of the current state-of-the-art in systems
analysis for water quality management has been conduct-
ed.  The survey is divided into two parts.  Part I
gives an introductory guide to the relevant analy-
tical considerations and techniques together with
assessments of the capabilities and limitations of
available systems analysis approaches.  Part II
gives relatively detailed abstracts of a represent-
ative sampling of papers in relevant analytical
input areas and in the major water quality model-
ing areas.  The abstracts give both technical con-
tent of the papers and critical assessments.
                       iii

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Section

I

II


III


IV


V



VI

VII



Section

A

B
D
F

G
                    CONTENTS

                Part I - Survey
Introduction

Procedures for Conducting a Systems
Analysis

Modeling Techniques in Water Quality
Management
  Page

     2
    11
Physical, Chemical and Biological Con-
siderations in Water Quality Management  26
Legal, Social, Demographic, Economic
and Other Related Aspects of Water
Quality

Acknowledgments

References

      Part II - Abstracts
Introduction

Basin and Stream Models for Alloca-
tion of Abatement Resources

Treatment Plant and Treatment Pro-
cess Models
    35

    46

    47
Page

A-l


B-l


C-l
Hydrological Models for Application
to Systems Analyses of Water Quality D-l

Studies and Models of Oxygen Balance
in Streams                           E-l

Modeling of Thermal Pollution        F-l

Studies and Models of Economic and
Social Aspects of Stream Systems
and Water Quality                    G-l
                        v

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Section                                       Page

H        Data Collection, Technical Data
         and Cost Data for Systems Ana-
         lyses of Water Quality               H-l

I        Computer Programs for Basin and
         Stream Water Quality/Hydrological
         Models                               1-1

J        Computer Programs for Treatment
         Process and Plant Analysis/Design    J-l

K        Computer Programs for Thermal
         Pollution Modeling                   K-l
                          VI

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PART I  -  SURVEY

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                     SECTION I

                   INTRODUCTION

         The increasing scale of national efforts
to improve the quality of our streams, rivers and
lakes has brought with it a demand for efficient
and rational planning, management and operation
of the resources being devoted to these efforts.
This demand has led naturally to a growing interest
in the application of systems analysis methods to
water quality problems.  Because of the rapid
growth of systems analysis techniques applicable
to the water quality area, it has become difficult
for non-specialists to acquaint themselves with
current methods, capabilities and limitations of
the analytical approach.

         This survey is intended to assist
potential users and practitioners of systems
analysis in understanding the current state-of-
the-art without extensive literature search efforts
on their part.  In addition, this survey should
provide an introduction to the voluminous and
growing literature available for those who wish to
pursue certain aspects in greater depth.

         The survey itself is addressed to the non-
specialist with only a basic background in water
quality and systems analysis concepts.  It has
been structured to emphasize the pragmatic aspects
of applying systems analysis to "real-world" water
quality problems.   This emphasis dictates the need
for a balanced view of the usefulness of the various
analytical approaches; as a result, at least as
much weight has been placed on the limitations of
systems analysis as on its possibilities.

         For the reader who wishes to skim this
survey as well as for. the reader who, intends to
pursue the issue in depth, it is recommended that
at least a sampling of the abstracts provided in
Part II be perused.  These abstracts have been
carefully structured to provide considerable in-
sight into fundamental assumptions as well as
results achieved and not achieved in the studies
reviewed.

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         To assist the reader, Part I has reference
numbers (indexed to the Section VII reference list)
at appropriate places in the text; where these num-
bers are followed by an asterisk, the reference
indicated has been abstracted in Part II.  Part II
is not, however, limited to only these asterisked
references; it has additional abstracts of papers
and computer programs of interest to potential users
and practitioners of systems analysis for water
quality planning, management or operations.

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                    SECTION II

   PROCEDURES FOR CONDUCTING A SYSTEMS ANALYSIS

Systems analysis, contrary to widespread belief, is
neither a separate and specialized discipline nor an
arcane art.  Instead, it is, or should be, simply_a
practical, rational and quantitative approach to il-
luminating, but not necessarily solving, decision is-
sues that involve costs and. benefits.

The approach as applied to specific water.quality mana-
gement problems can be briefly, described in terms of the
following steps:

1.  Understand the problem - the major, difficulty in
accomplishing the first step is that it requires the
analyst to suspend judgement in all the areas in which
he invariablv has prior biases:  key variables,.domi-
nant relationships, appropriate modeling techniques,
feasible alternatives.  Much of this prior bias normally
stems from the body of professional literature in any
given problem area and can be attributed to the strong
tendency of academic publications to redefine real-
world issues in terms that permit clean and elegant
solutions.  It is, in fact, essential for the analyst
to develop an understanding of all the problem aspects
and the interactions that are unquantifiable, uncer-
tain, controversial or obscure due to either technical
or socio-polit4cal factors, particularly since these
same factors may, and often do, dominate the "clean"
factors.  In water quality problems, the following is
a partial listing of the unpleasant factors that must
be at least assessed and understood prior to any formal
analysis:

     a.  Non-steady state or randomly variable discharges,
         flows, waste characteristics and biological pro-
         cesses .
                            1             !
     b.  Multiple pollutant/nutrient interactions (syner-
         gistic or inhibitory effects).

     c.  Unquantif led  (and possible ujiquantif iable)  eco-
         nomic and ecological impacts of pollutants.

     d.  Inadeauate, variable and/or biased economic in-
         puts:  project/equipment costs; economic benefits,
         .demand variations, prices, projections, etc.

     e.  Inadequate physical/chemical/biological inputs:
         flows, velocities, mixing processes, growth/
         decay/reaction rates, etc.

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     f.  Feasibility constraints due to social atti-
         tudes, institutional processes and relation-
         ships, political forces arid jurisdictions,
         legal considerations and precedents, etc.

2.  Restrict and formally define'the decision-rele-
    vant aspects of the problem - the transition
from a thorough understanding of the complexities
and uncertanties of a real world problem to a con-
siderably narrower and highly approximate formal
representation of its decision-relevant aspects is
the key step that determines ultimate success or
failure of an analysis. •

Unfortunately, many analyses begin with a one-sided
justification of a preconceived problem definition
rather than between the actual problem and its formal
representation.  At a minimum, this step must include
consideration and assessment of the following:

     1.  Benefit, effectiveness or return factors
         included and those excluded.             :

     2.  Cost  (economic or intangible) factors in-
         cluded and excluded.

     3. ' Basis for quantification and specific selec-
         ,tion of descriptive variables for those factors
         and/or processes that have been stated in
         quantitative terms, particularly where the
         descriptive variables have lower dimension-
         ality than their underlying factors.

     4.  Means employed to reflect the impact of un-
         quantified factors or, alternatively, the
         rationale for their absence.

     5.  Criteria for ranking better and poorer solu-
         tions  (e.g., minimizing cost to implement a
         defined quality level or maximixing direct
         economic benefits minus costs; both of these
         are simple enough to become "optimization
         criteria") - note that absolute optimization
         is not essential to a systems analysis.

The problem-narrowing process is by no means rigorous;
it involves both understanding of the relative magni-
tude of costs, effects and benefits as well as a good
deal of subjective judgment.  As a somewhat exaggerated
example, assume that the problem to be addressed is
the "best" means of cleaning up a single stream to a
level  suitable for recreational fishing, given a num-
ber of local industrial and municipal pollutant dis-
chargers.  Ideally, one would like to relate total

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local (or even national)  benefits due to aesthetic/
recreational values and increased tourism (as a
function of fish population density)  to total local
(or even national)  cost.   This is clearly impossi-
ble, given the state of economic and  biological
data and modeling.

Thus, the first step in narrowing the problem is to
substitute for total benefits a relatively arbitrary
determination of the type of fish population desired.
However, the fish population itself cannot be quan-
titatively related to pollutant concentrations in_
the stream.  Therefore, the next step is to substi-
tute a set of water standards approximately suitable
to the population desired in place of the actual fish
population density.

Regarding the total economic cost issue, it is highly
unlikely that the total projected effect on the local
economy of increased treatment costs  for local indus-
tries and municipal plants can be assessed.   Conse-
quently, a typical restriction of the problem would
involve substituting direct discounted present value
of treatment expenditures (including  low-flow augmen-
tation, in-stream aeration, treatment plants process
changes, etc.) for total economic impact.  Note that
not only has the scope of economic consideration been
sharply reduced, but the inherent multi-dimensionality
of cost has been reduced dramatically (and probably
arbitrarily) by combining public, private, present
and future costs into one single-dimensional measure.

A final simplifying step often undertaken is to elimi-
nate all nutrient and toxic pollutant standards from
consideration and proceed with a one  dimensional
stream standard consisting of only a  dissolved oxygen
threshold.  Unless oxygen demand is in fact the only
pollution problem in the stream  (a rare case for mixed
industrial/domestic wastes) or unless the costs of all
other pollutant removals are trivial  compared to BOD
removal, this step represents one simplification too
many.  That is, after demonstrating the minmum treat-
ment cost scheme for meeting the dissolved oxygen stan-
dard, the original problem remains completely unsolved
insofar as the desired fish population still cannot
survive in the stream until the other pollutant levels
fall below their respective standards."

3.  Define the complete range of feasible, promising
    alternatives - a surprising amount of analysis has
been expended on quality control alternatives that are
in no sense feasible.  Aside from technical consideration,
the major constraints on feasibility of alternatives
are as follows:

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     a.  Social attitudes - strongly entrenched atti-
         tudes (which may be purely local in nature)
         such as aesthetic objections to wastewater
         reuse or conservationist objections to in-
         stream aeration may rule out otherwise attrac-
         tive alternative solutions, depending on the
         problem and the area.

     b.  Institutional/political arrangements *- alter-
         natives that may have a good deal of economic
         merit, such as basin-wide control of treatment
         requirements and operations, are often in-
         feasible (particularly as near term solutions)
         due to the existence of multiple political
         jurisdictions within the basin combined with
         the lack of precedent for establishing a region-
         al commission with the requisite authority to
         allocate treatment resources.

     c.  Legal constraints - minimum cost treatment
         schemes for achieving a given dissolved ox-
         ygen standard in a stream or basin are often
         not implementable because they may call for
         no treatment or primary treatment, on cer-
         tain relatively clean reaches when the federal/
         state standard requires a minimum of secondary
         treatment for all wastes.  Another basin-wide
         minimization may find additional low-flow
         augmentation release a low cost solution to
         water quality problems but will run afoul of
         prior water rights.

     d.  Equity considerations - a recurring problem
         in imposing local and basin-wide treatment
         requirements is the issue of equity to in-
         dustrial firms facing competitors in areas
         with less stringent requirements.  Another
         major equity issue is the question of alloca-
         ting stream assimilative capacity among a num-
         ber of densely spaced discharges represent-
         ing a variety of industries  (each with dif-
         ferent and partially unknown costs of pollu-
         tion abatement) and municipalities.

A through appreciation of these constraints is essential
to structuring sound and practical alternatives.  How-
ever, it must be remembered that not all of these con-
straints are immutable; analyses addressing long term
solutions are obligated to consider the effect of modi-
fying such constraints where major efficiencies can
be achieved.

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Analysts often restrict themselves to considering only
previously proposed or promulgated alternatives on
the basis that technical experts should have the respon-
sibilitv of formulating the relevant alternatives.
In fact', it should be the responsibility of the systems
analyst to ensure that the full range of feasible pro-
blem solutions is represented, including the possibility
of new unconventional approaches.

4.  Collect and assess the relevant input data - unfor-
tunately this"step normally is not accomplished until
after the selection of modeling technique.  In_fact,
data availability and quality should have a major im-
pact on the type and complexity of model selected.  If
the hydrologic data base for the area is scant,  there
is little point in using sophisticated statistical
techniques for dealing with flow variability.  If pol-
lution sources/loads or treatment costs are poorly
measured or estimated, then it is hard to justify highly
precise optimization techniques.

One of the most critical data assessments will be the
evaluation of variability.  First of all, it is  es-
sential to separate variability due to inexact mea-
surements, approximate process models or deterministic
time variations from variability due to inherent random-
ness (e.g., are fluctuations in biological treatment
process rates due to random changes in influent com-
position, due to measurement deficiencies or due to
variables excluded from the process kinetics) .  Secondly,
the magnitude of the inherent variability will deter-
mine whether a convenient steady-state model can be
used or whether a stochastic model is necessary to de-
scribe major effects.  Given large random components, a
relatively primitive model that accounts for fluctua-
tions is normally better than a more exact model that
ignores them.  Similarly, if large deterministic trans-
ients with relatively short periods are involved, models
roughly approximating transient behavior are more
valuable than excellent representations of the steady-
state.

The final and most obvious reason for data collection
and assessment prior to model formulation is the need
to determine the possibility of simplifying assumptions,
e.g., linear costs, independence of variables, linear
rate processes, etc.

5.   Selection of modeling technique - given a thorough
development of the problem formulations in terms of for-
mal definition of key aspects, structuring of alterna-
tives and comprehensive data collection/evaluation, the
actual  choice of modeling technique is both less dif-
ficult  and perhaps less crucial than the literature
emphasis would indicate.

                        8

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The first and most important consideration in selec-
tion of a modeling technique is the extent to which
it realistically incorporates the critical factors
and relationships identified in the problem formu-
lation.  The criteria of ease of exact optimization
and computational efficiency are, by comparison,
secondary.  All too often there is a strong temptation
to accept serious distortions of the real problem
structure in order to be able to employ the elegance
and convenience of one of the classical optimizing
techniques  (e.g., linear programming, dynamic pro-
gramming, etc.)  Given the fact that the majority of
water quality management problems have input data
uncertainties of anywhere from 20% to well over 50%,
it can be seen that insistence on exact optimization
would be misplaced.  Furthermore, water quality ana-
lyses are generally neither "canned" nor repetitive
due to the prevalence of special local conditions and
constraints; therefore, computational efficiency is not
a prime consideration.

In view of these facts, the selection of modeling
technique should proceed by elimination, in the
following sequence:

     a.  Equations with closed form or direct itera-
         tive solutions  (e.g., based on differential
         equations, calculus of variations, probabilis-
         tic formulations, etc.) - these are normally
         the simplest and most efficient models to op-
         timize, through rarely applicable to highly
         multi-dimensional problems.

     b.  Standard algorithmic optimization techniques
         from the operations research repertoire  (e.g.,
         linear/geometric/dynamic programming, network
         analysis, etc.) - these techniques are well
         understood and convenient to use, provided
         they fit the problem and remain computationally
         feasible.

     c.  Deterministic or Monte Carlo simulations - these
         must be specially designed for the problem at
         hand, but have the best chance of realistically
         reproducing real world water quality situations
         and alternatives.  Approximate optimums can
         be derived, but only using a variety of heuris-
         tic and/or empirical search techniques.

The latter tool has received relatively little emphasis
in water quality management, although it has been ex-
tensively used in water resources planning.

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6.  Model verification, solution, sensitivity testing, -
unfortunately,"the scientific tradition of rigorous
empirical validation of models has not become an in-
tegral part of systems analysis practice   Nevertheless,
it should be a prerequisite of all analytical studies
in water quality that any model proposed (or at least
the water quality descriptive component of the ™°ael)
be compared with actual stream conditions over a range
of flows and inputs in order to establish at least the
degree of descriptive or predictive Precision involve^
Similarly, cost estimating relationships should be cor
related against actual projects or equipments to P£O-
duce a quantitative statement of their accuracy.  These
demonstrations should accompany any solution or recom
mendation; without them, analysis can easily create
spurious impression of exactness that can seriously
mislead decision makers.  A further important component
of thorough analysis is a display of the sensitivity
of solutions to perturbations in each of the dominant
constraints or variables and each of the input vari-
ables for which precise values cannot be determined.
In this respect the economic concept of shadow prices
is highly useful in displaying sensitivity and imputed
value of arbitrary constraints representing aesthetic
values, water quality "requirements", equity considera-
tions, etc.  (one of the attractive aspects of linear
programming is that these shadow prices are in integral
part of the computation and can be directly incorporated.
in output formats).

Equally important and rarely presented is a demonstra-
tion of the relative scale of costs, benefits and/or
savings involved in an "optimum" solution compared with
overall economic activity in a plant, industrial sector
or region  (e.g., studies of minimum cost treatment schemes
for a basin will quote x million dollars in savings  for
an optimum policy, but rarely give an idea of the total
size of the region's economy or even of the affected
industrial sector).

7.  Iteration of steps 1 through 6 - because real world
analyses are not conducted in the chronological sequence
used here for expository purposes, and because real
analysts do not have universal prescience, there is  fre-
quently a need to use the results of a later step to
modify determinations made at an earlier step.  It  is
important to allow time and effort in the course of
an analysis for the implementation of this learning
effect.  Examination of data quality and content may
make it necessary to restate the problem definition;
sensitivity runs of the model may demonstrate  the need
for returning to the data gathering phase for  several
key variables, etc.  The ultimate quality of an analysis
will often be closely related to the number of  such
iterations.

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                   SECTION III

 MODELING TECHNIQUES IN WATER QUALITY MANAGEMENT



1.     Introduction

Examination of the existing literature and the
problems currently being faced in water quality
management indicates that adequacy of modeling
techniques is not a major obstacle to problem
solution.  In fact, it would appear that the state
of the art in models has substantially outstripped
the basic data and physical/chemical/biological/
economic insight needed to make modeling and ana-
lytical solutions credible.

A preliminary categorization of problems in water
quality management potentially amenable to systems
analysis will serve to focus the discussion of
models:

A.     Planning
       a.  Allocation of abatement resources and
           selection of efficient abatement strategies
           by reach, river, basin and nation.
       b.  Regulation,  standard - setting  (stream
           and effluent), taxation and subsidies
B.     Management and Operations
       a.  Control of reservoir systems
       b.  Control of discharge, treatment and with-
           drawals
       c.  Allocation of monitoring and surveillance
           effort
       d.  Allocation of enforcement effort
C.     System Design
       a.  Biological - trickling filter, activated
           sludge, extended aeration, etc.
       b.  Physical/chemical - for BOD removal;
           removal of other pollutants
       c.  Instream aeration

Each of these areas will be discussed in more detail
below.

2.     Analysis in Water Quality

The great majority of analytical efforts in water
quality are directed towards the planning area.  The
analyses vary according to their treatment of the
following aspects of water quality planning:
                        11

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a.  Pollutants - the vast majority of models
    address only the BOD/DO problem.   A few
    deal with single pollutants of other types.
    suspended solids, single nutrients_ana
    salinity.  Very few deal with multiple
    pollutants.
b.  Water system:  models addressing  every
    level from single discharger stream
    reaches through full basin systems and
    national overviews have been constructed.
    Most address multiple reach single streams
    (with or without tributaries). Only a
    small number of ground water quality _
    analyses have been attempted  (except in
    the area of salt water intrusion).  There
    are no combined surface/groundwater quality
    models that the authors are aware of
    (though combined surface/groundwater
    hydrological models are relatively common) .
c.  Abatement alternatives - these cover the
    range of standard methods:  self-treatment
    and bypass piping for industrial  discharges,
    individual  and centralized treatment for
    multiple municipalities, instream aeration
    and low flow augmentation.  Most  analyses
    have not considered all these alternatives
    simultaneously, due to either model or
    data limitations.
d.  Costs and benefits - most planning models
    deal simply with direct capital or capitalized
    expenditures for abatement to predetermined
    stream standards.  Certain economic investi-
    gations deal with "multiplier effects"
    in local economies; this is done  fairly
    often for agriculture/irrigation  analyses
    but less frequently for water quality issues.
    Several attempts at quantifying recreational
    benefits of improved water quality are
    available.
e.  Regulation alternatives - most planning
    analysis assumes direct treatment "requirements"
    (% BOD removal) applied to individual or
    grouped discharges.  Equity constraints are
    limited almost exclusively to zoned discharge
    requirement schemes.  Taxation as a method
    of regulation has been treated mostly on
    an abstract level.  There has been only one
                12

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           major attempt to analyze a practical tax
           structure for an important stream system
           using actual data; it was forced to use
           restrictive simplifying assumptions due
           to lack of practical economic methods for
           predicting response of widely diverse
           industries to taxation.

3.     Analysis of Management and Operations

Because there exists no institutional mechanism in
the U.S. for real time control of stream quality
(except for reservoir release operations), little
analysis of the possibility of regulating discharges
and withdrawals during periods of critical pollutant
levels has been accomplished  (even though Kneese,
Kerri, and ORSANCO have recommended strongly the
desirability of such control).

There is no extensive literature on optimizing
reservoir operations for maximum returns from power
and water sales, subject to required releases for sat-
isfying water rights and predetermined minimum flows
for maintaining quality.  Unfortunately, this literature
contains little or no description of the criteria
for setting these low flow augmentation requirements.

Another operating area that offers excellent op-
portunities for analysis is the allocation of the
limited effort level  available in the monitoring,
surveillance and enforcement areas.  Unfortunately,
there is no published literature in this area and little
incentive to initiate analytical investigations.

4.     Analysis of Systems Design

Due to the well-established technology of domestic
waste treatment, there is an extensive literature on
preliminary design cost minimization of the various
types of biological treatment systems for BOD removal,
though this literature is limited mainly to steady-state
considerations.  Recently, there has been increased
emphasis on applications of the same methodologies
and similar technology to industrial biological
treatment systems.  Generally, tertiary treatment is
not considered in these analyses.
                        13

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There is somewhat less complete coverage of physical/
chemical treatment systems and very little other tnan
R & D literature on newer methods such as electrodi-
alysis, reverse osmosis and incineration.  The enptia-
sis in this literature is mostly on process feasibility
and basic economics rather than on optimization, due to
either the simplicity of the systems involved (e.g.,
direct chemical treatment) or the uncertain state of
the technology (e.g., reverse osmosis).

Formal analytic models for design of systems to achieve
fixed multiple pollutant effluent standards have yet to
be published; such problems are currently treated on a
case by case basis due to the diversity of standards and
pollutant loadings for parameters other than BOD.  An
equally important problem is the optimization of treat-
ment systems for the highly variable or transient loadings
common in many industries.  Given adequate modeling, this
area could offer significant potential for cost reduction
through automation and/or special supplementary treatment
for peak loads (e.g., chemical treatment backup for stand-
ard biological systems).

5.    Modeling Techniques - Planning

The most widely addressed problem in planning is simply
that of allocating treatment effort (or regulating loads)
of individual or grouped discharges on a multiple reach
stream, with or without tributaries.  The techniques com-
monly employed here are linear programming, integer pro-
gramming and dynamic programming.  The approach and range
of problems handled by each one is discussed below:

a.    Linear programming - useful general references
      in linear programming methodologies are Chung
      (1)  and Gass (2).   The basic linear programming
      formulation as presented by Deininger  (3*) and
      Thomann and Sobel (4), consists of minimizing
      the sum of BOD removal costs for each discharge
      (using linearized cost functions)  subject to the
      constraint that the DO deficit due to the com-
      bined effects of upstream discharges does not
      drop below a predetermined standard for a mesh
      of constraint points in each reach  (additional
      continuity-type constraints are also imposed).
                        14

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The method depends on computing linear trans-
fer coefficients between a given discharger's
load and the resulting effect on DO at each
constraint point downstream.  These are normally
determined using the Streeter-Phelps oxygen sag
equation or recent variations of the classical
linear rate BOD/DO stream relationships.  Since,
in fact, most treatment cost curves are non-
linear, the cost functions can be included in the
program as piecewise linear approximations (at
the cost of a significant increase in varia-
bles and constraints) or the solution can be
iterated to adjust the linear cost slopes locally;
either method requires convexity of the cost
function.  Similar approaches have been taken
by Revelle, Loucks and Lynn  (5*) and Anderson
and Day  (6*).  The method can be extended to
other than unindirectional flow (e.g., estuaries)
and to tributary systems.

However, realistically large numbers of dischargers
and reaches can lead to impractical computer
storage and time requirements unless large scale
programming concepts can be introduced, that
is, concepts that use more efficient specialized
algorithms tailored to particular symmetries
among constraint equations often found in ex-
tremely large linear programs.  An excellent
review of this important area has been prepared
by Geoffrion  (7).

Linear programming has also been applied to
optimization of multiple river - reservoir
systems for maximum economic return subject
to low-flow augmentation requirements and other
release constraints.  Parikh  (8.)  has developed
a useful decomposition of the multi-reservoir
problem into individual reservoir sub-opti-
mizations  iterated  for successive sets of
shadow prices generated by his "master" linear
program for integrating the operations of the
whole set of reservoirs.  The solution converges
to optimal individual and multiple reservoir
operating policies over a finite number of time
periods with varying flows, prices, constraints,
etc.
                  15

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A more comprehensive treatment of regional
water resources allocations maximizing total
regional economic benefit including water
quality flow constraints has been developed
in linear programming format (again using
the decomposition principle) by Heaney (9*).
The model allows competition for water with-
in the suboptimizing subregions; optimum
allocation between competing regions is accom-
plished by iterating artifical prices for the
water assigned to each subregion until the
regional maximum benefit point is reached.
A very large version of this program has been
successfully run for agricultural activities
(using total value added as the measure of
economic benefit) in the complete Colorado
River Basin; obtaining similar economic data
inputs for optimizing industrial activities
appears much more difficult.

An interesting and important application of
linear programming involves the computation
of effluent tax levels necessary to achieve
desired stream quality levels.   Johnson (10*)
applies a simplified form of the Thomann and
Sobel program for the Delaware Estuary to
comparison of total cost under the overall
minimim cost scheme, the single tax and the
zoned tax schemes; unfortunately he is forced
by lack of economic data to make simplifying
assumptions regarding industrial response to
taxation.

Integer programming - this technique has not
found wide applicability in water quality
modeling, since problems involving the linear pro-
gramming format with solutions restricted to in-
teger values for the independent variables are
not common in water quality.  However, Liebman
(11*) has devised an ingenious application of
integer programming which circumvents the some-
times serious convex cost restriction encountered
in the classical linear programming formulation
of minimum cost treatment allocation described
above.  Instead of using a continuous variable
                  16

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      to represent BOD removal efficiency for
      each discharger, Liebman uses a 0-1 in-
      dicator variable to represent which one
     ' of a number of discrete treatment levels
      (with a separate cost associated with
      each) is selected by a given discharger;
      this allows representation in discrete
      form'of the non-convex and even discon-
      tinuous cost functions frequently en-
      countered  (when groups of plants already
      emphasize certain levels of treatment).
      A moderate 'size problem using Delaware
      Estuary data was successfully run to com-
      pare discharge-by-discharge regional mini-
      mum cost treatment with zoned treatment
      requirements.  It should be noted that inte-
      ger programs df any size are normally computat-
      ionally infeasible> with the exception of special
      formats such as 0-1 variables with certain con-
      straint symmetries.

c.    Dynamic programming - this technique offers
      both advantages and disadvantages relative
      to linear programming as follows:

      (1)  The objective function can consist
           of the sum of non-linear  (as opposed
           to only linear or convex for LP) single
           variable functions, as can the constraints
           (this is by no means a method for oprimi-
           zation of generalized non-linbar proglems).

      (2)  For computing optimum decisions for sequenced
      ;     time  (or space) intervals, computing time in-
           creases only linearly with the number of de-
           cisions .
   i             >            •
      (3)  Problems -with more than 2-dimensional de-
           cision variables for each stage are rarely
           computationally feasible.

      For general references to dynamic programming tech-
      niques, Bellman and Dreyfus  (13) and Neuhauser  (14)
      are comprehensive sources.  Dynamic programming has
      been applied for some time in period-by-period op-
      timization of reservoir operations for maximum re-
      turns from power and water sales, where water quality
      is introduced only as a low flow constraint.  The
                         17

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pioneering work in this area is Hall and Buras
(15); Buras (16)  gives an excellent review
of the area.  Erickson et alia (17*) gives a
detailed specific single reservoir application
involving hydroelectric, irrigation, urban and
recreational benefits/losses resulting in a
four decision variable dynamic program forcing
the use of pattern search techniques.

Dynamic programming has been applied to the
standard single stream minimum cost treatment
allocation problem described under linear pro-
gramming.  Liebman  (18)  solved an eleven dis-
charge/eleven reach representation of the Willa-
mette River (an interesting finding is that
better solution stability is obtained by solving
sequentially in the downstream direction or for-
ward in time, as opposed to the usual dynamic
programming practice).  However,  as Revelle, Loucks
and Lynn show  (5*), the Liebman solution can be
almost exactly duplicated using a far simpler linear
program with only a two-piece linear approximation
to the non-linear treatment cost curve.  Meier and
Beighter   (19)  extend the basic Liebman approach to
allow inclusion of tributaries through a decomposit-
ion of the program into serial programs.  A similar
approach is taken by Joeres (20*)  in treating the
problem of minimum cost sediment control on a multi-
branch stream/reservoir system.  However, the method
is still restricted to undirectional flow whereas
the LP approach can treat tidal streams and estuar-
ies  (given the possibility of linearization of indivi-
dual discharge effects).

Simulation models  (Monte Carlo and deterministic) -
it is to be noted that all of the above techniques
are incapable of simultaneously handling stochastic
flows/loads, non-linear discharge, effects and treat-
ment costs, multiple pollutants, etc.  The only tech-
nique currently available for dealing with these levels
of complexity is simulation, an approach relativelv
unused to  date in water quality studies.  The technioue
has been extensively used in reservoir system studies
since an initial Corps of Engineers experiment in TQ^.
Manzer and Barnett  (21) give a useful description  f
the technique as applied in the Harvard Water Pro
                   18

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Although simulation has the advantage of
allowing considerably more realism in the
description of the physical/economic water
system, it has been avoided in water quality
analysis because it requires empirical
search techniques to arrive at approximate
optima.  In other words, the simulation can
only compute points on the model's response
surface (usually multidimensional) for speci-
fied input values; thus, the success or failure
of simulation optimization depends on the sur-
face search technique used.  An excellent practi-
cal review of search techniques applied to multiple
reservoir problems is given by Hufschmidt (22) re-
porting on Harvard Water Program experience.  It
is to be noted that complete search is rarely ne-
cessary in water quality problems where both heuris-
tic insight and real world feasibility constraints
on alternative policies can greatly reduce the size
of the space to be searched.  Direct simulation
of randomly time-varying flows and multiple pollu-
tant loads in a moderately complex stream system
has been successfully accomplished by Pisano  (12*);
Moreau (79) has also developed a successful water
quality stream simulator.  A simplified queueing
format simulation model for a reservoir/treatment
plant/effluent holding tank system on a single stream
reach with variable stream flows, waste flows and
waste loads has been developed by Montgomery and
Lynn (23*) .  The model treats flow in discrete in-
crements and is thus able to handle important aspects
such as treatment efficiency changes with variations
in holding times generated by random fluctuations
in waste flow.  There appears to have been little
further development based on this promising beginning,

A final and extremely important area of interest
in water quality planning is the development of
national assessments and national policy analysis.
Very little direct water quality system analysis
has been performed in this area; probably the
most significant work was accomplished as part
of the Wollman-Bonhem  (24) model developed for
the U.S. Senate Select Committee on Water Resources.
Reid et alia  (25*) have published their contribution
to the model, i.e., the basin-by-basin projection
of water quality for six pollutant characteristics
and the associated tradeoff of low flow augumentat-
ion vs. effluent treatment  (the application of the
model in the national assessment was to compute
the nation's storage requirements for low flow aug-
                  19

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       mentation).   The  individual  pollutant  models
       are based on  basin-wide  loads  (factored  for
       population concentration)  and  on  highly  sim-
       plified basin-wide  average decay/mixing  para-
       meters.  The  approximations  involved are
       sufficiently  gross  that  without detailed em-
       pirical validation  of  the  resulting treatment
       and dilution  requirements, the conclusions
       must be viewed as highly tentative.

       There is, in  fact,  reason  to doubt that  much
       progress in this  area  can  be made until  a much
       more comprehensive  data  base for  water use,
       discharge descriptions and stream pollutant
       levels is assembled and  integrated via detailed
       multiple pollutant  subregional models.

 6.     Model Techniques  -  Management  and Operations

 This area has received  considerably  less analytical
 attention than the  water  quality planning area.

 The literature previously referred to in linear and
 dynamic programming for water  resources is directly
 applicable to operations  of  existing reservoir/stream
 systems and, to a lesser  extent, ground water  systems.
 Unfortunately, the  only provision  for water  quality
 in  these models is  normally  through  predetermined
 flows or dilution requirements for water quality pur-
 poses.   There is a  considerable  need for additional
 field studies followed  by modeling to relate stream
 quality to these dilution flows, a highly non-linear
 relationship due to the strong effect of stream flow
 levels on reaeration rates,  sedimentation/scour rates
 plankton levels and temperature  (depending on  depth
 of  reservoir releases) .

 In  the area of regulation (particularly effluent controls),
 there is some overlap between  analysis  for planning and
 analysis for management or operations.  On an  abstract
 level,  Kneese (26)  discusses the relative merits of direct
 regulation of discharge contents -versus>effluent taxation/
 subsidy schemes and describes  the  operation  of the German
'effluent tax system for the  Ruhr.  Johnson  (10*) discusses
 in  general terms the relative  operating expenses   (self-
 monitoring,  surveillance  and billing) of effluent  regulat-
 ion vs.  taxation systems. He  raises the important consider-
 ation of special tax rates and controls for  intense trans-
 ient discharges.
                         20

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In this connection, Thomann  (27)  discusses the need
for and the fundamentals of near real time control
of effluent variability and treatment efficiency in
the face of the substantial short and seasonal vari-
ations in streamflow normally experienced.  He points
out the economic and ecological inadequacies of the
steady-state approach for achieving water quality
goals with high probability, when hourly and daily
fluctuations are taken into account.  He introduces
and gives examples of the important notion of stream
step-response to an instantaneous pollutant input;
this concept is applied to a simple feedback control
of a variable efficiency treatment plant responding
directly to stream conditions  (and possibly to seasonal
adjustments in water use/water standards).  Note that
this view of stream conditions requires abandoning the
entire structure of steady state one-dimensional stream
modeling and replacing it with transient models that
include the effect of longitudinal  (streamwise) diff-
usion.  Experimental dye study techniques for address-
ing this problem are well-established; however, con-
siderable measurement effort will be required to corre-
late diffusion behavior with channel geometry/hydrology.

Further important areas for analysis in water quality
operations concern allocation of effort in enforcement
and in monitoring and surveillance.  In monitoring
and surveillance, there is considerable need for models
accounting for effort scheduling, costs, statistical
strategies for sampling, continuous versus sampled
measurement tradeoffs, etc.  There has been almost no
analytic effort in this field, though both the statis-
tical foundations and the measurement technology are in
hand.  A related statistical treatment of sampling
frequency requirements using a power spectral approach
applied to estuarine data has been published by Gunn-
erson  (28).

In the enforcement area, analysis would be considerably
more difficult, since it would have to take into account
the diversity of standards, institutional arrangements
and local/state legal structure.  To initiate investiga-
tions of this type, several comprehensive surveys would
be needed; in particular, a detailed survey of exist-
ing standards in each state as well as a survey of the
permit/monitoring/surveillance/enforcement procedures,
techniques and effort levels of at least the more active
states.
                        21

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7.    Modeling Techniques - Systems Design

The greatest obstacles to realistic optimization of
treatment systems remain in the area of structuring
the basic performance versus cost models of individual
processes.  The single process most widely modeled
is the activated sludge process, almost always treated
in steady state, linear kinetics fashion.  Useful re-
views of the basic biological treatment kinetics are
given in Pearson (29*) and Eckenfelder  (30) together
with substantial data on the various rates, coeffici-
ents, etc. involved; results are applicable to acti-
vated sludge, trickling filters, anaerobic reactors
and aerated lagoons.  In these approaches, transient
and instability effects are only included by means
of experience limits on feasible values of loadings,
detention times, etc.  Direct attempts to model transi-
ent effects are reported by Smith and Eilers  (31*) who
present a time-varying computer model for linear
kinetics of the simultaneous action of carbonaceous
and nitrifying bacteria and by Andrews  (32*) who
presents a promising model for inhibitory, non-steady
state effects in anaerobic digestion.

The literature on process models including the effects
of N and P on the basic biological kinetics is scant;
likewise, models for N and P removal in biological
treatment are not widespread.  There is, however, a
growing basic data base due to strong interest in this
area - see Sachs and Sheets  (33) and Eliassen (92*).

