Formulation and Use of 

Practical Models for RiverQuality Assessment 

By W. G. Hines, D. A. Rickert, S. W. McKenzie, and J. P. Bennett 

RIVER-QUALITY ASSESSMENT OF THE WILLAMETTE RIVER BASIN, OREGON 

G E 0 L 0 G I CAL SURVEY CIRCULAR 715-B 

1975 
United States Department of the Interior 

Geological Survey 

V. E. McKelvey, Director 

First printing 1975 

Second printing 1980 

Library of Congress Cataloging in Publication D<~ta 

Hines, Walter G. 

Formulation and use of practical model5 for river-quality assessment. fRiver-quality assessment 

of the Willamette River Basin, Oregon) 

(Geological Survey Circular 715 -B) 

Bibliography: p. 812-B 13. 

l. Water quality~Mathematical models. 2. Water quality- Willamette River watershed--Mathematical models. I. Hines. Walter G. II. Series. Ill. Series: United States. Geological Survey. 

Circular 715-B. 

QE75.C5 No. 715-B [TD370] 628.1'61 75-28191 

Free on application to the U.S. Geological Survey, National Center, Reston, Va. 22092 
FOREWORD 

The American public has identified the enhancement and protection of river 

quality as an important national goal, and recent laws have given this commitment considerable force. As a consequence, a considerable investment has been 

made in the past few years to improve the quality of theN ation's rivers. Further 

improvements will require substantial expenditures and the consumption of 

large amounts of energy. For these reasons, it is important that alternative 

plans for river-quality management be scientifically assessed in terms of their 

relative ability to produce environmental benefits. To aid this endeavor, this 

circular series presents a case history of an intensive river-quality assessment 

in the Willamette River basin, Oregon. 

The series examines approaches to and results of critical aspects of riverquality assessment. The first several circulars describe approaches for providing 

technically sound, timely information for river-basin planning and management. Specific topics include practical approaches to mathematical modeling, 

analysis of river hydrology, analysis of earth resources-river quality relations, 

and development of data-collection programs for assessing specific problems. 

The later circulars describe the application of approaches to existing or potential 

river-quality problems in the Willamette River basin. Specific topics include 

maintenance of high-level dissolved oxygen in the river, effects of reservoir 

release patterns on downstream river quality, algal growth potential, distribution of toxic metals, and the significance of erosion potential to proposed future 

land and water uses. 

Each circular is the product of a study devoted to developing resource information for general use. The circulars are written to be informative and useful to 

informed laymen, resource planners, and resource scientists. This design stems 

from the recognition that the ultimate success of river-quality assessment 

depends on the clarity and utility of approaches and results as wen as their basic 

scientific validity. 

Individual circulars will be published in an alphabetical sequence in the 

Geological Survey Circular 715 series entitled ~tRiver-Quality Assessment of 

the Willamette River Basin, Oregon.'' 

J. S. Cragwall, Jr. 

Chief Hydrologist 

III 
Cover: Willometfe River as it winds through Portland, Oregon. Photograph taken by 

Hugh Ackroyd. 
CONTENTS 

Page 

Foreword __ _ ____ _ _ ___ _ _ ___ _ _ _ __ __ _______ _ __ _ __ _____ _ __ __ __ ___ _ ______ _ __ _ __ __ __ _ ___ _ _ III 

Abstract____________________________________________________________________________ Bl 

Introduction________________________________________________________________________ 1 

Important considerations in applied modeling ----------------------------------------- 2 

Modelability of variable or process ---------------------------------------------- 2 

Model configuration ______________________________________________ - ------------- 4 

Recognition of critical periods ______________________________________ ---- ______ ---- 5 

Calibration and verification requirements ----------------------------------------- 6 

Model data base ---------------------------------------------------------------- 7 

Willamette River data-collection program -------------------------------------- 8 

Communication and application of model outputs__________________________________ 10 

Summary --------------------------------------------------------------------------- 11 

References _________________________________________________________ -----~____________ 12 

ILLUSTRATIONS 

Page 

FIGURE 1. Diagram showing relative difficulty of applied modeling __________________________________________________ B2 

2. Willamette River, Oreg., map showing distinctive hydrologic reaches and elevation profile__________________ 9 

3. Hydrograph ofWillamette River discharge at Salem, Oreg., 1973 water year ------------------------------ 10 

4. Graph showing relation between DO and summer runoff for Willamette River, Oreg. (1950-51), at river mile 6 11 

5. Graph showing relation between DO and BOD waste loading for the Willamette River, Oreg. ( 1950-51 ), below 

river mile 50 __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ __ _ _ _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ _ __ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ ___ _ _ _ _ _ _ _ 12 

TABLES 

Page 

TABLE 1. Common deficiencies of applied river-quality models and suggestions for improvement -------------------- B3 

2. Comparison of applied river-quality models______________________________________________________________ 5 

3. Selected physical characteristics of the main stem Willamette River, Oreg. -------------------------------- 8 

CONVERSION FACTORS 

By To Obtazn 

Feet (ft l _____________________________ 0.3048 _____________ Metres (ml 

Miles (mi) ___________________________ 1.609 ______________ Kilometres (km l 

Pounds (lb l ____ ______ _ _ ________ _____ __ .4536 _____________ Kilograms (kg) 

Cubic feet per second (ft3/sl ___________ .02832 _____________ Cubic metres per second (m3/s) 

v 

Formulation And Use Of Practical Models 

For River-Quality Assessment 

By W. G. Hines, D. A. Rickert, S. W. McKenzie, and J. P. Bennett 

ABSTRACT 

Complexities inherent in the study of large rivers and the 

need for quantitative description of river-quality have generated increasing interest in mathematical modeling. In concept, 

mathematical models have great potential as practical tools for 

predicting the impact of alternative planning proposals on 

river quality. However, many planners and decisionmakers 

have failed to accept models for river-quality assessment, and 

many actually view models with considerable mistrust. This 

situation can be partly traced to six major deficiencies common 

to applied modeling efforts: ( 1) application of a model to a 

variable or process that is too complex for formulation of a 

practical, applied model; (2) application of a sophisticated, 

general-case model without adequate understanding of the 

particular river in question; (3) failure to recognize the nnportance of basin hydrology in defining the critical planning and 

management decision periods for model simulation; (4} misapplication of model calibration and verification procedures; (5) 

use of a poor data base for interpretation, calibration, and 

venfication; and (6) failure to format results for ease of user 

understanding. Overall, these deficiencies have caused an irrational progression of models from the conceptual to the applied 

states. With careful thought and interdisciplinary teamwork, 

these deficiencies can be corrected and conceptual models 

transformed into practical, useful tools for river-quality 

assessment. 

