m Instruction Report W-96-2

I 1 September 1996 Il@ll (Updated April 1999)

US Army Corps

of Engineers

Waterways Experiment

Station

Water Operations Technical Suppofl Program

Simplified Procedures

for Eutrophication Assessment

and Prediction: User Manual

by William W. Walker

Approved For Public Release; Distribution Is Unlimited

Prepared for Headquarters, U.S. Army Corps of Engineers
The contents of this report are not to be used for advertising,

publication, or promotional purposes. Citation of trade names

does not constitute an official endorsement or approval of the use

of such commercial products.

The findings of this report are not to be construed as an

official Department of the Army position, unless so designated by other authorized documents.

@

PRINTED ON RECYCLED PAPER
Water Operations Technical

Support Program

Simplified Procedures

for Eutrophication Assessment

and Prediction: User Manual

by William W. Walker

1127 Lowell Road

Concord, MA 01742

Final report

Approved for public release; distribution is unlimited

Prepared for U.S. Army Corps of Engineers

Washington, DC 20314-1000

Instruction Report W-96-2

September 1996

(Updated April 1999)

Monitored by U.S. Army Engineer Waterways Experiment Station

Vicksburg, MS 39180-6199
ENWROWENTAL -,”..,! ]:

Watenvays Experiment Station Cataloging-in-Publication Data

Walker, William W.

Simplified procedures for eutrophication assessment and prediction : user manual/by

William W. Walker; prepared for U.S. Army Corps of Engineers ; monitored by U.S. Army

Engineer Waterways Experiment Station.

235 p. : ill. ; 28 cm. – (Instruction reporl; W-96-2)

Includes bibliographic references.

1. Eutrophication — Mathematical models. 2. Resetvoir ecology. 3. Water quality —

Evaluation — Computer programs. 1. United States. Army. Corps of Engineers. Il. U.S.

Army Engineer Waterways Experiment Station. Ill. Water Quality Research Program. IV.

Title. V. Series: Instruction report (U.S. Army Engineer Waterways Experiment Station) ;

w-96-2.

TA7 W34i no.W-96-2
Contents

Prefae . . . .. o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..vi

l—Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Eutrophication Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3

Summary ofAssessmentProcedures . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14

DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18

2—FLUX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

FLUX Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

Input DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...2-2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-4

Program Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...2-14

Typical Application Sequence.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26

Procedure Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..2-29

Data-Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...2-31

DataFile Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-34

FLUX Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44

3—PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

PROFILE Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..3-1

Input DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Mixed-Layer WaterQualityData Summary . . . . . . . . . . . . . . . . . . . . . . 3-4

Oxygen Depletion Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7

Program Operation . . . . . . . . . . . . . . . . . $. . . . . . . . . . . . . . . . . . ...3-10

Input DataFile Format......,.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15

Data-Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20

Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...3-22

4-BATHTUB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-1

BATHTUB Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-1

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-2

Program Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-36

Application Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4-42

Procedure Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-51

Data-Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-53
Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-59

Instructional Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-79

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..R-1

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..B-1

Appendix A: Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..A1

Appendix B: Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..B1

SF 298

List of Figures

Figure 1.1.

Figure 1.2.

Figure 1.3.

Figure 1.4.

Figure 1.5.

Figure 1.6.

Figure 3.1.

Figure 3.2.

Figure 4.1.

Figure 4.2.

Figure 4.3.

Figure 4.4.

Figure 4.5.

Figure 4.6.

Control pathways in empirical eutrophication models

developed fornorthem lake applications . . . . . . . . . . . . . . . . . 1-4

Control pathways in empirical eutrophication models

developed for CEreservoirapplications . . . . . . . . . . . . . . . . . 1-5

Sensitivity analysis of first-order phosphorus sedimentation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12

Sensitivityanalysis ofsecond-order phosphorus sedimentation model ...,..... . . . . . . . . . . . . . . . . . . . . . . . . . 1-13

Assessment pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15

Estimated accuracy ofreservoirmean concentration

computed from sampling designs with betweenl and

30 sampling rounds overarange oftemporal CVS . . . . . . . . 1-29

Sample PROFILE output: Surface water qualitysummary . . . 3-5

Example box plot for Beaver Reservoir . . . . . . . . . . . . . . . . . 3-7

Schematic ofBATHTUB calculations . . . . . . . . . . . . . . . . . . 4-3

Control pathways inempirica.l eutrophication models

developed for CE reservoir applications . . . . . . . . . . . . . . . . . 4-5

BATHTUB segmentation schemes . . . . . . . . . . . . . . . . . . . . 4-17

Mean depth (Z)versus hydraulic residence time(T)

for Remodel developmentdataset LOGIOscales . . . . . . . . . 4-25

Relationships between nutnent residence times and

hydraulic residence times in Remodel development

dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27

Phosphorus, nitrogen, turbidity relationships for CE

reservoirs (nonalgal turbidity calculated as l/Secchi

(m)-0.025Chl a(mg/m3)) . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30

iv
Figure 4.7. Phosphorus, chlorophyll a, and transparency relationships for CE reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

Figure 4.8. Calibration factor for linear phosphorus/chlorophyll

model versus light limitation factors . . . . . . . . . . . . . . . . . . . 4-34

Figure 4.9. Model segmentation for Lake Keystone, Oldahom&

application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-59

List of Tables

Table 1.1.

Table 1.2.

Table 1.3

Table 1.4

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Table 2.5

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 4.6

Comparison of Lake and Reservoir Empirical

Eutrophication Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

Mass Balance Terrnsand Data Sources . . . . . . . . . . . . . . . . 1-22

Minimal and Desirable Designs for Tributary Monitoring Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23

General Guidelines for Designing Reservoir Pool

Monitoring Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-27

Estimation Algorithms Used in FLUX Program . . . . . . . . . . . 2-5

Stratified Sample Algorithm (Cochran 1977; Bodo

and Unny 1983) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10

Breakdown by Flow Stratum - Caddo River Example . . . . . 2-12

Typical Application Sequence . . . . . . . . . . . . . . . . . . . . . . . . 2-27

FLUX File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34

Symbol Definition s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6

BATHTUB Model Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8

Supplementary Response Models . . . . . . . . . . . . . . . . . . . . . 4-12

Error Statistics for Model Network Applied to Spatially Averaged CEReservoir Data . . . . . . . . . . . . . . . . . . . . 4-13

Diagnostic Variables and Their Interpretation . . . . . . . . . . . . 4-14

Equations for Estimating Nonalgal Turbidity, Mixed

Depth, and Hypolimnetic Depths in Absence of

Direct Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-33
Preface

The information reported herein is based on a series of technical reports

written by Dr. William W. Walker and published by the U.S. Army Engineer

Waterways Experiment Station (WES). These previous reports summarized

work conducted as part of the Environmental and Water Quality Operational

Studies Program, sponsored by the Headquarters, U.S. Army Corps of Engineers (HQUSACE). Preparation of this report was sponsored by HQUSACE,

as part of the Water Operations Technical Support (WOTS) Program. The

WOTS Program was assigned to WES under the purview of the Environmental

Laboratory (EL). Funding was provided under Department of the Army

Appropriation 96X3 123, Operations and Maintenance. The WOTS was managed under the Environmental Resources Research and Assistance Programs

(ERRAP), Mr. J. L. Decell, Manager. Mr. Robert C. Gunkel was Assistant

Manager, ERRAP, for the WOTS. Program Monitors for WOTS were

Messrs. Frederick B. Juhle and Rixie Hardy, HQUSACE.

The work was conducted under the direct WES supervision of

Dr. Robert H. Kennedy, Ecosystem Processes and Effects Branch (EPEB),

Environmental Processes and Effects Division (EPED), EL, and the general

supervision of Dr. Richard E. Price, Chief, EPEB, Mr. Donald L. Robey, Chief,

EPED, and Dr. John W. Keeley, Director, EL.

At the time of publication of this report, Director of WES was

Dr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN.

This report was updated in April 1999.

This report should be cited as follows:

Walker, W. W. (1996). “Simplified procedures for eutrophication assessment and prediction: User manual,” Instruction

Report W-96-2 (Updated April 1999), U.S. Army Engineer

Waterways Experiment Station, Vicksburg, MS.

lhe contents of this report are not to be used for adver~ising, publication,

or promotional putposes. Citation of trade names does not constitute an

oficial endorsement or approval of the use of such commercial products.

vi
Background

1 Introduction

This report describes simplified procedures for eutrophication assessment

and prediction. These techniques, initially developed for use at U.S. Army

Corps of Engineer (CE) reservoirs, are based upon research previously

described in a series of technical reports. These reports describe database

development (Report 1; Walker 1981); model testing (Report 2; Walker 1982);

model refinement (Report 3; Walker 1985); and applications procedures

(Report 4; Walker 1987). Reported here is detailed itiormation concerning

application of the latest versions of these techniques using a DOS-based

personal computer and also reported is an update of the original applications

manual (i.e., Report 4).

Three computer programs facilitate data reduction and model implementation. While the assessment procedures and programs can be “run” based upon

the information contained in this report, their intelligent “use” requires an

understanding of basic modeling concepts and familiarity with the supporting

research. Review of the above research reports and related references on this

topic (see References and Bibliography) will facilitate proper use of the techniques described below.

Eutrophication can be defined as the enrichment of water bodies leading to

an excessive production of organic materials by algae and/or aquatic plants.

This process has several direct and indirect impacts on reservoir water quality

and beneficial uses. Common measures of eutrophication include total nutrient

concentrations (phosphorus and nitrogen), chlorophyll a (a measure of algal

density), Secchi depth (a measure of transparency), organic nutrient forms

(nitrogen and carbon), and hypolimnetic dissolved oxygen depletion.

The basis of the modeling approach described below is to relate eutrophication symptoms to external nutrient loadings, hydrology, and reservoir morphometry using statistical models derived from a representative cross section of

reservoirs. When applied to existing reservoirs, the models provide a framework for interpreting water quality monitoring data and predicting

Chapter 1 Introduction 1-1
effects of fhture changes in external nutrient loadings. The models can also be

used to predict water quality conditions in a proposed reservoir.

Three basic phases are involved in applying the methodolo~ to an existing

or proposed reservoir:

a. Analysis and reduction of tributary water quality data.

b. Analysis and reduction of pool water quality data.

c. Model implementation,

A separate computer program has been developed for each phase. The datareduction phases are critical steps in the modeling process. The programs can

also be used in other aspects of reservoir operation and management, including

monitoring program design and generalized data analysis. The model implementation program is designed so that it can be applied to a single reservoir

(mixed or spatially segmented), networks of reservoirs (hydrologically linked),

or collections of reservoirs (hydrologically independent). The last type of

application can support regional comparative assessments of reservoir conditions and controlling factors.

This report is organized in four chapters. Chapter 1 reviews basic empirical

modeling concepts, presents an overview of the assessment procedures which

have been developed for reservoir application, and summarizes basic data

requirements and recommended monitoring strategies. Chapter 2 describes the

FLUX program, which is designed for analysis and reduction of tributary monitoring data. Chapter 3 describes PROFILE, a program designed for analysis

and reduction of pool monitoring data. Chapter 4 describes BATHTUB, a

program designed for model implementation. Appendix A describes the necessary procedures for installing the programs on an IBM-compatible personal

computer.

Several levels of involvement are offered to potential users of this methodology. The following steps are suggested:

Step 1: Review summary information (Chapter 1).

Step 2: Review supporting research and basic reference documents.

Step 3: Review program documentation (Chapters 2,3, and 4).

Step 4: Review documented output listings.

Step 5: Acquire and install programs (Appendix A) on an accessible computer system.

1-2

Step 6: Run programs using several sample input files provided.

Chapter 1 Introduction
Step 7: Apply program to user-defined problems.

The above procedures provide a gradual and logical introduction of the techniques and a foundation for their application in a reservoir management

context.

Eutrophication Modeling Techniques

Models for reservoir eutrophication can be broadly classified as theoretical

or empirical. While all models are empirical to some extent, they are distinguished by their levels of empiricism. General characteristics and limitations of

these model types are discussed below.

Theoretical models generally involve direct simulation of physical, chemical,

and biological processes superimposed upon a simulation of reservoir hydrodynamics. These methods generally have extensive resource requirements in

terms of input dat~ computing facilities, and user expertise. They can be usefbl for problems requiring high spatial and temporal resolution and/or simulation of cause-effect relationships which cannot be represented using simpler

models. Their relative complexity does not guarantee that simulation models

are more accurate or more reliable than simplified models for certain types of

applications.

Although based upon theoretical concepts (such as mass balance and nutrient limitation of algal growth), empirical models do not attempt explicit simulation of biochemical processes and use simplified hydrodynamic representations.

They generally deal with spatially and temporally averaged conditions. The

simple structures, low resolution, limited number of input variables, and initial

calibration to data from groups of impoundments result in relatively low data

requirements. At the same time, the above characteristics limit model applicability. In one sense, empirical models attempt to “interpolate” the gross

responses of a given impoundment, based upon observed responses of other

impoundments and levels of certain controlling variables. They also provide a

quantitative framework for interpreting monitoring data from a given impoundment and describing eutrophication-related water quality conditions and controlling factors both in absolute and relative terms.

Empirical model structures and evolution

Empirical prediction of reservoir eutrophication can be described as a twostage procedure involving the following types of models:

a. Nutrient Balance Models. These relate pool or discharge nutrient levels

to external nutrient loadings, morphometry, and hydrology. (Note that

the term “pool” refers to the lake or reservoir impounded by a dam.)

Chapter 1 Introduction 1-3
b. Eutrophication Response Models. These describe relationships among

eutrophication indicators within the pool, including nutrient levels,

chlorophyll a, transparency, and hypolimnetic oxygen depletion.

Generally, models of each type must be linked to relate external nutrient

loadings to reservoir water quality responses. In the absence of loading information, however, application of eutrophication response models alone can

provide useful diagnostic tiormation on existing water quality conditions and

controlling factors.

The literature contains a wide array of empirical eutrophication models

which have been calibrated and tested using data from various lake and/or

reservoir data sets. Many of these models, particularly the early ones, were

based primarily upon data from northern, natural lakes. While the equations

and coefficients vary considerably among the lake models, they share the same

sets of variables and basic assumptions, as depicted in Figure 1.1.

INFLOW

TOTAL P

MEAN DEPTH

+

LAKE

TOTAL P CHL-A— SECCHI

HYDRAULIC

RESIDENCE TIME

Figure 1.1. Control pathways in empirical eutrophication models developed for

northern lake applications

Inputs to these models can be summarized in three terms:

a. Inflow total phosphorus concentration. External loading/discharge rate,

a nutrient supply factor.

b. Mean depth. Reservoir volume/surface are% a morphometric factor.

c. Hydraulic residence time. Reservoir volume/discharge rate, a hydrologic fwtor.

Empirical nutrient balance models have generally evolved from a simplistic

“black-box” model which represents the impoundment as a continuous stirredtank reactor at steady state and the sedimentation of phosphorus as a first order

reaction. Phosphorus is assumed to control algal growth and other

eutrophication-related water quality conditions. Response models generally

consist of bivariate regression equations relating each pair of response measurements (e.g., phosphorus/chlorophyll, chlorophyllk.nsparency).

1-4

Chapter 1 Introduction
In adapting these models for use in CE and other reservoirs (Walker 1981,

1982, 1985), modifications have been designed to include additional input variables, controlling factors, and response variables, as depicted in Figure 1.2.

Table 1.1 compares the variables and assumptions of the reservoir models

documented in this manual. The reservoir modifications are designed to

improve generality by incorporating additional independent variables and controlling factors found to be important in model testing.

INFLOWTOTAL METALIMNETIC ~

DEPLETION RATE

INFLOW ORTHO-P

MEANTOTAL DEPTH

NYD. RESIDENCE TIME

HLOROPHYLL-A

INFLCW TOTAL N

tNFLW bNORGANIC N

SECCHI

SUMMER FLUSHING RATE ORGANIC N

MEAN OEPTH OF TOTAL P-ORTNO-p MO(ED IAYER

NONALGAL TRU6JDITY

Figure 1.2. Control pathways in empirical eutrophication models developed for

CE reservoir applications

Refinements are focused in the following areas:

a. Effects of nonlinear sedimentation kinetics on nutrient balances. A

second-order kinetic model appears to be more general than a firstorder model for predicting both among-reservoir, spatially averaged

variations and within-reservoir, spatial variations.

b. Effects of inflow nutrient partitioning (dissolved versus particulate or

organic versus inorganic) on nutrient balances and chlorophyll a levels.

Because of differences in biological availability and sedimentation rates,

reservoir responses appear to be much more sensitive to the orthophosphorus loading component than to the nonortho (total minus ortho)

component.

Chapter 1 Introduction 1-5
Table 1.1

Comparison of Lake and Reservoir “Empirical Eutrophication

Models

Model

Characteristics Lake Models Reservoir Models

Input Inflow total P concentration Inflow total P concentration

variables Mean depth Inflow ortho-P concentration

Annual hydraulic residence Inflow total N concentration

time Inflow inorganic N

Mean hypolimnetic depth concentration

Mean depth

Mean hypolimnetic depth

Mean depth of mixed layer

Seasonal hydraulic residence

time

Nonalgal turbidity

Spatial Mixed Mixed or spatially segmented

variability

Temporal Steady state Steady state

variability

Nutrient Linear (first-order) Nonlinear (second-order)

sedimentation

kinetics

Factors Phosphorus Phosphorus

controlling Nitrogen

algal growth Light

Flushing rate

output Total phosphorus Total phosphorus

variables Chlorophyll a Total nitrogen

Transparency Chlorophyll a

Hypolimnetic oxygen Transparency

depletion Nonortho-phosphorus

Organic nitrogen

Hypolimnetic oxygen

depletion

Metalimnetic oxygen

depletion

1-6

c. Effects of seasonal variations in nutrient loadings, morphomet~, and

hydrology on nutrient balances. Pool water quality conditions are

related more directly to seasonal than to annual nutrient balances in

impoundments with relatively high flushing rates.

Chapter 1 Introduction
d Effects of algal growth limitation by phosphorus, nitrogen, light, and

flushing rate on chlorophyll a concentrations. Simple phosphorus/

chlorophyll a relationships are of limited use in reservoirs because

nitrogen, light, and/or flushing rate may also regulate algal growth,

depending upon site-specific conditions.

e. Effects of spatial variations in nutrients and related variables, as controlled by reservoir morphometry, hydrology, and the spatial distribution

of tributary nutrient loads. Nutrient-balance models can be implemented in a spatially segmented framework which accounts for advection, dispersion, and sedimentation to predict water quality variations

among and within major tributary arms. This spatial resolution can be

important for evaluating impacts on reservoir uses, depending upon

locations of water-use points (e.g., water-supply intakes, bathing

beaches, parks, fishing areas, and/or wildlife refiges).

Model structures have been tested against several independent reservoir data

sets. Details on model development and testing are described in the supporting

research reports (Walker 1982, 1985).

Applications

Potential model applications can be classified into two general categories:

diagnostic and predictive. Characteristics and limitations of these applications

are described below.

In a diagnostic mode, the models provide a framework for analysis and

interpretation of monitoring data from a given reservoir. This yields perspective on eutrophication-related water quality conditions and controlling factors.

Assessments can be expressed in absolute terms (nationwide, e.g., with respect

to water quality objectives, criteri~ or standards) and/or relative terms (e.g.,

comparisons with other impoundments, or regionally). Using routines and

statistical summaries included in the BATHTUB program, observed or predicted reservoir characteristics can be ranked against characteristics of CE

reservoirs used in model development.

In a predictive mode, the models are used to project fiture conditions in

either existing or planned reservoirs. The distinction between the two types of

predictive applications is important. In the first case, monitoring data from an

existing reservoir can be used, in combination with the models and diagnostic

analyses, as a “starting point” for “extrapolation” to future conditions. Because

of the opportunity for site-specific calibration, projections of future conditions

in an existing reservoir are generally subject to less uncertainty than projections

of water quality conditions in a proposed reservoir.

In a predictive mode, the models project steady-state responses to changes

in controlling variables which are explicitly represented in the model network

Chapter 1 Introduction 1-7
(Figure 1.2). Such projections can be used in impact assessments and in evaluations of water-quality-control strategies. For example, fhture scenarios

involving changes in seasonal or annual-mean values of the following factors

can be evaluated:

a. Inflow nutrient concentrations or loadings (total phosphorus, ortho

phosphorus, total nitrogen, and/or inorganic nitrogen).

b. Pool elevation, as it influences mean depth, mixed-layer depth, mean

hypolimnetic depth, and hydraulic residence time.

c. Inflow volume and changes in hydraulic residence time.

d. Pool segmentation, as it influences longitudinal nutrient transport, sedimentation, and the spatial distribution of nutrients and related water

quality conditions.

Applications of the first type are of primary importance because control strategies for reservoir eutrophication are usually focused on external nutrient

(especially, phosphorus) supplies.

Examples of impacts and control strategies which cannot be explicitly evaluated with these models include the following:

a. Variations in pool level or other model input variables which occur over

time scales shorter than the growing season (typically, 6 months).

b. Changes in outlet levels.

c. Structural modifications, such as the construction of weirs.

d. Hypolimnetic aeration or destratification.

e. Other in-reservoir management techniques, including dredging and

chemical treatment to control internal nutrient recycling.

In such cases, implementation of the models in a diagnostic mode can provide

useful baseline water quality perspectives; however, simulation or other

approaches must be used for predictive purposes.

Although the supporting research has focused on reservoirs, the computational framework can also be applied to natural lakes. Certain procedures and

concepts are essential to evaluating eutrophication problems in lakes or reservoirs. These include calculation of tributary nutrient loads, summary of

observed water quality conditions, construction of water balances, and construction of mass balances. In adapting the empirical lake models (Figure 1.1)

for use in reservoirs, the goal has been to increase model generality, so that the

resulting formulations can be applied within certain constraints to lakes or to

1-8

Chapter 1 Introduction
reservoirs. The limits and extent of model testing against lake data sets are

summarized in the supporting research reports (Walker 1982, 1985). Options

for implementing empirical models previously developed exclusively from lake

data sets are also included in the software.

Error, variability, and sensitivity analysis

The distinction between “error” and “variability” is important. Error refers

to a difference between an observed and a predicted mean value. Variability

refers to spatial or temporal fluctuations in concentration about the mean.

Prediction of temporal variability is generally beyond the scope of empirical

modeling efforts, although such variability is important because it influences

the precision of observed mean values calculated from limited monitoring data.

Because both measurement and model errors tend to increase with concentration scale, errors are most conveniently expressed on a percentage basis or

logarithmic scales. This stabilizes variance over the ranges of concentration

encountered, an important requirement for application of common statistical

techniques (e.g., regression). This report frequently uses the mean coefllcient

of variation (CV) as a measure of error. The CV equals the standard error of

the estimate expressed as a fraction of the predicted value. For example, a CV

of 0.2 indicates that the standard error is 20 percent of the mean predicted

value. Assuming that the errors are log-normally distributed about the predicted value, 95-percent confidence limits can be estimated from the following

equation:

yme-2cv<y<yme2cv

where

Ym= predicted mean value

CV = error mean coefficient of variation

Y = 95-percent confidence range for mean value

Magnitudes, sources, and interpretations of error are discussed below.

Error CVS for the reservoir model network (Figure 1.2) are on the order of

0.27 for predicting total phosphorus and 0.35 for predicting mean chlorophyll a. According to the above equation, these statistics translate into

95-percent confidence factors of 1.72 and 2.00, respectively. In applying these

models in a reservoir management context, limitations imposed by errors of this

magnitude are less severe than immediately apparent because of the following

factors:

Chapter 1 Introduction 1-9
a. Despite the relatively wide confidence bands, the models explain 91

percent and 79 percent of the observed variances in total phosphorus

and chlorophyll a across reservoirs, respectively. This reflects the relatively wide ranges of conditions encountered and suggests that the

models are adequate for broad comparative analyses of reservoir

conditions (i.e., ranking).

b. Error statistics are calculatedfiom “imperfect” data sets. Errors are

partially attributed to random sampling, measurement, and estimation

errors in the input and output (i.e., observed) conditions, which inflate

the total error but do not reflect model performance.

c. Error magnitudes refer to predictions which are made without the

beneJt of site-specl@c water quality information. In applications to

existing reservoirs, prediction errors can be reduced by calibrating the

model (adjusting certain model coefficients) so that predictions match

observed water quality conditions. The calibrated model can subsequently be used to project water quality changes likely to result from

changes in nutrient loads or other controlling factors.

d. Year-to-year water quality variations induced by climate, hydrology,

nutrient loading, and other factors are substantial in many reservoirs.

It would be difficult to detect modest errors in predicting average conditions without several years of intensive monitoring.

e. Ability to de$ne objective criteria or standards is limited. The “penalty” or “risk” associated with modest errors in predicting average

responses may be low when expressed in terms of impacts on water

uses. The measured and modeled variables (chlorophyll a, etc.) are

reasonable and practical, but impefiect, surrogates for potential wateruse impacts.

$ Ability to predict changes in loading resultingfiom adoption of specl~c management strategies is limited. This applies particularly to

implementation of nonpoint source loading controls with performances

evaluated using watershed simulation models. In such situations, errors

associated with predicting reservoir response may be swamped by errors

associated with predicting loadings; i.e., the reservoir response model

may not be the limiting factor in the analysis.

Error-analysis concepts discussed below provide additional perspectives on the

above points.

1-1o

Differences between observed and predicted reservoir conditions can be

attributed to the combined effects of a number of error sources, as described

below:

Chapter 1 Introduction
a. Independent variable error. These are errors in the estimates of model

input variables, including external nutrient loadings, flows, and reservoir morphometry.

b. Dependent variable error. These are errors in the estimates of mean

observed reservoir water quality conditions, based upon limited monitoring data.

c. Parameter error. These errors are attributed to biases or random errors

in the model coefficients estimated from cross-sectional data sets.

d. Model error. These errors are attributed to errors in model structure or

effects of factors which are not explicitly represented.

The user has direct control over the first two error sources (i.e., independent

and dependent variable error), primarily through design and implementation of

appropriate monitoring programs and use of proper data reduction techniques.

The last two sources (i.e., parameter and model error) are also under user

control to the extent that the user selects the model(s) deemed appropriate for

specific application. Research (Walker 1981, 1982, 1985) has been directed at

minimizing the last two error sources by reviewing, screening, refining, calibrating, and testing arrays of models which are appropriate for reservoir

applications under specific conditions.

The impacts of errors in speci$ing model input variables or coefficients

depend upon the sensitivities of model predictions to those inputs. Sensitivities,

in turn, reflect model structure and variable ranges. A sensitivity coefficient

can be conveniently expressed as a normalized first derivative, or as the percent

change in a model output variable induced by a 1-percent change in a model

input. For example, a sensitivity coefficient of 1.0 would indicate that the output is proportional to the input; in this situation, for example, a 5-percent error

in speci&ing the input would propagate through the model and cause a

5-percent error in the predicted output. For a sensitivity coefficient of 0.2,

however, a 5-percent input error would cause only a 1-percent output error.

Sensitivity coefficients provide insights into which model variables and coefflcients are the most important to measure or estimate accurately.

Figures 1.3 and 1.4 display sensitivity coefficients for models predicting

mean phosphorus concentrations in reservoirs assuming first- and second-order

sedimentation reactions, respectively. In both cases, the output variable is the

error term or the ratio of the observed to the predicted mean phosphorus concentration. Input variables used to calculate this ratio include the observed

pool concentration, inflow concentration (flow-weighted over all sources),

flushing rate (outflow/volume), and sedimentation coefficient.

Sensitivities vary with flushing rate over the approximate range encountered

in CE impoundments (median value for reservoirs used in model testing

= 7/year. At low flushing rates (or long hydraulic residence times), sensitivities

Chapter 1 Introduction 1-11
1.0

0.8

0.6

0.4

0.2

0

- —— — ———

SED!MENTA TION RATE -

-

-

FLUSHING RATE

0.1 1 10 100

FLUSHING RATE. l/YR

I% CHANGE IN ERROR ~ SENSITIVITY COEF = 1% CHANGE Ihl FACTOR I

ERROR = OBSERVE() POOL P

PREDICTED POOL P

P, F

PREDICTED POOL P = F+K1

WHERE: Pi = INFLOW TOTAL PHOSPHORUS CONCENTRATION (mg/m3)

F = FLUSHING RATE (1/yr )

K, = FIRST-ORDER SEDIMENTATION COEFFICIENT = 2.5 1/ Yf

Figure 1.3. Sensitivity analysis of first-order phosphorus sedimentation model

to the sedimentation coefficient and flushing rate are relatively high (approach

ing 1.0 for the first-order model and 0.5 for the second-order model). This

reflects the relative importance of the sedimentation term in the overall phosphorus balance of the reservoir. At high flushing rates, sensitivities to the sedimentation coefficient and flushing rate approach zero for both models. In this

situation, the sedimentation process is relatively unimportant, and modest

errors in the specified flushing rate a.dor sedimentation coefficient can be

tolerated without having major impacts on the predicted pool concentration.

Because the sedimentation coefficient is estimated from highly simplified

empirical models (whereas the other input terms can be directly measured), its

sensitivity characteristics have a strong influence on model performance and

uncertainty over the range of flushing rates.

1-12

Chapter 1 Introduction
1.0

0.6

0.6

0.4

02

0

——— ——— —

p(J~, ,7 ~

,0-,~,,~~ ,

/0

/“

r ,.~”~” r SEDIMENTATION RATE

-

FLUSHING RATE

1 I i

0.1 1 10 1(KI

FLUSHING RATE, 1/ Yf

SENSITIVITY COEF = % CHANGE IN ERROR I

11%OHANGE IN FACTOR I

ERROR = OBSERVED POOL P

PREDICTED POOL P

+ +~~”

PREDICTED POOL P =

2%

WHERE: F = FLUSHING RATE (1/Yr)

P, = INFLOW TOTAL PHOSPHORUS CONCENTRATION = 50 mg/m3

K2 = SECOND-ORDER SEDIMENTATION COEFFICIENT = .1 m3/mg-yr

Figure 1.4. Sensitivity analysis of second-order phosphorus sedimentation

model

Figures 1.3 and 1.4 are intended primarily to demonstrate sensitivity analysis

concepts. They also illustrate some important basic characteristics of

empirical nutrient balance models:

a. Sensitivities are highest for inflow and pool phosphorus concentrations

over the entire range of flushing rates. This emphasizes the importance

of monitoring programs (tributary and pool) and data reduction procedures to modeling efforts.

b. Because of a higher sensitivity to phosphorus sedimentation, potential

prediction errors are greater for reservoirs with lower flushing rates.

Chapter 1 introduction 1-13
While pool nutrient concentrations can be predicted relatively easily from

inflow concentrations in reservoirs with high flushing rates, predictions of biological responses (as measured by chlorophyll a) may be more difficult because

of temporal variability in nutrient levels (induced by storm events, for example)

and/or controlling effects of turbidity and flushing rate. The importance of

obtaining accurate inflow and pool concentration estimates for model implementation has led to the development of the computer programs described in

subsequent chapters. FLUX and PROFILE are designed to make efficient use

of tributary and pool monitoring da~ respectively, in calculating the required

summary statistics.

Summary of Assessment Procedures

Figure 1.5 depicts the basic steps involved in applying the eutrophication

assessment procedures described in this and subsequent chapters. The “pathway” comprises four general stages:

a. Problem identification.

b. Data compilation.

c. Data reduction.

d. Model implementation.

Once the user has developed a working understanding of the model structures,

assumptions, and limitations by reviewing basic references and supporting

research (see References and Bibliography), most of the effort and cost would

typically be involved in the data compilation and data reduction stages. Three

computer programs have been written to assist at various stages of the analysis.

The functions of these programs are outlined below:

a. FLUX - estimation of tributary mass discharges (loadings) from grab

sample concentration data and continuous flow records.

b. PROFILE - display and reduction of pool water quality data.

c. BATHTUB - implementation of nutrient balance and eutrophication

response models.

Figure 1.5 summarizes the basic inputs, functions, and outputs of each supporting program. This chapter provides an overview of each analytical stage.

Details are given in subsequent chapters, along with examples and guidance for

use of the computer software.

1-14 Chapter 1 Introduction
PATHWAY PROCEDURES

PROBLEM ● DESCRIBE RESERVOIR AND/OR WATERSHED CHARACTERISTICS

DEFINITION ● DEFINE UATER WALITY MANAGEMENT OBJECTIVES

● IDENTIFY IMPACTS/CONTROL STRATEGIES TO BE EVALUATED

● DETERMINE STUDY TYPE:

DIAGNOSTIC

PREDICTIVE

● DETERMINE MODEL TYPE:

NUTRIENT BALANCE

EUTROPHICATION RESPONSE

DATA CCM4PILE TRIBUTARY C(NJIPILE RESERVOIR

CWPILATION AND DISCHARGE DATA POOL DATA

● HYDROLOGY ● HYDROLOGY

● UATERSHED ● MORPHWETRY

CHARACTERISTICS ● WATER QUALITY

● UATER QUALITY

DATA RUN FLUX PROGRAM RUN PROFILE PROGRAM

REDUCTION ● DATA ENTRY ● DATA ENTRY

● DIAGNOSTIC DISPLAYS ● DIAGNOSTIC DISPLAYS

● DATA STRATIFICATION ● OXYGEN DEPLETION

● LOADING CALCULATIONS CALCULATIONS

ANNUAL ● MIXED-LAYER SUMMARIES

SEASONAL

M(X)EL RUN BATHTUB PROGRAM

IMPLEMENTATION ● SEGMENTATION

● SUBMCX)EL SELECTION

NUTRIENT BALANCE

EUTROPHICATION RESPONSE

● DATA ENTRY

● CALIBRATION AND TESTING

● SENSITIVITY ANALYSIS

● ERROR ANALYSIS

● APPLICATIONS

DIAGNOSTIC

PREDICTIVE

Figure l.5. Assessment pathways

Problem identification

The problem identification stage defines thescope ofthe modeling effort.

The following factors are specified:

a. The reservoir, watershed, and water uses.

b. Water quality standards andmanagement objectives.

c. Whether the reservoir is existing or planned.

d. Specific managementstrategies orimpacts to reevaluated.

Chapterl Introduction 1-15
e. Types of evaluations to be performed.

(1) Diagnostic.

(2) Predictive.

J Classes of models to be used.

(1) Nutrient balance.

(2) Eutrophication response.

If the analysis is not directed toward evaluating specific management strategies

or impacts, the general objective may be to develop perspectives on reservoir

water quality conditions and controlling factors as part of a “diagnostic” study.

This may lead, in turn, to future evaluations of specific management strategies

designed for water quality control.

Two general types of evaluations maybe pefiormed. In a diagnostic mode,

the models are used as a framework for interpreting monitoring data from the

reservoir and/or its tributaries. A diagnostic study provides insights into factors

controlling algal productivity and rankings of trophic state indicators versus

water quality criteria and/or data from other CE reservoirs. In a predictive

mode, the models are applied to predict future conditions in a planned reservoir

or in an existing reservoir undergoing changes in nutrient loading regime and/or

other controlling factors.

Model classes are determined by the types of analyses to be performed.

Both nutrient balance and eutrophication response models are required for a

predictive analysis. Diagnostic studies of existing reservoirs can be based

exclusively upon response models and pool water quality data; this provides a

basis for defining existing conditions and controlling factors, but not for evaluating watershed/reservoir or load/response relationships. Monitoring requirements are generally more stringent for implementing nutrient-balance models

than for implementing eutrophication-response models.

Response models and pool monitoring data may be used in preliminary

diagnostic studies aimed at defining reservoir conditions. In some reservoirs,

this may be followed by implementation of a more elaborate monitoring program designed to quanti~ nutrient loadings and to support nutrient-balance

modeling. Priorities can be established based upon the severities of existing

eutrophication-related problems (if any), intensities and types of water use, and

potential for future improvement or degradation owing to changes in loading

regime.

1-16 Chapter 1 Introduction
Data compilation

As shown in Figure 1.5 data compilation occurs in two general areas. The

reservoir data required for implementation of eutrophication-response models

include morphometric characteristics, outflow hydrology, and pool water quality obtained over at least one complete growing season (three preferred). The

watershed data required for implementation of nutrient-balance models include

basic watershed characteristics (e.g., subwatershed delineations, topography,

geology, land uses, point source inventories) and tributary flow and nutrient

concentration data taken at reservoir entry points over at least one full water

year (three preferred). Details on data requirements and suggested monitoring

designs are given later in this chapter.

Data reduction

In the data reduction phase, pool and tributary water quality data are

reduced or summarized in forms which can serve as model input. Since the

models generally deal with conditions averaged over a growing season within

defined reservoir areas (segments), data reduction involves the averaging or

integration of individual measurements, sometimes with appropriate weighting

factors.

The FLUX program is designed to facilitate reduction of tributary inflow

monitoring data and reservoir outflow monitoring data. Using a variety of calculation techniques, FLUX estimates the average mass discharge or loading

that passes a given tributary monitoring station, based upon grab-sample concentration data and a continuous flow record. Potential errors in the estimates

are also quantified and can be used to (a) select the “best” or least error loading

estimate, (b) assess data adequacy, and (c) improve future tributary monitoring

efficiency via optimal allocation of sampling effort among seasons and/or flow

regimes. Graphic displays of concentration, flow, and loading data are also

provided for diagnostic purposes.

The PROFILE program facilitates analysis and reduction of pool water quality data from existing reservoirs. A variety of display formats are provided to

assist the user in developing perspectives on spatial and temporal water quality

variations within a given reservoir. Algorithms are included for calculation of

hypolirnnetic oxygen depletion rates and for robust estimation of areaweighted, surface-layer mean concentrations of nutrients and other response

measurements used in subsequent modeling steps.

ModeI implementation

The BATHTUB program applies empirical eutrophication models to

morphometncally complex reservoirs or to collections of reservoirs. The program performs water and nutrient balance calculations in a steady-state,

Chapter 1 Introduction 1-17
spatially segmented hydraulic network which accounts for advective transport,

diilbsive transport, and nutrient sedimentation. Eutrophication-related water

quality conditions (expressed in terms of total phosphorus, total nitrogen,

chlorophyll a, transparency, organic nitrogen, particulate phosphorus, and

hypolimnetic oxygen depletion rate) are predicted using empirical relationships

previously developed and tested for reservoir applications (Walker 1983).

To reflect data limitations or other sources of uncertainty, key inputs to the

model can be specified in probabilistic terms (mean and CV). Outputs are

expressed in terms of a mean value and CV for each mass balance term and

response variable. Output CVS are based upon a first-order error analysis

which accounts for input variable uncertainty and inherent model error.

As shown in Figure 1.5, applications of BATHTUB would normally follow

use of the FLUX program for reducing tributary monitoring data and use of the

PROFILE program for reducing pool monitoring data. Use of the data reduction programs is optional if independent estimates of tributary loadings and/or

average pool water quality conditions are used.

Data Requirements

This section summarizes data requirements to support model applications.

The following categories are discussed:

a. Watershed characteristics.

b. Water and nutrient loadings.

c. Reservoir morphometry.

d Pool water quality and hydrology.

Before describing each area in detail, it is appropriate to discuss some general

concepts and guidelines that may be helpful in the design of a reservoir study.

IrI a typical application, most of the effort and cost would be expended in

the critical data-gathering phase, Information sources would generally include

project design memorand~ basin planning reports, historical hydrologic and

water quality dat~ and water quality data gathered specifically for the study.

Data requirements can be given rather explicitly, as determined by the list of

model input variables. Specific data sources and monitoring program designs

cannot be dictated, however, because they are influenced by unique aspects of

each reservoir and its watersheds, the extent of existing dat~ logistic considerations, and study resources.

1-18

Chapter 1 Introduction
Compilation and review of existing data are important initial steps in conducting a reservoir study. Preliminary application of models using existing data

(even if inadequate) can highlight data strengths and weaknesses and help to

focus fhture monitoring activities. In some cases, existing data maybe adequate to support modeling efforts. When existing data are inadequate or

unavailable, a phased monitoring program is generally indicated. The first

phase involves a small-scale program designed to obtain preliminary data for

use in designing efficient monitoring programs for subsequent years. A phased

study can be a relatively cost-effective means of data acquisition.

Given specific objectives (e.g., quanti@ng annual total phosphorus load or

growing-season mean chlorophyll a concentration in an existing reservoir),

statistical methods can be applied to improve monitoring efficiency. As the

efficiency of a monitoring program increases, the amount of uncertainty (variance) in the measured variable decreases. Monitoring efficiency may be

improved by optimizing the allocation of sampling effort, subject to logistic and

economic constraints. Examples of such optimization procedures include the

following:

a. Allocation of samples among flow regimes to estimate loadings from a

given tributary.

b. Allocation of samples among tributaries to estimate total reservoir

loading.

c. Allocation of samples among stations, depths, and dates to estimate

reservoir-mean concentrations.

Phased studies or useful existing databases are required to implement these

optimization procedures. Because of logistic constraints, multiple monitoring

objectives, and other factors, “optimal” designs are rarely implemented;

instead, they can be used to indicate appropriate directions for adjusting existing sampling designs.

Watershed characteristics

Basic watershed information is used in the development and interpretation

of hydrologic and nutrient loading dat~ in the design of tributary monitoring

programs, and in the assessment of problem sources and control strategies.

Maps (U.S. Geological Survey topographic or other) are the most useful formats for this type of information. Separate maps (or a series of transparent

overlays) can be used to summarize the following types of watershed

tiormation:

a. Elevation contours.

b. Subwatershed delineations.

Chapter 1 Introduction 1-19
c.

d.

e.

J

Dominant land uses.

Soil types.

(1) Hydrologic soil groups.

(2) Erosion potential.

Point sources.

Monitoring station locations.

Aerial photos, regional planning agencies, design memorand~ Geographic

Information System (GIS) databases, and/or published basin reports are generally usefid sources of watershed Mormation. Soils information would also be

available from the Soil Conservation Service. The information should be

summarized in a tabular form by subwatershed.

Land uses, soil types, topography, and point sources are important factors in

dete rmining runoff and nutrient export from a given subwatershed. This type

of tiormation is used to do the following:

a. Design tributary monitoring programs (place stations).

b. Interpret watershed monitoring data (compare monitored runoff and

loads from different subwatersheds to develop perspectives on regional

land use/nutrient-export relationships).

c. Estimate loadings from unmonitored watersheds (use land use/nutrientexport factors or proportion monitored loads from a nearby watershed

with similar land uses and soil types, based upon drainage area).

Projections of future land use and point-source nutrient loads are also required

for predicting impacts of watershed development.

Water and nutrient loadings

The formulation of water and nutrient balances for the reservoir is a critical

step in the empirical modeling process. The following components are of

concern:

1-20

a. Water.

b. Total phosphorus.

c. ortho phosphorus.

Chapter 1 Introduction
d. Total nitrogen.

e. Inorganic nitrogen (Ammonia+ Nitrate+ Nitrite),

f Conservative substance (e.g., chloride).

Water and total phosphorus balances are essential. The other components are

optional, While nitrogen balances are desirable, they may be omitted if monitoring data and/or preliminary mass balance calculations indicate that the reservoir is clearly not nitrogen limited under existing and future loading conditions.

The ortho-phosphorus and inorganic nitrogen (ammoni~ nitrate, and nitrite)

loading components are required for (optional) implementation of nutrient sedimentation models which account for the “availability” or partitioning of total

nutrient loads between dissolved and particulate (or inorganic and organic)

fractions. Conservative substance balances are useful for testing water balances and calibrating diffhsive transport rates in segmented reservoirs.

The nutrient species listed above correspond to those monitored by the

U.S. Environmental Protection Agency (EPA) National Eutrophication Survey,

the primary data source used in model development and testing. Monitoring of

other species (particularly, total dissolved phosphorus) may be desirable for

deftig inflow nutrient partitioning and availability. Because of existing data

constraints, however, the models are based upon the above species.

Generally, balances should be formulated over both annual and seasonal

(e.g., May-September) time periods. Annual balances should be calculated on

a water-year (versus calendar-year) basis. While traditional nutrient loading

models deal with annual time scales, seasonal loadings are better predictors of

trophic status in many reservoirs. The methodologies presented in subsequent

sections can be applied separately to annual and seasonal nutrient balance data.

Nutrient residence time criteria are used to assess the appropriate time scale for

each reservoir.