In addition to a voluminous literature of models and
programs for non-formally optimized complete treatment
system designed based on engineering experience, there
are a number of models for describing performance
versus cost of multi-process treatment systems in
which a wide range of process parameters can be spe-
cified, among them Smith  (34*) dealing with municipal-
type paints and Parker (35*) who gives a thorough
examination of treatment process alternatives for
the canning industry.  Both references employ basic
relations based on linear, steady state kinetics.
The data base for processes such as final settlers is
considerably less reliable than for the widely in-
vestigated activated sludge or trickling filter
processes.
                        22

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There is a relatively less voluminous literature on
optimization of full, multi-process treatment systems;
the main techniques available are described below:

a.    Surface search - naturally, any of the deter-
      ministic performance  versus cost models de-
      scribed above  (or simulation models suitable
      for describing more complex interactions and
      transients) can be approximately optimized
      using the same surface search techniques re-
      ferred to under planning models.  McBeth and
      Eliasson  (36) report a surface exploration
      for minimizing cost of activated sludge
      processes based on grouping parameters by
      sensitivity.  Less formal trial and error
      optimization based on engineering insight is
      common in current engineering practice.

b.    Linear programming - due to the evident non-
      linearity of costs and performance in treat-
      ment systems, direct linear programming applicat-
      ions are rare.  However, techniques for iteration
      of linear programs to approximate non-linear
      (convex) costs and constraints  (i.e., convex pro-
      gramming) have been successfully applied.  An
      excellent example is the optimization of trickling
      filter design by Caller and Gotaas (37*) using a
      non-linear empirical performance equation and non-
      linear costs.  A markedly different application
      and approach is used by Lynn  (38)  in examining
      the problem of selecting rational planning periods
      over which to minimize the cost of treatment plant
      ownership; he gives a non-linear model of the com-
      plete stream of expenses and receipts over time and
      then bounds solutions from above and below with a
      linear programming formulation.

c.    Dynamic programming - the application of dynamic
      programming to treatment systems that can be de-
      composed into unit processes connected in series
      is immediate and obvious, due to the serial staged
                         23

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      nature of such systems.   A straightforward
      example for tertiary treatment systems based
      on empirical unit process fits is given by
      Shih and Krishman (39) .   A more detailed
      examination using standard dynamic programming
      format is given by Evenson, Orlob and Monser (40)
      and applied to the cannery treatment processes
      referred to above.

      It is important to note  that these dynamic
      programming formulations cannot deal with
      processes within a feedback (recirculation)
      loop; such loops must be treated as complete
      stages in the dynamic program.  Where such a
      stage contains too many  decision parameters
      to be handled computationally, the process is
      normally empirically suboptimized to reduce de-
      cision variables.

d.    Geometric programming -  a promising though not
      yet practically applied  technique for optimizing
      individual non-linear processes (as opposed to
      full systems with processes in series)  that can
      be described using polynomial costs and constraints
      is geometric programming (non-integral positive
      exponents for the polynomials are permissible).
      Meier et alia (41*)  give an introduction to the
      technique with a simple  tank/pump system example.

e.    Pontryagin maximum principle - this standard
      optimization technique in control theory has
      been applied to rather abstract system design
      problems with relatively artificial cost functions.
      It represents in essence a generalization of class-
      ical calculus of variations.  Erickson, Yo and Fan
      (41*) applied a discrete version of the maximizat-
      ion principle to optimum allocation of loads be-
      tween stages of completely mixed and plug flow
      step aeration systems.  Unfortunately, the optimi-
      zation criterion is  minimum volume which is by no
      means equivalent to  minimum cost; nevertheless  the
      results yield interesting insights into the marginal
      benefits of extra stages and the comparison of com-
      pletely mixed with plug  flow processes.  Tarassov
      et alia  (42) , solving for optimum river reaeration
      policies, apply the  maximization principle to a system
      of partial differential  equations describing DO as
      a  function of artificial reaeration effort distributed
                        24

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quasi-continuously down a stream reach.  Again,
the optimization criterion is relatively artifi-
cial: it is the streamwise integral of squared
DO deficits weighted by an arbitrary cost plus
the integral of the square of the DO artifically
added.
                   25

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                    SECTION IV

PHYSICAL, CHEMICAL AND BIOLOGICAL CONSIDERATIONS IN
WATER-QUALITY MODELLING
1.    Introduction:  The Complexity of the Problem

Models, however complex and sophisticated they may be,
are simplifications and approximations of natural
phenomena.  When the natural phenomena are well under-
stood, carefully measured, and confirmed by years of
accurate observation, a model may have excellent de-
scriptive and predictive power.  However, when the
underlying phenomena are thoroughly understood, de-
scribed and confirmed, any model based on them must
be used with caution, intellectual humility, and some
appreciation for its relative strengths and weaknesses.
In this chapter we shall discuss some of the most im-
portant physical, chemical and biological matters that
must be borne in mind in evaluating a water-quality
model.  The most important lesson is that water-quality
phenomena are complex, dynamic, and interrelated; the
chemical, physical, and biological aspects of water-
quality are alloyed in reality.  When this alloy is
decomposed and simplified for analytical convenience
in modeling, one must take care not to confuse the
analytical solution with the often insoluble complex-
ities of real water-quality problems.

An example or two may help.  Many water-quality pheno-
mena are closely related to mixing.  Wastes are di-
luted by mixture with flowing water; they are chem-
cally changed by the action of oxygen that has been
dissolved in the water; they settle as sludge or
are caught up in the streamflow, depending on the
strength of turbulent mixing in the water.  Many
determinants of mixing are to be found in the stream-
bed:  its slope, contours, geometry, roughness, twists
and turns.  In sections of a stream where the bed
slopes gently, where the contours and geometry of the
cross-section change frequently, where the bed is rough,
and the channel twists and turns every few yards,
mixing will be excellent, wastes will be quickly dis-
persed and thus offer themselves more readily for
cleansing by a variety of physical, chemical and bio-
logical processes.  Where the bed is deep, straight,
smooth and invariant, there will be much less mixing
and much less opportunity for chemical, physical and
biological purification.  Many water-quality models
pay no direct attention to the streambed; they deal
instead with certain derived attributes generally
treated from a steady state pont of view  (such as
                        26

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mean flow, reaeration coefficients, mean velocity,
mean depth).  These attributes are analytically
convenient but less informative and often downright mis-
leading, because the variations in depth, flow, etc.,
are usually much more significant than the correspond-
ing averages.  Perhaps the most telling example is
average concentration of toxic matter:  it is not
necessarily the long term average concentration
of a poison that converts a river into a biological
disaster; rather, it may be the maximum concentra-
tion over a few minutes or hours that determines whether
the organisms that depend on the river will live or die.
One lethal dose kills, even if the river is free of
poison for the next six months and even if the six-
month average is innocuous.

The system analyst who must deal, with water-quality
models is advised to spend some time in familiariz-
ing himself with (1) the body of water that is being
modelled and  (2) the most important fundamental con-
cepts in physics, chemistry, and biology of water-
quality research.  Maps, charts, and other decrip-
tive materials -- often excellent -- are available
from a variety of sources:  state agencies (such as
departments of natural resources, water boards,
pollution-control agencies, engineering advisory of-
fices, etc.), interstate and regional agencies (such
as interstate compact commissions and regional inter-
state river-basin commissions), and a wide variety
of Federal agencies  (including the Geological Survey,
and the Coast Guard, the Array Corps of Engineers, the
Bureau of Reclamation, the Soil Conservation Service,
the Fish and Wildlife Service, and the Bureau of
Outdoor Recreation).  Several excellent introductory
treatments of water quality are generally available;
Kittrell's superb handbook  (43) and the "Green Book",
Water Quality Criteria  (44) are especially recommended.

2.    Basic Considerations and Terms

There are two principal  types of water-quality models:
(1) those that model water quality due to a single dis-
charge, such as the outlet of a sewage-treatment plant,
and (2) models of related points.  The second type of
model is usually more complex because it must deal with
water quality as multiple functions of distance and/
or time of travel in the flow.  Roughly speaking,
the first type of model is Eulerian, the second La-
garangian.  For expository convenience, we shall con-
cern ourselves mostly with the latter because they in-
clude the full scope of physical, chemical,  and bio-
                        27

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logical phenomena that pertain to water quality.

Models of water quality must begin with waste sources.
There are two general types:  (1) point sources,
usually limited to municipal and industrial wastes,
and  (2) area sources, principally agricultural wastes.
Very little has been done to model area sources, al-
though agricultural pollutants (such as pesticides,
herbicides, fertilizers, salts leached from soils by
extensive irrigation, and microbial nutrients leached
from manure piles in animal feedlots) have begun to
receive a great deal of attention.  In fact, area
sources are all too often ignored in studies of
optimum allocation of treatment resources.  Although
some industrial wastes are included in municipal wastes,
municipal wastes generally are of two related types:
 (1) so-called sanitary wastes, and (2) miscellaneous
wastes such as garbage that enters the sewer  system
through such routes as garbage disposal units.  Both
types of municipal wastes are predominantly organic
materials of biological origin,  largely food, its
digestive end-products, food scraps,  and street litter.

Industrial wastes are not so easily categorized:  Each
industry produces wastes that are characteristic of the
manufacturing processes it employs.  The wastes from
a petroleum refinery are vastly different from those
of a sugar-refining plant, a paper factory, a thermal-
electric power plant, a mineral-processing plant, a
soap factory, or an industrial chemical plant.  The
types of pollution problems that these wastes create
are similarly diverse, ranging from thermal pollu-
tion  (hot -- or more usually simply warm -- water,
which can damage aquatic life and disrupt the chemis-
try of the stream) to weak acids that drain from aban-
doned mines, to tons of pulverized tailings from mine-
ral processing plants, to a variety of offensive colors,
odors, and toxic chemicals.

The system analyst must constantly keep in mind the
enormous diversity of wastes that may be dumped into
water.  Unfortunately, due in part to traditional
emphases in sanitary engineering, most water quality
models are concerned only with BOD or COD  (biological
and chemical oxygen demand), which only measure --
and not too precisely, at that — the amount of oxygen
that is required to convert organic wastes into carbon
dioxide, water, and other simple oxides.  Many kinds
of wastes, however, exert little or no BOD or COD.
                        28

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Hot water discharged from a power plant may cause
a serious pollution problem, without affecting
oxygenation  (other than through temperature effects
on oxygen saturation and on metabolic rates) in the
least.  Taconite tailings from an ore-dressing plant
may smother a lake bottom and all the life that dwells
there without contributing BOD or COD at all.

Nevertheless, most models are concerned only with one
or another aspect of oxygen demand, as though water
pollution were synonymous with oxygen depletion.  The
oxygen content of water is usually cited as DO  (dis-
solved oxygen).  When readily oxidized matter is in-
troduced into water, microorganisms will metabolize
it, thereby consuming some of the DO.  A graph that
depicts the lowering and recovery of DO vs. distance
below a BOD discharge point is called and "oxygen-
sag curve."  At the same time that DO is being con-
sumed, the water will dissolve fresh quantities of ox-
ygen as it continues to flow; this process is called re-
aeration, and it is exceedingly complex. Although there
is a variety of models that purport to describe the
relationship between oxygen-demanding wastes, DO, and
reaeration, the system analyst is warned that the re-
lationship is in fact not very well understood at all:
It is obscured by any number of unknowns, unaccounted
factors, and an insufficient data base.

DO is not the only measure of water quality, and a
body of water may "assimilate" many kinds of waste
besides oxygen-demanding wastes.  A stream may have
a perfectly acceptable DO, yet be dangerously polluted.
It may be loaded with pathogenic bacteria, viruses,
protozoa, and parasites; it may be excessively acid
or alkaline;-it may be too warm, too turbid, or con-
tain unacceptable concentrations of hazardous inor-
ganics such as boron, cadmium, lead, or mercury;
it may have dangerously high levels of agricultural
pesticides and herbicides; it may simply be too saline
(which is one of the principal water-quality pro-
blems of the Lower Colorado River Basin).  Never-
theless, the system analyst will discover that the
vast majority of models are concerned only with DO,
BOD, or COD, the oxygen-sag curve, and reaeration.

Once the wastes have been introduced into the water,
they become part of an extraordinarily complex and
intricate ^reaction system whose physical, chemical,
and biological parameters are dynamic and interrelated.
They are mixed in three dimensions  (vertically,
laterally, and longitudinally); precipitated and
scoured; exposed to many kinds and sources of energy
(mechanical, thermal, optical, chemical, and bio-
chemical); passed by and over a variety of filters

                        29

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and adsorptive sites — ranging from clays, gravels,
sand, rubble, cellulosic materials, and biological
detritus to dense populations of aquatic plants and
animals, whose surfaces (including the surfaces of
their digestive and respiratory tracts) offer excel-
lent reaction sites; and put into contact with all
the other chemical compounds in the water.

When we speak of a stream "assimilating" wastes, we
are compressing into one word all the physical,
chemical, and biological processes that purify_
water.  The chemical mechanisms alone include ion
exchange, acid and alkaline hydrolysis, auto-oxi-
dation, photolysis, catalytic oxidation, enzymatic
oxidation, and a long gamut of addition and sub-
stitution reactions.  As the wastes are carried along
by the current of water, they are progressively
exposed to these purifying processes; but the pro-
gression of processes cannot be predicted with any
confidence; thus, it will be seen that most models
of instream processes are largely empirical and
rarely precise.

The physical factors of a stream or current are so
interrelated that it is almost impossible to separate
the effects that they bring about.  The slope and
roughness of the water course influence both depth
and speed of flow, which together control turbulence.
Turbulence, in turn, affects mixing rates, reaeration,
sedimentation and scour, growths of biological forms
attached to the bottom and sides of the channel, and
rates of natural purification.  Water temperature
affects the rate at which wastes are decomposed, the
amount of dissolved gases (especially oxygen)  that
the water can hold, and the forms of life that can
flourish in the water.  Turbidity and color affect
the quantity of light that can penetrate the water's
surface to sustain photosynthesis by aquatic light-
dependent chemical reactions.

3.    Hydrological Inputs, for Analytical Modeling

For general background in hydrology, Chow (45)  re-
presents a useful reference.  Specifically, an
essential input (or set of test conditions)  for anv
water quality model that accounts for flow variations
over time is a streamflow record that 'realistically1
represents the flow that can be expected over the
planning period employed.   Where historical records
of sufficient length and accuracy are available, these
are often used in raw form.   In
                        30

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the more common case where such records are un-
available , synthetic flows derived from available
or correlated records must be generated.  The basic
references for monthly streamflow generators are
Beard (46) and Thomas and Fiering (47).  Matalas (48)
has a -useful review of the methods of synthetic hy-
drology.  Monthly  (or yearly) generators are generally
based on a transformation and distribution fit  (us-
ually log Pearson Type III or log normal) to the
available data with serial correlation coefficient
estimates for each month; normally, correlation with
any month before the immediate predecessor has been
found insignificant.  The resulting statistical para-
meters" are then used to transform the output of a
random number generator to any desired length of re-
cord.  This same basic technique is extended to cor-
relate different gaging stations on the same or
different streams when inputs for modeling of multiple
reaches or streams are required.  A further exten-
sion developed by Benson and Matalas (49*) allows the
generation of synthetic monthly and annual flows for
multiple ungaged locations in a basin; the technique
developed is simply the regression of means and stan-
dard deviations for the gaged locations within the
basin on six basin/climatic variables.  The regression
formula then predicts the statistical parameters of
flow for any other location in the basin, though with
considerable prediction error.

The generation of daily  (or shorter period) synthetic
hydrographs is considerably more difficult due to the
need to preserve realistic behavior of the ascension
and recession curves around peak and low flows; the
behavior of these curves appears to have a strong
deterministic component not accounted for by straight-
forward statistical methods such as Beard's second-
order Markovian daily generator  (46).  A non-rigorous
but considerably more realistic  (and impressively
validated) technique is presented by Payne, Newman,
and Kerri  (50*); the technique is based on rearrange-
ment of the daily records around the critical event(s)
in each month in order to preserve ascension/recession
behavior.  After rearrangement, the statistical treat-
ment follows the standard methods described for
monthly generators.

Of more specialized interest in water quality model-
ing is surface runoff hydrology; Betson et alia  (51*)
have a successful simplified empirical model for pre-
                         31

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dieting runoff from rainfall data; Huggins and Monks
 (52*) present a theoretical model based on micro-
detail .

For groundwater hydrology there exists a voluminous
literatures good basic reference is Todd  (53).
The area of most direct interest to the water quality
analyst invlolves the fitting of a ground water model
for elevations, heads, storage, etc. to the usually
inadequate data available.  Although least squares and
linear programming techniques for fitting the requisite
parameters exist, e.g., Kleinecke (54), they generally
do not provide satisfactory results.  Two interesting
practical approaches are available:   Vemuri and Kar-
plus  (55*) present a practical hybrid computation pro-
cedure based on Pontrayagin's maximization princi-
ple that allows direct application of hydrological
insight and experience; Meyer  (56*)  develops a direct
stochastic perturbation technique for sensitivity
analysis of groundwater models.

4.    Dissolved Oxygen Modeling

The bulk of water quality models are concerned with
DO as the measure of stream pollution.  DO is in
fact one of the most important aspects of pollution,
though it does not necessarily dominate water quality
considerations in all stream situations.  Due to the
long history of interest in this parameter, there
exists more literature on BOD/DO modeling than on
any other stream pollutant.  Unfortunately, this
does not imply either completeness or satisfactory
accuracy in current methods.

The basis of most work today remains the Streeter-
Phelps equation which assumes steady state condi-
tions and linear deoxygenation rates proportional
to BOD5 loads plus linear reoxygenation rates that are
constant for a given stream reach.  Various authors,
Dobbins (57), O'Connor (90*), etc.,  added other
linear rates or constants to represent benthic de-
mands, photosynthetic contributions, sedimentation,
etc.

Falk (58)  has made a significant advance in realism
by developing a model which accounts for two stage
BOD (carbonaceous and nitrogenous) from multiple
sources and varying temperature profiles  (and
associated saturation levels), heat loads and stream
cross sections.  Li (59*)has developed a variety
of non-steady state solutions  (retaining one-dimen-
sional flow,  however) to represent diurnal variations
in load/photosynthetic contribution, cross-section
and runoff input variations,  etc.

                        32

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An extremely useful area is the prediction of stream
behavior without a need for in-stream measurements.
Churchill et alia  (60*) made a significant step in
this direction with an excellent series of field
•studies on reaeration constants in clean streams,
resulting in an empirical fitting equation using
depth and velocity.  Isaacs  (61*) significantly
improved the fit and the theoretical validity of
the predictive model.  To complete the capability
of approximately predicting stream DO behavior with-
out in-stream measurement, the following are needed:

a.    A predictive characterization of the effect
      of general pollutant concentrations in chang-
      ing reaeration rates from the basic clean water
      rate.

b.    A predictive characterization by industry or
      process of both the basic deoxygenation rate
      and the general shape of the BOD curve for a
      comprehensive cross-section of important
      wastes.

A number of authors have conducted field studies on
photosynthetic contributions and diurnal variations,
including Meritt et alia  (62*), Rudolfs et alia  (63*)
and Ignjatovic  (64*).  It is clear that photosynthesis
is a major oxygen contributor  (up to 75% of total
reaeration has been reported); unfortunately, despite
the successful fitting of Fourier series approximations
to the diurnal cycle by Kartchner et alia  (65*) it is
not clear that the data base is sufficiently complete
to allow prediction of amplitudes as a function of
algal density, ambient light, turbidity, nutrients,
etc.

Another important area is the analysis of stochastic
variations in DO, due to load, streamflow and bio-
logical process variations.  An interesting model has
been presented by Thayer and Krutchkoff  (66*) based
on a probabilistic formulation of the Dobbins deter-
ministic approach; mean DO results coincide with
Dobbins but DO variability is shown to increase as
DO decreases, implying that the worst fluctuations
can be expected under the worst pollution conditions.
Other authors have recognized the inadequacy of
planning deterministically to a deterministic DO
standard, notably Loucks and Lynn  (67).
                        33

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A final area, as yet uninvestigated for stream situa-
tions, is the modeling of large transient BOD inputs
including the effect of longitudinal mixing (thus
eliminating the usual one-dimensional assumption),
in accordance with Thomann's concept of a stream step
response (27*).  Such modeling would require extensive
dye studies in the field in  order to be able to
predict the mixing properties of a stream from its
physical configuration.  The importance of such studies
derives from that fact that  they are required in
order to be able to impose needed peak effluent re-
gulations on discharges (slug discharges are respon-
sible for a significant portion of fish kills).
                       34

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                     SECTION V

       LEGAL, SOCIAL, DEMOGRAPHIC, ECONOMIC,
     AND OTHER RELATED ASPECTS OF WATER QUALITY
1.    Introduction

Because water is one of the Nation's most important
basic resources, a resource that is tapped by almost
every human activity, systematic studies of water and
water quality have inevitably grown to include almost
every major activity and to incorporate every in-
tellectual discipline.  Every principal water agency
of the Federal Government now conducts systematic
studies of water requirements (both present and pro-
jected) that include demographic patterns and trends,
economic analysis, sociological and political trends,
and legal considerations, in addition to hydrology
and water-quality sciences.  The literature on these
related factors is enormous; in this short chapter
we can do little more than refer the interested
reader to the most important sources, and quickly
summarize the most important trends in recent studies.
Some of the most important on-going research is also
discussed.

Adequate supplies of water of acceptable quality are
essential to the Nation's health, welfare, and prosperity.
As the nation has grown, pressures on its water resources
have become acute; in some regions (such as the High
Plains of Texas and the Lower Colorado Basin), water is
already the limiting resource for certain critical
economic activities, such as agriculture.  To conserve
and make the wisest use of the Nation's water, comprehensive
planning studies of water in relation to economic growth,
environmental policy, demographic shifts, technological
development, interregional and intersectoral competition,
are conducted by administrative policy in all of the
Federal agencies that participate in the Water Resources
Council. The universities (especially those that have
Water Resources Research Institutes that were established
by the Water Resources Research Act), private or semi-
public research institutes (such as Resources for the
Future and the Brookings Institution), and lower levels
of government also conduct or sponsor studies of water
quality that include these related factors.

While comprehensive scope and global perspective are
admirable in any truly systematic study, these same
qualities can also lead to formidable practical problems
such as incomplete or grossly inadequate data to support
such ambitious analyses, insufficient sensitivity to
interactions among factors, and uncritical extrapolations

                       35

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 of purely  fortuitous historical trends into the nebulous
 future.  The most ambitious of these studies are vir-
 tually indistinguishable from master plans for national
 economic growth; those that concentrate on purely local
 water-quality problems often suffer because they are
 unduly negligent of larger regional and national issues
 whose resolution must necessarily affect the pattern
 of water use in every locality.

 All  systems studies of water must ultimately be framed
 in terms of two categories:  water quantity and water
 quality.   Every other category of analysis depends on
 these two, for these other categories are all concerned
 with allocation of the resource among competing uses and
 users, incidence and distribution of the associated
 costs and  benefits, restraints on use, and provision  for
 future use by generations yet unborn.

 The  definiencies of water quality studies that fail
 to consider the most important related factors (such
 as economics) are usually readily apparent and need no
 further comment here.  The problems of global inclusiveness,
'however, merit some analysis.  One of the most instructive
 examples is the Water Resources Council's plans for the
 Second National Assessment of the Nation's Water Resources
 (2d  Assessment, hereinafter).

 The  Water  Resources Planning Act of 1968 (P.L. 89-80,
 42 USC 1962a et seq.) created the Water Resources Council
 as a forum for coordinating the activities of all the
 Federal water agencies.  One of the Act's provisions
 empowers the Council to assess the Nation's water
 resources  from time to time and to report the results
 to the President and the Congress.  The principal
 objective of these assessments is to alert the Nation
 to its water problems (i.e. insufficient quantity,
 inadequate quality, and their consequences) so that pre-
 ventive or corrective action can be taken.  The 1st
Assessment was prepared and published soon after the Council's
 establishment; it was hastily prepared and torn apart
 at leisure.  The principal deficiencies of the 1st Assess-
ment included insufficient data (especially on water
quality and water use), inadequate analysis of interactions
 among factors (e.g. regional ambitious for water-related
economic growth as opposed to balanced national economic
growth or national economic efficiency), marked over-
simplification of dynamic factors (such as population
growth,  demographic s5lifts, the direction and pace of
technological development), and insensitive techniques
 (based on simple extrapolations of recent historical
trends)  for projecting future water requirements.

                         36

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The Council began planning for its 2d Assessment almost
immediately.   A contract was awarded  to A.D. Little,
Inc. , to draw up plans for the 2,d Assessment; the final
report for this contract was published in 1970, but not
widely distributed.  These plans were made public at a sym-
posium sponsored by the U.S. National Bureau of Standards
(7-8 May 1970) and criticized by an audience that included
hydrologists, engineers, economists, planners, and system
analysts from several prominent university facilities,
the Geological Survey, the Federal Water Quality Admin-
istration, the Office of Water Resources Research, the
National Water Commission, the General Accounting Office,
the Economic Research Service, the Office of Business
Economics, and the Corps of Engineers.  Much of the following
analysis is summarized from that discussion.

A.D. Little's plans were comprehensive indeed.  Two
layers of analysis were defined: a hydrological layer,
and a superimposed economic-demographic layer.  The
hydrological layer called for a complete quantity-quality
model of all the Nation's water, both surface water and
ground water.  The Nation was to be divided into approximately
20 hydrological regions (roughly >corresponding to the
river-basin regions of the 1st Assessment); these regions
were to be subdivided into subregions, and the subregions
subdivided  into  zones.  The model was to describe and
predict the quality and quantity of water as it flowed
from zone to zone within subregions, and from subregion
to subregion within regions; interregional transfer of
water was explicitly excluded, partly for legal reasons.

Several hydrologists inquired where all the data on
quality and quantity would come from.  The fluctuating
quality of the Nation's waters is not at all well documented:
there are great gaps in the data base, and much of the
available data (such as BOD measurements)  are notoriously
erratic.  While the data on water quantity are more complete,
they are not up to the zone-by-zone analysis A.D. Little
calls for, particularly in the arid West,  where much of
the scarce water is from ground-water sources that are
incompletely charted, and whose flows are not well documented.
Several in the audience commented that if this large and
expensive model could only :guess at hydrological data for
the arid West where problems of water quantity are already
the most severe in the Nation, why  bother with it at all?

The superimposed grid of demographic-economic data creates
other problems.  The purpose of constructing this second
grid is to compare, analyze, and predict probable water
demands in relation to the probable water supply  (which
the underlying hydrologic grid was to have shown).   The
three principle types of data in the superimposed grid

                        37

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 are:   (1) demographic data (population densities,
 distributions, and growth patterns); (2) agricultural
 data  (consumptive uses of water for irrigated farming,
 and alterations in water quality by fertilizers, herbicides,
 pesticides, agricultural and feedlot wastes; and  (3)
 industrial data (location of industries and specification
 of their waste effluents).   These data were to be supplied
 by two principal Governmental sources:   the Office of
 Business Economics (QBE) of the Department of Commerce
 and the Economic Research Service  (ERS) of the Department
 of Agriculture (the initials of these two agencies were
 combined into one acronym,  OBERS, and the OBERS system
 for producing joint demographic-agricultural-industrial
 data  for water-management studies has become an important
 data  source).

 There are several difficulties in the OBERS system, and
 they  are the familiar ones:  inadequate data, controversial
 (many would say "mistaken") methods of analysis, and
 insufficient sensitivity to the dynamic factors that will
 shape future needs for water.

 The fundamental demographic data are certainly sound
 enough since they are based on the U.S. Census.  Projections
 of these data are another matter altogether.  Estimates
 of the population growth rates have been shrinking every
 year for the last several years; the great population
 increases that the experts predicted just ten years ago
 have fallen far short of the mark; the experts now predict
 a very slow growth rate, but they could be just as wrong.
 There is ample reason to doubt the accuracy of the estimates.
 Yet our pollution-abatement activities today must be
 synchronized with the growing pressures for water for
 tomorrow.  It makes a great difference in our water-quality
 activities to know when we must have sufficient clean water
 for a population of 400 million.  Much depends on our
knowing with some precision how many people will live in
which areas at what time in the future.  If people continue
to congregate in a few densely populated urban areas,
water quality problems will be concentrated there.  If
they continue to migrate heavily to the arid Southwest,
the competition for water between cities, industries, and
agriculture in that semi-desert region will be exacerbated.

One powerful reason that the experts guess wrong is that
demography is sensitive to a variety of governmental policies
that may be as fickle as election results.  Population
growth is very sensitive to such factors as wars, depressions


                        38

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inflations, and the whole constellation of factors that
encourage upward mobility.  Population shifts are also
sensitive to governmental policy.  A combination of
technological advances and federal policies on agriculture
and irrigation helped accelerate the depopulation of
farm communities, and contributed to the substantial
shift of agriculture from the wet Southeast to the arid
Southwest.  The development of large industrial complexes
in certain rapidly growing urban areas (such as Phoenix,
Los Angeles, and Houston) has been intimately related to
the award of large Government contracts.  In the absence
of sustained and explicit governmental policies on such
matters as population growth, population distribution,
regional economic growth, national economic efficiency,
and similarly fundamental issues, demographic prediction
is subject to large errors.  The systems analyst must be
distrustful of all models whose results depend in any
way on long-term demographic projections.

Hydroeconomic data on agriculture are even more restricted.
The dynamic factors in this area are even more dependent
on governmental policies and on the predictable pace and
direction of technological development.  The enormous
labor of sorting out the contribution of irrigated
agriculture to our national production of food and fiber
is just now being undertaken systematically by Prof.  Earl
O. Heady and his colleagues at the State University of
Iowa.  Until Heady's analysis is complete, one can only
approximate the quantities of water that the nation must
set aside for irrigated agriculture.  The whole question
of agriculture's needs for water is intimately bound up
with such policy issues as the soil bank, price quotas
and acreage restrictions, agriculture export and import
restrictions, and substantial food give-away programs.
Change any of these policies, and agriculture's needs
for water will be affected.  Shifting large segments
of agriculture from the Southwest to the Southeast
through changes in irrigation policy would necessarily
affect water quality in both regions: agricultural
pollution would increase in the Southeast and decrease in
the Southwest.  Removing the subsidy on sugar beets would
eliminate beet sugar and its attendant pollutant loads
(and as a concomitant, would create the problem of
finding some use for the displaced land, labor and faci-
lities)".  No model of national water-quality problems
can afford to ignore these problems, but none can deal
with them either, except by postulation.  These cir-
cumstances create a modeller's nightmare, none-the-less,
it is incontrovertible that many of the major determinants
of water quality depend
                        39

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on policy factors that cannot be accurately defined or
predicted.  Although the OBERS system draws on all the
accumulated experience of the U.S. Department of Agriculture,
it is virtually helpless to deal with dynamic factors
in agricultural water consumption.

Considerations similar to those in agriculture apply to
industry's needs for water and the associated water-
quality problems.  A few sizeable changes in international
trade agreements and in federal tax law could create
or wipe out whole segments of industry.  The discovery
of a reliable and cheap source of new energy (such as
the direct conversion of atomic energy to electrical
energy) could revolutionize American industry, and
utterly change industry's needs for water and its
water-quality problems.  Here again, the national
assessment models of A.D. Little cannot begin to deal with
the challenge of prediction in the face  of changing policy
and technology.  And here, too, the available data on
industry's water needs and waste-disposal problems are
simply not adequate.  One observer from the General
Accounting Office seemed to crystallize the sense of the
adverse comments when he noted that if we have to guess
about future demography, about current and future agricultural
economic data, about almost all aspects of water-quality
problems due to cities or industries or to farming, about
the movement of water from zone to zone, and so forth; if
we have to guess about all this, why not just make one or
two big quesses at the end about water quality and water
quantity rather than spending so much time and money fab-
ricating data to feed into an extremely expensive computer
model that will do no more than produce a highly compounded
guess.

Because these complex policy and technology factors must
be considered but cannot be incorporated except by some
axiomatic method, it is now increasingly common for modellers
to run their analytical and simulation routines against a
variety of policy and technology factors combined into
various scenarios.  Current examples of policy scenarios
in water quality models include the Heady model for irrigated
agriculture,  the interregional and intersectoral models of
the National Water Commission (R.G. Thompson) and the
very influential Wollman-Bonem model for quality, quantity,
and cost in 22 major water resources region   The Wollman-
Bonem model (24)  has been widely circulated in manuscript,
and has just been published.  Because this model has be-
come so well-known, it is worth devoting a few paragraphs
to a summary description.

                        40

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The Wollman-Bonem model emphasizes national and basin level
water quality considerations; the model was constructed
to evaluate three water-quality policies or strategies:

1.    least flow of water to dilute wastes; waste treat-
      ment is maximized, thereby bypassing the requirement
      for releasing water stored in reservoirs to dilute
      wastes to acceptable levels of water quality.

2.    least treatment of wastes; storage of water in reser-
      voirs is maximized, thereby creating the largest
      volume of stored water being kept at the ready to
      dilute waste-filled waters.  Dilution replaces
      waste treatment.

3.    least cost; water storage and waste treatment are
      selected in combinations so as to minimize cost for
      a specified level of water quality.

Each of these policies  (or strategies) is run against
a range of assumptions and specifications that cover other
variants such as projected withdrawal and consumptive uses,
storage costs, interest rates, amortization rates, water-
quality standards, and probability of minimum streamflow.
Because this model was first published in 1960 and has
been extensively criticized, refined and extended during
the last ten years, it is one of the pioneering attempts
in national water quality analysis.  In the latest version
of the manuscript reviewed by the authors of this report,
stream quality was represented by three parameters:
dissolved oxygen, phosphorus, and nitrogen; it was assumed
that pollution due to microbes, chemicals, and suspended
solids would be reduced to acceptable levels by the
dilution flows that would be required to meet stream standards
for dissolved oxygen.  Although the model has been widely
acclaimed, the systems analyst is warned that the Wollman-
Bonem model involves major unverified approximations and
is not self-contained:  it requires data on water use,
on the costs of regulated streamflow versus treatment,
and on pollution loading.  The difficulty of obtaining
reliable and accurate data on any of these three is well
known; the results of the model must be interpreted with
the limitations on data and basin-wide approximations in
mind.

The following sections represent a brief introduction
to major concepts, literature and data of importance
to the analysis of water quality management.


                        41

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 2.    Legal/Social/Political Aspects Relevant to Water
      Quality Analysis

 Water resources in the United States are subject to a
 bewildering variety of governmental c°ntr°JS *?f,^"_
 tions due to the diversity of interests and political geo
 graphies involved.  The tradition of public control of water
 predates the American legal system by many centuries; it is
 universally recognized that water resources cannot be managed
 through the normal operations of a competitive market and
 private property system.

 The  fundamental body of law controlling water resources
 is concerned with the right to use of water.  Water rights
 law  is divided into two general doctrines, the riparian
 rights concept which holds in the East and the appropriative
 rights concept which applies throughout the West.

 The  former operates under the principle that every owner
 of property adjoining a water body has a right to have
 the  flow continue undiminished in quantity or quality, a
 condition that is clearly impossible to guarantee literally.
 In practice, this principle allows the riparian owner to
 sue  upstream dischargers or withdrawers for any damage
 that he can demonstrate he has sustained.  Such suits have
 not, in general, been effective in preserving the quality
 of Eastern streams due to the difficulty of proving sub-
 stantial damages.

 The  western appropriative rights doctrine holds that
 surface waters may be appropriated for beneficial use
 by any person, subject only to non-interference with
 previously established appropriative rights (these
 rights fall under state rather than federal sovereignty).
 This system also has substantial drawbacks, particularly
 with respect to overall social/economic benefits, not
 to mention the inequities that can be created through
 purchase of land with its associated water right by
 powerful economic interests (e.g., the famous Owens
 Valley War in which Los Angeles purchased and diverted
 enough water rights in the Owens Valley to wreck the
 Valley's economy and land values). An excellent review
 of water rights law is contained in Hutchins (68) .

 It is to be noted that the status of percolating ground-
water is considerably different.   By and large
percolating groundwater has legal status similar to
 underground mineral resources; with the exception of
 certain states such as New Mexico, groundwater is
privately owned as a direct concomitant of land ownership.
Where well defined underground channels exist, the sur-
 face water rights doctrines can be (but are not always)

                       42

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applied.  Needless to say, these legal distinctions
cannot be sustained hydrologically; thus, there is
an increasing trend toward local (and possibly national)
regulation of groundwater use and quality, through
special groundwater districts, powers of taxation,
permit systems,

Useful references concerning existing legal arrange-
ments specifically related to water quality and their
variations across the country are Wollman (69) and Sax
 (70),  (71).  Due to the rapid development of legal
precedents in this area, periodicals such as the Bulletins
of the Environmental Law Institute and the Environmental
Reporter may be important to the analyst concerned
with constructing legally feasible alternatives
for water quality management in various areas.