INTRODUCTION 

Environmental awareness and new laws such as 

Public Law 92-500 have established improved 

river quality as a major goal of comprehensive 

river-basin planning. River quality can be defined 

as the physical, chemical, and biological character 

of a river with regard to its suitability for a specified purpose. In this context, river quality concerns not only the observed quality of water in a 

river, but also involves the analysis of environmental factors on land, water, and in air that are 

responsibile for the observed quality. 

To achieve improved river quality with a 

minimum of environmental, social, and ec·_ ~wmic 

cost, it is imperative that basin-planning decisions 

and the need for river-quality management 

Bl 

facilities be based on scientific assessment rather 

than on arbitrary edicts and assumptions. Thus, 

the objective of river-quality assessment is to 

evaluate, before the fact, the beneficial or adverse 

environmental impacts of planning alternatives 

on the quality of the river. Once the environmental 

impacts have been examined, economic, social, 

and energy costs can be weighed and compared for 

each planning alternative. 

The complexities inherent in the scientific study 

of large rivers, coupled with the need for quantitative description of river-quality behavior, have 

created great interest in mathematical models (referred to hereafter as river-quality models) as tools 

for simulating the response of river-quality variables to alternative basin-planning proposals. The 

study of dissolved oxygen-biochemical oxygen demand <DO-BOD) relationships by Streeter and 

Phelps (1925) is generally considered to be the 

pioneering effort at applied river-quality modeling. Although DO continues to be the subject of a 

majority of river-quality models, other variables 

and processes are receiving increasing attention. 

The subjects range in contplexity from relatively 

simple variables such as temperature to highly 

complex long-term processes such as eutrophication (fig. 1). 

In concept, river-quality models provide a great 

potential for problem-solving to resource planners 

and managers, pollution-control officers, and government decisionmakers. In general, however, 

these people have not only failed to accept riverquality models as a practical tool, but often view 

mathematical modeling with considerable mistrust. The authors have concluded that this failure 

to accept and trust models stems from the fact that 

many river-quality models have not been formulated on the basis of sound data nor effectively 

applied to planning and management situations. 
EROSION 

EUTROPHICATION 

NUTRIENT AND PESTICIDE TRANSPORT 

INDICATOR BACTERIA SEDIMENT TRANSPORT 

DO TEMPERATURE DISSOLVED SOLIDS 

FIGURE I.-Relative difficulty of applied modeling. 

Similar conclusions have been cited by several 

other investigators, including Mar (1971), Lombardo (1973), Weber, Kisiel, and Duckstein (1973), 

and Velz (1970). 

The objective of this circular is to describe considerations vital to the formulation and use of 

practical river-quality models intended for application to planning problems. The focus is on current deficiencies in modeling rationale and suggestions for improvement. The discussion is not 

meant to convey an indictment of models or modelers, nor is it intended solely as a critique of currently prevalent modeling approaches. Rather, the 

primary intent is to provide a basis for examining 

potential shortcomings in proposed river-quality 

models and to propose ideas and hypotheses useful 

for improving these models. 

IMPORTANT CONSIDERATIONS 

IN APPLIED MODELING 

To be an effective assessment and planning tool, 

a river-quality model must proceed from a conceptual state to an applied state. In the conceptual 

state, mathematical configuration, mathematical 

solution techniques, and computer adaption are of 

primary concern. In the applied state, a basic understanding of the particular river system is 

needed to formulate the model and quantify its 

parameters. 

(A model parameter is an element of a 

mathematical model used to define a reaction rate, 

proportionality constant, or other processdescribing characteristic. For example, in the 

basic DO reaeration equation of Streeter and 

Phelps ( 1925) 

dD 

- =K1L -K2D 

d t ' 

where 

D = the DO deficit with respect to the saturation value, 

L = the stream BOD concentration, and 

K 1 andK2 are parameters defining the rate of 

biochemical oxidation (or deoxygenation) and the 

rate of stream reaeration, respectively.) 

Irrational progression from the conceptual to 

the applied state is a major cause for the current 

poor utility of many applied river-quality models. 

Table 1 summarizes major deficiencies that are 

prevalent in applied river-quality models, and 

presents suggestions for improvement. Each deficiency and suggestion is amplified in the discussion that follows. Where pertinent, examples are 

presented from a river-quality study of the Willamette River, Oreg. 

MODELABILITY OF VARIABLE OR PROCESS 

Mathematical equations have long been utilized 

for describing, at least in a conceptual sense, the 

behavior of certain river-quality variables and 

processes. In fact, most of the phenomena shown in 

figure 1 have been the subject of conceptual models. However, such models can be translated into 

applied river-quality models only when complemented by reasonable assumptions and quantified model parameters. These assumptions and 

model parameters are the driving force of all 

applied models because they describe the rates and 

relative importance of the factors that govern the 

behavior of river-quality phenomena. The quality 

of assumptions and model parameter values is 

based almost entirely on the level of understanding and empirical evidence concerning the variable, process, and river system in question. Measurement or determination of model parameters 

and assumptions increases in difficulty for each 

higher level in figure 1 and is a major reason that 

models become less quantitative at each higher 

level. 