The nominal definition of seasonal (May-September) can be adjusted in

specific applications, depending upon seasonal variations in inflow hydrology

and, especially, pool level. For example, if a full recreational pool were maintained June through August and much lower elevations were maintained during

other months for flood control purposes, then a June-August time scale may be

more appropriate for seasonal nutrient balances. Generally, seasonal balances

are less important in projects with little or no inflow or outflow during the summer months. The formulation of both seasonal and annual balances is generally

recommended for all applications and does not substantially increase monitoring requirements, since both sets of loading estimates can be derived from the

same monitoring program.

For each component and time scale, a control volume is drawn around the

reservoir (or reservoir segment) and the following mass balance terms are

quantified:

Chapter 1 Introduction 1-21
a. Total inputs.

b. Total OU@ltS.

c. Increase in storage.

d. Net loss.

Table 1.2 outlines the specific elements of each term and general data sources.

Since water is conservative, the net loss term in the water balance (estimated by

difference) reflects errors in the estimates of the other water balance terms. For

nutrients, the net loss term can be estimated by difference or, in a predictive

mode, by using empirical nutrient sedimentation models which have been calibrated and tested for reservoir applications.

Table 1.2

Mass Balance Terms and Data Sources

Mass Balance Terms General Data Sources

Inputs

Gauged tributaries Direct monitoring

Ungauged tributaries Drainage area approximations

Watershed models

Direct point sources Direct monitoring

Per capita loading factors

Shoreline septic systems Per capita loading factors

Hydrogeologic studies

Direct groundwater inputs Hydrogeologic studies

Atmospheric Local precipitation data

Regional atmospheric deposition

outputs

Outflows and withdrawals Direct monitoring

Evaporation Local climatologic data

Increase in storage Pool elevation and morphometry data

Vet loss Calculated by difference

Represents error in water balance

Emperical nutrient sedimentation models

In general, direct monitoring is recommended to quanti& major flow and

nutrient sources. Table 1.3 summarizes “minimal” and “desirable” designs for

1-22

tributary monitoring programs and methods for quanti&ing other loading components. These are intended as general guidelines to be modified based

Chapter 1 Introduction
Chapter 1 Introduction 1-23
1-24

Chapter1 Introduction
upon site-specific conditions. The basic design for major tributaries and outflows consists of continuous flow monitoring and a combination of periodic

grab-sampling and event monitoring for concentration. A sampling program

weighted toward high-flow regimes is generally desirable for estimation of

loadings. The multiple objectives of estimating both annual and seasonal loadings should be considered in designing surveys. The FLUX program can be

applied to historical and/or preliminary monitoring data to assist in sampling

design.

While balances are formulated for the study (monitored) period, a historical

hydrologic record is desirable to provide perspective on study conditions in

relation to long-term averages and extremes. Long-term hydrologic records are

usually available for reservoir discharge sites and major tributary inflows. If

not, records from a nearby, long-term station, possibly outside the watershed(s), can be correlated with monitoring data from study sites and used to

extrapolate the record.

Reservoir morphometry

Reservoir morphometric information is required for nutrient balance and

eutrophication response models. It is usually readily available from project

design memoranda and other sources. A map indicating the following basic

idormation is useful:

a. Distance scale.

b. Shoreline for typical and extreme pool levels.

c. Bottom elevation contours or soundings.

d. Tributary inflows and any direct point sources.

e. Pool and tributary monitoring station locations.

The following morphometric data should also be compiled in tabular form:

a. Elevation/area volume table.

b. Typical operating pool elevations (rule curve).

c. Reservoir bottom elevation at each pool sampling station.

d. Volumes, surface areas, and lengths of major reservoir segments at

typical operating elevations.

This tiormation is used in data reduction (PROFILE) and modeling

(BATHTUB).

Chapter 1 Introduction 1-25
Pool water quality and hydrology

In studies of existing reservoirs, pool water quality and hydrologic data are

used for the following purposes:

a. Assessing trophic state, related water quality conditions, and controlling

factors.

b. Model testing and calibration.

Expressed in terms of model variables, the primary objectives of the monitoring program are to obtain the data required for calculation of growingseason, mixed-layer, average concentrations of the following variables:

a. Total phosphorus.

b. Dissolved ortho-phosphorus.

c. Total nitrogen.

d Total inorganic nitrogen.

e. Organic nitrogen.

J Chlorophyll a (corrected for phaeophytin).

g. Transparency (Secchi depth).

J Conservative substance.

In stratified reservoirs, another primary objective is to estimate hypolimnetic

and metalimnetic oxygen depletion rates. Secondary objectives are to develop

perspectives on spatial variations, vertical stratification, basic water chemistry,

and other variables which are directly or indirectly related to eutrophication.

General guidelines for designing pool monitoring programs are outlined in

Table 1.4. Basic design features include component coverage, station locations, sample depths, temporal frequency, and duration. An appreciation for

spatial and temporal variability of conditions within the reservoir may be

obtainable from historical data and can be very useful in designing future

surveys.

1-26

The objectives of identifying spatial gradients and calculating reservoirmean conditions suggest somewhat different emphasis for station placement.

Generally, horizontal variations parallel to the net advective flow along the

main axis of a major tributary arm are much more important than variations

perpendicular to the flow. If they exist, longitudinal gradients in nutrients, algal

biomass, and transparency are usually steepest in upper pool areas; this

Chapter 1 Introduction
Table 1.4

General Guidelines for Designing Reservoir Pool Monitoring Programs

Feature Minimal Design Desirable Design

Water quality Temperature Dissolved Oxygen Add:

components Total P Ortho-P Total Silica Total Organic Carbon

Organic N Ammonia N Total Iron Total Manganese

Nitrite-Nitrate N Transparency True Color Sulfides

Alkalinity pH Suspended Solids (total and organic)

Conductivity Turbidity Oxidation reduction potential

Chlorophyll a (corrected for Phaeophytin) Algal cell counts (ASU) by type

Dominant algal types

Station locations Minimum of three stations/reservoir Add stations in smaller tributary arms and

(near-dam, midpooi, upper-pool) embayments

Distributed along thalweg of each major Critical reservoir use areas

tributary arm in representative areas Above and below junctions of tributary

Maximum distance between stations along arms

thalweg = 20 km Maximum distance between stations along

thalweg = 10 km

Duration of sampling One growing season Three growing seasons

(typically April-October)

Bracket stratified period, including one round

each during spring and fail isothermal

periods

Frequency - laboratory Monthly or biweekly Biweekly or weekly

samples

Depths - laboratory Mixed-1ayer composite Unstratified reservoirs: surface,

samples Depth-integrated hose sampling mid-depth, and 1 m off bottom

Stratified reservoirs:

3 samples in mixed layer

1 sample in thermocline

3 samples in hypolimnion

1 m from top of hypolimnion

mid-depth

1 m off bottom

Frequency - field profiles Unstratified reservoirs: same as laboratory Unstratified reservoirs: same as laboratory

Unstratified reservoirs: samples samples

Temperature Stratified reservoirs: biweekly in spring to Stratified reservoirs: weekly in spring to

Dissolved oxygen early summer (until onset of anoxia), then early summer (until onset of anoxia), then

monthly biweekly

Depths - field profiles 1-m intervals, top to bottom Increase spatial frequency in thermocline

Temperature and other zones with steep gradients

Dissolved oxygen

Reservoir hydrology Month-end values Daily values

Surface elevation Monthly totals Daily totals

Outflow volumes

Chapter 1 Introduction 1-27
suggests that stations should be more closely spaced in upper pool areas to

permit adequate resolution of gradients. Most of the reservoir volume, however, is usually located in the lower pool areas, where width and depth tend to

be greater and spatial gradients tend to be less pronounced; this suggests a

greater emphasis on lower pool stations for the purposes of calculating reservoir means. Because of these trade-offs, it is difficult to use a statistical

approach for optimizing station placement within a given reservoir.

Ghen multiple sampling objectives, a reasonable design rule is to distribute

stations throughout representative areas of the reservoir. The size, morphometric complexity, and loading distribution of a reservoir largely determine the

required number of stations. A minimum of three stations (upper-pool, midpool, and near-dam) are recommended for small projects with simple morphometry. Based upon reservoir morphometnc information, weighting factors

can be applied to data from each station in calculating area-weighted reservoir

means (see PROFILE).

To provide bases for characterizing variability and developing robust statistical summaries, surveys should be designed to provide replication (some

overlap in information content) of measurements made in each reservoir area

or segment during each sampling round. There are several ways in which

replication can be built into survey designs, including the following:

a. Multiple sampling at a given date, station, and depth.

b. Multiple sampling with depth within the mixed layer at a given date and

station.

c. Multiple sampling stations within a given reservoir segment or area,

d. High temporal sampling frequencies, permitting aggregation of data

from adjacent sampling dates.

In designing surveys, combinations of the above strategies can be employed

to provide data which include at least three measurements for each reservoir

segment and sampling round. In the “desirable” design (see Table 1.4), three

samples are suggested within the mixed layer for each station and date. Since

the stratum is mixed, on the average, the three samples can be treated as replicates. Other strategies listed above can be used in conjunction with depth

sampling to provide replication. Another monitoring objective is to sample

each station on each sampling round; this greatly simplifies reduction of the

data and error analysis, as implemented in the PROFILE program.

1-28

Assuming representative station distribution and proper sampling and analytical techniques, the “precision” of a mean, surface-layer, growing-season

value depends largely upon the number of sampling rounds and the inherent

temporal variabilities of water quality components in the reservoir being studied. For sampling periods of roughly a week or longer, the variance of the

Chapter 1 Introduction
mean is roughly inversely proportional to the number of rounds. Based upon

analyses of variance applied to model development data sets (Walker 1980,

198 1), temporal variance components of phosphorus, transparency, and chlorophyll a are typically 0.31,0.33, and 0.62, respectively, expressed as CVS. Figure 1.6 shows the estimated accuracies of reservoir mean concentrations

computed from sampling designs with between 1 and 30 sampling rounds over

a range of temporal CVS. The “value” of each additional round, as measured

by the reduction in the mean CV, decreases as the total number of rounds

increases. This figure provides a rough perspective on design sensitivity and a

basis for interpreting the reliability of data from historical monitoring activities,

provided the sampling regimes were both specified and representative.

TEMPORALCOEPflCKt4TOF VARIATION

o 0.2 0.4 0.6 0.8 1.0

1

90

TYPICAL VALUES FOR GE RESERVOIRS

a

CHL-A

TOTALP ~

BIMONTH1.Y

MONIHLY

BIWEEKLY

WEEKLY

Figure 1.6. Estimated accuracy of reservoir mean concentration computed from

sampling designs with between 1 and 30 sampling rounds over a

range of temporal CVS

The “adequacy” of a given monitoring program is partially determined by

the precision of the mean concentration estimates calculated from the data.

Because of the limited pool sampling schedule employed by the EPA National

Eutrophication Survey (three to four sampling rounds per growing season),

typical error CVS were on the order of 0.18 for mean total phosphorus, 0.18 for

mean transparency, and 0.28 for mean chlorophyll a. More precise estimates

(e.g., mean CVS less than 0.10 for nutrients and transparency and 0.15 for

mean chlorophyll a) are desirable for model applications in a reservoir management context.

Chapter 1 Introduction 1-29
The purpose of sampling in and below the thermocline (Table 1.4) is to

provide information on vertical stratification and the accumulation and transformation of nutrients within the hypolimnion. Many important secondary

water quality effects of eutrophication are expressed in bottom waters, including oxygen depletion, development of reducing conditions, nutrient accumulation, iron and manganese releases, and sulfide and ammonia generation. While

nutrient data from the hypolimnion are not used exclusively in the models, they

are important for developing an understanding of nutrient cycling and reservoir

processes. Since metaiimnetic and hypolimnetic samples are less important for

trophic state assessment and model implementation, however, sampling fi-equencies in and below the thermocline can be lower than those used for the

mixed layer.

1-30

Chapter 1 Introduction
2 FLUX

FLUX Overview

FLUX is an interactive program designed for use in estimating the loadings

of nutrients or other water quality components passing a tributary sampling

station over a given period of time. These estimates can be used in formulating

reservoir nutrient balances over annual or seasonal averaging periods appropriate for application of empirical eutrophication models. Data requirements

include (a) grab-sample nutrient concentrations, typically measured at a weekly

to monthly frequency for a period of at least 1 year, (b) corresponding flow

measurements (instantaneous or daily mean values), and (c) a complete flow

record (mean daily flows) for the period of interest.

Using six calculation techniques, FLUX maps the flow/concentration relationship developed from the sample record onto the entire flow record to

calculate total mass discharge and associated error statistics. An option to

strati~ the data into groups based upon flow, date, and/or season is also

included. In many cases, strati&ing the data increases the accuracy and precision of loading estimates. Uncertainty is characterized by error variances of the

loading estimates. A variety of graphic and tabular output formats are available

to assist the user in evaluating data adequacy and in selecting the most appropriate calculation method and stratification scheme for each application. FLUX

provides Mormation which can be used to improve the efficiencies of future

monitoring programs designed to provide data for calculating loadings and

reservoir mass balances.

The succeeding sections of this chapter contain descriptions of the following

topics:

a. Input data requirements.

b. Theory.

c. Program operation.

d Typical application sequence.

Chapter 2 FLUX 2-1
e. Procedure outline.

f Data-entry screens.

g. Data file formats.

h. Documented session.

Input Data Requirements

Two data sets are required to run FLUX. One defines sample characteristics (date of collection, concentration, and instantaneous flow). The other

describes the complete flow record (date, mean daily flow) over the period of

interest. Most of the effort in applying FLUX is generally involved in setting up

the required data files. To facilitate this effort, FLUX can read files in a variety

of formats, as described in a subsequent section (see Data file formats).

The function of the program is to use the water quality information in the

sample data set to estimate the mean (or total) loading which corresponds to

the complete flow distribution over the period of interest. All program calculations and output are in metric units, with flows expressed in million cubic

meters (= cubic hectometers, hm3) per year, concentration in milligrams per

cubic meter (parts per billion), and loading in kilograms per year. The data can

be stored in other units and converted to the appropriate units when accessed

by FLUX (see Appendix B). For a typical nutrient-balance study, sample data

sets would include the following components: instantaneous flow, total phosphorus, ortho-phosphorus, total nitrogen, inorganic nitrogen, and a conservative

substance such as chloride. Potential applications of the program are not

restricted to these constituents, however.

The sample data are normally derived from periodic grab-sampling. Flow

measurements stored with the water quality data should correspond to the times

of sampling. Daily mean flows can be used in the absence of instantaneous

flow measurements; FLUX can automatically pair sample concentrations with

corresponding daily mean flows specified in the complete flow record. Generally, samples are collected periodically (weekly to monthly) over a year and

over a range of flow regimes. If intensive storm-event monitoring has been

conducted, resulting discrete or composite samples should be summarized

before they are accessed by FLUX; in this case, each record in the sample data

set includes an event mean flow and a flow-weighted mean concentration for

each component. Differences in the duration of composite samples are not

considered in the current version of FLUX. If continuously sampled events

represent a significant fraction of the total loading over the estimation period,

the program may overestimate the error variance of the loading estimates. To

avoid severe biases in the load estimates, special consideration must be given to

2-2

Chapter 2 FLUX
the specification of sample flows in small, flashy streams or storm sewers (see

Typical application sequence).

The reliability of loading estimates strongly reflects monitoring program

designs. Water quality samples should be taken over the ranges of flow regime

and season which are represented in the complete flow record. For a given

number of concentration samples, loading estimates will usually be of greater

precision if the sampling schedule is weighted toward high-flow seasons and

storm events, which usually account for a high percentage of the annual or seasonal loading. While the calculation methods described below are designed to

make efficient use of the available datq they cannot work miracles. If the basin

dynamics are such that annual loadings are dominated strongly by a few

extreme events, no calculation procedure will give an acceptable answer without representative samples from at least some of the major events. FLUX

provides graphic and tabular output which can help to evaluate the adequacy of

the sample data set for use in load calculations.

Sample data files can include up to 64 fields representing different water

quality components and other sample descriptors. Loading calculations are

performed for only one component at a time. Concentrations which are entered

as zero or negative values are assumed to be missing. Sample records with

zero or negative flow values are not used in load calculations. All FLUX calculations are performed in computer memory; source data files are not modified.

The flow data set specifies the complete flow distribution, which is generally

derived from continuous stage or velocity measurements made at or near the

water quality monitoring site. Typically, flow records consist of a mean flow

for each day in the period of interest. In the absence of daily measurements,

other averaging flow periods can also be used (weekly, monthly), but with

some loss of accuracy. If a continuous flow record is not available for a particular site, one might be constructed using simulation techniques or correlating

available flow measurements with simultaneous data from a nearby benchmark

station with a continuous flow record and similar watershed.

Missing values are permitted in the flow distribution file, but they should be

avoided by estimating them independently. Zero flow values are acceptable to

permit applications to intermittent streams. Negative flow values (reverse

flows) are treated as zeros. Average flow rates and loads calculated by FLUX

reflect total transport in the downstream direction. This may be different from

the net transport estimates appropriate for use in BATHTUB or other massbalance models. If the stream contains significant reverse flows, an option is

available for calculating total transport in the upstream direction; this essentially

involves reversing the sign of the sample flow and daily flow data. The net

downstream transport can subsequently be calculated by subtracting the total

upstream transport rates from the total downstream transport rates.

It is convenient to define the time period represented in the sample data set

as the “sampling period” and that represented in flow data set as the “averaging

Chapter 2 FLUX 2-3
period.” Normally, these two periods correspond, i.e., the flow data set contains a mean daily flow value for each day in the year of water quality sampling.

If the sampling and averaging periods do not correspond (e.g., the sample set

might contain data from 1978 through 1981, and the flow set might contain

daily flows for 198 1), then the user is making the assumption that the flow/

concentration dynamics of the stream are stable, i.e., that concentrations

measured between 1979 and 1980 are also representative of those measured in

1981. Using samples from outside the averaging period can increase the

accuracy and precision of the loading estimates (by increasing the number of

samples and improving the coverage of flow regimes); this may introduce bias

in the loading estimates, however, if there are significant year-to-year variations

in the flow/concentration relationship caused by variations in climate, hydrology, or watershed land use. In each program run, the user specifies the date

ranges and/or season ranges to be used for samples and flows; this permits

estimation of both annual and seasonal loadings from source data files containing data from 1 or more years of monitoring.

The flow data set may include daily flows from the year(s) of water quality

monitoring, as well as other periods which may represent “low-flow,”

“average,” and “high-flow” years. Provided that a sufficiently wide range of

flow regimes are sampled, this permits extrapolation of the sample record, i.e.,

estimation of year-to-year variations in loadings based upon sample data from a

specific year or years.

FLUX can handle problems containing up to 900 samples and 8,000 daily

flow records (-22 years), These constraints apply to data read into computer

memory at the start of program execution, not the size of the input data files.

Since the user is prompted for the ranges of sample and flow dates to be used

in a given run, the input data files can be much larger than indicated above.

Users should check the online documentation file (accessed through the HELP

option of the main menu) for maximum problem dimensions and other program changes in updated versions of FLUX (Version 5.0 is documented here).

Theory

Loading calculation methods

Table 2.1 lists the equations used to calculate the mean loading and error

variance using six alternative methods. Method applicability depends upon

flow/ concentration dynamics and sampling program design in each application.

Walker (198 1,1987) provides details on the derivation and testing of each

method. The FLUX procedure “Calculate/Loads” provides a one-page summary of loadings calculated using each method. The user must decide which

method is most appropriate for each application, based upon factors discussed

below. In most cases, particularly if the data are properly stratified (see Data

stratification), the calculation methods will give estimates which are not

2-4

Chapter 2 FLUX
Table 2.1

Estimation Algorithms Used in FLUX Program

Method 1 - Direct Mean Loading

w, = Mean(w)

Method 2- Flow-Weighted Concentration (Ratio Estimate)

W2 = WI Mean(Q) /Mean(q)

Method 3- Modified Ratio Estimate (Bodo and Unny 1983)

W3 = W2(1 + FWJn)/( 1 + FJn)

Method 4- Regression, First-Order (Walker 1981)

W4 = W1[Mean(Q)/Mean( q)lb+’

Method 5- Regression, Second-Order (Walker 1987)

W5 = W4(1 + r FJ/(1 + r Fq)

Method 6- Regression Applied to Individual Daily Flows

w= = ~jexp [ a + (b+ l)ln(Qi) + SE2/2 ]

where

Ci =

qi =

b =

a =

Wi =

F = wq

Fq =

F~ =

Qj =

n =

N =

w“ =

Vm =

r =

Xj =

SE =

Mean(x)

Var(x)

Cov(xry)

measured concentration in sample i (mg/m3)

measured flow during sample i (hm3/year)

slope of In(c) versus In(q) regression

intercept of In(c) versus In(q) regression

measured flux during sample i = qi Ci (kg/year)

Cov(w,q) / [Mean(w) Mean(q)]

Var(q) / [Mean(q) Mean(q)]

Var(Q) / [Mean(Q) Mean(Q)]

mean flow on day j (hm3/year)

number of samples (i)

number of daily flows (j)

estimated mean flux over N days, method m (kg/year)

variance of estimated mean flux, method m (kg/year)z

0.5 b(b + 1)

sum over N dates in daily flow record

standard error of estimate for In(c) versus In(q)

regression

= mean of vector x

= variance of vector x

= covariance of vectors x and y

Chapter 2 FLUX 2-5
significantly different from each other. Thus, the choice of method will not be

critical.

Desired properties of the loading estimates include minimum bias and minimum variance. The distinction between bias and variance (analogous to

“accuracy” and “precision”) is important. A biased procedure will give the

wrong answer, even for an infinite number of samples, whereas variance in the

mean can generally be reduced by increasing the number of independent random samples. The seriousness of bias depends upon its size relative to the

variance of the mean or the standard error of estimate. Biases less than 10 percent of the standard error account for less than 1 percent of the total mean

squared error and are generally considered negligible (Cochran 1977). Bias in

a loading estimate can come from two sources: unrepresentative sampling or

the use of an inappropriate calculation method. These sources are discussed

below.

Consistent problems with sample collection, handling, and analytical procedures can cause one type of unrepresentative sampling; there is little that can be

done about these problems at the calculation stage. Another, more subtle, but

generally more common type of unrepresentative sampling results from differences in the distributions of flows between the sampling dates and the entire

averaging period. Sampled flows may tend to be higher or lower, on the

average, than the complete distribution of flows or contain a higher or lower

percentage of extreme flows. This can lead to bias in the estimate if the calculation procedure does not take the relative flow distributions into consideration

by directly representing the flow/concentration relationship and/or by strati~ing

the sample, as described below.

Even if the sampled and total flow distributions are equivalent, bias can be

introduced as a result of the calculation method. For example, loading calculated as the product of the mean sample concentration and the mean flow over

the averaging period would be badly biased if flow and concentration are (even

weakly) correlated (Walker 198 1). Because of the potential bias associated

with this method, it is not included in the program. The six included methods

have been selected and tested so that, for representative samples, they should

not introduce significant bias except under special conditions discussed below

for each method. The extent to which the methods can minimize variance in

the loading estimates is limited ultimately by the sample data sets.

Method applicability depends upon the relationship between concentration

and flow. In FLUX, this characteristic is represented by the slope of a

log(Concentration) versus log(Flow) regression (C/Q slope) derived from the

sample data set. Typically, the C/Q slope approaches -1 at monitoring stations

which are downstream of major point sources. The slope may approach or

exceed 1 at monitoring stations where the load is generated as a result of runoff

or high-flow events, particularly for particulate components. In many watersheds, the C/Q slope for total phosphorus varies with flow (negative at low

flows to positive at high flows). FLUX graphic and tabular output helps to

2-6

Chapter 2 FLUX
characterize the concentratiordflow relationship; this characterization is essential to selecting the appropriate calculation method and developing reliable

loading estimates.

Method 1 (direct load averaging) is the simplest of the calculation schemes.

It gives unbiased results only if the samples are taken randomly with respect to

flow regime. This method completely ignores the unsampled flow record and

generally has higher variance than the other methods because the flow record

on the unsampled days is not considered. This method is most appropriate for

situations in which concentration tends to be inversely related to flow (C/Q

slope approaching -1; loading does not vary with flow). This might occur, for

example, at a station which is below a major point source and the flow/

concentration relationship is controlled by dilution.

Method 2 bases the loading estimate on the flow-weighted average concentration times the mean flow over the averaging period. This amounts to a “ratio

estimate” according to classical sampling theo~ (Cochran 1977). This method

performs best when flow and concentration are unrelated or weakly related.

Some bias may occur for extreme flow/concentration relationships. In test

simulations of a stream with a C/Q slope 0.75, Method 2 overestimated loadings by an average of 10 percent (Walker 1987). This bias can be substantially

reduced by stratifying the samples into groups of relatively homogeneous concentration and applying the method separately to each group, as described in

more detail below. This is perhaps the most robust and widely applicable

method, especially when applied to stratified data sets.

Method 3 modifies the Method 2 estimate by a factor that is designed to

adjust for potential bias in situations where concentration varies with flow. The

factor was developed byBeale(1962) and applied in a load estimation method

developed by the International Joint Commission(IJC)(1977), as described by

Bodo andUnny(1983, 1984). Trial simulations indicate that, compared with

Method 2, this procedure is moderately successful at reducing bias but tends to

have slightly higher mean squared error for streams with C/Q slopes greater

than or equal to zero (Walker 1987).

Method 4 is the regression method developed by Walker (1981). This

method adjusts the flow-weighted mean concentration for differences between

the average sampled flow and the average total flow using the C/Q slope. It

should not be used in cases where the daily flow data set contains a significant

number of zero flow values. This method petiorms well over a range of C/Q

slopes. Some bias is introduced at high C/Q slopes. At a slope of 0.75, for

example, simulated bias is 13 percent of the mean loading but accounts for only

6 percent of the total mean squared error (Walker 1987). Additional simulations indicate that bias also occurs if the C/Q slope is highly nonlinear (i.e.,

quadratic or higher order polynomial). This problem can be resolved by strati-

&ing the sample so that the relationship is approximately linear within each

group.

Chapter 2 FLUX 2-7
Method 5 modifies the Method 4 estimate by a factor accounting for differences in variance between the sampled and total flow distributions (Walker

1987). The derivation of the method is based upon expected value theory

(Benjamin and Cornell 1970). Method 5 should not be used in cases where the

daily flow data set contains a significant number of zero flow values. As for

Method 4, bias resulting from nonlinearity in the log (c) versus log (q) relationship can be reduced by strati$ing the data.

Method 6 is another regression-based calculation method. For each stratum, the C/Q regression equation is applied individually to each daily flow

value. In contrast, Methods 4 and 5 use only the flow means and variances. A

small correction for bias resulting from the log transformation is also included.

This method is often appropriate for generating daily, monthly, or yearly load

time series using an optional FLUX procedure designed for this purpose

(Calculate/Series). Relatively intensive sample data sets and well- defined

concentration/flow relationships are required for reliable application of this

method. Method 6 is generally preferred over the other regression-based

methods when the flow/concentration relationship is well defined. In applications to small, flashy streams, special consideration must be given to the specification of sample flows to avoid bias in Method 6 estimates (see Typical

application sequence). Error analysis calculations are time-consuming relative

to the other methods. An option to turn off the error analysis for Method 6 is

included (Utilities/Set/Method 6).

For each method, the jackknife procedure (Mosteller and Tukey 1978) is

used to estimate error variance. This involves excluding each sampling event,

one at a time, and recalculating loadings, as described in Table 2.2. While

alternative, direct estimators of variance are available from classical sampling

theory for most of the methods (Cochran 1977; Walker 1981; Bodo and Unny

1983, 1984), such formulas tend to rely upon distributional assumptions. The

direct estimators are generally applicable to large samples and normal distributions, neither of which is typical of this application. As described by Cochran

(1977), the jackknife has improved properties for ratio estimators derived from

small, skewed samples. Use of the jackknife procedure also provides a uniform

basis for comparing calculation methods with respect to estimated variance.

Simulations (Walker 1987) indicate that jackknifing provides a reasonably

unbiased estimate for error variance for a range of C/Q slopes. Two important

factors should be considered in interpreting the variance estimates. First, the

estimates are themselves subject to error and are of limited accuracy in small

sample sizes, particularly if the sampled flow distribution is not representative.

Second, the variance estimates do not reflect effects of biases associated with

some calculation methods under certain conditions, as discussed above. Thus,

while the estimated variances are important factors to consider in selecting the

“best” loading estimation method, the sample characteristics and bias potential

should also be considered. FLUX diagnostic procedures assist in this process,

as described below.

2-8

Chapter 2 FLUX
Error variance estimates developed by FLUX assume that the samples are

statistically independent. This may not be the case if the file contains large

numbers of discrete samples taken within relatively short periods of time. One

approach to solving this problem is to composite the samples by event prior to

calculating loadings. Important Wormation on the flow/concentration relationship may be lost in compositing, however. As an alternative to compositing,

discrete samples can be grouped by event only for the purposes of error analysis. In FLUX, sampling events are defined by the program parameter T. =

Maximum Event Duration (days). Samples collected within T, days of each

other are considered part of the same sampling event. The default setting for T.

is 1 day. This setting only influences the error variance estimates (not the mean

loading estimates). It only influences error variance estimates developed from

relatively intensive sample data sets containing multiple samples on the same

day or within the current N~ setting.

Data stratification

FLUX includes an option to divide the input flow and concentration data

into a series of groups and calculate loadings separately within each group

using the methods described above. Using formulas derived from classical

sampling theo~ (Cochran 1977), the mean and variance estimates within each

group are subsequently combined across groups using weighting factors which

are proportional to the frequency of each group in the total flow distribution

(see Table 2.2).

The groups, or “strat~” can be defined based upon flow, season, and/or

date. Stratification can serve three basic functions:

a. Adjust for differences in the frequency distributions of sampled and

unsampled flow regimes.

b. Reduce potential biases associated with some calculation methods and/

or sampling program designs.

c. Reduce the error variance of the mean loading estimate.

When sample data are adequate, stratification can offer significant advantages

over the direct methods and provide insights that can be used to improve

sampling efficiency in future years.

In most applications, the groups are defined based upon flow. The “flowinterval” method was developed by the U.S. Army Engineer District, Buffalo

(1975), for use in the Lake Erie Wastewater Management Study and is

described by Verhoff, Yaksich, and Melfi (1980) and Westerdald et al. (198 1).

This procedure applies the direct load averaging (Method 1) separately to

different data groups, defined based upon flow regimes. Since loading usually

increases with flow, grouping the data based upon flow reduces the loading

Chapter 2 FLUX 2-9
2-1o

Table 2.2

stratified Sample Algorithm (Cochran 1977; Bodo and Unny 1983)

definitions:

s = subscript indicating stratum

m= subscript indicating estimation method

N, = number of daily flows in stratum s

N, = total number of daily flows

ns,. = optimal number of samples in stratum s, given nt

w = total number of sampled concentrations

w=m,s mean flux in stratum s estimated by method m

v=m,s variance of mean flux in stratum s estimated by m

s = m,s effective standard deviation within stratum s for method m

w m,t = mean flux over all strata estimated by method m

v=m,t variance of mean flux over all strata estimated by method m

V*=m,t variance of mean flux over all strata estimated by method m for optimal

allocation of nt samples according to n~,.

z= sum over all strata (s)

Equations:

N, = ~N~

% = ~n~

w m,t = Z (wm,JJ6)/Nt

vm,t = Z (Vm,JJ$2)/Nt2

s = m,s [n, Vm,J0”5

n~. = ntN~Sm, / ~ ~ (N&J

V*=m,t x (V~,SN~2nJn~,.)/N~

variance within each group and results in lower variance for the total loading

estimate. A flow-stratified version of Method 2 written in SAS (Statistical

Analysis System) was developed and applied to estimate phosphorus loadings

in a Vermont lake study (Walker 1983). The IJC method described by Bodo

and Unny (1983, 1984) is a flow-stratified version of Method 3.

In FLUX, data groups or strata can be defined based upon flow range, date

range, and/or season range. Generally, flow ranges would be used and the data

would be stratified into two or three groups based upon flow. In some situations, however, it maybe desirable to strati~ based upon sampling date or

Chapter 2 FLUX
season. Stratification based upon season may be usefti in situations where

there is a strong seasonal variation in concentration which is independent of

flow or for streams with highly regulated flows, such as a reservoir outflow

station (particularly when intake levels are varied seasonally). Flowindependent, seasonal variance components are more likely to be detected in

analysis of dissolved or inorganic nutrient concentrations (particularly nitrate)

than in analysis of particulate or total nutrient concentrations.

In deftig stra~ one objective is to isolate homogeneous subgroups, based

upon the flow/concentration relationship assumed by the calculation method

(constant loading for Method 1, constant concentration for Methods 2 and 3,

and log-linear flow/concentration relationship for Methods 4-6). A second

objective is to set stratum boundaries so that the sampled and total flow distributions are equivalent within each stratum. This protects against bias in the

loading estimates and applies particularly to high-flow strata. As described

above, the method used to estimate error variance does not detect bias. If the

flow distributions are not equivalent within each stratum, then minimum variance is less reliable as a criterion for selecting the “best” calculation method

and loading estimate. Statistical and graphical tests are provided to compare

flow distributions within each stratum.

Robustness of the loading estimate decreases as the number of statistical

parameters which must be estimated from the sample data set increases. The

number of parameters which must be estimated depends upon the calculation

method and upon the number of strata. Methods 1 and 2 require one parameter estimate for each stratum. Methods 3, 4, 5, and 6 require two parameter

estimates per stratum. Strati&ing the data into two or three groups based upon

flow and using Method 2 is generally adequate to capture the flow/

concentration relationship while requiring the fewest parameter estimates (in

statistical terms, using up the fewest degrees of freedom). If concentration

does not vary systematically with flow, the need for flow stratification

decreases.

Uncertainty in the loading estimate is reflected by the CV estimate reported

for each calculation method. The CV equals the standard error of the mean

loading divided by the mean loading. The CV reflects sampling error in the

flow-weighted mean concentration. Potential error variance in the flow measurements are not considered in these calculations. In practice, CV values <0.1

are usually adequate for use in mass-balance modeling, especially considering

that uncertainty in flow measurements is usually in this range. Depending on

stream dynamics, CV values <0.1 may be very difficult to achieve, especially in

small, flashy streams with strong C/Q relationships. CV values between 0.1

and 0.2 may be adequate for modeling purposes, especially for minor tributaries. If higher CVS are found, the user should consider refining and extending

the stream monitoring program to obtain better data sets for load estimation

before proceeding with modeling efforts. This particularly applies if the CV

values are high for major tributaries.

Chapter 2 FLUX 2-11
For each calculation method, FLUX generates an invento~ of sample and

flow data in addition to a breakdown of the flow, load, and variance components within each stratum, as well as for the total strat~ as demonstrated in

Table 2.3, for the Caddo River example. Samples have been divided into three

flow intervals. Complete output for this example is given at the end of this

chapter.

Table 2.3

Breakdown by Flow Stratum - Caddo River Example

FLUX Breakdown by Stratum:

FREQ FLOU FLUX VOLUME Wiss CONC CV

ST NS NE DAYS HM3/YR KG/YR HM3 KG PPB -

1 93 93 582.0 120.23 2761.4 191.58 4400.1 23.0 .050

2 61 61 407.0 397.42 14501.1 442.85 16158.7 36.5 .092

3 14 14 107.0 2070.70 259357.2 606.61 75978.7 125.3 .148 *** 168 168 1096.0 413.59 32171.8 1241.05 96537.5 77.8 .118

Optimal Sample Allocation:

ST NE NE% NEOPT% FREQ% VOL% MASS% VAR% VARIANCE CV

1 :: 93 55.4 3.8 53.1 15.4 4.6 .0 . 5276E+04 .050

2 61 61 36.3 20.8 37.1 35.7 16.7 1.7 . 2442E+06 .092

3 14 14 8.3 75.5 9.8 48.9 78.7 98.3 . 1407E+08 .148 *** 168 168 100.0 100.0 100.0 100.0 100.0 100.0 .1432E+08 .118

Notes:

Output from the lList/Breakdownl Procedure for Caddo River with 3 Flow Strata

The top part of the screen lists the distribution of samples, flows, fluxes,

volume, and mass across strata for the current calculation method.

The middle part of the screen lists the distribution of sampling effort, flow

days, flow volume, mass, and error variance, each expressed as percentage of the

total.

The bottom part of the screen describes the potential benefit of optimizing the

sample allocation across strata to obtain the lowest error variance for a fixed

number of sampling events.

NE% = percent of total sample events in stratun

NEOPT% = optimal percent of total sample events in stratum

The reduction in error CV attributed to shifting from the current sample

distribution (NE%) to the optimal distribution (NEOPT%) is listed. This can be

used to refine future monitoring program designs. Generally, a shift towards

more intense sampling of high-flow strata ~ill be indicated.

Typically,mostof theloadanderror varianceisinthe high-flowstratum.

Since the variance component is roughly inversely related to sampling frequency within each stratum, the “breakdown by stratum” given in Table 2.3 is

useful for evaluating sampling strategies. The low-flow stratum accounts for

55.4 percent of the total samples but only 4.6 percent of the total mass discharge. In future sampling, moving some ofthesamples fromthelow-flow to

the high-flow stratum would reduce the variance ofthe total loading estimate.

Alternatively, to reduce monitoring costs, the low-flowsampling frequencies

2-12

Chapter2 FLUX
could be reduced without substantially increasing the variance of the total

loading estimate. FLUX also provides an estimate of the “optimal” sample

distribution (expressed as percent of the total sampling effort allocated to each

stra~ NEOPTO/Oin Table 2.3) which would minimize the variance of the

total loading estimate for a given total number of independent samples, using

the equations specified in Table 2.2. Comparing the observed variance with the

optimal variance provides an approximate indication of the potential benefits of

optimizing the sample design. In this case, shifting from the historical sample

distribution across flow strata (55%/36%/8%) to the optimal sample distribution (4%/2 1%/76%) would decrease the CV of the load estimate from O.118 to

0.045.

As described by Bodo and Umy (1983, 1984), stratum breakdowns can be

used to refine monitoring program designs for future years, subject to practical

limitations in sample scheduling and total budget and to requirements imposed

by other monitoring objectives. The “optimal” distribution of sampling effort

indicated by the program may be difficult to achieve without automated equipment. An important statistical limitation is that the “optimal” allocation

assumes that the samples are serially independent, and it may be impossible to

take the recommended number of independent samples from intensively monitored strata. Five samples taken from different storm events would tend to be

less serially dependent than five samples taken within one event, for example.

Because of these limitations, the “optimal” design should not be viewed as

an absolute objective, but as a general direction for adjusting previous survey

designs within practical constraints.

Diagnostics

FLUX includes several routines for generating scatter plots and histograms

of flow, concentration, loading, and sample dates, as illustrated at the end of

this chapter. The relationship between flow and concentration partially determines the appropriate calculation method and should be reviewed in each

application. Flow frequency distributions (sampled versus total) can also be

graphically compared. These displays characterize the flow and concentration

distributions and can assist the user in assessing data adequacy, identi~ing

appropriate stratification schemes, and evaluating calculation methods.

The calculation methods differ with respect to the schemes used to estimate

the loadings on the unsampled days or periods. For a given method, observed

and predicted fluxes can be compared for each water quality sample. This

provides one measure of performance. Ideally, the flux residuals

(loglO(observed flux) minus loglO(predicted flux) should be random and

independent of flow season. In practice, this independence is sometimes difflcuh to achieve with the relatively simplistic models upon which the calculation

methods are based. The residuals analysis procedure generates plots of

observed versus predicted loadings, residuals versus flow, and residuals versus

Chapter 2 FLUX 2-13
date. Alternative stratification schemes can be investigated to reduce the flowdependence and/or time-dependence of the residuals.

Listings of residuals and jackknifed loading estimates are useful for identi&-

ing outliers and determining sensitivity of the loading estimates to individual

samples. FLUX includes an outlier detection routine which can be used to

delete suspected outliers from the sample data set. Outliers are detected based

upon deviations of the residuals from a lognormal distribution (Snedecor and

Cochran 1989). This procedure should be used conservatively. Detection of

outliers depends upon the current stratification scheme and calculation method.

Important information may be lost if an apparent outlier is actually an important

signal. Suspected outliers are usually apparent on the concentration versus

flow scatter plots. Developing confidence with the program, stratification

scheme, and calculation method are suggested before using the outlier deletion

procedure.

Program Operation

Introduction

This section describes the FLUX menu structure and operation procedures.

When the program is run (from the DOS prompt), a series of help screens summarizing model features is first encountered. If error messages appear, it generally means that one of the FLUX program files has been corrupted or that

your computer does not have enough available memory. TV reinstalling the

program. Try unloading any memory-resident software. If you are trying to

run the program from Windows, try exiting Windows and running directly from

DOS. The program permits selection of ‘user mode’ at startup after introductory screens. The selection of user mode is followed by a menu which

provides interactive access to eight types of procedures with the following

fhnctions:

FLUX- VERSION 5.0

Data Calculate Method Plot List Utilities Help Quit

Data Read and/or Strati fy Data

Calculate Calculate Loads Using Current Data & Stratification Scheme

Method Select Flux Calculation Method Used in Plots & Tables

Plot Plot Load, Flow, and/or Concentration Data

List List Output Formats for Current Calculation Method

Utilities Program Uti lities & Options

Help View Help Screens

Quit End Session

2-14

A procedure category is selected by moving the cursor (using arrow keys) or by

pressing the first letter of the procedure name. Selected procedures in the

menu box are highlighted on the screen and underlined in the following

documentation. Assistance in navigating around the menu can be obtained by

Chapter 2 FLUX
pressing the <F7> fiction key. A Help screen describing the selected procedure can be viewed by pressing <Fl>. After each procedure is completed,

control returns to the above menu screen. Essential features of the current data

set are summarized below the menu box (not shown here).

Data procedures

Data procedures control input, stratification, listing, and other manipulations of sample and./or flow data used in load calculations:

Read Read New Sanple and/or Flow Data

Stratify Divide Sanples & Flows into Groups for Load Calculations

Delete Delete a Specific Sanple or Delete Excluded Samples

Composite Composite Samples by Date

FlowSub Substitute Daily Mean Flows for Sample Flows

Title Enter New Title for Labeling Output

List List Sanple or Flow Input Data

Four methods for reading in new sample or flow data are available under

Data/Read:

Reset Read New Sa~le & Flow Data; Reset Stratification Scheme

Keep Read New Sa~le & Flow Data; Keep Current Stratification Sch

Sanples Read New Sanple Data Only; Keep Current Stratification Schern

I nd,X Read Sample & Flow Data from Station Index File

In the first three procedures, a data-entry screen is presented for defining all

input specifications (data file names, variable labels, time periods, and units

conversion factors). Use Reset to read in new flow data and reset the stratification scheme. Use Keep to read in new data without changing the current

stratification scheme. Use Samples to read in new sample data only, without

changing the current daily flow data or stratification scheme. Use Index to

read in new data from a station index file, which is a user-created ASCII file

defining the storage locations and formats for concentration and flow data

referring to specific stations. Using index files greatly speeds and simplifies the

specification of input data. (See Data-entry screens.)

If variable labels (for daily flows, sample flows, and concentration) are left

blank on data entry screens, the user is prompted to select the appropriate field

from a list of all fields contained in the source data file. Screen messages track

the progress of data retrieval from disk files. If the specified data set has fewer

than three samples or no daily flows, an error message appears and control

returns to the main menu. Note that this may occur if the file names or variable

labels are entered incorrectly. If a valid data set is retrieved, subsequent

screens include a listing of missing or out-of-sequence daily flows (Data/List/

Chapter 2 FLUX 2-15
Missing procedure) and a summary of the current stratification scheme (Data/

Stratify/List procedure). Control then returns to the main menu.