The local variations in applicable law correspond to
the great variety of interlocking and overlapping
political mechanisms and jurisdictions controlling
water, from township and special purpose water or sanitary
districts through regional authorities, interstate compacts
and federal river basin agencies.  An important general
reference is Davies (72).  An excellent case study of
the functioning of such multiple political institutions
in the complex Los Angeles area has been compiled by
Warren (73); Mann (74) has studied Arizona.  Various
proposals for different political arrangements have
been published; notable is Kneese's (26) description
of the functioning of regional water resource/quality
cooperatives in the Ruhr.

There have been various attempts at sociological
analysis of water-related institutions and water
interest groups; perhaps the most ambitious is the
attempt to develop a quantitative model of institutional
behavior by Males et alia (75*) for the case of a
California Regional Water Quality Control Board.  The
National Water Commission (76) is publishing a survey
of public reactions to water problems and policies.
By and large, these attempts are not directly usuable  in
systems analysis due to lack  of validation.  Never-
theless, it is certainly important for the analyst
to understand clearly the interest groups and institutional
history relevant to water quality in any given region
under analysis.

3.    Economic Issues in Water Quality Analysis

A background in the overall economics of water is

                         43

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essential for accomplishing useful systems analysis
in water quality.  Of particular importance is an under-
standing of the economic impact of water on_the develop-
ment, growth and prosperity of regions and_industries,
as well as the conflict of regional economic interest
with national economic interest.  Important general
references here are Maas et alia (77)  and Smith and
Castle  (78).  In the specific area of economics of water
quality, major references are Kneese (26) , Jarret (80)
and FWPCA  (81).  Howe and Easter (82)  have dealt with_the
more specialized subject of interbasin transfers; their
book is valuable for the variety of construction cost
data and economic benefit data (particularly for
agriculture) presented.  It is particularly important
that the analyst be familiar with the areas of economic
benefit that have been usefully quantified and those_
that have not.  Extensive and useful regional analysis
of agricultural economic benefits has been accomplished
for irrigated regions in the West;  e.g., Heaney (9*)
has modeled water benefits and optimum allocation for
44 regions in the Colorado River Basin.  However, indirect
or multiplier benefits beyond direct gross value-
added measures remain highly uncertain.  Direct economic
benefits of water for Eastern agriculture have not
been studied intensively and little data is available
to the analyst.  Industrial economic behavior with respect
to water quantity, price and quality variations, though
understood in theory, has generally not been  reduced
to empirical, numerical results useful for water quality
planning.  Recreational benefits have neen extensively
studied and at least useful lower bounds on the dollar
value of recreational use have been estimated; general
references in this area  are Knetsch (83) and Davis (84).

In long range water quality planning, projections
of water use and quality as related to economic and
demographic considerations are an essential input.
A good appreciation of the uncertainties and weaknesses
involved in such projections can be obtained from Wollman
(24)  for national projections and Goldstone et alia
(85*)for detailed regional projections of the Susquehanna
River Basin.

A special topic of interest in water quality economics
is the question of direct regulation of discharges
versus effluent changes and/or subsidies.  Besides
the major review by Kneese (26), Upton (86*)  addresses
the question of optimal taxation in the absence  of
knowledge of individual discharge cost functions.
Johnson (10*)  computes actual charges necessary to
achieve prescribed DO standards for the Delaware
Estuary, based on estimates of discharger treatment

                         44

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costs and simplified assumptions concerning industrial
responses.

A final major economic input to water quality analysis
is the area of costs, particularly costs of low-flow
augmentation, in-stream aeration, centralized and in-
dividual discharger treatment/disposal.  Basin references
in this area are FWPCA (87) and  (88).  Costs for in-stream
aeration are given in Davis (89); details of biological
treatment costs can be found in Smith  (91) and Parker
(35*); generalized costs of reservoir storage are given
in Maas et alia (77) and Howe and Easter  (82).  Needless
to say, the precision of cost estimates in these areas
is relatively poor; it is essential  for the analyst
to have an appreciation of the range of uncertainty
in each case.

Important areas in which almost no cost data base is
available are the direct costs of pollutional damage
to downstream users and the costs of industrial
pollution abatement versus improved housekeeping or
process changes.  These can and have effected surprisingly
large reductions in pollutant loads  for a substantial
number of plants at low or even negative cost; ignoring
the possibility of major industrial pollution abatement
without the normally assumed capital investment in
standard treatment facilities is a serious source of
cost overestimation in most assessments.
                       45

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                   SECTION VI

                ACKNOWLEDGMENTS

The survey and abstracts were developed by a
team from Enviro Control, Inc., consisting of
Messrs. Pierre Sprey, Paul Cleveland, Altaf Ahmed
and Mrs. Theodora Kunec.  They were advised and
assisted by Dr. Leon Weinberger.

The support of the project by the Water Quality
Office, Environmental Protection Agency, and the
guidance provided by Mr. W.  P. Somers is acknowl-
edged with gratitude.
                       46

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                    SECTION VII

                    REFERENCES

             NOTE: reference numbers followed
             by an asterisk are abstracted in
             Part II; their Part II page num-
             bers are given in the parentheses
             following the complete reference

1.  Chung, A., Linear Programming, Merrill Books,
    Columbus, Ohio, 1963.

2.  Gass, S. I., Linear Programming, McGraw - Hill,
    New York, 1964.

3?  Deininger, R. A., "Water Quality Management -
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4.  Thomann, R. V., and Sobel, M. S., "Estuarine Water
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5?  ReVelle, C. S., Loucks, D. P., and Lynn, W. R.,
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    September, 1966.

                         47

-------
 9*  Heaney, J. P., "Mathematical Programming Analysis
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11*  Liebman, J. C. , "A Branch-and-Bound Algorithm for
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15.  Hall, W. A., and Buras, N., "The Dynamic Pro-
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16.  Buras, N.,"Dynamic Programming in Water Resources
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                         48

-------
20.  Joeres, E. F., "An Operations Research Approach
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30.  Eckenfelder, W. W. Jr., "Biological Treatment of
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                       49

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31*  Smith, R.,  and Eilers,  R.  G.,  "Simulation
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32*  Andrews,  J. F.,  "A Dynamic Model of the
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34*  Smith, R.,  "Preliminary Design of  Waste-
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35*  Parker, D.  S., Mcnser,  J.  R. ,  Spicher, R. G. ,
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36.  McBeath,  B. C.,  and'Eliasson,  R.,  "Sensitivity
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37*  Galler, W.  S., and Gotaas, H.  B.,  "Optimization
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38.  Lynn, W.  R., "Stage Development of Wastewater
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39.  Shih, C.  S., and Krishman, P., "Dynamic Optimization
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     1969, Purdue University,  Lafayette, Indiana, 1969.


                        50

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40.  Evenson, D. E., Orlob, G. T., and Monser, J. R.,
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41*  Meier, W. L. Jr., Lawless, R., Beightler, C.,
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42.  Tarassov, V. J., Perlis, H. J., and Davidson, B.,
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43.  Kittrell, F. W., A Practical Guide to Water
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44.  Water Quality Criteria, Report of the National
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45.  Chow, V. T., Handbook of Applied Hydrology,
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46.  Beard, L. R., "Use of Interrelated Records to
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     Division, ASCE, Volume 91, Number HY5, 1965.

47.  Thomas, H. A. Jr., and Fiering, M. B., Chapter
     12,Maas, A. M.,pp.459-493 et.al., The Design
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48.  Matalas, N. C.,"Mathematical Assessment of
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49*  Benson, M. A., and Matalas, N. C., "Synthetic
     Hydrology Based on Regional Statistical Para-
     meters," Water Resources Research,  Volume 3,
     Number 4, 1967, pages 931 -935.(D-2).

50*  Payne, K., Neuman, W. R., and Kerri, K. D.,
     "Daily Streamflow Simulation."  Journal of the
     Hydraulics Division,Proceedings of the American
     Society of Civil Engineers,  pages 1165 - HY4,
     July, 1969. (D-10).

                        51

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51*  Betson, R. P., Tucker,  R.  L.  and Haller, F. M. ,
     "Using Analytical Methods  to Develop a Surface -
     Runoff Model", Water Resources Research, Volume 5,
     Number 19, February, 1969.  (D-4) .

52*  Huggins, L. and Manke ,  E. ,  "A Mathematical Model
     for Simulating the Hydrologic Response to a Water-
     shed, IIWaterR£sojar£ej_^esej.rch, Volume 4, Number 3,
     pages 529 -539, 1968. (D-8)  .

53.  Todd, D. K., Ground Water  Hydrology, John Wiley &
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54.  Kleinecke, D. C., "The Use of Linear Programming
     for Estimating Geohydroldgical Parameters of
     Groundwater Basins," 70 TMP - 43, General Electric-
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55*  Vernuri, R. and Karplus , W. ,  "Identification
     of Nonlinear Parameters of Groundwater Basins
     by Hybrid Computation," Water Resources  Research,
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56*  Meyer, Charles, F. ,  "Using Experimental  Models to
     Guide Data Gathering," Journal of the Hydraulics
     Division, ASCE , July, 1970. (H-6) .

57.  Dobbins, W. E. , "BOD and Oxygen Relationships
     in Streams," Proceedings of the American Society
     of Civil Engineers,  Volume 90, Number SA3 , 19687

58.  Frankel, R. J. , and Hansen, W. W. , "Biological
     and Physical Responses in a Fresh Water Dissolved
     Oxygen Model," Gloyra, E. F.  and Eckenf elder, W. W. Jr.,
     Advances in Water Quality Improvement, University
     of Texas Press, Austin, Texas, 1967.

59*  Wen-Hsiung Li, "Unsteady Dissolved-Oxygen Sag in
     a Stream," Journal of the Sanitary Engineering
     Division, Volume 88, Number SA3, pages 75 - 85,
     May, 1962. (E-10) .

60*  Churchill, M. A., Elmore, H.  L. , Buckingham, R. A.,
     "The Prediction of Stream Aeration Rates, " Journal
     of the Sanitary Engineering Division ASCE, Volume
     88, Number SA4, 1 - 46, 1962. (E-12).

61.  Isaacs,  W. P., and Maag, J. A., "Investigation of the
     Effects  of Channel Geometry and Surface Velocity on
     the Reaeration Coefficient,"  Proceedings of the
     Twenty-Third Industrial Waste Conference, Purdue
     University, Lafayette, Indiana, 1968.
                       52

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62?  Merritt, C. A., McDonald, D. B., Paulson, W. L.,
     "The Effect of Photosynthesis on the Oxygen
     Balance in a Midwestern Stream," Proceedings
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     1968, Purdue University, Lafayette, Indiana. 1968. (E-13)

63*  Rudolfs, W. and Heukelekian, H., "Effect of
     Sunlight and Green Organisms on Re-aeration on
     Streams," Biology of Water Pollution, pages
     52 - 56, 1967. (E-17) .

64?  Ignjatovic, L. R., "Effect of Photosynthesis
     on Oxygen Saturation," Journal Water Pollution
     Control Federation, Volume 40, Number 5, Part Two,
     May, 1968. (E-4) .

65?  Kartchner, A. D. et. al. "Modeling Diurnal
     Fluctuations in Stream Temperature and Dissolved
     Oxygen," Proceedings of the Twenty-Fourth In-
     dustrial Waste Conference, 1969, Engineering
     Bulletin of Purdue University Engineering
     Extension Series Number 135, Part One, Purdue
     University, 1969. (E-8).

66?  Thayer, R., and Krutchkoff, R. G., "Stochastic
     Model for BOD and DD in Streams," American
     Society of Civil Engineers, Journal of the
     Sanitary Engineering Division, Volume 93,
     Number  3, pages 59 - 83, June, 1967.  (E-18).

67.  Loucks, D. P. and Lynn, W.  R., "Probabilistic
     Models  for Predicting Stream Quality," Water
     Resources Research, Volume 2, Number 3,  1966.

68.  Hutchins, W. A. , "The California Law of Water
     Rights," State of California, Sacramento, 1956.

69.  Wollman, N., The Value of Water in Alternative
     Uses, University of New Mexico Press,
     Albuquerque, New Mexico, 1962.


70.  Sax, Water Law, Planning and Policy,  Bobbs -
     Me rr ill, 1968

71.  Sax, Defending the Environment, Alfred Knopf,
     New York, 1968.
                        53

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72.  Gaffney, M.,  "Diseconomies  Inherent  in Western Water
     Laws:  California Case  Study,"  Western Resources and
     Economic Development of  the West  Report,  Number 9,
     1961.

73.  Warren, R.,  "Changing  Patterns of Governmental
     Organization  in the Los  Angeles Metropolitan
     Area," Doctoral Dissertation,  University  of
     California, Los Angeles,  1963.

74.  Arizona Game  and Fish  Department, "A Summary
     of the Pacific Southwest Water Plan, Including
     the Central Arizona Project,"  1964.

75*  Males, R. N.,  Gates, W.  E. , and Walker,_J.  P.,
     "A Dynamic Model of Water Quality Decision
     Making," Engineering-Science,  Incorporated,
     OWWR Contract Number 14-01-0001-1989, May,
     1970.  (G-10).

76.  National Water Commission - "Survey  of Public
     Attitudes Toward Water Policy," to be published.

77.  Maas,  A. M.,  et. al.,  The  Design of Water
     Resources Systems, Harvard  University,
     Cambridge, Massachusetts, 1962.

78.  Smith, S. C.,  and Castle, E. N.,  Economics  and
     Public Policy in Water Resource Development,
     Iowa State University  Press, Ames, Iowa,  19~64.

79.  Moreau, D. H., and Pyatt, E. E.,  "Uncertainty
     and Data Requirements  in Water Quality Fore-
     casting, A Simulation  Study,"  University  of
     Florida, Gainesville,  Florida, 1968.

80.  Jarret, H., Comparisons  in  Resource  Management,
     John Hopkins  Press, Baltimore, Maryland,  1961

81.  Cost of Clean Water, Volume I, FWPCA, U.  S.
     Department of Interior,  1968.

82.  Howe,  C. W.,  and Easter, K. W., Interbasin
     Transfers of  Water, Johns Hopkins Press,
     Baltimore, Maryland  1971

83.  Knetsch, J. L., "Outdoor Recreation Demand
     and Benefits," Land Economics, Volume 39, 1963.
                       54

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84.  Davis, R. K., and Knetsch, J. L. "Comparison of
     Methods for Recreation Evaluation," Water
     Research, Johns Hopkins Press, Baltimore,
     Maryland, 1966.

85*  Hamilton, H. R., Goldstone, S. E., et alia,"
     A Dynamic Model of the Economy of the Susquehanna
     River Basin: Phase II", Susquehanna River Basin
     Group, Battelle Memorial Institute, Columbus, Ohio,
     August, 1966.(G-5).

86*  Upton, C., "Optimal Taxing of Water Pollution,"
     Water Resources Research, Volume 4, Number 5,
     October, 1968. (G-13).

87.  Cost of Clean Water, Volume II - Detailed Analyses,
     FWPCA, U.S. Department of the Interior,  1968.

88.  Cost of Clean Water, Volume III - Industrial
     Waste Profiles  (1-10), FWPCA, U.S. Department
     of the Interior, 1968.

89.  Davis, R. K., The Range of Choice in Water
     Management, Johns Hopkins Press, Baltimore,
     Maryland, 1968.

90*  O'Connor, D. J. , "The Temporal and Spatial
     Distribution of Dissolved Oxygen in Streams,"
     Water Resources Research, Volume 3, Number 1,
     1967.(E-15).

91.  Smith, R., Cost of Conventional and Advanced
     Treatment of Wastewater, Journal Water Pollution
     Control Federation, 40, 1546, 1968.

92*  Eliassen, R. and Tchobanoglous, G.,"Removal of
     Nitrogen and Phosphorus", Proceedings of the 23rd
     Industrial Waste Conference, 1968, Purdue Univer-
     sity, Indiana, 1966. (C-6).
                       55

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PART II - ABSTRACTS

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                     SECTION A

    INTRODUCTION TO ABSTRACTED PAPERS AND PROGRAMS
The paper and programs selected for inclusion in this
section are intended to be a representative sampling
of current work and emphases in systems analysis of
water quality.  The abstracts themselves are more de-
tailed and more critical than the usual practice in
scientific abstracts.  This approach has been taken
to allow the abstracts to serve as a balanced intro-
duction to both the capabilities and the limitations
of systems analysis in water quality planning, manage-
ment and operations.

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                     SECTION B

     BASIN AND STREAM MODELS FOR ALLOCATION OF
       ABATEMENT RESOURCES - ABSTRACTED PAPERS

Author and Title

Anderson, N.W., and Day, H.J., "Regional
Management of Water Quality - A Systems
Approach"                                       B-2

Dysart, B.C., Ill, "An Economic Approach to
Regional Industrial Waste Management"           B-4

Graves, G.W., Hatfield, G.B., and Whinston,
A., "Water Pollution Control Using By-Pass
Piping"                                         B-6

Joere, E.F.,"An Operations Research Approach
to Basin Sediment Control"                      B-8

Johnson, E.L., "A Study in the Economics of
Water Quality Management"                       B-10

Liebman, J.C., "A Branch-and-Bound Algorthim
for Minimizing the Costs of Waste Treatment,
Subject to Equity Constraints"                  B-14

Montgomery, M.M. and Lynn, W.R., "Analysis of
Sewage Treatment Systems by Simulation"         B-17

Reid, G.W., et.al., "Model of Optimal Combina-
tion of Treatment and Dilution"                 B-19

ReVelle, C.S., Loucks, D.P., and Lynn, W.R.,
"A Management Model for Water Quality
Control"                                        B-23

Water Resources Engineers, Inc., Systems
Analysis of Urban Water Management              B-25
                        B-l

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Anderson, N. W. and Day, H. J., "Regional Management of
Water Quality - A Systems Approach", Journal Water ^±^u
tion Control Federation, Vol. 40, No. 10, pp. 1679-16°/,
October 1968.

DESCRIPTORS
OBJECTIVE
      This paper deals with an investigation of regional
management of organic pollution in the Great Miami basin
of Southwestern Ohio using both linear programming and
simulation techniques.  The objective of the study was to
determine individual plant monthly treatment levels nece-
ssary to minimize regional operating costs  (excluding in-
vestment costs and amortization)  of conventional waste
treatment (BOD removal) without violating river standards
 (D.O. level).

MODEL/METHOD
      An oxygen sag model for the Miami River was developed
using the modified Streeter-Phelps linear differential
equations to describe DO deficit at various locations along
the river in one-dimensional terms.  The river was divided
into short uniform reaches and the sag model was used to
determine linear "influence" coefficients relating individual
discharge treatment efficiency to oxygen deficits in down-
stream reaches.  A standard linear programming format is
adapted to minimizing the sum of treatment operating costs
while meeting oxygen deficit constraints with monthly treat-
ment efficiency policies.  These policies are then tested
in a simulation using 400 years of synthetic flows to compare
frequency of violation of standards among policies.

ASSUMPTIONS MADE
      1.  The river system can be approximated in terms of
          a series of short uniform reaches
      2.  The effect of upstream pollution loads on each
          reach can be described by linear coefficients
          based on a modified form of the Streeter-Phelps
          equation
      3.  The level of BOD reduction at a particular plant
          can be varied uniformly from 45 to 90% each
          month and operating costs for each month will
          vary in direct proportion to BOD reduction.

DATA REQUIRED
      1.  Number of reaches, length of reaches, and
          location of waste outfall;
      2.  Waste loadings received by treatment facilities;
      3.  Treatment efficiencies available at each outfall;
                       B-2

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      4.  Operating cost vs. efficiency at each waste
          treatment facility;
      5.  Quantity, velocity and quality of main and
          tributary flows in each reach;
      6.  Deoxygenation and reoxygenation coefficients;
      7.  River standards for dissolved oxygen in each
          reach.

RESULTS/COMMENTS
      A claimed saving of 40% in operating costs over a
uniform 85% removal effluent standard is claimed for the
derived optimum policy with standard compliance 96% of
the time.  However, severe restrictions on the model and
findings exist:
      1.  Variability other than that associated with
          extreme low river flow such as waste loads,
          temperature and DO is not included.
      2.  In some cases operating cost and average BOD
          reduction were synthesized from other facili-
          ties instead of actual data.  Cost was Iin3ar-
          ized based on reported yearly operating costs
          and removal efficiencv.  It is by no means
          clear that operating  for costs treatment plants have
          much flexibility on a month-to-month basis.
          Furthermore, the model cannot trade investment
          costs for new facilities against existing opera-
          ting costs; this is certainly necessary to
          achieve overall regional optimization.
      3.  Effects of photosynthesis and benthic deposits
          are included only by means of fitted deoxygena-
          tion and reoxygenation coefficients in each reach.
          Fixed contributions of BOD from runoff are not
          included.  The potentially substantial cost of
          treatment for meeting standards other than DO
          are not incorporated.
      The formulation of treatment and costs in this
manner does not correspond to the real world of today.
For though it is possible to operate a treatment plant at
any particular level of a wide efficiency range, this is
not normally done nor is it clear that significant cost
savings  (relative to total life-cycle cost) are feasible
through operating efficiencies below design level.

RELATED REFERENCES
1.    Anderson, M. W. , "Regional Water Quality Management
      in the Miami Basin," Ph.D. Dissertation, Carnegie-
      Mellon University, Pittsburgh, Pennsylvania (1967) .
                        B-3

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Dysart, B.C., Ill, "An Economic Approach to Regional
Industrial Waste Management,:  Proceedings of the 24th
Industrial Waste Conference, Purdue University, Lafay-
ette, Indiana, 1969.
DESCRIPTORS
OBJECTIVE
      The study demonstrates an economic approach to
regional industrial waste management.   The modeling
technique employed involves discrete,  one-dimensional
dynamic programming.  Two principal problem areas are
addressed:
      1.  Allocation of resources in which the object-
          ive is to minimize economic  costs (i.e.,
          optimize the treatment levels) of a multiple-
          facility basin system within dissolved oxygen
          standards as constraints.
      2.  Investigation of response or sensitivity of
          the minimum total system costs and the optimum
          management policy to system  variation.

MODEL/METHOD
      The approach is illustrated by a hypothetical
river basin system involving three stream reaches
 (stages) in series.  An industrial waste outfall is
located at the head of each reach.  The Streeter-Phelps
formulation is used to compute the transfer function re-
lating upstream BOD and DO inputs to downstream BOD
and DO concentrations in each computation, the program
checks for each reach that the minimum DO is above the
reach DO standard and yields the input BOD and DO for
the next reach.
      The dynamic program written starts with coarse
increments in treatment level, input BOD and input DO
and reduces increment size on each iteration.

ASSUMPTIONS MADE
      1.  Steady state is assumed with regard to waste
          production at each discharge and with respect
          to stream flow.
      2.  Deoxygenation and reaeration can be represented
          by first-order processes and the basic Streeter-
          Phelps dissolved oxygen sag  equation is applicable.
      3.  DO is the pollutant standard that dominates total
          regional treatment costs.
                        B-4

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FACTORS INCLUDED
      Factors included in the policy-optimization,
minimum cost phase of the study are waste production
and waste treatment levels, costs at each discharge,
stream BOD/DO balance, flows by reach and BOD/DO inputs
at head of stream system.  Factors examined in the
sensitivity analysis phase include varying dissolved
oxygen standards, varying streamflow  (i.e., effect of
augmented flow) and total costs.

DATA REQUIRED
      1.  Waste production at each industrial site in
          terms of BOD per unit of time.
      2.  Cost data for various levels of treatment
          at each industrial site.
      3.  BOD and DO concentrations entering at the up-
          stream end of the system.
      4.  Mean stream flow rates within each reach.
      5.  Deoxygenation and reaeration coefficients
          for each reach.

RESULTS/COMMENTS
      An example of minimum cost assessment is presented
using hypothetical data in a hypothetical three-stage
river basin system.  Three iterations of the standard
dynamic programming search procedure using successively
smaller increments of treatment levels, input BOD, and
input DO converged effectively on the optimal policy
to produce minimum cost.  Cost and policy sensitivity to
system changes are analyzed for potential incremental
adjustments of streamflow and DO standards.  The response
of optimal cost to variations of streamflow and standards,
and the response of optimal treatment levels to the same
parameters are presented in graphical format for considera-
tion by authorities in making rational policy decisions.
For the example shown, sensitivity to small changes in
standard was high, while sizable changes in streamflow had
surprisingly small effects.
      The hypothetical basin system with simplifying
assumptions is adequate to illustrate the methodology.
However, none of the stated assumptions is completely real-
istic.  In any adaption of the method to a real situation,
time varying and/or stochastic measures of waste production,
streamflow, oxygen sag, and physical stream conditions should
be considered.  Stage transfer functions involving additional
factors such as algal and Kenthic take-up of oxygen and
photosynthesis contributions to DO levels are becoming avail-
able and should be considered.  The methodology may be suit-
able for addressing multiple pollutant standards, an import-
ant consideration for achieving realistic total cost minimi-
zation.
                         B-5

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Graves, G.W., Hatfield, G.B., and Whinston, A.,
"Water Pollution Control Using By-Pass Piping1,
Water Resources Research, Vol. 5, No.  1, Feb.,
1969.

OBJECTIVE

To demonstrate the cost of savings possible using
optimum arrangements of bypass piping  to achieve
desired minimum DO standards in the Delaware Esturay.

MODEL/METHOD

The Thomann-Marks programming formulation was used
in attempt to determine the minimum cost bypass
piping configuration for achieving the desired
DO standards.  Due to the number of variables and
constraints a special large scale programming tech-
nique was developed and applied.

FACTORS INCLUDED

1.    Only various bypass configurations are considered;
      no combinations of treatment and bypass are handl-
      ed by the model.

2.    The Thomann-Marks formulation of linear transfer
      coefficients between BOD discharges and DO levels
      in each reach of the estuary is  used.

3.    Cost savings through joint rather than redundant
      pipeline sections are considered.

ASSUMPTIONS

1.    Empirical pipeline cost relations are assumed;
      no extra costs for river cross-overs or urban
      areas are assessed.

2.    Steady-state, linear deoxygenation/reaeration
      rates as required by the Thomann-Marks formula-
      tion are assumed.

3.    Optimum joint pipeline configuration can be
      determined by inspection  (the model does not
      eliminate duplicate piping automatically).

4.    DO degradations in above-minimum reaches will
      be permitted (these constitute violations of
      current anti-degradation regulations).
                        B-6

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RESULTS/COMMENTS

The optimal levels and discharge locations for major
polluters along the Delaware River have been determined
using the Thomann-Marks model.  The sensitivity of
the cost minimizing solutions has been determined;
it is found that for  fixed waste loads and costs the
solutions are particularly sensitive to the reaeration
coefficients and much less sensitive to diffusion and
decay terms.  The paper indicates the marginal savings
achieved through bypass piping  as compared with on-
site treatment, amounting to one to two orders of
magnitude.

SIMILAR/RELATED REFERENCES

Thomann, R.V. , and Marks, D.H.,  "Results  from a
Systems Analysis Approach to the Optimum  Control
of Estuarine Water Quality", Third Conference of
the International Association on Water Pollution,
Munich, Germany,September,1966~~
                         B-7

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Joeres, E. F., "An Operations Research Approach to Basin
Sediment Control," Third American Water Resources Confer-
encexProc'eedings, American Water Resources Association,
UrbanaT,Illinois, November, 1967.

DESCRIPTORS
OBJECTIVE
      The paper presents a 'scheme for minimizing the total
cost of basin sediment control and sediment damages result-
ing from a!greatly increased basin load due to new upstream
construction.

MODEL/METHOD
      A dynamic programming model is developed in considerat-
ion of a basin comprised of an estuary, a main stream, an
upstream sediment-producing construction site, a tributary,
and a reservoir.  The basin is divided into five stages; each
stage incurs a cost .for sediment control as a non-linear
function of amount trapped plus another cost for sediment
damage in that stage's reach.  Stage transfer functions are
written starting at the downstream end.  At each stage, the
cumulative cost of all downstream damages is minimized re-
lative to the sediment control decision(s) available in that
stage, taking into account optimization in prior downstream
stages.  This process relates downstream optimum stage control
decisions to the control decision at the upstream construction
site; iterations of the latter decision then converge on the
best at-site control effort to minimize basin cost.

ASSUMPTIONS MADE
      1.  The sediment yield resulting from construction
          activity in the upstream reach is a fixed total
          amount which is known.
      2.  Prior to the development situation, an equili-
          brium condition existed and few or no control
          measures were needed.
      3.  Sediment damage costs in each reach are known
          (e.g., dredging, stream overflow, industrial
          pre-treatment requirements, drain clogging,
          pumping failures, etc.)
      4.  The decision as to the degree of control to be
          provided at a particular location and the damage
          caused downstream by bypassed sediment are in-
          dependent of the size distribution of the in-
          coming sediment load  (problem exists due to
          preferential settling of heavier particles).
                        B-8

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      5.  The reservoir size is small; thus its
          sediment trap efficiency can vary widely
          and be considered a control decision'
          variable.

FACTORS INCLUDED
      Sediment loads, settling rates, control options,
and costs, sediment damages.

DATA REQUIRED
      1.  Cost-treatment functions for all measures
          taken at each control point.
      2.  Cost-damage functions resulting in each
          reach as a result of sediment allowed to
          pas
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Johnson, E.L., "A Study in the Economics of Water
Quality Management", Water Resources Research,
Volume 3, No. 2, Second Quarter 1967.
DESCRIPTORS
OBJECTIVE

Purpose of this report is to present and compare
several methods of allocating waste reductions among
dischargers using Delaware Estuary Study data.
Specifically, this study sought to demonstrate the
effluent charge (in terms of $/lb. of BOD)  required
to attain each of several desired levels of DO,
assuming steady state conditions.

MODEL/METHOD  ,

Four policies were considered:

1.    Uniform treatment  (UT) - all dischargers must
remove a specified equal proportion of their respect-
ive waste loads before discharging to the water body.

2.    Least cost  (LG) - allowable waste discharges
are allocated on the basis of marginal costs of
increasing removal efficiency in such a manner as to
minimize the total (basinwide) ,cost of meeting a
dissolved oxygen goal..

3.    Single effluent charge  (SECH) - a uniform price
per unit of oxygen-demanding material discharged to
the water body is applied to each waste source.

4.    Zone effluent charge  (ZECH) - an effluent charge
constant within zones is levied on each unit of
oxygen-demanding material discharged.

All solutions must satisfy the basic physical con-
straints :
 1   '    !       i
1.    Additional waste removal must be sufficient to
      meet the specified quality improvement.

2.    Removals must be zero or positive; that  is, no
      one is allowed to reduce his level of waste
      removal.

3.    The total amount of waste removed by any dis-
      charger, the sum of the current plus ad-
                        B-10

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       ditional removals must be less than his total
       load before any removal;  (i.e., each discharger
       cannot reduce his waste discharge by more
       than 100%).

 Additional conditions are imposed on the three basic
 constraints to form computational models for each
 of the load allocation techniques.

 a.   -The program (UT) selects a vector f such that the
       basic constraints are satisfied and all dis-
       chargers additionally remove the same proportion
       of their raw wastes before discharging, except
       that those who are already removing an equal or
       greater proportion must continue to do so.

 b.    The least cost model  (LC) is obtained by forming
       the linear programming problem which minimizes
       the total cost  (sum of costs of each discharger)
       subject to the three basic constraints.

:c.    The model  (SECH) treats the removal as a function
       of charge.  The level of removal of each dis-
       charger induced by a charge is determined by
       investigating the response curve of that dis-
       charger, assuming cost minimizing behavior.  SECH
       selects an arbitrary nominal charge for all
       dischargers which in turn, maps into an induced
       increase in removal; then it converges to a
       charge such that the induced waste reduction
       satisfies the three basic constraints.

 d.    The effluent charge model (ZECH) performs exactly
       as SECH, except that a different charge may ob-
       tain in each zone of the water body, and con-
       ceivably more than one set of such charges will
       induce sufficient removals to satisfy the quality
       improvement constraint.  Therefore, an additional
       condition is specified that selects from^among
       all feasible sets of charges that set which in
       duces the least total waste reduction expenditure
       and which satisfies the three basic constraints
       as well as the requiement that the total annual
       cost of the induced waste reduction should be less
       than or equal to the total annual cost for the
       current removal.
                         B-ll

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FACTORS INCLUDED

BOD/DO balance for the estaurine case, simplified cost-
minimizing behavior for dischargers,  Not considered
explicitly were the following:  storm water over-
flows, urban drainage, benthic and photosynthetic
oxygenation effects as well as cost reduction through
regional treatment alternatives.

ASSUMPTIONS MADE

1.    Only steady-state conditions are considered.

2.    Control authorities do not permit individual
      dischargers to reduce their levels of waste
      reduction below that currently being practiced.

3.    Costs of waste reduction are not important
      enough to result in significant production
      changes.

4.    Dischargers select between investment in treat-
      ment or payment of effluent charges based only
      on cost-minimization critera.

5.    All treatment costs and quality requirements
      are associated only with BOD rather than
      other pollutants.

KEY DATA REQUIRED

Input data to each model are basically the same,
consisting of:  (1) a matrix relating the effect
on DO level in each reach to a unit removal of
oxygen-demanding material in any other reach; and
(2) a piecewise linear cost function for each dis-
charger, showing his waste removal cost.

RESULTS/COMMENTS

1.    Effluent charges should be seriously considered
      as a method of attaining water quality im-
      provement;

2.    Cost of waste treatment induced by a zoned charge
      level will approach overall regional minimum cost
      treatment plan;

3.    A charge level of 8 to 10 cents per pound of
      oxygen demanding material discharged appears
      to produce relatively high increases in
      critical dissolved oxygen levels;

                        B-12

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4.    Major regional economic readjustments result-
    •  ing from a charge of that level are not anti-
      cipated to occur in the study area;

5.    Administrative costs and difficulties of manag-
      ing an effluent charge method are greater than
      conventional methods of quality improvement.
      However, the problems are not insurmountable
      and are not sufficiently great to negate the
      advantages of the charge method;

6.    Compared with a conventional method of improving
      water quality, the charge method attains the
      same goal at lower costs of treatment, with
      a more equitable impact on polluters. Also,
      the charge provides a continuing incentive for
      the polluter to reduce his waste discharge
      and provides a guide to public investment
      decisions;

7.    More study is needed of the technical problems
      of coping with differential charges related to
      transient waste load discharges prediction
      of induced responses, administrative problems
      associated with sampling of discharges, and
      damage estimation.

8.    All four of the allocation schemes will satisfy
      the goal.  The LC is the most efficient pro-
      gram for meeting the quality goal.  ZECH can
      be made to approach the LC solution as closely
      as desired by increasing the number of zones, but
      costs of administration and data gathering would,
      of course, also tend to increase.  The UT
      scheme is the most inefficient in that it not
      only requires unnecessary waste reductions
      but requires such reduction regardless of the
      marginal cost of undertaking them.
                         B-13

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Liebman, J.C., "A Branch-and-Bound Algorithm for Minimizing ^
the Costs of Waste Treatment, Subject to Equity Constraints,
Proceedings of IBM Scientific Computing Symposium on water
and Air Resource Management, Oct. 1967.
DESCRIPTORS
OBJECTIVE

Purpose of this report is to minimize the regional cost of
wastewater treatment to meet DO stream standards without
violating subjective equity constraints (equal treatment
for all dischargers in a geographical or industrial category).

MODEL/METHOD

A zoned minimization approach is followed in which dischar-
gers are grouped into categories, an equal treatment restrict-
ion is imposed upon all the plants within each category, and
the cost of the entire basin treatment is then minimized.
The river basin (with or without estuary)  is divided into
relatively uniform reaches with a DO standard for each.

The difficulties of treating this problem by dynamic program-
ming are shown.  Next, a linear programming formulation of
the problem is given which fails due to both nonlinearities
and discontinuities in costs of improved treatment.  This is
reformulated into a 0-1 integer programming problem (in order
to circumvent nonlinearities);  the 0-1 variable represents
the non-employment or employment of one of a preset number of
discrete levels of treatment at a given plant.  The objective
function to be minimized is:

The summation over all categories of the cost for providing
the appropriate level of treatment in each category required
to meet the DO standards in all reaches.  The cost function
has a discrete jump at each point where the existing level
of treatment at a plant is reached; this is easily represent-
ed since cost coefficients represent total cost of reaching
a certain treatment level for all plants in a category.

The constraints are:

1.    The sum of DO reductions in a given reach contributed
      by all plants should be at least equal to the required
      DO reduction for that reach.