At present, many complex processes such as 

those appearing in the mid and upper levels of the 

triangle in figure 1 are difficult, if not impossible, 

to model in a practical, applied sense. This stems 

from the fact that appropriate assumptions and 

accurate model parameters are difficult to develop 

because of the poor state ofknowledge about many 

B2 
river-quality processes and the effects of various 

environmental factors on process rates. 

In the absence of reliable data and sound understanding of river phenomena, conceptual models 

have been used to make predictions of impacts 

related to planning and management alternatives. 

There can be little doubt that conceptual models 

are valuable for this and many other purposes, 

although their utility and validity compared with 

less sophisticated approaches have not been fully 

tested. 

In lieu of modeling, particularly for the more 

complex river-quality variables and processes, 

semiquantitative descriptive studies may prove to 

be more useful. An example of such a case can be 

described for the Willamette River, Oreg. 

In the Willamette River, a future potential for 

excessive algal growth exists because total nitrogen and phosphorus loads discharged to the river 

during summer low-flow conditions are increasing 

while BOD (carbon) loads have been dramatically 

reduced by new secondary waste-treatment plants 

(Gleeson, 1972). Jaworski, Lear, and Villa (1971) 

documented a severe algal-growth problem in the 

upper Potomac estuary under similar conditions. 

Concern about future algal growth in the Willamette led to a scrutiny of methods that could give 

predictive insight into the potential problem. 

Originally, a model to simulate algal growth was 

considered. However, a review of data indicated 

that only limited information was available for the 

Willamette on species and population of algae, the 

concentration of nutrients in the river and in 

waste-water discharges, and river DO, turbidity, 

TABLE 1.-Common deficiencies of applied river-quality models and suggestions for improvement 

[For discussion see text that follows) 

Deficiencies 

Application to a variable or process that is too complex for 

formulation of a practical applied model. 

Application of a sophisticated, general-case model without 

adequate understanding of the particular river in question. 

Failure to recognize the importance of basin hydrology in 

defining the critical planning and management decision 

periods for simulation by the model. 

Misapplication of model calibration and verification procedures. 

Use of a poor data base for interpretation, model calibration, 

and model verification. 

Failure to format results for easy user understanding. 

B3 

Suggestions for improvement 

Model only those variables and processes for which major 

parameters and assumptions can be qualified or verified 

through field and laboratory study. 

Define model applications, limitations, biases, and predictive accuracy commensurate with the level of understanding surrounding the variable or process. 

Use semiquantitative descriptive studies when knowledge 

is inadequate to formulate a practical, applied model. 

Conduct premodeling studies to develop a better understanding of river hydrology and important river-quality 

processes and tailor the model to reflect these determined 

characteristics. 

Consult with independent mathematicians and computer 

scientists concerning model configuration, solution 

techniques, and other technical model questions prior to 

selection or use of any particular model. 

Conduct a detailed assessment of natural and man- influenced basin hydrology to determine the critical re- curring conditions with respect to river quality. 

Establish recurrence probabilities for these conditions. 

Base production runs of the model (that is, predictions) 

wihthin the framework of these recurrence probabilities. 

Use separate, independent sets of data for calibration and 

verification. 

Minimize reliance on mathematical "curve-fitting" 

techniques by independently establishing reasonable 

ranges for model parameters and assumptions through 

field and laboratory investigation. 

Collect a statistically reliable set of data specifically suited 

for analysis ofthe river-quality variable or process being 

modeled. 

Concentrate data-collection and analysis effort within 

periods when critical hydrologic and river-quality conditions occur. 

Consult continually with intended model users in order to 

update needs and instill familiarity with the model and 

its capabilities. 

Write user reports and products in nontechnical language. 

Include discussion ofmodellimitations and applications. 

Display results of model production runs in graphical form 

whenever possible. 
and light penetration. Thus it was apparent that a 

reliable algal-growth model would be most 

difficult to formulate and test within the 2%-year 

times pan of the study. 

Instead of a model, a descriptive study was designed to assess the potential for algal problems. 

The study is composed of several elements: 

1. Compilation and analysis of historical data 

from the Willamette (and other rivers) to 

relate present conditions in the river to 

past conditions, and to anticipate problems 

observed under similar conditions in other 

rivers. 

2. A network of stations that are sampled frequently during summer low-flow, hightemperature conditions to determine 

species and populations of algae, river and 

algal-cell nutrient concentrations, DO concentration (instantaneous and diel), and 

physical conditions such as temperature 

and light penetration. The stations are also 

sampled periodically during other periods 

of the yea:r. 

3. Intensive studies involving algal primary 

productivity tests (light-and-dark-bottle 

BOD's) and enrichment bioassays. 

Results of the study should allow better understanding of the algal system of the W illamette 

River and serve as a baseline from which trends 

can be established and predictions made using 

subsequent data sets for comparison. In contrast to 

a model, the study will not hide the fact that with 

current knowledge quantitative predictions are 

questionable at best. 

The credibility of models can be improved 

through recognition of the fact that many riverquality phenomena are presently modelable only 

in a conceptual sense. Attempts to "sell" conceptual models as suitable for direct application to 

planning and management situations should be 

discouraged. All proposed river-quality models, 

whether conceptual or applied, should be accompanied by a statement of limitations, predictive 

accuracy, and suggested applications. Potential 

users could then exercise independent judgment as 

to whether a model or another technique should be 

applied to the river-quality problem in question. 