Data/Stratify procedures divide the sample and flow data into groups

based upon flow, date, and/or season. In many cases, stratification increases

the accuracy and precision of load estimates. At least three samples are

required in each stratum. Four options are available:

Flow Define Strata Based Upon Flow; Reset Data & Season Limits

Genera 1 Define General Stratification Scheme vs. Flow, Date, Season

Reset Reset Stratification Scheme - Use 1 Stratum Only

List List Current Strati f i cat ion Scheme & Sanple Counts

Strati&ing based upon flow is often appropriate, especially when concentration is correlated with flow:

2 Strata Use 2 Flow Strata - Boundary at QMEAN

3 Strata Use 3 Flow Strata - Boundaries at QMEAN/2, QMEAN x 2

4 Strata Use 4 Flow Strata - Boundaries at QMEAN/2, QMEAN x 2, QMEAN x 8

Other Use Flows to Define Strata; Enter Flow Bounds Directly

The first three procedures defineflow boundaries automatically. Dividing the

dataintotwo strata based uponflow(low-flow andhigh-flow)is often appropriate. Three or more flow stratamaybe appropriate for relatively intensive

datasetswithstrongflow/concentration relationships. The last procedure

permits direct entry offlow boundaries. Each stratum must contain atleast

three sample events. Ifastratum contains fewer thenthree events, theuseris

asked to redefine the flow boundaries until a valid stratification scheme is

defined or the stratification scheme is reset.

Data/Delete procedures operate only on data stored in memory; they do not

change disk files:

One Delete a Specific Sample

Excluded Delete All Sanples Excluded from Current Stratification Sche

The Data/Composite procedure combines samples collected on the same

date or in the date interval into a single composite sample:

2-16

Chapter 2 FLUX
Ccmposite Canposite Sanples by Date

The user is prompted for the time interval (number of days) to be used for

compositing samples. This optional procedure may be appropriate for data

derived from intensive monitoring programs providing multiple samples per

date. The composite sample concentration is the flow-weighted mean of the

individual samples. The composite sample flow is the average of the sample

flows. Because of possible variations in actual event duration, it is generally

preferable to composite samples prior to running FLUX; i.e., to specifi event

mean flows and event flow-weighted mean concentrations in the source data

files.

The Data/FlowSub procedure can be used to test the sensitivity of load

estimates to the types of flow measurements which are paired with sample

concentrations:

F 1ousub Substitute Dai ly Mean Flows for Sanple Flows

Depending upon source data files, input sample flows may be instantaneous

flows measured at the time of sampling. The Data/FlowSub procedure

replaces sample flows with daily mean flows on the corresponding sample

dates. Samples are deleted if the corresponding daily mean flow is missing or

zero. This flow substitution may also be performed in the Data/Read

procedures by entering “Lookup” in the sample flow field.

Data/List procedures summarize the sample and/or flow data which have

been retrieved from disk files:

Samples List Sample Data

F t OMS List F1OH Data

Missing List Missing or Out-of-Sequence Daily Flows

Before proceeding with load calculations, data listings should be reviewed to

make sure that the correct sample and flow data have been retrieved from disk

files. Both sample flows and corresponding daily mean flows are listed by the

first two procedures. Daily flow data files read by FLUX are assumed to be

sorted by date. The Data/List/Missing procedure lists missing or out-of

sequence daily flow records. If any are detected, FLUX can still operate. It is

desirable, however, to estimate any missing flows independently and to sort

flow files before running FLUX.

Chapter 2 FLUX 2-17
Calculate procedures

Calculate procedures can be accessed tier valid sample and flow data sets

have been read and a valid stratification scheme has been defined. Three

options are available:

FLUX- VERSION 5.0

Data e Method Plot List Utilities Help Quit

Conpare Series

Corrpare Compare Sample Flow & Total Flow Distributions

Loads Calculate Loads Using Each Method

Series Generate Load Time Series

The Calculate/Compare procedure provides information which can be used to

assess adequacy ofthe sample dataand/orstratificationscheme. The Calculate/Loadsprocedure lists average flows, flux rates, flow-weighted mean concentrations, and error estimates using each calculation method; this provides

the basic tiormation needed for BATHTUB applications.

The Calculate/Series procedure lists flow, load, and concentration time

series using the currently selected calculation method. Four options are

available:

Yearly Generate Load Time Series by Calendar Year

WtrYearly Generate Load Time Series by Water Year

Monthly Generate Monthly Load Time Series

Daily Generate Daily Load Time Series

Time-series output does not include error estimates. These procedures are

included primarily for generating load time series for use in applications other

than BATHTUB which may require daily or monthly estimates.

Method procedure

The Method procedure asks the user to select the loading calculation

method to be used in generating subsequent plots and output tables. Six

choices are provided:

FLUX - VERSION 5.0

Data Calculate !!!Q@d Plot List Utilities Help Quit

1 AVG LOAD 2QWTDC 3 IJC 4 REG 1 5 REG 2 6 REG 3

1 AVG LOAD Method 1 - Mean Load

2QWTDC Method 2 - Flow-Wtd-Hean Cone.

3 IJC Method 3 - Flow-Wtd-Nean Cone. (IJC Modification)

4 REG 1 Method 4 - Regression Model 1

5 REG 2 Method 5 - Regression Model 2

6 REG 3 Method 6 - Regression Model 3 - log(C) vs. log(Q) Separate

2-18 Chapter2 FLUX
Method 2 is initially selected as the default calculation method when the program is started. Descriptions of each method are given above (see Loading

calculation methods); summary descriptions can be viewed by selecting a

method and pressing the Help key <F 1> or by running the Help procedure.

Plot procedures

Plot procedures provide important diagnostic information which can help in

evaluating the adequacy of the current data set, stratification scheme, and calculation method:

Barchart

Cone

Load

Flow

Daily

Qfreq

Residuals

GridOpt

Barcharts of Load, Mass, or Concentration Estimates

Plot Sample Concentrations (ppb)

Plot Sample Loads ( kg/yr)

Plot Sample Flows (hm3/yr)

Plot Daily Flows (hfi/yr)

Plot Flow Frequency Distributions

Plot Residuals = LOGlO ( Observed Load /Estimated Load )

Toggle Plot Grids On or Off

The Plot/Barchart procedures plot load, mass, flow-weighted mean

concentration, or flow as a function of calculation method or stratum:

Load Load (kg/yr) Barcharts vs. Calculation Method or Stratum

Method Plot Load Estimates (kglyr) vs. Calculation Method

Stratum Plot Load Estimates (kg/yr) vs. Stratwn

Mass Mass (kg) Barcharts vs. Calculation t4ethod or Stratum

Method Plot Mass Estimates (kg) vs. Calculation Method

Stratun Plot Mass Estimates (kg) vs. Stratum

Cones Flow-Ueighted Concentration (ppb) vs. Calc. Method or Stratu

Method Flow-bleighted Concentration (p@) vs. Calculation Method

Stratun Flow-Ueighted Concentration (ppb) vs. Stratum

Flow Mean Flow (hm3/yr) vs. Stratun

Each bar chart (exceptFlow) shows estimates+ l standard error. Plotting

against method shows the sensitivityof the estimate (total across all strata) to

thecalculation method. Generally, alowsensitivity tocalculation method

would support the reliability ofthe load estimates. Plotting against stratum

shows estimates foreach data group using the currently selected calculation

method.

Plot/Concprocedures display sample concentrations against four independent (x-axis) variables or a histogram:

Chapter2 FLUX 2-19
Flow Plot Sanple Concentration (ppb) vs. Flow (hm3/yr)

Date Plot Sample Concentration (ppb) vs. Date

Month Plot Sample Concentration (ppb) vs. Month

Estimated Plot Observed vs. Estimated Cone. for Current Calc. Method

Histogram of Observed Concentrations (ppb)

Both theobserved and theestimated sample concentrations areshown inthe

first three procedures. The``estimated'' sample concentration is based uponthe

currently selected calculation method. Different symbols are usedto indicate

samples indifferent strata.

TheP1ot/Loadand Plot/Flowprocedures generate similar displays ofsarnple data:

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart Cone Flow Daily Qfreq Residuals GridOpt

Flow Date Month Estimated Histogram

Flow Plot Load (kg/yr) vs. Flow (hti/yr)

Date Plot Load (kg/yr) vs. Date

t40nth Plot Load (kg/yr) vs. Month

Estimated Plot Observed vs. Estimated Load

Histogram Histogram of Observed Loads (kg/yr)

FLUX- VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart Cone Load Daily Qfreq Residuals GridOpt

Date Month Histogram Comparison Both

Date Plot Sample Flows (hfi/yr) vs. Date

Uonth Plot Sanple Flows (hm3/yr) vs. Month

Histogram Histogram of Sanple Flous (hm3/yr)

Comparison Sample & Total Flow Histograms

Both Plot Sanple Flow vs. Daily Mean Flow

Plot/Dailyprocedures display theentireflow record against date ormonth

or as ahistogram:

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart Cone Load Flow I)ailv Qfreq Residuals GridOpt

Date Month Histogram

Date Plot Daily Flows (hti/yr) vs. Date

Month Plot Daily Flows (hm3/yr) vs. Month

Histogram Histogram of Daily Flows (hfi/yr)

Three format options are available for plotting daily flow against date:

2-20

lLinear Plot Daily Flows (hti/yr) vs. Date - Linear Scale

2Log Plot Daily Flows (hm3/yr) vs. Date - Log Scale

3Filled Plot Daily Flows (hm3/yr) vs. Date - Filled

Chapter2 FLUX
In addition to plotting the daily flow values, each of these formats also indicates

daily flows on the dates of sample collection (red squares). These displays are

usefhl for identi&ing gaps in the sample record and for assessing sample coverage of major hydrographyfeatures. The lLinear and 2Log displays use different symbols to identi& strata. The 3Fi11ed display does not identifi strata. If

zero flows are contained in the record, these are plotted as one-half of the lowest positive flow value in the 2Log displays.

The PlotiQfreq procedures display cumulative frequency distributions of

sampled flow and total flow:

T Freq Time Frequency Distributions for Sample & Total Flow

V Freq Volune Frequency Distributions for Sample & Total Flow

In the first case, they axis reflects the cumulative percentage of total samples

or total flow days. In the second case, they axis is the cumulative percentage

of the total sample volume or total flow volume.

Plot/Residuals procedures display residuals for the current calculation

method:

Cone Plot Residuals vs. Estimated Concentration (F@)

Load Plot Residuals vs. Estimated Load (kg/yr)

Flow Plot Residuals vs. Sanple Flow (hfi/yr)

Date Plot Residuals vs. Sample Date

Month Plot Residuals vs. Sample Month

Histogram Histogram of Residuals for Current Calculation Method

Autocor Plot Residual Autocorrelation - Resid(t) vs. Resid(t-1)

The residual is defined as log 10(observed sample flux/estimated sample flux).

Different symbols areused toidenti& strata. The Autocor procedure shows

tielag-l setidcomelation ofresiduds titismple order bwedupon date. As

discussed above (see Theory), serial correlation can influence the accuracy of

error estimates and determine the appropriateness of time-series methods for

estimating loads.

List procedures

List procedures can be accessed only if a valid data set and stratification

scheme have been defined. Three tabular output formats are provided using

the currently selected calculation method:

Chapter 2 FLUX 2-21
Residuals List Residuals & Screen for Outliers

Breakdowns List Load & Flow Breakdowns by Stratwn; Optimal Sample Allot

Jackknife List Jackknife Table for Current Calculation Method

List/Residualsprocedures provide detailed listing ofobservedandpredieted concentrations forthe currently selected calculation method:

All List All Residuals Uithout Screening for Outliers

Out 1 iers List Outliers

Signif Set Significance Level for Outlier Screening

The first procedure lists observed concentrations, estimated concentrations, and

residua.ls(loglO(observed/estimated)) foreach sample. The second procedure

hwasitilm fomat, butlists odysmples wtichme suspected outliers. Outliersare detected based upon deviation from alognormal distribution; seethe

associated help screen for a description oftheoutlier detection method. Ifany

outliers are detected, the user may elect to delete therefrom the current sample

list; source data files arenot modified. Theoutlier detection procedure is

iterative mdautomaticdly repeats i~elfmtil nooutliers we detected. The last

procedure sets the significance level for outlier screening (default= 0.05).

The List/Breakdowns procedure provides detailed information on the distribution of flow, flux, and error variance as a fuction of stratum for the current calculation method:

Breakdowns List Load & Flow Breakdowns by Stratun; Optimal Sample Allot

The top half of this output screen shows the sample properties. The bottom

half estimates the optimal sample allocation across strata based upon the current sample properties. The optimal allocation is defined as the distribution of

sampling effort (percentage of total sample events in each stratum) which leads

to the lowest error in the load estimate. This information can be used to refine

future data-collection efforts.

The List/Jackknife procedure shows the derivation of the error variance

estimate for the current calculation method:

2-22

Jackknife List Jackknife Table for Current Calculation Method

Chapter 2 FLUX
Each sample event is excluded, one at a time, from the sample set and the load

estimate is recalculated using data from the remaining sample events. The procedure lists and displays the distribution of load estimates with each sample

event excluded. This can be used to identi~ samples which have a relatively

large impact on the computed average loads.

Utilities procedures

Utilities procedures allow the user to redirect program output, view disk

files, or modi@ the default settings for various program options:

~L”;’o; ‘Y:;y’f’i(i’ies “1’ ‘“i’

output Select Output Destination for Text

View View any DOS File

Set Set Hiscel laneous Program Options & Parameters

The Utilities/Output procedure redirects program output to a disk file or to

screen:

Screen Send Output to Screen (Default)

File Send Output to Disk File

The selected output destination remains in effect until it is reset. Even if

Screen is selected, individual output screens can be copied to disk files after

viewing.

The Utilities/View procedure views any DOS file stored in ASCII format:

View View any DOS File

Only the first 80 columns of each record are displayed.

Utilities/Set procedures modi~ the default settings for various program

options:

Chapter 2 FLUX

Events Define Maximum Event Duration (Days) For Grouping Samples

Signif Set Significance Level for Testing Flow/Cone Regression

Restrict Toggle Option to Restrict Flow Ranges for Model Application

Method 6 Toggle Option for Error Analysis Using Calc Method 6

2-23
The Utilities/Set/Events procedure sets the maximum duration of an independent sampling event for the purpose of estimating error variances:

Events Define Maximum Event Duration (Days) For Grouping Samples

This setting does not influence mean load estimates. The default setting is

1 day. Iftiesmple record conttis hydro~aptic events l~tig longertim

1 day and if multiple samples are collected within events, settings longer than

1 day maybe appropriate.

The Utilities/Set/Signif sets the statistical significance level required before

flow/concentration regression models are applied in calculating loads:

FLUX- VERSION 5.0

Data Calculate Method Plot List utilities Help Quit

output Vie~

Events ~ Rest~t Method 6

L

Signif Set Significance Level for Testing FloWConc Regression

This setting only influences loads calculated using Method4, Method 5,0r

Method6. The Signifsetting hasavalid range of O.Otol.O. If Signif=O.0,

the sample regressions are never used; the slope of the log concentration versus

log flow relationship is always set to 0.0 before calculating loads. If Signif =

1.0 (default), the regression slope calculated from the sample record is always

used (regardless of its significance level). If Signif = 0.05, the sample regression slope is used only if it is different from zero at the 0.05 significance level.

The Utilities/Set/Restrict toggles the option to restrict concentration versus

flow regressions to the range of sampled flows:

Restrict Toggle Option to Restrict Flow Ranges for Model Application

This setting only influences loads calculated using Method 6. If the Restrict

setting is on (default), daily flows are restricted to the range of sample flows

before applying the regression to calculate loads. For example, if the maximum

sampled flow is 98 hm3/year, the predicted concentration at a flow of

98 hm3/year is applied to all days when the flow exceeds 98 hm3/year. If the

Restrict setting is off, extrapolation of the regression beyond the range of

sampled flows is permitted; this is risky, but may be appropriate if the slope is

well defined from the sample data and if the extrapolation is not over a wide

flow range. This option will have no effect if the range of sample flows equals

or exceeds the range of daily flows, which is the desired situation when data are

derived from an ideal sampling program. The setting turns on and off each

2-24

Chapter 2 FLUX
time the Restrict procedure is selected. A screen message beneath the menu

indicates the current setting.

The Utilities/Set/Method 6 procedure toggles the option to conduct error

analysis calculations using Method 6:

Method 6 Toggle Option for Error Analysis Using Calc Method 6

If Method 6 setting is on (default), error estimates are calculated for Method 6.

Depending upon the numbers of sample and daily flow records, these calculations can be time-consuming because the concentration/flow regression is

applied separately to each daily flow. If the Method 6 setting is off, error

analyses are not conducted and the CV of the Method 6 load estimate is set to

0.0. The setting turns on and off each time the procedure is selected.

Help procedure

Supplementary help screens can be viewed from the program menu by

selecting the Help procedure:

1 FLUX- VERSION 5.0

Data Calculate Method Plot List Utilities Quit

Help View Help Screens

Quit End Session

This provides access to help screens that are organized in seven categories, as

summarized below:

HELP TOPICS

I NTROOUCTORYSCREENS

PROGRAHtlECHANI CS

GLOSSARY

DATA FILE FORMATS

CALCULATION METHODS

OUTPUT FORHATS

GENERALGUIDANCE

A help category is selected by moving the cursor and pressing <Enter>. A list

of the help screens available in the selected category is presented. Contextsensitive help screens can also be accessed during execution of other procedures by pressing the <F 1> fiction key. The general Help menu can also be

accessed from any Data-Entry screen by pressing <F9>.

Chapter 2 FLUX 2-25
Quit procedure

I FLUX - VERSION 5.0

Data Calculate Method Plot List Utilities Help ~

Quit End Session

Selecting Quit from the main menu ends the current session after user

verification.

Typical Application Sequence

Flux input data files can be generated using formats described below (see

Data File Formats). The user directs the flow of the program through the fourlevel tree menu screen described in the previous section. A Documented

Session showing steps involved in a typical application is provided at the end of

this chapter. The program starts by reading in the concentration and flow data

and using the data files and date ranges specified by the user. Data stratification can be definedhedefined at any time, based upon flow, date, and/or season

ranges, The analysis is subsequently directed from the main menu, which

includes categories of procedures. After executing a given procedure, the program returns to the main menu for another selection.

Because each loading estimation problem is unique, it is impossible to

speci~ a “universal” pathway for the analysis. In some cases, a few iterations

(mainly involving alternative strata definitions) would be required before

arriving at an acceptable loading estimate. Generally, however, a typical program application sequence is outlined in Table 2.4.

Further steps would involve, but not be limited to, refinement of the stratification scheme, testing of alternative models, deletion of outliers, and testing

for trends.

The selection of the “best” loading estimate to be used in subsequent modeling efforts is up to the user, based upon the following criteria:

a. Calculation method and stratification scheme yielding minimum

estimated variance in the mean loading estimate.

b. Sensitivity of the loading estimate to alternative calculation methods,

stratification schemes, and individual samples.

c. Residuals analysis results.

2-26

The selection can be based primarily upon minimum estimated variance,

provided that the following conditions are met (corresponding FLUX procedures are listed in parentheses):

Chapter 2 FLUX
Table 2.4

Typical Application Sequence

I I

Step Menu Selections Function

1 Data/Read/Reset Read sample and flow data

or Data/Read/Index from disk

2 Plot/DaiI y/Date Plot daily flow record,

showing sample dates

3 Calculate/Compare Compare sample and total

flow distributions

4 Data/Stratif y/Flo w/2Strata Stratify into two groups at

mean flow

5 I Plot/Cone/Flo w I Plot concentration versus flow

6 Calculate/Loads Calculate loads using each

method

7 Plot/Barchart/Loads/Method Plot loads versus calculation

method

8 Method Select calculation method

start with Method 2

9 Plot/Loads/Estimated Observed versus estimated

loads on sample dates

10 IPlot/Residuals/Date Test for time dependence of

residuals

11 Plot/Residuals/Month Test for seasonal dependence

of residuals

12 Plot/Residuals/Flow Test for flow dependence of

residuals

13 [ Reiterate 1 Review results

Return to Step 4 or 8

Increase flow strata until

methods converge

Try other calculation methods

Try using daily flows in

place of inst. flows

14 I.WBreakdo wns List breakdown by stratum

optimal sample allocation

a. Sampling is representative; date and flow ranges are reasonably well

covered. (P1ot/Daily/Date, Calculate/Compare).

b. Sampled and total flow means are equal within each stratum

(CaIculate/Compare, Calculate/Loads).

c. Residuals are reasonably independent of date, season, and flow.

(Plot/Residuals/Date,Month,Flow).

Chapter 2 FLUX 2-27
d Residuals are serially independent. (P1ot/Residuals/Autocorr).

e. Sampling events are independent; for intensive data sets only.

(Utilities/Set/Events).

If the above conditions are marginally satisfied or cannot be met because of

existing data limitations, factors other than minimum variance (sensitivity and

residuals analyses) should be given greater weight. Further sampling may be

indicated, particularly if the tributary accounts for a major portion of the total

reservoir loading.

Differences among the various calculation methods should be interpreted in

relation to the estimated variances. For example, a range of 45 to 50 kg/year in

the mean loading estimate is of little significance if the estimated coefficients of

variation are on the order of 0.1 or greater. Provided that flow regimes are

adequately sampled, limited variation among calculation methods suggests

robust results. Calculation Methods 2 or 3 are generally the most robust and

should be used (typically with flow stratification into two groups with the

boundary set near the mean flow) if load estimates must be generated from

limited data not conforming rigidly to the above criteria.

A general approach is to refine the stratification scheme so that estimates for

six calculation methods converge to a common result. This occurs when the

mean estimates for Methods 1-6 are not significantly different from each other.

The uncertainty of the estimates (CVS) may differ substantially, however. In

most cases, the Method 2 estimate will have the lowest uncertainty and should

be used if convergence is reached. A regression estimate (usually Method 6)

may have the lowest uncertainty if stratification alone does not capture essential

features of the flow/concentration relationship, especially if flow and concentration are strongly correlated within the highest flow stratum.

In applications to small, flashy streams or storm sewers, special consideration must be given to the specification of sample flows. In flashy streams, the

variance and extremes of instantaneous sample flows will be considerably

higher than the variance and extremes of daily mean flows. This can cause

severe bias in the load estimates when (a) concentration varies with flow, and

(b) either the data are stratified based upon flow or a regression method (4-6) is

used. To avoid this bias, the time scale (averaging period) of the sample flows

should be equivalent to the time scale of the daily flows. This can be accomplished in one of two ways:

a. Preprocess the instantaneous flows and sample concentrations so

that each sample record read by FLUX represents a daily mean

flow and daily flow-weighted mean concentration.

2-28

b. Read the instantaneous flows and sample concentrations into

FLUX. Run the “Data/Composite” procedure to calculate a

daily flow-weighted mean concentration for each sample day.

Chapter 2 FLUX
Then run the “Data/FlowSub” procedure to substitute daily mean

flows for sample mean flows. Then proceed with load

calculations.

This type of problem is generally indicated when the mean sample flow in

the highest flow stratum is significantly higher than the mean daily flow

(Calculate/Compare or Calculate/Loads procedures). It is also revealed by

plotting sample flows against daily mean flows (Plot/Flow/Both procedure). If

the sample flow rates generally exceed the daily flow rates (particularly in the

high-flow range), one of the preprocessing steps outlined above should be

taken. In any application where instantaneous samples are used, it is generally

a good idea to test whether substitution of daily mean flows has an effect on the

load estimates. If such an effect is indicated, estimates based upon daily mean

flows are less likely to be biased.

In a reservoir eutrophication study, FLUX can be used to estimate annual

(October-September) and seasonal (May-September) loadings of total phosphorus, ortho-phosphorus, total nitrogen, inorganic nitrogen, and a conservative

substance for each sampled tributary and outflow. For annual calculations,

water-year loadings (October-September) are generally more appropriate than

calendar-year loadings for use in predicting growing-season water quality in the

reservoir pool. Unless flow/concentration/seasonal dynamics differ markedly

among the nutrient components, it is a good idea to use the same stratification

scheme for each component. The stratification scheme can be optimized for

calculating total phosphorus loading (usually the most important) and subsequently used in calculating other component loadings.

Procedure

Following is

Outline

a list of all FLUX procedures. Names are listed on the left.

Indentation reflects Menu level (Lines 1-4). A brief description of each procedure is given on the right.

Data

Read

Reset

Keep

Samples

Index

Stratify

F1OH

2 Strata

3 Strata

4 Strata

Other

General

Reset

List

Delete

Excluded

Coq30site

F 1ousub

Read and/or Stratify Data

Read New Sample and/or Flow Data

Read New S~le & Flow Data; Reset Stratification Scheme

Read New Sanple & Flow Data; Keep Current Stratification Sch

Read New Sanple Data Only; Keep Current Stratification Schem

Read Sample & Flow Data from Station Index File

Divide Samples & Flows into Groups for Load Calculations

Define Strata Based Upon Flow; Reset Data & Season Limits

2 Flow Strata - Boundary at QMEAN

3 Flow Strata - Boundaries at QNEAN/2, QhlEAN x 2

4 Flow Strata - Boundaries at QMEAN/2, QHEAN x 2, QFIEAN x 8

Use Flows to Define Strata; Enter Flow Bounds Directly

Define General Stratification Scheme vs. Flow, Date, Season

Reset Strati f i cat ion Scheme - Use 1 Stratum Only

List Current Stratification Scheme & Sample Counts

Delete a Specific Sample or Delete Excluded Sanples

Delete a Specific Sample

Delete Al 1 S~les Excluded from Current Stratification Sche

Conposite Samples by Date

Substitute Daily Mean Flows for Simple Flows

Chapter 2 FLUX 2-29
Title

List

Samples

F 10MS

Missing

Calculate

Compare

Loads

Series

Yearly

UtrYearly

Monthly

Daily

Method

1 AVG LOAD

2QUTDC

3 IJC

4 REG 1

5 REG 2

6 REG 3

Plot

Barchart

Load

Method

Stratum

Mass

Method

Stratum

Cones

Method

Stratum

Flow

Cone

Flow

Date

Month

Estimated

Histogram

Load

Flow

Date

Month

Estimated

Histogram

Flou

Date

Month

Histogram

Comparison

Both

Daily

Date

lLinear

2Log

3Filled

Month

Histogram

Qfreq

T Freq

V Freq

Residuals

Cone

Load

Flou

Date

Month

Enter Neu Title for Labeling Output

List Sample or F1OM Input Data

List Sample Data

List Flow Data

List Missing or Out-of-Sequence Daily Flows

Calculate Loads Using Current Data & Stratification Scheme

Compare Sample Flow & Total Flow Distributions

Calculate Loads Using Each Method

Generate Load Time Series Using Current Model

Generate Load Time Series by Calendar Year

Generate Load Time Series by Uater Year

Generate Monthly Load Time Series

Generate Daily Load Time Series

Select Flux Calculation Method Used in Plots & Tables

Method 1 - Mean Load

Method 2 - Flow-Utd-Mean Cone.

Method 3 - Flow-Utd-Mean Cone. (IJC Modification)

Method 4 - Regression !hdel 1

Method 5 - Regression Uodel 2

Method 6 - Regression Model 3 - log(C) vs. log(Q) Separate

Plot Load, Flow, and/or Concentration Data

Barcharts of Load, Mass, or Concentration Estimates

Load (kg/yr) Barcharts vs. Calculation Method or Stratun

Plot Load Estimates (kg/yr) vs. Calculation Method

Plot Load Estimates (kg/yr) vs. Stratum

Mass (kg) Barcharts vs. Calculation Method or Stratum

Plot Mass Estimates (kg) vs. Calculation Method

Plot Mass Estimates (kg) vs. Stratum

Flow-Ueighted Concentration (@) vs. Calc. Method or Stratu

Flow-Ueighted Concentration (p@) vs. Calculation Method

Flow-Ueighted Concentration (p@) vs. Stratum

Mean Flow (hm3/yr) vs. Stratum

Plot Sample Concentrations (p@)

Plot Sanple Concentration (p@) vs. F1OW (hm3/yr)

Plot Sample Concentration (P@) vs. Date

plot Sample concentration (p@) VS. Month

Plot Observed vs. Estimated Cone. for Current Calc. Method

Histogram of Observed Concentrations (p@)

Plot Sanple Loads (kg/yr)

Plot Load (kg/yr) vs. Flow (hm3/yr)

Plot Load (kg/yr) vs. Date

Plot Load (kg/yr) vs. Month

Plot Observed vs. Estimated Load

Histogram of Observed Loads (kg/yr)

Plot Sqle Flows (hm3/yr)

Plot Sarple Flows (hm3/yr) vs. Date

Plot Sanple Flows (hm3/yr) vs. Month

Histogram of Sample Flows (hm3/yr)

Sample & Total Flow Histograms

Plot Sample Flow vs. Daily Mean Flow

Plot Daily Flows (hfi/yr)

Plot Daily Flows (hn3/yr) vs. Date

Plot Daily Flows (hn3/yr) vs. Date - Linear Scale

Plot Daily Flows (hm3/yr) vs. Date - Log Scale

Plot Daily Flows (hti/yr) vs. Date - Filled

Plot Daily Flows (hm3/yr) vs. Month

Histogram of Daily Flows (hfi/yr)

Plot Flow Frequency Distributions

Time Frequency Distributions for Sample & Total Flow

Volune Frequency Distributions for Sample & Total Flow

Plot Residuals = LOG1O (Ohs./Est.) Loads with Regression

Plot Residuals vs. Estimated Concentration (F@)

Plot Residuals vs. Estimated Load (kg/yr)

Plot Residuals vs. Sample Flow (hnif/yr)

Plot Residuals vs. Sample Date

Plot Residuals vs. Sample Month

2-30 Chapter2 FLUX
Histogram

Autocor

GridOpt

List

Residuals

All

Out 1 i ers

Signif

Breakdowns

Jackknife

Utilities

output

Screen

File

View

Set

Events

Signif

Restrict

Method 6

Help

Quit

Data-Entry

Histogram of Residuals for Current Calculation Method

Plot Residua[ Autocorrelation - Resid(t) vs. Resid(t-1)

Toggle Plot Grids On or Off

List Output Formats for Current Calculation Method

List Residuals & Screen for Outliers

List All Residuals Uithout Screening for Outliers

List Outliers

Set Significance Level for Outlier Screening

List Load & Flow Breakdowns by Stratum; Optimal Sample Allot

List Jackknife Table for Current Calculation Method

Program Utilities & Options

Select Output Destination for Text

Send Output to Screen (Default)

Send Output to Disk File

View anyDOS File

Set Program Options & Parameters

Define Maximm Event Duration (Days) For Grouping Samples

Set Significance Level for Testing Flow/Cone Regression

Toggle Option to Restrict Flow Ranges for Model Application

Toggle Option for Error Analysis Using Calc Method 6

View Help Screens

End Session

Screens

Following isalisting ofeach data-entry screen inFLUX and itsassociated

HELP file. TheseareaccessedviatheData/Read or DattiStrati@ procedures.

The help screens areaccessedby hitting <Fl>. Additional help screens containing more detailed information on specific fields maybe obtained by moving

thecursorto thefield andhitting<F8>; thisworks onlywhen themessage

“<F8>=HELP FIELD’’appears inthelowerright comerofthescreen.

DATA-ENTRY SCREEN: Data/Read/Reset,Keep,orSamples

TITLE:

DOS PATH:

FLOU DATA FILE:

FLOU LABEL:

SAMPLE DATA FILE:

SAUPLE STATION CODE:

CONC VARIABLE:

FLOU VARIABLE:

SCREENING VARIABLE:

FLUX INPUT SCREEN

CONC UNIT FACTOR:

FLOU UNIT FACTOR:

FLOU SIGN (1 or -1)

RANGE : TO

SAPIPLE DATE RANGE: >= < (YYMMDD)

FLOU DATE RANGE: >= < (YYt4MDD)

SEASON RANGE: >= < (MMDD )

Chapter2 FLUX 2-31
HELP SCREEN:

Data Read

Read input sanple & flo~ data from disk files.

PATH specifies directory for input files (e.g., C:\FLUX)

Input file formats specified by file extensions:

‘file.FLX’ - original FLUX format

‘file.HKl’ - LOTUS-123 Uorksheet

‘file.DAT’ - free-format ASCII File

‘ffle.ASC’ - alternative free-format ASCII

Ofile.FLO’ - alternative free-format for daily flow

Use Procedure lHelp’ or <F9> to get description of file formats.

CONCENTRATION & FLOU SCALE FACTORS are read from .FLX files. They

must be entered on screen for other input file formats. Use a flow

scale factor of .8937 if file flows are in ft3/sec (cfs).

If CONCor FLOU labels are blank, user will be asked to select them

from list of all fields contained in file.

Press <F8> to get help on specific inout fields.

DATA-ENTRY SCREEN: Data/Read/Index:

READ SAMPLE & FLOU DATA FROM STATION INDEX FILE

TITLE:

DOS PATH:

STATION INDEX FILE:

SCREENING VARIABLE: RANGE : TO

SAMPLE DATE RANGE: >= < (YYMMDD)

FLOU DATE RANGE: >= < (YYMMDD)

SEASON RANGE: >= < (MMDD)

HELP SCREEN:

Data Read Index

Reads New Samples & Flows from data files specified in a

Station Index File (*.IDX). Station Index Files facilitate

access to sample and flow data. Suggest creating a separate

index file for each project or reservoir.

An ASCII text editor (e.g. DOS EDIT) is required to create

or edit an index file (outside of FLUX).

Use one of the s~le index files (*.IDX) as a teinplate.

If the TITLE is blank, station label will be assigned.

If the index file name is blank, user will be pro@ed to select

from a list of all index files stored in the current PATH.

Resets stratification scheme after data are read.

See ‘Help - Station Index File FormatC for details.

2-32 Chapter2 FLUX
DATA-ENTRY SCREEN: Data/Stratify/Flow

STRATI FY BASED UPON FLW

UNITS = HM3/YEAR

MEAN FLOU:

MAXIMUMFLOU:

SAMPLE FLOU

STRATUU UPPER FLOU LIMIT COUNT CWNT

1<

2<

3<

4<

5<

HELP SCREEN:

Data Stratify FlobJ

Divide sanple & flow data into groups or strata based upon flow.

Set upper bound for flow in each stratun.

Sample included in stratum if flow < upper bound.

Season & date ranges are reset.

Flow bounds must be in increasing order.

To include all data, upper bound of last defined stratum

should exceed maximum flow.

Set upper flow limit to O for unused strata.

DATA-ENTRY SCREEN: Data/Stratify/General

—

DEFINE STRATIFICATION SCHEME

FLous-(HM3/YR) DATE-(YYMMDD) SEASON-(M14DD) PREVIOUS

STR >=MIN < HAX >=MIN < MAX >=MIN < MAX SAMP FLOUS

1 —— —

2 —— ——

3 —— —.

4 —— —

5 —— .— —

Chapter2 FLUX 2-33
HELP SCREEN:

Data Stratify General

Divide sample & flow data into groups or strata based upon flow,

date, and/or season.

Sample & flow counts for previous stratification scheme (before

editing) are shown on right.

Set limits to 0,0 to

Also, if MIN=MAX, al

Seasonal Definitions

inclde all data.

data are included.

Wraparound Calendar, e.g.:

MIN= 0401, MAX=1OOI ‘(sanples between-April 1 & Sept 30)

MIN= 1001, HAX=0401 (samples between Oct 1 &March 31)

Samples and flows not within any defined stratun are excluded

from load calculations & displays.

Data File Formats

FLUX requires input data files containing sample data(i.e. ,theconcentrations and instantaneous flows)andflowdata (i.e., thecontinuous flow record

fortheperiod ofinterest). Experiencewiththe program indicates thatmostof

theeffortrequired to applytheprogram involves settingup therequired data

files. Several format options are provided to facilitate this task. Five data-file

formats aresupported forsample and flowdata records. One format is supported fortheoptional station index file. Brief descriptions, naming conventions, and file names are given in Table 2.5.

Table 2.5

FLUX File Formats

File Naming File

Format Convention Contents Examples

FLUX formatted ●.FLX Sample and flow data CADDO.FLX

ASCII *.DAT Sample data CADDO_S.DAT

Flow data CADDO_O.DAT

ASCII * .ASC Sample data cADDo_s2.Asc

ASCII *.FLO Flow data CADDO.FLO

Lotus- 123 ●.WK1 Sample data CADDO_S.WKl

Release 2.X “ CADDO_S1.WKl w cADDo_s2.wKl

Flow data CADDO_Q.WKl

ASCII ●.IDX Station index CADDO.IDX

2-34

Although only one spreadsheet format is provided (*.WK1), most other

spreadsheet programs (including Windows versions) can export files in the

Chapter 2 FLUX
.WK1 format. Lotus WK3 and WK4 (Windows) file formats are not equivalent to the WKl format. If a Windows version of Lotus is being used, all of the

data must be stored on the first page of the worksheet, and the .WK1 extension

must be specified in saving the file. If the user’s spreadsheet program cannot

save or convert files to the .WK 1 format, data can be printed to a disk as an

ASCII file and edited to comply with one of the ASCII formats described

below.

The following general rules apply to all file formats (except where noted):

a.

b.

c.

d.

e.

$

/3

h.

i.

j.

A Date field must be included, labeled at the top of the file as follows:

DATE Lotus-123 date (Days from Jan 1, 1900), or

YYMMDD year-month-day format, numeric value

(This does not apply to the *.FLX format in which dates are always

assumed to be in YYMMDD format). Dates cannot be specified as

character strings.

Spreadsheet columns must be contiguous starting with Column A (no

blank CO1lllllllS).

Spreadsheet Rows must be contiguous (reading stops at first blank

row). Entries beyond the first blank row in a spreadsheet are ignored.

Sample files can be sorted in any order.

Daily flow files should be sorted by date.

Missing values are identified using the missing value codes specified at

the top of the file (ASCII formats).

Blank fields in spreadsheets are assumed missing. If a blank field is

intended, make sure that it is truly blank and not a character field filled

with spaces; the latter will be interpreted as zero (not necessarily

missing).

For concentrations, blank, negative, zero values, or character strings are

assumed missing.

For daily flows, negative or zero values (other than the specified missing

value code) or character strings are interpreted as zeroes (no flow).

With the exception of the optional station field in the first column of

sample worksheets, all spreadsheet entries should be numeric values or

blank. Character constants are interpreted as zeroes. Computed fields

in spreadsheets (numeric values assigned by formulas) are acceptable

for all fields except the optional station field (character string).

Chapter 2 FLUX 2-35
k. In speci&ing file names, variable labels, and station codes, case is not

significant (i.e., “stal” = “STA 1” = “StA 1” ).

1. A maximum of 64 fields (columns) can be contained in the sample or

flow data sets. FLX format files can contain up to seven fields.

Each file format is described in detail below. Examples are provided on the

program diskette.

* .FLX Format for Sample & Flow Data

This format is indicated by the .FLX file extension. This fixed-format file

contains both sample data and daily flow data. The file contains four groups:

Group 1: Title (maximum =48 characters)

FORMAT (6A8)

Group 2: Variable Index - ID, LABEL, CF

FORMAT (12,1X,A8,F8.0)

ID = Integer subscript (maximum = 7)

LABEL = Flow and water quality variable label (e.g.,TOTALP, FLOW)

(maximum = 8 characters)

CF = Factor to convert data units to program units

Program Units = MILLION M3NR (hm3/yr) for flow

Program Units = MG/M3 = PPB for concentration

NOTES:

a. Conversion factors contained in the input file will override those

specified on the input screen.

b. If the flow lookup option is used (sample flows retrieved from daily

flows), the appropriate flow conversion factor must be specified on the

FLUX data-ent~ screen.

c. The order of variable labels must correspond to that specified in Data

Group 3 (columns).

d The last record of Data Group 2 must be - “00”.

2-36

Group 3: Water Quality Records - DATE, S, (C(I),I=l,N)

FORMAT (F6.0,2x,7F8.0)

Chapter 2 FLUX
DATE =

C(I) =

N =

NOTES:

Date in YYMMDD 6-character format (e.g., 840126) or

YYYYMMDD 8-character format (e.g., 19840126)

Data value (include decimal points or right-justi~ in field;

entries that are blank, zero, or negative are assumed to be

missing). At least one of these should refer to sample

concentration. The sample flow field is optional if the

‘Lookup’ option is specified when retrieving data.

Number of variable indexes defined in Group 2

a. The last record of Data Group 3 must be - “000000”.

b. Include one record for each sample (maximum samples= 500).

c. Use blanks, zeros, or negative values for missing concentrations or

sample flows.

Group 4: F1OWDistribution Records - DATE, FLOW

FORMAT (F6.0,2x,F8.0)

DATE = Date in YYMMDD 6-character format or YYYYMMDD 8-

character format

Use a consistent format within each file. A 6-character

DATE field is interpreted as follows:

YYMMDD Year Month Day

990113 1999 01 13

000113 2000 01 13

Rule:

YY0113 19YY 01 13 IfYY >=50

YY0113 20YY 01 13 IfYY <50

FLOW = Flow must be in the same units as the sample flows specified

in Group 3. Include decimal point or right-justi$ in field.

Zero or negative entries are valid. Blank values are interpreted as zeros (omit the entire record if flow is missing for a

given date).

NOTES:

a. The last record of Data Group 4 must be - “000000”.

b. Include one record for each mean daily flow (maximum flow

records = 7000).

Chapter 2 FLUX 2-37
The file ‘CADDO.FLX’ is an example of the 6-character date format:

degray inflow, Jan 78 - Dec 80 - flows in cms

id- label----cf -----

01 flow 31.56

02 total p 1.

03 total dp 1.

04 ortho p 1.

00

dates flow total p tdp ortho p

780102 4.70 12.00 4.00 4.00

780109 4.39 11.00 10.00 4.00

780117 47.00 71.00 0.00 4.00

780123 9.08 18.00 0.00 8.00

780130 16.30 19.00 0.00 0.00

etc.

810922 2.98 16.00 9.00 8.00

810929 13.80 23.00 14.00 10.00

000000

date flow

780101 5.09

780102 4.66

780103 4.66

780104 4.66

etc.

801229 4.35

801230 4.25

801231 4.13

000000

<EOF>

Group 1

Group 2

Group 3

Group 4

The file ‘CADD02K.FLX’ is an example of the 8-character date format.

*.DATASCII FormatforSample orFlowData

This format is specified bythe ’.DAT’ file extension.

format ASCII file. Column locations are not significant.

by spaces or commas. The layout is as follows:

Line 1 Title

This is a freeEntries are separated

Line 2 Number of Variables= M (columns in database)

Line 3 Missing Value Code (Typicallyzeroor negative)

Line 4 to 3+M Variable Labels (Max 8 Characters Per Label)

Line3+M...n DataRecords (Any Number, Max500 used atonetime)

Variable labels must include a date field labeled as:

YYMMDD for dates in YYMMDD Format, or

DATE for dates in Lotus Format (# Days from Jan 1, 1900)

For compatibility after 1999, sample or flow dates specified

using the YYMMDD format are interpreted as follows:

YYMMDD Year Month Day

980113 1998 01 13

000113 2000 01 13

113 2000 01 13

1000113 2000 01 13

2-38

Chapter 2 FLUX
Rule:

YY0113 19YY 01 13 IfYY >= 50

YY0113 20YY 01 13 If YY<50

It is recommended that the alternative DATE format (Sequence

@om 1900/1/1) be used in spreadsheet~les (“.WKI).

If the *.WK1format is used, DATE or YX!l.4MDDvalues must

be stored in the spreadsheet as numerical values (not labels or

characters!~.

Variable labels may include sample flows, concentrations, screening variables, or other record identifiers. Columns must be contiguous (no blank

columns). Rows (data records) must also be contiguous. Sample records can

be sorted in any order.

Units conversion factors are not included in the file. These must be specified on the FLUX Input Screen or in the station index file (see below).

The file ‘CADDO_S.DAT’ is an example of this format for sample records:

degray inflow flows in cms

5

+

tp

total dp

ortho p

780102 4.7 12 4 4

780109 4.39 11 10 4

etc.

810922 2.98 16 9 8

810929 13.8 23 14 10

<EOF>

The file ‘CADDO_Q.DAT’ is an example of this format for daily flow records:

degray inflow, Jan 78 - Dec 80 - flows in cms

2

-999

yymndd

flow

780101 5.09

780102 4.66

780103 4.66

etc.

801230 4.25

801231 4.13

<EOF>

*.ASC ASCII Format for Sample Records

This alternative ASCII format for sample data can be used (instead of

*.DAT format) for files containing data for more than one station. The file

layout is as follows:

Chapter 2 FLUX 2-39
Line 1 ‘Title’ (enclosed in single quotes)

Line 2 Number of Fields (columns) = Nfields

Line 3 Missing Value Code

Lines 4 thru 3+Nfields ‘Field Labels’ (enclosed in single quotes)

Lines 4+Nfields etc Sample Records, free-format

Each sample record contains station code, date, and numeric fields.