2.    The sum of the 0-1 indicator variable over all alter-
      nate levels of treatment for any plant should be one.

                        B-14

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This formulation has increased the number of variables
over the linear program by a factor equal to the number
of discrete treatment levels.  To solve the zoned problem
a modified Geoffrion algorithm is used.  This is a branch-
and-bound technique which is used on the 0-1 integer
problems.  In this approach, at each iteration all of the
variables of the problem are contained in one of three
groups: a) those variables which are "free" (values have
not been specified), b) those variables whose values has
been set equal to 0 in a previous iteration, c) those
variables whose value has been set equal to 1 in a
previous iteration; each iteration consists of selecting
a free variable and setting it equal to 1 or selecting
a variable with value 1 and setting it equal to 0.  In
this way a "tree" of possibilities is developed.  The
model was applied to the Delaware Estuary with 7 categories
(zones) , 13 levels of treatment and 15 constraints.

FACTORS INCLUDED

Cost non-linearities including existing treatment; BOD/DO
balance by reach including loads of plants outside the
reach; equal treatment requirements for each discharger
category.

ASSUMPTIONS MADE

a.    Cost vs. treatment level for any category is mono-
      tone nondecreasing {required by Geoffrion algori-
      thm) .

b.    Stream standards for all other pollutants will be
      met when DO standards are met (or treatment costs
      for other pollutants are independent of BOD treat-
      ment .)

c.    DO reductions due to individual plant BOD reductions
      are additive in a given reach (this is only literally
      true if all discharges occur at a point.)

DATA REQUIRED

Reach and category definitions, DO standards by reach,
effect on each reach of BOD reduction at every plant,
total cost by discharger category of implementing each
level of treatment.

RESULTS/COMMENTS

The application of zoned treatment requirements using
this model in the Delaware case gave an overall cost of
$116.6M as contrasted with $78M for a minimum  cost


                     B-15

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solution with no need for equal treatment and $157M
for regionally uniform treatment.  A zone treatment
approach for planning problems on a river basin
leads to sufficient flexibility to permit subjective
notions of equity to be introduced into the solution
at considerably lower cost than uniform treatment.
The branch and bound algorithm is a feasible method
of solving such problems, though running time was 27
minutes for the Delaware case using an IBM 7094.

The method stands or falls on the extent to which DO
dominates total cost of meeting water quality standards
and on the accuracy of predicting oxygen sag due to an
individual discharger's load.
                       B-16

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Montgomery, M.M. and Lynn, W.R.  "Analysis of Sewaae
Treatment Systems by Simulation", A.S.C.E. Journal
of the Sanitary Engineering Division, vol. 90—No~ 1
1964.                      ~~	             '  '
DESCRIPTORS
OBJECTIVE
     This paper deals with a  sewage treatment system
that includes the possibility of using effluent storage
and low-flow augmentation.  Objective of the study was
to develop insight  into the operation of the system using
various combinations of "treatment" elements and operat-
ing disciplines and to measure the resulting frequency
of stream quality violations.

MODEL/METHOD
     The description which follows is applicable for a
single sewage treatment plant discharge and continuous
stream flow.
     The elements of the model are: treatment plant,
effluent storage reservoir and stream augmentation
reservoir.  Inputs  are randomly varying sewage flow,
sewage strength, and stream flow.  These demands are
handled in standard queueing  theory format.  The treat-
ment plant accepts  immediately all arrivals of sewage
input.  The plant changes the characteristics of the
arriving sewage and then releases it to the effluent
storage reservoir.  The degree of treatment is described
by operating curves that depend on the retention time and
strength.  Since the treatment plant essentially operates
at full capacity  (such that the treatment costs will be
minimized) every arrival forces an equal quantity to be
released  (into the  effluent storage reservoir, when employed).
For a given arrival, the rate of subsequent arrivals deter-
mines the detention time.
     The effluent storage reservoir releases only an amount
of effluent that will not violate the stream's maximum allow-
able oxygen deficit (as determined by a Streeter-Phelps
oxygen sag formulation), given the effluent resevoir is be-
low capacity.
     The capacity of the stream  (actually the distribution
of its capacity over time) is varied by the introduction of
the low-flow augmentation reservoir.  The reservoir release
is a function of the normal stream flow and the demand for
release as dictated by the requirement to accept effluent
from the sewage treatment plant.
     The digital simulation program is constructed  so that
it may be operated  in any one of four configurations:
treatment plant/stream; treatment plant/augmentation reservoir/
stream; treatment plant/effluent storage/stream; and treatment
plant/augmentation  reservoir/effluent storage/stream.

                        B-17

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     Varying capacities and operating rules may be
studied using synthetic stream hydrology and synthesized
sewage flows and strengths (normally distributed around
diurnal cycles).

FACTORS INCLUDED                                     . , ,
     Stream standards and assimilative capacity, variable
stream flows/sewage flows and strength.

KEY ASSUMPTIONS
1) Uniform quantity and quality of flow exists in both_the
stream and sewage for the duration of one simulation time
period.
2) "Plug-flow" is assumed such that a quantity of sewage
flow entering the plant in a period is not mixed with sewage
that had arrived in earlier periods.
3) BOD concentration of the entering sewage is independent
of the sewage flow.
4) Stream reoxygenation and reaeration rates plus input stream
DO remain constant at all flows (not in accordance with ob-
served stream characteristics).

KEY DATA REQUIRED
     Stream hydrographs, sewage flow statistics, sewage BOD
concentration statistics, initial DOD in the stream, reaera-
tion and reoxygenation coefficients, plant operating curves
as function of detention time and BOD influent.

RESULTS/COMMENTS
     Comparing the four configurations (based on hypothetical
data) the plant/ stream system yielded standard violations
10% of the time; 8% for plant/effluent reservoir/stream; 1.4%
for plant/augmentation/stream and 1% for all four components.
Utilization of total stream assimilative capacity varied only
slightly.  Given more realistic formulations of plant behavior
and of stream assimilative capacity with flow plus the addi-
tion of cost considerations, the queuing simulation  approach
appears to be one of the more promising methods for  considering
variability in stream systems with small numbers of  discharges.
                        B-18

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Reid, G.W., et.al.  "Model of Optimal Combination of
Treatment and Dilution," Proceedings of the Third
Annual American Water Resources Conference, San—
Francisco, Nov., 1967, pp.  339-35CK

DESCRIPTORS
OBJECTIVE

The ultimate objective  of  this  continuing work is the
development of nationwide  input-output model relation-
ships that will  cover all  major pollutant categories
in sufficient detail to address specific basin storage
project  issues.   The specific objective of this study
is the development  of dilution  requirements as a
function of municipal and  industrial waste treatment
levels by basin  for use in setting  low flow augmen-
tation requirements that minimize the cost of dilution
plus treatment.   This forms an  input to the Wollman
Supply-Demand Model for national assessments.  The study
develops stream  response sub-models for each of 6 major
pollutant categories.

MODEL/METHOD

General  problem  constraints:

1.    Economic projections are  provided in aggregate
      terms for  a basin.

2.    Physical stream characteristics are fixed and
      known  (including  seasonal variations).

3.    In-stream  water quality standards are given.

Major factors included  in  the study are those related
to consideration of the following pollutant categories:

1.    Organic oxygen demanding  substances  (biodegradable
      wastes)
2.    Infectious agents (bacterial)
3.    Plant nutrients  (aggregated eutrophication - N and P)
4 .*    Persistent chemicals (conservative substances —
      brines, metallic  ions, etc.)
                          B-19

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5.    Heat  (thermal pollution)
6.    Sediment  (suspended solids)

Specific component models are not developed for sediment
and infectious  aaents; they are considered as additional
constraints  (minimum standards) in the overall systems
model.  Input-output (dilution flow required vs. treatment
level and loads) relationships are developed for each of
the four remaining pollutant categories.

      Biodegradable Model

The domestic waste load on a stream is expressed for
the total basin load in terms of population equivalents
and the fraction of waste load discharges after treatment.
The model includes a linear (Streeter-Phelps)  estimate of
BOD assimilation capacity of a given river system  (depending
on basin-wide reaeration constraints, average branching
effects and average point-to-uniform loading ratios derived
from urban population fraction, plus a single oxygen
demand rate for all BOD).  Industrial loads are incor-
porated analagously, with projections based on national
economic growth and a statistical survey of waste  loads
per unit production.  Estimated constants are given for each
of twenty-two major stream basins of the United States.

      Accelerated   Eutrophication Model

Parallel models are developed for both nitrogenous and
phosphorus nutrients.  The models are simple mass balances
of N or P removed by treatment plus the N or P removed by
in-stream bacterial action; the remaining quantity is used
to compute a concentration in the fraction of the basin
flow that is impounded  (since water storage areas  are the
critical zones  in terms of algal blooms).  Dilution flow
requirements to reduce the concentration to an acceptable
Oswald AGP index (Algal Growth Potential) are computed,
based on both average N and P loads per capita and project-
ed industrial loads (based on estimated N and P raw load
per unit production) for each basin.

      Thermal Model

A simple basin-wide thermal mixing model is derived in
terms of waste flow and temperature differential, basin-
wide allowable stream temperature changes, and basin-
wide mixing constants.  The model computes dilution flow
required to meet basin standards of allowable temperature
increases over normal maximum summer temperatures.
                        B-20

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      Conserved  or Persistent  Chemical Waste Model

The persistent waste model  simply  computes the dilution
necessary to reduce persistent chemical concentrations
to a basin standard, given  the chemical loads and the
standards for  each persistent  pollutant.

ASSUMPTIONS MADE

1.    Biodegradable model:  linear  stream oxygen balance
      with basin-wide  average  parameters has usable
      accuracy.   Benthic  demand, photosynthesis and run-
      off BOD  (independent  of  population and industry)
      can be ignored.

2.    Eutrophication model:  basin-wide average water
      storage  conditions  related to AGP index  (based
      only on  the worse of  N or P) are adequate to
      compute  treatment and flows  required to prevent
      eutrophication.  Organic carbon, temperature and
      salinity interactions can be ignored.

3.    Thermal  model: basin-wide average mixing conditions
      and basin-wide standards are adequate to balance
      effluent cooling against flow augmentation for pre-
      vention  of  thermal  damage.

4.    Persistent  chemicals  model — standards and loads
      in each  important category of persistent chemicals
       (e.g., mercury,  chlorinated  hydrocarbons, brines,
      etc.) can be defined  on  a basin-wide basis.  Natural
       (or population industry  unrelated) fixed sources can
      be ignored.

5.    In general, reasonable and quantitative basin-wide
      water standards  can be defined and projected for
      30 years, despite the multiplicity and vagueness
      of current  standards  within  any given basin.

RESULTS/COMMENTS

The component  models are  to be integrated into a computer
system  for use in basin analyses.  Analysis is to be per-
formed  by considering  the optimal  treatment of pollutants
 (i e    four types) and augmented flow rates to produce
a minimum cost solution for meeting the water quality stand-
ards established  for each pollutant.  Basin-wide costs are
assigned to each  of four  levels of treatment  (secondary,
nitrogen removal, phosphorus removal and tertiary treatment)
plus to each of the low flow augmentation storage require-
ments associated  with  each  treatment level.
                         B-21

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Details of the development of the basin-wide constants
and load projections are not included in the present
work.  No validation of the component models is presented.

The input-output models may provide estimates suitable
for assessing long-range water resource requirements
on a gross national basis.  The severe assumptions and
basin-wide approximations involved in the method reduce
the probable accuracy of the results to a questionable
level for optimization of water resources and minimization
of costs or sub-basin or individual project levels.

SIMILAR/RELATED REFERENCES

1.    Reid, G.W., "Low Flow Augmentation Requirements,"
Committee Print No.  29, U.S.  Senate Select Committee
on Water Resources,  1959.
                       B-22

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DESCRIPTORS
OBJECTIVE
     A model based on  linear programming and the oxygen-
sag equation is presented which determines the degree of
treatment required from  individual waste water dischargers
in such a fashion that the  total treatment cost is mini-
mum and the stream standards are met.

MODEL/METHOD
     For convenience the river is divided into reaches
with one discharger at the  head of each reach.  In each
reach is an arbitrary  number of control points for check-
ing oxygen sag.  The objective total cost function that is
to be minimized is the sum  of individual treatment costs,
each linear with respect to BOD removal.
     The linear constraints are as follows:
1)   In each reach the treatment efficiency plus the ef-
fluent BOD concentration divided by the influent BOD con-
centration sums to-1.
2)   A mass balance equation is written at the head of each
reach for the oxygen deficit.
3)   A mass balance equation is written at the head of each
for the BOD.
4)   The treatment plant efficiency must fall within a given
range  (35-90%) to preserve  treatment cost linearity.
5)   The oxygen deficit  at  the top of each reach and at each
control point  (sags calculated from the classical linear
Streeter-Phelps equation) must be at most equal to the maxi-
mum deficit allowed by the  reach standard.  These constraints
are linear in load and deficit at the head of each reach.

FACTORS INCLUDED
     BOD, DO

ASSUMPTIONS MADE
1)   Cost of treatment is linear vs. efficiency within the
range 35-90% removal.
2)   Perfect mixing of the  waste water and stream flow oc-
curs at the beginning  of each reach.
3)   The bioxidation rate at each  reach is  an accumulative
average of the rates of  wastes of the previous reaches
(including this last one -  the linear ozygen  sag differ-
ential equations are valid.
4)   Oxygen sag control  points are close enough together  to
prevent significant violations from occuring  between them.


                         B-23

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KEY DAT A REQUIRED                                         ,
      Bioxidation constant, reaeration constant, slope and
intercept of individual treatment cost curves, discharge
and stream flows, and BOD loads and DO standards.

RESULTS/COMMENTS
      The advantages of this procedure are:
a)    The algebra of the constraints, especially the inven-
tory equations, provides a consise and clear statement of
the relations of variables.
b)    There is no limitation as to configuration of the
river system; tributaries are easily handled.
c)    Standard linear programming software packages can be
used.

      There are, however, significant problems with this
formulation including possibly serious non-linearities
of treatment cost, the inequity of applying different
treatment standards to discharges depending on their location
and proximity to other dischargers, excessive computational
load for any sizable industrialized region, and the lack
of realism in setting effluent treatment requirements based
on BOD as the only significant pollutant.

SIMILAR/RELATED REFERENCES
1)    Deininger, R. A., "Water Quality Management - The
Planning of Economically Optimal Pollution Control
Systems," Systems Research Memorandum, No. 125, North-
western Univ., Evanston, 111;, The Technological Insti-
tute (1965) .
2)    Liebman, J. C., "The Optimal Allocation of Stream
Dissolved Oxygen Resources," Doctoral Thesis, Cornell
Univ., Ithaca, N. Y. (1965).
3)    ReVelle, C. S., Loucks, D. P., and Lynn, W. R. ,
"Linear Programming Applied to Water Quality Management,"
Water Resources Research, Vol. 4, No. 1, February, 1968.
4)    ReVelle, C. S., Dietrich, G. and Stensel, D., "The
Improvement of Water Quality under a Financial Constraint -
A Commentary on Linear Programming Applied to Water Quality
Management," Water Resources: Research, Vol. 5, No. 2, April,
1969.
                        B-24

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Water Resources Engineers,  Inc.,  Systems Analysis for
Urban Water Management.   Office ot Water Resources	
Research, Department  of  the Interior, by Water Resources
Engineers, Inc.,  September,  1970.
DESCRIPTORS
OBJECTIVE

The study  is  limited  to  a  demonstration of the systems
concept as_a  viable guide  for  planning, implementation,
and operation of  total metropolitan water resource  (cov-
ering inflows,  storage,  outflows  and quality at each
stage) systems, and for  fundamental research.

MODEL/METHODS

The modeling  technique involves simulation of the behavior
of a pilot urban  system  (includes river hydrology/quality,
storm sewer system/urban hydrology, storage, water supply
treatment,  user systems  with reclamation  treatment possi-
bilities,  waste collection,  waste treatment with reclamat-
ion alternative,  and  disposal  system).  These sub-systems
are represented by highly  simplified equations; the model
computes the  stepwise solution of this large number of
approximate simulation equations  in a sequence of monthly
time periods.

In addition to the overall engineering/physical simulation
model,smaller-scale economic models are developed to compute
benefits and  costs for two specific selected subsystems
using technical outputs  of the engineering model as basic
input information.

ASSUMPTIONS MADE

Key assumptions and approximations of the model develop-
ment include:

1.    The  feedback and interactions as simulated for a
      limited set of  sub-systems  are representative of
      complex interactions that will occur in a compre-
      hensive simulation of  all aspects of urban water.

2     The  gross operational  and economic functions  assumed
      for  illustration in  the  study are adequate for water
      quality system  evaluations  in general or, if more
      complex functions  are  required, they can be evaluated
      satisfactorily  by  the  stepwise solution of the approx-
      imate equations.


                         B-25

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DATA REQUIRED

Direct application of the methodology to existing
situations would require the development of specific
situation-appropriate technical and cost data as
follows:

1.    Information on physical interrelationships of
      facilities
2.    Monthly rainfall quantities and qualities
3.    Monthly stream flows and/or groundwater hydrology
4.    Monthly water quantity and quality demands of all
      users
5.    Available import quantities and qualities
6.    Value of water at specified qualities to each user
7.    Capital, operational and maintenance costs for
      treatment and delivery of water quantities and
      qualities
8.    Present work factors and capital recovery factors
9.    Factors to accommodate intangible benefits.

RESULTS/COMMENTS

The physical models developed produced only gross
simulation of urban water systems behavior.  Other work
by the authors dealing with the feasibility and current succ-
esses of increasing the detail of simulation to represent
realistically the time varying behavior of each sybsystem
is summarized.

Several components of the technical evaluation model are
developed for demonstration and applied to a hypothetical
urban system  (with hypothetical input data) comprised of
three separate users, three import sources each containing
five quality constituents, facilities for storage and treat-
ment of water, and wastes-water reclamation facilities for each
user.  Economic modeling demonstration was performed for only
one combination of import source yields and user demands.
Four analyses were made for a schedule of waste removal
efficiencies involving three different types of treatment.
Economic evaluation was performed for water use and water
treatment examples.  Results of both technical and economic
evaluations are included in the report in tabular form.

The authors believe the model development format is general
enough to permit its application to multiple urban water
systems comprising a region or a basin and that the method
may be extended to include social, demographic, and political
models along with the technical and economic components.
In addition, an executive simulation-optimization program is
recommended.
                         B-26

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This study suffices as a basic demonstration of ability
to model a logical sequence of events taking place in
a simplified metropolitan water system.  The models
developed may be practical as a tool for limited exam-
ination of sensitivity of subsystem performance or of
costs to gross changes.  They would become very cumber-
some, even with computers, if applied to the overall
optimization of water supply, water treatment and waste
treatment costs, benefits, and consequences for a real
major urban location, much less a multiple-facility
multiple-use basin system.  Furthermore, the use of 30
day evaluation steps may prove unacceptable for evaluat-
ing subsystem interactions which involve critical factors
of widely varying periodicity down to cycles as short
as half-hour storms.

SIMILAR/RELATED REFERENCES

1.    Water Resources Engineers, Inc.  "Comprehensive Systems
      Study Engineering Analysis of All Aspects of Urban
Water, A Prefeasibility  Study," Appendix H, Urban Water
Resources  Research,  First  Year Report  to OWRR, ASCE Urban
Hydrology  Research  Council,  September,  1968.
                          B-27

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                   SECTION C

       TREATMENT PLANT AND TREATMENT PROCESS
           MODELS - ABSTRACTED PAPERS
Author and Title                              Page

Andrews, J.F.,  "A Dynamic Model of the Anae-
robic Digestion Process"                       C-2

DeBruhl, J.M. and Smallwood, C., Jr., "The
Applicability of Optimization Techniques
in Textile Mill Waste Treatment"               C-4

Eliassen, R. and Tchobanoglous, G.,  "Removal
of Nitrogen and Phosphorus"                    C-6

Erickson, L.E., Ho, V.S. and Fan, L.T.,
"Modeling and Optimization of Step Aeration
Waste Treatment Systems"                       C-7

Caller, W.S. and Gotaas, H.B.,  "Optimization
Analysis for Biological Filter  Design"         C-9

Meier, W.L., Lawless, R.W., and Beightler,
C.S., "Geometric Programming: New Optimi-
zation Technique for Water Resource  Ana-       C-12
lysts"

Parker, D.S., Monser, J.R., and Spicher,
R.G., "Unit Process Performance Modeling
and Economics for Cannery Waste Treat-
ment"                                          c~14

Pearson, E.A.,  "Kinetics of Biological
Treatment"                                     C-16

Smith, R.,  "Preliminary Design  of Waste-
water Treatment Systems"                       c~19
                       C-l

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Andrews, J.F., "A Dynamic Model of the Anaerobic Digestion
Process," Proceedings of the 23rd Industrial Waste Confer-
ence, 1968, Part I, Purdue University, 1968.
DESCRIPTORS
OBJECTIVE
     This paper presents a dynamic model for the anaerobic
digestion process to be used in analyzing start-up, bulk-
ing and other transient instability problems in anaerobic
treatment.

MODEL/METHOD
     This model uses an inhibitory function to relate un-
ionized volatile acid concentration and specific growth rate
for the methane bacteria assuming the unionized acid as the
growth limiting substance and inhibiting agent.  This con-
sideration resolves the conflict existing between volatile
acid inhibition and pH inhibition since the concentration
of unionized acid is a function of both total volatile acid
and pH.  A pair of first order differential equations are
used to describe organism growth and substrate concentration.
Since an inhibition function is used, the model can predict
growth lag variations in batch processes and failures of
continous flow processes at residence times exceeding the
"wash out" residence time.
     Experimental laboratory reactor evidence and evidence
from the bacteriological literature are presented in support
of the model.  Using the model to simulate both batch and
continous flow systems provides additional supporting evi-
dence by predicting results which are commonly observed
in the field (e.g., increasing pH to improve stability and
decrease starting time; use of 'ramp' load increases rather
than step inputs to avoid digester failure; dilution to save
a failing digester, etc.).

FACTORS INCLUDED
     Time varying growth rate, behavior of methane bacteria,
and limiting substrate concentrations in the absence of in-
hibition, inhibition effect.

FACTORS NOT INCLUDED
     Effect of 1) organism death, 2) utilization of substrate
for maintenance energy, 3) inhibition by other substances,
4) delay of organism response to changes in substrate con-
centration, 5)  modeling of acid-producing bacteria which pro-
vide substrate for methane bacteria, 6) decrease in pH due
to increase in volatile acids, and 7) known differences in
inhibitory effects of the various volatile acids.
                        C-2

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ASSUMPTIONS MADE

Simplifying assumptions  include:

a)    Linear growth  rates  and  linear inhibition
      effects  (using the assumed  inhibition func-
      tional form).
b)    Omission of  lag phase, organism death, endo-
      genous respiration,  use  of  substrate for
      maintenance  energy or  inhibition byproducts.
c)    Bacterial volatile acid  production rates do
      not constrain  methane  bacteria processes.
d)    Digester pH  control  eliminates change in pH
      with volatile  concentrations changes.
e)    Differences  in inhibitory effect of different
      volatile acids can be  averaged through single
      invariant inhibition constant.

DATA REQUIRED

Maximum specific growth  rate,  limiting substrate
concentration, saturation  constant, yield coef-
ficient, ionization  constant and  inhibition con-
stant for the bacterial  conversion of volatile
acids to methane.

RESULTS/COMMENTS

The model indicates  that:

1)    Increasing the quantity  of  seed sludge or
      increasing pH  (up  to 7.3) will decrease the
      time required  for  batch  digestion and start-
      up time for  continuous flow digestion;
2)    Digester failure may occur  a) if insufficient
      seed sludge  is present;  b)  if the pH is too
      low when a continuous  flow  digester is
      started; or  c)  if  step increases in loading
      are applied;
3)    Digester failure during  start-up may be avoided
      by slowly bringing the digester loading to its
      full value;  and
4)    pH control and/or  decrease  of process loading
      are effective  techniques for "curing" a failing
      digester.

The studies presented here should be considered semi-
quantitative in nature since reliable values of the
growth parameters  are not  available.  Estimates were
made from laboratory data  presented by Lawrence and
McCarthy.  Growth  parameters in the pilot reactor
runs conducted for model verification were not esti-
mated.  The inhibition function will require modi-
fication so that it  will include  the factors men-
tioned previously  as omitted.

                         C-3

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DeBruhl, J.M., Smallwood, C.,Jr., "The Applicability
of Optimization  Techniques in Textile Mill Waste
Treatment", Proceedings of 15th Southern Water Resources
and Pollution Control Conference, Raleigh, North Carolina,
pp. 63-80, April, 1966.

DESCRIPTORS
OBJECTIVE
     The purpose of this investigation was to use linear
programming to set production rates and waste treatment
plant investment in such a way as to maximize mill profits
while meeting stream dissolved oxygen standards.

MODEL/METHOD
     Stream oxygen standards were converted to maximum
allowable BOD discharge using the Thomas formulation for
oxygen sag.
     An objective function for the present discounted value
of net mill profits (difference between production times
profit per unit and cost of treatment plant investment
plus operations) was established as an exponential function
of production and treatment capacity and then linearized
in the range of 50,000-100,000 Ibs/day of products.
With linearized profits and assuring linear waste load vs.
production rate plus constant BOD removal efficiency up
to the treatment plant capacity, it becomes possible
to use the standard simplex tableau method of linear
programming (manual solution).
     The linear program constraints were:
1)   Production per day between 50,000 and 100,000
pounds of goods.
2)   Plant effluent equals treated effluent plus bypass
effluent.
3)   Plant effluent equals constant times production rate.
4)   Bypass effluent load plus treated effluent load can-
not exceed allowable BOD limit.

FACTORS INCLUDED
     Oxygen sag in stream plus allowable BOD load, non-
linear treatment plant costs vs. capacity, possibility
of treatment bypass.

ASSUMPTIONS MADE
1)   Constant profit per product unit at any production
rate.
2)   Constant BOD removal efficiency independently of
treatment plant capacity
3)   BOD represents only significant pollutant in textile
plant effluent that potentially violates stream standards
and affects treatment plant capacity/costs.

                        C-4

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KEY DATA REQUIRED
1)  Process flow, BOD  load  and  profit per unit of production
2)  Cost vs. capacity  of  treatment plant at constant remov-
al efficiency.
3)  Oxygen sag equation  for stream or maximum allowable BOD
RESULTS/COMMENTS
     For the  simple  cost and waste  relationships assumed,
the model  permits  the determination of  (a)  the optimum
production level,  and (b)  the equivalent  value  (shadow
prices) of inplant housekeeping pollution abatement
practices,  reductions in stream standards,  etc. Limita-
tions  are  the rarely achieved linearity of profit  and
waste  load with production as well  as constant BOD removal
efficiency vs.  capacity.  The model does  not  deal  with
multiple pollution components.
                         C-5

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Eliassen, R. and Tchobanoglous, G., "Removal of Nitrogen
and Phosphorus", Proceedings of the 23rd Industrial Waste
Conference, 1968, Purdue University, Lafayette, Indiana, 1968.

DESCRIPTORS
OBJECTIVE
     The purpose of this paper is to present_and discuss
unit operations and processes which are applicable to the
removal of nitrogen and phosphorus compounds from waste-
waters in order to avoid stimulating the undesirable growth
of algae and aquatic plants.

MODEL/METHOD
     Important forms of nitrogen in wastewater are ammonia,
nitrites and nitrates. Phosphorus compounds of importance
include organic phosphorus and soluble inorganic phos-
phates .       .
     Nitrogen and phosphorus removal methods may be classi-
fied as biological, chemical and physical.  Removal methods
for nitrogen compounds include ammonia stripping (80-98%
removal efficiency), biological treatment (30-50%) , anaero-
bic dentrification (60-95%) , algae harvesting (50-90%) ,
ion exchange (80-92%), electrochemical treatment (80-85%),
electrodialysis (30-50%), reverse osmosis (65-95%) , distil-
lation (90-98%), and land application.  For phosphorus, the
major methods are biological treatment (10-30%) , chemical
precipitation (88-95%), sorbtion (90-98%) , ion exchange  (86-
98%), modified activated sludge  (60-80%),electrochemical
(81-85%).  Also the cost range per volume treated for each
process was given as well as the cost and type of process
waste to be disposed, a highly significant cost factor.
     Key factors which must be considered in planning and
designing facilities for removal of nitrogen and phosphorus
are:
1)   The use to be made of the treated wastewater.
2)   Whether compounds of one or both are to be removed.
3)   The available means for disposing of the ultimate
contaminants.
4)   The economic feasibility of the selected process or
processes.

RESULTS/COMMENTS
     Results are given in the three tables of comparison of
alternate removal methods.
                        C-6

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Erickson, L.E., Ho,  V.S.,  and  Fan,  L.T.,  "Modeling and
Optimization of Step Aeration  Waste Treatment Systems,"
Journal Water Pollution  Control  Federation  Vol  40
No. 5, Part I, pp. 717-732,  1968.  	      '
DESCRIPTORS
OBJECTIVE
     In_this  study  the  optimization  (with respect to
minimizing total  aeration  tank  volume  for a fixed
level of organic  removal)  of  various step aeration
waste treatment processes  is  investigated by considering
sequences of  tanks  arranged in  series  with the possi-
bility of introducing variable  quanities of influent
to each compartment or  tank.

MODEL/METHOD
     The discrete version  of  the maximum principle then
is used to determine the individual tank volumes with
their assigned organic  loads  which minimize the total re-
quired volume for such  a system.  First order micro-
organism growth and nutrient  consumption kinetics are used.
Complete-mixing flow and plug-flow material balance equa-
tions were used to  describe the resulting concentrations
at each type  of aeration stage.
     Four types of  systems are  considered:  a sequence
of complete-mixing  aeration compartments, a sequence of
plug-flow aeration  compartments, a complete-mixing com-
partment followed by a  plug-flow compartment, and a
plug-flow compartment with continous distribution of feed
along the length  of the compartment.

FACTORS INCLUDED
     Steady state microorganism growth rates and limits,
nutrient concentrations, nutrient consumption rates and
conversion yields.

ASSUMPTIONS MADE
1)   The system is  isothermal and under steady state con-
dition  (including constant flows, nutrient concentrations/
compositions, microorganism population, density, diffusity
and viscosity).
2)   The effect of  endogenous respiration is assumed negli-
gible.
3)   The nutrient conversion yield factor is constant and
independent of the  age  of  the organisms.
4)   The sludge and waste  streams are  mixed completely
and instantaneously at  each point where the waste is intro-
duced; mixing requires  no  additional volume over and above
volume required for aeration.
5)   Oxygen is sufficiently supplied for oxidation.
6)   The plug-flow  model assumes that  there is no mixing
of fluid longitudinally along the flow path.

                        C-7

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KEY DATA REQUIRED
1)   Growth rate of sludge microorganisms vs. nutrient
concentration  (linearized) for the specific sludge and
waste considered.
2)   Nutrient consumption rate and conversion yield
3)   Influent and effluent nutrient concentrations

RESULTS/COMMENTS
     The minimum total volume and optimum load allocation
for each stage for a specific degree of treatment in each
of the four examined systems was presented.  Using non-
dimensionalized inputs, the findings are:
1)   A plug-flow system with continuous feed allocation
along it minimizes the required volume for the step aera-
tion system (54% of volume of single stage completely-
mixed flow aeration);
2)   Single stage plug-flow requires 63% of completely-
mixed flow single stage volume and is equivalent to 5
stage completely-mixed flow volume; two stage plug-flow^
requires 57%  (54% is theoretical minimum) thus eliminating
incentive to consider more than 2 stages.
3)   Plug-flow is most beneficial at the back end of
the system and complete mixing does not greatly increase
the volume requirements at the front end of the aeration
system (while probably increasing stability for non-steady
state conditions).
     The model may not identify optimum systems in a prac-
tical sense insofar as a) treatment plant cost is not
linear with volume; b) plug-flow configurations are more
expensive than completely-mixed flow and do not achieve
zero longitudinal mixing; c) susceptibility to instabili-
ties and input transients is not considered; d) optimal
distribution of loads among stages changes with varia-
tions in influent.
                        C-8

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Caller, W.S. and H.B. Gotaas,  "Optimization Analysis
for Biological Filter Design," Ann. Soc. Div. Eng.,
Journal of the Sanitary Engineering Division—Vol  9?
No. 1, pp. 163-182, 1966:	   	~'        '

DESCRIPTORS
OBJECTIVE

This study presents  a method  for optimization design
of the biological  filter  for  a minimum total cost.
For a given known  stream  flow and BOD, the analysis
permits the selection of  the  number of filter, radius,
depth and recirculation rate  that will permit the
minimum cost.

MODEL/METHOD

The problem of minimizing the sum of  filter component
costs subject to certain  performance  requirements
can be adapted to  a  linear programming format.  In
the cost of the biological filter, the nonlinear pro-
cess constraint equations and the nonlinear cost
functional can be  linearized  using the cutting place
method of Kelly.   Once linearized, a  solution is
obtained by using  the dual method developed by Lemke.

Four cases of filter design minimizing the costs of
construction and operation were studied  in detail,
namely,(a) the trickling  filter,  (b)  the trickling
filter with settling basins,  (c) the  trickling filter
with forced ventilation,  and  (d) maximizing the BOD
removal from a liquid waste subject to a fixed in-
vestment cost.

FACTORS INCLUDED

BOD, DO deficit, filter radius, depth and recirculat-
ion rate, process  nonlinearities, nonlinear cost re-
lationships.

KEY ASSUMPTIONS

1.    The labor costs involved in the operation of
      a sewage treatment  plant are relatively con-
      stant for plants of a given capacity.

2.    Maintenance  costs are relatively constant
      for plants of  a given capacity.
                         C-9

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3.    The cost of recirculation piping is a relat-
      ively small fraction of the total costs, and
      therefore, if the conditions for determining
      the piping (flow rate, length, etc) can be
      found from the optimization of the biological
      filter and the plant layout, the pipe sizing
      can be optimized separately with almost no
      effect on the overall optimization.

4.    The cost of excavation is not included but
      can be readily included.

5.    The filters are circular; however, the for-
      mulation can be adapted to other shapes.

6.    Steady state process kinetics.

KEY DATA REQUIRED

Design requirements  (plant influent and effluent,
BOD in influent),component cost relationships.

RESULTS/COMMENTS

1.    In studying optimization of trickling filter
      design, it was found that the depth and re-
      circulation ratio are dependent on the BOD
      in the filter influent and desired BOD
      reduction, and are independent of the plant
      influent volumetric rate.

2.    Variation of the cost parameters within
      reasonable limits does not affect the design
      variables when cost is being minimized.

3.    For optimum design conditions, the hydraulic
      rate through the filter will be at the maximum
      level permitted until the recirculation ratio
      is approximately 4 to 1.  After this ratio is
      achieved, the hydraulic rate will decrease
      (equation for decrease is given).

4.    At recirculation ratios lower than the maximum
      effective limit of about four, the cost of in-
      creasing the diameter and size of the filter
      is greater than increasing the recirculation
      to obtain increased BOD removal.

5.    The inclusion of settling basins does not
      alter the optimum design characteristics of
      the filter.

6.    Deep filters having forced ventilation are
      more economical than shallow filters only for
      high reductions in BOD.

-------
7.    Theoretically, one filter provides optimum
      cost conditions; the most economical design
      will have the minimum number of units to
      provide the necessary operating flexibility.

The equations and curves presented provide optimum
biological filter system designs subject to the
validity of the accepted process models incorporated
in the linear program.
                           C-ll

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Meier, W.L., R.W. Lawless, C.S. Beightler, "Geometric
Programming: New Optimization Technique for Water
Resource Analysts," Proceedings of the Fourth American
Water Resources Conference, AWRA, Urbana, III., 1968.
DESCRIPTORS
OBJECTIVE

An optimization technique called "geometric programming"
is demonstrated for application to water resource
analysis, particularly engineering design optimization.
Basic theory and formal proofs are not considered in
the paper.

MODEL/METHOD

Geometric programming is a recent algorithmic method
for solving non-linear mathematical programming problems
(e.g., function to be maximized or minimized subject
to constraints) with non-linear objective functions and/
or constraints.

The technique of geometric programming is illustrated
by two examples.  In the first example, the objective
function is to find the optimal dimensions of a cylin-
drical storage tank that would minimize the costs of
construction of the tank and its operation as a storage
reservoir.  A non-linear cost equation of three non-
linear terms is developed which includes tank dimensions,
total volume to be supplied from storage per unit of time,
and cost coefficients which are related to the costs of
filling the tank, material for the base, and material
for the sides.