MODEL CONFIGURATION 

General applicability to any river is sometimes a 

stated objective of river-quality models (Pacific 

Northwest Laboratories, 1972; Texas Water Development Board, 1970a, b). Usually models with 

this objective are sophisticated in configuration 

because they must have dynamic mathematical 

components and model parameters to simulate 

any conceivable perturbation of the phenomena in 

question. For example, a general-case DO model 

must include mathematical equations and model 

parameters for simulating carbonaceous deoxygenation, reaeration, photosynthesis, respiration, 

nitrification, and benthal oxygen demand. In addition, the model must account for extremes in river 

discharge, hydraulic conditions, river temperature, and other environmental factors. The resulting sophisticated model configuration is seldom 

justified by conditions or needs for any particular 

basin. 

Unfortunately, the proliferation of sophisticated, general-case river-quality models has 

caused a preoccupation with mathematical development, solution techniques, and computer 

programing. Although such technical model problems are important and deserve continuing attention, they tend to divert attention from analysis 

and understanding· 'of river hydrology and the 

phenomena being modeled. In a publication describing the mismatch between data and models, 

Weber, Kisiel, and Duckstein (1973) stated:''*** 

the increased availability of library computer 

programs tends to encourage analysis of data and 

generation of numbers without serious consideration of the assumptions on which these analyses 

are based." In light of this tendency, future efforts 

at applied modeling should minimize extraneous 

mathematical sophistication and maximize the 

understanding of river phenomena. 

In cases where technical model problems persist 

or where there is uncertainty concerning the 

mathematical integrity of a particular model, 

users should consult with independent mathematicians or computer scientists. 

Before the selection of a particular model or 

model configuration, many rivers can be assessed 

as to the required level of mathematical sophistication. The concept here is to fit the model to the 

river rather than the river to the model. The assessment can be partly based on a short premodeling data-collection and analysis program designed 

to determine such factors as mixing and wasteloading characteristics, streamflow patterns, expected ranges of model parameter values, and the 

presence or absence of benthal deposits. Insight 

into such factors before formulation of the model 

B4 
and the implementation of an intensive model 

data collection program will greatly enhance the 

compatibility of the model with actual river conditions. 

In the Willamette River basin, a reconnaissance-level study was conducted on the river before a decision on the configuration of a DO model. 

The study indicated that several major changes 

had occurred since 1951 and 1960 when Velz 

(1951, 1961) studied the DO dynamics ofthe Willamette: BOD loading was much lower because of 

basinwide secondary treatment; waste-water discharges were less variable because oflarge aerated 

stabilization ponds at all pulp and paper mills; 

deoxygenation rates in the river and in waste water were much lower; significant benthal deposits 

were absent; algal photosynthesis and respiration 

were now active in many areas; and detention time 

and river channel geometry (and thus reaeration 

rates) had been affected by dredging. Conversely, 

several important river phenomena and conditions had not changed: the river was still well 

mixed in most reaches, DO concentration was lowest in the lower 55 miles (88 km) of the river, and 

streamflow during the late summer was still 

steady and low despite increased flow augmentation from reservoirs. Such findings led to the formulation of a model of simpler configuration than 

originally considered and allowed the design and 

implementation of a more efficient model-

~alibration and verification program. In other 

words, the premodeling study allowed more inves-

+igative effort to be placed on those factors having 

the largest effect on the DO system of the W illamette. 

RECOGNITION OF CRITICAL PERIODS 

The size and complexity of most river basins 

limit the capability for modeling all seasonal 

changes in a particular river-quality variable or 

process. There is a mystique, perhaps fostered by 

reliance on general-case river-quality models, that 

because seasonal changes in water quality do occur, a useful model must simulate all these 

changes. In reality, attempts to formulate 

perennial-simulation models may obscure important objectives and waste money and time. 

' . In many river basins there exists a particular 

seasonal period, controlled by cyclical hydrologic 

processes, for which a river-quality model can be 

aimed. This is particularly true for the more commonly modeled variables-DO, temperature, and 

dissolved solids. For example, in the Willamette 

River, critically low DO conditions have historically been experienced only during the annually 

recurring low-flow high-temperature summer season (Gleeson, 1972). River-quality planning and 

management decisions in the Willamette Basin 

and many other basins have been predicated 

primarily on poor water-quality conditions that 

recur during the summer. Thus, river-quality 

models for DO can be highly useful for planning 

and management purposes, although intended to 

simulate only this specific condition. 

The critical-condition rationale for model application also offers other advantages (table 2). First, 

critical conditions for many river-quality variables and processes (for example, DO, temperature, and dissolved solids) often occur during lowflow, steady-state hydrologic conditions. Therefore, the need for dynamic model components is 

drastically reduced. Steady, plug-flow conditions 

can usually be realistically assumed, and only 

small ranges in associated variables and processes 

need be considered. Second, because critical conditions are often governed by hydrology and commonly recur on a cyclical basis, it is often possible 

to s·~atistically evaluate the recurrence probability 

TABLE 2.---Comparison of applied river-quality models 

Category Applications Mathematical 

sophistication 

Model 

parameters Data requirements 

Perennialcondition 

Criticalcondition 

Perennial simulation. 

Real-time management. 

Assessment of planning 

alternatives. 

Impact prediction. 

Critical-condition 

simulation. 

Management during 

critical condition. 

Assessment of planning 

alternatives. 

Impact prediction. 

High, numerous 

dynamic elements 

necessary. 

Low to moderate, 

primarily steadystate elements. 

B5 

Numerous. 

Difficult to 

quantify. 

Few. 

Easier to 

quantify. 

Detailed year-round 

hydrologic and quality 

data. 

Continuous monitoring. 

Detailed hydrologic and 

quality data only 

during critical 

condition. 
of the hydrologic event and to relate the results of 

model predictions to this probability. Third, data 

needs for calibration and verification of the riverquality model are reduced. Because sampling is 

needed only for a short period of the year, analysis 

is greatly simplified. 

On the basis of extensive experience in a number 

of river basins, Velz { 1970) described a detailed 

approach for analyzing low-flow hydrology to base 

formulation and application of river-quality 

models for DO, temperature, and several other 

variables. 