All character entries in this file must be enclosed in ‘single quotes’. This

includes the title line, field labels, and station labels. Fields are delimited by

spaces or commas.

The first data field (column) is used to speci& 8-character station codes,

enclosed in ‘single quotes’.

The file ‘CADDO_S2.ASC’ is an example of this format for sample

records:

‘degray inflow, flows in m3/sec - dates in yymmdd format’

6

-999.999

‘Station’

‘YYmmdd’

‘flow’

‘Q’

‘tdp’

‘Orthop’

‘Caddo’ 7801024.71244

‘Caddo’ 7801094.3911104

‘Caddo’ 7801174771-999.9994

etc.

‘Caddo’ 8109153.25481515

‘Caddo’ 8109222.981698

‘Caddo’ 81092913.8231410

<EOF>

Although this example includes data from only one station, records from

other stations can be included in the file; the program will select the appropriate

records based upon the sample station code specified on the FLUX Input

Screen. If the specified sample station code is blank, all records are selected.

* .FLO ASCII Format for Daily Flow Data

2-40

This ASCII format for daily flow records is indicated by the ‘.FLO’ extension. This is a free-format file containing one record per month:

Chapter 2 FLUX
Line 1 Title (station descriptor, etc.)

Line 2 Missing Value Code (must be a negative number)

Line 3.n Daily Flows (one record per month)

YY MM Q1 Q2 Q3 Q4 Q5 .... Qn, or

YYYY MM Q1 Q2 Q3 Q4 Q5 .... Qn, wheren=# days in month

Data records are fi-eeformat, delimited by commas or spaces (one line/month).

The program will read the appropriate number of days per line, depending

upon specified year and month.

If Line 2 (missing value code) is omitted, all negative values in the flow file

are interpreted as missing.

The year can be in 2-character ~) or 4-character (YYYY) format (e.g.,

80 or 1984). Years between Oand 49 are interpreted as 2000 to 2049.

The file ‘CADDO.FLO’ is an example of this format for daily flow records:

ca*_q. f 10

-1

78 1 5.094.664.66 (etc. for 31 values) 18.29 15.81 13.42

78 2 11.72 10.51 9.73 (etc. for 28 values) 9.08 9.8

etc.

80 12 5.38 5.23 (etc. for 31 values) 4.35 4.25 4.13

* .WK1 Lotus-1 23 (Rel. 2.x) File Format for Sample Data

This spreadsheet format for sample data is indicated by the .WKI extension.

The layout is as follows:

ROU A B c D E F <-- COLUMN

1 Uorksheet Title < -- title

2 STAT 10N DATE VAR1 VAR2 VAR3 etc. <-- labels (<=64)

3 stal 01/01/86 10.0 20. < -- data records

4 stal 02/03/87 15. 23. 34. II

5 sta2 01/02/86 23. 100. II

etc. . . (records cent i guous )

The STATION field (optional) can be used to select data from a specific

station. If included, STATION codes must be stored as character constants in

COLUMN A of the worksheet. If the STATION column is excluded, FLUX

will read all data from the file.

One field may refer to sample flows, others to concentrations (Example:

VAR1 = flow, VAR1 = total p, VAR2 = ortho p, etc.) or to sample identifiers.

The Date label (Cell B2 in this example) must be DATE if dates are stored

in Lotus format (days fkom January 1, 1990). The Date label must be

WMMDD if dates are stored in YYMMDD format (numeric values only).

The file ‘CADDO_S. WK1’ is an example of this format with the optional

station field included and dates stored in Lotus format:

Chapter 2 FLUX 2-41
A B c D E F

1 degray inflow, flows in m3/sec

2 Station date flow tp tdp orthop

3 UK 456 01123178 3.61 28 22 13

4 U1568 09/29/81 3.01 24 17 12

5 Xxxx 09/08/81 3.57 18 15 13

6 1234 04/24/78 26.59 42 36 22

7 Caddo 01/02/78 4.7 12 4 4

8 Caddo 01/09/78 4.39 11 10 4

9 Caddo 01/17/78 47 71 4

10 Other 03/06/78 7.92 25 25 12

11 Caddo 01/23/78 9.08 18 8

12 Caddo 01/30/78 16.3 19

etc.

The file ‘CADDO_S 1.WK1’ is an example of this format with the optional

station field excluded and dates stored inLotusformat:

A B c D E F

1 degray inflow, flows in m3/sec

2 date flow tp tdp orthop

3 01/02/78 4.7 12 4 4

4 01/09/78 4.39 11 10 4

5 01/17/78 47 71 4

6 01/23/78 9.08 18 8

7 01/30/78 16.3 19

The file ‘CADDO_S2. WK1’ is an example of this format with the optional

station field included and dates stored inYYMMDD format:

A B c D E F

1 degray inflow, flows in m3/sec - dates in yymndd format

2 Station Z flow tp tdp orthop

3 Caddo 4.7 12 4 4

4 Caddo 780109 4.39 11 10 4

5 Caddo 780117 47 71 4

6 Caddo 780123 9.08 18 8

*.WK1 Lotus-123 (Rel. 2.x) File Format for Daily Flow Data

This spreadsheetformat can be used forcompact storage offlow data from

multiple stations:

ROU A B c D E <-- COLUMN

1 Daily Flow Data Base < -- title

2 DATE STA1 STA2 STA3 etc. <-- labels (<=64)

3 01/01/86 10. 20. <-- data records

4 01/02/86 15. 23. 34. II

5 01/03/86 23. 100. II

etc...

Columns B+ contain daily flow data from different stations.

(e.g., STA1 = flow data from station 1, STA2 = data from station 2)

If flow data are missing, omit the entire row or leave field blank.

2-42

DATE or FLOW fields can be formulas or numeric constants.

Chapter2 FLUX
The file ‘CADDO_Q.WKl’ is an example of this format for daily flow

records:

A B c D E

1 degray daily flows in m3/sec

2 date Caddo Sta2 Sta3 etc. . .

3 01/01/78 5.09

4 01/02/78 4.66

5 01/03/78 4.66

6 01/04/78 4.66

7 01/05/78 4.66

etc. . .

* .IDX Format for Station Index

A separate index of station codes can be maintained on disk to facilitate

reading of sample and flow data. The default extension of’ *.IDX’ is suggested

to identi~ a station index file. A maximum of 63 stations can be indexed in a

given file. An index file is accessed through the Data/Read/ Index procedure.

The format is as follows:

Line 1 Title (for user reference)

Line 2 Flow Scale Factor (default, can be modified when read)

Line 3 Concentration Scale Factor (“”)

Lines 4+ Station Record, fields enclosed in ‘quotes’

Station Record Format:

Field Description

1 station identifier (<= 8 characters)

2 sample station code (reference values in sample file)

3 sample file name

4 sample flow variable (’lookup’ to retrieve from daily flow data)

5 flow station code (for .WK1 or .DAT data file types)

6 daily flow file

7 flow sign (+1 or -1) not enclosed in quotes

This is a free-format file with fields delimited by spaces or commas. All

character strings must be enclosed in single quotes.

It is usefhl to create a separate index for each reservoir or group of stations

in a common application.

The file ‘CADDO.IDX’ is an example:

‘Station Index for Caddo R - Each Reads Equiv. Data from Different Fi le Forrnatsl

31.56 ‘Default Flow Scale Factor (except for *.FLX files)!

1 ‘Default Cone Scale Factor (except for *. FLX f i les)’

‘Caddol’ ‘ ‘ ‘Caddo. fix’ ‘flow’ II ‘caddo. fix’ 1

‘ Caddo2’ ‘ ‘ ‘ caddo_s .dat’ ‘flow’ II ‘caddo_q. flo’ 1

‘caddo3’‘ ‘ ‘caddo_s .dat I ‘flow’ ‘flow’ ‘ caddo_q. dat’ 1

‘ Caddo4’ ‘ Caddo’ ‘ caddo_s. wkl I ‘flow’ ‘caDDo’ I caddo_q. wkl I 1

‘Caddo5’ ‘ ‘ ‘ caddo_sl .wkl I ‘flow’ ‘ CaddO’ ‘ caddo_q. wkl’ 1

‘Caddo6’ ‘ CADDO’ ‘ caddo_s2. wkl’ ‘flow’ II ‘caddo_q. flo’ 1

Chapter 2 FLUX 2-43
‘ Caddo7’ ‘Caddo’ ‘caddo_s2. asc’ ‘ fLOw’ II ‘caddo_q.f 10’ 1

‘Caddo8’ ‘ ‘ ‘caddo.flx’ ‘flow’ ‘flow’ ‘caddo_q.dat’ 1

‘ Caddo9’ ‘Caddo’ ‘caddo_s.wkl’ ‘flow’ II ‘caddo_q.flo’ 1

‘Caddo10’ ‘Caddo’ ‘caddo_s.wkl’ ‘flow’ ‘ CADDO ‘ ‘caddo_q.wkl ’ 1

‘Caddoll’ ‘ ‘ ‘caddo_s.dat’ ‘flow’ II ‘caddo.flx’ 1

Field 1 2 3. 4 5 6 7

Once the station index file is created, the need to speci& sample and flow

data files ondata-entry screens is eliminated. Theuser selects thedesiredstation (Caddol thru Caddoll) froma menu and the remaining details areread

fromtheindexfile.

This example illustrates the widevarietyof options which are available for

setting up FLUX input files. Each ofthe ’Stations’ identified above ’Caddol’

through ‘Caddo 11’ reads in exactly the same data by accessing files with different formats. hactudapplications, each station would refer to a different

location or data set. Examples of other *.IDX files are included on the program diskette.

FLUX Documented Session

This section demonstrates a typical FLUX session. As a training exercise,

the user should be able to recreate this session by running FLUX and accessing

the data files for Caddo River supplied with the program. Notes to the user are

provided in italics below. Selected menu options are underlined. To begin,

enter ‘flux’ at the prompt.

FLUX

FLUX

STREAM LOAD COMPUTAT IONS

VERSION 5.0

Envi ronrnental Laboratory

USAE Uaterways Experiment Station

Vicksburg, Mississippi

December 1998

PRESS KEY TO CONTINUE, <ESC> RETURN TO MENU 100

Aseries ofintroductory screens appear. These contain brief descriptionsof

the program and summarize any new features not documented in this manual.

To bypass these screens, press KESC>and the program menu will appear.

E::;L::;::F5;’’:;”S ““ ““t

1 MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F I,F7> HELP

2-44

Chapter2 FLUX
.00 HM3/YR

.00 HM3/YR

VARIABLE =

SAMPLE FILE = STATION =

SAMPLES = O, DATES = o to o, UEAN FL(XJ =

FLOU FILE = FIELD =

FLCWS = O, DATES = o to o, HEAN FL(IU =

MAX EVENT DURATION = 1 DAYS, FLOU RESTRICTION = YES

STRATUM : 1 EXCLU TOTAL

SAMPLE CWNTS: o 0 0

EVENT CCXJNTS: o 0 0

FLCNJ COUNTS: o 0 0

WTPUT TO: SCREEN CALC METHOD: Q UTD C

Aone-linemessage describingthe currently selectedprocedure appearsatthe

bottom ofthe menu box. Characteristics ofthe currentdata setandprogram

option settings are listedon the bottom halfofthe screen. Since no data set

hasbeen loaded, the above valuesarezeroes orblank.

SelectIlatalReadlhdex toreadinadata setfor CaddoRiver:

FLUX - VERSION 5.0

Calcu(ate Method Plot List Utilities Help Quit

t Stratify Delete Composite F 1owsub Title List

I

Reset Keep Samples -1nde~

1 Read Sample & Flow Data from Station Index File

1 MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <FI,F7> HELP

READ SAMPLE & FLOU DATA FROM STATION INDEX FILE

TITLE: Caddo River

DOS PATH: d:\coe\flux\caddo

STATION INDEX FILE: caddo.idx

SCREENING VARIABLE: RANGE: O TO O

SAMPLE DATE RANGE: >= O <0 (YyHMDD)

FLOU DATE RANGE: >= o <0 (YYMMDD)

SEASON RANGE: >= o <0 (HMDD)

station index file name F8=HELP/FIELD

FI=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

l_heprogramreads the station indexJle ‘caddo.idx’andlists theindexed

stations. As discussed intheData File Formats section, this example index

file illustrates a variety of data set con~gurations all accessing the same data.

I.npractice, users can create separate indexJles tofacilitate access todatafor

dl~erent stations within a given projector reservoir. Caddol is selected here.

Date orseason limits can reentered on thisscreen. Press <F2> toproceed.

Chapter2 FLUX 2-45
> FIELD

caddo2

caddo3

caddo4

Caddo5

caddo6

caddo7

caddo8

caddo9

Caddolo

Caddol 1

Sample atiJow$les for the selected station are opened. i%e program reads

thejile headers and asks the user to select the variable to be analyzed (total p)

@om a list of all~elds contained in the sample~le.

Locating Sanple File . . . .

OPENING SAMPLE FILE = caddo. flx

>

—

FIELD

flow

@tat Q

total dp

ortho p

DEFINE FIELD FOR: CONCENTRATION

Locating Sample File . . . .

OPENING SAMPLE FILE = caddo. flx

SAMPLE CONCENTRATION FIELD = total D

CONCENTRATION UNITS FACTOR = ‘1.000000

Define Flow Scale Factor

Scale Factor ? < 31.5600” > ?

Define Concentration Scale Factor for: total p

Scale Factor ? < 1.00000 > ?

Flow Scale Factor = 31.5600

Cone Scale Factor = 1.0000

Reading Sanples...

degray inflow, Jan 78 - Dec 80 - flows in CMS

NUMBER OF SAMPLES = 168

Reading Flows...

OPENING FLOU FILE = caddo.flx

degray inflow, Jan 78 - Dec 80 - flows in cms

NUMBER OF FLOU RECORDS = 1096

<H>

Sample andjlow countsare listedas the dhta$lesareread. 7he,S’malefactor

promptspermituser to changedefault scalefactorsstored in thestation index

jVe. Press <llnter >toacceptdefaul tvalues.

Caddo River VAR=total p METH~= 2 Q UTD C

TABULATION OF HISSING DAILY FLOUS:

Flow File =caddo.flx I Station =

Daily Flows frcm 780101 to 801231

Sumnary:

Reported Flows = 1096

Hissing Flows = O

Zero Flows = o

Positive Flows = 1096

<EOF>

2-46

Chapter2 FLUX
An inventory of daily~ows is presented, including date range, missing values,

and zero values. Anyflow records out of sequence would also be listed here.

Control returns to the main menu.

— =FLUX - VERSION 5.0

Data Calculate Method Plot List Utilities Help Quit

Read Stratify Delete Composite F 1ousub Title List

Read and/or Stratify Data

MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN RWTINE, <FI, F7> HELP

P

Caddo River VARIABLE =

SAMPLE FILE = caddo.flx STATION =

SAMPLES = 168, DATES = 780102 to 810929, MEAN FLOU =

FLOU FILE = caddo.flx FIELD =

FLCMS = 1096, DATES = 780101 to 801231, HEAN FLOU =

MAX EVENT DURATION = 1 DAYS, FLOU RESTRICTION = YES

STRATUM : 1 EXCLU TOTAL

SAMPLE COUNTS: 168 0 168

EVENT COUNTS: 168 0 168

FL(IU COUNTS: 1096 0 1096

OUTPUT TO: SCREEN

i%ebottom ha~ofthe screen summarizes thecurrent

can be listed using the DatalListlS amplesprocedure:

total p

405.16 HM3/YR

413.59 HM3/YR

CALC METHOD: Q WTD C

case data. Sample data

FLUX- VERSION 5.0s

Calculate Method Plot List Utilities Help Quit

Read Stratify Delete Composite

~ F1OWS Sanples

F 1owsub Title U

List Sample Data

I MOVE CURSOR&HIT <Enter>OR <First Letter> TO RUN ROUTINE, <F1, F7> HELP

Caddo River VAR=total p METHOD= 2 Q UTD C

SAMPLE DATE EVENT STRATUM DAILY-FL(IU SA14PLE-FLOU CONC FLUX

1 780102 1 1 147.07 148.33 12.00 1779.98

2 780109 2 1 142.97 138.55 11.00 1524.03

3 780117 3 1 1313.53 1483.32 71.00 105315.70

etc...

USE KEYPAD, <F1>=HELP, <F8>=SAVE, <ESC>=QUIT OUTPUT

Bothahi[ymean jlowsandsample jlowsarelisted alongwithsample concentrations. Zhelistingextends beyondthe bottom ofthe screen. [Jse thekeypad

arrows toforwardor backward through thejle. Zhelisting canbesavedon

disk bypressing <F8>. Press <Esc> to continue.

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart Cone Load Flow Daily Qfreq Residuals GridOpt

Month Histogram

~ 2Log 3Filled

Plot Daily Flows (hrn3/yr) vs. Date - Linear Scale

I MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN RCNJTINE, <F1,F7> HELP

Chapter2 FLUX 2-47
Caddol

M30Eq

Oaee -

D

6080 -

F

L

o

u 4000 -

29W3-

t3

78

I T

79 80

Df3TE

Plotting the dailyflow record (Plot/Daily/Date/Linear) shows hydrography

ji?atures and the dates of sample collection (squares). Note that relatively few

high--ow samples were collected during the high-runoflperiod in late 1978 to

early 1979. The square symbols indicate the daily fiows on the dates of

sample collection (not the sample flows).

7ke CaIculatelCompare procedure provides a more quantitative comparison

of sample and totalflow distributions.

v;”’[’tvER’;’:’”’’ Compare Sample and Total Flow Distributions “lP‘“i’

Comparison of Sanpled & Total Flow Distributions

------ SAMPLED ----- ------- TOTAL -. -.. .

STRAT N MEAN STD D“ MEAN STD D“ DIFF T PROB(>T)

1 168 405.16 795.10 109! 413.59 781.02 -8.43 .13 .894 *** 168 405.16 795.10 1096 413.59 781.02 -8.43 .13 .894

Average Sarrple Interval = 8.1 Days, Date Range = 780102 to 810929

Uaximum Sanple Interval = 41 Days, Date Range = 790123 to 790306

Percent of Total Flow Volune Occurring In This Interval = 6.4%

Total Flow Volune on Sampled Days = 47003.2 hfi

Total Flow Volune on All Days = 453292.5 hm3

Percent of Total Flow Volume Sa~led = 10.4%

Maximum Sampled Flow Rate = 6406.68hfi/yr

Maximum Total Flow Rate = 9305.78hm3/yr

Nunber of Days when Flow Exceeded Maximun Sampled Flow = 4 out of 1096

Percent of Total Flow Volume Occurring at Flow Rates Exceeding the

Maximum Sampled Flow Rate = 7.1%

2-48

Chapter2 FLUX
The last statistic indicates that the high-flow regimes are not represented very

well in this case. Xhis is consistent with impressions derived above from the

dailyflow plot. Plotting concentration against~ow is generally appropriate

here.

—FLUX- VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart ~ Load Flou Dai [y Qfreq Residuals GridOpt

Date Month Estimated Histogram

Plot Sanple Concentration vs. S~le F1OM

c

o

N

c

Caddol

NETNOD: 2 0 MTDC

I

❑

❑

o

6d-

❑ ❑ ❑

0

0000

00

0

‘%

I I

100 mm S FLOn

. ES?IMTE

Concentration increases with~ow. Since the ahta are not stratljied and

Method 2 is selected, the predicted concentration is constant. Regression

methoak attempt to represent concentration variations with~ow within each

stratum. i%is can be demonstrated by selecting Method 6 and repotting.

=f:i!’f-z:::!::=it

FLUX - VERSIOH 5.0

Data Calculate Method List Utilities Help Quit

Barchart ~ Load Flow Daily Qfreq Residuals GridOpt

Date Uonth Estimated Histogram

Plot Sanple Concentration vs. Sample Flow

Chapter 2 FLUX 2-49
Caddol

NET~D: 6 REC-3

c

o

N

c

o

L, 1 * , , I , ,

lm lme

s FLon

When Method 6 is selected, the predicted concentration varies with flow.

Some nonlinearity is evident. Concentrations are underpredicted at high

jlows. This suggests that moreflow strata are needed to capture the~ow/

concentration relationship.

I’_hefollowing sequence demonstrates the ejiects of stratlfiing the data on

the load estimates. Loads arejirst calculated without stratljication.

Method 2 is reselected.

FLUX - VERSION 5.0

Data Qlculate Method Plot List Utilities

Compare w Series

Help Quit

Calculate Loads Using Each Method

Caddo River VAR=total p METHOD= 2 Q UTD C

CCMfPARI SON OF SAMPLED AND TOTAL FL(3U DISTRIBUTIONS

STR NQ NC NE VOL% TOTAL FLOU SAMPLED FLOU C/Q SLOPE SIGN I F

1 1096 168 168 100.0 413.588 405.163 .396 .000

*** 1096 168 168 100.0 413.588 405.163

FL(IU STATISTICS

FLW DURATION =

MEAN FLOU RATE =

TOTAL FLOU VOLUUE

FL(XJ DATE RANGE

SAMPLE DATE RANGE

1096.0 DAYS = 3.001 YEARS

413.588 HM3/YR

= 1241.05 HM3

= 780101 TO 801231

= 780102 TO 810929

2-50

Chapter2 FLUX
METHOD MASS (KG) FLUX (KG/YR) FLUX VARIANCE CONC (PPB) Cv

1 AV LOAD 93253.1 31077.3 .7923E+08 75.14 .286

2QUTDC 95192.3 31723.5 .2872E+08 76.70 .169

3 IJC 96738.0 32238.7 .2913E+08 77.95 .167

4 REG-1 95971.5 31983.2 .1927E+08 77.33 .137

5 REG-2 92308.6 30762.5 .2024E+08 74.38 .146

6 REG-3 73497.2 24493.5 .7845E+07 59.22 .114

<EOF>

Results (both the loadestimateand C~forMethod6 aresomewhatlower

than resultsfor the other calculation methods. ResultsforA4ethods l-5are

within arelatively narrow range. 7%isisshown graphicaUy using the Plotl

Barchart procedure:

—FLU X - VERSION 5.0-

Data Calculate Method List Utilities Help Quit

~ ConC Load Flow Daily Qfreq Residuals GridOpt

Mass Cones Flow

lfethml Stratun

Plot Load Estimates (kg/yr) vs. Calculation Method

W+R: total p LORD(KG/YR)

ESTINRIE 4/- 1 STRNDfiRD ERROR

4

I r I n—

4HHHHFl II I I I I l— I l—

R 2aeed- 1

W IJxu) Q MTDC IJC REG-1 REG-2 REG-3

NE TNOD

cM-SE M+SE

Wewillnow trystratlfiing thedata using2flow intervals.

FLUX- VERSION 5.0

Calculate Uethod Plot List Utilities Help Quit

Read ~ Delete Composite F 1owsub Title List

General Reset List

2 strata 3 Strata 4 Strata Other

2 Flow Strata - Boundary at QMEAN

Chapter2 FLUX 2-51
STRATIFY BASED UPON FLOU

UNITS = HM3/YEAR

MEAN FLOW: 413.588

MAXIMUM FLOU: 9305.78

SAMPLE FLOU

STRATUM UPPER FLW LIHIT CWNT COUNT

1 < 413.588 0 0

2 < 10236.3 0 0

3 <0 0 0

4 <0 0 0

5 <0 0 0

< mm flou hund for stratum 1 (hm3/yr)

F1=HELP, F2=DtiE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

The valuesshownon the editscreenare automaticallycalculatedfiom the

totaljlowdistribution. i’heseca nbeeditedatthispoint. Press <F2> when

you are done editingor toaccept thedefaultvalues. An inventoryofsample

countsandJow values in each stratum is listed:

Caddo River VAR=total p METH~= 2 Q UTD C

STRATIFICATION SCHEME:

-- DATE -- -- SEASON -- -------- FLOU --- . . . . .

ST! >=MIN < MAX >=MIN < MAX >=MIN < MAX

o 0 0 0 .00 413.59

2 0 0 0 0 413.59 10236.36

STR SAMPLES EVENTS FLOW VOLUME %

1 129 129 833 31.56

2 39 39 263 68.44

EXCLUDED O 0 0 .00

TOTAL 168 168 1096 100.00

Now repeat the concentration versusflowplot:

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart ~ Load Flow Daily Qfreq Residuals GridOpt

Date Month Estimated Histogram

Plot Sample Concentration vs. Sample Flow

Chapter2 FLUX
c

o

N

c

Caddo River

METHOD: 2 Q MTD C

*

* O*

1 n o : ❑ 0

0

I , 1

lm mm s FLON

❑ SIWT-1 e STll~r-2 . ESIlWT~

The predicted concentrations using Method 2 now have two levels, one for

each flow stratum.

Loaak can be recalculated using the current stratljication scheme:

PLu’lO’_ Calculate Loads Using Each Method “’’’’”T

Caddo River VAR=total p METH(XI= 2 Q UTD C

CCMIPARISON OF SAMPLED AND TOTAL FLOW DISTRIBUTIONS

STR NQ NC NE VOL% TOTAL FLOU SAMPLED FLOU C/Q SLOPE SIGNIF

1 833 129 129 31.6 171.762 165.135 .034 .677

2 263 39 39 68.4 1179.523 1199.102 .647 .000 *** 1096 168 168 100.0 413.588 405.163

FL(N STATISTICS

FL(XJ DURATION = 1096.0 DAYS = 3.001 YEARS

MEAN FLOW RATE = 413.588 HM3/YR

TOTAL FLOU VOLUME = 1241.05 HM3

FL(M DATE RANGE = 780101 TO 801231

SAMPLE DATE RANGE = 780102 TO 810929

METHOD MASS (KG) FLUX (KG/YR) FLUX VARIANCE CONC (PPB) c’

1 A’ LOAD 95976.8 31985.0 .7069E+08 77.34 .263

2QUTDC 94942.0 31640.1 .1924E+08 76.50 .139

3 IJC 96125.2 32034.4 .1878E+08 77.45 .135

4 REG-1 94052.8 31343.8 .1539E+08 75.79 .125

5 REG-2 92137.3 30705.4 .2581E+08 74.24 .165

6 REG-3 101996.6 33991.1 .3880E+08 82.19 .183

<EOF>

Estimates are compared using the PMIBarchart procedure:

Chapter2 FLUX 2-53
FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

~ cm Load F1OM Daily Qfreq Resi~als Gri~pt

Mass Cones Flow

Pethod Stratun

Plot Load Estimates (kg/yr) vs. Calculation Method

URR: total p LOfaD (KG/YR)

ESTIIU+TE +/- 1 SIRNDRRD ERROR

aO

+E400

L

o

R

D

El

RULORD Q UTD C IJC REC-1 REG-2 REG-3

METHOD

cM-SE m +SE

Estimatesforallmethodshaveconverged. i%isisa desiredresult. Nowtry3

jlow strata to see whether precision can be improved.

— — FLUX - VERSION 5.0

Calculate Method Plot List Utilities Help Quit

Read ~ Delete Coaposite F 1owsub Title List

Genera 1 Reset List

2 Strata 3 strata 4 Strata Other

3 Flow Strata - Boundaries at QMEAN/2, QMEAN x 2

STRATIFY BASED UPON FLOU

UNITS = H#!3/YEAR

MEAN FLOU: 413.588

MAXIMUM FLOW: 9305.78

SAMPLE FLOU

STRATUM UPPER FLOU LIMIT CWNT COUNT

1 < 206.794 0 0

2 x 827.176 0 0

3 < 10236.3 0 0

4 <0 0 0

5 <0 0 0

2-54

Caddo River VAR=total p METHOD= 2 Q UTD C

Chapter2 FLUX
STRATIFICATION SCHEME:

-- DATE -- -- SEASON -- -------- FLOU --------

STR >=MIN < MAX >=MIN < MAX >=MIN < MAX

1 0 0 0 0 .00 206.79

2 0 0 0 0 206.79 827.18

3 0 0 0 0 827.18 10236.36

STR SAMPLES EVENTS FLOUS VOLU!4E %

1 93 93 582 15.44

2 61 61 407 35.68

3 14 14 107 48.88

EXCLUDED O 0 0 .00

TOTAL 168 168 1096 100.00

<H>

FLUX- VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart ~ Load Flow Daily Qfreq Residuals GridOpt

Date Month Estimated Histogram

Plot Sample Concentration vs. Sample Flow

c

o

N

c

o sTRllT-1

Caddo River

METNOD: 2 0 HTD C

280 I 0

0

00 . . . . . . . . . . .- .

0 0 0 0

* 0

* 0

lea mea 3Bee

S FLCM

* STRf W-2 o STRRT-3 . EST IMflTE

Using 3jlow strata provides a better fit of the flow/concentration relationship.

FLU””; Calculate Loads Using Each Method “’’’5tCaddo River VAR=total p METHOD= 2 Q UTD C

COMPARISON OF SAMPLED AND TOTAL FL(IU DISTRIBUTIONS

STR NQ NC NE VOL% TOTAL FLOU SAMPLED FLOU C/Q SLOPE SIGNIF

1 582 93 93 15.4 120.233 119.816 -.316 .035

2 407 61 61 35.7 397.424 399.808 .543 .001

3 107 14 14 48.9 2070.698 2324.010 .515 .064 *** 1096168 168 100.0 413.588 405.163

Chapter2 FLUX 2-55
FLOU STATISTICS

FLOU DURATION = 1096.0 DAYS = 3.001 YEARS

MEAN FLW RATE = 413.588 HM3/YR

TOTAL FLOU VOLUME = 1241.05 HM3

FL(W DATE RANGE = 780101 T0801231

SAMPLE DATE RANGE = 780102 TO 810929

METH~ MASS (KG) FLUX (KG/YR) FLUX VARIANCE CONC (PPB) Cv

1 AV LOAD 105913.8 35296.5 .6190E+08 85.34 .223

2QUTDC 96537.5 32171.8 .1432E+08 77.79 .118

3 IJC 96872.4 32283.4 .1304E+08 78.06 .112

4 REG-1 92095.1 30691.4 .1783E+08 74.21 .138

5 REG-2 93187.2 31055.3 .1890E+08 75.09 .140

6 REG-3 102935.2 34303.9 .4579E+08 82.94 .197

Precision hasimproved. 7he CVforA4ethod2isdown to0.118.

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

~ COIW Load F1OW Daily Qfreq Residuals GridOpt

Mass Cones Flow

)leth~ Stratum

Plot Load Estimates (kg/yr) vs. Calculation Method

UflR: tota[ p LORD (IUWYR)

ESTIMRTE +/- 1 STRMDRRD ERROR

!51mm3

4em8

L 3-8

0 H

n

D

2mee -

1

T

El El El E El

W LORD Q MID C IJC REG–1 REG-2 REG-3

METHOD

cM-SE ~+sE

Khemethodsarestillconvergent. Now try 4jlowstrata.

FLUX - VERSION 5.0

~ Calculate Method Plot List Utilities Help Quit

~ Delete Composite F 1owsub Title List

General Reset List

2 Strata 3 Strata 4 Strata Other

4 Flow Strata - Boundaries at Q14EAN/2, QMEAN*2, QMEAN*8

2-56

Chapter2 FLUX
STRATIFY BASED UPON FLW

UNITS = HM3/YEAR

MEAN FLOU: 413.588

MAXIMUM FLOU: 9305.78

SAMPLE FLOU

STRATUM UPPER FLOU LIMIT COUNT CWNT

1 < 206.794 0 0

2 < 827.176 0 0

3 < 3308.70 0 0

4 < 10236.3 0 0

5 <0 0 0

Caddo River VAR=total p METH~= 2 Q UTD C

STRATIFICATION SCHEME:

-- DATE -- -- SEASON -- -------- FLOU . . . . . . --

ST! >=MIN < MAX >=PIIN < MAX >=!!IN < MAX

o 0 0 0 .00 206.79

2 0 0 0 0 206.79 827.18

3 0 0 0 0 827.18 3308.70

4 0 0 0 0 3308.70 10236.36

STR SAMPLES EVENTS FLOUS VOLUME %

1 93 93 582 15.44

2 61 61 407 35.68

3 11 11 89 27.53

4 3 3 18 21.35

EXCLUDED O 0 0 .00

TOTAL 168 168 1096 100.00

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart ~ Load Flow Daily Qfreq Residuals GridOpt

Date Month Estimated Histogram

Plot Sample Concentration vs. Sample Flow

Caddo River

METHOD: 2 Q MTD C

‘m 0 0

I 0 I

k

100

8 ❑

b~ . . . .. . . . . . .- .

e o 0 A

0 0

0 0

6L— t I , I

100 lfiuM3 3013B

s FLon

❑ STRRT-1 + STWiT-2 o STRflT-3 A S?RRT-’ ● ESTIkWiTE

Chapter2 FLUX 2-57
i%e highestflow stratum (4) now contains only three samples. Zhis is not a

desirable situation.

I

Data Lalcw Method Plot List Utilities Help Quit

Conpare - Series

Calculate Loads Using Each Method

Caddo River VAR=total p METH~= 2 Q UTD C

COMPARISON OF SAMPLED AND TOTAL FLOU DISTRIBUTIONS

STR NQ NC NE VOL% TOTAL FL(M SAMPLED FLOU C/Q SLOPE SIGNIF

1 582 93 93 15.4 120.233 119.816 -.316

2 407 61 61 35.7 397.424 399.808 .543

3 89 11 11 27.5 1402.069 1450.153 1.011

4 18 3 3 21.4 5376.702 5528.155 1.165 *** 1096 168 168 100.0 413.588 405.163

FLOU STATISTICS

FLOW DURATIOU = 1096.0 DAYS = 3.001 YEARS

MEAN FLW RATE = 413.588 HM3/YR

TOTAL FLOU VOLUME = 1241.05 HM3

FLW DATE RANGE = 780101 T0801231

SAMPLE DATE RANGE = 780102 TO 810929

METH~ MASS (KG) FLUX (KG/YR) FLUX VARIANCE CONC (PPB)

1 AV LOAD 98784.8 32920.7 .2992E+08 79.60

2QUTDC 96312.5 32096.8 .1965E+08 77.61

3 IJC 96872.1 32283.3 .1999E+08 78.06

4 REG-1 93773.0 31250.5 .2775E+08 75.56

5 REG-2 95141.0 31706.4 .3722E+09 76.66

6 REG-3 93901.5 31293.4 .6185E+08 75.66

.035

.001

.087

.467

Cv

.166

.138

.139

.169

.608

.251

Zhe CVvalues using 4~owstrata have increasedrelative to resultsfor 3flow

strata. 7hissuggests thatthesampling intensi~is notsuf~cient tosupport

4 strata.

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

~ cm Load F1OW Daily Qfreq Residuals Gridopt

Mass Cones Flow

Kthi Stratum

Plot Load Estimates (kg/yr) vs. Calculation Method

Chapter2 FLUX
UflR: tOtai p LORD (KG/YR)

EST IMRTE +/- 1 STRNMRD ERROR

-t

4

L

o

~E f33me

D E

lam

T

E

—

W LORD Q UTD C IJC REG-1 REG-2 REG-3

WETHOD

KM-SE ~+sE

The load estimatesfiom each method are in reasonable agreement. Convergence of load estimates as the number of strata increases is a desired result.

The following table summarizes the eflect of increasing the number ofjlow

strata on the estimated flow-weighted mean concentration for Method 2:

Number of Strata Flow- Weighted-Mean Cv

1 76.7 .169

2 76.5 .139

3 77.8 .118

4 77.6 .138

i%e mean estimates did not change signljicantly, and the error W was lowest

for 3 strata. The increase in error at 4 strata reJects data limitations (only

three samples injlow interval 4). This causes instability, particularly in the

regression methods (4-6), when 4 strata are used. Based upon these results,

the load estimate based upon 3JOW strata and Method 2 is selected. This

could be firther re~ned by adjusting thejlow strata boundaries (using the

DaWStratify/FJowl Other procedure) to obtain a better C/Q~t and reduce

the CV estimate.

We can reset the stratljication scheme to 3flow strata and examine residuals.

Chapter 2 FLUX 2-59
FLUX - VERSION 5.0—

~ Calculate Method Plot List Utilities Help Quit

~ Delete Composite F 1owsub Title List

Genera 1 Reset List

2 Strata 3 strata 4 Strata Other

3 FlobJ Strata - Boundaries at QMEAN/2, QMEAN x 2

. FLUX- VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart Cone Load Flow Dai [y Qfreq Resi- GridOpt

Flow Month Estimated Histogram Autocorr

Plot Residuals vs. Date

R

E

s

I

D

u

6

L

Caddo River

METHOD:2 ClMTDC

-.

4

-11 , , ,

7H 79 86 81

DfiTE

❑ STRflT-1 o STRRT-2 o STRRT-3 . REGRESS

I’_hisplotca nbeused to testfor trend, i.e., increasingordecreasing concentrations, adjustedfor variations inflow. Generah’y, severalyears ofmonitoringdda collected overawide range offlowregimes are requiredin orderto

make areliable testfor trend. Stratljicationb asedupondute maybe appropriatel~signljicanttrendorstep change isapparent. An alternative approach

wouldbe to estimate loads separatelyfor different timeperiods byspeclfiing

appropriate date ranges in the DatalIlead procedures.

2-60

FLUX - VERSION 5.0

Data Calculate Method List Utilities Help Quit

Barchart Cone Load Flow Daily Qfreq Be sid@_ s GridOpt

Flow Date Estimated Histogram Autocorr

Plot Residuals vs. Month

Chapter2 FLUX
R

E

s

I

D

u

f+

L

Caddo R iuer

METHOD : 2 Cl HTD C

m +

-1 , , , m , , , 8

1234567 89 le 11 12

MONTH

o STRftT-1 Q S~T-2 o STRftT-3 . REGRESS

This plot can be used to test for seasonality. If signljlcant seasonal patterns in

the residuals are evident, stratl~cation based upon season maybe

appropriate. This is accomplished by using the Ik.itdStratify/General

procedure. Now examine the load breakdown byflow stratum.

vL’Lu’’’ick::K5;ti’ieses List Load & Flow Breakdowns by Stratun; Optimal Sample Al“lP10C. ‘“i’

Caddo River VAR=total p METHOD= 2 Q UTD C

FLUX Breakdown by Stratum:

FREQ FLOU FLUX VOLUME MASS CONC CV

ST NS NE DAYS HM3/YR KG/YR HM3 PPB -

1 93 93 582.0 120.23 2761.4 191.58 4400:! 23.0 .050

2 61 61 407.0 397.42 14501.1 442.85 16158.7 36.5 .092

3 14 14 107.0 2070.70 259357.2 606.61 75978.7 125.3 .148 *** la 168 1096.0 413.59 32171.8 1241.05 96537.5 77.8 .118

Optimal Sample Allocation:

ST NE NE% NEOPT% FREQ% VOL% MASS% VAR% VARIANCE CV

1 ;: 93 55.4 3.8 53.1 15.4 4.6 .0 .5276E+04.050

2 61 61 36.3 20.8 37.1 35.7 16.7 1.7 .2442E+06.092

3 14 14 8.3 75.5 9.8 48.9 78.7 98.3 .1407E+08.148 *** 168 168 100.0 100.0 100.0 100.0 100.0 100.0 .1432E+08 .118

Optimal Allocation of 168 Sampled Events Across Strata (According to NEOPT%)

Uould Reduce CV of FLUX Estimate from O.118 to 0.045

l%etoppartofthe table shows thedistribution of~ow,flux,v olume, andmass

acrossjlowstrata. l%erniddlepartofthe table lists the distributionof

sampling effort,flow days,jlow volume, mass, anderrorvariance, each

expressedaspercentage of the total. i%ebottompart ofthe table estimates

thepotential bene$t ofoptimizing the sample allocation across stratato

obtain the lowest error variance fora]xednumber ofsamplingeven ts.

Chapter2 FLUX 2-61
NE% =percent of total sample events in stratum

NEOPT?? = optimal percent of total sample events in stratum

i%e reduction in error CVattributed to shlftingfiom the current sample

distribution (NE%) to the optimal distribution (NEOPT!?!?)is listed. This can

be used to re~nefiture monitoring program designs.

In this example, 98.3 percent of the variance in the load estimate is attributed

to the Stratum 3. This received only 8.3 percent of the sampling effort WE%).

An optimal sampling design would devote 75.5 percent of the eflort to

Stratum 3. 7he optimal design would reduce the error CVflom 0.118 to

0.045.

2-62

Chapter 2 FLUX
3 PROFILE

PROFILE Overview

PROFILE is an interactive program designed to assist in the analysis and

reduction of pool water quality measurements. The user supplies a data file

containing basic information on the morphometry of the reservoir, monitoring

station locations, surface elevation record, and water quality monitoring data

referenced by station, date, and depth. The program’s fbnctions are in three

general areas:

a. Display of concentrations as a fhnction of elevation, location, and/or

date.

b. Calculation of mixed-layer summary statistics and standard errors.

c. Calculation of hypolimnetic and metalimnetic oxygen depletion rates

from temperature and oxygen profiles.

These applications are introduced in the following paragraphs. Details are

given in subsequent sections.

Several display formats support exploratory analysis of reservoir water

quality data. These elucidate important spatial and temporal variance components. Reviewing these displays can help the user in evaluating data adequacy,

designing future monitoring programs, and specifying appropriate segmentation

schemes for modeling. The various display formats and options are described

in detail in the Program Operation section and demonstrated in the Documented Session section of this chapter.

Mixed-layer water quality data can be summarized in a two-way table format that depicts variations as a function of space (station or reservoir segment)

and time (sampling date) over date, depth, and station ranges specified by the

user. In the two-way analysis, filtering and weighing algorithms are used to

generate robust sumnuuy statistics (median, mean, and coefficient of variation

of the mean) for characterization of reservoir trophic status, evaluations of data

Chapter 3 PROFILE 3-1
adequacy, and application of BATHTUB (Chapter 4) or other empirical

models.

Hypolimnetic oxygen depletion rates are important symptoms of eutrophication in stratified reservoirs. Using input oxygen and temperature profiles, the

program applies interpolation and area-weighing procedures to calculate depletion rates. Graphic and tabular outputs assist the user in selecting appropriate

sampling dates and thermocline boundaries for oxygen depletion

calculations.

The following sections of this chapter describe:

a.

b.

c.

d

e.

$

Input data requirements.

Application procedures.

Program operation.

Input data file format.

Data-entry screens.

Documented session.

Input Data Requirements

PROFILE requires an input file containing data in the following groups:

Group 1: Title

Group 2: Parameters and Unit Conversion Factors

Group 3: Reservoir Morphometry

Group 4: Component Key (water quality variables)

Group 5: Station Key (monitoring locations)

Group 6: Elevation Data (reservoir surface elevations)

Group 7: Profile Data (water quality measurements)

All of this information can be specified in a single, fixed-format ASCII file, as

described in the section entitled Input Data File Format. As an option, water

quality measurements (Group 7) can also be read from spreadsheet files or

free-format ASCII files.

3-2

Group 2 contains scale factors to convert input are% elevation, and depth

units to metric units used by the program (square kilometers for area and

meters for elevation and depth). Missing concentration values are flagged with

a speckl code specified in Group 2. The “date blocking factor” is used to

combine data for summary purposes. In large reservoirs, it may be difficult to

Chapter 3 PROFILE
sample all pool monitoring stations in 1 day. If a blocking factor of 2 is specified, for example, sample dates differing by <=2 days will be associated with

the same sampling round for data-summary purposes.

Group 3 contains an elevation versus surface area table for the reservoir.

This information is used only in computing areal hypolimnetic oxygen depletion

rates.

Group 4 defines water quality components and concentrations interval for

contour plotting. In eutrophication studies, the input file would normally contain measurements of oxygen, temperature, total phosphorus, ortho phosphorus, inorganic nitrogen, organic nitrogen, total nitrogen, chlorophyll a, and

Secchi depth. Output is formatted to provide one place to the right of the decimal point; thus, input units should be milligrams per cubic meter (or parts per

billion) for nutrients and chlorophyll a and meters for Secchi depth. Other

components should be scaled accordingly. Groups 4 and 7 can contain up to

64 water quality components. A maximum of 10 water quality components

can be read from disk files and analyzed in a given session.