Any generalized polynomial (termed posynomial) with,
positive real coefficients and real exponents is suit-
able.  Partial derivatives are taken with respect to
the values to be optimized.  A change of variable based
on duality theory is introduced so that three optimum
weights are defined as the portion of the total cost
attributed to each term of the posynomial. Using the
fact that the sum of the weights must equal one, and
simplification of the partial derivative equations
yields 3 simultaneous linear equations in the 3 weights
from which a solution of optimum weights independent
of the cost coefficients is derived.  The distribution
of costs thus obtained remains invariant regardless
of the values of the cost coefficients, an important


                        C-12

-------
unique feature of the algorithm.  Further substitution
of the optimum weights yields minimum cost values
in terms of the original cost coefficients and con-
stants .

In the second example, an additional term is added
to the original cost posynomial, adding an additional
optimum weight.  This additional weight gives an
underdetermined system of 3 linear equations in 4
weights, therefore all weights are expressed in terms
of one of the weights.  A "substituted dual function"
is developed by substituting these expressions for
the weights  (in terms of the single "representing
weight") into the objective function.  It has been
proved in geometric programming theory that when the
substituted dual function is maximized this maximum
value is equal to the minimum cost.  The optimum value
of the representing weight is found by obtaining the
first derivative of the logarithm of thfe substituted
dual function, setting it to zero, and solving.  The
remaining minimizing variables can be obtained follow-
ing procedures given in the first example.

The number of weight terms minus the number of linear
equations in the weights is termed "degree of difficulty"
 (first example had zero, second had one).

Both examples are free of physical constraints.  Such
constraints, if they occur, are handled in geometric
programming procedures by defining additional weights
and augmenting the dual function with terms generated
by the constraints.

RESULTS/COMMENTS

The geometric programming technique is in its infancy.
Use of the technique permits direct solution of a large
class of non-linear optimization problems in engineer-
ing design and basin optimization which heretofore had
to be solved by approximation techniques.  However,
it appears that very few problems of degree of difficulty
more than one are computationally tractable, a serious
limitation of the algorithm.  An IBM 360/65 FORTRAN
program has been written.

SIMILAR/RELATED REFERENCES

1.    Duffin, R.J., E.L. Peterson, and C.M. Zener,
      Geometric Programming, John Wilder and Sons,
      Inc., New York, 1967.
                         C-13

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Parker, D.S., J.R. Monser, R.G. Spicher, "Unit Process
Performance Modeling and Economics for Cannery Waste
Treatment," Resources Engineers, Inc., Walnut Creek,
California.  In: Proceedings of the 23rd Industrial
Waste Conference, 1968.  Purdue University, Lafayette,
Indiana, 1968.
DESCRIPTORS
OBJECTIVE

Individual treatment and process models are formulated
to determine which processes are "best" and at what
level of removal each of the alternative processes
should be operated to minimize cost of the entire treat-
ment for a specific cannery's wastes.   Details are given
for 6 out of the 16 processes considered.

MODEL/METHOD

For each process there are essentially two analyses:
                                            i
a.    A deterministic engineering "performance model"
      relating process removal efficiency and the
      equipment/operational parameters that affect
      efficiency is formulated based on available
      design and experience data.  Capital, operat-
      ing and land costs are then estimated as a
      function of the equipment/operational para-
      meters .

b.    Straightforward minimization or search tech-
      niques are then used to establish minimum
      cost combinations of equipment/operating
      parameters for each total flow/removal efficiency
      combination.  This is the cost-size-efficiency
      (C-S-E) relationship for each process.

For simplicity, a set of second order polynomial fits
(one each for capital costs, operations and land) to
the C-S-E relationships for each of 12 treatment
processes was established and tabulated.  The result-
ing data fits generally had correlation coefficients
greater than 0.98.

Processes for which C-S-E relations are given are:
                         C-14

-------
      1.   Screen
      2.   Sedimentation
      3.   Chemical precipitation
    .. 4 .   Chemical oxidation
      5.   Trickling filter
      6.   Activated sludge
      7.   Aerated lagoons
      8.   Anaerobic ponds
      9.   Facultative ponds
     10.   Aerobic pond
     11.   Spray irrigation
     12.   Evaporation and percolation

ASSUMPTIONS MADE:

1.    Activated sludge: first-order, steady state
      kinetics and COD removal proportional to
      BOD removal are assumed.

2.    Ponds: regression fits for existing ponds
      using only areal waste loading and detent-
      ion time give adequate prediction of eff-
      iciency.

3.    Chemical oxidation: laboratory-scale chemical
      oxidation removal efficiencies will apply
      to full-scale processes.

4.    Second order polynomials are adequate fits
      for all C-S-E relationships.
                         C-15

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Pearson, E.A., "Kinetics of Biological Treatment,"
Special Lectures Series: Advances in Water Quality
Improvement, University of Texas, Austin, April 6,
1966.

DESCRIPTORS
OBJECTIVE

The objectives of this paper are:

1.    To present a consistent and rational basis for
      kinetic modeling of biological waste treat-
      ment processes.

2.    To indicate, demonstrate and emphasize the
      value of kinetic modeling in process evaluat-
      ion and in the analytical comparison of differ-
      ent biological processes (viz, aerobic and
      anaerobic).

MODEL/METHOD

A unified kinetic description of both aerobic and
anaerobic waste treatment systems in the absence
of inhibitory effects is presented.  The kinetic
model for growth and substrate removal is based
upon that of Michaelis-Menten  (linear cell growth
rate and substrate removal rate including a linear
cell decay term constitute the basic kinetic des-
criptions of the process). Basic steady state relat-
ions for influent load, residence time, effluent
quality and cell recycling are presented.  In addi-
tion, operating conditions for maximizing cell
production (i.e., maximizing P or N removal in the
form of cellular material) are desired; these con-
ditions are quite different from maximum BOD removal,

The need for additional laboratory and field deter-
mination of the applicable kinetic constants is
emphasized.  Most of the currently available data
on aerobic and anaerobic process constants are
presented in tabular form.

FACTORS INCLUDED

Steady-state first order bacterial growth and sub-
strate (BOD or COD) removal, cell decay, cell re-
cycling,  reactor volumes and hydraulic retention
times.
          !
                         C-16

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ASSUMPTIONS MADE

1.    For Michaelis-Menten model :
      a.  The  enzyme plus the enzyme-substrate
           complex  is  proportional to the total
            active  solids" concentration.

      b.   The growth  rate is proportional to the
           enzyme substrate complex concentration .

2.    For the  process  material balance:
      a.   The process is at steady state; no in-
           hibition effects occur at any load/growth
           rate combinations .

      b.   The reactor volume includes the volume
           of  the cell separator; both the separator
           volume and  the cell mass in the separator
           are negligible  (true only for laboratory
           studies) .

      c.   The wastage of cells  (net growth) is equal
           to  the cell concentration in the effluent
           stream times the flow rate.

DATA REQUIRED

The following  microbiological kinetic constants of
aerobic and anaerobic  treatment systems are required:

1.    Substrate concentration at one half maximum
      growth rate;  maximum growth rate.

'2.    Flow, load and cell mass leaving and entering
      reactor;  reactor volume.

3.    Yield coefficient; endogenous respiration rate
      (decay);  oxygen requirement constants for oxidized
      cells and for substrate removed.

RESULTS/COMMENTS

If aerobic  and anaerobic processes are to be evaluated
for a specific waste treatment problem on a rational
economic feasibility basis, the development of accurate
kinetic constants for  both processes is an absolute
requirement.   Unfortunately the data used here were
obtained from  laboratory studies.  Additional studies
of full scale  plants are needed to develop more reliable
estimates of treatment kinetics, particularly for  anaer-
obic systems.
                         C-17

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This approach does not address transients due to
variable flows, loads or start up nor does it
address inhibitory effects; both considerations
are important in addressing  process stability.

SIMILAR/RELATED REFERENCES

1.    Stewart, M.J., Reaction Kinetics and Operat-
ional Parameters of Continuous Flow Anaerobic	
Fermentation Processes.  Sanitary Engineering Research
Laboratory Publication No. 4 IER Series 90; Berkley,
University of California  (June 1958).
                         C-18

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q^h' VB"Preliminarv  Design  of Wastewater Treatment
Systems," Proceedings, American snn-j^7 ^ civil Engine
  Journal of th«  ^nxrary  Division.  Vol.  osr ^  car
pp. 117-145, Feb.,  1969.:~

DESCRIPTORS
OBJECTIVE

Purpose of this paper  is  to  bring together in one comput-
ational scheme the  significant  cost and performance relat-
ionships for a group of wastewater treatment processes
(arranged in a single  typical configuration for domestic
sewage treatment) and  to  attempt to calculate the perfor-
mance and cost of the  system as a whole based on relation-
ships which have been  developed for the processes indivi-
dually.

MODEL/METHOD

A separate model is adapted  for each individual process,
which describes the relationship of equipment engineer-
ing parameters to process performance variables.  The
resulting engineering  parameters are used to compute the
unit process capital costs   and operating costs using full
size plant compilations by Russell and by Swanson.  Domestic
wastes are characterized  in  the models by 10 categories:
biodegradable carbon,  non-degradable carbon, N, Pf and
inorganic fixed matter (dissolved and solid for each).   The
unit processes described  are:  (a) primary settler, described
by a linear model with two parameters;  (b) aerator and final
settler, steady-state  kinetics  (Eckenfelder) are used   (c)
nitrification in the aerator, steady-state kinetics for the
Nitrosomonas material  describe  balance;  (d) the thickener,
with performance described linearly by two parameters (so-
lids recovery ratio and the  total solids in the underflow
stream); (e) digester, exponential relationships were used
to describe the digester  (McCarthy);  (f) sludge elutriation,
the single-stage washing  step is specified by the solids
recovery ratio and the concentration of solids at a given
station; (g) vacuum filtration  and sludge drying beds,
described by McCarthy's empirical relationship between the
concentration of solids at a given station; (h) vacuum
filtration and sludge  drying beds, described by McCarthy's
empirical relationship between  the concentration of sludge
entering the vacuum filter and  the moisture content of
                         C-19

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the filtered sludge; (j)  sludge incineration, the
total cost of sludge incinerated per year is given;
(k) disinfection, standard engineering procedure was
used (chlorine contact  tank).

Sample costs (capital,  total  cost per 1000 gallons
treated and process costs)  have been computed for
plants from 1-100 MGD capacity and 8-40 ppm of
effluent BOD.

FACTORS INCLUDED

Steady state activated  sludge  kinetics, limiting con-
ditions for nitrification processes, temperature sen-
sitivity of bacterial processes, distinction between
biodegradable and non-degradable carbon as well as
dissolved vs. solid BOD.

ASSUMPTIONS

1.    PRIMARY SETTLER:

      a.  All classes of  suspended solids in primary
          settler are treated  with the same efficiency
          (same for final settler).
2.    AERATOR AND FINAL SETTLER:

      a.  In achieving  the effluent BOD all of the
          soluble food  is used first.
      b.  Steady-state  conditions hold and waste
          composition has constant average properties
          of domestic waste (fixed proportions of
          nitrogen, phosphorus, solids, etc.).
3.    NITRIFICATION IN  THE AERATOR;

      a.  Organic nitrogen required for new sludge
          is assumed equal to  organic nitrogen avail-
          able from nutrients  under nitrifying con-
          ditions; therefore  the ammonia to be oxidized
          is assumed equal to  the influent ammonia.
      b.  Sufficient oxygen for substaining nitrifica-
          tion is supplied and no inhibitory substances
          are present;  99% of  ammonia is converted to
          nitrate if nitrifying conditions are met.
      c.  Each element  of water moves down the aeration
          tank without  mixing; steady state nitrifica-
          tion kinetics hold with constants as given
          by Downing.
4.    AIR REQUIREMENTS;

      a.  When the detention  time to achieve nitrifica-
          tion is less  than or equal to the detention
          time required for BOD removal, it is assumed
          that sufficient oxygen must be supplied to
          convert ammonia to  nitrate.
                        C-20

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5.    DIGESTER;

      a.  Anaerobic steady state laboratory kinetics
          and laboratory constants hold.
      b.  Organic nitrogen decomposition occurs at
          65% of organic carbon rates.
6.    VACUUM FILTRATION AND SLUDGE DRYING BEDS;

      a.  Dissolved species at stations 16 and 15
          are equal.

KEY DATA REQUIRED

Plant design capacity, influent BOD load, effluent
BOD desired primary and final settler performance,
mixed liquor suspended solids concentration in
aerator, digester detention time.

RESULTS

With a fair degree of reliability the program computes
the capital cost, amortization or debt service cost,
and operating and maintenance cost of the entire plant
(or of individual processes or groups of processes)
for conventionally arranged secondary treatment plants
of the type modeled.  No attempt is made to optimize
or to account for influent variability.

SIMILAR/RELATED REFERENCES

1.    Smith, R.,  "Operations Research Activities at
      Cincinnati Water Research Laboratory," Proceed-
      ings, American Water Resources Assn., Symposium
      on the Analysis of Water Resources Systems
       (1968).

2.    Smith, R.,  "Cost of conventional and advanced
      treatment of waste water," Journal WPCF, Vol.
      40, No. 9, pp. 1546-1577, September, 1968.
                         C-21

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                     SECTION D

     HYDROLOGICAL MODELS FOR APPLICATION TO
SYSTEMS ANALYSES OF WATER QUALITY-ABSTRACTED PAPERS
Author" and Title                                 Page

Benson, M.A., and  Matalas, N.C.,  "Synthetic
Hydrology Based on Regional Statistical Pa-
rameters"                                        D-2

Betson, R.P., Tucker, R.L., and Haller, F.M.,
"Using Analytical Methods to Develop a
Surface-Runoff Model"                            D-4

Garrison, J.M., et.  al.,  "Unsteady Flow Simula-
tion in Rivers and Reservoirs"                   D-6

Huggins, L.  and Monke,  E. , "A Mathematical Model
for Simulating the Hydrologic Response to a
Watershed"                                       D-8

Payne, Kip,  Neuman,  W.R., and Kerri, K.D.,
"Daily Streamflow  Simulation"                    D-10

Vemuri, R. and Karplus, W.,  "Identification of
Nonlinear Parameters of Groundwater Basins
by Hybrid Computation"                           D-12
                         D-l

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Benson, M.A., and N.C. Matalas , "Synthetic Hydrology
Based on Regional Statistical Parameters," Water
REsources  Research, Vol. 3, No. 4, 1967, pp. 931-935.

DESCRIPTORS
OBJECTIVE

Purpose of this report is to propose a method that
corrects the space and time deficiencies in the
procedure for synthesizing long hydrologic series
for design and planning purposes.

MODEL/METHOD

This method is an extension of the Harvard "synthetic
hydrology" methodology, e.g., fitting of means, stand-
ard deviations, skewness and first order serial correlat-
ions to log-transformed  monthly and annual single station
stream flow series in order to establish distribution
characteristics for computer generation of long artifical
sequences.

The extension involves multiple regression of individual
station means and standard deviations against six statis-
tically selected basin and climatological variables,  (e.g.,
drainage area, percent forested, percent surface storage
area, annual precipitation, annual snowfall, and slope
of main channel).  Skewness and serial correlation were
found to have poor relationships with these six variables,
therefore, they are given standard monthly values for an
entire region.  The form of the regression function is
multiplicative with unknown exponents (e.g., linear
equation in logarithms).  Relating stream flow statistical
parameters to regional climatological and basin variables
allows use of all long-term records in an area, thus
reducing spatial and temporal sampling errors involved in
single station statistical fits.  Furthermore, given the
six parameter values for an ungaged location, synthetic
stream flows can be generated despite the absence of
historical records.  Actual fitted relationships for the
Potomac basin are presented.

FACTORS INCLUDED

Drainage basin characteristics, climatological factors
(monthly and annual)
                        D-2

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KEY ASSUMPTIONS MADE

1.    The statistical model underlying the synthetic
      hydrology method  is an adequate description of
      single  station flows.

2.    The multiplicative function of the six basin/
      climatological variables  is an adequate descript-
      ion of  their  relation to  mean and standard de-
      viation of  individual station flows.

KEY DATA REQUIRED

Long term stream  flow records at locations throughout
a given region plus values of the six basin/climatolo-
gical variables for each location.

RESULTS/COMMENTS

The method  was applied  to  Potomac River Basin data.
Standard prediction error  for monthly mean flows was
8-24%;  for  monthly standard  deviations, prediction
error was  19-45%.  The  coefficients  of  the regressions
against basin/climatological  variables  show  somewhat
erratic monthly trends  which leave  the  validity of  the
regression  function and selected variables in  some
doubt.  Nevertheless,  the  present method  is  one of  the
few available for generating synthetic  flows for ungaged
locations.
                          D-3

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Betson, R.P., Tucker, R.L.,  and Haller, P.M.,
"Using Analytical Methods to Develop a Surface-
Runoff Model", Water Resources Research, Vol. 5,
No. 19, Feb. 1969.
DESCRIPTORS
OBJECTIVE

By using analytical methods, successive restric-
tions were imposed on a mathematical version of
the U.S. Weather Bureau's graphical surface-runoff
model to develop a simplified analytical model
that expresses the API (antecedent precipitation
index)--runoff relations.  The objectives set for
the model were rationality, model conciseness,
goodness of fit and coefficient consistency.

MODEL/METHOD

An analytical fitting technique (TVA, 1967) was used
for the simplification process; it determines an
optimal set of coefficient values associated with
a minimal sum of squares of the prediction error.

The mathematical API  model  developed  by  the  U.S.
Weather Bureau retains the concept of the season
quadrant, i.e., a set of functions relating runoff
index (RI) to antecedent precipitation for each
week of the year.   In the Weather  Bureau model all
these functions lie between two extreme curves de-
scribing summer (low runoff) and winter  (high run-
off) .  The SI  (season index, a function of week
number)  interpolates between two extreme  curves
to determine R.I.  for a given storm a given week.
In the Weather Bureau formulation, 28 coefficients
are required for the extreme curve plus interpolation
function fit; this was simplified to one exponential
equation with five coefficients expressing RI as a
function of API.  The surface runoff quadrant relations
(surface runoff, SRO, as a function of RI) of the
coaxial-method were replaced by a single polynomial
function of storm rainfall  (RF) and RI with one
coefficient to be fitted.

The resultant analytical model expresses API-runoff
relations with two equations and five coefficients.
                        D-4

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FACTORS INCLUDED

Surface runoff, rainfall, antecedent precipitation by
watershed and by week of the year.

ASSUMPTIONS MADE

The API measure coupled with week number, is a rea-
sonable indicator of antecedent moisture conditions.

Historically fitted SRO vs. API/week number relation-
ship adequately encompass all  factors involved  in
individual sub-basin runoff.

KEY DATA REQUIRED
Historical API, RF, SRO records.

RESULTS/COMMENTS

When tested, runoff relations, derived with the
analytical model over selected watersheds, pre-
dicted  surface runoff from  those watersheds
somewhat better than the regional graphical
relations developed for the Tennessee Valley.

The model coefficients are sensitive  to watershed
characteristics.   The concise  relations  of the sim-
plified analytical model can be rapidly  derived from
a historical storm list by  computer.  Therefore
it becomes economically feasible to  derive runoff
vs. storm relationships for individual watersheds
whose  storms are not  adequately predicted by  the re-
gional  relations currently  used.
                         D-5

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Garrison, J.M., et. al.,  "Unsteady Flow Simulation  in
Rivers and Reservoirs," Am. Soc. Civ. Eng., Journal of
the Hydraulics Division, Vol. 95, No. 5, pp.1559-1576,
Sept., 1969.
DESCRIPTORS
OBJECTIVE
     The purpose of this report is to develop a mathemati-
cal model for unsteady flow simulation in rivers  and  re-
servoirs, including effects such as flow reversals, wave
travel, flood phenomena, etc.

MODEL/METHOD
     The basic model described here involves the  solution
of two linear, first order, first degree partial  differen-
tial equations with two independent variables  (longitudinal
direction, x, and time) and two unknowns  (water surface
elevation and mean velocity).  These two equations of
unsteady one-dimensional stream flow are the continuity
equation and the equation of motion (lateral inflows  and
variation in channel cross-section in the x direction are
included).  Although no closed form solution exists,  these
can be solved numerically by writing them in finite dif-
ference form for digital computer manipulation.   The  advan-
tages of computation with a fixed rather than variable net
of discrete solution points are retained by using Stoker's1
centered difference scheme to compute transient flows (spac-
ing of .3-2.3 miles and 18-180 seconds).  The boundary con-
ditions are given  (using computer tables) as discharge
vs. time, water-surface elevation vs. time, or as a stage-
discharge relationships.  For initial conditions  a steady-
flow profile, a flat pool-zero flow profile    a  transient
flow profile from previous computations may be used.   From
properly calibrating the appropriate model for a  particular
river or reservoir channel,cross sections, slopes and hy-
draulic resistance, time variations in stage, velocity, and
water flow can be accurately predicted at any desired loca-
tion along the channel from  prescribed flow conditions at
each end of the channel and prescribed tributary  or. dis-
tributed lateral inflows (or withdrawals).  Other models
have been developed to complement and extend the  basic model
and to handle special flow situations.

FACTORS INCLUDED
     Local and distributed inflows and withdrawals ,  varying
hydraulic resistance, and varying channel geometry.

ASSUMPTIONS MADE
     One dimensional characteristics are assumed  (e.g.,
depth and velocity vary only in the longitudinal  direc-
tion and with time).
                        D-6

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KEY DATA REQUIRED
     Local and distributed  inflows,  channel geometry, hy-
draulic resistance, time-varying  boundary conditions.

RESULTS/COMMENTS
     This model has been  applied  to  five specific TVA
site studies; three were  used  to  directly verify model
accuracies of  .1 to  .3  feet in stage and almost perfect re-
production of transient event timing   after model cal-
ibration.  (Velocity verification  was poorer due to diffi-
culty of comparing the  mean velocities modeled vs. actual
in-channel measurements).   Important uses of the ,model are:
1)   To guide timing  and  location of measurement effort for
transient phenomena  and basic  resistance coefficients.
2)  For water quality modeling and measurement the model can
show the actual movement  of a  mass of water in a flow sys-
tem, giving  accurate  definitions  of  decay times, uptake
times, exposure times,  etc., regardless of the system un-
steadiness .
3)   To select the best locations for future power plant
sites on the basis of the most desirable flow conditions,
including critical transient phenomena.
4)   To regulate  stream reservoir system flows including
control of transient  effects.
5)   To route  large   flows-  through a reservoir or river
reach based  on accurate predictions  of staged and flows
vs. location and  time.
6)   To study  dam failure problems.
The following  limitations of the  mathmatical model have
been found:
1)   Stability and convergence of the computation scheme
depending on the  gomputation net  used.
2)   Supercritical flows  cannot be calculated.
3)   Bores cannot be  computed.
4)   Branching flows  or complex system flows can only be
computed by  successive  applications  of the model for each
branch.
5)   Stratified  flows cannot be computed with the model
described herein.                           ,
6)   Distortion of wave speed  occurs in regions where rapid
changes occur  between computation net points.
7)   Extensive and relatively  accurate field measurements
of  both basic  channel properties  and observed transient flows
are necessary  to  calibrate the model.           ,
8)   Fairly  high  computer time expenditures are  involved
 (e.g.  2-7 min. of IBM 360 time per day of  simulation).
                         D-7

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Huggins, L. and Monke, E., "A Mathematical Model for
Simulating the Hydrologic Response to a Watershed,"
Water Resources Research, Vol. 4, No. 3, 1968, pp.529-539.
DESCRIPTORS
OBJECTIVE
     A generalized mathematical model is developed to simu-
late, e.g.the surface runoff from watersheds.

MODEL/METHOD
     The model avoids the use of lumped parameters by de-
lineating the watershed as a grid of small, independent
elements.  The element must be of sufficiently small size
so that all hydrologically significant parameters e.g.
slope steepness and direction, vegetation, rainfall and
infiltration rates, etc. are uniform within the bound-
aries of each element.  The composite run-off hydrograph
from the entire watershed is assuming a model for the
runoff hydrograph for each element and applying the equa-
tion of continuity to integrate the responses from all
elements.
     This model was applied to two small watersheds.

FACTORS INCLUDED
     Slope steepness and direction, vegetation, rainfall
infiltration rates, rate of surface runoff, rate of evap-
oration, drainage rate, porosity of the soil, soil moisture,
depth of flow for each grid element of the watershed.

ASSUMPTIONS MADE
1)   The entire watershed is composed of a composite
group of essentially independent internally uniform
elements.
2)   At every point within the watershed a functional
relationship exists between the rate of surface run-
off (dependent variable) and the hydrologic parameters
of soil properties, topography, vegetation, temperature,
time and rainfall from the beginning of the storm event
and the depth of flow.
3)   That the rate which water was intercepted before
satisfying the interception storage could be computed
as the percentage of the total area covered by the hori-
zontal projected leaf surfaces times the rainfall rate.
4)   Holtan's empirical infiltration equation was assumed.
Measurements of constants were based on:  (a) the drain-
age rate was assumed to be equal to the infiltration rate
as required by continuity considerations when the soil was
saturated,  (b)  the drainage rate was taken to be  zero when
the soil moisture content was less than field capacity,
                        D-8

-------
(c)  an arbitary polynomial relation was used to calculate
the drainage rate with respect  to unsaturated pore vol-
ume when the soil water  content was between field capa-
city and saturation.
5)    The typical soils of the area being studied are such
that interflow was  assumed to be negligible.
6)    For surface runoff, the hydraulic gradient in Man-
ning's equation was assumed to  be equal to the slope of
the element and the hydraulic radius was assumed to be
equal to the average  depth of water in excess of the sur-
face retention within the element.

KEY DATA REQUIRED
     Quantitative measurement  (of all factors included
previously) for each  grid element.

RESULTS/COMMENTS
     Application of this model  to two small experimental
watersheds  (251 square grid elements) indicated a need
for additional research  to define better the relation-
ships for  surface runoff and infiltration to improve
the reliability of  the simulated runoff hydrographs.
     A general purpose Fortran  4 program to implement
the watershed model for  arbitrary watershed conditions
is available  (Huggins and Monke, 1966) .
     The model has  the following advantages:
1)   An ability to  readily simulate  watershed conditions
and both spatial and  temporal  storm distributions.
2)   Elimination of the  requirement for lumped parameter
coefficients that must represent  'effective averages'
for a spatially varied parameter.
3)   Independence between the basic model formulation
and the relationship  chosen to  model each of the
component  hydrologic  processes.
4)   Subdivision of the  model  into small elements facili-
ties independent study of the  component parts and a re-
sultant improvement in model accuracy.
     Current major  weaknesses  are the  imprecise empirical
nature of  the assumed infiltration and surface runoff
relationships plus  inadequate  descriptions of antecedent
soil moisture.
                         D-9

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Payne, Kip, Neuman, W.R., and Kerri, K.D., "Daily
Streamflow Simulation," Journal of the Hydraulics
Division, Proceedings of the American Society of
Civil Engineers, pp. 1165, HY4, July 1969.
DESCRIPTORS
OBJECTIVE
     The objective is to develop a multiple-station
daily streamflow generator capable of simulating daily
flow sequences with frequency characteristics similar
to those of the historical records.

MODEL/METHOD
     The present simulator is an extension of the
monthly simulator developed by Beard, but differs
from Beard's second order Markovian single station
daily simulator in two respects:   (1) Historical hy-
drographs are rearranged; and (2) Simulation of monthly
flows to adjust daily flows is not necessary.
     The hydrographs within each month are rearranged
around critical hydrologic events  (peak and minimum flow
days) to preserve the ascension and recession curve
behavior.  The Log-Pearson T#pe m method was used to
transform the rearranged flows to normal distributions
and to determine regression coefficients between stations
and days.  A chi-squared goodness of fit test was used
to test for the normality of the transformed flows.
Flows are simulated by transforming generated random
numbers on the basis of the statistical parameters com-
puted from the rearranged daily flows.  The adequacy
of the technique is tested by comparing the frequency
distributions of the important statistical properties
of the historical flows  (distributions of annual means,
maximum and minimum daily, maximum 3-day average, mini-
mum 7-day average flow, etc.) with those of the simu-
lated flows for two gaging stations on the Calapooia
River in Oregon.  To reduce the excess variation that
the minimum and maximum simulated daily flows exhibited,
two empirical dampening constants were introduced into
the simulator.

FACTORS INCLUDED
     Daily streamflow, multiple station correlations,
monthly peaks with ascension and recession behavior.

ASSUMPTIONS MADE
     Hydrograph rearrangement does not affect time
series behavior; Log-Pearson Type  m transformation
and regression method applied monthly preserves essen-
tial statistics.

                         D-10

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KEY DATA REQUIRED
     Sufficient  station-years of daily hydrographs.

RESULTS/COMMENTS
     The proposed  simulator  is  capable of generating
both nonhistorical flow  sequences with statistical
properties  and hydrographs  similar  to historical flows.
Therefore it  can be used to  analyze the response of
proposed and  existing water  resources systems to poten-
tial nonhistorical flow  sequences of longer duration
than historical  records.  Empirical judgment is required
in  rearranging daily hydrographs and selecting dampen-
ing constants.   The model demonstrated reasonable extreme
value  statistical  behavior using the flow records of the
two gaging  station  selected.
                           D-ll

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Vemuri, R. and Karplus, W., "Identification of Nonlinear-
Parameters of Groundwater Basins by Hybrid Computation,
Water Resources Research, Vol. 5, No. 1, pp. 172-185,
1969 .
DESCRIPTORS -
OBJECTIVE
     The purpose of this report is to identify the para-
meter (transmissifcrlrty, storage coefficient and the bound-
ary) of an unconfined aquifer.

MODEL/METHOD
     Identification of parameters of an unconfined aquifer
in which the dynamics of the water table are describable
by a partial differential equation are looked upon as a
control system problem in distributed parameter systems.
     Using a maximum priciple in conjunction with a
steepest descent algorithm, the transmissibility of an
aquifer is identified, starting from observed values of
input-output as data.  This algorithmic procedure is
blended with a heuristic empirical method to identify
the storage coefficient and the boundary of an aquifer.
This was done by taking full advantage of the flexibility
offered by the  computer via the analog patch board.  Re-
sults of computations carried out on a hybrid computer
(digital computer plus passive resistance network) are
presented.

FACTORS INCLUDED
     Locally varying transmissibility, boundaries and
storage coefficients of the aquifer.

ASSUMPTIONS MADE
1)   Hybrid identification is achieved by assuming a nominal
shape to the boundary of the aquifer and a nominal set of
values to the storage coefficients.
2)   A ground-water flow field is characterized by a qua-
silinear partial differential equation piecewise linear
in the time domain. (Vemuri and Dracup, 1967) .
3)   The transmissibility of the aquifer and the storage
coefficient are only functions of spatial coordinates and
independent of the water elevation level during each time
subinterval.
4)   Assuming that the aquifer is bounded on all sides by
vertical imaginary impermeable barriers it follows that
the boundary of the aquifer is not a function of the
water elevation level.

KEY DATA REQUIRED
     Historical water elevation level and water flow at
points expressed in a Cartesian system plus precipita-
tion inflow, artificial recharge and pumpage.


                        D-12

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RESULTS/COMMENTS
     The technique was  applied  to  study the San Fernando
Valley basin  in the City  of  Los Angeles and some typical
results for transmissibility contours, storage coefficient
contours and  for  the  boundary of the  aquifer are presented
in graphs.
        transmissibilities and  storage coefficients tend
        to decrease with  declining water  tables.
        the shape of  the  boundary  that gives the best
        model can be  seen from  the shape  of the resis-
        tance network on  the analog patch board.
                          D-13

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                    SECTION E

       STUDIES AND MODELS OF OXYGEN BALANCE
         IN STREAMS - ABSTRACTED PAPERS
Author and Title
Churchill, M.A., Elmore,
H.L. and Buckingham, R.A.,
"The Prediction of Stream
Aeration Rates,"                         E-2

Ignjatovic, Lasar, R.
"Effect of Photosynthesis
on Oxygen Saturation,"                   E-4

Isaacs, W.P. and Maag, J.A.,
"Investigation of the Effects
of Channel Geometry and  Surface
Velocity on the Reaeration  Coef-
ficient,"                                E-6

Kartenner, A.D., N. Dixon,  &
D.W. Hendricks,  "Modeling
Diurnal Fluctuations in  Stream
Temperature and Dissolved Oxygen,"       E-8

Li, W.,  "Unsteady Dissolved -
Oxygen Sag in  a  Stream,"               E-10

McKeown, James J.,  "Studies on
In-Stream Aeration,"                    E~12

Merritt, C.A., D.B. McDonald, W.
L. Paulson,  "The Effect  of  Photo-
synthesis on the Oxygen  Balance
in a Midwestern  Stream,"               E~13

O'Connor, D.J.,  "The Temporal and
Spatial  Distribution of  Dissolved
Oxygen in Streams,"                     E"15

Thayer,  R.,  and  R.G- Krutchkoff,
"Stochastic Model for BOD and DO
in Streams,"
                          E-l

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Churchill, M.A., Elmore, H.L. and Buckingham, R.A. ,
"The Prediction of Stream Aeration Rates," Journal
of the Sanitary Engineering Division ASCE, Vol. 88,
No. SA4, pp. 1-46, 1962.

DESCRIPTORS

OBJECTIVE
      The purpose of this investigation is to develop a
fundamental formula based on field measurments for pre-
dicting the reaeration rate  (K2) of natural stream chan-
nels  (non-stratified, non-"white water," free of organic
pollution) as a function of the hydraulic properties of
the channels.

MODEL/METHOD
      Reaches for this study were selected to fulfill the
following requirements: a) location downstream from a deep
reservoir so that water released is low in DO (and es-
sentially free of BOD) during some summer and fall period
and close enough to the reservoir so as to be unsaturated?
b) relatively uniform hydraulic properties and essentially
no benthic organic pollution; c) wide range of flow, vel-
ocity and depth.  Flows were held steady for approximately
24 hour periods during the study at the upstream hydroplants
DO samples for each end of each reach were taken at 7 posi-
tions across the stream hourly.  The laboratory analysis
and research included new measurements of DO saturation
concentrations, effect of temperature on reaeration rate,
and oxygen contribution of indigenous aquatic plants to
correct raw DO readings from streams.  From the above re-
sults K2' s were calculated based on the linear differ-
ential equation for reaeration rate proportional to oxygen
deficit.  509 geometric means of K2 values for each steady
state measurement period on each reach were fitted  (multi-
ple regression least squares) to 19 different equations in
9 variables  (velocity, mean depth, energy slope, resistance
coefficient, density, viscosity, surface tension, molecular
diffusion and vertical diffusion coefficient).  The equation
tested were based on dimensional analysis.  Goodness of fit
was measured using the multiple correlation coefficient.

FACTORS INCLUDED
      DO variation with time and cross-channel position
for each reach; bay hydraulic properties of channels;
correction and/or checks for : BOD, plankton and benthic
photosynthesis, mineral and temperature effects.

KEY DATA REQUIRED
      Channel geometry and hydraulic parameters, flow
velocity,  hourly DO measurements, temperature, labora-
tory determinations of pollutant effect on reaeration rate.
                     E-2

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RESULTS/COMMENTS
1)    19 dimensionally correct exponential-multiplicative
equations in  the  9  key hydraulic variables  were  fitted to
predict K2 over the range of reaches:  all equations had
approximately equally good fits (multiple correlations of
.805-.846).
2)    The simplest  satisfactory equation used only powers
of velocity and mean depth to predict  K2 (valid  for clean
water and uniform reaches in the absence of stratification
and white water).   No significant improvement is obtained
by including  more variables.  Note that slope and  reisitanoe
are strongly  correlated with depth in  the basic  sample of
reaches; therefore, they exert an indirect  effect  through
depth in the  simple equation.  The simple equation is ac-
curate to + 5% with 95% confidence at  the mean of  the data;
at the extremes  it  still predicts K2 within + 15% .
3)    The prediction equation can be applied to  polluted
water by adjusting  K2 by the percentage difference in clean
vs. polluted  water  reaeration rate (laboratory impeller
tests on samples of each).
4)    The  Streeter-Phelps equation cannot be used  directly
for K2 determination  (due to errors through BOD, contamin-
ants, benthic demand, etc).
5)    The  O'Connor  and Dobbins fits for K2  are theoretical-
ly and empirically  deficient.
6)    DO  sampling must take into account significant cross-
stream variations  (as much as 1 ppm.); vertical  gradients
are  insignificant in unstratified stream.
7)    Photosynthesis even in clean streams  can leave a signi-
ficant effect and must be corrected for.
8)    Mineralization and pH have negligible effect of  DO.
9)    The  reaeration rate increases with water temperature
at the geometric rate of 2.41% per degree centigrade.
      Large unexplained cyclic variation (2-12 hour period)
as a  function of time for each reach should be noted  (as
large as + 100%) ; these are simply averaged out  in the final
fits.  The" simplest equation's accuracy may be degraded when
applied  to other regions due to possibly differing cor-
relations  of  slope  and resistance with depth as  compared to
the  correlation for the Tennessee Valley reaches used in
the  data base.
                          E-3

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Ignjatovic, Lazar R., "Effect of Photosynthesis on
Oxygen Saturation," Journal Water Pollution Control
Federation, Vol. 40, No. 5, Part 2, May, 1968.
DESCRIPTORS
OBJECTIVE
     The goal of this paper is to prove the existence
of oxygen supersaturation in a natural body of water
and to search for its source.