Certain river-quality variables, especially those 

associated with erosion and sediment-transport 

phenomena, are most important during high~flow 

periods. Soils and transported sediment are repositories for pesticides, trace metals, and nutrients such as nitrogen and phosphorus. These materials often reach their concentration peaks in 

rivers during storm-runoff events, particularly in 

reaches below erodible areas or below agricultural 

and urban development. 

The significance of river-quality problems associated with high flows depends primarily on the 

antecedent conditions of land surfaces in the basin 

and on the hydraulic regime of the river. For 

example, in an agricultural area, the first large 

runoff event of the year may transport a large 

quantity of sediment-associated nitrogen and 

phosphorus to the river. If streamflow and channel 

geometry are such that the sediment does not deposit in the river, the nutrients will be flushed 

from the basin. In this case, the inputs of nutrients 

will have little or no effect on subsequent algal 

growth within the river. However, if the sediment 

deposits in the river or behind a downstream dam, 

the attached nutrients may profoundly affect algal 

growth during spring and summer growth periods. 

Obviously, the activities of man play a particularly important role in determining the magnitude 

of river-quality problems associated with high 

flows. Land-use activities affect the nature and 

quantity of materials transported to the river by 

runoff. River developments such as dams and 

navigation works change the hydraulic regime of 

the river and affect the fate and impact of transported materials. 

Generally, mathematical models intended for 

simulatation of river-quality phenomena during 

high-flow periods are more difficult to formulate 

and apply than models intended for steady, lowflow periods. High-flow phenomena are so variable 

in time and space that they cannot presently be 

adequately studied and quantified for river-basin 

sized watersheds. Bennett {1974) described the 

chronic problems encountered in obtaining adequate data for formulating a quantitative 

watershed model for erosion and sediment transport. This situation is another example of the basic 

problem mentioned previously in the section, 

ttModelability of Variable or Process." 

In summary, the failure to recognize critical 

periods for river-quality model application is usually attributable to a failure to recognize the overriding importance that river hydrology has in controlling river quality. To formulate a simulatory, 

predictive model and to define the periods of the 

year in which the model can be validly applied, 

river hydrology-quality interactions must be understood. Subsequent circulars in this series will 

deal with the quantification of certain hydrologic 

factors as a prerequisite to modeling and riverquality analysis. 

CALIBRATION AND VERIFICATION REQUlREMENTS 

Calibration is the procedure whereby model 

parameters are adjusted so that the model outputs 

{for a particular set of input data such as streamflow, temperature, and waste loads) approximate a 

set of observed river-quality data. The ranges 

within which model parameters can be realistically adjusted are important to the credibility of 

the calibration. 

Unfortunately, modelers are often faced with 

poor data for calibration and have tended to rely 

heavily on mathematical optimization techniques 

to quantify model parameters. In simple terms, 

optimization involves two steps. First, a numerical 

range is established within which each model 

parameter can vary. The range, which is typically 

quite large, is usually obtained from a review of 

modeling literature. Second, numerou~ computer 

runs are conducted, and values for each parameter 

are simultaneously varied within the ranges previously established. During the computer runs, a 

least-squares procedure is used to obtain a ~~best 

fit" of model outputs to a set of observed riverquality data. The model parameter values resulting in the ~~best fit" are considered to be the optimum values. Often these values are not checked 

independently for accuracy within the river system being modeled. 

B6 
When conducted in the manner described above, 

calibration in effect becomes little more than a 

computerized ((curve-fitting" process instead of a 

((fine-tuning" process governed by scientific understanding. 

Numerical ranges for most parameters can and 

should be established by independent field and 

laboratory study. For example, in the case of a DO 

model, a range of reasonable river deoxygenation 

rates can be established by a carefully conducted 

BOD sampling and analysis program. Similarly 

reaeration coefficients, though not directly 

measurable, can be approximated for any river 

reach for which detailed flow and channel geometry data are available (Bennett and Rathbun, 

1972; Velz, 1970). It is also important that the 

major underlying assumptions are checked for 

reasonableness. 

Verification is the essential step for substantiating the predictive capability of a river-quality 

model. The procedure involves the use of a calibrated model (that is, the same model parameter 

values developed during calibration) and a new set 

of observed data. Some of the new data establish 

the boundary conditions necessary to ~~start" and 

((run" the model. The rest of the data serve as an 

independent set of observations for comparison 

with model predictions (or outputs). 

If the model predictions are Hacceptably close" to 

the independent observations, the model is considered verified. If the predictions are not t~acceptably 

close" or if model parameter values must be juggled to make the model ((fit" the observations, the 

verification has failed. The nacceptably close" 

criterion can be established before verification and 

can, in part, be based on the ((goodness of fit" obtained during calibration as defined by the standard error of estimate. Readers desiring criteria for 

judging the credibility of model calibration and 

verification should read Dawdy (1969). 

Bella (1969) noted that model verification, by 

definition, implies the ttproof of the truth of the 

model." He cautioned, however, that this definition does not describe the process of relating the 

model results to the real world and that a model 

cannot be truly verified-only its use justified for 

the situation in which it is used. The authors agree 

with this hypothesis. 

Verification has been abused in many riverquality modeling efforts. As noted by Mar (1971), 

verification and calibration have often been based 

on the same set of observed data. In others, verification has not even been attempted. Such practices discredit the predictive capabilities of riverquality models. 

The predictive capability of a river-quality model, and thus the integrity and utility of the model 

for assessing proposed planning alternatives, deserves careful scrutiny. A basic necessity is the 

collection and analysis of independent sets of 

statistically reliable data (see subsequent section, 

ftModel Data Base") for calibration and for verification. In this regard, Dawdy (1969, p. D9) 

stated that in order to present a measure of utility 

of the model to a potential user, the data used in 

verification should not include any data used to 

calibrate the model or develop its parameters. It is 

also well to assume that the model will have to be 

recalibrated and reverified at a future date should 

drastic changes in the river system occur (for 

example, a change from primary to secondary 

waste treatment, extensive dredging or diversion 

of a large percentage of streamflow). 