Integers (range 01- 15) are used to identi~ sampling stations and are cross-

-referenced to user-defined station codes and descriptions in Group 5. To

facilitate interpretation of data displays and tables, station numbers should be

assigned in a logical order (e.g., upstream or downstream order within each

tributary arm). The optional “river kilometer” input for each station would

normally represent the distance along the thalweg from the reservoir inflow;

since the river kilometer index is used only for spatial display purposes, any

frame of reference can be used.

In computing summary statistics, “segment numbers” specified in Group 5

can be used to combine data from specific stations based upon their relative

proximities, major tributary arms, horizontal mixing characteristics, etc. For

example, if the file contains two adjacent stations (or two stations with similar

observed water quality), data from these stations can be grouped by assigning

them the same segment number. Segment numbers can refer directly to the

spatial segments used in reservoir modeling (see BATHTUB). If oxygen

depletion calculations are not desired, it is also possible to use segment numbers to refer to stations in different reservoirs.

“Areal weights” specified in Group 5 are used in calculating area-weighted

summ~ statistics over the entire reservoir and should reflect the approximate

surface area represented by each station. These can be estimated by plotting

stations on a reservoir map and allocating a given area to each station, based

upon relative station locations and bisecting lines between adjacent stations.

Since they are resealed in calculations, the weighing factors do not have to sum

to 1.0.

Group 6 contains daily measurements of reservoir surface elevation over the

period of water quality measurements. The program uses this information in

Chapter 3 PROFILE 3-3
generating concentration versus elevation plots and in calculating hypolimnetic

oxygen depletion rates. Only the elevations on sampling dates are used; thus,

the entire daily elevation record is not required. If an elevation value is not

specified for a particular sampling date, it is estimated by interpolation from

adjacent dates with specified elevation values.

PROFILE can handle problems with the following maximum dimensions:

Elevation/Area pairs = 29

Number of stations = 50

Number of samples = 2,500

Number of water quality components = 10

Number of sample dates = 250

Number of measurements = 12,000

Water quality records must speci& the station, date, and depth, in addition to

measurements. If the depth field is missing, a sample depth of Ois assumed.

Note that limitations on sample numbers and number of water quality components apply only to data read into the computer memory at the time of program

execution, not to the data file itself. Since the user is prompted for the ranges

of station numbers, sample years, and water quality components to be considered in a given run, the data file can be much larger than indicated above

(except for the maximum number of stations). Users should check the online

documentation file (accessed through the HELP menu) for maximum problem

dimensions or other program changes in updated versions of PROFILE

(Version 5.0 is documented here).

Mixed-Layer Water Quality Data Summary

A major fiction of PROFILE is the calculation of mixed-layer, summary

statistics for characterization of reservoir trophic status, evaluations of data

adequacy and monitoring program designs, and application of empirical

models. Calculation steps (outlined in the Documented Session section)

include the following:

a. Setting the data window to include mixed-layer samples.

b. Generating box plots to depict spatial and temporal variations.

c. Summarizing the data in a two-way table format.

These steps are described below.

3-4

The data window defines the ranges of stations, dates, and depths to be

included in displays and statistical summaries. For characterization of reservoir

trophic status, the window would normally be set to include all stations, dates

Chapter 3 PROFILE
in the growing season (e.g., April-October), and depths in the mixed layer. In

model development research, a mixed-layer depth of 15 ft (4.6 m) was used for

data summary purposes; this value should be adjusted in specific applications,

based on a review of midsummer temperature profile data. Because the

data-summary procedure does not apply weighting factors with depth, use

outside of the mixed layer (or in nonhomogeneous depth layers) is not

recommended.

The data-summary procedure organizes the data in a two-way table depicting spatial (columns) and temporal (rows) variations. This is illustrated in

Figure 3.1 using Beaver Reservoir data. Spatial groups can be defined by

station or reservoir segment. Temporal groups are defined by sampling round,

which is determined by sample date and date blocking factor specified in the

input file. The purpose of date blocking is discussed below, A summary value

(mean or median) is computed for each cell (row/column combination). For

each row (sampling date), summary values are weighted by surface area and

averaged across cohmms (stations or segments) to compute a reservoir mean

concentration. Values are subsequently analyzed vertically to estimate a

median, mean, coefficient of variation (CV, standard deviation/mean), and

coefficient of variation of the mean (CV(MEAN), standard error/mean).

Beaver Reservoir

C~PONENT: total p , DEPTHS: .0 TO 10.0 M

total p SAMPLE FREQUENCIES:

SEGMENT 1 4 6 8 10 12 RESERV

DATE UTS> .050 .100 .150 .250 .250 .200 -------- -------- -------- -------- -------- -------- . . . . . . . . .

740405 4 4 3 3 3 3 20

740618 4 4 5 3 4 4 24

740830 4 4 4 3 3 3 21

741009 4 4 4 4 4 4 24

--------- --------- . . . . . . . . . . -------- . . . . . . . . . . . . . . . . . . . . .

SAMPLES 16 16 16 13 14 14 89

DATES 4 4 4 4 4 4 4

total p SUMMARY VALUES:

SEGMENT 1 4 6 8 10 12 RESERV

DATE UTS> .050 .100 .150 .250 .250 .200 -------- -------- -------- -------- . ------- -------- -------- -

740405 67.0 47.0 37.0 36.0 16.0 9.0 28.4

740618 61.5 89.0 32.0 16.0 9.0 9.5 24.9

740830 49.5 41.5 21.0 15.0 12.0 12.0 18.9

741009 48.0 37.5 21.5 11.0 10.5 10.0 16.8 -------- -------- -------- -------- -------- . . . . . . . . -------- -

SAMPLES 16 16 16 13 14 14 89

DATES 4 4 4 4 4 4 4

MEDIANS 55.5 44.3 26.8 15.5 11.3 9.8 21.9

MEANS 56.5 53.8 27.9 19.5 11.9 10.1 22.3

Cv .164 .443 .284 .575 .254 .130 .241

CV(UEAN) .082 .222 .142 .287 .127 .065 .121

Figure 3.1. Sample PROFILE output: Surface water quality summary

Chapter 3 PROFILE 3-5
The distinction between the last two statistics (CV and CV(MEAN)) is

important. CV is a measure of temporal variability in conditions at a given

station (standard deviation expressed as a fraction of the mean). CV(MEAN) is

a measure of potential error in the estimate of the MEAN value. From classical

sampling theory (Snedecor and Cochran 1979), CV(MEAN) is calculated from

the CV divided by the square root of the number of nonmissing rows (sample

dates). This assumes that the rows are statistically independent. The calculation

of CV(MEANS) for the entire reservoir (last column in Figure 3.1) considers

only temporal and random variance components and assumes that the stations

are distributed throughout representative areas of the reservoir.

Estimates of “mean” conditions are generally required for trophic state

assessment and empirical modeling (Chapter 4). Direct calculation of arithmetic mean concentrations from all mixed-layer data would be one way of computing desired summary statistics. However, this approach may be undesirable

for two reasons:

a. Lack of robustness (a single errant value can have a major impact on the

computed mean).

b. Nonrandomness in samples (multiple samples taken within the mixed

layer on the same date would tend to be highly correlated).

The PROFILE data summary algorithm has been designed to provide more

robust estimates of the mean and coefficient of variation than would be derived

from simple averaging.

“Robustness” can be introduced by using medians to compute summ~

values within each cell. Cells may contain more than one observation as a

result of the following:

a. Replicate sampling at a given station, date, and depth.

b. Sampling with depth within the mixed layer (e.g., O,2,4 m).

c. Including more than one station per segment (if segments are used to

define columns).

d Blocking of adjacent sampling dates (speci&ing date-blocking factors

greater than 1 in the input file).

In the Beaver Reservoir example (Figure 3. 1), cells contain between two and

four observations as a result of sampling with depth. Use of the median in

computing a summary value provides some protection against “errant” observations and yields summary statistics (across stations and across dates) that are

less sensitive to outliers. For example, a cell containing five observations ( 10,

20, 15, 12, 100) would be summarizedbyameanof31 and a median of 15.

The median is less dramatically influenced by the single high value.

3-6 Chapter 3 PROFILE
Medians provide “filtering” of outliers only in cells containing at least three

observations, which may be achieved by replicate sampling, sampling with

depth, including more than one station per reservoir segment and/or blocking

of adjacent dates. Generally, date blocking should not be used unless the

sampling frequency is at least biweekly and the resulting number of rows is at

least three. In such cases, date blocking may also improve the CV and

CV(MEAN) estimates by reducing serial dependence in the rows.

While the calculation procedure accounts for missing values in the two-way

table, the usefulness and reliability of the surface water quality summary are

enhanced by complete sampling designs (i.e., each station sampled on each

date). Based upon review of box plots and two-way tables, monitoring programs can be refined by reducing excessive redundancy across stations,

improving characterization of spatial gradients, and modi&ing temporal sampling frequency to achieve the desired precision in summ~ statistics.

Figure 3.2 illustrates the use of a Box Plot to summarize spatial variations in

mixed-layer total phosphorus concentrations. In generating Box Plots, data can

be grouped by station, segment, month, round, year, or depth interval. An

accompanying table (not shown) summarizes the distribution of measurements

with each data group (percentiles, median, mean, CV).

Btmver Reservoir

PERCENTILES: 18 - 25 - 58 - 75 - ~ x

““~

t

o

t

a

1

P

STfi 1 Srfl 2 STf3 3 STtl 4 SIR 5 ST13 6

STRTION

Figure 3.2. Example box plot for Beaver Reservoir

Oxygen Depletion Calculations

This section presents an overview of the procedures for calculating oxygen

depletion rates in stratified reservoir using PROFILE. Calculations are

Chapter 3 PROFILE 3-7
illustrated in the Documented Session section of this chapter. Calculations are

applied to vertical oxygen profiles at a given station; simultaneous measurements of temperature are also required to characterize thermal stratification.

Empirical models have been developed for relating near-dam oxygen depletion

rates to surface-layer chlorophyll a concentrations (Walker 1985). Accordhgly, the procedure would normally be applied to data from near-dam

stations.

For the present purposes, the areal hypolimnetic oxygen depletion rate

(HOD~ mg/m2-day) is defined as the rate of decrease of dissolved oxygen mass

(mg/day) in the reservoir hypolimnion divided by the surface area of the hypolimnion (m*). The rate is also expressed on a volumetric basis (HODV,

mg/m3-day), which is essentially the rate of decrease of the volume-weightedaverage dissolved oxygen concentration in the hypolimnion between two dates,

or HODa divided by the mean depth of the hypolimnion (m). These rates are

symptoms of eutrophication because they partially reflect the decay of organic

loadings resulting from surface algal growth and sedimentation.

The initial oxygen concentration at the onset of stratification (usually on the

order of 10 to 12 g/m3) and HODV determine the days of oxygen supply. Subtracting the days of oxygen supply from the length of the stratified period

(typically 120 to 200 days) provides an estimate of the duration of anaerobic

conditions. While HODV is of more immediate concern for water quality

management purposes, HODa is a more direct measure of surface productivity

because it is relatively independent of reservoir morphometric characteristics.

For a given surface productivity and HOD% HODV is inversely related to mean

hypolimnetic depth. Thus, the morphometry of the reservoir has a major

impact on the severity of hypolimnetic oxygen depletion at a given surface

water quality condition.

In a given stratified season, the areal and volumetric depletion rates are

calculated between two monitored dates, the selection of which is important.

The following criteria are suggested for selection of appropriate dates:

a. Reasonable top-to-bottom distribution of oxygen and temperature

measurements.

b. Vertically stratified conditions, defined as top-to-bottom temperature

difference of at least 4 ‘C.

c. Mean hypolimnetic oxygen concentrations in excess of 2 g/m3.

3-8

The first criterion provides adequate data for characterizing thermal stratification and volume-weighting (estimation of total oxygen mass and volumeweighted concentration) within the hypolimnion on each sampling date. The

second criterion is based upon the concept that HODa is valid as a measure of

productivity only in water bodies that have stable vertical stratification. The

calculation is meaningless in unstratified or intermittently stratified reservoirs

Chapter 3 PROFILE
because of oxygen transport into bottom waters. The 4 ‘C temperature

difference is an operational criterion employed in developing data sets for

model calibration and testing (Walker 1985). Special consideration must be

given to water bodies with density stratification that is not related to temperature. The third criterion is designed to minimize negative biases caused by

calculating HODa values under oxygen-limited conditions. The underlying

model assumes that the depletion rate is limited by the organic supply, not the

oxygen supply.

The first date generally corresponds to the first profile taken after the onset

of stratification. The last date corresponds to the last profile taken before the

end of August, the loss of stratification, or the loss of hypolimnetic dissolved

oxygen (mean <2g/m3), whichever occurs first. Due to existing data limitations, it is sometimes difficult to cotiorm to all of the above criteria in selecting

dates. Small deviations may be acceptable, but should be noted and considered

in interpreting subsequent modeling results.

To permit calculation of hypolimnetic and metalimnetic depletion rates

between two dates, fixed thermocline boundaries (top and bottom) must be

specified. Temperature profile displays can assist in the selection of appropriate boundaries. The bottom of the thermocline (metalimnetic/hypolimnetic

boundary) is set at the intersection of one line tangent to the region of maximum temperature gradient and another line tangent to the bottom of the profile.

The top of the thermocline (epilimnetic/metalimnetic boundary) is set at the

intersection of one line tangent to the region of maximum temperature gradient

and another line tangent to the top of the profile. If significant thermocline

migration has occurred between the two sampling dates, calculations should be

based upon the thermocline levels at the last sampling date. A degree of subjective judgment must be exercised in interpreting temperature profiles and

setting thermocline boundaries, Program output provides perspective on the

sensitivity of the calculated depletion rates to the dates and thermocline

boundaries employed.

In response to program prompts, the user specifies temperature and oxygen

variables, near-dam station description, elevation increment (meters), first and

last sampling rounds, and thermocline boundaries. Profiles are interpolated and

integrated at the specified elevation increment from the bottom of the reservoir

to the top of the water column. At elevations below the deepest sampling

point, concentrations and temperatures are set equal to those measured at the

deepest sampling point. Results are most reliable when the profiles are complete and the morphometnc table (Input Data Group 3) has been specified in

detail.

Procedure output is in the form of several tables and plots that are useful for

tracking the calculations and evaluating sensitivity to sampling date and

thermocline selections. Interpolated profiles and the summary table for Beaver

Reservoir are displayed in the Documented Session section. The summary

table can be considered the “bottom line” in the calculations. The Beaver

Chapter 3 PROFILE 3-9
Reservoir example illustrates a pronounced metalimnetic oxygen depletion,

which is often found in relatively deep reservoirs.

Program Operation

Introduction

This section describes the PROFILE menu structure and operation procedures. When the program is run (from the DOS prompt), a series of help

screens summarizing model features is first encountered. If error messages

appear, it generally means that one of the PROFILE program files has been

corrupted or that your computer does not have enough available memory. Try

reinstalling the program. Try unloading any memo~-resident sofbwi.re. If you

are trying to run the program from Windows, try exiting Windows and running

directly from DOS. The program permits selection of ‘user mode’ at startup,

after the introductory screens. The selection of user mode is followed by a

menu that provides interactive access to eight types of procedures with the

following functions:

PRO FILE -VERSION 5.0

Plot Calculate Utilities Help Quit

Data Read or List Data

Ui ndou Set Data Uindow

Plot Select Plot Formats

Calculate Calculate Oxygen Depletion Rates or Mixed-Layer Smries

Utilities Program Utilities

Help Display Help Screens

Quit End Profile Session

A procedure category is selected by moving the cursor (using arrow keys) or by

pressing the first letter of the procedure name. Selected procedures in the

menu box are highlighted on the screen and underlined in the following documentation. Assistance in navigating around the menu can be obtained by

pressing the <F7> fhnction key. A Help screen describing the selected procedure can be viewed by pressing <Fl>. Afler each procedure is completed,

control returns to the above menu screen.

Data procedures

Data procedures control input and listing of sample data and other

information derived from the input file:

3-1o

Read Read Input Data File

List List Sample Data

Keys List Morphometric Table, Station Key, Date Key

Invent ory Inventory Data By Component, Station, and Date

Chapter 3 PROFILE
The Data/List lists the sample data in one of two sort sequences:

PRo FILE -vERsIoN5.0—

Hi ndoM Plot Calculate Utilities Help Quit

Read w Keys Inventory

1 Sort 2 Sort

1 Sort List Data Sorted by Station, Date, Depth

2 Sort List Data Sorted by Date, Station, Depth

Window procedures

Windowprocedures are usedto select subsets ofthe data forsubsequent

calculationsand plotting:

~:e:t::a:c::~:ii:::;y’:’f:~

Date/Depth Define Date, Season, & Depth Ranges

Components Define Uater Quality Components

Stations Define Sanpling Stations

All Define Date, Season, Depth, Station, & Components

Reset Reset Uindou to Include All Data

Window parameters remain in effect until another data file is read or one of the

Window/Resetprocedures isselected:

Date/Depth Reset Uindow to Include All Dates and Depths

components Reset Window to Include All Components

Stations Reset Window to Include All Stations

All Reset Uindow to Include All Dates, Depths, Components, Stati

Plot procedures

Plot procedures permit display of water quality data in several formats:

1~ PRO FILE -VERSION5.0 d , Data Ui ndow Calculate Utilities Help Quit

Line Contour Genera 1 Histograms Box-Plots Opt ions

Line Use Pre-Defined Line Plot Format

Contour Use Pre-Defined Contour Plot Format

Genera 1 Create a Custom Plot Format

Histograms Plot Histograms

Box-Plots Data Sumnaries & Box Plots by Station, Date, Etc...

Opt ions Set Graphics Options

Plot/Lineprocedures include eightpredefined formats:

Chapter3 PROFILE 3-11
I

Data Uindou Calculate Utilities Help Quit

li,ils Contour Genera 1 Histograms Box-Plots Opt ions

lPR/S/D 2PR/D/S 3PR/D/Y 4C/R/D 5C/D/S 6C/S/SY 7C/D/ZS 8C/D/ZY

lPR/S/D

2PR/D/s

3PR/D/Y

4c/R/D

5C/D/S

6c/s/sY

7C/D/ZS

8c/D/zY

Vertical Profiles, Symbol = Station, Repeated for Each Date

Vertical Profiles, Symbol = Date, Repeated for Each Station

Vertical Profiles, Symbol = Date, Repeated for Each Year

Concentration vs. RKM, Syrbol = Date

Concentration vs. Date, Symbol = Station

Cone. vs. Season, Symbol = Station, Repeated for Each Year

Cone. vs. Date, Symbol = Depth Interval, For Each Station

Cone. vs. Season, Symbol = Depth Interval, For Each Year

Plot/Contourprocedures include fourpredefmed formats:

lE/S/S Elevation vs. Season Contour Plot, Repeated for Each Station

2E/S/Y Elevation vs. Season Contour Plot, Repeated for Each Year

3E/D/s Elevation vs. Date Contour Plot, Repeated for Each Station

4E/R/D Elevation vs. RKM Contour Plot, Repeated for Each Date

UsingthePlot/General procedures, theuser can create acustom plotformat:

Prompt Create Custom Plot Format - Prompt Method

Screen Create Custom Plot Format - Screen Method

Plot formats aredefmed bythewaterquality component displayed, X-axis

variable, Y-axis variable, symbol variable, and repeat variable. A separate plot

is generated for each unique value ofthe repeat variable. Frequency distributions are displayed usingtheP1ot/Histograms procedure:

Histograms Plot Histograms

Plot/Box-Plotsincludes vertical orhorizontal formats:

Vertical Vertical Box Plot

Horizont Horizontal Box Plot

Boxplots area.ccompanied byatable with summary statistics. Use Plot/

Options to set any of eight options:

3-12

Chapter3 PROFILE
Intervals Edit Contour Intervals & Depth Intervals for Plotting

LogScale Select Variables to Be Plotted on Logarithmic Scales

Seal ing Set Automatic or Manual Plot Scaling

Grouping Set Scaling Options for Plot Groups

Reduction Method for Summarizing Multiple Values at Same Plot Location

Break Set Option to Break Lines at End of Year

Contour Set Contour Plot Resolution & Format

Calculate procedures

Calculate procedures can be selected to estimate oxygen depletion rates

andto generate mixed-layer water quality summaries:

~p::t+- ‘ERti:l;’:e~

HOD Calculate Hypolinmetic Oxygen Depletion Rates

Sumnaries Sumnarize Hater Quality Data - Calculate Area-Weighted Means

Opt ions Set Options for Data Summaries

Select Calculate/Options to change default settings for options controlling the

calculationof mixed-layer summaries:

mpRkR-vER’’l’”es ‘e’pQuit

Length Set Output Format: Short or Long (default)

co 1l.nnns Set Column Option: Segments (default) or Stations

Uethod Set Cell Smnary Method: Medians (default) or Means

Calculate/Options/Length defines the output format:

mp*-vER’’L’”es ‘eLp“Uit

Long Long Output Format (Default)

Short Short Output Format - BATHTUB Inputs Only

TheLongformat contains atableof sample frequencies and atable ofconcentrations foreachcomponent. The Short format contains only the means

and coefficients ofvariation for each column and forthe entire reservoir.

CaIculate/Options/Columns defines thecolumn attribute ofthedata-summ~

table:

Chapter3 PROFILE 3-13
m:.&-vER’’l’’’p=’p ‘“i’

lSegtnents Table Colunns = Reservoir Segments (default)

2Stations Tabte Colunns = Sampling Stations

Calculate/Options/Method sets the method used for summarizing multiple

observations in a given cell of the data-summary table:

EPk=v’’’’’’”es ‘e” ‘u”

llkdi an. Use Medians to Smnarize Table Cel 1s (default)

2Means Use Means to Sumnarize Table Cel 1s

Utilities procedures

Utilities procedures

any disk file:

can be selected to route output to a disk file or to view

PRO FILE -VERSION 5.0

Data Ui ndow Plot Calculate !Jtlllt es . . i Help Quit

output View

output Select Output Destination

View View Any ASCII File

mpRO’a’c’l:t’vER’:’’”es ‘eLp Qui’

Disk Direct Output To Disk File

Screen Direct Output to Screen (Default)

Help procedures

The Help procedure provides access to supplementary

nized in four topics:

help screens, orgaPRO FILE -VERSION 5.0

Calculate Utilities !if2!J2 Quit

Help Display Help Screens

3-14

HELP TOPICS

INTRODUCTORY SCREENS

I

PROCEDURES

PLOTTING

PROGRAM MECHANICS

Chapter3 PROFILE
Quit procedure

The Quit procedure ends the current session, after asking for verification:

~PRo FILE -vERsIoN5. o

Calculate Utilities Help ~

Quit End Profile Session

Input Data File Format

PROFILE requires aformatted ASCII input data file containing seven

groups of data. The specified formats, descriptions, and limitations of each

group are given in detail below.

Group 1: Title (maximum = 40 characters)

FORMAT(5A8)

Group 2: Parameters and Conversion Factors

FORMAT (F8.4)

NOTES:

a. There are seven records (one value per record) in Data Group 2.

b. The values should be entered in the following order:

Reservoir Length (km or Miles) - record 1

Missing Value Code (Suggest -9) - record 2

Conversion Factor - Elevations to Meters - record 3

Conversion Factor - Surface Areas to km2 - record 4

Conversion Factor - Distance to km - record 5

Conversion Factor - Sample Depths to Meters - record 6

Date Blocking Factor, Days (Normally = 1) - record 7

c. The conversion factors are multiplied by the input units to get the

program units (metric).

Area units = SQUARE KILOMETERS (km2)

Elevation and Depth units = METERS (m)

Group 3: Reservoir Morphometry - ELEV, AREA

FORMAT (2F8.0)

Chapter 3 PROFILE 3-15
EIJZV = Surface elevation, inincreasing order (maximum =

29 entries)

AREA = Surface Area

NOTES:

a. The first entry must be the bottom of the reservoir (invert,

AREA = O).

b. The units should be consistent with the conversion factors in Data

Group 2.

c. Decimal points should be included or right-justified.

d. The last record of Data Group 3 must be - “00”.

Group 4: Component Key - IC, LABEL, V1, .. .. V6

FORMAT (12,1X,A8,6F5.0)

IC = Component sequence number in Data Group 7

LABEL = Variable name (e.g., TEMP, OXYGEN, TOTAL P)

(maximum = 8 characters)

v = Cutpoints to be used to define contour intervals

NOTES:

a. Include the decimal points in V1-V6, or right-justify the entries.

b. The last record of Data Group 4 must be - “00”.

c, Cutpoints can be edited from within the program using the Plot/

Options/Interval procedure.

Group 5: Station Key - ST, CODE, ELEV, RINDEX, WT, SEG, DESC

FORMAT (12,1X,A8,3F8.0,14,2A8)

ST = Station number used in sample records (must be in

ascending order)

CODE = User station code (for general reference)

(maximum = 8 characters)

ELEV = Elevation of reservoir bottom at the station

3-16 Chapter 3 PROFILE
RINDEX =

WT=

SEG =

DSC =

NOTES:

Distance along thalweg from the major inflow (mainstream

stations) (used only for plotting purposes, ignored if c O)

Factors used in area-weighted averaging across stations

(relative surface area represented by station (estimated

from maps) - weights are resealed by the program and do

not have to sum to 1.0)

Integer segment number, used for grouping stations by the

reservoir area

Station location description (maximum = 16 characters)

a. Include one record for each station in Data Group 7 (maximum = 50)

b. Include the decimal point in ELEV, RINDEX, WEIGHT, or rightjusti~ the entries.

c. Input units must be consistent with the conversion factors specified in

Data Group 2.

d. The last record of Data Group 5 must be - “00”.

Group 6: Elevation Key - DATE, SELEV

FORMAT (312,F10.0) for 6-character dates or

(I4,2I2,F1O.O) for 8-character dates

The program will detect which format is used, based upon the~rst record

in each group. Use one or the other (do not mix).

DATE = Sample date in YYMMDD format (e.g., 840126) or

YYYYMMDD format (e.g., 19840126)

If 6-character dates are used, they are interpreted asfollows:

Y Y M M D D Year Month Day

990113 1999 01 13

000113 2000 01 13

Rule:

YY0113 19YY01 13 if YY>=50

YY0113 20YY01 13 if YY<50

SELEV = Surface elevation of the reservoir at the dam on the sample

date

NOTES:

Chapter 3 PROFILE 3-17
a.

b.

c.

d.

e.

Include one record for each sample date in Date Group 7.

Dates must beinchronological order (maximum = 100 dates).

Input units must be consistent with the conversion factors specified in

Data Group 2.

Group must contain at least two records; if an elevation record is not

specified for a given sample date, it is estimated by interpolation from

adjacent elevation records.

The last record of Data Group 6 must be - ‘00”.

Group 7: Profile Data - ST, DATE, DEPTH, C1, ..., C10

FORMAT (12,1X,312,11F5.0) for 6-character dates or

(12,1X,14,212,11F5.0) for 8-character dates

ST =

DATE =

DEPTH =

c =

NOTES:

Station number, indexed in Data Group 5

Sample date in YYMMDD or YYYYMMDD format,

indexed in Data Group 6

Sample depth

Component concentrations, indexed in Data Group 4

(IC value) (maximum = 10)

a.

b,

c.

d.

Note:

Records may be in any order.

Include the decimal point in DEPTH and C1-C1O, or right-justify the

entries.

Input units must be consistent with the conversion factors specified in

Data Group 2.

The last record of Data Group 7 must be - “00”.

Inclusion of data in Group 7 is optional. The file name(s) of spread3-18

sheet or free-format ASCII data files containing sample data may be substituted. Any number of file names may be specified (one per line). The

component labels in Group 4 should correspond with the field labels in the

data files (not necessarily a 1-to-1 correspondence). PROFILE will read data

from any components contained in both Group 4 and the data file. Station

codes in the data files should correspond to the Station codes (8-character

Chapter 3 PROFILE
alphanumeric) specified in Group 5. The following file formats are

supported:

*o~ I - LOWS-123worksheet

*.ASC - ASCII

File formats and conventions are described in Chapter 2 (FLUX - Data File

Formats).

A sample input data>le, BM VER.PRF(6-character dates), is listed below:

Beaver Reservoir - EPA/NES Data

120. *** length (kilometers)

-9. *** missing value code

.305 *** elevation conversion to m

.00405 ***area conversion to km2

1.0 *** rkm conversion to km

.305 *** depth unit conversion factor to m

1. *** date fuzz factor

elev --->area---> ** hypsiographic curve in increasing order ft, acres

914. 0.

938. 240.

982. 1830.

1050. 9750.

1077. 15540.

1080. 16210.

1090. 18800.

1093. 19690.

1100. 21830.

1110. 24950.

1120. 28220.

1130. 31700.

1137. 35860.

1142. 36260.

00

ic label <---><---><---><---><---><- -->

01 tenp 8. 12. 16. 20. 24. 28.

02 oxygen 2. 4. 6. 8. 10. 12.

03 total p 20. 40. 80. 160. 320.

00

st c~e..->e[ev- ..>rkm ---->weight-> seg description----> *** station key

01 STA 1 916. 119.0 .20 12 above dam

02 STA 2 951. 100.0 .25 10 big city

03 STA 3 999. 76.0 .25 08 below rogers

04 STA 4 1018. 51.8 .15 06 above rogers

05 STA 5 1054. 32.0 .10 04 below war eagle

06 STA 6 1073. 5.7 .05 01 headwater

00

date--selev--->

740405 1124.

740618 1124.

740830 1118.

741009 1119.

00

st date-- depth terp 02 ptot

01 740405 0 9.

01 740405 5 11.6 10.0 9.

01 740405 15 11.6 10.0 16.

01 740405 50 11.5 10.0 10.

etc.

00

*** component key

*** eievation key

*** sample records

BEA VER2K.PRF is an example of an 8-character ddefile.

Chapter3 PROFILE 3-19
NOTE: Spreadsheet file names for free-format ASCII file names may be

substituted for sample records. See example file ‘BEAVER2.PRF’

(6-character date) or BEAVER2K.PRF (8-character date).

Data-Entry Screens

DATA-ENTRY SCREEN: Data/Read

PROFILE DATA INPUT SCREEN

CASE TITLE:

PATH:

DATA FILE :

SAMPLE DATE RANGE : —— TO <YYMMDD>

SEASON RANGE: TO <MMDD>

DEPTH RANGE: TO <METERS>

HELP SCREEN:

Data Read

Reads Input Data File.

If FILE

sets

Can def

NAME is blank, user selects from list of all Profile data

in PATH (Default File Extension = *.PRF)

ne date, season, depth ranges to be read.

Set limits to 0,0 to read all data.

Up to 10 variables can be read.

DATA-ENTRY SCREEN: Window/Date/Depth

PROFILE DATA UINDOU

SAMPLE DATE RANGE: TO <yyMMDD>

SEASON RANGE: TO <~DD>

DEPTH RANGE: TO <METERS>

3-20 Chapter3 PROFILE
HELP SCREEN:

Data Uindou Date/Depth

Defines Date, Season, Depth Ranges for Data to Be Used in

Plotting, Listing, Smnary Procedures.

Limits are Inclusive, e.g., MIN<= value <=MAX.

Limits of (0,0) or (141N=MAX) will include all sanples.

Season Limits Urap Around Calendar, e.g.,

MIN=0401, MAX=0930 : Satples between April 1 and Sept 30

MIN=0930, HAX=0401 : Samples between Sept 30 and April 1

DATA-ENTRY SCREEN: Plot/Options/Intervals

EDIT VARIABLE AND DEPTH CUTPOINTS

Upper Limit ( c = ) of Contour Interval

VARIABLE 123456

1 —— —. —— -

i —— —— ——

e —— —— —— >

6

7

8

9

10

—— —— ——

—— —— ——

—— —— ——

—— —— ——

—— —— ——

—— .— ——

DEPTH (M) —— —— ——

Values Must be In Increasing Order, O = Missing

HELP SCREEN:

Plot Options Intervals

Edit Contour Intervals for each variable.

Edit Depth Intervals used to group data in line plots.

Each Entry Defines the Upper Limit (<=) of an Interval.

Entries Must Be in Increasing Order.

A ’01 Signals End of List, So Cutpoints of O Are Illegal.

VALID :2 4 68 10 0 < 5 intervals (trailing O ignored)

VALID :24 0 0 0 0 < 2 intervals

INVALID: 2 6 4 0 0 0 < wrong order

INVALID: O 2 4 6 < 0 intervals (leading O invalid)

VALID : 2 4 6 8 1012 < 6 intervals

Last Row Defines Depth Ranges for Plots using Depth Intervals.

Chapter3 PROFILE 3-21
DATA-ENTRY SCREEN: Plot/General/Screen

I PLOT TITLE:

1

1- 2- 3- 4- 5-

6- 7- 8- 9- 10

I

COMPONENT NUMBERS PLOTTED: < —— — ---all on same plot

X-AXIS: _ l=DATE 2=SEASON 3=JULIAN 4=RKM 5=CONC 6=LOG(C)

7=YEAR 8=MONTH 9=YR-MONTH

1

Y-AXIS: _ O=NONE I=ELEV 2=CONC 3=LOG(CONC) 4=-DEPTH

I

SYMBOL VARIABLE: _ O=NONE l=STATION 2=SEGMENT 3=DATE 4=YEAR

5=DEPTH INTERVAL 6=CONC INTERVAL (CONTOUR

I

REPEAT VARIABLE: _ O=NONE l=STATION 2=SEGMENT 3=DATE 4=YR

I SUMMARY METHCXI :_ O=NONE l=MEANS 2=MEDIANS

HELP SCREEN:

Plot General Screen

Fill in Table As Indicated - Choices Shown on Right.

At Least One Component and X-Axis Must Be Specified.

To Specify Histogram, Set X-Axis to CONC or LOG(C) and

Set Y-Axis to NONE.

If More Than One Component is Specified, All Uill Appear

on Same Plot and SYMBOL Choice Mill be Ignored.

Press <ESC> to Return to Main Menu

Documented Session

The PROFILE documented session uses the BEAVER.PRF file (found on

the distribution diskette and copied tothehard drive during installation) asthe

inputdataset. This file contains dataforBeaver Reservoir inArkansasforthe

growingseasonof 1974,andthesedata weretakenaspa.rt oftheNational

Eutrophication Survey. The documented session illustrates the screens asthey

would appear as the program is run. Notes to the user are in italics below.

Selected menu items are underlined. To begin, enter ‘profile’ at the prompt.

3-22 Chapter3 PROFILE
>PROFILE

PROFILE

RESERVOIR DATA ANALYSIS

VERSION 5.0

Envirorunental Laboratory

USAE Uaterways Experiment Station

Vicksburg, Mississippi

December 1998

PRESS KEY TO CONTINUE, <ESC> RETURN TO MENU 100

Aseries ofintroductoryscreensappear. These contain briefdescriptionsof

theprogramand summarizeanynew features notdocumented in this manual.

To by~ssthese screens, press <Esc> andtheprogram menu wi[lappear.

PRO FILE -VERSION5.0

U i ndow Plot Calculate Utilities He~p Quit

List Keys Inventory

Read or List Data

MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <FI,F7> HELP

CASE =

DATA FILE =

UINDOU

STATIONS = O

DATES = o

COMPONENTS = O

RECORDS = O

OUTPUT FILE = SCREEN

Aone-linemessage

TOTAL

o

0

0

0

describing

PLOT OPTIONS:

SCALING = AUTOMATI MANUAL

GROUP I NG = SEPARATE GROUPED

REDUCTION = POINTS MEANS MEDIANS

LINE BREAK = NO YES

the currently selected procedure appears atthe

bottom ofthe menu box. Characteristics ofthe currentdata setandprogram

option settings are listedon the bottom halfofthe scrcen. ,S’inceno data set

has beenloa~ed, the above valuesarezeroes or blank.

SelectIhtalRead to readin a data setfor Beaver Reservoir:

Chapter 3 PROFILE 3-23
PROFILE DATA INPUT SCREEN

CASE TITLE: Beaver Reservoir

PATH:

DATA FILE: beaver.prf

SAMPLE DATE RANGE: O TO O <yy~DD>

SEASON RANGE: o TO O <MMDD>

DEPTH RABIGE: o TO O <METERS>

case title

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/ED1TOR, <ESC>=ABORT

l%isscreen sthedata~l eanddat arangest obeselected. Hit<F2> a~er

editingandthe jileisread:

OPENING INPUT FILE: beaver.prf

Beaver Reservoir - EPA/NES Data

READING MORPHOMETRY...

READING C(BIPONENT KEY...

READING STATION KEY...

6 STATIONS O SAMPLES O DATES 3 COMPONENTS LOADED

SELECT STATIONS

STATIONS

* above dam

* big city

* below rogers

* above rogers

* belou uar eagle

* headwater

PRESS <SPACE> TO SELECT(*) OR NO( ), <ENTER>=DONE, <a>= ALL, <n>=NONE

Select the stations to beusedin this window. Allareselected(*) inthis

example.

OPENING INPUT FILE: beaver.prf

Beaver Reservoir - EPAINES Data

READING MORPH~ETRY...

READING CCN4PONENT KEY...

READING STATION KEY...

6 STATIONS O SAMPLES O DATES 3 CCN!PONENTS LOADED

PERCENT OF PROGRAM CAPACITY = . o%

STATIONS SELECTED = 6/ 6

SELECT VARIABLES

n

VARIABLE

* temp

* oxygen

* total p

3-24

PRESS <SPACE> TO SELECT(*) OR NO( ), <ENTER>=DoNE, += ALL, <n~=NoNE

Chapter3 PROFILE
Select the variables to be usedfiom the above list of all variables contained in

the dilta~le. Hit <Enter> to continue.

OPENING INPUT FILE: beaver. prf

Beaver Reservoir - EPA/NES Data

READING MORPHOMETRY. . .

READING C~PONENT KEY...

READING STATION KEY...

6 STATIONS O SAMPLES O DATES 3 C~PONENTS LOADED

PERCENT OF PROGRAM CAPACITY = . o%

STATIONS SELECTED = 6/ 6

C~PONENTS SELECTED = 3/ 3

OPENING INPUT FILE: beaver.prf

Beaver Reservoir - EPA/NES Data

READING MORPHCNETRY...

READING COMPONENT KEY...

READING STATION KEY...

READING DATE KEY...

READING PROFILE DATA...

DEVELOPING SAMPLE INDEX...

6 STATIONS 169 SAMPLES 4 DATES 3 COMPONENTS LOADED

PERCENT OF PROGRAM CAPACITY = 4.2%

<H>

Xheahtafileha sbeensuccessjidly loaded. Hit <Enter> in response tothe

<H>prompttoreturn toprogram menu.

F~ro’F*:i’il;’0N5”’tiL “’’””i’

II Read or List Data

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

CASE = Beaver Reservoir

DATA FILE = beaver.prf

UINDOU TOTAL

STATIONS = 6 6 PLOT OPTIONS:

DATES = 4 4 SCALING = AUTOMATI MANUAL

COMPONENTS = 3 3 GROUP I NG = SEPARATE GROUPED

RECORDS = 169 169 REDUCTION = POINTS MEANS MEDIANS

LINE BREAK = NO YES

WTPUT FILE = SCREEN

Casea?izta canbe listeu!using the DataJListl lSortprocedure:

F~:o’F*;iQF:’lON;’’L ‘eLp ‘“i’

II List Data Sorted by Station, Date, Depth

I MOVE CURSOR &HIT <Enter>OR <First Letter> TO RUN RWTINE, <F1, F7> HELP

Beaver Reservoir

ST C~E DATE DEPTH teip oxygen total p

1 STA 1 740405 .0 9.0

1 STA 1 740405 1.5 11.6 10.0 9.0

1 STA 1 740405 4.6 11.6 10.0 16.0

Chapter3 PROFILE 3-25
1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

1 STA 1

740405

740405

740405

740405

740618

740618

740618

740618

740618

740618

740618

740618

740618

740830

740830

740830

740830

740830

15.3

30.5

45.8

61.0

.0

1.5

4.6

7.6

12.2

16.8

27.5

39.7

52.2

.0

3.1

6.1

11.6

18.3

11.5

8.4

7.5

7.3

24.4

24.2

21.9

20.4

16.5

12.6

10.8

8.5

26.3

26.3

26.3

20.4

17.6

10.0 10.0

9.6 11.0

8.8 12.0

8.4 100.0

10.0

9.0 9.0

9.0 8.0

7.8 13.0

5.8 9.0

6.4 7.0

7.8 10.0

7.6 12.0

5.4 22.0

7.6 14.0

7.5 12.0

7.8 12.0

.4 12.0

1.0 11.0

USE KEYPAD, <F1>=HELP, <F8>=SAVE, <ESC>=QUIT OUTPUT

The DaWList12Sort procedure generates similar output, but sorted in a dl~

ferent order. ~eDatdKeysprocedure lists thestation, variable, sampling

date keys:

Fi”’’’:k;f;;”;;’’;’’ities ‘“P ““i’

II List Morphometric Table, Station Key, Date Key

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, cFl,F7> HELP

STA CODE ELEVATION RKM UEIGHT SEGMENT DESCRIPTION

1 STA 1 279.4 119.0 .200 12 above dam

2 STA 2 290.1 100.0 .250 10 big city

3 STA 3 304.7 76.0 .250 8 below rogers

4 STA 4 310.5 51.8 .150 6 above rogers

5 STA 5 321.5 32.0 .100 4 below war eagle

6 STA 6 327.3 5.7 .050 1 headwater

MAXIMUM CONCENTRATION

LEVEL ‘em’ oxygen total p

1 8.0 2.0 20.0

2 12.0 4.0 40.0

3 16.0 6.0 80.0

4 20.0 8.0 160.0

5 24.0 10.0 320.0

6 28.0 12.0 .0

RWND DATE JULIAN SURFACE ELEVATION

1 740405 95 342.8

2 740618 169 342.8

3 740830 242 341.0

4 741009 282 341.3

<E()’>

7he DataiInventory procedure lists the number ofconcentration

stationanddzte foreach component:

valuesby

Chapter3 PROFILE
PRO FILE -VERSION 5.0

Calculate Utilities Help Quit

List Data Inventory

MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

—

DATA INVENTORY FOR COMPONENT: 1 telnp STATION: 1 above dam

ROUND DATE JULIAN SELEV SAMPLES ZMIN ZMAX CMIN CMAX

M M--

1 740405 95 34! .8 6 1.5 61.0 7.3 11.6

2 740618 169 342.8 8 1.5 52.2 8.5 24.4

3 740830 242 341.0 9 .0 51.9 9.2 26.3

4 741009 282 341.3 10 .0 53.4 9.5 19.6

DATA INVENTORY FOR COMPONENT: 1 tellp STATION: 2 big city

ROUND DATE JULIAN SELEV SAMPLES ZMIN ZMAX CMIN CMAX

M

1 740405 95 34!.8 5 1.5 4!.8 7.2 10.5

2 740618 169 342.8 9 1.5 49.1 8.7 24.6

3 740830 242 341.0 8 .0 45.8 9.9 25.9

4 741009 282 341.3 9 .0 46.4 10.7 19.6

DATA INVENTORY FOR C@!PONENT: 1 tellp STATION: 3 below rogers

RWND DATE JULIAN SELEV SAMPLES ZMIN ZMAX CMIN CMAX

M

1 740405 95 34! .8 5 1.5 3!.1 7.3 10.7

2 740618 169 342.8 7 1.5 36.9 9.7 25.0

3 740830 242 341.0 6 .0 33.5 11.3 26.1

4 741009 282 341.3 8 .0 25.6 16.0 19.7

USE KEYPAD, <F1>=HELP, <F8>=SAVE, <ESC>=QUIT OUTPUT

The I)aWWimlow procedures are used to restrict subsequent analyses (Plot

or Calculate)to certain data ranges.

PRO FILE -VERSION5.0

Data M Plot Calculate Utilities Help Quit

Pat~/D~Oth Components Stations All Reset

Define Date, Season, & Depth Ranges

MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <FI,F7> HELP

PROFILE DATA UINDOU

SAMPLE DATE RANGE: 740405 TO 741009 <YYMMDD>

SEASON RANGE: o TO O <MMDD>

DEPTH RANGE: o TO 61 <METERS>

Window parameters are initially set to include the entire range of values in the

dataset. lftheminimum andrnaximu revaluesare equal, allvaluesare

selected. Following are demonstrations ofvariousplotprocedures.