MODEL/METHOD
     Since the solubility (of O2) is a function of
temperature, pressure, and salinity these factors
are discussed and evaluated within existing_data for
the Roanoke Rapids Reservoir in North Carolina.J-
     A hypothesis was made that supersaturation is^
due to photosynthesis.  The method of elimination is
used to test the above hypothesis. It is shown that the ob-
served   degree of supersaturation cannot be produced
in a natural water body by:   (a)  temperature changes,
(b) pressure changes, (c) vertical mixing or strati-
fied water, (d) vertical diffusion, or  (e) evapora-
tion.
     Samples of the Roanoke Rapids Reservoir were
taken at 2 stations at 5- ft. depth to obtain DO,
temperature patterns, turbidity and the other factors
related to solubility.
     Turbidity was determined by comparing a sample
in a French square 200-ml bottle with the standards
in the same type of bottle.
     The samples which represent consecutive clear days
with 80% sunshine and consecutive cloudy days with 40%
or less sunshine were selected to test the hypothesis
of photosynthetic oxygen production.  Calculations with
regard to the level of oxygen supersaturation are based
on the Truesdale  et. al. values for oxygen saturation.

FACTORS INCLUDED
     DO, temperature, pressure, salinity, evaporation,
diffusion, light intensity.

ASSUMPTIONS MADE
     It is assumed that a normal biological picture
exists in the reservoir water and that it is not changed
appreciably during the two-month sampling period.

RESULTS/COMMENTS
1)   Dissolved oxygen supersaturation was observed to be
                        E-4

-------
as high as 25% at the  5-Ft. depth at an average temper-
ature of 25°C and over 80% of possible sunshine in sum-
mer at the latitude  35 to  40 degrees N (an additional
9% per day of supersaturated oxygen was consumed by the
existing natural BOD load).
2)  This value of supersaturation cannot be produced by
temperature  changes, pressure  changes, vertical mixing
of stratified water, vertical  diffusion, or evaporation,
whether these  factors act  separately or together.  Photo-
synthesis  is the  only force  capable of producing this
magnitude  of supersaturation.
3)  The effect  of sunshine and algae on oxygen levels in
streams should be recognized as having considerable
significance (average DO levels for  80% or above sun-
shine days were 25% higher than for  40% or below sun-
shine) .   The problems associated with  algae growth and
death appear to be quite important in  stream  pollution
assessment and control.
                          E-5

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Isaacs, W.P. and Maag, J.A., "Investigation of the Effects
of Channel Geometry and Surface Velocity on the Reaeration
Coefficient," Proceedings of the 23rd Industrial Waste
Conference, Purdue University, Lafayette, Indiana, 1968.

DESCRIPTORS
OBJECTIVE
     To predict as a function of channel characteristics
the reaeration rate coefficient, K2, based.on existing
empirical data and theoretical considerations.

MODEL/METHOD
     The authors begin by reviewing existing prediction at-
tempts .
     Adeney and Becker (1919) showed that the change in ox-
ygen deficit was a first order kinetic reaction involving
the reaeration rate constant.
     W.G. Whitman and W.K. Lewis'• (1923) two film theory pro-
posing the existence of laminar layers of gas and liquid at
the two phases interface made their model impractical due
to immeasurable film thickness.
     R. Higbie's idea  (1935) that the constant K  is a func-
tion of contact-time of turbulent eddies at an interface was
rejected due to indeterminacy of "contact time."
     Danckwert's proposal (1951) that the constant is a func-
tion of water surface renewal rate also met the same fate
due to indeterminacy of the parameters.
     Streeter (1926) proposed a model  (suprisingly similar
to Churchill's fit in 1962)  involving average stream velo-
city and average depth of flow controlled by constant co-
efficients which were never explained in terms of stream
parameters.
     The validity of the 0"Conner and Dobbins equation in-
volving mean stream velocity, average depth and slope was
doubted due to inconsistency between prediction and ac-
tual data plus theoretical flaws.
     Churchill's model (1962) based on extensive correlation
analysis performed upon measured stream variables and actual
data from streams although dimensionally non-homogeneous
is considered the best field study.  The parameters in-
volved are the mean stream velocity, the average depth and
water temperature.
     Krenkel and Orlob (1962) proposed an equation(developed
from collected data involving gas activation energy for
molecule  transfer into turbulent fluid)with absolute temp-
erature, gas constant and longitudinal dispersion coefficient.
The Whitman and Lewis film concept was combined with the
Dobbins model but the evaluation technique for film replace-
ment frequency and film thickness received much criticism.
     Thackston and Krenkel  (1966) definition of reaeration
                          E-6

-------
constant using recirulation     is believed to be in-
valid due to the  lack  of  similarity  between flume and stream.
     Owens, Edwards, and  Gibbs  (1964)  empirical equation
appears biased due  to  data base emphasizing streams with
high. K2ls.
     Langbein and Durum (1967)  have  proposed that reaera-
tion rate constant  is  a function of  mean velocity, mean
depth, position along  the stream and the geomorphic
characteristics based  on  Churchill's data.  Churchill
measured only 30  stream reaches but  Langbein and Durum plot-
ted only 24 of these reaches; no correlation coefficients
were reported.
     Tsivoglou's  (1965) approach to  the reaeration con-
stant through the use  of  inert  gases showed excellent com-
parison between reaeration  coefficient and transfer rate
of inert gases.
     Isaacs  (1967)  using  simulated  streams defined the re-
aeration constant in measurable stream parameters  (for
rectangular cross sections).  This model was fitted to
Churchill's data  on streams  for evaluating the linear
constant used in  the model  -  20% discrepancy was found be-
tween simulated and natural  stream  fits.
     The present  study modifies the  original Isaacs fit
by adding a specific non-dimensional shape factor  (to
account for non-rectangular  stream  cross section and a
non-dimensional empirical factor of  proportionality
between mean velocity   (as used  by Churchill) and surface
velocity  (clearly important in  reaeration).

KEY DATA REQUIRED
     Mean velocity  or  preferably surface velocity, temp-
erature, mean depth,  accurate stream cross sections  (for
computing  shape  factors)  and for polluted  stream pre-
dictions  reaeration  rate percentage difference from clean
water value.

RESULTS/COMMENTS
     The  fit  obtained is  significantly better  than Churchill s
original  fit  (.95 vs.   .82 correlation) while at_the  same
time offering  a  dimensionally homogeneous  equation that
also fits  laboratory simulated stream data.  The current
model appears  to  be a highly satisfactory  mean of pre-
dieting  reaeration  rate for clean streams  based on their
physical  characteristics.
                           E-7

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Kartchner, A.D., N. Dixon, & D. W. Hendricks, "Mod-
eling Diurnal Fluctuations in Stream Temperature
and Dissolved Oxygen," Utah Water Research Laboratory,
Utah State University, Logan, Utah.  In: Proceedings
of the 24th Industrial Waste Conference, Purdue Univ-
ersity, Lafayette, Indiana, 1969

DESCRIPTORS
OBJECTIVE

Dissolved oxygen and temperature exhibit significant
diurnal fluctuations which could impact upon the biotic
community of streams.  Use of these parameters in basic
simulation models therefore requires short-time^ (e.g. ,
hourly) time incrementation.  This study is designed
to illustrate the characteristics and possible implica-
tions of these diurnal fluctuation parameters in small,
rapidly flowing streams.

MODEL/METHOD

Two alternative techniques by which short-time varia-
tions can be represented are presented: a Fourier series
curve fitting approach and a time series index approach.

Both models are empirically derived and require sequences
of hourly data relative to the pertinent parameters.

Models were developed by fitting and/or analyzing DO
and temperature data for periods of several days to
one week.  The Fourier model is fitted to data utilizing
least square methods.  The time series analysis is
performed by the ratio-to-moving average method.   To
ascertain the character of seasonal changes, 22 data
blocks of several days each representing different times
of the year are analyzed (summer data used was incomplete)
Diurnal patterns of variation characteristic of each
season are then developed.  Diurnal indexes are based on
ratios of observed hourly parameter values to seasonal
data block means in the time series approach.  Fourier
coefficient seasonal trends are shown through fitted
values for each block of data.

ASSUMPTIONS MADE

1.    A two term Fourier series model can provide
      an adequate fit to DO and stream temperature
      diurnal cycles.
                          E-8

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2.    For the time series approach, the values of
      DO and stream temperatures have only seasonal
      and diurnal cyclical components.

RESULTS/COMMENTS

The authors conclude  the modeling techniques presen-
ted provide a systematic method for assessing DO
and temperature  fluctuations,  and they can be used
to adjust currently available  mean data which is
frequently based on daytime-only sampling procedures.
Either model accounts for about 90% of the DO vari-
ability  and 75%  of the temperature over a one week
period;  annual  fits are considerably poorer.  Weekly
standard deviations are approximately  .25 ppm and  .67°.
These models are limited by  the characteristics of
the data from which the model  was derived.  Extraneous
factors, present at other  locations  (even in the same
stream) , can alter the basic data and may lead to
substantially  different sets of diurnal and seasonal
indexes.

Unfortunately,  extensive in-stream measurement records
are needed for every  location to be modeled.  The  DO
extreme  fluctuations  about the diurnal  trend are of the
greatest interest in  terms  of effects  on biota; these
are riot  directly statistically analyzed or modeled.
                           E-9

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Li. W. , "Unsteady Dissolved - Oxygen Sag in a Stream1,'
Journal of the Sanitary Engineering Division, ASCE,
Vol. 88, No. SA3, May, 1962
DESCRIPTORS
OBJECTIVE

The paper aims at finding a solution of the distribution
of dissolved oxygen at any cross section of a polluted
stream in which the volume and velocity of flow are
steady but not necessarily uniform at all cross sections,
It also attempts to compute the unsteady distribution of
DO due to unsteady initial oxygen content and BOD load
along the stream.

MODEL/METHOD

The deoxygenation of polluted water and atmospheric
reaeration cause variation in DO concentration with
respect to time and distance.  The difference in the
mass inflow and outflow of oxygen and BOD causes
relative changes both in oxygen content and BOD in the
volume bounded by two cross sections a certain distance
apart.  There is a linear relationship between the BOD
changes, BOD of added discharge and the residual BOD
in the stream.  The residual BOD is determined from the
linear differential equations describing their relation-
ship.  Similarly, the dissolved oxygen deficit for the
general case  (varying cross section, velocity and dis-
charge BOD/DO load) is calculated from the first order
equations.

The author develops the differential equations and
solutions for the following special cases:

a.    Steady-state BOD and DO loading;
b.    BOD discharge loading fluctuations as
      a function of time;
c.    BOD and DO discharge loading fluctuations
      of one cycle per day.

ASSUMPTIONS

1.    Constant stream discharge.
2.    The sewage is well mixed both
      vertically and laterally.
3.    No effect of longitudinal turbulent diffusion.
1.    Deoxygenation and reaeration are linear pro-
      cesses .
5.    Benthic and photosynthetic contributions to
      the oxygen balance can be excluded.
                          E-10

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CONCLUSION

The equations predicting the DO/BOD balance are
useful generalized  solutions, given the simpli-
fications inherent  in  the  linear rate assumptions
for the oxygen  depletion and rearation processes.
The often ignored movement of the oxygen sag
point with  fluctuations in BOD  and DO loading
is clearly  demonstrated.
                          E-ll

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McKeown, James J., "Studies on In-Stream Aeration,"
Department of Civil Engineering, Tufts University,
Medford, Massachusetts. In: Proceedings of the 23rd
Industrial Waste Conference, Purdue University,
Lafayette, Indiana, 1968.

DESCRIPTORS
OBJECTIVE

The paper presents a discussion of field measurements
of dissolved oxygen and estimates of oxygen transfer
capabilities of dams and short sections of turbulence
in streams due to rapid loss of elevations.  The use
of mechanical aeration for the purpose of increasing
the DO content at critical oxygen sections of streams
is also evaluated.

RESULTS/COMMENTS

Previous work involving analysis of data collected above
and below numerous weirs and cascades is summarized.
Existing, validated models for calculating deficit ratio
 (of dissolved oxygen) as a function of pollution levels,
height of fall, and water temperature are summarized.
No new models are derived.

New data are presented on dissolved oxygen contributions
from dams and spillways.  Data on the transfer efficiency
 (Ibs. of 02 per hr. per HP) of mechanical surface aerators
is developed and presented.  DO profiles resulting from
various location configurations and numbers of aerators
are presented.  Operational scheduling patterns  (i.e.,
on-off periods), water recycling patterns, and special
horizontal flow or circulation enhancers are examined
as methods of optimizing DO profiles in shallow waters.
Unfortunately, cost data is not included though it is
implied that in-stream aeration is often substantially
more economical than equivalent effluent treatment.
                         E-12

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        f£'l   'B\McDonald' W.L. Paulson, "The
       of Photosynthesis on the Oxygen Balance
in a Midwestern  Stream," Department of Civil En-
gineering, University of Iowa, Iowa City, Iowa
In: Proceedings  of the  23rd Industrial Waste Con-
ference iyb», Purdue University, Lafayette, Indiana
iy b o
DESCRIPTORS
OBJECTIVE

The purpose of this  study was to determine the oxygen
contributed by planktonic photosynthesis in the Ohio River,
which contains ample nutrients due to agricultural activity
in the area, but almost  no benthic vegetation.

MODEL/METHOD

Six 24-hour series were  conducted using separately light
and dark 300 ml. bottles (and 5.5 gallon plastic boxes)
at depths of 0,2.5 and 4.5 feet with readings every 4
hours.  DO measurement were  conducted in the bottles
 (by Winkler method)  and  in the plastic boxes  (at com-
parable times) using the oxygen probes and a micro-
meter; BOD measurements  plus algal counts were also
taken.

RESULTS/COMMENTS

When evaluating the  oxygen resource of a stream, photo-
synthesis must be considered despite its high vari-
ability.  In the present study plankton counts ranged
from 3,600 to 8,900  organisms/ml.  Photosynthetic oxygen
production exceeded  total respiration by 1. 9:1; photo-
synthesis provided 75% of river oxygen.  Total oxygen
produced by photosynthesis in a one foot wide cross-
section of the river was 13.2 gm/day or 1.2 gm/sq.m./day,
as opposed to 4.3 gm/day of  reaeration.

Other important observations include:

1.    Photosynthesis peaks in the early morning
      and levels off during  the rest of the day
      with a sharp drop  after twilight; respira-
      tion has a similarly non-sinusoidal rate
      during the night hours; 10% of full sunlight
      gives peak activity while more is harmful.
                          E-13

-------
2.    A presented plot shows a roughly exponential
      rise in DO with increasing plankton count to
      a slightly supersaturated asymptote (about
      1 ppm) with a very wide scatter band.

3.    Net photosynthetic oxygen contribution at 5
      foot depth is approximately 0 and maximizes
      near the surface with a roughly linear trend
      in between, respiration is approximately
      constant with depth requiring .30 mg/1 of 02•

Unfortunately, no measurements were made to  correlate
results with either stream nutrients or light intensity
at the sample depth.

SIMILAR/RELATED REFERENCES

1.    O'Connell, R.L. and N.A. Thomas, "Effect of
      Benthic Algae on Stream Dissolved Oxygen,"
      Journal of the Sanitary Engineering Division,
      ASCE, Vol, 91, No. SA3, June 1956, pp. 0-16

2.    Hull, C.H.K., Discussion of "Effect of Benthic
      Algae on Stream Dissolved Oxygen," by  Richard
      L. O'Connell and Nelson A. Thomas, Journal of
      the Sanitary Engineering Division, ASCE, Vol.  91
      No. SA1, Feb. 1966, pp. 306-313.

3.    Odum, H.T., "Primary Production in Flowing
      Waters," Limnology and Oceanography, Vol. 1,
      1956, pp. 102-117.
                          E-14

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                 "The.TemP°ral and Spatial Distribution
      v i        ge? in Streams>" Water Resources
      Vol. 3, No. 1, pp.  65  (1967)
DESCRIPTORS
OBJECTIVE

Purpose of this paper is to present methods of incor-
porating temporally and spatially varying factors in
linear differential equation models for dissolved
oxygen streams.

MODEL/METHOD

A_general equation describing the temporal and spatial
distribution of dissolved oxygen in a steady-state
one dimensional river  (e.g., no variation in cross-
stream properties, no longitudinal mixing) is given.
Commonly fitted functions expressing the variation of
the freshwater flow  (due to drainage area changes
and/or groundwater contributions or losses) and cross
sectional area are included as well as the various sources
and sinks of oxygen  (approximated as linear processes) :
natural and artificial aeration, the photosynthetic con-
tribution, distributed and point sources of BOD, bacterial
and algae respiration, carbonaceous and nitrogeneous
oxidation, and benthal deposits.  The system is treated
as a linear in nature: therefore the individually com-
puted oxygen demand/contribution components are simply
added to determine the total  oxygen deficit.  The general
equation is not solved; special cases are solved for linear
increase in drainage area; 24 hours sinusoidal photosynthetic
variations; constant, linear or expodential changes in cross-
section; point and uniformly distributed sources of BOD,
recession from peak flows, diurnal BOD load variations.

FACTORS INCLUDED

DO, BOD, natural and artificial aeration, photosynthetic
contribution, bacterial and algae respiration, carbonaceous/
nitrogenous oxidation, benthal deposits, time varying flows
and loads.
                        E-15

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ASSUMPTIONS MADE

1.    One-dimensional flow.

2.    All oxygen contributing or demanding processes
      are linear in time.

3.    All processes depend only on BOD and DO levels;
      no inhibitory or stimulatory effects of toxins,
      P or N are modeled.

RESULTS/COMMENTS

Methods are shown for developing linear dissolved oxygen
models in the many cases where temporal and spatial
variations are important.  Empirical validation is nbt_
included.  Important observations are made on the signi-
ficant magnitude and lag of nitrogenous BOD in wastes
and the necessity for carefully controlled in-stream
measurements  (even when measuring linear rates of
composite effects of multiple sinks and sources)  Not
addressed is the fact that the one-dimensional approach
can significantly overestimate peak concentrations down-
stream from slug and rapidly varying discharges due to
the failure to account for important longitudinal mixing
effects.

SIMILAR/RELATED REFERENCES

1.    Li, W., Unsteady dissolved oxygen sag in a stream,
      Proc. Paper 3129, J. Sanit. Eng. Div., Am. Soc.
      Civil Engrs., 88 (75), 1962

2.    O'Connor, D.J., and D.M. DiToro, An analysis of
      the dissolved oxygen variation in a flowing
      stream, Proceedings, Special Lecture Series on
      Advances in Water Quality Improvement, University
      of Texas, Austin, Texas, April, 1966.
                         E-16

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DESCRIPTORS
OBJECTIVE
 f ^Thi!  paper  reports  a  combined  laboratory/field study
ot tne effect  of sunlight  and  green organisms on reaeration
of running streams.

MODEL/METHOD
     Data  were obtained  by sampling Delaware River for 24-
hour periods;  samples  were taken  in the middle and two
quarter points at mid  depth.   For the  laboratory experi-
ments large samples  were obtained from different points
in the Delaware  River.   Some samples were exposed to light
or kept in the dark  in open containers with uniform depth.
Others were distributed  into glass-stoppered bottles, which
were immersed  in a water bath  and the  temperature regulated
with hot and cold water.   At frequent  intervals  (2 to 1-1/2
hours) the temperature and dissolved oxygen content were
determined.  All transfers of  water were made by siphon im-
mersed under water to  avoid bubbles.   Analyses were made to
complete 24 hour cycle according  to the standard A.P.H.A.
methods.

FACTORS INCLUDED
     DO, BOD,  photosynthesis,  algal count, light and temp-
erature effects.

RESULTS/COMMENTS
       In- stream measurements  showed both strong diurnal
and strong tidal effects;  diurnal changes covered the
range of 80-115% saturation.   Laboratory experiments with
river water containing green algae  showed that small temper-
ature changes  had practically  no  effect; DO increased or
decreased  depending  almost only upon light and darkness.
     Direct sunlight produced  the same DO level as diffused
light.  Do in  water  containing large quantities of blue-
green and  green  algae  could be decreased from supersatura-
tion to 17% saturation by  placing the  water in darkness,
and could  also be increased to 282% saturation (after 4 1/2
days)  by subjecting  it to  diffused  light.  Large changes
in pH values (6.9 to 9.6)  followed  changes in oxygen sat-
uration.   Under  similar  conditions  the oxygen dissolved
could be decreased'by  almost half where the number of or-
ganisms were decreased by  half.
     Stream measurement  results previously obtained for
dissolved  oxygen (without  consideration of algae) have been
interpreted as meaning far more than was actually warranted,
     In stream pollutions  surveys algal factors must be
taken into  consideration and great  care must be taken in
distinguishing night surveys from day  samples.

                         E-17

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Thayer, R., and R.G. Krutchkoff, "Stochastic Model
for BOD and DO in Streams," Ann. Soc. Civ. Eng.,
Journal of the Sanitary Engineering Division, Vol. 93
No. 3, pp. 59-83, June, 1967
DESCRIPTORS
OBJECTIVE

To model the statistics of oxygen demand and dissolved
oxygen simultaneously at any downstream point.

MODEL/METHOD
The model consists of the following five independent
probabilities of small discrete changes in oxygen
demand and dissolved oxygen concentrations in the stream;

1.    The probability of a unit decrease in oxygen
      demand and dissolved oxygen due to bacterial
      action in a unit time interval is linearly
      proportional to the amount of oxygen demand
      present.

2.    The probability of a dissolved oxygen unit
      increase in a unit time interval due to reaera-
      tion is proportional to the dissolved oxygen
      deficit.

3.    The probability of a unit decrease in oxygen
      demand in a unit time interval as a result
      of sedimentation and stream bed absorption
      is proportional to total oxygen demands.

4.    The probability of a unit increase in oxygen
      demand  (due to uniformly distributed waste
      inputs along the stream) is proportional to
      a constant (input load rate).

5.    The probability of a unit decrease per time
      interval in dissolved oxygen  (due to the net
      effect of benthal demand, photosynthetic
      respiration and photosynthesis) a propor-
      tional to a constant (net deoxygenation rate).

The joint probability of any given dissolved oxygen
and oxygen demand state is computed as the sum of
probabilities of all the first order discrete steps
leading to that state.  All intervals are allowed to
approach zero to yield a continuous formulation.
                         E-18

-------
Means and variances  vs.  time  for  both  variables are
calculated from probability generating functions.

ASSUMPTIONS MADE

1.    Uniform one  dimensional steady flow with steady-
      state deoxygenation-reaeration processes.

2.    Bacterial action,  reaeration, sedimentation,
      oxygen demand  inputs, benthal demand, photo-
      synthetic respiration/photosynthesis  operate
      on oxygen demand  and dissolved oxygen linearly
      as stated above.

3.    Other pollutants  (e.g., N,  P, or toxins) have
      no significant interaction  with  the oxygen
      balance.

4.    Oxygen demand  and dissolved oxygen are  stochastic
      variables whose joint state can  change-, due to 5
      independent  transit transition probabilities.

DATA REQUIRED

1.    Oxygen demand, (BOD, COD or  TOD)  and dissolved
      oxygen measurements from river stations for
      fitting sedimentation deoxygenation, reaeration
      and waste load input rates.

2.    Travel time  and flows.

RESULTS/COMMENTS

The equations for  mean  amounts of oxygen demand and
dissolved oxygen vs. time derived from this model
are identical to the Dobbins  equations obtained from
a deterministic differential  equation  approach based
on the  same linearity assumptions.

The key and most surprising result is  that the variance
of dissolved oxygen  vs.  time  or distance increases
with decreasing mean DO.   This indicates the  serious
shortcomings of deterministic standards and using deter-
ministic oxygen sag  predictions to meet standards.  Note
that even if mean  DO is slightly  above standards at the
sag point, this is precisely  where variability is max-
imized; thus the probability  of random standard violation
becomes quite high.
                         E-19

-------
Actual experimentation carried out under controlled
conditions in polythylene waste cans with random
samples of river water artifically polluted and
reaerated supports the predicted increase in vari-
ability at the sag point.  Likewise, stream data
from the Sacramento River shows worst variability
at the sag point though the data given for both
cases is not adequate to verify the specific form
of the variance prediction.

Computer programs for doing the necessary arithmetic
are available.
                        E-20

-------
                     SECTION F

         MODELING OF THERMAL POLLUTION



Author and Title                             Page

Christiansen, A.G., and Tichenor, B.A.,
Industrial Waste Guide on Thermal
Pollution                                    F-2

Stolzenbach, K.D., and Harleman, D.R.F.,
"An Analytic and Experimental Investiga-
tion of  Surface Discharges and Heated
Water"                                       F-4

Water Resources Engineers, Inc., Mathe-
matical  Models  for the Prediction of
Thermal  Energy  Changes in Impound-
ments                                        F~8
                        F-l

-------
Christiansen, A.G. and Tichenor, B.A., Industrial
Waste Guide on Thermal Pollution, Federal Water
Pollution Control Administration, Northwest Region,
Pacific Northwest Water Laboratory, Corvallis/. Oregon,
September, 1968

DESCRIPTORS
OBJECTIVE

The objective is to develop a practical guide.providing
basic orientation in the subject area of thermal pollu-
tion and, further, to identify sources of more detailed
information as an aid to State, Federal, and local regu-
latory personnel, community and regional planners, and
industrialists in making sound decisions with respect
to thermal pollution.

RESULTS/COMMENTS

The study presents a comprehensive coverage of subject
matter in handbook format.  Each subject area covered
(see factors covered below) includes brief orientation
statements concerning the sources of thermal problem
areas, time-projections of major problem situations, use-
ful statistics and facts, tables and/or graphs of perti-
nent data, and mathematical models or equations for gen-
erating additional practical information.

The use of information and formulae contained in the
guide book is illustrated by a concise summary of the
steps leading to solution of two ty.pical example
problems in thermal pollution.  Cross referencing to
material in the book is extensive in the example
solutions,and references to related research reports
are included in the text.

FACTORS INCLUDED

The subject matter of the guide book is divided
broadly into three parts;

1.    Industrial waste and heat loads

2.    Effects of thermal pollution

3.    Control techniques and devices
                       F-2

-------
The section on waste and heat loads summarizes
information for both the electric power and manu-
facturing industries.  Effects of thermal pollution
includes physical, chemical and biological aspects
of heated discharges.  By  far the largest and most
important subcategory of this section is on bio-
logical effects which includes effects on bacteria,
fish and shellfish, algae  and other aquatic plants.
The control techniques section delves into process
changes, energy utilization, cooling devices, and
heat plume behavior manipulation.                •

Both the attributes and the liabilities of a tech-
nical guide book  are illustrated in this report.
The simple, concise presentation of information  is
an attractive asset for engineers and other workers
in the  field.  Generous cross-indexing throughout
the book and illustrated examples enhance its useful-
ness.

The foreword to the guide  book admits to omissions
of important information in this first attempt to
provide a guide for thermal pollution.  Updating
has apparently not been accomplished in almost three
years during which considerable research activity has
occured and new information has been developed in
the field.
                         F-3

-------
Stolzenbach, K. D., and Harleman, D. R. F., "An
Analytic and Experimental Investigation of Surface
Discharges of Heated Water," Department of Civil
Engineering, Massachusetts Institute of Technology,
Cambridge, Massachusetts, Feb., 1971.
DESCRIPTORS
OBJECTIVE

The objective of the study is the theoretical develop-
ment and experimental validation of a steady-state
analytic model for computation of temperature dis-
tributions in the near field (the zone within which
jet-like behavior prevails) of an ambient body of
water receiving discharges of heated water.  Such
a model is needed for evaluation of thermal effects
upon the natural environment, to develop techniques
for the prevention of recirculation of heated dis-
charges into cooling-water intakes, for improved de-
sign of laboratory scale models, and for insuring
that discharge configurations meet legal tempera-
ture regulations.

MODEL/METHOD

The approach involves, first, a review of th§
available scientific literature in the areas :>f
turbulent jets, stratified flows, and surface heat
loss to provide guidelines and departure points for
the development of basic governing equations.  An
extensive, detailed review of the best available
analytical and experimental investigations of
turbulent jets, flows with stable gradients, and
heat transfer in turbulent fluids is presented.  A
tabular summary of previous theoretical investigations
is presented to show the number of physical dimensions
and the factors affecting temperature distribution
considered by each.

The model developed is a three-dimensional turbulent
jet simulation of a horizontal discharge of heated
water at the surface of a large body of ambient water
which is either stagnant or flowing.  In the initial
model development, theory is developed for predicting
the three-dimensional velocity and temperature dis-
tribution within a discharge jet.  The governing equa-
tions include basic equations for water flow in three
                        F-4

-------
dimensions, incorporating the Boussinesq approximation.
Simplifications and assumptions required to develop a
soluble set of equations are presented.  A solution for
a non-buoyant horizontal discharge is obtained by
proposing similarity forms for velocity and tempera-
ture and by assuming linear jet spreading.

The case of a buoyant jet with no cross current is
developed taking into account the structure of the
jet, lateral momentum, and vertical entrainment.
For ambient cross flows, the governing equations
are the same as those for the buoyant jet with extra
terms to account for jet curvature.  Contingent upon
an extensive set of assumptions, the integrated
equations governing a deflected, buoyant jet are
developed and summarized in a four-page table.

The solutions of all governing equations are per-
formed using a fourth-order Runge-Kutta integration
technique which is contained in the IBM FORTRAN
Scientific Subroutine Package.

FACTORS INCLUDED

Turbulent jets; turbulent flows with density gradients,
surface heat exchange, surface discharges of heated
water, basic governing equations, nonbuoyant surface
jets, buoyant jets, deflected jets, bottom slopes and
jet separation from bottoms.

KEY ASSUMPTIONS

1)    Turbulent Jet (basic)

      (a)  The discharge  is three-dimensional, with
unsheared critical core and turbulent region in which
the velocity and temperature distributions are re-
lated to centerline values by similarity functions.

      (b)  Horizontal and vertical entrainment of
ambient water into the jet is proportional to the
jet centerline velocity.

      (c)  The vertical entrainment is a function
of the local vertical stability of the jet.

      (d)  The buoyancy of the discharge increases
lateral spreading.
                        F-5

-------
2)     Deflected and Buoyant Jets

      (a)   The deflection of the jet is sufficiently
gradual that locally a cylindrical coordinate system
may be defined in terms of the coordinate system
moving with the jet and the fixed coordinate system.

      (b)   Cross flow velocity is small compared to
the jet centerline velocities and distortion of the
jet is small.

      (c)   The lateral spreading velocity is related
to the difference in buoyant and nonbuoyant spreading.

      (d)   Other specific and detailed assumptions
to permit application of the governing equations to
each of four separate jet regions.

      (e)   A jet will not separate from the bottom,
over the entire width of the jet, until the buoyant
effects of lateral spreading cause the slope of the
bottom of the jet to be less than the bottom slope.

      (f)   Until buoyant separation occurs, the
buoyant terms of the model have no effect on the
jet.

      (g)   Frictional effects are negligible and the
longitudinal momentum equations are valid.

      (h)   Once separation occurs, losses in the
entrained flow between the jet and the bottom are
small.

KEY DATA REQUIRED

Initial temperature difference between discharge and
ambient water, the discharge velocity, discharge chan-
nel geometry, surface heat transfer coefficients,
ambient cross flow, and bottom slope.

RESULTS/COMMENT                :

A heated discharge is physically modeled in a laboratory
basin.  All of the important parameters, including the
cross flow and bottom slope are varied and three dimen-
sional temperatures are measured in a series of experi-
mental heated discharges.  The validity of the theoretical
models is verified by comparisions of theoretical and
experimental values.

The results of experiment and computations show that
the rate of temperature decrease in the jet and the

                        F-6

-------
vertical and lateral spreading are controlled by the
initiial densimetric Froude number, the ratio of
discharge channel depth to width, and the bottom
slope.  A cross flow is shown to deflect the jet,
but does not greatly affect the temperature dis-
tribution.  Surface loss does not significantly
affect the temperature distribution in the heated
discharge within the region treated by the theory.

The theoretical model predicts the limits of the
near field temperature distribution in which tem-
perature rises are significant.  The diversion of
natural flows by jet entrainment can also be
observed by theoretical calculations.

The dependence of the maximum vertical discharge
depth on the densimetric Froude number enables the
design of a bimmer wall structure which requires
knowledge of the depth of the heated layer at the
intake.  The calculated dimensions, temperature
and position of the discharge jet aids in the loca-
tion of an intake for prevention of recirculation
as well as the evaluation of the success of dis-
charge configurations in meeting temperature
standards.

The authors conclude that satisfactory field appli-
cation of the theory to prediction of temperature
in an actual heated discharge is possible if tem-
peratures, velocities and the geometry of the discharge
can be schematized by means of steady state tempera-
tures and velocities, and by an equivalent rectan-
gular channel.  However, if it is not clear whether
the jet will entrain water from one or both sides, or
if irregularly shaped solid boundaries (including
bottom) will distort the jet from the form assumed
in the theory, then meaningful schematization is
not possible.

SIMILAR/RELATED REFERENCES

"Mathematical Models for the Production of Thermal
Energy Changes in Impoundments" Water Resources
Engineers, Inc., Walnut Creek, California, December,
1969.

"Mathematical Models for the Prediction of Temperature
Distributions Resulting from the Discharge of Heated
Water into Large Bodies of Water," Tetra Tech, Inc., 630
N. Rosemead Blvd., Pasadena, California  91107, Oct., 1970
                      F-7

-------
 Water Resources  Engineers,  Inc.,  Mathematical Models
 for the Prediction of Thermal Energy Changes  in Im-
 poundments .   Environmental  Protection Agency, Water
 Quality Office,  Water Pollution Control  Research
 Series 16130  EXT,  December,  1969.
 DESCRIPTORS
 OBJECTIVE

 Purpose  of  this  study was  to devise  a mathematical
 model which would  represent the thermal  changes which
 may  be expected  under alternative hydrologic, hydraulic
 and  climatologic condition for operating reservoirs.
 This work is  to  supplement the model developed pre-
 viously  by  Water Resources Engineers, Inc. in their
 investigation of the Columbia River  System.

 MODEL/METHOD

 Two  improvements of the original model were made:

 a.    A  generalized empirical expression for the
      eddy  conductivity coefficient  was  derived, and
       (b) the influence of reservoir stability
      on the  vertical extension of the with-
      drawal  zone  for reservoir outlets  and the
      zone  influence for inflows was accounted
      for.

 The  resulting model accounts for external heat ex-
 change by the usual budget components.   Internal
 heat transfer is accomplished by the penetration of
 short-wave  radiation, eddy diffusion, and vertical
 advection.  The  model also simulates weakly stra-
 tified reservoirs.  These  are represented as a set
 of smaller  reservoirs coupled to each other by the
 heat and mass conservation requirement.  Each small
 reservoir is  described by  the basic model, and the
 tilted isotherms are produced by connecting the
 temperature profiles at the longitudinal midpoints
 of the segments.

 FACTORS INCLUDED

The basic hydrologic, meteorologic and hydraulic fac-
 tors affecting reservoirs were considered.
                        F-8

-------
KEY ASSUMPTIONS MADE

1.    Weakly stratified reservoir  is characterized
      by tilted isotherms along the longitudinal
      axis.

2.    The eddy conductivity efficient is described
      by an empirical  linear log-log relationship
      between the eddy conductivity coefficient
      and stabilities.

3.    A uniform velocity distribution is assumed.

4.    Energy input by  the wind is an exponential
      function of depth.

5.    The selective withdrawal feature of the model
      assumes that the reservoir outlets are slots
      which extend laterally across the face of the
      dam.

KEY DATE REQUIRED

1.    Physical data;   location, elevation, intake ele-
      vations^spillway, mean gaged inflow, mean
      ungaged inflow,  average reservoir discharge
      to volume ratio.