In some cases, the model's predictive ability can 

be further checked by comparing model predictions with results of past river-quality surveys. 

Care must be taken, however, to ensure that the 

old surveys were of high quality and accompanied 

by data on related factors such as waste loads, 

streamflow, river temperature, and channel 

geometry. MODEL DATA BASE 

In many basins, the existing river-quality data 

base has been compiled largely through 

pollution-monitoring and surveillance programs. 

Such programs are usually concerned with determining compliance with State and Federal 

water-quality standards or with detecting trends. 

Monitoring and surveillance programs usually involve routine grab sampling and rigid temporal 

and spatial guidelines. For example, in a particular river, 10 sites might be designated for sampling 

once or twice a month (commonly during daylight 

hours only) for temperature, DO, pH, specific conductance, alkalinity, turbidity, BOD, and coliform 

bacteria. Periodic samples may be collected for 

other selected constituents such as nitrogen and 

phosphorus. Continuous monitors for temperature 

or pH might also be operated at one or two sites. 

Attempts are often made to use such data for 

calibration and verification of river-quality models, particularly DO models. Unfortunately, these 

B7 
data are almost always poorly suited for model 

calibration or verification. Several reasons can be 

cited for this poor suitability: 

1. Lin1ited samples at widely dispersed sites are 

not sufficient to give an indication of large 

diel or cross-sectional variations in quality 

that may be occurring. This is especially 

true for a nonconservati ve variable such as 

DO. 

2. Correlative data on hydrology and waste discharges are seldom available to relate with 

sampling of the river. As a result, most 

monitoring and surveillance data give an 

indication only of an effect and do not permit much insight into causes of the effect. 

3. The relation between streamflow and time of 

travel is seldom known or is overlooked 

when interpreting results. Therefore, results obtained from individual sites will 

represent a concurrent picture of the river 

only if samples happen to be collected during a long-term steady-state flow period 

and at the same time of day. This is rarely 

the case. 

4. Inherent sampling and analysis errors for 

river-quality variables are relatively large. 

Consequently, a number of samples are 

usually necessary to define a statistically 

reliable mean and index of variability. 

Thus, single grab-sample values cannot be 

realistically utilized for modeling data. 

In spite of these factors, much existing monitoring and surveillance data can be useful for designing definitive, intensive studies of river-quality 

phenomena and for providing checks on conclusions and predictions derived by a model. The 

value of existing data for these purposes (assuming the appropriate variables were sampled) is determined by several conditions: (1) the length of 

time during which the data were collected, (2) the 

frequency with which data were collected, l3) the 

location and number of sampling stations, and 

perhaps most importantly, ( 4) the compatibility of 

the data for segregation and collation on the basis 

of hydrology. Hydrologic segregation and collation 

are necessary to expunge the cyclical variability in 

river-quality conditions due to temporal and spatial changes in streamflow, water temperature, 

channel morphology, and other hydrologic conditions. 

To overcome the deficiencies inherent in an inadequate model data base, a set of data specifically 

suited for analysis of the river-quality phenomena 

in question should be collected. The final data 

program should have as its goals (1) a quantitative 

description of the system being modeled, and (2) an 

independent evaluation and quantification of each 

model parameter and assumption. If these goals 

are met, the program should form a sound basis for 

analyzing the river system and permit suitable 

calibration and verification of a model. 

WILLAMETTE RIVER DATA-COLLECTION PROGRAM 

The data-collection program for the Willamette 

River DO model exemplifies the kinds of data required for applied river-quality models. The program was begun in summer, 1973. 

1. General hydrologic characteristics of the 

river were determined from existing data 

on streamflow, water temperature, bed 

slope, bed material, and cross-sectional 

geometry. On the basis of similarity in hydraulic regime, the 187 -mile (30 1-km) 

main stem of the river can be sectioned into 

three reaches. Figure 2 shows the location 

and elevation profiles of the three reaches, 

and table 3 includes descriptive data on 

each reach. (The locations of waste discharges and tributaries, in-reach time of 

travel, and availability of sampling sites 

TABLE 3.-Selected physical characteristics of the main stem Willamette River, Oreg. 

(Characteristics refer to summer low-flow conditions of 6 ><103 ft3/s at Salemi 

Length A~roximate Reach Bed matenal (mit d slope 

(fttmil 

Tidal 26.5 <0.1 Intem1ixed clay, sand, and 

Reach(1) gravel. 

Newberg 25.5 .12 Intermixed clay, sand, and 

Pool (2) gravel with some cobbles. 

Upstream Reach(3) 135 2.8 Mostly cobbles and gravel. 

•Calculated by volume displacement method using channel cross-!>Cctional data. 2C'alculated from dye study conducted by U.S. Geological Survey (Harris, 19681 

B8 

Representative 

midchannel Velocity Approximate 

traveltime war.er depth 

(ft) 

(mi/hrl in reach 

(hrsl 

40 10.11 240 

25 1 .27 94 

7 2 2.0 68 
26.5 mi (43 km) 

2 25.5 mi (41 km) 

187 m1 \301 km) 

3 135 m1 (21 7 km) 

0 30 MILES 

I 11 I ', 

0 50 KM 

A 

300 200 100 0 

DISTANCE, IN RIVER KILOMETRES ABOVE MOUTH 

B 

FIGURE 2.-Willamette River, Oreg. A, Distinctive hydrologic reaches. B, Elevation profile. 

and stream gages necessitated minor 

changes in the reaches finally selected for 

sampling.) 