Chapter3 PROFILE 3-27
—P R O F I L E - VERSION 5.0

Data Ui ndow Calculate Utilities Quit

M Contwr Genera 1 Histograms Box-Plots Opt ions

~ 2PR/D/S 3PR/D/Y 4C/R/D 5C/D/S 6C/S/SY 7C/D/ZS 8C/D/ZY

Vertical Profiles, Synbol = Station, Repeated for Each Date

MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

VARIABLE

temp

* oxygen

total p

Beaver Reseruoir

DRTE : 746485 SYMBOL: STRTION Uf3R : ox~gen

340 –

33e –

. . . . . . . ...............................................

E 320 – ................................................... ................. ........... ..

L

E

u 310 –

I I I 7 8 9 la 11

Ommn

■ STfi 1 X SIR 2 A STfl 3 0 STR 4 ~ STfl 5 + STR 6

RESS R to Rescale, D to Dump

Select thewater quali~component(s) to beplotted(o~gen). HotlLinell

generates vertical pro@les using dl~ferent symbols toidentlfi stations. A

separateplotis producedforeach sampling date.

3-28 Chapter3 PROFILE
E

L

:

● Sm 1

IRESS R to

B6iauer Reservoir

Df)TE : 741889 SYIIIiUIL: STfiTIOM URR : ox~gen

34B - .........................!.............................................. ...........

........................... .

320 – ........................................................

...........................l.............................l.............................

.................................................................. a -.

. .. .........................................&............................... .. . .. . . ...............,,.,..,...,..,

I i I I e 2 4 6 8 la

oxwen

xsIfi2AsT~30sT~ 4* STf15+STfJ6

Resca [e. D to ))urm

Select PlotlContour14 to display a longitudinal pro~le (y = elevation, x =

distance along thalweg (i.e., old river channel)). I%isformat only makes

sense when all selected stations are in the same tributary arm.

—P R O F I L E - VERSION 5.0

Data Ui ndou Calculate Utilities Help Quit

Line ~onto~ General Histograms Box-Plots Opt ions

lE/S/S 2E/S/Y 3E/D/s 4F/R/D

Elevation vs. RKM Contour Plot, Repeated for Each Date

UOVE CURSOR & HIT <Enter> OR cFirst Letter> TO RUN ROUTINE, <Fl ,F7> HELP

Chapter 3 PROFILE 3-29
Beauer Resexwoir

MTE : 740630 SwlmL: C(MC UfiR: total p

34e

/

........ .. ........a”_-y .......................!....

1. ~..---..~ l-i: . . t .................... ........................................

$,~F~::

..:%-.+-> . ... . ...... : .. ...............+~....... ‘

............................................................ ...........7...........1............ ~

26el -y I I I I I

e 26 40 60 80 166 120

RKM

● 213~4fl =68=168=326

Dl~ferent colors are used to represent contour intervals (not discernible here).

Select PiotlGeneral to define your own plot format. Remember that all plots

use a!hta in the current window.

—P R O F I L E - VERSION 5.0

Data Ui ndow Calculate Utilities Help Quit

Line Contour General Histograms Box-Plots Opt ions

Pronpt screeq

Create Your Own Plot Format - Screen Method

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

PLOT TITLE: Beaver Reservoir

l-temp 2-oxygen 3-total p 4- 5-

6- 7- 8- 9- 10

COMPONENT NUMBERS PLOTTED: 3 0 0 <--- all on same plot

X-AXIS: 4 l=DATE 2=SEASON 3=JULIAN 4=RKM 5=CONC 6=LOG(C)

7=YEAR 8=MONTH 9=YR-MONTH

Y-AXIS: 1 O=NONE l=ELEV 2=CONC 3=LOG(CONC) 4=-DEPTH

SYMBOL VARIABLE: 6 O=NONE l=STATION 2=SEGMENT 3=DATE 4=YEAR

5=DEPTH INTERVAL 6=CONC INTERVAL (CONTOUR)

REPEAT VARIABLE: 3 O=NONE l=STATION 2=SEGMENT 3=DATE 4=YR

SUMMARY METHOD : 0 O=NONE l=MEANS 2=MEDIANS

-—

3-30 Chapter3 PROFILE
This screen provides a high degree of~exibility for de~ning plots. In this

example, a phosphorus contour plot (elevation versus rkm) is specljied. The

plot is repeated for each sampling &te (only one is shown below).

8ewer Reseruo ir

DRTE : 74883$3 sYMmL : C(INC UfiR : tots 1 p

- –

~_________

.......................................... .........

E 320 - .....................................

L

E

u 318 – ............................................................

286 I I I I I

a 28 4e 68 88 188 120

RI(M

.2e*48=8e. lm .32a

Select PlotlContourll to display an elevation versus season (month) contour

plot.

PRO FILE -VERSION 5.0

Data Uindow Calculate Utilities Help Quit

Line $ontour General Histograms Box-Plots Opt ions

2E/S/Y 3E/D/s 4E/R/D

Elevation vs. Season Contour Plot, Repeated for Each Station

j MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <Fl ,F7> HELP

Chapter 3 PROFILE 3-31
E

L

E

u

98912

Beauer Reeeruoir

STfiTION : STll 1 SYNBOL: CONC w: tenp

33

32 ........................................................ -------------i---

.........................................................

—

-> :“

33 . .. . . . .. .. . . ....................................... ........... . ........................................ .. . ..........

; - [.,

:,

.................... .......................................................................................}.. . ...... :.

I I

4 6 18 12

SER&lN

● 16=29 =24m2B

Plot contour intervals can be set using the Plot/Options/Intervals procedure.

PRO FILE -VERSION 5.0

Data Ui ndow Calculate Utilities Help Quit

Line Contour Genera 1 Histograms Box-Plots !21W@S

~ LogScale Scat ing Growing Reduction Break Contour

Edit Conponent & Depth Intervals for Plotting

NOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

EDIT VARIABLE AND DEPTH CUTPOINTS

Upper Limit ( < = ) of Contour Interval

VARIABLE 123456

1 tenp 8 12 16 20 24 28

2 oxygen 2 4 6 8 10 12

3 total p 20 40 80 160 320 0

4 000000

5 000000

6 000000

7 000000

8 000000

9 000000

10 000000

DEPTH (M) 6 8 10 18 0 0

Values Must be In Increasing Order, O = Missing

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

3-32

SelectPlot/Options/LogScale tode~ne variables to beplottedon log scales

(open appropriate for nutrient and chlorophyll data, not appropriate-for

oxygen or temperature).

Chapter3 PROFILE
Data Uindou

Line Contour General

Interval ~cal~ Sca 1 i ng

FILE- VERSION 5.0-

Calculate Utilities Help Quit

Histograms Box-Plots @S.@!3S

Grouping Reduction Break Contour

II Select Variables to Be Plotted on Logarithmic Scales

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

SELECT(*) VARIABLES TO BE PLOTTED ON LOG SCALES

VARIABLE

temp

oxygen

* total p

Select PkM30x-Plots to display t.hta summaries by de$ned groupings.

PRO FILE -VERSION5.0

Data Ui ndow Calculate Utilities Help Quit

Line Contour General Histograms Box-Plots Opt ions

~ Horizont

Vertical Box Plot

II MOVE CURSOR&HIT <Enter>OR <First Letter> TO RUN RWTINE, <F1, F7> HELP

DEFINE GRWPING VARIABLE

CATEGORY

STAT 10N

SEGMENT

DATE

YEAR

MONTH

CONC- I

DEPTH- I

NONE

Chapter3 PROFILE 3-33
t

o

t

a

1

P

Baauer Rosarvo ir

PERCENTILES: 18 - 2S - W - 75 - S x

2~~:f::~::u................. x.....................!.....................................

lul

Sm 1 STfi 2 SIR 3 sTfl 4 SIR 5 SIR 6

STflTION

0NE-UA% DATA SUMMARY FOR: 3 total D GROUPED BY: STATION

DATE RANGE: 740405 741009 SEASON RANGE: O 0 DEPTH RANGE: .0 61.0

STATION MIN 10% 25% 50% 75% 90% MAX MEAN Cv CV(M)

STA 1 3; 7.0 8.6 10.0 11.0 13.0 19.0 100.0 14.4 1.068 .180

STA 2 33 4.0 8.4 10.0 13.0 17.5 31.8 65.0 16.3 .773 .134

STA 3 28 11.0 11.0 15.3 20.5 39.0 53.0 136.0 30.5 .821 .155

WA 4 29 20.0 21.0 21.5 32.0 57.0 91.0 212.0 50.1 .981 .182

STA 5 23 29.0 33.8 43.0 53.0 90.0 134.6 182.0 70.3 .562 .117

STA 6 20 39.0 41.3 50.5 62.0 68.8 96.2 180.0 67.2 .449 .100

<EOF>

Theasterisb(w )showthemedian value in eachdatagroup. The boxesshow

the 25- to 75-percentrange. Zhelines show the 10- to 90-percent range.

Select CalculatelJiIOD tocalculate arealhypolimneticdepletionrates. I%isis

applicable onty to stratljiedreservoirs andto data sets containing late spring/

early summer oxygen andtemperature projilesfiom anear-damstation.

PRO FILE -VERSION5.0

Data Ui ndow Plot Calculate Utilities Help Quit

li$!il Smnaries Opt ions

Catculate Hypolimnetic Oxygen Depletion Rates

3-34

Chapter3 PROFILE
PROFILE: OXYGEN DEPLETION CALCULATIONS

This routine uorks best if you first set the UINDOU

to consider data from only one year, preferably

during the late spring and early summer when profiles

are most likely to be useful for oxygen depletion

calculations.

Otherwise, you may be overwhelmed with lots of output.

The UINDOU has already been reset to include data

from all stations.

Date limits can be set with the following screen...

! PROFILE DATA UINDOU

SAMPLE DATE RANGE: 740405 TO 741009 <yyMMDD>

SEASON RANGE: o TO O <MMDD>

DEPTH RANGE: o TO 61 <METERS>

first sample date >= yymndd

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

As indicatedin the abovehelpscreen, selectthesample date anddepth ranges

containing thepro~les tobe usedinoxygen depletion cala.dations. Next,

de~ne the temperature variable, oxygen variables, andstation:

HYPOLIMNETIC OXYGEN DEPLETION (HOD) CALCULATIONS

SELECT TEMPERATURE VARIABLE

>

VARIABLE

1

oxygen

total p

HYPOLIMNETIC OXYGEN DEPLETION (HOD) CALCULATIONS

SELECT DISSOLVED OXYGEN VARIABLE

❑

VARIABLE

tellp

>Q.XYWIl

total p

HYPOLIMNETIC OXYGEN DEPLETION (HOD) CALCULATIONS

SELECT STATION FOR HOD CALCS

STAT 10N

W

below rogers

above rogers

below war eagle

headwater

FOR NEAR-DAM STATIONS

FOR NEAR-DAM STATIONS

FOR NEAR-DAM STATIONS

Chapter3 PROFILE 3-35
Calculations begin. Hit < I%nter> to select the default depth interval for the

calculations:

TOTAL ELEVATION RANGE = 278.8 342.8 METERS

N~INAL ELEVATION INCREMENT = 3.20 METERS

ELEVATION INCREMENT ? 3.2

DATA INVENTORY FOR COMPONENT: 1 terp STATION: 1 above dam

RWND DATE JULIAN SELEV SAMPLES ZMIN ZMAX CMIN CMAX

M M--

1 740405 95 34!.8 6 1.5 61.0 7.3 11.6

2 740618 169 342.8 8 1.5 52.2 8.5 24.4

3 740830 242 341.0 9 .0 51.9 9.2 26.3

4 741009 282 341.3 10 .0 53.4 9.5 19.6

DATA INVENTORY FOR COMPONENT: 2 oxygen STATION: 1 above dam

RCNJND DATE JULIAN SELEV SAMPLES ZNIN ZMAX CMIN CMAX

M M--

1 740405 95 34! .8 6 1.5 61.0 8.4 10.0

2 740618 169 342.8 8 1.5 52.2 5.4 9.0

3 740830 242 341.0 9 .0 51.9 .4 7.8

4 741009 282 341.3 10 .0 53.4 .2 7.6

Above isan inventory oftheoxygenand temperature data in thecurrent

window. Next, select thejlrstand lastsampling round tobeusedin oxygen

depletion calculations. Generally, the~rstprojileshouki bethe~rstround

after the onset ofstratljication, andthelastpro$le shouldbe the last round

withoutanoxic conditions. Seetextforr noredetails.

DEFINE SAMPLING ROUNDS FOR HOD CALCS

FIRST SAMPLING RWND <##>? 1

LAST SAMPLING ROUND <##>? 3

Vertical Profile Plots for the Selected Dates Follow.

Later, You Uill Be Asked to Specify the Upper & Lower Boundaries

of the Thermocline for Use in H(X) Calculations.

Press <Enter> to Continue

<H>

Fiveplotsfollow, showing vertical pro~les oftemperature, oxygen, areal

oxygen depletion rate and total oxygen demand @elow each elevation incremen~, andvolumetric oxygen depletion rates, View thejirstplot

(temperature) to select appropriate thermocline boundaries (top, bottom):

3-36

Chapter3 PROFILE
Beausr Reservoir - EPfUNES Data - STfl 1

INTERPOMTED PROFILES

L

E

u

!(34 .................................. ...............

328 ........................ .“”””””””””””””””””””

33

~

........... .............. .....................

......... .. . ...........................

I

5 10

■ 74W05 x 740030

IRESS R to Reeca Ie. D to DunP

I I

20 25 :

tenp

Beaver Reservoir - EPfWNES Data - STR 1

INTERPOLATED PROFILES

E

u

m

t:

.....................................~

288 .. ............................................ V

2681 I

B 2

........................

.......................

,................l...

........... .............;

. . . . . .......

........... ................. /

0 1

■ 740405 x 740838

‘RESS R to Resca le , D to Dump

Chapter 3 PROFILE 3-37
Beaver Rsserw Ir - STR 1

RREfiL DEPLETION )WTE (MC/M2-D ) 7464B5-74883B

t

338 ................-

32‘l--........................ E

L

E 31

+

........................

u

-T.............

0 2

J

.........

.........

........,.

)6 4

............................... ... .. ............................

................................................................

I I

B 680 688

■ Hoi)-ft

RESS R to Reeca le, D to Dump

E

L

E

u

Beaver Reservo 1r – STR 1

TOTRL OXYGEN DEWWD (XC/IM3Y) 746485–748638

340

.,......... ......

32 ......................;............................................ ...............!..

310 ............................................................................... . ...........

386

290 ............................................................................................................... ............

28

8 28660 4e136e 68086 86006

~9en

■ XOD

JRESS R to Resca [e . D to Dufm

3-38 Chapter 3 PROFILE
Beaver Ramruo ir - STfi 1

UOLUMETR IC DEPEL . IU3TE W(VM3-D ) 74t34B5-74B838

....................................................... ........................................................

E 328 – .............................................+.......................+

L

E

u

=8 – .............................................+.................. ................................

280 . ............................................................................................!...... ......................

1 I I I I 10 2a m 40 50 w 70

--n

m f)l ELEU X M-

‘RESS R to Resca le, D to Dump

?he upper plot shows the total oxygen demand (@#day) below each elevation.

This may be usefil for sizing hypolimnetic aerators. The lower plot shows

volumetric oxygen depletion rate at each elevation and the mean depletion

rate below each elevation.

Thermocline boundaries are dejined in the following screen:

ENTER THERMOCLINE BCMJNDARIES BETUEEN 278.8 AND 342.8 IN METERS

ELEV AT TOP OF HYPOLIMNION? 305

ELEV AT TOP OF METAL IMNION? 325

7he following output table shows calculation results:

Beaver Reservoir COIPONENT :

STAT ION : 1 above darn RKM: 119.0 BASE ELEV:

DATES : 740405 TO 740830

STAT I ST I C HYPOLIMNION METAL IMNION

ELEVATION M 305.00 325.00

SURFACE AREA KM2 15.90 53.01

VOLLH4E HM3 125.66 643.67

MEAN DEPTH n 7.90 12.14

MAXIMUM DEPTH M 26.23 20.00

INITIAL CONC G/M3 8.93 9.70

FINAL CONC G/M3 2.79 2.70

AREAL DEPL. RATE MG/M2-DAY 330.03 578.02

VOL. DEPL. RATE MG/M3-DAY 41.76 47.61

2 oxygen

279.4

BOTH

325.00

53.01

769.33

14.51

46.23

9.57

2.72

677.02

46.65

Youmayrepeat thecalculations using dl~erent thermocline boundaries, f

desired.

Chapter3 PROFILE 3-39
TRY OTHER BOUNDARIES <O.=NO,l.=YES>? O

The following plot shows the time series of volume-weighted mean oxygen

concentrations in the hypolimnion and metalimnion. Xhe slopes of these lines

are proportional to the volume-weighted mean oxygen depletion rates.

Beauem Remervo ir - STfl 1

UOLUME-NEIHITED CCWWENTRRT IONS

le6 - ..........................

0

x 6 - ................................................................... .........................................

u

9

e

n 4 – .....................................................................................i.. ........................

e I I I I 50 1= 150 200 2s6 300

JIJLIflN

m HYPOLIM X METRLIM

PRESS R to Resca Ie, D to Dump

View Calculation File ? n

I

Hit y to view details of oxygen depletion calculations.

program menu.

Hit n to return to

Following is a demonstration of the CalculatelSummaries procedure. This

procedure constructs a two-way table with columns de$ned by station/segment

and rows defined by sampling round. First set the data window to include

phosphorus:

1 Define Water Quality Components

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <Fl ,F7> HELP

3-40

❑

VARIABLE

temp

oxygen

* total p

Chapter 3 PROFILE
PRO FILE -VERSION 5.0

Data Uindw Plot Utilities Quit

H(X) Opt ions

Smnarize Uater Quality Data - Calculate Area-Ueighted Means

MOVE CURSOR& HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

Ahelp screen appears:

Mixed-Layer Uater Quality Smnaries

On the next screen, you will specify the data to be smmarized.

Set the DEPTH range to reflect the mixed layer of the reservoir.

Set the SEASON range to reflect the growing season.

Constraints:

Maxinnm Sanples = 4000

Maximum Rows (Sa~ling Dates) = 200

Maxinnnn Columns (Stations or Segments) = 20

PRESS KEY TO CONTINUE, <ESC> RETURN TO MENU

Set theahteanddepth ranges accordingly:

21

PROFILE DATA UINDOU

SAMPLE DATE RANGE: 740405 TO 741009 <YYMMDD>

SEASON RANGE: o TO O <MMDD>

DEPTH RANGE: o TO 10 <METERS>

Results:

Columns = Segments

Cell Smnaries = Medians

Output Format = Long

Beaver Reservoir

C~PONENT: total p , DEPTHS: .0 TO 10.0 M

total p SAMPLE FREQUENCIES:

SEGMENT 1 4 6 8 10 12 RESERV

DATE UTS> .050 .100 .150 .250 .250 .200 - -- - -- - - - - - - - - - - - - - - - - . - - - - - . . . . . . - - - - . - - . - . . . . . - - - . . . . - -

740405 4 4 3 3 3 3 20

740618 4 4 5 3 4 4 24

740830 4 4 4 3 3 3 21

741009 4 4 4 4 4 4 24 . --- ------- . --- ----- . --- . --. . . . . --- --. . . ------- ----------

SAMPLES 16 16 16 13 14 14 89

DATES 4 4 4 4 4 4 4

Chapter3 PROFILE 3-41
total p SUMUARY VALUES:

SEGMENT 1 4 6 8 10 12 RESERV

DATE UTS> .050 .100 .150 .250 .250 .200 -------- ------- -------- -------- ------- -------- ------- ----

740405 67.0 47.0 37.0 36.0 16.0 9.0 28.4

740618 61.5 89.0 32.0 16.0 9.0 9.5 24.9

740830 49.5 41.5 21.0 15.0 12.0 12.0 18.9

741009 48.0 37.5 21.5 11.0 10.5 10.0 16.8 ------- ------- ------ ------- . . ----- ------- ------- -- . . . . ---

SAMPLES 16 16 16 13 14 14 89

DATES 4 4 4

MEDIANS 55.; 44.3 26.; 15.5 11.: 9.8 21.9

HEANS 56.5 53.8 27.9 19.5 11.9 10.1 22.3

Cv .164 .443 .284 .575 .254 .130 .241

CV(MEAN) .082 .222 .142 .287 .127 .065 .121

Zheright-handcolumn contains reservoir mean values, weighted bythe area

ofeach segment. SelectCalculate/Optionsto setother data-summary options.

Select Help to view supplementary help screens in various categories.

rpRO’a’c’L:’’vER’yL * ‘“it

1 Display Help Screens

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <F1,F7> HELP

PRESS <ESC> TO QUIT

HELP TOPICS

INTRCK)UCTORY SCREENS

PROCEDURES

PLOTTING

PROGRAM MECHANICS

Select Quit to end session:

rpRO’a’c’L’’’vER’:L II End Profile Session‘e” w

1 MOVE CURSOR&HIT <Enter>OR <First Letter> TO RUN ROUTINE, <FI, F7> HELP

3-42 Chapter3 PROFILE
4 BATHTUB

BATHTUB Overview

BATHTUB is designed to facilitate application of empirical eutrophication

models to morphometrically complex reservoirs. The program performs water

and nutrient balance calculations in a steady-state, spatially segmented hydraulic network that accounts for advective transport, diffusive transport, and

nutrient sedimentation. Eutrophication-related water quality conditions

(expressed in terms of total phosphorus, total nitrogen, chlorophyll a, transparency, organic nitrogen, nonortho-phosphorus, and hypolimnetic oxygen

depletion rate) are predicted using empirical relationships previously developed

and tested for reservoir applications (Walker 1985). To provide regional perspectives on reservoir water quality, controlling factors, and model performance, BATHTUB can also be configured for simultaneous application to

collections or networks of reservoirs. As described in Chapter 1, applications

of the program would normally follow use of the FLUX program for reducing

tributary monitoring data and use of the PROFILE program for reducing pool

monitoring dat~ although use of the data reduction programs is optional if

independent estimates of tributary loadings and/or average pool water quality

conditions are used.

The fhnctions of the program can be broadly classified as diagnostic or predictive. Typical applications would include the following:

a. Diagnostic.

(1)

(2)

(3)

Formulation of water and nutrient balances, including identification

and ranking of potential error sources.

Ranking of trophic state indicators in relation to user-defined

reservoir groups and/or the CE reservoir database.

Identification of factors controlling algal production.

b. Predictive.

Chapter 4 BATHTUB 4-1
(1)

(2)

(3)

Assessing impacts of changes in water and/or nutrient loadings.

Assessing impacts of changes in mean pool level.

Estimating nutrient loadings consistent with given water quality

management objectives.

The program generates output in various formats, as appropriate for specific

applications. Predicted confidence limits can be calculated for each output variable using a first-order error analysis scheme that incorporates effects of

uncertainty in model input values (e.g., tributary flows and loadings, reservoir

morphometry, monitored water quality) and inherent model errors.

A detailed description of the following topics is given in the remaining

sections of this chapter.

a.

b.

c.

d.

e.

$

g.

Theory

Program operation.

Application steps.

Procedure outline.

Data entry screens.

Documented session.

Instructional cases.

These and other features of the program maybe examined by reviewing the

example data sets supplied at the end of this chapter and by viewing help

screens supplied with the program.

Theory

Introduction

A flow diagram for BATHTUB calculations is given in Figure 4.1. This

section describes calculations performed in the model core:

a.

b.

c.

Water balance.

Nutrient balance.

Eutrophication response.

4-2 Chapter 4 BATHTUB
INPUT

ENTER/EDIT CASE DATA

LIST CASE DATA

MODEL CORE

CALCULATE UATER BALANCE

CALCULATE CIXIPONENT BALANCES:

● CONSERVATIVE TRACER

● PHOSPHORUS

● NITROGEN

CALCULATE UATER QUALITY RESPONSES:

● CHLOROPHYLL-a

● SECCHI

● ORGANIC N

● PARTICULATE P

● OXYGEN DEPLETION

f

ERROR ANALYSIS

ALTER INPUT OR MODEL ERROR TERM

ACCUMULATE OUTPUT SENSITIVITIES

EXECUTE MODEL CORE

CALCULATE WTPUT VARIANCES

OUTPUT

LIST SEGMENT HYDRAULICS AND DISPERSION

LIST GROSS UATER AND COMPONENT BALANCES

LIST BALANCES BY SEGMENT

LIST OBSERVED VS. PREDICTED STATISTICS

LIST DIAGNOSTICS AND RANKINGS

LIST SUMMARY CXJTPUT TABLES

PLOT OBSERVED AND PREDICTED CONFIDENCE LIMITS

END

Figure 4.1. Schematic of BATHTUB calculations

Chapter4 BATHTUB 4-3
Using a first-order error analysis procedure (Walker 1982), the model core is

executed repeatedly in order to estimate output sensitivity to each input variable

and submodel and to develop variance estimates and confidence limits for each

output variable. The remainder of the program consists of graphic and tabular

output routines designed to summarize results.

Control pathways for predicting nutrient levels and eutrophication response

in a given model segment are illustrated in Figure 4.2.

Predictions are based upon empirical models which have been calibrated

and tested for reservoir applications (Walker 1985). Model features are documented as follows: symbol definitions (Table 4.1), model equations and

options (Table 4.2), supplementary response models (Table 4.3), error statistics

(Table 4.4), and diagnostic variables (Table 4.5).

As listed in Table 4.2, several options are provided for modeling nutrient

sedimentation, chlorophyll a, and transparency. In each case, Models 1 and 2

are the most general formulations, based upon model testing results. Alternativemodels are included to permit sensitivity analyses and application of the

program under various data constraints (see Table 4.2). Table 4.3 specifies

submodels for predicting supplementmy response variables (organic nitrogen,

particulate phosphorus, principal components, oxygen depletion rates, trophic

state indices, algal nuisance frequencies). Error statistics for applications of the

model network to predict spatially averaged conditions are summarized in

Table 4.4.

The following sections describe underlying theory. The development and

testing of the network equations (Walker 1985) should be reviewed prior to

using the program.

Segmentation

Through appropriate configuration of model segments, BATHTUB can be

applied to a wide range of reservoir morphometries and management problems.

Figure 4.3 depicts segmentation schemes in six general categories:

a. Single reservoir, spatially averaged.

b. Single reservoir, segmented.

c. Partial reservoir or embayment, segmented.

d Single reservoir, spatially averaged, multiple scenario.

e. Collection of reservoirs, spatially averaged.

4-4

J Network of reservoirs, spatially averaged.

Chapter 4 BATHTUB
z

s

~

UJ

o

Chapter 4 BATHTUB 4-5
Table 4.1

Symbol Definitions

a = Nonalgal Turbidity (m”’) = 1/S -0.025 B

As = Surface Area of Segment (km*)

Ac = Cross-Sectional Area of Segment (km*m)

Al = Intercept of Phosphorus Sedimentation Term

A2 = Exponent of Phosphorus Sedimentation Term

B1 = Intercept of Nitrogen Sedimentation Term

B2 = Exponent of Nitrogen Sedimentation Term

B = Chlorophyll a Concentration (mg/m3)

Bm = Reservoir Area-Weighted Mean Chlorophyll a Concentration (mg/m3)

Bp = Phosphorus-Potential Chlorophyll a Concentration (mg/m3)

Bx = Nutrient-Potential Chlorophyll a Concentration (mg/m3)

CB = Calibration Factor for Chlorophyll a

CD = Calibration Factor for Dispersion

CN = Calibration Factor for N Sedimentation Rate

co = Calibration Factor for Oxygen Depletion

CP = Calibration Factor for P Sedimentation Rate

Cs = Calibration Factor for Secchi Depth

D = Dispersion Rate (km*/year)

Dn = Numeric Dispersion Rate (km*/year)

E = Diffusive Exchange Rate between Adjacent Segments (hm3/year)

Fs = Summer Flushing Rate = (inflow-Evaporation) /Volume (year-’)

Fin = Tributary Inorganic N Load/Tributary Total N Load

Fot = Tributary Ortho-P Load/Tributary ”Total P Load

FD = Dispersion Calibration Factor (applied to all segments)

G= Kinetic Factor Used in Chlorophyll a Model

HODV = Near-Dam Hypolimnetic Oxygen Depletion Rate (mg/m3-day)

L = Segment Length (km)

MODV = Near-Dam Metalimnetic Oxygen Depletion Rate (mg/m3-day)

N = Reservoir Total Nitrogen Concentration (mg/m3)

(Continued)

4-6 Chapter 4 BATHTUB
Table 4.1 (Concluded)

Ni

Nin

Nia

Ninorg

Norg

P

Pi

Pio

Pia

Portho

Pc- 1

PC-2

Q

Qs

s

T

TSlp

TSIC

TSIS

u

v

w

Wp

Wn

Xpn

z

Zx =

Zh

Inflow Total Nitrogen Concentration (mg/m3)

Inflow Inorganic N Concentration (mg/m3)

Inflow Available N Concentration (mg/m3)

Inorganic Nitrogen Concentration (mg/m3)

Organic Nitrogen Concentration (mg/m3)

Total Phosphorus Concentration (mg/m3)

Inflow Total P Concentration (mg/m3)

Inflow Ortho-P Concentration (mg/m3)

Inflow Available P Concentration (mg/m3)

Ortho-Phosphorus Concentration (mg/m3)

First Principal Component of Response Measurements

Second Principal Component of Response Measurements

Segment Total Outflow (hm3/year)

Surface Overflow Rate (m/year)

Secchi Depth (m)

Hydraulic Residence Time (years)

Carlson Trophic State Index (Phosphorus)

Carlson Trophic State Index (Chlorophyll a)

Carlson Trophic State Index (Transparency)

Mean Advective Velocity (km/year)

Total Volume (hm3)

Mean Segment Width (km)

Total Phosphorus Loading (kg/year)

Total Nitrogen Loading (kg/year)

Composite Nutrient Concentration (mg/m3)

Total Depth (m)

Maximum Total Depth (m)

= Mean Hypolimnetic Depth of Entire Reservoir (m)

Zmix = Mean Deoth of Mixed Laver (m)

Chapter 4 BATHTUB 4-7
Table 4.2

BATHTUB Model Options

Model O: Do Not Compute (Set Predicted = Observed) [defeultl

Model 1: Compute Mass Balances

Phosphorus Sedimentation

Unit P Sedimentation Rate (mg/m3-year) = CP A 1 ~z

Solution for Mixed Segment:

Second-Order Models (A2 = 2)

P = [-1 + (1 + 4 Cp Al Pi T)Osl/(2 CP Al T)

First-Order Models (A2 = 1)

P = Pi/(l + CP Al T)

Model Al u

O - Do Not Compute (Set Predicted = Observed) -- --

1 - Second-Order, Available P [default] 0.17 Qs/(Qs + 13.3) 2

as = MAx(z/T,4)

Inflow Available P = 0.33 Pi + 1.93 Pio

2- Second-Order Decay Rate Function 0.056 Fot”’Qs/(Qs + 13.3) 2

3- Second-Order 0.10 2

4- Canfield and Bachman (1 981) 0.11 (wp/v)O’5’ 1

5- Vollenweider (1 976) T-0.5 1

6- Simple First-Order 1 1

7- First-Order Settling 1/z 1

(Sheet 7 of 4) )

Note: For purposes of computing effective rate coefficients (Al), Qs, Wp, Fot, T, and V are

evaluated separately for each segment group based upon external loadings and segment

hydraulics.

4-8

Chapter 4 BATHTUB
Table 4.2 (Continued)

JJitrOaensedirnm$alim

Unit N Sedimentation Rate (mg/m3-year) = CN B1 N82

Solutions for Mixed Segment:

Second-Order Models (B2 = 2)

N = [-1 + (1 + 4 Chl B1 INiT)Osl/(2 CN B1 T)

First-Order Models (B2 = 1)

N = Ni/(1 + CN B1 T)

Model ~E.z

O - Do Not Compute -- --

(Set Predicted = Observed)

1 - Second-Order, Available N [default] 0.0045 @/(@ + 7.2) 2

QS = Maximum (Z/T,4)

Inflow Available N =0.59 Ni + 0.79 Nin

2- Second-Order Decay Rate Function 0.0035 Fin-OwQs/(Qs + 17.3) 2

Qs = Maximum (Z/T,4)

Fin = Tributary Inorganic N/Total N Load

3- Second-Order 2

4- Bachman (1 980)/Volumetric Load 1

5- Bechman (1 980)/Flushing Rate 1

6- Simple First Order 1

7- First-Order Settling 1

(Sheet 2 of 4)

Note: For purposes of computing effective rate coefficients (Bl ), Qs, Wn, Fin, T, and V are

evaluated separately for each segment group based upon external loadings and segment

hydraulics.

Nitrogen Model 1 differs slightly from that developed in Walker (1 985). The coefficients

have been adjusted so that predictions will be unbiased if inflow inorganic nitrogen data are

not available (inflow available N = inflow total N). These adjustments have negligible

influence on model error statistics.

0.00315

0.0159 (Wn/V)05g

0.693 T-055

1

1/z

Chapter 4 BATHTUB 4-9
Table 4.2 (Continued)

Model O: Do Not Compute

Model 1: N, P, Light, Flushing Rate

Xpn = [P-2 + ((N-1 50)/12)-2]-0s

Bx = Xpn ‘“” /4.31

G = Zmix (0.14 + 0.0039 Fs)

B = CB Bx/[(1 + 0.025 Bx G) (1 + Ga)l

Model 2: P, Light, Flushing Rate [default]

BP = p’3714.88

G = Zmix (0.19 + 0.0042 Fs)

B = C8 Bp/[(1 + 0.025 Bp G) (1 + Ga)l

Model 3: P, N, Low-Turbidity

B = CB 0.2 Xpn’26

Model 4: P, Linear

B = CB 0.28 P

Model 5: Jones and Bachman (1 976)

B = CB 0.081 P’a

AmlimblW. .

General

Ninorg/Portho >7

(N-1 50)/P > 12

a C 0.4 m-’

Fs < 25 1/year

a< O.91/m

Ninorg/Portho > 7

(N-150)/P > 12

Fs < 25 1/year

a < 0.4 m-’

Ninorg/Portho > 7

(N-1 50)/P > 12

Fs < 25 1/year

@~ Iicability

Model O: Do Not Compute

Model 1: Secchi vs. Chl a and Turbidity [default] General

s = CS/(a + 0.025 B)

Model 2: Secchi vs. Composite Nutrient General

s = CS 16.2 Xpn”0”7g

Model 3: Secchi vs. Total P Ninorg/Portho > 7

s = CS 17.8 P“070

,. Is - Es~lon of ~ Flows men Adlacent Seaments

Model O: Do Not Compute

E=O.

Model 1: Fischer et al. (1 979) Dispersion Equation, Walker (1 985) [default]

W}dth w = AsIL

Cross-Section Ac =Wz

Velocity u = QIAc

Dispersion D = CD 100 W* Z-ow Maximum (U,l )

Numeric Dispersion Dn = U L/2

Exchange E = MAX(D-Dn, O) At/L

Model 2: Fixed Dispersion Rate

Same as Model 1, except with fixed dispersion rate of 1,000 km2/year

D= 1,000 CD

(Sheet 3 of 4)

4-1o Chapter 4 BATHTUB
Table 4.2 (Concluded)

Dispersion M@ds (Con@u@l

Model 3: Input Exchange Rates Directly

E = CD

Model 4: Fischer Equation, Not Adjusted for Numeric Dispersion

E = D At/L (D as defined in Model 1)

Model 5: Constant Dispersion Coefficient, Not Adjusted for Numeric Dispersion

E = 1,000 CD At/L

Note: For all options, E = O. always for segments discharging out of network

(outflow segment number = O).

Phosphorus c-ion Metl@ . .

Option O: Multiply Estimated Sedimentation Rates by Calibration Factors [default]

Option 1: Multiply Estimated Concentrations by Calibration Factors

Pitroaen Callbratlon Meth d . . 0

Option O: Multiply Estimated Sedimentation Rates by Calibration Factors [default]

Option 1: Multiply Estimated Concentrations by Segment Calibration Factors

Note: Segment calibration factors (defined via Case Edit Segment) are always

applied to sedimentation rates. The above options apply only to global

calibration factors (defined via Case Edit Mcoefs).

Use of Av-itv Factora . .

Option O: Do Not Apply Availability Factors

Calculate nutrient balances based upon Total P and Total N only.

Option 1: Apply Availability Factors to P & N Model 1 Only [ default I

When P Model 1 or N Model 1 is selected, calculate nutrient balances

based upon Available nutrient loads:

Inflow Available P = 0.22 Pi + 1.93 Pio

Inflow Available N = 0.59 Ni + 0.79 Nin

When other P or N models are selected, calculate nutrient balances based

upon Total P and Total N.

Option 3: Apply Availability Factors to all P & N models except Model 2.

Option O: Use Predicted Segment Concentrations to Calculate Outflow and Storage

Terms [default]

Option 1: Use Observed Segment Concentrations to Calculate Outflow and Storage

Terms

(Sheet 4 of 4)

Chapter 4 BATHTUB 4-11
Table 4.3

Supplementary Response Models

Norg = 157 + 22.8 B + 75.3 a

IP-OW

P - Portho = Maximum [ -4.1 + 1.78 B + 23.7 a , 1 ]

HODV = 240 Bms / Zh (for Zh >2 m)

MODV = 0.4 HODV Zh 0.38

PrlnCIDal cornwn.wls . .

With Chl a, Secchi, Nutrient, & Organic Nitrogen Data:

Pc- 1 = 0.554 log(B) + 0.359 log(Norg) + 0.583 log(Xpn) -

PC-2 = 0.689 log(B) + 0.162 log(Norg) -0.205 log(Xpn) +

With Chl a and Secchi Data Only:

Pc- 1 = 1.47 + 0.949 log(B) -0.932 log(S)

PC-2 = 0.13 + 0.673 log(B) + 0.779 log(S)

TSlp = 4.15 + 14.42 In(P)

TSIC = 30.6 + 9.84 In(B)

TSIS = 60.0-14.41 In(S)

Nuisance I evel Frequencies (Walker 19841

Percent of time during growing season that Chl a exceeds bloom

20, 30, 40, or 50 ppb.

0.474 log(s)

0.676 log (S)

criteria of 10,

Calculated from Mean Chl a assuming log-normal frequency distribution with

temporal coefficient of variation = 0.62

4-12

Chapter 4 BATHTUB
Table 4.4

Error Statistics for ModeI Network Applied to Spatially Averaged

CE Reservoir Data

Variable H,= comment

Total phosphorus 0.27 o.45tt 0.91 Models 1, 2

Total nitrogen 0.22 o.55tt 0.88 Models 1, 2

Chlorophyll a 0.35 0.26 0.79 Models 1, 2

0.47 0.37 Models 3-6

Secchi depth 0.28 0.10 0.89 Model 1

0.29 0.19 Model 2

Organic nitrogen 0.25 0.12 0.75

Total p - Ortho p 0.37 0.15 0.87

Hypoiimnetic oxygen 0.20 0.15 0.90 $

depletion

MetaJimnetic oxygen 0.33 0.22 0.76 *

depletion

Note: Error statistics for CE model development data set (n = 40).

* Total = total error (model + data components). ** Model = Estimated Model Error Component.

,2 = percent of observed variance explained.

& Model error CV applied to nutrient sedimentation rates

(versus concentrations).

$ Volumetric oxygen depletion (n = 16).

Segments can be modeled independently or linked in a network. Each segment

is defined in terms of its morphometry (are% mean depth, length, mixed layer

depth, hypolimnetic depth) and observed water quality (optional). Morphometric features refer to average conditions during the period being simulated.

Segment linkage is defined by assigning each segment an ID number (from 1 to

39) and speci@ing the ID number of the segment that is immediately downstream of each segment. Multiple external sources and/or withdrawals can be

specified for each segment. With certain limitations, combinations of the above

schemes are also possible. Characteristics and applications of each segmentation scheme are discussed below.

Chapter 4 BATHTUB 4-13
Table 4.5

Diagnostic Variables and Their Interpretation

Variable Units Explanation

TOTAL P mg/m3 Total phosphorus concentration

CE distrib (MEAN = 48, CV = 0.90, MIN = 9.9, MAX = 274)

Measure of nutrient supply under P-limited conditions

TOTAL N mg/m3 Total nitrogen concentration

CE distr (MEAN = 1002, CV = 0.64, MIN = 243, MAX = 4306)

Measure of nutrient supply under N-1imited conditions

C. NUTRIENT mg/m3 Composite nutrient concentration

CE distr (MEAN = 36, CV = 0.80, MIN = 6.6, MAX = 142)

Measure of nutrient supply independent of N versus P limitation; equals total P at high

N/P ratios

CHL A mg/m3 Mean chlorophyll a concentration

CE distrib (MEAN = 9.4, CV = 0.77, MIN = 2, MAX = 64)

Measure of algal standing crop based upon photosynthetic pigment

SECCHI m Secchi depth

CE distrib (MEAN = 1.1, CV=O.76, MIN = 0.19, MAX = 4.6)

Measure of water transparency as influenced by algae and nonalgal turbidity

ORGANIC N mg/m3 Organic nitrogen concentration

CE dist (MEAN = 474, CV = 0.51, MIN = 186, MAX = 1510)

Portion of nitrogen pool in organic forms; generally correlated with chlorophyll a

concentration

P-ORTHOP mg/m3 Total phosphorus - Ortho phosphorus

CE distrib (MEAN = 30, CV = 0.95, MIN = 4, MAX = 148)

Phosphorus in organic or particulate forms correlated with chlorophyll a and nonalgal

turbidity

HODV mg/m3-day Hypolimnetic oxygen depletion rate

CE distrib (MEAN = 77, CV = 0.75, MIN = 36, MAX = 443)

Rate of oxygen depletion below thermocline; related to organic supply from settling of

algae, external organic sediment loads, and hypolimnetic depth

For HOD-V > 100; hypolimnetic oxygen supply depleted within 120 days after onset

of stratification

MODV mg/m3-da y Metalimnetic oxygen depletion rate

CE distrib (MEAN = 68, CV = 0.71, MIN = 25, MAX = 286)

Rate of oxygen depletion within thermocline; generally more important than HODV in

deeper reservoirs (mean hypolimnetic depth >20 m)

ANTILOG .- First principal component of reserv. response variables

Pc-1 (chlorophyll ~, Secchi, Organic N, Composite Nutrient)

CE distrib (MEAN = 245, CV =1.3, MIN = 18, MAX = 2460)

Measure of nutrient supply:

Low: PC-1 <50

low nutrient supply

low eutrophication potential

High: PC-1 > 500

high nutrient supply

high eutrophication potential

(Sheet 7 of 3}

Notes: CE distribution based upon 41 reservoirs used in development and testing of the model network (MEAN, CV =

geometric mean and coefficient of variation). Low and high values are typical benchmarks for interpretation.