2.    Meteorological data: solar radiation, at-
      mospheric radiation, cloud cover, barometric
      pressure, wind speed, air temperature (wet
      bulb and dry bulb), solar radiation extinction
      coefficient in evaporation coefficient.

SESULTS/COMMENT S

The model was tested and verified on Hungry Horse
Reservoir for which the assumption of horizontal
isotherms is valid.  The primary difference between
the model results and  the observed behavior was
that the model tends to enter the cooling cycle one
to two weeks early.  A test of the segmented model
on Lake Roosevelt gave satisfactory results, although
some difficulties were encountered in simulating the
reservoir during the period of cooling in September.

The primary limitations of the model are:  (a)  it is
one dimensional while  the solution describes a three-
dimensional body of water and  (b) the selective
withdrawal feature, as incorporated into the model,
assumes that the reservoir outlets are slots which
extend laterally across the face of the dam.

                        F-9

-------
The functional form of the eddy conductivity co-
efficient must be used with caution until more ex-
perience is gained through the application of the
model to additional reservoirs.
                      F-10

-------
                    SECTION G

STUDIES AND MODELS OF ECONOMIC AND SOCIAL ASPECTS
OF STREAM SYSTEMS AND WATER QUALITY - ABSTRACTED
                    PAPERS
Author and Title                        Page
Hall, W.A., Butcher, W.S.
and  Esogbue, A., "Optimi-
zation of the Operation of a
Multiple Purpose Reservoir"              G-2

Hamilton, H.R., Goldstone,
S.E., et alia, "A Dynamic
Model of the Economy of the
Susquehanna River Basin:
Phase II "                                G-5

Heaney, J.P.,  "Mathematical
Programming Analysis of Re-
gional Water-Resource Systems"           G-7

Males, R.M., W.E. Gates, and
J.F., Walker, "A Dynamic
Model of Water Quality Manage-
ment Decision-Making"                   G-10

Upton, C.,  "Optimal Taxing
of Water Pollution"                     G-13

Wipple, William, Jr.,  "The
Economics of Water Quality,"            G-15

Kerri, K.D.,  "A Dynamic Model  for
Water Quality  Control"                  G-18
                         G-l

-------
Hall, W.A., Butcher, W.S. and Esogbue, A., "Opti-
mization of the Operation of a Multiple Purpose
Reservoir", Water Resources Research, Vol. 4, No. 3.
pp. 471-477, June 1968

DESCRIPTORS
OBJECTIVE

A technique of analysis is presented in this paper
by which the dynamic operation policies for planning
or operating a single multi-purpose reservoir stream^
system producing hydroelectric power and providing
water can be optimized for the maximum return from
"firm"  (on-peak) water, "firm" (on-peak) power, dump
(off-peak) water and dump (off-peak) power, while
meeting complex constraints (such as mandatory flood
control storage variable in time, fish, wildlife,
and recreational releases, navigation, salinity control
or water right minimum flows,  etc., as well as eva-
poration losses and inter-basin diversions).

MODEL/METHOD

The technique can be used as the suboptimization
portion of a multiple reservoir system optimization
by linear programming  (Parikh, 1966).   The fourth
decision variable, dump water, is determined by
the other three decision variables mentioned above and
the equation of continuity over time.   The procedure
provides for optimization of the individual stream
system in response to a given set of predetermined
time-varying prices and input flows (authors use the
"critical period hydrology" concept in use in Califor-
nia)over the total planning horizon for the three
decision variables.  The predetermined prices need not
be actual "contract" prices; they can be shadow prices
generated during iteration of the linear multiple
reservoir-optimization shceme.

The objective function for the single reservoir opti-
mization is given by the sum of income returns from
expected "sale" of firm.iand dump water and energy,
for the price schedule given for each of the N time
intervals.  Using the standard recursive procedures
of dynamic programming, a generalized equation is
written successively for one remaining time period,
two remaining time periods, etc.  Only the volume of
water released is carried over into the next time
period, and the power and water decisions are in-
herently interrelated in the model.  The constraints
used in the dynamic program are:

                        G-2

-------
1.    The allowable releases for each month must
      be greater than or equal to the minimum re-
      lease that will bring the reservoir to its
      maximum storage level for the next month,
      and these releases must be less than or equal
      to the maximum release that will bring the
      reservoir to its minimum storage level.

2.    The minimum release is the greater of either
      the feasible release for that month or the
      mandatory release.

3.    If the energy function is less than or equal
      to the capacity limit on peak energy, then
      all the energy that can be produced will be
      on-peak energy.

4.    If the energy function is greater than the
      capacity limit on peak energy but less than
      or equal to the capacity limit on total
      energy; then there will be two energy values:
      peak and non-peak energy.

5.    If the energy function is greater than the
      capacity on total energy, then the maximum
      possible peak energy is produced, and the
      excess energy is thereby non-peak, or dump,
      energy.

6.    The maximum allowable storage  in any time
      period may not exceed total storage less
      the flood control reservation for that time
      period.

KEY DATA REQUIRED

Inflows  (monthly), storages  (initial and end), re-
leases  (mandatory), prices  (monthly for dump and
firm energy, single value for water released)f
hours  (on peak hours, total hours in each month).

RESULTS/COMMENTS

1.    Against the additional returns from reduced
      end storage must be weighed the risk of fail-
      ure to regain normal  (initial) storage before
      the onset of a second critical period.  This
      aspect cannot be covered directly in the_ana-
      lysis, yet end storage decisions are an in-
      tegral part of an overall optimum operating
      policy.
                          G-3

-------
2.     A key advantage of this analysis is that it
      requires considerably less running time than
      the previously employed linear program add-
      ressing the same problem.

3.     The treatment of water quality as a simple
      low flow augmentation "requirement" or
      constraint is somewhat simplistic, from the
      point of view of water quality management.

SIMILAR/RELATED REFERENCES

1.     Hall, W.A., and D.  T. Howell,  The optimization
      of single-purpose reservoir design with the
      application of dynamic programming to synthetic
      hydrology samples,  J. Hydro!., 1, 355-363,
      December, 1963.

2.     Parikh, S.C. Linear dynamic decomposition
      programming of optimal long-range operation
      of a multiple multi-purpose reservoir system,
      Proc. Fourth Intern. Conf.  Operation Res.,
      Boston, Massachusetts, September, 1966.
                        G-4

-------
Hamilton, H.R   GoldRtone,  S.E., et alia," A Dynamic
5£f   ?T  c6 Eco£om*  Df the Susquehanna River Basin:
Phase II  Susquehanna River Basin Group", Battelle
Memorial Institute, Columbus, Ohio, August, 1966
DESCRIPTORS
OBJECTIVE

The report outlines progress toward the development
of a dynamic, mathematical model of the economy of
the Susquehanna River Basin.  In its present stage
of development the model has been used to make pro-
jections of the Basin's economy.  These projections
are reported with an analysis of water-resource
development in the Basin.

MODEL/METHOD

The study is separated into two phases: Phase I in-
vestigated the feasibility of building a dynamic model
and Phase II has been directed primarily toward ana-
lyzing and tying together factors judged to have sig-
nificant impact on the growth of the economy of the
Basin.

Two primary divisions are established.  The first is
the division of the Basin into economic subregions,
and the second is the division of each of these sub-
regions into subsectors of interrelated variables
for each major factor; these are demography, employ-
ment, water, electric power.  Each subregion has
been described by a series of fitted equations that
are divided into subsectors.  In each subsector are
equations that tie the subsector to other subsectors.

The complete dynamic model can and has been used to
accomplish the following functions: (1) To make
economic and water-use projections for the Basin.
Projections, by subregions, of population, employ-
ment, wages, unemployment, water-consumption, pollu-
tion, and many other variables can be made._ (2) To
project electric power demand.   (3) As a guide to
point out major influences on the economic develop-
ment of the Basin.   (4) To test the economic impact
of building various alternative systems of river
works.  (5) As a guide to facilities planning.
                         G-5

-------
RESULTS/COMMENTS

1.     The relationship of economic growth to water-
      resource development in the Basin has been
      described through equations fitted to the major
      economic variables.

2.     A useful dynamic model of the economy of the
      Basin has been developed and adopted for
      computer simulation.

Two overall conclusions of interest are:

1.     Water is not a constraint upon the growth of
      the economy of the Susquehanna River Basin.

2.     in general the economy of the Basin will grow
      more slowly than the nation over the next 50
      years.

The study does not address water quality problems
or their economic effects on the Basin.  Furthermore,
it does not address past or predicted effects of
extreme low flows.
                         G-6

-------
Heaney, J.P., "Mathematical Programming Analysis
of Regional Water-Resource Systems," Proceedings
of the ARWA National Symposium on the"Analysis
of Water Resource Systems, July  1968'.
DESCRIPTORS
OBJECTIVE

The objective of the analysis is to allocate water
resources among regions within a water resource
system so as to achieve the  "best combination of
use"  giving consideration to both tangible and in-
tangible beneficial uses.

MODEL/METHOD

A river system is subdivided into study areas of two
categories  (a) headwater  (one which does not have
another study area upstream) and  (b) interior.  The
model employs the concept of economic demand and com-
petition for water rather than absolute requirements.
The "best combination of uses" is defined as that
combination which maximizes  regional net economic
benefits  (gross value-added) while supplying certain
minimum flows for intangible beneficial uses  (e.g.,
preserving stream quality, fish, wildlife, esthetic
values, etc.).  Maximization is achieved by linear
programming format which decomposes the problem into
individual study area optimization schemes based on
the Dantzig and Wolfe decomposition principle.

Each of the study areas determines its optimal water
allocation  (depending en cost of water, supply avail-
able and total value-added differences for alternate
uses) and the associated imputed value of water to the
area  (change in net benefit  if water supply is altered
by one unit) , using a linear program.  The regional
optimization consists of giving each study area an
estimated quantity and value of water supplied (zero
value for the first iteration), based on which each
study area is optimized.  Under these conditions,
each study area solution yields an imputed value^of
water for the area.  The process is iterated until
all imputed values for headwater areas are equal
plus all imputed values for  interior areas are equal
and less than the headwater  value (barring areas with
an oversupply of water, where value is zero).
                         G-7

-------
This point represents the regional optimum.  Using
this optimum, the imputed cost  (benefits foregone)
of the flows reserved for intangible beneficial
uses can be computed.

The model has been applied to the Colorado Basin
divided into 44 study areas, using published
economic data.

ASSUMPTIONS MADE

1.    Basic economic inputs can be estimated.
2.    Value-added is linear with water quantity
      for each alternate water use.
3.    Time variations in water supply can be
      ignored or averaged out for the purposes
      of economic analysis.
4.    There is no interaction with groundwater
      supply.              ;
5.    Total gross -value-added is an adequate in-
      dicator of regional economic benefits.

DATA REQUIRED

1.    Regional and study area water supply constraints
2.    Value-added for each alternate use vs. water
      quantity for each study area.
3.    Supply quantities necessary for intangible bene-
      ficial uses.

FACTORS INCLUDED

Supply available; competition among alternate uses and
subregions; overall regional economic benefits; water
supply restrictions for intangible beneficial uses.

RESULTS/COMMENTS

In examining possible system states with respect to
the imputed resource valuation, it can be determined
whether or not river basin planning yields major
economic advantages.  The model offers a quantitative
technique for evaluating the sub-region interdepen-
dencies that are the prime concern of regional opti-
mization.  By recognizing the decomposable nature of
the river basin planning problem, it is possible to
evaluate large systems in a consistent manner and  a
computationally feasible manner.
                         G-8

-------
Applications of the model to the Colorado Basin
show that major economic misallocations result
from current water appropriations and current cost/
benefit justifications of Bureau of Reclamation
irrigation projects.

SIMILAR/RELATED REFERENCES

1.    Heaney, J.P.,  "Mathematical Programming Model
      for Long-Range  River Basin Planning with
      Emphasis on the Colorado River Basin," Ph.D.
      Dissertation, Northwestern University, Evanston,
      ill.,  215 pp.,  1968.

2.    Heaney, J.P., A. Charnes, R.S, Gemmell, and
      H.B. Gotaas,  "Impact of Institutional Arrange-
      ments  on the Available Alternative Developmen-
      tal  Paths for Water Allocation and Pollution
      Control in  the  Colorado River Basin," Proc.
      Third  American  Water Resources Associaiton
      Conference/ San Francisco, California, 12
      pp., 1967.
                          G-9

-------
Males, R.M., W.E. Gates, and J.F. Walker, A Dynamic
Model of Water Quality Management Decision-Making,
Final Report, Engineering Science, Inc., May, 1970.

DESCRIPTORS
OBJECTIVE

The study investigates the regional board decision
making process.  The disciplines of behavioral science
and systems analysis are used in combination to assess
the California system of Regional Water Quality Control
Boards.  The overall objective is the derivation of
broadly applicable techniques of water quality manage-
ment.  Specific objectives are:

1.    Assessment of the formal and informal object-
      ives and attitudes of groups and/or individuals
      identified as participating in the decision-
      making process.

2.    Determinations of procedures by which decisions
      are achieved.

3.    Determination and evaluation of the consequences
      of a postulated informal decision-making struct-
      ure for water quality management.

MODEL/METHODS

Since broadly applicable techniques are sought, it
is implicitly assumed that the California system of
regional control boards is representative of regional
boards in general.

The approach is termed "environmental systems dynamics",
It involves simulation modeling of the behavior of the
components of a regional decision-making system, in-
cluding feedback loops operative among components.
Model component structure and parameter are based on
quantitative assessment of qualitative information
gleaned from extensive interviews with persons in-
timately involved with water quality decisions.  The
model is brought to an empirical fit with observed
behavior patterns of a prototype California Regional
Board System by arbitrary adjustment of non-measur-
able parameter values.
                         G-10

-------
FACTORS INCLUDED

Key factors included in the model development involve
the structuring and assessment of:

1.    The hierarchy of management organization.
2.    Dynamic interactions of pertinent factors and
      personnel pertaining to decision making.
3.    Relationships among- relevant water interest
       (objective) groups.
4.    Regional versus centralized management.
5.    The decision making process.
6.    Perceptions of water quality management functions.
7.    Perceptions of goals, conflicts, identities, etc.,
      for all interest groups.
8.    Regional board meeting procedures.

DATA REQUIRED

Classes of data collected and/or estimated subject-
ively from interviews include:

1.    Scales of public and interest-group attitudes.
2 .    Response functions.
3 .    Impact functions.
4.    Measures of public awareness of pollution
      problems,
5.    Flow charts of decision processes and pro-
      cedures .

RESULTS/COMMENTS

Structuring and testing of the model and an example
of use is described for the limited situation of
two distinct interest groups  (industrial and con-
servationist) interacting with an extended board.
Five functional areas are structured: generation of
pollution, desired quality of water based on uses,
perceived quality of water based on pollution levels,
negotiation of responses based on magnitude of the
problem and time factors, and response.  Within the
situation content, the model is used to examine the
sensitivity of the decision-making process to be-
havioral and technical parameters.  Partial results
of the case are presented as time simulations of
actual pollution levels.
                         G-ll

-------
1.    The structure and philosphy of the regional
      board relies heavily on the concept of
      assimilative capacity, i.e., the capacity
      of the environment to assimulate wastes.

2.    System response to discharger behavior
      patterns is critical, i.e., the relative
      independence of the board with respect
      to waste dischargers determines the rate
      at which abatement is achieved.

The simulation model as structured in this paper
is comprised of a series of basic block diagrams.
The text infers the existence of a mathematical
model fitted empirically to information given in
case studies, but the mathematical model is never
formally presented.  A major difficulty in•social
system research, that of quantification of data',
is acknowledged, but the specific relationships
developed for use as hard data in the mathematical
model are not presented.   It is therefore diff-
icult to judge the full validity of the conclusions
and recommendations provided.
                         G-12

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Upton, C., "Optimal Taxing of Water Pollution"
Water Resources Research, Vol.  4, No. 5, October,
1968.

DESCRIPTORS
OBJECTIVE

This paper deals with the problem of achieving effi-
cient water quality management through effluent taxes.
       ?
MODEL/METHOD    >    . i •  *

The model uses standard calculus methods to minimize
cost of maintaining a specified water quality (DO
level) by minimizing the sum of low flow augmentation
costs  (publicly funded) and amount of treatment ex-
penditure for each polluting discharger (privately
funded), where cost of augmentation is a fixed function
of flow.  Cost of augmentation is only assumed to be
a convex increasing function of the amount of pollutant
load removed.

It is shown that optimum taxes on pollution discharges
can be set in such a way as to drive dischargers to
the minimum total cost operating point, at least when
the individual plant treatment cost functions are known.
Using this framework two tax schemes which do not re-
quire knowledge of the treatment cost function on the
part of the taxing authority are examined as to optima-
lity.

The first one, the increased permissible waste load
method, makes each firm's assessment proportional to
its share of excess DO deficit contributed over and
above the total DO deficit contribution that results
in acceptable water quality standards without augmen-
tation.  This scheme is equivalent to the "required
dilution water method" where tax is based on the amount
of dilution water required to maintain stream quality.
These taxes are optimal only if cost of augmentation
is directly proportional to amount of augmentation flow.
In the second scheme, the waste discharge method, the
firm's assessment is proportional to its share of the
total discharge.

This scheme is optimal only if cost of augmentation
is directly proportional to total stream flow.
                         G-13

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KEY ASSUMPTIONS

1.    There is only one form of central treatment
      available:low flow augmentation.

2.    The only alternative way for a firm to reduce
      pollution is to treat waste at the plant site
      after the pollutants are created in the pro-
      duction processes.

3.    The marginal cost for both low flow augmentation
      and decentralized treatment is positive.

4.    A one dimensional parameter,DO deficit,can des-
      cribe total stream water quality; this para-
      meter consists of a simple weighted sum of
      individual discharge loads (e.g., measured as
      BOD) divided by total stream flow.  It is assumed
      that the weights used are constant and independ-
      ent of stream flow  (though this is not true even
      under linear rate DO stream models unless all
      discharges occur at a single stream location).

5.    The level of output of each firm and the amount
      of pollutants produced by each firm's product-
      ion process are fixed.

DATA REQUIRED

Waste load of each firm, downstream linearized effects
of each discharge, cost vs. scale of low flow augmen-
tation.

RESULTS/COMMENT

1.    The cost of maintaining a minimum water quality
      standard is minimized when the marginal cost
      of treatment at each plant, weighted by the
      plant's marginal effect on the water quality,
      is set equal to the marginal cost of low flow
      augmentation.
                           i
2.    Results demonstrate that the second taxation
      scheme is preferable to the first scheme if
      the cost of augmentation is continuous and
      concave upward  (decreasing return to scale).
      No general results are available.

The unrealistic nature of strong assumptions such
as 4. and 5. considerably restrict the applicability
of this model.
                         G-14

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Wippie, William, Jr.,  "The Economics of Water Quality,"
Water Resources Research  Institute, Rutgers - The
State University, New  Brunswick, New Jersey.  In:
Proceedings of the First  Annual Meeting of the American
Water Resources Association, AWRA. Urbana r Til-inni gf	
1965 .
DESCRIPTORS
OBJECTIVE

This paper is an expository discussion of the economics
of water quality intended to develop a rationale for
an economic approach to quality control analysis.
Water use concepts and principles of economic costs and
benefits, including treatment of aesthetics, are dis-
cussed.  It is concluded that it should be possible
to make fair evaluations of all economic benefits that
accrue as a result of improved water quality.

MODEL/METHOD

Supply-demand concepts developed in economics are con-
sidered for application to analysis of total usable
streamflow, including return flows.  The technique is
rejected as insufficient to solve major problems.

The graphical procedure of indifference curves is
introduced as applicable to the process of assessing
alternatives for obtaining usable  (within standards)
water at downstream points.  The indifference curve
method is illustrated by an example involving graphic
contours of all combinations of waste treatment re-
duction and low-flow augmentation capable of achieving
a given stream quality level.  Straight line contours
representing equal cost combinations of the two alter-
natives are superimposed on the same graph; points
of tangency between the equal cost and equal "quality"
contours identify optimum combinations (in the sense
of minimum cost for a given quality level).  The ex-
ample problem is constrained to analysis of a single
pollutant.

A concept of "pollution sets" is explored.  Pollution
sets are defined as.combinations of multiple pollu-
tant concentrations in a stream.  A set encompasses
a range within which an optimum solution is likely
to be found.  Each pollution set thus represents a
                         G-15

-------
criterion range for BOD, heat, chemical wastes, etc.
There exist corresponding costs for reducing pollu-
tion to the levels specified by a set, and corres-
ponding economic losses caused by pollutants in the
stream.  For each set there also corresponds an
optimum combination of effluent treatment, flow
augmentation or alternate means of reducing pollu-
tion, and a corresponding lowest total cost of achie-
ving the given degree of control of the various wastes
embraced by the set.  It is proposed that various sets
can be compared using appropriate incremental costs,
benefits, and quality criteria to arrive at an optimal
result.

ASSUMPTIONS MADE

1.    Each damage caused by waste can be identified
      and the costs of treatment can be associated
      directly with that damage to determine net
      benefit.

2.    Treatment levels can be related to corresponding
      changes in receiving stream water quality.

3.    Stream water quality is assumed to be uniform.

RESULTS/COMMENTS

The economic bases for effluent charges and subsidies
are discussed by means of an example and graphic
illustration involving an optimal solution for a single
pollutant and three points of water use.  The object-
ive function is to minimize total costs by optimizing
the costs of treating versus accepting pollutants dis-
charged by the involved users.  The problem is con-
strained to a single additive measure of pollution.
Assumptions include:

1.    The economic costs to downstream users of
      accepting residual wastes of upstream
      polluters are known.

2.    Pollutant effects from upstream outfalls are
      directly additive at downstream points for
      purposes of estimating intake treatment re-
      quirements and costs.

It is concluded from the example that definite re-
lationships can be determined between the costs of
treating effluent wastes at various points and the
                         G-16

-------
economic costs occasioned by the residual wastes
discharged.  Using marginal and total costs cal-
culated for the various users of the example, a
philosophical discussion is presented concerning
the economic implications of various approaches
for imposing effluent charges in a basin system.

This paper provides graphic insight into the
principles of economic benefit and cost/benefit/
tradeoffs.  However, practical application of the
techniques presented is essentially negated by
the highly multidimensional nature of real world
problems compared to the simplification and approx-
imations necessary to implement the proposed graphical
techniques in a comprehensible format.  Identical
concepts have since been implemented in large scale
mathematical programming models.
                          G-17

-------
Kerri, K. D.,  "A Dynamic Model  for Water Quality
Control," Journal of the Water  Pollution Control
Federation, Vol. 39, No. 5, May,  1967, pp.  772-786.
DESCRIPTORS
OBJECTIVE

The  qualitative  structuring of an acceptable approach
to an  equitable  system of effluent charges as an
economic means of providing a monetary incentive  for
waste  dischargers to reduce the quantity of waste  in
their  effluents.

RES ULTS/COMMENTS

The  report  is an expository discussion of a proposed
method of handling effluent charges.  A cooperative
or association composed of waste dischargers is
proposed.   Waste treatment costs are reduced for
an example  of five industrial waste dischargers
by merging  their individual waste treatment re-
sources into a single, controlled system in lieu
of attempting to conform separately to an effluent
standard.   The water quality objective (e. g. a
specified,  in-stream DO concentration) is achieved
through a pollution control system that is based
on economic analysis.

Digital computer programs are necessary to compute
the  optimal economic solution, but the programs
are  identified by references to other research
efforts and are not included in the discussions of
this study.

In general  terms, a minimum cost solution is ob-
tained from a dissolved oxygen cost of treatment
matrix solved by nonlinear programming techniques.
This solution is inserted into a program that
analyzes the influence of the major dischargers in
a basin on  the dissolved oxygen concentrations in
receiving waters and the assimulative powers of
numerous reaches of a main stream and its tributaries.

The  association members pay the total cost  (only
institutional costs are included) estimated by the
economic solution,  the costs being distributed among
the  discharger members in proportion to the quantity
of waste generated by each member.  A key feature of the
proposed association is the implementation of a pivotal
waste treatment facility.  The pivotal facility may
be any member of the association selected (and if
                        G-18

-------
necessary upgraded) to meet specified characteristics
concerning size, location with respect to critical
reaches, and flexibility with respect to marginal
costs of treatment over a broad range of treatment
requirements.

Based on the degree of treatment  (indicated for each
member) to achieve a basic quality condition of the
entire receiving stream by reaches, the nonpivotal
facilities maintain relatively constant rates of
waste removal regardless of the condition of the
receiving stream.  The pivotal facility (by its
design) is able to vary the amount of wastes it
removes over a considerable range.  The pivotal
facility, thus, acts to reduce its level of
treatment (and hence costs) during periods when
water quality is far above standard, and increases
the level of treatment during adverse conditions.
By careful design of the entire system, utilization
of the pivotal facility concept leads to considerable
reduction of association total costs.

Bases for eligibility in the association, are pro-
posed.  Possibilities include legal requirements for
all basin dischargers to join, pressure tactics
based on unreasonable effluent discharge require-
ments to force membership, or the simple option
of joining the association as opposed to otherwise
conforming to the regulatory agency established
standards.  The last option is recommended.

Relationships between the association and the res-
ponsible, basin, regulatory agency are examined.
Cooperation and coordination between the association
and the agency are deemed essential.

The problems of compensation to individual association
members for their existing facilities are analyzed
and arrangements for equitable settlements are
proposed.

Rigorous economic analysis of existing facilities
and of required new construction is essential.  The
operating'strategy for the association system must
be developed, using high speed computers and systems
analysis techniques, to specify the removal of wastes
from a critical reach (or reaches) at minimum cost.  An
approximating graphical approach to the analytic pro-
cedure is illustrated.

Dynamic conditions that will confront an association
are addressed.  The increased costs (to the association)


                        G-19

-------
from increased volumes of wastes to be treated as
basin industrial activity increases (outside the
association) are concluded to be a reasonable
exchange for the privilege of using all of the
available assimilative capacity of the receiving
stream.  Conditions for the acceptance of new,
participating or nonparticipating association
members, and special considerations for expansion
of production processes at existing sites (both
association and nonassociation)  are addressed.  If
changes in water quality standards occur, it is
concluded that advantages accrue to the association
because of system flexibility permJ tting selective
upgrading of parts (only) of the system -- costs
being distributed throughout the system.  Problems
of jurisdictional boundaries and association mergers
are evaluated, and the handling of costs sustained
by the association when a member chooses to leave
the group are analyzed.

Cost savings is the major advantage observed in the
proposed association concept.   At one extreme (all
basin waste dischargers included), , the association
concept would approach that of a basin authority;
at the other extreme (a multiplicity of associations),
it would approach the zoning concept proposed by
other authors.
                        ;-2o

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                         SECTION H

     DATA COLLECTION TECHNICAL DATA AND COST DATA FOR
     SYSTEMS ANALYSES OF WATER QUALITY - ABSTRACTED PAPERS
     Author and Title                        Paqe
1.    Gannon, J.j. and C.T.
     Wezernak, "Collection and
     Interpretation of Stream
     Water Quality Data,"                     H-2

2.    Kalinske, A.A., "Economics
     of Aeration in Waste Treat-
     ment ,"                                   H-4

3.    McKeown, James J., "Studies
     on In-Stream Aeration,"                  H-5

4.    Meyer, C.F., "Using Experi-
     mental Models to Guide Data
     Gathering,"                              H~6

5.    Stone, Ralph and C. Schmidt,
     "A Survey of Industrial
     Waste Treatment Costs and
     Charges,"               .                H~8

5.    Warner, D.L.,  "Deep Wells
     for Industrial Waste In-
     jection in  the United
     States: Summary of Data,"               H-10
                              H-l

-------
Gannon, J.J. and C.T. Wezernak, "Collection and
Interpretation of Stream Water Quality Data,"
Third American Water Resources Conference, AWRA,
San Francisco, November, 1967.

DESCRIPTORS
OBJECTIVE

In this paper the steps involved in designing and
executing practical stream surveys are described.
                                          i
MODEL/METHOD

The steps include:

1.    Continuous physical measurements of the river
      flow at a number of key locations.

2.    Preparation of hydrographs consisting of a
      graph of the daily average flow with respect
      to time, relating water quality data to flow
      conditions during the sampling period.  This
      includes high or low runoff, ascension and
      recession hydrograph curves and normal flows.

3.    Knowledge of discharge rates from all the
      known pollution points including waste treat-
      ment plants, storm and sanitary sewers and
      drainage ditches, etc.

4.    Accurate time of travel or velocity record
      along the stream.  The authors use a Rhod-
      amine B dye as an external tracer in con-
      junction with a fluorometer operating either
      in a boat for times through an impoundment,
      or at bridges for times in free flowing
      river sections for measuring the time of
      travel.

5.    Collection of water quality samples and test-
      ing including measurements of the coliforms,
      dissolved oxygen and BOD.

6.    Exploration of existing information on water
      quality from sources such as water treatment
      plants, sewage treatment plants, private
      industries, and governmental agencies at the
      State and Federal level.
                         H-2

-------
7.    Measurement of thermal stratification with
      associated influence on water quality (e.g.,
      where a river flows through an impoundment).

8.    Summarization and interpretation of the
      collected information.  A number of suggest-
      ions have been given by the authors.

RESULTS/COMMENTS

A case study of a survey of the Clinton River is
described.  The survey investigated research on
abnormal river BOD reductions and arrived at sig-
nificant conclusions regarding the influence of
such  factors as photosynthesis on dissolved oxygen
level by means of carefully controlled day and night
sampling.
                          H-3

-------
Kalinske, A.A., "Economics of Aeration in Waste
Treatment," Eimco Corporation, Salt Lake City,
Utah.  In: Proceedings of the 23rd Industrial
Waste Conference, Purdue University, Lafayette,
Indiana, 1968.

DESCRIPTORS
OBJECTIVE

The paper is confined to discussions of the efficiency
and power consumption of the three aeration methods
for those aerobic processes where the organisms are
kept in suspension in liquid waste—primarily the
activated sludge process.

RESULTS/COMMENTS

The three principal oxygenation methods presently in
use in liquid waste treatment are discussed, i.e.,
these are diffusion of compressed air, air diffusion
with submerged turbine dispensers, and mechanical
surface entrainment aerators.  Methods for calculating
power requirements and oxygen absorbed are presented
and discussed.  Factors pertinent to the assessment
of true cost are identified for each oxygenation method.
Three principal methods for evaluating the performance
of aerators either under test conditions or in the field
under actual operating conditions and the implications
of aerator performance on cost are discussed.  It is
concluded that diffusion methods require double the
power of mechanical surface aerators for large-scale
installations.  Capital and operating costs are not
given.
                         H-4

-------
McKeown, James J., "Studies on  In-Stream Aeration,"
Proceedings of the 23rd Industrial Waste Conference,
Purdue University, Lafayette, Indiana, 1968	
DESCRIPTORS
OBJECTIVE

The paper presents a discussion of field measurements
of dissolved oxygen and estimates of oxygen transfer
capabilities of dams and  short sections of turbulence
in streams due to rapid loss of elevation.  The use
of mechanical aeration for  the purpose of increasing
the DO  content at critical  oxygen sections of streams
is also evaluated.

RESULTS/COMMENTS

Previous work involving analysis of data collected
above and below numerous  weirs and cascades is
summarized.  Existing, validated models for calcu-
lating  deficit rates of dissolved oxygen as a
function of pollution  levels, height of fall, and
water temperature are  summarized.

Useful, new data are presented on dissolved oxygen
determinations from dam and spillway investigations.
Data on the transfer efficiency of mechanical, sur-
face aerators is developed  and presented.  DO pro-
files resulting from various location configurations
and numbers of aerators are presented.  Operational
scheduling patterns  (i.e. on-off periods), water
recycling patterns, and special horizontal flow or
circulation enhancers  are examined as methods of
optimizing DO profiles in shallow waters.

Although no models have been developed  in this paper,
the data presented are useful as input  for studies
to improve mechanical  aeration coefficients  for
inclusion of  in-stream aeration as pollution abate-
ment alternatives  in basin  planning  and stream model-
ing .
                          H-5

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Meyer, C.F., "Using Experimental Models to Guide
Data Gathering," Journal of the Hydraulics Division,
ASCE, 1970.

DESCRIPTORS
OBJECTIVE

The use of a series of analytical models is examined
as a possible minimal-cost approach to guiding data-
gathering programs while simultaneously developing
a plausible model to be used for predicting the con-
sequences of management decisions.

MODEL/METHOD

The technique employed is an empirical sensitivity
analysis of the parameters defining the mathematical
model; the example used is a groundwater basin model
with 144 nodes, 482 parameters defining the mathematical
record.  A number of ways of systematically varying the
model parameters are examined:

1.    Simple multiplication of each parameter set (e.g.,
      all storage coefficients)by a factor.

2.    Application of statistical perturbations to each
      parameter set using random number generation.

In either case, a small number of runs (not full Monte
Carlo procedure) of the entire model with perturbed
values proportional to the estimated measurement error
for each parameter set are executed; the results are
displayed to give time records or map displays of
the difference between the base case solution and the
perturbed solution (e.g., in terms of piezometric heada
for the groundwater model).  Data-gathering effort is
then allocated proportionally to the sensitivity in
model output observed for each parameter set.

RESULTS/COMMENT

It is concluded that straight multiplication of an
entire parameter set by a single factor introduce
skew into the results which produces an illogical
representation of basin groundwater.  Statistical
measures such as normal, lognormal, and triangular
distributions can eliminate or minimize skewed results.
                         H-6

-------
The extremes of Gaussian distributions can lead to
unlikely or impossible negative results in ground-
water studies.  The  lognormal distribution over-
comes the problem  of negative values, but extreme
values continue to pose difficulties.

Triangular and  log-triangular probability distri-
butions covering the range  of  estimated measurement
error are  suggested  as the  most suitable methods for
perturbing groundwater system parameters for sensi-
tivity  studies, the  latter  being  suitable where error
is  measured  in  percentages.

Time  saving  techniques utilizing  direct computer
print out of key  sensitivity summaries and displays
in  a  suitable format for  easy data comparison  and
analysis  are proposed.
                           H-7

-------
Stone, Ralph and C. Schmidt, "A Survey of Industrial
Waste Treatment Costs and Charges," Proceedings of
the 23rd Industrial Waste Conference,  Purdue Univ-
ersity, Lafayette, Indiana, 1968.

DESCRIPTORS
OBJECTIVE

The paper gives data on the types and extent of
sewerage/treatment charges imposed by United States
cities  (based on mailed questionnaire) plus data
on national industrial waste volumes and strengths.

RESULTS/COMMENTS

Through a questionnaire circulated among sewering
agencies it was found that about 33% of responding
cities provide separate waste charges while the
remaining two-thirds make no distinction between
residential, commercial and industrial sewerage
service.  Most of those providing separate rate
schedules  used volume or sewer size as the basis
for charges.  About 5% of the agencies billed the
industry on the basis of the amount of BOD and suspen-
ded solids in addition to basic volume charges.  The
sample results indicate that collection and treatment
costs generally decrease as served population increases;
the average cost per citizen in a community of under
100,000 inhabitants is approximately $20.00 per month,
and it falls to $14.00 per month in larger cities.

The sewerage charge ordinances of four cities were
applied to nine hypothetical firms with equal volume
and same BOD component.  It was found that charge
variations were as high as 100 fold.  The interesting
thing was the relationship between the degree of pollu-
tion and cost in the case of one city; for a waste
volume of 0.5 mgd containing an average BOD of 2000 mg/
Ibs. the sewer charge was $3,500.00 per month where as
with other cities the charge for same amount of BOD was
as little as $30.00 per month.  It follows that in many
cases heavy sewer users get a "free ride" with the ad-
ditional cost of treating their waste being absorbed
by the public and other industries through taxation.

The following types of sewer service charges were
found:

1.    Fixed, uniform charges per sewer connection.
2.    Charge per plumbing fixture.
3.    Fixed percentage of waste bill.
4.    Sliding scale of water consumption.
                         H-8

-------
 5.     Size of sewer connection.
 6.     Size of water meter.
 7.     Corporate revenue  taxes.
 8.     Volume of sewage.
 9.     1 through 8 with separate rate schedules
       by type of industry.
10.     Volume plus surcharge for BOD suspended solids,
       grease, or other special waste constituents.

 Analysis shows that the most equitable arrangement
 is generally that whereby a part of the revenue is
 obtained by charges based on BOD, suspended solids,
 and volume of waste discharge to the sewer and
 another portion by property taxes on all properties.
                           H-9

-------
Warner, D.L., "Deep Wells for Industrial Waste In-
jection in the United States: Summary of Data,"
Federal Water Pollution Control Administration,
Water Pollution Control Research Series Publication
No. WD-20-10, Cincinnati, Ohio, November, 1967.