2. Each reach was studied intensively during 

72-hour periods within the July-August 

high-temperature, steady low-flow period 

(fig. 3). During the 72-hour studies, 5 to 10 

stations were sampled in each reach from 

dawn until dusk. Every 2 hours, DO and 

water temperature were measured using a 

meter and field probe, and, where warB9 

ranted, horizontal and vertical traverses 

were made. BOD samples of the river were 

collected every 2-4 hours. Samples to determine BOD loading were collected at 

least daily from tributaries and all municipal and industrial waste-treatment plants. 

Collection of BOD samples began 2-7 days 

before each 72-hour study, depending on 

time of travel through the reach. 

3. During the 72-hour period, four recording 

monitors were operated continuously in 
0 100.000 JOOO 0 

z z 0 0 

~ 50,000 ~ II) 

a: a: 1000 w ~ 0.. II) 

~ w 20,000 500 a: 

t- u. ~ u 10,000 iii u ::> iii u 5000 ::> 

~ u 

100 ~ w· 

c.:> u.i a: c.:> <( 2000 a: :r <( 

u I II) 

1000 u 0 II) 

0 N D j F M A M j A s 0 

1973 WATER YEAR 

FIGURE 3.-Willamette River discharge at Salem, Oreg., 1973 

water year. 

each reach to record diel variations in 

temperature, DO, specific conductance, and 

pH. (Algal photo-synthesis and respiration 

were discernible at several sites from these 

data.) 

4. All river- and waste-BOD samples were incubated for 20 days, and DO measurements 

were made at frequent intervals to determine BOD rate curves and ultimate BOD. 

The possibility of nitrification in the river 

was assessed by (a) running inhibited (Tuffey, 1973) and noninhibited BOD's and (b) 

analyzing Kjeldahl-N, ammonia-N, and 

nitrate-N samples of river water and waste 

water collected during several of the 72-

hour studies. 

5. The significance of benthal oxygen demand 

was evaluated by sampling bed material 

from areas that had historically contained 

benthal deposits and by examining results 

of vertical DO traverses at numerous cross 

sections. 

6. Refined calculations of time-of-travel and 

reaeration rates were made for short subreaches of the river using detailed crosssectional geometry data obtained from the 

U.S. Army Corps of Engineers. In reaches 

where there was reason to suspect recent 

changes from the Corps data, new crosssectional data were obtained using a 

fathometer. 

7. False-color infrared and black-and-white 

photographs of the main stem of the Willamette were obtained f1·om the NASA 

Earth Resources Assessment Project and 

the U .8. Army Corps of Engineers. The 

photography was used, in conjunction with 

field observations, to examine river morphology and other physical factors. 

COMMUNICATION AND APPLICATION OF 

MODEL OUTPUTS 

The ultimate goal of an applied river-·quality 

model is acceptance and use by planners and other 

decisionmakers for evaluating the impacts of 

planning alternatives on river quality. Typically, 

reports and products of modeling work are too 

technical for these users, many of whom have little 

background in mathematics or computers. Computer users' manuals and card decks, which commonly appear as final products, are useful for t•running the model." However, they give users little 

guidance in applying the model to the riverquality planning and management questions at 

hand. This deficiency can be greatly improved if 

modelers and intended users consult frequently 

concerning the nature and progress of the model. 

Workshops, seminars, and ttbrainstorming sessions" can be invaluable for fostering communication and for establishing trust in the model. 

User reports and products should be written in 

nontechnical language and specifically designed 

for application to the river-quality planning and 

management problems of the basin. Reports on 

model <(production runs" are a key to the successful 

application of river-quality models. 

t•Production runs" produce the applied output of 

a calibrated-verified river-quality model. A different output is generated for each set of inputs. The 

inputs are based on future alternatives for wastetreatment plants, streamflow regulation, land-use 

zoning, etc. These alternatives, in turn, are functions of expected population growth, industrial development, water needs, new water-quality standards, and other social and environmental factors 

as identified by planners, managers, and the public. Information used as inputs for <(production 

runs" should be carefully designed with intended 

model users to ensure the assessment of all 

reasonable river-quality planning and management alternatives. 

An excellent technique for presenting results of 

"production runs" is the "control-curve" concept 

described by Velz (1970). Two "control curves" 

generated by an early DO model of the Willamette 

River (Velz, 1951) are shown in figures 4 and 5. 

Note that the curves are simple, user oriented, 

and permit assessment of multiple factors on one 

graph. Given a reliable river-quality model, the 

B10 
DISCHARGE, IN CUBIC METRES PER SECOND, AT SALEM GAGE 

100 150 200 

z 

0 

1-

<{ 

a: 

:::::> 

1- 60 

<{ 

U) 

1-

z 

w 

u 

a: 

w 

Q.. 

z 40 

z 

w 

(.!) 

>-

X 

0 

0 

~ 20 -l 

0 

~ 

0 

Percentage reduction in 

1950 BOD waste load"'-..80 percent 

0 ~----~--~~--~~--~~--~----~----~----~----~----_. ____ _. ____ ~ 

2000 4000 6000 8000 

DISCHARGE, IN CUBIC FEET PER SECOND, AT SALEM GAGE 

FIGURE 4.-Relation between DO and summer runoff for Willamette River, Oreg. 0950-51), at river mile 6. (See fig. 2.) 

Curves represent DO-runoff relations at different BOD waste-loading conditions. <Adapted from Velz, 1951, p. 68a.) 

computer can easily produce a suite of curves for 

any given reach or station on the river. Such 

curves enable the simultaneous evaluation of 

numerous planning and management alternatives 

without separate production runs on the computer. 

SUMMARY 

A river-quality model can be a powerful predictive tool for river-basin planning and management 

provided that premises and limitations are recognized and that the model is properly calibrated and 

verified. These criteria can only be satisfied 

through a competent scientific appraisal of the environmental factors and processes affecting the 

river-quality phenomena being modeled. The ability to perform such an appraisal is related to the 

complexity of physical conditions within each 

river basin and to the background of available 

scientific knowledge concerning the relevant processes and variables. There are times when complex 

physical conditions or limited scientific understanding prevent formulation of a reliable, applied 

model. In such cases, semiquantitative descriptive 

studies are warranted in lieu of models to provide 

insight into river-quality processes and variables 

and to form a basis for future modeling work. 