4-14

Chapter 4 BATHTUB
Table 4.5 (Continued)

Variable Unite Explanation

ANTILOG PC-2 -- Second principal component of reserv. response variables

CE distrib (MEAN = 6.4, CV =0.53, MIN = 1.6, MAX = 13.4)

Nutrient association with organic vs. inorganic forms; related to light-limited areal

productivity

Low: PC-2 <4

turbidity-dominated, light-limited, low nutrient response

High: PC-2 > 10

algae-dominated, light unimportant, high nutrient response

(N-150)/P -- (Total N - 150)flotal P ratio

CE distrib. (MEAN = 17, CV = 0.68, MIN = 4.7, MAX = 73)

Indicator of limiting nutrient

Low: (N-1 50)/P c 10-12 nitrogen-limited

High: (N-1 50)/P > 12-15 phosphorus-limited

INORGANIC NIP -- Inorganic nitrogen/ortho-phosphorus ratio

Ratio CE distrib. (MEAN = 30, CV = 0.99, MIN = 1.6, MAX = 127)

Indicator of limiting nutrient

Low: N/P <7-10 nitrogen-limited

High: N/P >7-10 phosphorus-limited

TURBIDITY m-’ Nonalgal turbidity (1 /SECCH1 -0.025 x CHL-A)

CE distrib. (MEAN = 0.61, CV=O.88, MIN = 0.13, MAX = 5.2)

Inverse Secchi corrected for light extinction by Chl a

Reflects color and/or inorganic suspended solids

Influences algal response to nutrients:

Low: Turbidity c 0.4

allochthonous particulate unimportant

high algal response to nutrients

High: Turbidity > 1

allochthonous particulate possibly important

low algal response to nutrients

ZMIX * -- Mixed-1ayer depth x turbidity

TURBIDITY CE distrib. (MEAN = 3.2, CV = 0.78, MIN = 1.0, MAX = 17)

Effect of turbidity on light intensity in mixed layer

Low: <3

light availability high; turbidity unimportant

high algal response to nutrients

High: > 6

light availability low; turbidity important

low algal response to nutrients

ZMIXI SECCHI -- Mixed-1ayer depth/Secchi depth (dimensionless)

CE distrib (MEAN = 4.8, CV = 0.58, MIN = 1.5, MAX = 19)

Inversely proportional to mean light intensity in mixed layer for a given surface light

intensity:

Low: <3

light availability high

high algal response to nutrients expected

High: > 6

light availability low

low algal response to nutrients expected

{Sheet 2 of 3)

Chapter 4 BATHTUB 4-15
Table 4.5 (Concluded)

Variabla Units Explanation

CHL A SECCHI -- Chlorophyll 8 x transparency (mg/m2)

CE distrib (MEAN = 10, CV = 0.71, MIN = 1.8, MAX = 31)

Partitioning of light extinction between algae turbidity

Measure of light-limited productivity

Correlated with PC-2 (second principal component)

LOW: < 6

turbidity-dominated, light-limited

low nutrient response expected

High: > 16

algae-dominated, nutrient-limited

high nutrient response expected

CHL A .- Mean Chlorophyll a / Mean Total P

TOTAL P CE distrib (MEAN = 0.20, CV=O.64, MIN =0.04, MAX = 0.60)

Measure of algal use of phosphorus supply

Related to nitrogen-limited and light-limitation factors

Low: c 0.13

low phosphorus response

algae limited by N, light, or flushing rate

High: >0.40

high phosphorus response (northern lakes)

N, light, and flushing unimportant

P limited (typical of northern lakes)

TSI-P -- Trophic State Indices (Carlson 1977)

TSI-B Developed from Northern Lake Data Sets

TSI-S Calculated from P, Chl a, and Secchi Depths

TSI <40 “Oligotrophic”

41 < TSI < 50 “Mesotrophic”

51 < TSI < 70 “Eutrophic”

TSI > 70 “Hypereutrophic”

FREQ > 10”A Algal Nuisance Frequencies or Bloom Frequencies

FREQ > 20”A Estimated from Mean Chlorophyll a

FREQ > 30°A Percent of Time During Growing Season that Chl a Exceeds

FREQ > 40”A 10, 20, 30, 40, 50, or 60 ppb

FREQ > 50°A Related to Risk or Frequency of Use Impairment

FREQ > 60”A “Blooms” generally defined at Chl a > 30-40 ppb

(Sheet 3 of 3)

Scheme 1 (Figure 4.3) is the simplest configuration. It is applicable to

reservoirs in which spatial variations in nutrient concentrations and related

trophic state indicators are relatively unimportant. It can also be applied to

predict area-weighted mean conditions in reservoirs with significant spatial

variations. This is the simplest type of application, primarily because transport

characteristics within the reservoir (particularly, longitudinal dispersion) are not

considered. The development of submodels for nutrient sedimentation and

eutrophication response has been based primarily upon application of this

segmentation scheme to spatially averaged data from 41 CE reservoirs (Walker

4-16

1985).

Chapter 4 BATHTUB
SCHEME 1. SCHEME 2.

SINGLE RESERVOIR, SPATIALLY AVERAGEO

SINGLE RESERVOIR, SEGMENTED

SCHEME 3. SCHEME 4.

PART(ALRESEFWOIR OR EMBAYMENT, SEGMENTED SINGLE FIESERVOIR. SPATIALLY AVERAGED,

. MULTIPLE LOADING REGIMES

SCHEME 5. SCHEME 6.

COLLEC710N OF RESERVOIRS. SPATIALLY AVERAGED NETWORK OF RESERVOIRS, SPATIALLY AVERAGED

Figure 4.3. BATHTUB segmentation schemes

Scheme 2 involves dividing the reservoir into a network of segments for

predicting spatial variations in water quality. Segments represent different

areas of the reservoir (e.g., upper pool, midpool, near dam). Longitudinal

nutrient profiles are predicted based upon simulations of advective transport,

diffusive transport, and nutrient sedimentation. Reversed arrows in Figure 4.3

reflect simulation of longitudinal dispersion. Branches in the segmentation

scheme reflect major tributary arms or embayments. Multiple and higher order

branches are also permitted. Segment boundaries can be defined based upon

consideration of the following:

a. Reservoir morphometry.

b. Locations of major inflows and nutrient sources.

c. Observed spatial variations in water quality.

d Locations of critical reservoir use areas.

e. Numeric dispersion potential (calculated by the program).

Chapter 4 BATHTUB 4-17
If pool monitoring data are available, spatial displays generated by

PROFILE can be useful for identi&ing appropriate model segmentation. A

degree of subjective judgment is normally involved in speci~g segment

boundaries, and sensitivity to alternative segmentation schemes should be

investigated. Sensitivity to assumed segmentation should be low if longitudinal

transport characteristics are adequately represented. Experience with the program indicates that segment lengths on the order ofs to 20 km are generally

appropriate. Segmentation should be done conservatively (i.e., use the minimum number required for each application).

Scheme 3 illustrates the use of BATHTUB for modeling partial reservoirs or

embayments. This is similar to Scheme 2, except the entire reservoir is not

being simulated and the downstream water quality boundary condition is fixed.

DiiTusive exchange with the downstream water body is represented by the

bidirectional arrows attached to the last (most downstream) segment. An independent estimate of diffusive exchange with the downstream water body is

required for this type of application.

Scheme 4 involves modeling multiple loading scenarios for a single reservoir in a spatially averaged mode. Each “segment” represents the same reservoir, but under a different “condition,” as defined by external nutrient loading,

reservoir morphometry, or other input variables. This scheme is useful primarilyin a predictive mode for evaluation and rapid comparison of alternative

management plans or loading scenarios. For example, Segment 1 might reflect

existing conditions; Segment 2 might reflect projected future loadings as a

result of land development; and Segment 3 might reflect projected future loadings with specific control options. By defining segments to reflect a wide range

of loading conditions, loadings consistent with specific water quality objectives

(expressed in terms of mean phosphorus concentration, chlorophyll a, and/or

transparency) can be identified. One limitation of Scheme 4 is that certain

input variables, namely precipitation, evaporation, and change in storage, are

assumed to be constant for each segment. If year-to-year variations in these

factors are significant, a separate input file should be constructed for each year.

Scheme 5 involves modeling a collection of reservoirs in a spatially averaged mode. Each segment represents a different reservoir. This is useful for

regional assessments of reservoir conditions (i.e., rankings) and evaluations of

model performance. Using this scheme, a single file can be set up to include

input conditions (water and nutrient loadings, morphometry, etc.) and observed

water quality conditions for each reservoir in a given region (e.g., state, ecoregion). As for Scheme 4, a separate input file must be constructed for each

reservoir if there are significant differences in precipitation, evaporation, or

change in storage across reservoirs.

4-18

Scheme 6 represents a network of reservoirs in which flow and nutrients can

be routed from one impoundment to another. Each reservoir is modeled in a

spatially averaged mode, For example, this scheme could be used to represent

a network of tributmy and main stem impoundments. This type of

Chapter 4 BATHTUB
application is feasible in theory but has been less extensively tested than those

described above. One limitation is that nutrient losses in streams linking the

reservoirs are not directly represented. Such losses may be important in some

systems, depending upon such factors as stream segment length and time of

travel. In practice, losses in transport could be approximately handled by

defining “stream segments,” provided that field data are available for calibration of sedimentation coefficients (particularly in the case of nitrogen). Networking of reservoirs is most reliable for mass balances formulated on a

seasonal basis and for reservoirs that are unstratified or have surface outlets.

As illustrated in Figure 4.3, a high degree of flexibility is available for speci-

&ing model segments. Combinations of schemes are also possible within one

input file. While each segment is modeled as vertically mixed, BATHTUB is

applicable to stratified systems because the formulations have been empirically

calibrated to data from a wide variety of reservoir types, including well-mixed

and vertically stratified systems. Effects of vertical variations are incorporated

in the model parameter estimates and error terms.

Segment groups

As indicated in Table 4.2, nutrient sedimentation coefficients may depend

upon morphometric and hydrologic characteristics. To provide consistency

with the data sets used in model calibration, segments must be aggregated for

the purpose of computing effective sedimentation rate coefficients (Al and B1

in Table 4.2). A “Segment Group Number” is defined for this purpose. Ratecoefflcient computations are based upon the following variables summarized

by segment group:

a. Surface overflow rate.

b. Flushing rate (or residence time).

c. Total external nutrient load.

d Tributary total nutrient load.

e. Tributary ortho or inorganic nutrient load.

Flushing rate is also used in chlorophyll a Models 1 and 2. Area-weighted

mean chlorophyll a values are computed for each segment group and used in

the computation of hypolimnetic oxygen depletion rates (see Table 4.3).

Group numbers are integers ranging from 1 up to the total number of segments defined for the current case. Generally, if a case involves simulation of a

single reservoir with multiple segments, all segments should be assigned the

same group number (1). If the segments represent reservoir regions (tributary

arms) with distinctly different morphometric, hydrologic, and water quality

Chapter 4 BATHTUB 4-19
characteristics, different group numbers can be assigned to each region. If the

case involves simulation of multiple reservoirs (Schemes 5 or 6 in Figure 4.3),

different group numbers are assigned to each reservoir.

Tributaries

Multiple of external inflows (’Tributaries’) can be specified for any model

segment. Tributaries are identified by name and a sequence number between

1 and 99. Each tributary is assigned to a specific segment number and classified using the following ‘Type Codes’:

1 Monitored Inflow

2 Nonpoint Inflow

3 Point-Source Inflow

4 Outflow or Withdrawal

5 Internal Load

6 Diffusive Source

Type 1 describes tributaries with monitored inflows and concentrations.

Type 2 describes tributaries or watershed areas that are not monitored; inflow

volumes and concentrations are estimated from user-defined land-use categories and export coefficients. In order to invoke this tributary type, the user must

supply independent estimates of export coefficients (runoff (m/year) and typical

runoff concentrations for each land use) developed from regional data. Type 3

describes point sources (e.g., wastewater treatment plant eflluents) that discharge directly to the reservoir. Type 4 describes measured outflows or withdrawals; these are optional, since the model predicts outflow from the last

segment based upon water-balance calculations. Specification of outflow

streams is usefbl for checking water-balance calculations (by comparing

observed and predicted outflow volumes). Type 5 can be used to define internal nutrient loading rates (recycling from bottom sediments); this option would

be invoked in rare circumstances where independent estimates of sediment

nutrient fluxes are available. Type 6 defines diffusive exchange with downstream water bodies in simulating embayments (e.g., Scheme 3 in Figure 4.3).

Transport channels

In normal segmentation schemes, outflow from each segment discharges to

the next downstream segment or out of the system. An option for specifying

additional advective and/or diffusive transport between any pair of segments is

also provided. A maximum of 10 ‘Transport Channels’ can be defined for this

purpose. Independent measurements or estimates of advective and/or diffusive

flow are required to invoke this option. Definition of transport channels is not

required for simulating typical one-dimensional branched networks in which

each segment discharges only to one downstream segment.

4-20

Chapter 4 BATHTUB
Mass balances

The mass-balance concept is fimdamental to reservoir eutrophication modeling. BATHTUB formulates water andnutrient balances by establishinga

control volume around each segment and evaluating the following terms:

Inflows = Outflows + Increase-in-storage+ Net Loss

(External) (Discharge)

(Advective) (Advective)

(Diflhsive) (Diffusive)

(Atmospheric) (Evaporation)

The external, atmospheric, discharge, evaporation, and increase-in-storage

terms are calculated directly from information provided by the user in the

input file. The remaining are discussed below.

Advective terms reflect net discharge from one segment into another and are

derived from water-balance calculations. Diffusive transport terms are applicable only to problems involving simulation of spatial variations within reservoirs. They reflect eddy diffusion (as driven by random currents and wind

mixing) and are represented by bulk exchange flows between adjacent segment

pairs. Chapra andReckhow(1983) present examples of lake/embayment

models that consider diffusive transport.

As outlined in Table 4.2, five methods are available for estimating diffusive

transport rates. Each leads to the calculation of bulk exchange flows which

occur in both directions at each segment interface. Dispersion coefficients,

calculated from the Fischer et al. (1979) equation (Model 1) or from a fixed

longitudinal dispersion coefficient (Model 2), are adjusted to account for

effects of numeric dispersion (“artificial” dispersion or mixing that is a consequence of model segmentation). Model 3 can be used for direct input of bulk

exchange flows.

Despite its original development based upon data from river systems, the

applicability of the Fischer et al. equation for estimating longitudinal dispersion

rates in reservoirs has been demonstrated previously (Walker 1985). For a

given segment width, mean depth, and outflow, numeric dispersion is proportional to segment length. By selecting segment lengths to keep numeric dispersion rates less than the estimated values, the effects of numeric dispersion on

the calculations can be approximately controlled. Based upon Fischer’s dispersion equation, the numeric dispersion rate will be less than the calculated dispersion rate if the following condition holds:

L < 200w2Z-084°

where

L = segment length, km

Chapter 4 BATHTUB 4-21
W = mean top width= surface aredlength, km

Z = mean depth, m

The above equation can be applied to reservoir-average conditions in order to

estimate an upper bound for the appropriate segment length. In most cases,

simulated nutrient profiles are relatively insensitive to longitudinal dispersion

rates. Fine-tuning of exchange flows can be achieved via the use of segmentspecific calibration factors.

While, in theory, the increase-in-storage term should reflect both changes in

pool volume and concentration, only the volume change is considered in massbalance calculations, and concentrations are assumed to be at steady state. The

increase-in-storage term is used primarily in veri@ng the overall water balance.

Predictions are more reliable under steady pool levels or when changes in pool

volume are small in relation to total inflow and outflow.

Nutrient sedimentation models

For a water balance or conservative substance balance, the net sedimentation term is zero. Nutrient retention submodels are used to estimate net sedimentation of phosphorus or nitrogen in each segment according to the

equations specified in Table 4.2. Based upon research results, a second-order

decay model is the most generally applicable formulation for representing

phosphorus and nitrogen sedimentation in reservoirs:

W== KZC2

where,

W,= nutrient sedimentation rate, mg/m3-year

K2= effective second-order decay rate, m3/mg-year

C = pool nutrient concentration, mg/m3

Other options are provided for users interested in testing alternative models

(see Table 4.2). The default model error coefficients supplied with the program, however, have been estimated from the model development data set

using the second-order sedimentation formulations. Accordingly, error analysis

results (predicted coefficients of variation) will be invalid for other formulations (i.e., model codes 3 through 7 for phosphorus or nitrogen), unless the user

supplies independent estimates of model error terms.

4-22

Effective second-order sedimentation coefficients are on the order of

0.1 m3/mg-year for total phosphorus and 0.0032 m3/mg-year for total nitrogen,

as specified under “Model 3“ in Table 4.2. With these coefficients, nutrient

Chapter 4 BATHTUB
sedimentation models explain 83 and 84 percent of the between-reservoir

variance in average phosphorus and nitrogen concentrations, respectively.

Residuals from these models are systematically related to inflow nutrient partitioning (dissolved versus particulate or inorganic versus organic) and to surface overflow rate over the data set range of 4 to 1,000 m/year. Effective rate

coefficients tend to be lower in systems with high ortho-P/total P (and high

inorganic N/total N) loading ratios or with low overflow rates (4 to 10 m/year).

Refinements to the second-order formulations (Models 1 and 2) are designed to

account for these dependencies (Walker 1985).

As indicated in Table 4.2, Sedimentation Models 1 and 2 use different

schemes to account for effects of inflow nutrient partitioning. In the case of

phosphorus, Model 1 performs mass balance calculations on “available P,” a

weighted sum of ortho-P and nonortho-P which places a heavier emphasis on

the ortho-P (more biologically available) component. Model 2 uses total phosphorus concentrations but represents the effective sedimentation rate as

inversely related to the tributary ortho-P/total P ratio, so that predicted sedimentation rates are higher in systems dominated by nonortho (particulate or

organic) P loadings and lower in systems dominated by ortho-P or dissolved P

loadings. The nitrogen models are structured similarly, although nitrogen

balances are much less sensitive to inflow nutrient partitioning than are phosphorus balances, probably because inflow nitrogen tends to be less strongly

associated with suspended sediments.

Model 1 accounts for inflow nutrient partitioning by adjusting the inflow

concentrations, and Model 2 accounts for inflow nutrient partitioning by

adjusting the effective sedimentation rate coefllcient. While Model 2 seems

physically reasonable, Model 1 has advantages in reservoirs with complex

loading patterns because a fixed sedimentation coefficient can be used and

effects of inflow partitioning are incorporated prior to the mass balance calculations. Because existing data sets do not permit general discrimination between

these two approaches, each method should be tested for applicability to a particular case. In most situations, predictions will be relatively insensitive to the

particular sedimentation model employed, especially if the ortho-P/total P

loading ratio is in a moderate range (roughly 0.25 to 0.60). Additional model

application experiences suggest that Method 2 may have an edge over Model 1

in systems with relatively long hydraulic residence times (roughly, exceeding

1 year), although further testing is needed. Because the coefficients are concentration- or load-dependent and because the models do not predict nutrient

partitioning in reservoir outflows, Sedimentation Models 2 and 4 cannot be

applied to simulations of reservoir networks (Scheme 6 in Figure 4.3).

Based upon error analysis calculations, the models discussed above provide

estimates of second-order sedimentation coefllcients which are generally

accurate to within a factor of 2 for phosphorus and a factor of 3 for nitrogen.

In many applications, especially reservoirs with low hydraulic residence times,

this level of accuracy is adequate because the nutrient balances are dominated

by other terms (especially, inflow and outflow). In applications to existing

Chapter 4 BATHTUB 4-23
4-24

reservoirs, sedimentation coefficients estimated from the above models can be

adjusted within certain ranges (roughly a factor of 2 for P, factor of 3 for N) to

improve agreement between observed and predicted nutrient concentrations.

Such “tuning” of sedimentation coefficients should be approached cautiously

because differences between observed and predicted nutrient levels may be

attributed to factors other than errors in the estimated sedimentation rates, particularly if external loadings and pool concentrations are not at steady state.

Figure 4.4 shows the relationship between hydraulic residence time and

mean depth in the reservoirs used in model development. Predictions of nutrient sedimentation rates are less reliable in reservoirs lying outside the data set

range. This applies primarily to reservoirs with residence times exceeding

2 years, mean depths greater than 30 m, or overflow rates less than 4 m./year.

Tests based upon independent data sets indicate that the sedimentation models

are unbiased under these conditions but have higher error variances. In such

situations, the modeling exercise should include a sensitivity analysis to model

selection and, if possible, calibration of sedimentation coefficients to match

observed concentration data. Deviations at the other extremes (reservoirs with

lower residence times or higher overflow rates than those represented in the

model development data set) are of less concern because the sedimentation

term is generally an insignificant portion of the total nutrient budget in such

systems (i.e., predicted pool concentrations are highly insensitive to estimated

sedimentation rate).

Because the sedimentation models have been empirically calibrated, effects

of “internal loading” or phosphorus recycling from bottom sediments are

inherently reflected in the model parameter values and error statistics. Generally, internal recycling potential is enhanced in reservoirs with the following

characteristics:

a.

b.

c.

d.

High concentrations of ortho-phosphorus (or high ortho-P/totalP ratios)

in nonpoint-source tributary drainage (indicative of natural sediments

that are phosphorus-rich and have high equilibrium phosphorus

concentrations).

Low summer sufiace overflow rates, typically <10 m/year (indicative of

low dilution potential for internal loadings generated on a mass per unit

area basis and low external sediment loadings).

Intermittent periods of stratification and anoxic conditions at the

sedimentiwater interface (contribute to periodic releases of soluble

phosphorus from bottom sediments and transport into the mixed layer).

Low iron/phosphorus ratios (typically <3 on a mass basis) in sediment

interstitial waters or anaerobic bottom waters (permits migration of

phosphorus into aerobic zones without iron phosphate precipitation).

The above conditions are often found in relatively shallow prairie reservoirs;

Lake Ashtabula (U.S. Army Engineer District, St. Paul) is an example

Chapter 4 BATHTUB
1.8

1.5

0

0

d 0.6

0.3

o

●

●

● ☛

●

●

●☛ ●“*

Q

● ●

●

●

I I 1 1 I J

-2.0 -1.5 -1.0 -0.5 0 0.5

LOG HYDRAULIC RESIOENCE TIME. YR

=2YR

YR

Figure 4.4. Mean depth (Z) versus hydraulic residence time (T) for CE model

development data set LOGIO scales

included in the CE reservoir data set. In such situations, empirical sedimentation models will underpredict reservoir phosphorus concentrations. Depending

upon the efficiency of the internal recycling process, steady-state phosphorus

responses can be approximately simulated by reducing the effective sedimentation coefficient (e.g., roughly to O.in the case of Ashtabula). An option for

direct specification of internal loading rates is also provided for use in situations

where independent measurements or estimates are available.

Nutrient residence time and turnover ratio

The “averaging period” is defined as the period of time over which water

and mass balance calculations are petiormed. The selection of an appropriate

averaging period is an important step in applying this type of model to reservoirs. Two variables must be considered in this process:

Mass residence time, year = Nutrient mass in reservoir, kg

External nutrient loading, kg/year

Turnover ratio = Length of averaging period, year

Mass residence time, year

Chapter 4 BATHTUB 4-25
The estimates of reservoir nutrient mass and external loading correspond to the

averaging period. The turnover ratio approximates the number of times that

the nutrient mass in the reservoir is displaced during the averaging period.

Ideally, the turnover ratio should exceed 2.0. If the ratio is too low, then pool

and outflow water quality measurements would increasingly reflect loading

conditions experienced prior to the start of the averaging period, which would

be especially problematical if there were substantial year-to-year variations in

loadings.

At extremely high turnover ratios and low nutrient residence times

(s2 weeks), the variability of loading conditions within the averaging period (as

attributed to storm events, etc.) would be increasingly reflected in the pool and

outflow water quality measurements. In such cases, pool measurement variability may be relatively high, and the biological response (e.g., chlorophyll a

production) may not be in equilibrium with ambient nutrient levels, particularly

immediately following storm events.

Figure 4.5 shows that the hydraulic residence time is an important factor in

determining phosphorus and nitrogen residence times, based upon annual mass

balances from 40 CE reservoirs used in model development. For a conservative substance, the mass and hydraulic residence times would be equal at steady

state. The envelopes in Figure 4.5 show that the spread of nutrient residence

times increases with hydraulic residence time; this reflects the increasing

importance of sedimentation as a component of the overall nutrient balance. At

low hydraulic residence times, there is relatively little opportunity for nutrient

sedimentation, and pool nutrient concentrations and residence times can be

predicted relatively easily from inflow concentrations. At high hydraulic residence times, predicted pool nutrient concentrations and residence times

become increasingly dependent upon the empirical formulations used to represent nutrient sedimentation. This behavior is reflected in the sensitivity curves

discussed in Chapter 1.

Normally, the appropriate averaging period for water and mass balance

calculations would be 1 year for reservoirs with relatively long nutrient residence times or seasonal (May-September) for reservoirs with relatively short

nutrient residence times. As shown in Figure 4.5, most of the reservoirs in the

model development data set had phosphorus residence times less than 0.2 year,

which corresponds roughly to a nutrient turnover ratio of 2 for a 5-month seasonal averaging period. Thus, assuming that the reservoirs used in model

development are representative, seasonal balances would be appropriate for

most CE reservoir studies. BATHTUB calculates mass residence times and

turnover ratios using observed or predicted pool concentration data. Results

can be used to select an appropriate averaging period for each application.

4-26

Chapter 4 BATHTUB
0.5

0.0

--

z

“2.0

-2.5

t

“2*!5 -2.0 -1.5 -1.0 -0.s 0.0 0.5

LOG 14YDf3AULlC

RESIOENCE TIME, LOG (YR)

0.5

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5

LOG HYDRAULIC

RESIDENCE TIME, LOG (YR)

Figure 4.5. Relationships between nutrient residence times and hydraulic residence times in CE model development data set

Chapter 4 BATHTUB 4-27
Solution algorithms

The water balances are expressed as a system of simultaneous linear equations that are solved via matrix inversion to estimate the advective out-flow

from each model segment. The mass balances are expressed as a system of

simultaneous nonlinear equations which are solved iteratively via Newton’s

Method (Burden, Fakes, and Reynolds 198 1). Mass-balance solutions can be

obtained for up to three constituents (total phosphorus, total nitrogen, and a

user-defined conservative substance). Total phosphorus and total nitrogen

concentrations are subsequently input to the model network (Figure 4.2) to

estimate eutrophication responses in each segment. Conservative substances

(e.g., chloride, conductivity) can be modeled to veri~ water budgets and calibrate longitudinal dispersion rates.

Eutrophication response models

Eutrophication response models relate observed or predicted pool nutrient

levels to measures of algal density and related water quality conditions.

Table 4.5 lists diagnostic variables included in BATHTUB output and guidelines for their interpretation. They may be categorized as follows:

a.

b.

c.

d.

e.

f

g.

Basic network variables.

(1) Total P, Total N.

(2) Chlorophyll a, Secchi depth.

(3) Organic Nitrogen, Total P - Ortho-P.

(4) Hypolimnetic and Metalimnetic Oxygen Depletion Rates.

Principal components of network variables: first and second principal

components.

Indicators of nitrogen versus phosphorus limitation (Total N- 150)/Total

P, and Inorganic N/P ratios.

Indicators of light limitation.

(1) Nonalgal turbidity, mixed depth x turbidity.

(2) Mixed depth/Secchi depth, and chlorophyll a x Secchi Depth.

Chlorophyll a response to phosphorus: chlorophyll a/total P.

Algal Nuisance Frequencies.

Carlson Trophic State Indices.

4-28

Chapter 4 BATHTUB
Statistical summaries derived from the CE model development data set provide

one frame of reference. Low and high ranges given for specific variables provide approximate bases for assessing controlling processes and factors, including growth limitation by light, nitrogen, and phosphorus.

The ranges of conditions under which the empirical models have been

developed should be considered in each application. Figure 4.6 depicts relationships among three key variables determining eutrophication responses (total

phosphorus, total nitrogen, and nonalgal turbidity) in the CE model development data set. Figure 4.7 depicts relationships among phosphorus, chlorophyll

a, and transparency. Plotting data from a given application on each of these

figures permits comparative assessment of reservoir conditions and evaluations

of model applicability. If reservoir data fall outside the clusters in Figure 4.5,

4.6, or 4.7, potential model errors are greater than indicated by the statistics in

Table 4.4.

The prediction of mean chlorophyll a from observed or predicted nutrient

concentrations can be based on one of the five models listed in Table 4.2.

Error analyses indicate that it is generally more difficult to predict chlorophyll a

from nutrient concentrations and other controlling factors than to predict nutnent concentrations from external loadings and morphometry. This partially

reflects greater inherent variability of chlorophyll a. Chlorophyll a models can

be described according to limiting factors:

MQdd Limitirw Factors

1 P, N, light, flushing

2 P, light, flushing

3 P, N

4 P (linear)

5 P (exponential)

Approximate applicability constraints are given in Table 4.2. “Northern lake”

eutrophication models are based upon phosphorus/chlorophyll regressions

(similar to Models 4 and 5). Research objectives (Walker 1985) have been to

define the approximate ranges of conditions under which simple phosphorus/

chlorophyll relationships are appropriate and to develop more elaborate models

(Models 1-3) which explicitly account for additional controlling factors (nitrogen, light, flushing rate).

While model refinements have been successful in reducing error variance

associated with simple phosphorus/chlorophyll relationships by approximately

58 percent, a “penalty” is paid in terms of increased data requirements (e.g.,

nonalgal turbidity, mixed-layer depths, nitrogen, and flushing rate). For existing reservoirs, these additional data requirements can be satisfied from pool

monitoring and nutrient loading information. Otherwise, estimates must be

based upon subjective estimates, independent hydrodynamic models, and/or

regional data from similar reservoirs. Empirical models for developing independent estimates of turbidity, mixed-layer depth, and mean hypolimnetic

Chapter 4 BATHTUB 4-29
●

●

●

●

‘e

●

0.s to I*S 2,0 2,s

TOTAL PHOSPHORUS,LOG (MG/Ms)

0.8 r na! 1- U.CB r

“ -O*1 Iii =

z“0,4

4s7

-1.0

●

●

**

*

@

0.5 1,0 14s 8,0 B$8

TOTAL PHO$PHORU%LOQ(WMO)

Figure 4.6. Phosphorus, nitrogen, turbidity relationships for CEresewoirs

(nonalgal turbidity calculated as l/Secchi (m) -0.025 Chl a (mg/m’))

4-30

Chapter4 BATHTUB
1.0

1.5

1.2

0.9

0.6

0.3

0

0.9

0.6

0.0

-0.3

-0.6

-0.9

.

●

● 0 ●

am ●

● ●. #

00

● 1 1 1 J

1.0 1.5 2.0 2.5

TOTAL PHOSPHORUS, LOG (MG/M3)

●

%

●

●*P

● * -m

● ●h &

4 ● 9

● O*

●.*e:‘s● & ●

●

@%@.** ‘e

●

●

●

1 1 1 1 I J

o 0.3 0.6 0.9 1.2 1.5 1.8

CHLOROPHYLL-a, LOG (MG/M3)

Figure 4.7. Phosphorus, chlorophyll a, and transparency relationships for CE

reservoirs

Chapter 4 BATHTUB 4-31
depth are summarized in Table 4.6. These should be used only in the absence

of site-specific measurements.

Since mechanistic models for predicting nonalgal turbidity levels as a function of deterministic factors (e.g., suspended-solids loadings and the sedimentation process) have not been developed, it is possible to predict chlorophyll a

responses to changes in nutrient loading in light-limited reservoirs only under

stable turbidity conditions. Projections of chlorophyll a concentrations should

include a sensitivity analysis over a reasonable range of turbidity levels.

Estimates of nonalgal turbidity in each segment (minimum= 0.08 m-l) are

required for chlorophyll a Models 1 and 2, Secchi Model 1 (Table 4.2), and

Nutrient Partitioning Models (Table 4.3). Ideally, turbidity is calculated from

observed Secchi and chlorophyll a data in each segment. If the turbidity input

field is lefl blank, the program calculates turbidity values automatically from

observed chlorophyll a and Secchi values (if specified). An error message is

printed, and program execution is terminated if all of the following conditions

hold:

a. Turbidity value missing or zero.

b. Observed Chlorophyll a or Secchi missing or zero.

c. Chlorophyll a Models 1,2 or Secchi Model 1 used.

In the absence of direct turbidity measurements, the multivariate regression

equation specified in Table 4.6 can be used (outside of the program) to estimate a reservoir-average value. Such estimates can be modified to based upon

regional databases.

Model calibration and testing have been based primarily upon data sets

describing reservoir-average conditions (Walker 1985). Of the above options,

Model 4 (linear phosphorus/chlorophyll a relationship) has been most extensively tested for use in predicting spatial variations within reservoirs. The

chlorophyll/phosphorus ratio is systematically related to measures of light

limitation, including the chlorophyll a and transparency product, and the product of mixed-layer depth and turbidity. If nitrogen is not limiting, then lightlimitation effects may be approximately considered by calibrating the

chlorophyll/phosphorus ratio to field data; this is an alternative to using the

direct models (i.e., Models 1 and 2) that require estimates of turbidity and

mixed-layer depth in each segment. The relationships depicted in Figure 4.8

may be used to obtain approximate estimates of reservoir-average calibration

coefficients for use in Model 4 based upon observed monitoring data or independent estimates of turbidity and mixed-layer depth (Table 4.6).

Models 1 and 3 attempt to account for the effects of nitrogen limitation on

chlorophyll a levels.

nitrogen budget and

Nitrogen concentrations are predicted from the external

do not account for potential fixation of atmospheric

4-32

Chapter 4 BATHTUB
Table 4.6

Equations for Estimating Nonalgal Turbidity, Mixed Depth, and

Hypolimnetic Depths in Absence of Direct Measurements

Based upon measured chlorophyll a and Secchi depth:

a = 1/S -0.025 B (minimum value = 0.08 1/m)

where

s = Secchi dapth, m

B = chlorophyll a, mg/m3

Multivariate turbidity model:

log (a) = 0.23-0.28 log (Z) + 0.20 log (FS) + 0.36 log (P) -0.027

LAT + 0.35 du (R2 = 0.75, SE2 = 0.037)

whera

LAT = dam latitude, deg N

du = regional dummy variable, (1 for U.S. Army Engineer (USAE) Divisions

North Pacific, South Pacific, Missouri River, and Southwest (except USAE

District, Little Rock) and USAE District, Vicksburg, and O for other

locations)

Fa = summer flushing rate (year”’) or 0.2, whichever is greater

z = mean total depth, m

P = total phosphorus concentration, mg/m3

log (Zmix) = -0.06 + 1.36 log (Z) -0.47 [log (Z)]*

(R2 = 0.93, SE2 = 0.0026)

Mean deDth of hvDollmnlon (retire reservoir . .

log (Zh) = -0.58 + 0.57 log (zx) + 0.50 log (Z)

(R2 = 0.85, SE2 = 0.0076)

nitrogen by bluegreen algae. Nitrogen fixation may be important in some

impoundments, as indicated by the presence of algal types known to fix nitrogen,

low N/P ratios, and/or negative retention coeftkients for total nitrogen (Outflow N > Inflow N). In such situations, nitrogen could be viewed more as a

trophic response variable (controlled by biologic response) than as a causal

factor related directly to external nitrogen loads. Use of Models 1 and 3 may

be inappropriate in these cases; modeling of nitrogen budgets would be usefil

for descriptive purposes, but not useful (or necessary) for predicting chlorophyll a levels.

Chapter 4 BATHTUB 4-33
0.6

0.4

0.2

0.0

-’0.2

-O*4

-0.6

-0.8

-1.0

0.0 0.3 0.6 0.9 1.2 1.5

LOG (CHL-A * SECCHI)

0.6

0.4

r -

0.0

-0.2

-0.4

-0.6

-0.8

1- * ? =.62

r ●

-1.0 1 1 1 I I 1 J

0.3 0.o 0.3 0.6 0.9 1.2 1.5

LOG (ZMIX ● TURBIDITY)

4-34

Figure 4.8. Calibration factor for linear phosphorus/chlorophyll model versus

light limitation factors

Chapter 4 BATHTUB
If the reservoir is stratified and oxygen depletion calculations are desired,

temperature profile data taken from the period of depletion measurements

(typically late spring to early summer) are used to estimate the mean depth of

the hypolimnion. If mean hypolimnetic depth is not specified (=0.0), the reservoir is assumed to be unstratified and oxygen depletion calculations are

bypassed. The oxygen depletion models are based upon data from near-dam

stations. Accordingly, mean hypolimnetic depths should be specified only for

near-dam segments, based upon the morphometry of the entire reservoir (not

the individual segment). In modeling collections or networks of reservoirs

(Schemes 5 and 6 in Figure 4.3), a mean hypolimnetic depth can be specified

separately for each segment (i.e., each reservoir). Table 4.6 gives an empirical

relationship that can be used to estimate mean hypolimnetic depth in the

absence of direct measurements.

Calibration factors

The empirical models implemented in BATHTUB are generalizations about

reservoir behavior. When applied to data from a particular reservoir, observations may differ from predictions by a factor of two or more. Such differences

reflect data limitations (measurement or estimation errors in the average inflow

and outflow concentrations), as well as unique features of the particular reservoir. A facility to calibrate the model to match observed reservoir conditions is

provided in BATHTUB. This is accomplished by application of ‘Calibration

Factors’, which modi~ reservoir responses predicted by the empirical models,

nutrient sedimentation rates, chlorophyll a concentrations, Secchi depths, oxygen depletion rates, and dispersion coefficients. The calibrated model can be

applied subsequently to predict changes in reservoir conditions likely to result

from specific management scenarios under the assumption that the calibration

factors remain constant.

For convenience, calibration factors can be applied on two spatial scales:

global (applying to all segments) and individual (applying to each segment).

The product of the global and individual calibration factors is multiplied by the

reservoir response predicted by the empirical model to produce the “calibrated”

prediction. All calibration factors have a default value of 1.0. Separate sets of

calibration factors can be applied to any or all the following response

predictions:

Nutrient Sedimentation Rates (or Concentrations)

Chlorophyll a Concentrations

Secchi Depths

Longitudinal Dispersion Rates

Oxygen Depletion Rates

Recognizing that differences between observed and predicted responses are at

least partially due to measurement errors, calibration factors should be used

very conservatively. Program output includes statistical tests to assist the user

Chapter 4 BATHTUB 4-35
in assessing whether calibration is appropriate. General guidance is presented

in a subsequent section (see Application Steps).

Error analysis

The first-order error analysis procedure implemented by BATHTUB can be

used to estimate the uncertainty in model predictions derived from uncertainty

in model inputs and uncertainty inherent in the empirical models. To express

uncertainty in inputs, key input variables are specified using two quantities:

Mean = Best Estimate

CV = Standard Error of Mean/Mean

The CV reflects the uncertainty in the input value, expressed as a fraction of the

mean or best estimate. CV values carI be specified for most input categories,

including atmospheric fluxes (rainfall, evaporation, nutrient loads), tributary

flows and inflow concentrations, dispersion rates, and observed reservoir

quality. FLUX and PROFILE can be used to estimate Mean and CV values for

inflow and reservoir concentrations, respectively. Model uncertainty is considered by specifing a CV value for each global calibration factor; default CV

values derived from CE reservoir data sets are supplied (see Table 4.4). Erroranalysis calculations provide only rough indications of output uncertainty. Four

error analysis options are provided:

None

Inputs (Consider input uncertainty only)

Model (Consider model uncertainty only)

All (Consider input and model uncertainty)

Specified CV values are not used in the calculations if error analyses are not

requested.

Program Operation

Introduction

4-36

This section summarizes procedures for running the BATHTUB program.

When the program is run (from the DOS prompt), a series of help screens

summarizing model features is first encountered. These are followed by a

menu that provides interactive access to seven types of procedures with the

following functions:

Chapter 4 BATHTUB
1 BATHTUB - VERSION 5.4—

Case Run List Plot Utilities Help Quit

Case Define Case - Read, Enter, Edit, or List Input Values

List List Wdel Output

Run Check Input Values & Run Model

Help View Supplementary Help Screens

Quit End Current Session

A procedurecategory is selected bymoving the cursor(usingarrow keys) orby

pressing the first letter of theprocedure name. Assistance innavigating around

themenu can reobtained bypressing the<F7> function key. Generally, Case,

Run, List, and Plot procedures would be implemented sequentially in a given

session. Program control returns to the top of the menu after executing a procedure. A Help screen describing the selected procedure can be viewed by

pressing <Fl>.

Case procedures

Case procedures are invoked to define, edit, save, retrieve, or list input

values. Once Case is selected, the menu expands by one line to show further

choices. The following procedure categories are available:

Edit

Models

Read

Save

Neu

Change

List

Morpho

Edit Case Data

Set Model Opt ions

Read Case Data Fi [e

Save Case Input Data File

Reset Input Values & Start New Case

Delete, Insert, or Copy Segments or Tributaries

List Current Case Input Values

List Segment Morphometry

Entry and editing of data is accomplished by selecting Edit, which provides

access to data-entry screens in the following categories:

Dimensions

Globals

Segments

Tribs

Nonpoint

Mcoefs

Channels

Ail

Edit

Edit

Edit

Edit

Edit

Edit

Edit

Edit

Case Dimensions, File Name, Title, User Notes

Global Parameters, Precip., Evap., Atrnos. Loads

Segment Data

Tributary and Point-Source Data

Nonpoint Landuse Categories & Export Coefficients

Default Model Coefficients & Error Terms

Transport Channels

All Inout Data Groups

Each ofthe above procedures provides accessto

These are listed along with their associated Help

Chapter4 BATHTUB

adifferent data-entry screen.

screens below:

4-37
Once the case input values have been entered, the Case/Models procedure

can be used to define model options in the following categories:

Model Categories:

Conservative Substance Balance

Phosphorus Sedimental ion Model

Nitrogen Sedimental ion Model

Chlorophyll 1 a Model

Secch i Model

Dispersion Model

Phosphorus C. 1 i brat i on Method

Nitrogen Cal i brat ion Method

Nutrient Availability Factors

Mass-Balance Calculation Method

Subsequent menus are presented that allow the user to set model options in any

of the above categories. Option settings are documented in Table 4.2. For most

options, a setting of zero will bypass the corresponding calculations. Conservative substance (e.g., chloride) balances may be useful for veri@ng water

balances and calibrating diffusive transport coefficients. For the phosphorus,

nitrogen, and chlorophyll models, settings of 1 or 2 correspond to the most

general formulations identified in model testing. If the conservative substance,

phosphorus, or nitrogen sedimentation model is set to O, corresponding mass

balance calculations are bypassed, and predicted concentrations are set equal to

observed values in each segment. This feature is useful for assessing pool

nutrientfchlorophyll relationships and controlling factors in the absence of

nutrient loading information.

The Case/Read procedure is used to read existing data sets and has two

choices beneath it:

Data Read Version 5.4 Data set

Translate Read Data Set Created with Previous Versions of Program

Case input data can be saved (along with selected model options) on disk

(CasedSave) for retrieval in subsequent sessions (Case/Retrieve). Case files

should be named with an extension of’. BIN’ to facilitate future identification

and retrieval. The Case/Save procedure saves the current data set. The

Case/New procedure resets all data and model coefficients to their default

values and begins a new data set. The Case/List procedure lists all input

values for the current case. The Case/Morpho option lists a brief summary of

segment morphometric features.

4-38

Chapter 4 BATHTUB
Run procedures

Once a complete set of input values have been entered and saved on disk,

the model can be run using the following procedures:

-:l’:l!’;O” ‘u:’’’’:s’”4-

NoError Run Model Uithout Error Analysis

Inputs Error Analysis - Case Input Variables Only

Mode1 Error Analysis - Model Error Terms & Calib Factors

All Error Analysis - All Input Variables and Model Parameters

Thefirstprocedure (Run/Model/NoError) is suggestedfortrial runs ofnewly

entered cases. The program first checks for valid input data and lists any

errors identified. Error messages describe the error type and ofien referto a

particular segment ortributarynumber. Ifanerror is encou.ntered, execution

stops and control is returned tothe main menu. The user would then access

Caseprocedures toidenti& andcorrect theinvalid input data. Ifthe numberof

error messages encountered fills up more than one screen, a copy of the error

messages is saved in a disk file which can be accessed using the Utilities/Error

procedure.

If no input errors are detected, the program attempts to solve the massbalance equations. In rare cases, solutions cannot be reached and an error

message appears. This type of problem may occur when the segmentation

scheme is not defined correctly (outflow segment numbers are not correctly

specified) or when the solution of the water-balance equation indicates that

there is no net outflow from the reservoir (evaporation and/or withdrawals

exceed inflows). Steady-state solutions cannot be reached in such situations.

If a solution is reached, control is returned to the main menu. The message

‘MODEL EXECUTED’ appears in the lower right hand comer of the screen.

This indicates that List and Plot procedures can be accessed to review output.

If input values are subsequently edited or a new data file is read, the model

must be executed again before output can be viewed. As indicated above, the

Run/Model procedures can be implemented with four levels of error analysis.

Error analysis procedures require longer execution times because the model

must be solved many times to test sensitivity to each input variable and/or

model error term.

The Run/Sensitivity procedures test the sensitivity of predicted nutrient

concentrations in each segment to variations in nutrient sedimentation rate and

in longitudinal dispersion rate:

-BAT:!:,: ‘“’’’’:’’s’”4 ‘e” ‘Ui’

Chapter 4 BATHTUB 4-39
Conserv Run Sensitivity Analysis for

Total P Run Sensitivity Analysis for

Total N Run Sensitivity Analysis for

List procedures

Conservative Substance

Total Phosphorus

Total Nitrogen

Several tabuh.rformats are provided tosummarize and highlight various

aspects ofthe model output. These are accessed by selecting Listfrom the

main menu:

Hydrau 1

Balances/

Gross

By Segment

Smnary

Compar

D i agnos

Profiles

F 1ownet

Table

Short

List Uorphometry/Hydraulics/Dispersion Table

List Water and Mass Balances

Gross Uater and Mass Balances - All Segments

Uater and Mass Balances by Segment - Detailed

Uater and Mass Balances by Segment - Sunn’iary

Compare Observed & Predicted Values

List Observed & Predicted Diagnostic Variables

List Summary of Predicted Values

List Flow Network Sumnary

List Table of Predicted Values for Selected Variables

Short Table of All Predicted Values by Segment

Each procedure writes resultsto atemporay disk file. When output iscomplete, a utility is executed to permit interactive viewing of the output file.