DESCRIPTORS
OBJECTIVE

The paper is confined to a summary of the available
current information regarding the location, design,
and operating experience of existing industrial waste
injection deep wells; an important waste disposal
technique for concentrated, relatively untreatable
wastes.

RESULTS/COMMENT

Data on one hundred and ten industrial waste injection
wells  located in 16 states are summarized.  Information
on distribution of injection wells by geography and
type of industry plus rate of increase is developed.
Statistics such as distribution of well depths, type
of rock used for injection, rates of waste injection,
pressure at which waste is injected are also developed.
Cost data are not presented.

SIMILAR/RELATED REFERENCES

Manning, J.C., "Deep Well Injection of Industrial Wastes",
Hydro-Development, Inc., Bakersfield, California.  In:
Proceedings of the 23rd Industrial Waste Conference,
Purdue University, Lafayette, Indiana, 1968.
                         H-10

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                         SECTION I

          COMPUTER PROGRAMS FOR BASIN AND STREAM
  WATER QUALITY/HYDROLOGICAL MODELS - ABSTRACTED PROGRAMS
     Program Title                           Page
1.   A BRANCH-AND-BOUND ALGORITHM
     FOR MINIMIZING COSTS OF WASTE
     TREATMENT                                1-2
2.   DYNAMIC PROGRAM FOR OPTIMIZA-
     TION OF WATER QUANTITY AND
     QUALITY IN STREAM BASINS                 1-4
3.   LOW FLOW AUGMENTATION MODEL
     FOR MAINTAINING DISSOLVED OXYGEN         1-5
4.   RIVER BASIN SIMULATION PROGRAM           1-6


5.   WATERSHED HYDROLOGY  SIMULATION
     MODEL                                    I~8
                              1-1

-------
                COMPUTER PROGRAM

         A BRANCH-AND-BOUND ALGORITHM FOR
        MINIMIZING COSTS OF WASTE TREATMENT
DESCRIPTORS
PURPOSE OF COMPUTATION

A modified Geoffrion algorithm is used to solve the
integer programming formulation of the problem of
finding the minimum regional cost of wastewater treat-
ment to meet DO stream standards using zoned treatment
requirements.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
IBM 7094

TYPICAL RUNNING TIME
1.    A problem with 8 categories, 10 treatment levels,
      and only 4 quality constraints, ran in about 6
      minutes.

2.    A problem which was modeled with Delaware Estuary
      data, contained 7 categories, 13 treatment levels,
      and 15 constraints.  Running time was about 27
      minutes.

INPUT REQUIREMENTS

Reach dimensions, influence coefficients for each reach,
costs by treatment levels, discharger categories.

OUTPUTS

Outputs are tabular in format and include optimal levels
of treatment and cost by category  (or zone), minimum
total costs for basin, and the dual solution.

AVAILABILITY

The model and method are described in: Liebman, J.C.,
"A Branch-and-Bcund Algorithm for Minimizing the
Costs of Waste Treatment, Subject to Equity Constraints",
Proceedings of IBM Scientific Computing Symposium
on Water and Air Resource Management, October, 1967
                         1-2

-------
Documentation and source decks are available on  re-
quest from:

      Dr. J.C. Liebman
      John Hopkins University
      Baltimore, Maryland
                           1-3

-------
                COMPUTER PROGRAM

       DYNAMIC PROGRAM FOR OPTIMIZATION OF
     WATER QUANTITY AND QUALITY IN STREAM BASINS

DESCRIPTORS



PURPOSE OF COMPUTATION

Program will compute optimal costs of water quantity
and quality for multi-stage river basins involving
complex combinations of treatment costs and waste
return flows.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
IBM 360/65 adaptable to wide variety of computer
types.

TYPICAL RUNNING TIME
The IBM 360/65 can perform cost optimization cal-
culations for basin systep comprised of several
reaches with a waste outfall in each reach in approx-
imately 45 seconds.

INPUT REQUIREMENTS

Tabular inputs for physical and biological state
variables as well as costs.  Three dimensional
table look-up and interpolation routines are required.

OUTPUTS

Tables of individual stage returns, combined stage
returns, and optimal management policies with
minimum annual costs.

AVAILABILITY

Complete description of model is available in report
by L.W. Meier, Jr. and C.S. Shih, Application of	
Specialized Optimization Techniques in Water Quantity
and Quality Management with Respect to Planning for
the Trinity River Basin, Final Report, Water Resources
Institute, Texas, 1970.  (Computer program in research
code only, i.e., not developed for general use.  Plan
to develop and document complete program for field use
and general availability in near future).
                         1-4

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                 COMPUTER PROGRAM

           LOW FLOW AUGMENTATION MODEL
         FOR MAINTAINING DISSOLVED "OXYGEN
DESCRIPTORS
PURPOSE OF COMPUTATION

A model is presented  for use  in predicting the dissolved
oxygen distribution in  a river basin for discrete waste
sources.  When  flow augmentation is available the model
can be used to  compute  the additional flow required to
maintain dissolved oxygen at  a given level.

LANGUAGE
FORTRAN

MACHINE COMPATIBILITY
N/A

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Key input data  include  point  discharge loadings of BOD,
initial values  for DO,  deoxygenation rates as a function
of reach, relationship  between discharge, river velocity
and sources of  flow augmentation.

OUTPUTS

Outputs include dissolved oxygen profiles by reaches
in a river basin and  specification of amounts of flow
augmentation needed to  maintain specified DO levels.

AVAILABILITY

Details of the  mathematical model are described in
A Systems Analysis Method for Water Quality Management
by Flow Augmentation  by J.L.  Worley, Environmental
Protection Agency, Water Quality Office, Region X,
Portland, Oregon.
                          1-5

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                 COMPUTER PROGRAM

          RIVER BASIN SIMULATION PROGRAM
DESCRIPTORS
PURPOSE OF COMPUTATION

Provides Monte Carlo simulation of the monthly hydrology ,
flow routing and mixing of a river system with tributaries ,
reservoirs and waste discharges (up to 15 reaches, 10
confluence points, 10 discharges, 15 reservoirs, one de-
gradable pollutant and 4 conservative pollutants).  The
program can simulate the in-stream effects of time-varying
flows, discharges, withdrawals, pollutant loads and reservoir
release schedules as well as compute quantity and quality
deficiencies.

LANGUAGE
FORTRAN IV

MACHINE COMPATABILITY
IBM 360/65

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

a.    System geometry-locations and distances of confluence
      points, gaging stations, reaches, discharge points
      and reservoirs

b.    Fixed hydrological inputs-flow and runoff statistical
      parameters, fixed withdrawals, fixed flow and guality
      requirements, reservoir capacities, minimum pool
      storage, starting storage, reservoir losses, re-
      oxygenation/deoxygenation parameters, etc.

c.    Variable system design choices-reservoir operating
      policy rules, discharge pollutant loads, variable
      withdrawals, variable flow and quality requirements,

OUTPUTS

Outputs consist of hydrographs and stream quality records
for any of 50 gaging stations as well as deficiencies
in flow or quality when compared with pre-set requirements.
Additional outputs include reservoir storage/release
records.

                        1-6

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AVAILABILITY

Complete program description is available in a report
titled River Basin Simulation Program, W.C. Pisano
FWPCA, August,  1968, distributed on request through
the Environmental Protection Agency, Washington, D.C.
                          1-7

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                COMPUTER PROGRAM

       WATERSHED HYDROLOGY SIMULATION MODEL
DESCRIPTORS
PURPOSE OF COMPUTATION

Flood routing program for square-shaped watershed
elements chosen small enough so that hydrologic
properties are uniform over element.  Program com-
bines elements to form total watershed.  Events re-
lated to runoff included through flood routing
procedures to produce composite result for the entire
watershed.  Use is constrained to small watersheds.

LANGUAGE
FORTRAN

MACHINE COMPATIBILITY
Adaptable to wide variety of computer types.

TYPICAL RUNNING TIMES
Indicated in report referenced below.

INPUT REQUIREMENTS
Include basic hydrologic data, e.g. water
infiltration rates, rainfall rates, etc...
plus physical/topographic characteristics
for each watershed element.

OUTPUTS

Runoff hydrograph as function of spatial differ-
ences over the watershed.  Hydrograph printout
as watershed contours in process of development.

AVAILABILITY

Complete details of the computer program are in-
cluded in report by L.F. Huggins and E.F. Monk,
The Mathematical Simulation of the Hydrology of
Small Watersheds, Technical Report No. 1, Water
Resources Research Institutes, Purdue University,
Lafayette, Indiana.

(Note: Preceding source now out of print, but copies
available through Department of Interior, Office of
Water Resources Research, Washington, D.C.)
                           1-8

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                          SECTION J

          COMPUTER PROGRAMS FOR TREATMENT PROCESS AND
          PLANT  ANALYSIS/DESIGN - ABSTRACTED PROGRAMS


     Program Title                           Page

1.   A COMPUTER  ALGORITHM FOR SOLVING
     THE  POSYNOMIAL GEOMETRIC PROGRAM-
     MING PROBLEM                             j-2

2.   COMPLETE DOMESTIC WASTE TREATMENT
     SYSTEM DESIGN CCO71                      J-4

3.   COST ESTIMATING COMPUTER PROGRAM
     FOR  WASTEWATER TREATMENT PLANTS          J-5

4.   ENVIROTECH MUNICIPAL EQUIPMENT
     PROGRAM                                  J-6

5.   EXECUTIVE PROGRAM FOR PRELIMINARY
     DESIGN OF WASTEWATER TREATMENT
     SYSTEMS                                  J-7

6.   A GENERALIZED COMPUTER MODEL FOR
     STEADY-STATE PERFORMANCE OF THE
     ACTIVATED SLUDGE PROCESS  (CSSAS)         J~9

7.   MATHEMATICAL MODEL FOR COMPLETE
     SECONDARY TREATMENT SYSTEM              J-ll

 8.   MATHEMATICAL MODEL FOR TERTIARY
     TREATMENT BY LIME ADDITION              J-13

 9.   MATHEMATICAL MODEL FOR A TRICK-
     LING FILTER                             J~14

10.   A MATHEMATICAL MODEL FOR A WASTE
      STABILIZATION POND                      J~16

11.    TIME-DEPENDENT COMPUTER MODEL
     FOR THE ACTIVATED SLUDGE PROCESS        J-17
                               J-l

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                 COMPUTER PROGRAM          :

      A COMPUTER ALGORITHM  FOR SOLVING THE
        POSYNOMIAL GEOMETRIC PROGRAMMING
                    PROBLEM

DESCRIPTORS



PURPOSE OF COMPUTATION

Solves the posynomial geometric programming problem.
The program includes a main program which acts as an
executive controller.  Several subroutines partici-
pate in the mechanics of the geometric programming
solution.  Program includes an accuracy control feature
with automatic recycling of subroutines until the
optimum weights found meet the requirement of the
control.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
IBM 360/65

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Inputs include variables and constants associated
with the objective function and the constraints.
The matrix of exponents of the posynomial variables
is read along with cost coefficients, controls con-
cerning accuracy of solution, and starting values for
the primal problem variables.

OUTPUTS

Output includes printed solutions for both the primal
and the dual programs.

AVAILABILITY

The computer program is described briefly in "Geo-
metric Programming: New Optimization Techniques for
Water Resource Analysts" by W.L. Meier, R.W. Lawless,
and C.S. Beightler, Texas A&M University, College
Station, Texas, Proceedings of the Fourth American
                         J-2

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Water Resources Conference, AWRA, Urbana, Illinois,
1968.  (Computer program currently in research code
only and not  available  for general use) .
                            J-3

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                 COMPUTER PROGRAM

        COMPLETE DOMESTIC WASTE TREATMENT
                SYSTEM DESIGN CC071

DESCRIPTORS



PURPOSE OF COMPUTATION

This design and costing program uses Dorr-Oliver
design concepts and equipment sixing relationships
for three separate process systems:  ABC systems
for complete mixed activated sludge, PEP system for
phosphorus removal, and Farrar plus FS disposal for
sludge dewatering and incineration.

LANGUAGE
N/A

MACHINE COMPATIBILITY
N/A

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Key inputs include flow, specific pollutant con-
centrations of the influent stream and effluent
requirements.

OUTPUTS

The program sizes all equipment and structures to meet
given performance requirements.  It computes the vol-
ume of all side streams, the consumption of electrical
power and chemicals, and equipment cost estimates
which can be provided separately.

AVAILABILITY

The program is available only at Dorr-Oliver, Inc.
Computations using the program are made at no charge
to the customer by Dorr-Oliver.  Inquries should be
directed to Dorr-Oliver, Inc., 77 Havemyer Lane,
Stanford, Connecticut 06904, Environmental Equip-
ment and Systems Division, Attention:  Marketing
Department.
                         J-4

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                COMPUTER PROGRAM

       COST ESTIMATING COMPUTER PROGRAM FOR
            WASTEWATER TREATMENT PLANTS
DESCRIPTORS
PURPOSE OF COMPUTATION

The program estimates capital, amortization, operations
and. maintenance, and total treatment costs for stand-
ard wastewater treatment plants.  Cost calculations are
based on standard design parameters.  Rule of thumb
relationships are used to size equipment, structures
and internal streams.

LANGUAGE
FORTRAN

MACHINE COMPATIBILITY
IBM 1130/8K

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Inputs include design parameters, amortization factors,
construction cost index, and hourly wage rates.

OUTPUTS
Total and  component  cost breakouts, size and capacity
estimates, operating costs.

AVAILABILITY

Computer program documentation and source deck avail-
able  (no cost) through R.C. Eilers, Advanced Waste
Treatment  Research Laboratory, 4676 Columbia Parkway,
Cincinnati, Ohio, 45226.
                          J-5

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                COMPUTER PROGRAM

      ENVIROTECH MUNICIPAL EQUIPMENT PROGRAM
DESCRIPTORS
PURPOSE OF COMPUTATION

The program is designed to provide the consulting
engineer with a complete equipment analysis of a
sewage plant system comprised of'primary and second-
ary treatment processes to meet fixed performance
specifications.  The speed of the program permits
modification of input data for the development and
examination of alternative results.  -      :

LANGUAGE
N/A
                        I
MACHINE CAPABILITY
Suitable for terminal system; computer type/model
not indicated.

TYPICAL TUNNING TIME
Typical running time indicated as "minutes".

INPUT REQUIREMENTS

Program input requires at least influent flow,,
BOD load and removal required, but can use up
to 1000 variables related to engineering and
cost functions.

OUTPUTS

Output includes equipment sizing, capital costs,
operating costs and engineering component data
for the complete primary-secondary treatment system.

AVAILABILITY

The program is available as a terminal computer system
installed in customer's office for a monthly fee.
Inquiries should be directed to Mr. Robert Sherwood,
Municipal Equipment Division, Envirotech Corporation,
100 Valley Drive, Brisbane, California  94005.
                         J-6

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                 COMPUTER PROGRAM

        EXECUTIVE PROGRAM FOR PRELIMINARY
          DESIGN OF WASTEWATER TREATMENT"
                     ~SYSTEMS"
DESCRIPTORS
PURPOSE OF COMPUTATION

Computes quasi-steady-state performance and cost of
groups of conventional and advanced wastewater treat-
ment processes arranged in any configuration.  The
program^contains a main program and twelve process
subroutines.  Each subroutine computes the perform-
ance and cost of a single wastewater treatment process
based on empirical relationships.  Additional sub-
routines are developed and can be used to total costs
for the various processes in a variety of cost cate-
gorizations and to print all pertinent data relative
to each process in a specific format.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
IBM 1130/8K

INPUT REQUIREMENTS

Inputs include influent stream flows and specific
pollutant concentrations, effluent load requirements,
the tolerable error when recycle streams are invloved,
cost coefficients and process decision variables.

OUTPUTS

Output is printed in the following sequence:
a.    Description of system simulated.
b.    Volume, flow and concentrations of 15 contaminants
      in each stream number*
c     Names of all processes involved with pertinent
      data including capital costs for each process;
      operating cost, amortization cost, and total
      treatment cost.                            .
d     General cost items including capital cost  xndex,
      amortization factor,  cost of engineering, con-
                         J-7

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      tractor profit, contingencies and omissions, and
      land.
e.    Total costs including total capital cost, total a-
      mortization cost, total operating and maintenance
      cost, and total treatment cost for the system.

AVAILABILITY

Description of model contained in Executive Digital
Computer Program for Preliminary Design of Waste-
water Treatment Systems, No. WP-20-14, U.S. De-
partment of the Interior, Federal Water Quality Ad-
ministration, Advanced Waste Treatment Branch, Divi-
sion of Research, Cincinnati, Ohio, November 1970.

(Report and source deck available at no charge through
R.C. Eilers, Advanced Waste Treatment Research Lab-
oratory, 4676 Columbia Parkway, Cincinnati, Ohio
45226).
                         J-8

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                 COMPUTER PROGRAM

   A GENERALIZED COMPUTER MODEL FOR STEADY-STATE
PERFORMANCE OF THE ACTIVATED  SLUDGE PROCESS	(CSSAS)

 DESCRIPTORS
 PURPOSE OF COMPUTATION

 The CSSAS Program has been developed to aid in under-
 standing the relationships which govern the quasi-
 steady-state performance of the activated sludge
 process.  The model can be arranged to simulate con-
 ventional, modified, extended aeration, or contact
 stabilization.   It provides for simulation of all
 known^aspects of the process though several important
 questions relating to design and operation of the
 process remain  unresolved.  The model has been partly
 validated using data ranging from the short detention
 time, low mixed liquor suspended solids "modified
 process" to the extended aeration process.

 LANGUAGE
 FORTRAN

 MACHINE CAPABILITY
 IBM 1130/8K

 TYPICAL RUNNING TIME
 N/A

 INPUT REQUIREMENTS

 For both heterotroph and nitrosomona bacteria, growth
 equation parameters are required as well as total aerator
 volume, the number of equal volume sub-aerators, the
 compaction ratio for the final  settler, and a number of
 stream characteristics' such as  volume flow, concentration
 of particulate  and dissolved 5-day BOD, concentration
 of non-biodegradable volatile  suspended solids, etc.

 OUTPUTS

 A larae number  of output variables are available in-
 cluding volatile suspended  solids, total BOD out, waste
 stream flow,  active solids, concentrations of various
 solids etc.
                           J-9

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AVAILABILITY

Complete description of model contained in A Genera-
lized Computer Model for Steady State Performance
of the Relivated Sludge Process, R. Smith and R.C.
Eilers, U.S. Department of the Interios, Federal
Water Quality Administration, Advanced Waste Treat-
ment Branch, Division of Research, Cincinnati, Ohio,
October 1969.  Report and source deck available at
no charge through R.C. Eilers, Advanced Waste Treat-
ment Research Laboratory, 4676 Columbia Parkway,
Cincinnati, Ohio 45226.
                        J-10

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                COMPUTER PROGRAM

         MATHEMATICAL MODEL FOR COMPLETE
            SECONDARY TREATMENT SYSTEM—
DESCRIPTORS
PURPOSE OF COMPUTATION

A computational program  to handle the significant
preliminary design  cost  and performance relation-
ships for conventional municipal treatment systems
including primary settling, activated sludge, sludge
thickening, anaerobic digestion of primary and waste
activated sludge, sludge elutriation, vacuum filtra-
tion of sludge, sludge incineration, and sludge dry-
ing beds.  The program represents an attempt to pro-
vide a program capable of calculating the performance
and cost of treatment systems as a whole, based on
empirical relationships  which have been developed for
the processes individually.  The model computes per-
formance and cost as a function of the characteristics
of the feed streams as well as the operating and design
decisions associated with each process.  The program
is in a developmental state and remains to be fully
validated through precise data from full-scale plant
operations.

LANGUAGE
FORTRAN IV

MACHINE CAPABILITY
IBM 1130/8K

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Key inputs  include  a quantitative description of the
influent raw  sewage stream  in terms of volume, tempera-
ture  specific pollutant loads, etc.  Decision para-  _
meters which  specify the mode of operation or the design
criteria for  each individual process are also required.

OUTPUTS

Include construction costs; operating and maintenance
cost, cost  of  consumable items such as chemicals and
power, and  total  costs  for  each process and  for the
entire system.
                         J-ll

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AVAILABILITY

The details of the mathematical model are included
in Preliminary Design and Simulation of Conventional
Wastewater Renovation Systems Using the Digital	
Computer, Report No. WP-20-9, U.S Department of the
Interior, Federal Water Quality Administration,
Advanced Waste Treatment Branch, Division of Research,
Cincinnati, Ohio, March 1969.  Technical Report and
source deck available at no charge through R.C. Eilers,
Advanced Waste Treatment Research Laboratory, 4676
Columbia Parkway, Cincinnati, Ohio 45226.)
                        J-12

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                COMPUTER PROGRAM

         MATHEMATICAL MODEL FOR TERTIARY
            TREATMENT BY LIME ADDITION—
DESCRIPTORS
PURPOSE OF COMPUTATION

A cost-estimating routine for the lime clarifica-
tion process used downstream from an activated
sludge secondary treatment process.  The program
computes the size of process equipment, the amount
of chemicals,  electrical power, operating and maint-
enance labor,  capital and installation costs, and
operating and  maintenance costs.

LANGUAGE
FORTRAN

MACHINE CAPABILITY
IBM  1130/8K

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Quality variables and flows  for the secondary treat-
ment effluent; required quality of the tertiary treat-
ment effluent.

OUTPUTS

Cost breakouts for  tertiary  treatment equipment,
supplies power and  operating costs.

AVAILABILITY

Details of  the mathematical  model  are contained in
Robert R. Taft Water Research  Center Report  No.
TWRC-14;  source deck available at  no cost  through
R C  Eilers, Advanced Waste  Treatment Research Lab-
oratory,  4676  Columbia  Parkway, Cincinnati,  Ohxo
45226.
                         J-13

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                 COMPUTER PROGRAM

        MATHEMATICAL MODEL FOR A TRICKLING
                      FILTER

DESCRIPTORS



PURPOSE OF COMPUTATION

A mathematical model of the trickling filter-final
settling process based on empirical relationships
is used to compute the relationship of the various
physical properties of the trickling filter and the
final settler necessary for least cost preliminary
design based on desired BOD removals.  The model also
includes capital, operating, and maintenance costs.

LANGUAGE
FORTRAN

MACHINE COMPATIBILITY
IBM 360/65

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Inputs include a large number of parameters related
to waste characteristics, physical properties of the
trickling filter, effluent requirements, and a variety
of cost factors.

OUTPUTS

Outputs include component sizing estimates, character-
istics of internal streams, BOD removals, and total
cost plus cost breakdowns.

AVAILABILITY

A description of the model is contained in A Mathe-
matical Model for a Trickling Filter, by J.F. Roesler
and R. Smith, U.S. Department of the Interior, Federal
Water Quality Office, Advanced Waste Treatment Research
Laboratory, Robert A. Taft Water Research Center, Cin-
cinnati, Ohio, February 1969.
                        J-14

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(Report and source deck  available at no charge
through Mr. Joesph Roesler, Advance Waste Treat-
ment Research Laboratory,  4676 Columbia Parkway, Cin-
cinnati, Ohio 45226.)
                           J-15

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                 COMPUTER PROGRAM

          A MATHEMATICAL MODEL FOR A WASTE
                STABILIZATION POND

DESCRIPTORS



PURPOSE OF COMPUTATION

The model provides estimates of preliminary design
and cost data for aerobic waste stabilization ponds
to meet specified capacity and removal efficiency;
the model is based on empirically fitted process
relationships.

LANGUAGE
FORTRAN

MACHINE CAPABILITY
IBM 1130/8K

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Major input parameters are temperature, dissolved
oxygen levels, sunlight radiation, gains and losses
due to rain and evaporation, desired BOD removal
and influent flows with specific pollutant loads.

OUTPUTS

In addition to sizing estimates for components, the
program also computes capital, operating, and
maintenance costs.

AVAILABILITY

The details of the program are included in a report
which is available at no charge through Mr. Joseph
Roesler, Advanced Waste Treatment Research Laboratory,
4676 Columbia Parkway, Cincinnati, Ohio 45226.
                         J-16

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                 COMPUTER PROGRAM
          TIME-DEPENDENT COMPUTER MODEL
        FOR THE ACTIVATED SLUDGE PROCESS
DESCRIPTORS
COMPUTES  WHAT
       This  digital computer program consists  of  a numeri
cal  integration with respect to time of  the  rate of  syn-
thesis and  mass balance equations for each of the aeration
sub-volumes and for the process as a whole.   The kinetic
behavior  of three classes of microorganisms  is considerea ;
these classes are: heterotrophs which convert biodegradable
carbon to new cells, Nitrosomanas which converts ammonia
to new cells and nitrite, and Nitrobacter which converts
nitrite to new cells and nitrate. , This model has ^Jn
used to investigate a number of scaemes for  automatic con
trol of the activated sludge process.

 LANGUAGE
       Fortran  IV.

 COMPATIBLE WITH  WHAT MACHINES?
       IBM  1130/8K

 TYPICAL  RUNNING  TIME        sirmlation with only the  time
                                       to the  15th day


                                           '
  time to run this simulation.

  SPECIAL INPUT REQUIREMENTS          red for input.   A
        Large masses of da ta are r e         dependent data
  step method was used to simulate th     ^ ^ togel
  that was ^thered at the "y e^    £   the concentration of
  The volume flow at the first st ati      ^ ^^
  substrate at the first stat ion ^g/        as a step input
                            «Y.a* by -ans of matrix input.
  SPECIAL OUTPUTS        Drovisions  for printing process

  variables SE°SS  ti^polnt  and  electromechanical

  plotting.

  AVAILABILITY                    d  Richard G.  Eilers
         Report  by  Robert S mitn            dent  Performance
  entitled,  "Simulation o f  ^^ .^^P  ^ ^      [ computer'

                   ou     - ato  cost ^-^1^1 rie,

                                      Ohio   45226.

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                          SECTION K

             COMPUTER PROGRAMS FOR THERMAL POLLUTION
                 MODELING  -  ABSTRACTED PROGRAMS
     Program Title                           Paqe
1.   MATHEMATICAL MODELS  FOR  THE
     PREDICTION OF  TEMPERATURE
     DISTRIBUTIONS  -  PROGRAM  UTD               K~2

2.   MATHEMATICAL MODELS  FOR  THE
     PREDICTION OF  TEMPERATURE
     DISTRIBUTIONS  -  PROGRAM  JTD               K-3

3.   MATHEMATICAL MODELS  FOR  THE
     PREDICTION OF  TEMPERATURE
     DISBRITUTIONS  -  PROGRAM  SBJ2              K-4

4.   MATHEMATICAL MODELS  FOR  THE
     PREDICTION OF  TEMPERATURE  DIS-
     TRIBUTIONS - PROGRAM RBJ                 K-5

5.   A MATHEMATICAL MODEL FOR PRE-
     DICTING  TEMPERATURES TN  RIVERS
     AND  RIVER-RUN  RESERVOIRS                 K-6

6.   THEORETICAL CALCULATIONS OF
     HEATED DISCHARGE  BEHAVIOR               K-8
                              K-l

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                 COMPUTER PROGRAM

    MATHEMATICAL MODELS FOR THE PREDICTION OF
    TEMPERATURE DISTRIBUTIONS - PROGRAM UTD

DESCRIPTORS
PURPOSE OF COMPUTATION

Solves for the distribution of excess temperature
due to the effects of ambient turbulence, current,
and surface heat exchange.  Specifically, the
program treats the case where the discharge, the
ambient uniform current, and the surface heat
exchange coefficient are time varying.  The Crank-
Nicolson method was employed in solving this pro-
blem numerically.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
N/A

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Program control number, time steps, sizes and time
mesh schemes, characteristic velocity (u), at specified
time points, kinetic surface heat exchange coefficient
(Ke) and source strength  (Fco) values, dimensionless
dissipation parameter, source thickness, characteristic
velocity, four y coordinates and two coefficients for
defining vertical diffusion coefficient profiles, values
of u, Ke, and FCO at specified time; spacing in x for
each printout variable.

OUTPUTS

Two decay coefficients, time profiles for major input
and output variables, zero-order moment of concentration,
plume width characteristic, maximum value of concentra-
tion.

AVAILABILITY

Report and program are included in Koh, R.C.U., and Fan,
L., Mathematical models for the prediction of tempera-
ture distributions resulting from the discharge of heated
water into large bodies of water.  Environmental Protect-
ion Agency, Water Quality Office, Water Pollution Control
Research Series 16130DW01/70, October, 1970.
                         K-2

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                 COMPUTER PROGRAM
DESCRIPTORS


PURPOSE  OP COMPUTATION

Solves for the distribution of excess  temperature
due  to the effects of ambient turbulence, current,
and  surface heat exchange.   Specifically, the program
treates  the case of a steady release into a steady
undirectional shear current (current varies with depth
but  not  with time) .  This program  is based on Crank-
Nicolson method.

LANGUAGE
FORTRAN  IV

MACHINE  COMPATIBILITY
N/A

TYPICAL  RUNNING TIME
N/A

INPUT REQUIREMENTS

Program  control number, mesh and step  sizes, dimen-
sionless dissipation parameter, source level, source
thickness,  characteristic velocity, two y coordinates
defining velocity in the  x  direction profile, four
coordinates and two coefficients for defining vertical
diffusion coefficient profiles, kinematic heat exchange
coefficient,  decay  coefficient.

OUTPUTS

Space profiles  of major input  and output variables,
zero-order  moment of concentration, plume width
characteristic,  and maximum value of concentration.

AVAILABILITY

Report and  program  are included at: Koh, R.C.Y., and
Fan, L.,  Mathematical models for the prediction of
temperature distributions~resulting from the discharge
of heated water into large  bodies of water.Environ-
mental Protection Agency, Water Quality Office, Water
Pollution Control Research  Series 16130DW010/70, Oct., 1970
                         K-3

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                COMPUTER PROGRAM

        MATHEMATICAL MODELS FOR THE PREDICTION
        OF TEMPERATURE DISTRIBUTIONS - PROGRAM SBJ2
DESCRIPTORS
PURPOSE OF COMPUTATION

Solves for the dispersion of heat resulting from the
horizontal discharge of a two-dimensional warm jet
at the surface into a quiescent, cooler ambient.
The effects of source momentum, source buoyancy,
entrainment, surface heat exchange, and interfacial
shear are all included in the computation.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
N/A

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Entrainment coefficient, dimensionless surface heat
exchange coefficient, densimetric Froude number,
inverse of Reynolds number, integration limits, two
control variables for step size.

OUTPUTS

Dimensionless distance, dimensionless density
deficiency, dimensionless thickness, local densimetric
Froude number, layer thickness after jump, Froude
number after jump.

AVAILABILITY

Report and program are included at: Koh, R.C.Y., and
Fan, L., Mathematical models for the prediction of
temperature distributions resulting from the discharge
of heated water into large bodies of water.  Environ-
mental Protection Agency, Water Quality Office, Water
Pollution Control Research Series 16130DWQ10/70, Oct.,  1970,
                         K-4

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                COMPUTER PROGRAM

        MATHEMATICAL MODELS FOR THK
       OF TEMPERATURE DISTRIBUTIONS -"pROGRAM^RBJ

DESCRIPTORS



PURPOSE OF COMPUTATION

Solves for the  distribution of excess temperature
resulting from  the  subsurface discharge of warm
cooling water from  power plants into an ambient
fluid which may be  stratified in arbitrary manner.
The numerical integration used for the solution
of this problem utilizes a fourth order Runge-
Kutta scheme.

LANGUAGE
FORTRAN IV

MACHINE COMPATIBILITY
N/A

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Jet velocity, jet diameter, jet temperature, jet
density, jet discharge  angle, jet discharae depth,
jet spacing, entrainment coefficient for round jet or
for slot jet, density and temperature depth profiles
in the ambient  in tabular form,


OUTPUTS

Space profiles  of jet width, dilution, jet temperature,
jet density, ambient density, ambient temperature, and
temperature excess.

AVAILABILITY

Report and program  are  included at: Koh, R.C.Y., and
Fan, L., Mathematical models for the prediciton of
temperature distributions resulting from the discharge
O-F hpat-tgd water into large bodies of water.  Environ-
mental Protection Agency; Water Quality gtfice. Water
Pollution Control Research Series 16130DW010/70,
October, 1970.
                          K-5

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                 COMPUTER PROGRAM

 A MATHEMATICAL MODEL FOR PREDICTING TEMPERATURES
        IN RIVERS AND RIVER-RUN RESERVOIRS

DESCRIPTORS



PURPOSE OF COMPUTATION

A steady-state, one-dimensional model is solved
primarily for use in predicting temperatures in rivers
which are regulated by dams with run-of-the-river
 (or small usable storage capacity) reservoirs.  The
model may also be used in systems having reaches which
are free-flowing.  The method considers finite volumes
of water, or water parcels, which are released from
an upstream starting point at specified intervals of
time.  Individual parcels are followed downstream
through open river reaches and reservoirs, and a history
of temperature changes is computed.  The program includes
one main program and nine subroutines

LANGUAGE
The model is coded in FORTRAN H.

MACHINE COMPATIBILITY
N/A

TYPICAL RUNNING TIME
N/A

INPUT REQUIREMENTS

Key input data includes river cross-sectional characteristics,
meteorological/runoff data, water surface elevation data,
evaporation and sensible heat data.

OUTPUTS

Output is given by parcel number and reach location.
Results are in terms of changes in parcel temperature
due to weather, flow regulation, and advected sources.

AVAILABILITY

The mathematical model is described in detail in A
Mathematical Model for Predicting Temperature in Rivers
and River Run Reservoirs by John R. Yearsley, Working
                        K-6

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Paper No. 65, United States Department of the Interior,
Federal Water Pollution Control Administration, North-
west Region, Protland, Oregon, March 1969.

 ( The program deck  can be  obtained  from the EPA  Northwest
Regional Office, Portland, Oregon)
                          K-7

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               COMPUTER PROGRAM

           THEORETICAL CALCULATIONS OF
            HEATED DISCHARGE BEHAVIOR

DESCRIPTORS
PURPOSE OF COMPUTATION

The program solves an analytic model predicting
the temperature distributions in the near field
of an ambient body of water which result from
discharges of heated water.  The discharge is as-
sumed horizontal from a rectangular open channel
at the surface of a large receiving body of water
which may have a bottom slope or crop flow at _
right angles to the discharge.  The theoretical
model development  (which has been validated by
a series of laboratory experiments)assumes a three
dimensional turbulent jet discharge with unsheared
initial core and a turbulent region in which velocity
and temperature distributions are related to center-
line values by similarity functions.

The computer program consists of a main program and
subroutines.  The main program sets up the initial
conditions for each calculation and calls the appro-
priate subroutines.  Computation is in terms of
velocity and temperature fields comprising the
near field of the heated jet for a series of time
steps.

LANGUAGE
FORTRAN IV, G level, Mod 3.

MACHINE COMPATIBILITY
IBM 360/65

TYPICAL RUNNING TIMES
N/A

INPUT REQUIREMENTS

Inputs include an  indicator  for number of calculations
and sets of the following parameters  for each calcula-
tions: initial densimetric   Froude number, bottom
slope, channel aspect  ratios,  surface heat  loss coef-
 ficient   initial  angle of the discharge, flow,  tempera-
ture and dimensions of the discharge  channel and re-
                          K-8

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ceiving stream,  initial  values  for  jet dimensions,
maximum allowable  numerical truncation error  for
each dependent variable  at each time step,  and
spreading  rate of  the turbulent regions of  a
nonbuoyant jet.

OUTPUTS

Outputs  are printed in terms of sets of independent
variables  and nondimensional parameters relative  to
velocities, temperatures, and" jet boundary  dimensions,
let core region dimensions, the spread rate of the
jet and  the location of the jet in terms of a fixed
coordinate system.  Jet dilution and heat flow are
also computed and printed.

AVAILABILITY

Complete details of the mathematical model and a
 summary of the computer program are included in
An Analytical and Experimental Investigation of
 Surface Discharges of Heated Water, Department of
 Civil Engineering, Massachusetts Institute of Tech-
 nology ,Cambridge , Massachusetts, February,  1971
 [For further  information  concerning availability
 of source  deck contact  author  K.D.  Stolsenbach or
 D.R.F. Harleman,  Ralph  M.  Parsons Laboratory for
 Water Resources and  Hydrodynamics,  Massachusetts
 Institute  of  Technology,  Cambridge, Mass., 02139].
                                4U8 90Vf RNMENT fRINTINQ OMICI: 1972 i84-482/6 1-3

                           K-9

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