The analysis of river hydrology, particularly 

runoff and water-temperature patterns and channel morphology, is essential to the formulation of 

an applied river-quality model. River hydrology is 

the single most important factor governing the 

time-and-space variability in river quality. Know-

.ledge of this time-and-space variability helps to 

identify critical time periods and reaches of the 

river for which a river-quality model can be most 

effectively applied. 

Calibration and verification of river-quality 

models must be based on separate, statistically 

reliable sets of data for the variables and processes 

being modeled. Periodic grab-sample data comBll 
z 

Q 80 

1-

<( 

a: 

:J 

1-

<( 

(/) 

1-

z 

w 60 u 

a: 

w 

a.. 

z 

z 

w 

(.!) 40 

>-

X 

0 

0 

w 

> 

_, 

0 

(/) 

(/) 20 

0 

OL----L----~-----L----~----J-----~L---L---~L---~~--~----~----~ 

0 200 400 600 800 1 000 1200 

POLLUTION LOAD AT NEWBERG, IN THOUSANDS OF BOD POPULATION EQUIVALENTS 

~ BOD5 discharge (lb/day)] BOD population equivalent = ---------

0.17 (lb/capita day) 

FIGURE 5.-Relation between DO and BOD waste loading for the Wil1amette River, Oreg. (195~51), below river mile 50. 

<See fig. 2.) Curves represent DO-BOD load relations at various river discharges as measured at Salem <river mile 85). 

IAdapted from Velz. 1951, p. 75a.) 

monly generated by pollution-monitoring and 

surveillance programs are almost never suitable 

for model calibration or verification. 

Even those river-quality models with proven 

predictive capability will be of little value for 

planning and management purposes unless results of model production runs are translated into 

formats that are understandable to users. In this 

regard, constant communication and interplay 

among modelers and users are necessary to establish understanding and trust in the model and to 

ensure assessment of all important planning and 

management alternatives. 

REFERENCES CITED 

Bel1a, D. A., 1969, Modeling the eutrophication process: A 

further note on verification: Proc. workshop sponsored by 

Federal Water Quality Adm. and Univ. Florida, St. 

Petersburg, Fla., November 19-21, 1969, p. 21-25. 

Bennett, J. P., 1974, Concepts of mathematical modeling of 

sediment yield: Water Resources Research, v. 10, no. 3, 

p. 485-492. 

Bennett, J.P., and Rathbun, R. E., 1972, Reaeration in openB12 
channel flow: U.S. Geol. Survey Prof. Paper 737, 75 p. 

Dawdy, D. R., 1969, Considerations involved in evaluating 

mathematical modeling of urban hydrologic systems: U.S. 

Geol. Survey Water-Supply Paper 1591-D. p. Dl-D18. 

Gleeson, G. W., 1972, The return of a river, the Wi1lamette 

River, Oregon: Advisory Comm. on Environmental ScL 

and Technology and the Water Resources Research Inst .. 

Oregon State Univ., Corvallis, 103 p. 

Harris, D. D., 1968, Travel ratesofwaterforselectedstreams in 

the Wilamette River basin. Oregon: U.S. Geol. Survey 

Hydrol. Inv Atlas HA-273. 

Jaworski, N. T .. l.Rar, D. W., Jr., and Villa, Orterio, Jr., 1971. 

Nutrient management in the Potomac Estuary: Environmental Protection Agency, Water Quality Office, Tech. 

Rept. 45, 61 p. 

Lombardo, P. S., 1973, Critical review of currently available 

water-quality models: Consultants rept. to U.S. Dept. Interior, contract no. 14--31-0001-3571, 85 p. 

Mar, B. W., 1971. Verification of models and basic data used in 

the management and control of water quality: Tech. Research Proj. Completion Rept., OWRR Proj. no. B023-

WASH, 51 p. 

Pacific Northwest Laboratories, 1972, Explore I: A river basin 

water quality model: Battelle Memorial Inst., Richland, 

Wash., 119 p. 

Streeter. H. W., and Phelps, E. B., 1925, A study of the pollution 

and natural purification of the Ohio River: U.S. Public 

Health Service, Public Health Bull. 146, 75 p. 

Texas Water Development Board, 1970a. Simulation of water 

quality in streams and canals: Texas Water Devel. Board, 

DOSAG--1, 51 p. 

--1970b, Simulation of water quality in streams and canals: Texas Water Devel. Board, QUAL-1, 64 p. 

Tuffey. T. J .. 1973, The detection and study of nitrification in 

streams and estuaries: Ph.D. thesis, Rutgers Univ., New 

Brunswick, N.J., 180 p. 

Velz, C. ,J., 1951, Report on natural purification capacities, 

Willamette River: Natl. Council for Stream Improvement 

ofthe Pulp, Paper, and Paperboard Industries, Inc., School 

of Public Health, Michigan Univ., Ann Arbor, Mich., 80 p. 

---1961, Supplementary report on lower Willamette River 

waste as.<:imilation capacity: Natl. Council for Stream Improvement of the Pulp, Paper, and Paperboard Industries, 

Inc., School of Public Health, Michigan Univ., Ann Arbor. 

Mich., 28 p. 

---1970, Applied Stream sanitation: New York, John Wiley 

and Sons, Inc .. 619 p. 

Weber, .J. E., Kisiel, C. C., and Duckstein. Lucien. 1973. On the 

mismatch between data and models of hydrologic and water resource systems: Water Resources Bull., v. 9, no. 6, p. 

1075-1088. 

,:. U.S. GOVERNMENT PRINTING OFFICE: 1975-0-690-036/11 Bl3