Cursorkeyscanbe usedtomoveforward orbackwardthough thefile.

Results canbecopied toapermanentdisk filebypressingthe <F8>function

key. AHeIpscreen describing tiecunent output fomatcm beaccessedby

pressing the <Fl>fh.nction key. Examples and explanation ofeach output

format aregivenin the ’Sample Output’ section.

Plot procedures

Graphs of observed and predicted concentrations can be viewed by

accessing the Plot procedures:

Nutrients Plot Total Phosphorus & Total Nitrogen Only

All Plot All Variables

some Plot Selected Variable(s)

Define/ Edit Plot Scale Options (Default, Linear, or Logarithmic)

lDefault Use Default Scale Types

2Linear Use Linear Scales for All Variables

3Log Use Logarithmic Scales for All Variables

4-40

After speci&ing one of these procedures, plot formats can be selected from

subsequent menu screens:

Chapter4 BATHTUB
1. Observed and Predicted vs. Model Segment

2. Observed vs. Predicted

3. Observed/Predicted Ratio vs. Model Segment

If error analysis calculations have been petiormed, Format 1 shows predicted

concentrations + 1 standard error. Similarly, observed concentrations are

shown * 1 standard error for observed variables with specified CV values. The

last model segment displayed in Formats 1 and 3 shows results for the areaweighted mean across all case segments; for example, if the case contains

4 segments, area-weighted means will be shown above segment number 5.

Samples of each plot format are given in the ‘Sample Output’ section.

Utility procedures

Program utilities can be accessed from the main menu to provide the

following fhnctions:

V;i;w’i:’;r’ ‘“’’’’’’’’”4-

output/ Set Output Destination - Screen or Fi [e

Screen Direct Output to Screen (Default)

File Direct Output to Disk File

Restrict Restrict Output & Plots to Specific Segment(s)

View View any DOS Text File

Error View Error Message File

Output can be redirected from the screen to a disk file. If Utilities/Output/

File is selected, all output listings will be routed to a user-specified disk file; no

screen output will occur until Utilities/Output./Screen is selected. This utility

is usefid for creating permanent log files of program output for future reference

or for inclusion in reports. The Utilities/Restrict procedure can be used to

restrict program output (listing and plots) to specific segments. As discussed

above, the Utilities/Error procedure permits viewing of any error messages

from the last execution of the model. This is useful for debugging input files.

Help procedure

Supplementary help screens can be viewed from the program menu by

selecting the Help:

*B A T H T U B - VERSION 5.4

This provides access to help screens that are organized in the following generaI

categories:

Chapter 4 BATHTUB 4-41
Introductory Screens

Input Topics

Uodel Variables and Options

Output Topics

Program Operation

Context-sensitivehelp screens canalsobe accessed during execution ofother

procedures bypressing the<Fl>function key.

Quit procedure

BATHTUB - VERSION 5.4

Utilities Help w

Selecting Quitfkom the mainmenu ends the currentsession, after checking

whether this is the user’s intention. The current casefileshould besaved

before quitting.

Application Steps

This section describes basic steps involved in applying BATHTUB to a

reservoir. Three application scenarios can be defined, based upon reservoir

status and data availability:

Data Avtib ilitv

Water/Nutrient Pool Water

~ Reservo ir Balance Datz @al ity Data

A Existing Yes Yes

B Existing No Yes

c Existing or Proposed Yes No

Scenario A normally applies to an existing reservoir with nutrient balance data

and pool water quality data. Under Scenario B, nutrient balance (loading)

information is lacking; in this case, the program can be used for diagnostic

purposes (e.g., assessing pool nutrientichlorophyll relationships and regional

ranking). Scenario C is distinguished by lack of pool water quality dat~ which

would otherwise be used for preliminary testing and calibration.

For each scenario, application procedures can be summarized in terms of

the following basic steps:

4-42

S$42 Descrbtion

1 Watershed Data Reduction

2 Reservoir Data Reduction

3 Data Entry and Verification

4 Water Balances

5 Nutrient Turnover

Chapter 4 BATHTUB
6 Diffusive Transport

7 Nutrient Balances

8 Chlorophyll a and Secchi

9 Verification

10 Diagnostics

11 Predictions

These steps are designed to be executed sequentially. Reiteration of previous

steps is common in typical modeling projects. As described below, not all

modeling steps are applicable to each scenario. The procedures are intended to

provide general indications of factors to be considered during the modeling

process. They are not intended as a rigid framework for applying the model.

User judgment must be exercised to account for unique aspects of each application. The Theory section of this chapter describes model formulations,

options, and other background information required to support applications.

Before considering each scenario, a few general aspects of developing model

applications are discussed.

It is important to define purpose and scope prior to undertaking the modeling effort. This includes speci~ing management issues to be evaluated and

types of model output required to support the evaluations. In typical applications, most of the effort and cost is devoted to data collection and data reduction. In situations where modeling is undertaken after the monitoring data have

been acquired, model results may be severely limited by data. This situation

can be avoided by initiating modeling before designing and undertaking additional monitoring. Modeling can be conducted in two phases. The first phase

is based upon historical data and helps to define data gaps that can be filled in

subsequent monitoring. The second phase is based upon more complete data.

Chapter 1 contains guidance for designing monitoring programs to support

model applications.

In defining study scope, the user must decide which components will be

modeled. In the most general case, a model application involves specification

of tributary loads (flows and concentrations) for a conservative tracer, total

phosphorus, ortho phosphorus, total nitrogen, and inorganic nitrogen. Of these,

only total phosphorus is absolutely necessary. Based upon the CE reservoir

data set used in developing the phosphorus sedimentation models, additional

consideration of ortho phosphorus loads reduces the standard error of predicted

reservoir-mean phosphorus concentrations by 16 to 32 percent, depending

upon model formulation. Considering total phosphorus loads only will provide

unbiased predictions of reservoir response, however, if the ratio of tributary

ortho phosphorus load to tributay total phosphorus load is in the range of 15 to

50 percent. Considering nitrogen loads provides additional descriptive information, but may not contribute significantly to predicting the trophic response

of the reservoir, as measured by chlorophyll a because nitrogen may not be

limiting algal growth or because external nitrogen loads maybe supplemented

by fixation of atmospheric nitrogen (see Eutrophication response models).

Modeling a conservative tracer, such as chloride or conductivity, provides a

Chapter 4 BATHTUB 4-43
means for calibrating and testing diffusive transport terms and for testing

overall water balances.

BATHTUB provides a facility for calibrating the empirical models to

account for site-specific conditions (see Calibration fwtors). Calibration

should be attempted only by experienced users working with intensive monitoring data sets. A potential need for site-specific calibration is indicated when

significant differences between observed and predicted concentrations are

found during initial model runs. A conservative approach to calibration is

recommended (adjusting the fewest number of coefficients within reasonable

ranges). Differences between observed and predicted concentrations result

from two basic sources: data errors and model errors. Random data errors

always occur in the specification of model input values (tributary loads,

observed reservoir water quality, flows, morphometry, etc.). Omission of

important nutrient sources in formulating the reservoir nutrient balance is

another type of random error. These are essentially artifacts of study design,

data collection, and data reduction. Model errors reflect true differences

between model predictions and reservoir response. Calibration to account for

model errors may be justified, but calibration to account for data errors is

generally not justified. One possible exception to this rule occurs when data

errors are not random, but are biases attributed to differences in measurement

methods; for example, calibration of the chlorophyll a model may be appropriate to account for differences in measurement technique. BATHTUB error

analyses can help to distinguish between model and data errors. Calibration is

generally not necessary when there is considerable overlap between observed

and predicted distributions (Plot procedures).

Each application should start with construction of a schematic diagram

showing major reservoir regions, inflow streams, point sources, outflow

streams, and monitoring stations. Examples of schematic diagrams are given in

the Documented Session and Instructional Cases sections at the end of this

chapter. The diagram can be overlaid on a reservoir map. Initial definitions of

model segments should be shown; these may be revised based upon subsequent

review and summary of monitoring data. Segments and tributaries should be

labeled and numbered. The diagram provides a useful frame of reference for

subsequent data reduction and modeling steps.

Scenario A - Existing reservoir with loading and pool water quality

data

Step 1 involves reduction of watershed data used in modeling. Formulation

of a drainage area “balance” is an important first step in summarizing watershed characteristics. The FLUX program (Chapter 2) can be used for estimating seasonal and/or annual loadings for gauged tributaries, point sources,

and discharges. An averaging period for calculating tributary inflows must be

selected. This is typically 1 year for reservoirs with relatively long hydraulic

residence times and one growing season (April-September or

Chapter 4 BATHTUB
May-September) for reservoirs with relatively short residence times (see

Nutrient residence time and turnover ratio). Sensitivity to choice of averaging

period can be tested by creating separate input files for different averaging

periods.

Ungauged inflows and stream concentrations can be estimated by drainagearea proportioning using data from other regional watersheds with similar land

uses. Alternatively, ungauged inflows and concentrations can be estimated by

calibrating and applying the nonpoint source model provided with BATHTUB

(TYPE=2 tributaries). Calibration requires specification of typicaJ runoff rates

and concentrations as a fiction of land use (Case/Edit/Non-Point

Procedure).

Step 2 involves reduction of reservoir morphometric and water quality data.

Morphometric inilormation can be estimated from contour maps and/or sediment accumulation surveys. PROFILE (Chapter 3) can be used to summarize

observed water quality conditions by segment and calculate oxygen depletion

rates in stratified reservoirs. Segment boundaries depicted on the schematic

diagram may be revised based upon review of pool monitoring data. Generally,

it is appropriate to aggregate adjacent reservoir areas with similar water quality

into a single segment. Box plots summarizing water quality data by station can

be usefid for this purpose (see PROFILE, Chapter 3). Even if significant

spatial variations in water quality are apparent, division of the reservoir into

multiple segments is not necessary for modeling. Modeling the entire reservoir

with one segment provides predictions of area-weighted mean concentrations,

which may be adequate to support management decisions. In such situations, it

will be particularly important to apply spatial weighting factors when averaging

observed water quality data. Defining multiple segments may be required to

support management decisions. Simulating spatial variations within the reservoir can provide evidence of model applicability and reliability that is not

available in single-segment applications.

In Step 3, an input data file is created by running the Case/Edit procedures

(see Data-Entry Screens). The input file should be listed and checked for dataentry errors and completeness. Default model options should be modified to

reflect the components being modeled (conservative substance, phosphorus,

nitrogen). If ortho phosphorus and/or inorganic nitrogen concentrations for all

stream inflows are not supplied, availability factors should not be used in calculating nutrient balances. This is achieved by setting the ‘Availability Factor’

option to Ousing the Case/Models procedure.

Water balances are checked and adjusted in Step 4 using the List/Balances/

Gross procedure. Measured flows for all major inflow and outflow streams

must be specified in order to check the water balance. It may be appropriate to

adjust certain inflow, outflow, and/or increase-in-storage terms until balances

are established. The appropriate terms to adjust vary from case to case,

depending upon watershed characteristics and flow monitoring networks.

Based upon familiarity with the flow data sources, the user should assess the

Chapter 4 BATHTUB 4-45
most likely source(s) of water balance error and adjust the appropriate value(s)

in the CASE file. Flow-balance errors are often attributed to ungauged surface

or groundwater inflows. If a water balance cannot be established with reasonable adjustments, additional monitoring with refinements to flow gauging

networks may be required.

Nutrient turnover ratios are checked in Step 5 using the List/Balances/

Gross procedure. As discussed above (see Nutrient residence time and turnoverratio), the appropriate averaging period for mass-balance calculations is

determined by the observed turnover ratio of the limiting nutrient (usually

phosphorus). A seasonal averaging period (April/May through September) is

usually appropriate if it results in a turnover ratio exceeding 2.0. An annual

averaging period may be used otherwise. The turnover ratio criterion is an

approximate guideline, which may be adjusted from case to case. Other considerations (such as comparisons of observed and predicted nutrient levels) can

also be used as a basis for selecting an appropriate averaging period, particularly if the turnover ratio is near 2.0. Note that if the reservoir is vertically

stratified and significant hypolimnetic accumulations of phosphorus occur,

seasonal phosphorus turnover ratios calculated from mixed-layer concentrations will be overestimated. In this situation, mixed-layer nutrient levels during

the growing season may reflect nutrient transport from the bottom waters via

diflision or mixing processes, as compared with nutrient inputs from external

sources. Both annual and seasonal balances should be tested in this situation.

Depending upon results of Step 5, it maybe necessary to repeat the calculation

of tributary loadings (Step 1) using a different averaging period.

Step 6 involves checking and possible calibration of diffusive transport

terms using the List/Hydrau procedure. If numeric dispersion exceeds the

estimated dispersion in a given segment, the user should consider revising the

segmentation scheme (e.g., increasing segment numbers and thus decreasing

segment lengths) until this criterion is satisfied. In some cases, this may be

difficult to achieve with a reasonable number of segments, particularly in

upper-pool segments, where advective velocities tend to be greater. The criterion may be waived if the sensitivity of predicted nutrient profiles to alternativesegmentation schemes is shown to be minimal.

Conservative tracer data (typically chloride or conductivity), maybe used to

calibrate diffusive transport terms in problems involving more than one segment. An overall tracer mass balance should be established (List/Balances)

prior to calibrating transport terms. Calibration involves adjusting the global

calibration factor for dispersion (Case/Edit/Mcoefs) and/or segment calibration factors (Case/Edit/Segments) to match observed tracer profiles. Generally, predicted concentration gradients will decrease with increasing

dispersion rates. The Run/Model/Sensitivity procedure shows the sensitivity

of predicted tracer concentrations to fourfold variations in dispersion rates.

Where possible, adjustments should be made only to the global calibration

factor (keeping segment calibration factors at their default setting of 1.0); this is

a more conservative calibration approach than adjusting values for each

4-46 Chapter 4 BATHTUB
segment individually. For Dispersion Model 1, the global calibration factor

should be in the range of 0.25 to 4.0, the approximate 95-percent confidence

limit for dispersion estimated fi-om Fischer’s equation. If adjustment outside

this range is required, other dispersion models and/or alternative segmentation

schemes should be investigated.

If there is a long wind fetch and segments are aligned along predominant

wind directions, upward adjustment of the dispersion factors may be necessary.

Conversely, downward adjustment may be necess~ in reservoirs or reservoir

areas that are sheltered from winds. The segment calibration fmtor for dispersion can be adjusted downward to reflect local restrictions caused by weirs,

bridges, etc. Calibration of dispersion rates based upon tracer data is feasible

only if significant tracer gradients are detected in the reservoir as a result of the

tracer loading distributions.

Step 7 involves selecting, testing, and possibly calibrating nutrient sedimentation models using List and/or Plot procedures. Calibrating dispersion rates

to match observed nutrient gradients is also feasible, provided that tracer data

are not available in Step 6. As discussed above, differences between

observed and predicted nutrient profiles may reflect random errors in the data,

as well as true differences between the model predictions and reservoir

responses. As discussed above, a conservative approach to calibration is

recommended.

The List/Compar procedure provides statistical comparisons of observed

and predicted concentrations. These are computed using three alternative measures of error: observed error only, T(1); error iypical of model development

data set, T(2); and observed and predicted error, T(3). Tests of model applicability are normally based upon T(2) and T(3). If their absolute values exceed

2 for the comparison of area-weighted mean concentrations, there is less than a

5-percent chance that nutrient sedimentation dynamics in the reservoir are

typical of those in the model development data set, assuming that input conditions have been specified in an unbiased manner. The applicability of the

models would be questionable in this case. If the discrepancy cannot be attributed to possible errors in the input data file (particularly, inflow concentrations), other options for modeling nutrient sedimentation should be

investigated.

Lack of fit may also result from unsteady-state loading conditions, particularly if the nutrient turnover ratio is less than 2 based upon annual loadings. In

such cases, averaging periods longer than a year may be required to establish a

valid loadhesponse relationship. This situation is more likely to occur for

nitrogen than phosphorus because unit sedimentation rates tend to be lower for

nitrogen.

Once an appropriate sedimentation model is selected, T(1) can be used as a

basis for deciding whether calibration is appropriate. If the absolute value of

T(1) exceeds 2, then there is less than a 5-percent chance that the observed and

Chapter 4 BATHTUB 4-47
predicted means are equal, given the error in the observed mean. In this situation, it maybe desirable to calibrate the model so that observed and predicted

nutrient concentrations match.

As outlined in Table 4.2, two calibration methods are provided for phosphorus and nitrogen: Method O- calibrate decay rates and Method 1- calibrate

concentrations. In the first case, the segment-specific calibration factors are

applied to estimated sedimentation rates in computing nutrient balances. In the

second case, the factors are applied to estimated concentrations. In Method O

(default), it is assumed that the error is attributed primarily to the sedimentation

model. In Method 1, the error source is unspecified (some combination of

input error, dispersion error, and sedimentation model error). The latter may be

used when predicted nutrient profiles are insensitive to errors in predicted sedimentation rate because the mass balance is dominated by inflow and outflow

terms (low hydraulic residence times, see Figures 1.3 and 1.4). Regardless of

the selected calibration option, global calibration factors for phosphorus and

nitrogen (specified on the Case/Edit/Mcoef screen) are always applied to the

nutrient sedimentation rates.

Nutrient Sedimentation Models 1 and 2 have been empirically calibrated

and tested for predicting reservoir-mean conditions. Error analysis calculations

indicate that sedimentation rates predicted by these models are generally

accurate to within a factor of 2 for phosphorus and a factor of 3 for nitrogen

(Walker 1985). To account for this error, nutrient calibration factors (Case/

Edit/Mcoefs screen) can be adjusted within the nominal ranges of 0.5 to 2.0

and 0.33 to 3 for phosphorus and nitrogen, respectively.

IrIsome cases, nutrient retention coefficients for phosphorus or nitrogen

may be negative. Even after setting the nutrient calibration coefficient to zero

(essentially treating the nutrient as a conservative substance), the model will

underpredict the observed nutrient concentration in the reservoir. This may

reflect net nutrient releases from bottom sediments (phosphorus or nitrogen) or

fixation of atmospheric nitrogen by bluegreen algae. These “internal sources”

can be represented in the model using tributaries with TYPE CODE=5.

Apparent negative retention coefficients may reflect use of an improper averaging period or underestimation of significant external loads. Independent evidence and estimates of sediment nutrient sources should be obtained before

speci&ing internal sources in the model. As discussed in the Theory section of

this chapter, reservoirs with negative nutrient retention coefficients were rarely

encountered in the supporting research (Walker 1985). If internal sources are

specified, estimates of model error derived from the supporting research are

invalid. While it is usually possible to “tune” the model predictions using the

internal source terms, this does not provide a way of predicting how the internal

sources will change in response to changes in external loads or other management strategies evaluated in Step 11.

Once nutrient balances have been established, eutrophication responses (as

measured by chlorophyll a, transparency, and hypolimnetic oxygen depletion

Chapter 4 BATHTUB
rate) are developed in Step 8. This involves model selection, testing, and possible calibration. As outlined in Tables 4.2 and 4.3, several options are available

for predicting chlorophyll a concentrations and Secchi depths as a function of

nutrient levels and other controlling factors. If nitrogen balances are considered

in addition to phosphorus, chlorophyll a Models 1 or 3 can be used; otherwise,

chlorophyll a Model 2 (default) is the most general for application to reservoirs. Secchi Model 1 (default) requires an estimate of nonalgal turbidity for

each model segment (see Theory). The interpretation and use oft-statistics

(List/Compar procedure) in testing and calibrating the chlorophyll a and

Secchi submodels follow the above discussion for nutrients (Step 7).

With the completion of Step 8, the model has been setup and possibly calibrated using pool and tributary data from a particular year or growing season.

Step 9 involves testing of the model based upon an independent data set

derived from a different monitoring period. Model options and calibration

factors are held constant, and performance isjudged based upon a comparison

of observed and predicted nutrient, chlorophyll a, and transparency profiles.

This procedure is especially recommended in systems with significant year-toyear variations in hydrology, loading, and pool water quality conditions or in

cases where extensive calibration is necessary. Generally, multiyear reservoir

studies are necessary in order to obtain adequate perspectives on water quality

variations driven by variations in climate or flow. A separate model input file

can be created for each study year; each file uses the same segmentation

scheme, model options, and calibration coefficients. Successful simulation of

year-to-year variations is important evidence of model validity. Reiteration of

previous modeling steps may be required to improve model performance over

the range of monitored conditions.

Step 10 involves application of the model for diagnostic purposes using the

List/Diag procedure. Observed and predicted variables are listed and ranked

against the model development data set. Diagnostic variables (Table 4.5)

reflect the relative importance of phosphorus, nitrogen, and light as factors

controlling algal productivity. Results are reviewed to ensure that controlling

factors are consistent with the chlorophyll a and transparency submodels

employed.

The model is applied to predict the impacts of alternative loading scenarios

or management strategies in Step 11. Typically, a separate input file is created

for each management strategy and hydrologic condition (e.g., wet year, average

year, dry year). Effects of management strategies under different hydrologic

conditions can be evaluated by comparing model predictions. Model output

from multiple runs can be routed to disk files and subsequently read into a

spreadsheet for tabulation, comparison, and display. In simple cases, multiple

loading scenarios can be specified within a single file (see Scheme 4 in Figure 4.3 or Instructional Cases at the end of this chapter).

Sensitivity to critical assumptions made in the modeling process can be

evaluated by repeating Steps 1-11 using alternative assumptions and comparing

Chapter 4 BATHTUB 4-49
results. Iftie~plication hwkvolved substitid calibration hSteps 6-8,

management scenarios should also be evaluated using model runs with the

uncalibrated model (all calibration coefficients set to 1.0). In many cases, the

relative impacts of alternative management strategies (expressed as percentage

differences in predicted mean chlorophyll a, for example) will be insensitive to

whether they are based upon the calibrated or the uncalibrated model.

Error analyses can be run to quanti~ uncertainty in each predicted response

variable for each scenario and hydrologic condition. Uncertainty is expressed

in terms of the mean coefficient of variation (CV). The error analysis will

overpredict this uncertainty in cases where the model has been calibrated and

tested based upon site-specific conditions. In all cases, the uncertainty associated with relative predictions (e.g., expressed as percent change in chlorophyll

a resulting from different management strategies) will be substantially lower

than that associated with absolute predictions (expressed in ppb).

In applying the model to predict future conditions, diagnostic variables are

checked to ensure that controlling factors are consistent with the chlorophyll a

and transparency submodels. For example, if a phosphorus-limited chlorophyll

a submodel (e.g., 4 or 5 in Table 4.2) is applied to existing conditions in Step

8, model predictions will be invalid for a future loading condition, which causes

a switch from phosphorus- to nitrogen-limited conditions. Similarly, if the

phosphorus sedimentation model does not account for inflow phosphorus

availability, predictions of future conditions involving a significant change in

the Ortho-P/Total P load ratio maybe invalid.

Scenario B - Existing reservoir with pool water quality data only

BATHTUB can be used to summarize and rank water quality conditions and

to evaluate controlling factors in segments representing different reservoirs or

different areas within one reservoir. Comparisons are based upon observed

water quality conditions and morphometric features specified for each segment.

Various nutrient/chlorophyll a and other eutrophication response models can be

tested. This type of analysis can be applied in the absence of nutrient loading

and water balance information. It is essentially descriptive or diagnostic in

nature and does not provide a predictive basis. Because water-balance and

nutrient-balance calculations are not involved, Steps 4-7 and 11 are not

petiormed.

Scenario C - Reservoir with loading data only

4-50

BATHTUB can be used to predict water quality conditions in a future reservoir or in an existing reservoir lacking observed water quality data. Lack of

observed water quality data precludes calibration and testing of diffusive

transport, nutrient sedimentation, and eutrophication-response models. If the

application is to an existing reservoir, a monitoring program should be

Chapter 4 BATHTUB
implemented to obtain data for calibration and testing before using the model to

evaluate management strategies. If the application is to a proposed reservoir,

the accuracy and credibility of model projections would be enhanced by first

applying it successfidly to an existing reservoir in the same region and, if possible, with similar morphometry and watershed characteristics.

Model predictions for a fiture reservoir refer to steady-state conditions and

do not apply to the initial “reservoir aging” period, during which significant

“internal” loadings may occur as a result of nutrient releases from inundated

soils and vegetation. The reservoir aging period is inherently dynamic and not

suited for direct simulation via the steady-state algorithms used in BATHTUB.

Approximate estimates of conditions during the reservoir aging period maybe

derived by speci@ing additional internal nutrient sources of appropriate magnitudes to reflect sediment releases during this period, based upon literature

reviews and/or field data.

Procedure Outline

Following is a list of all BATHTUB procedures. Names are listed on the

left. Indentation reflects Menu level (Lines 1-4). A brief description of each

procedure is given on the right.

Case

Edit

Dimensions

Globals

Segments

Tribs

NonPoint

First

Second

MCoefs

Channe 1s

All

Modets

Read

Data

T rans

Save

New

Change

ate

Segments

Delete

Insert

copy

Tribs

Delete

Insert

copy

List

Define Case - Read, Enter, Edit, or List Input Values

Edit Case Data

Edit Case Dimensions, File Name, Title, User Notes

Edit Global Parameters, Precip., Evap., Atmospheric Loads . . .

Edit Segments, Calib. Factors, Morphometry, Ohs. Water Qual.

Edit Tributary & Watershed Data - Areas, Flows, Cones . . .

Edit Nonpoint Landuse Categories & Exgurt Coefficients

Edit Coefficients for Landuse Categories 1-4

Edit Coefficients for Landuse Categories 5-8

Edit Default Model Coefficients & Error Terms

Edit Transport Channels

Edit Al 1 Input Data Groups

Set Model Opt ions

Read Case Data File

Read Input File (Filename = *.BIN, BATHTUB Version

Read Old Input File Format (Filename = *.BTH, Vers

Save Case Input Data File

Reset Input Values & Start New Case

Delete, Insert, or Copy Segments or Tributaries

Delete, Insert, or Copy Segments

Delete a Segment from the Existing Network

Insert a New Segment into the Network

Copy Data from One Segment to Other Segment(s)

Delete, Insert, or Copy Tributaries/Watersheds

Detete a Tributary from the Existing Network

Insert a New Tributary into the Network

Copy Data from One Tributary to Other Tributaries

List Input Values for Current Case

>= 5.0)

on <= 4.4

Chapter4 BATHTUB 4-51
Morpho List Segment Morphometry

Run Check Case Data & Run Uodel

Mode 1

NoError

Inputs

Model

All

Run Model

Run Model Uithout Error Analysis

Error Analysis - Case Input Variables Only

Error Analysis - Model Error Terms & Segment Calib Factors

Error Analysis - All Input Variables and Model Parameters

Sensitivity

Conserv

Total P

Total N

Run Sensitivity Analysis - Dispersion & Decay Factors

Run Sensitivity Analysis for Conservative Substance Balance

Run Sensitivity Analysis for Total Phosphorus Balance

Run Sensitivity Analysis for Total Nitrogen Balance

List List Model Output

Hydraul List Morphometry / Hydraulics/ Dispersion Table

Ba 1antes

Gross

By Segment

Wmnary

List Select Uater and Mass Balances

Gross Uater and Mass Balances - All Segments

Uater and Mass Balances by Segment - Detailed

Uater and Mass Balances by Segment - !Wmnary

Compar

All

Means

Conpare Observed & Predicted Values

All Segments + Area-Ueighted Mean

Area-Ueighted Means Only

D i agnos

All

Means

List Observed & Predicted Diagnostic Variables

All Segments + Area-Ueighted Mean

Area-Ueighted Means Only

Profiles

Predicted

Observed

Ratios

List Sumnaries of Predicted & Observed Values

List Predicted Values

List Observed Values

List Observed / Predicted Ratios

Flounet List Flow Network Sumnary

Table List Table of Predicted Values for Selected Variables

Short Short Table of Predicted Values by Segment

Plot Plot Observed & Predicted Variables

Nutrients Plot Total Phosphorus & Total Nitrogen Only

All Plot All Variables

some Plot Selected Variable(s)

Define

lDefault

2L i near

3Log

Define Plot Scale Types (Default, Linear, or Logarithmic)

Use Default Scale Type for Each Variable

Use Linear Scales for All Variables

Use Logarithmic Scales for All Variables

Utilities Program Utilities

output Set Output Destination - Screen or File

Screen Direct Output to Screen (Default)

File Direct Output to Disk File

Restrict Restrict Output & Plots to Specific Segment(s)

Vieu View any DOS Text File

Error View Error Message File

4-52 Chapter4 BATHTUB
Help

Quit

Data-Entry

View Supplementary Help Screens

End Current Session

Screens

Following is a listing of each data-entry screen in BATHTUB and its associated HELP file. These areaccessed viathe Case/Edit procedures. The help

screens areaccessed byhitting<Fl>. Additional help screens containing more

detailed information on specific fields maybe obtained by moving the cursor to

the field and hitting <F8>; this works only when the message ‘<F8>=HELP

FIELD’ appears in the lower right comer of the screen.

DATA-ENTRY SCREEN: Case/Edit/Dimensions

.

CASE DIMENSIONS

CASE TITLE:

DATA FILE NAME :

NUMBER OF UCM)EL SEGMENTS _ <=39

NUMBER OF TRIBUTARIES <=99

NOTES:

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

HELP SCREEN:

Case Edit Dimensions

Define problem TITLE for labeling output

Define DATA FILE NAME for storing input values. DOS PATH can also

be included. Examples:

KEYSTONE .BIN < ---- places file in same directory as program

C:\MYDIR\KEYSTONE .BIN

D:\WRK\SUB\KEYSTONE .BIN

Extension ‘.BIN’ should be used to indicate binary output format.

NUMBER OF SEGMENTS (Maxi- = 39)

NUMBER OF TRIBUTARIES (Maximtnn = 99)

includes inflow streams, outflow streams, & non-point watersheds

NOTES are for user reference

Chapter4 BATHTUB 4-53
DATA-ENTRY SCREEN: Case/Edit/GlobaIs

GLOBAL VARIABLES & ATMOSPHERE C LOADS

MEAN Cv

AVERAGING PERICXI (YRS)

PRECIPITATION (M)

EVAPORATION

STORAGE INCREASE $;

ATMOS. LOADS (KG/KM2-YR)

VARIABLE MEAN Cv AVAILABILITY-FACTOR

TOTAL PHOSPHORUS [0.331

ORTHO PHOSPHORUS [1 .331

TOTAL NITROGEN — [0=591

INORG. NITROGEN [0. 791

CONSERV. SUBST.

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

HELP SCREEN:

Case Edit Globals

Values entered in this screen apply to all segments in network

during the period of mass-balarke calculations.

Averaging Period =

(1 = annual, .;

Storage Increase =

duration of mass-balance calculations

period used in specifying tributary inf

= April-September, .42 = May-September)

increase in pool elevation between start

Ows

and end of Averaging Period-.

Default values for Availability Factors are shown in [brackets].

DATA-ENTRY SCREEN: Case/Edit/Segments

SEGMENT : NAME : OUTFLOU SEG: GROUP :

AREA (KM2~ MEAN DEPTH (M): LENGT~KM): —

VARIABLE UNITS MEAN Cv CALIBRATION

MIXED LAYER DEPTH (M) FACTORS

HYPOLIMNETIC DEPTH (M)

DISPERSION FACTOR -

OBSERVED HATER QUALITY...

NON-ALGAL TURBIDITY (1/M)

TOTAL PHOSPHORUS (PPB)

TOTAL NITROGEN (PPB)

CHLOROPHYLL-A (PPB)

SECCHI DEPTH (M)

ORGANIC NITROGEN (PPB)

TOTAL P - ORTHO P (PPB )

HYPOL. 02 DEPL. (PPB/DAY)

METAL. 02 DEPL. (PPB/DAY)

CONSERVATIVE SUBST. -

—

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

4-54 Chapter4 BATHTUB
HELP SCREEN:

Case Edit Segments

Edit all input data & observed water quality for a specific segment.

Use cursor or space bar to select segment to be edited; press <return>

to select segment, <esc> to quit.

If mixed layer depth =0., it Hill be estimated from mean depth.

Calibration factors normally = 1.0.

Observed water quality data should reflect growing season.

They are optional. ‘O’ indicates missing.

Estimates of non-algal turbidity are required if Chlorophyll-a Model

1 or 2 is used. If turbidity is set to 0.0, it is estimated from

observed Chl-a and Secchi if both are specified.

DATA-ENTRY SCREEN: Case/Edit/Tribs(TYPESl-4,6)

TRIBUTARY NUMBER:_ LABEL :

SEGMENT NUMBER: TYPE CODE:

MEAN Cv

DRAINAGE AREA (KM2)

FLOU (HM3/YR)

TOTAL PHOSPHORUS (PPB )

ORTHO PHOSPHORUS ( PPB )

TOTAL NITROGEN (PPB )

INORGANIC NITROGEN (PPB)

CONSERVATIVE SUBST. -

NON-POINT-SOURCE UATERSHED AREAS

CATEGORY :

AREA (KM2)

CATEGORY :

AREA (KM2)

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

Chapter4 BATHTUB 4-55
HELP SCREEN:

Case Edit Tributary

Edit tributary names, types, flows, drainage areas, & concentrations.

IJse cursor or space bar to select trib. to be edited;

press <return> to select tributary, <esc> to quit.

Tributary TYPE CCX.)ES:

1 = Gauged Tributary (flow, cones input)

2 = Ungauged Tributary (flows, cones estimated from land use)

3 = Point Source Discharging Directly to Reservoir

4 = Outflow or Withdrawal

5 = Internal Source (input areal loads in mg/m2-day)

6 = Diffusive Source

If TYPE=2, flow & concentrations will be estimated using the non-point

source model, otherwise, values entered in this screen will be used.

Non-Point Source Uatershed Areas:

-> only used in calculations if TYPE CODE=2

-> swn of subwatershed areas should equal total drainage area

-> landuse category definitions & export coefficients specified

in separate screen (lCase Edit Nonpointl)

DATA-ENTRY SCREEN: Case/Edit/Tribs (TYPE = 5)

TRIBUTARY NUMBER: LABEL :

SEGMENT NUMBER: TYPE C~E: =5

INTERNAL LOADING RATES (MG/M2-DAY)

MEAN Cv

TOTAL PHOSPHORUS

ORTHO PHOSPHORUS

TOTAL NITROGEN

INORGANIC NITROGEN

CONSERVATIVE SUBST.

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

HELP SCREEN:

Internal Load Rates

Use tributary type code = 5 to specify internal loads for each

constituent to any segment in units of mg/m2-day.

This can be used to represent nutrient recycling from bottom

sediments, if independent estimates or measurements are

available.

To use this feature, change the tributary type code to 5 and

press <F2>. The normal tributary input screen (used for

type codes 1-4) will switch to one with entry locations for

internal load rates and cvs for each constituent.

4-56 Chapter4 BATHTUB
DATA-ENTRY SCREEN: Case/Edit/Nonpoint

NON-POINT-SCNJRCE EXPORT COEFFICIENTS

LANDUSE CAT: 1 2 3 4

LABEL

MEAN CV MEAN CV MEAN CV MEAN CV

RUNOFF M/YR —— —. —. ——

TOTAL P PPB —— —. —. —.

ORTHO P PPB —— —. —— —.

TOTAL N PPB —. —. —— ——

INORG N PPB —— —— —. ——

CONS s --- —— —— —. ——

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

HELP SCREEN:

:ase Edit NonPoint

Edit Non-Point Source Export Coefficients

rhese values are used to estimate flou & concentration for TYPE=2

tributaries, according to the following model:

FLOU (hm3/yr) = SUM [ AREA (km2) x RUNOFF (m/yr) 1

LOAD (kg/yr) = SUM [ AREA (km2) x RUNOFF (m/yr) x CONC (ppb) 1

SUM = sun over land use categories

rhis screen is used to enter RUNOFF & CONC values for each landuse

:ategory.

rhis screen can be ignored if all inflows are measured directly.

DATA-ENTRY SCREEN: Case/Edit/Mcoefs

~EL CALIBRATION FACTORS

CURRENT-CASE

MEAN Cv

DISPERSION RATE

P DECAY RATE

N DECAY RATE

CHL-A MODEL

SECCHI MIEL

ORGANIC N U(X)EL

TP-OP MODEL

HCK)V WEL

MODV MODEL

SEC./CHLA SLOPE (M2/MG)

MINI14LJH 0S (M/YR)

CHL-A FLUSHING TERM

CHLOROPHYLL-A CV

DEFAULTMEAN

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

.025

4.0

1.0

.62

VALUES

Cv

.70

.45

.55

.26

.10

.12

.15

.15

.22

.0

.0

.0

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

Chapter4 BATHTUB 4-57
HELP SCREEN:

Case Edit MCoefs

Edit Model Coefficients & Error Terms.

Calibration factors apply to all segments.

For example, changing the mean value for coefficient 1 (P DECAY RATE)

from 1.0 (default value) to 0.5 will reduce the phosphorus sedimentation

rate in all segments by 50%, regardless of which option is selected for

predicting phosphorus sedimentation.

Default values are listed on right.

MINIMUM QS = lowest overflow rate used in computing sedimentation coef.s

FLUSHING EFFECT = 1 include flushing term in Chl-a Models 1 & 2,

= O exclude flushing term

CHL-A CV = Chl-a-a temporal coefficient of variation used in

conputing algal nuisance frequencies (typical value = .62)

DATA-ENTRY-SCREEN: Case/Edit/Channels

DEFINE CHANNELS - TRANSPORT BETUEEN SEGMENTS

SEGMENTS ADVECTIVE-FLOU DIFFUSIVE-EXCHANGE

LABEL FROM TO HM3/YR Cv HM3/YR Cv

.—

——

——

——

F1=HELP, F2=DoNE/sAvE, F3=EDIT FIELD, F7=HELP/EDITOR, <ESC>=ABORT

HELP SCREEN:

Case Edit Channels

Defines Transport Channels (optional).

Specification of “Normal Outflow Segments’ defines a typical application

consisting of a one-dimensional, branched network.

“Channels” can be used to specify additional advective flow and

diffusive transport between any pair of segments.

Solutions of the water-balance and mass-balance equations are modified

to account for these additional transport terms.

Flow values must be estimated independently.

Up to 10 channels can be defined for any case.

4-58 Chapter4 BATHTUB
Documented Session

This section describes examples of each output format using data from

Keystone Reservoir (located on the Arkansas and Cimarron rivers in

Oklahoma). Data from this reservoir are analyzed extensively in the supporting

research document (Walker 1985). Model segmentation for Keystone is

illustrated in Figure 4.9.

CIMARRO&V

R}VER

ARKANSAS

RIVER

J+?’( POINT SOURCE

~ DISCHARGE

POINT SOURCE

a. Morphologic features

ARKANSAS

RIVER

\

POINT SOURCE

\

CWARRON -

RIVER DISCHARGE

POINT SOURCE

b. Segmentation scheme

Figure 4.9. Model segmentation for Lake Keystone, Oklahoma, application

Chapter 4 BATHTUB 4-59
Pool and tributary water quality data were derived from measurements

made in 1974 and 1975 by the EPA National Eutrophication Survey (NES)

(U.S.’Environmental Protection Agency) (USEPA 1975). The Keystone pool

was sampled by the NES at nine stations four times between April and October

1975. The role of light limitation in Keystone has been previously discussed

(Walker 1985). Because of the relatively low summer hydraulic residence time

of the reservoir (0.08 year), seasonal nutrient turnover ratios are high, and

water and mass balance calculations are based on May through September

conditions during the pool monitoring year. Point sources include three sets of

municipal sewage effluents which have been aggregated by reservoir segment.

Since the NES estimated nutrient loadings but not flows for these ellluents, a

flow of 1 hm3/year has been assumed for each source (insignificant in relation

to reservoir water balance) and the nutrient concentrations have been adjusted

to correspond with the reported loadings.

The input data file ‘KEYSTONE.BIN’ file (found on the distribution diskette and copied to the hard drive during installation) is used to generate the

output listings. The following procedures are executed:

Case/Read/Data

Case/List

CaselMorpho

Run/Model/All

List/Hydraulics

List/Balances/Gross

List/Balances/By Segment

List/Balances/Summary

Lkt/Compar/All

List/Diagnos/All

List/Prot’iles/Predicted

LktiTable

List/Flownet

Run/Sensitivity/Total P

Plot/Some

Quit

Installing the program and running these procedures in sequence, while referring to comments and instructions below, will help users to become familiar

with program operation and output formats.

4-60

Start the program from the DOS prompt by entering:

Chapter 4 BATHTUB
>BATHTUB

BATHTUB

EM~IRICAL MODELING OF

RESERVOIR EUTROPHICATION

VERSION 5.4

Envirorunental Laboratory

USAE Uaterways Experiment Station

Vicksburg, Mississippi

December 1998

PRESS KEY TO CONTINUE, <ESC> RETURN TO MENU 100

Aseries ofintroductoryscrcens appear. Pressing ESC herebypasscsthe

introductory screens andproccdsto the mainprogram menu:

II Define Case - Read, Enter, Edit, or List Input Values

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <Fl ,F7> HELP

CASE = Default Input File

SEGMENTS = 1

MODEL OPTION ----->

CONSERVATIVE SUBSTANCE

PHOSPHORUS BALANCE

NITROGEN BALANCE

CHLOROPHYLL A

SECCHI DEPTH

DISPERSION

PHOSPHORUS CALIBRATION

NITROGEN CALIBRATION

DATA FILE =

TRIBUTARIES = 1

SELECTION . . . . . >

0 NOT COMPUTED

1 2ND ORDER, AVAIL P

O 2ND ORDER, AVAIL N

1 P, N, LIGHT, T

1 VS. CHLA& TURBIDITY

1 FISCHER-NUMERIC

1 DECAY RATES

1 DECAY RATES

Select CasdReadLData to reada BATHTUBd’ata set (selected choices are

underlined below butare highlighted on the screen). Choices aremade inone

oftwo ways: (a) bypressing thefirst letter of the desired command, orfi)by

using the cursor keys. Aone-line description of the selectedprocedureis

highlightedatthe bottom ofthe upper menu box.

BATHTUB - VERSION 5.4

Qxx Run List Plot Utilities Help Quit

Edit Models Save New Change List Morpho

Translat

Read Input File (Filename = *.BIN, BATHTUB Versions >=5.0

II MOVE CURSOR & HIT <Enter> OR <First Letter> TO RUN ROUTINE, <FI,F7> HELP

Chapter4 BATHTUB 4-61
The next screen asks the user to speclfi the DOSpath to the directory where

BATHTUB data sets are stored. If ahta sets are kept in the same directory as

the BATHTUB program (as is recommended and assumed here), press

<Enter>.

ENTER FILE PATH or PRESS <Esc> TO ENTER FILENAME DIRECTLY

ENTER FILE PATH: *. BIN

Press CEnter>.

Alisting ofinputjiles inthespec@edpath isgiven. Files areidentjjied bythe

.BIN extension.

POINT TO DESIRED FILE & PRESS <Enter> PATH = *.BIN

----------SELECT FILE ----------

BEAVER.BIN

CASE1.BIN

CASE2.BIN

CASE3.BIN

CASE4.BIN

CASE5.BIN

KEYSTONE.BIN

Move the cursor to the desiredinputjile andhit” Enter .

1

CLEARING CURRENT CASE, OK ?

Respondwitha Y (yes) to clearthecurrent datasetandload thespecljied~le.

Controlreturn stothemainmenu.

—BATHTUB - VERSION 5.4

~ Run List Plot Utilities Help Quit

Models Read Save New Change List Morpho

Define Case - Read, Enter, Edit, or List Input Values

CASE = Keystone Reservoir, Oklahoma DATA FILE = KEYSTONE.BIN

SEGMENTS = 7 TRIBUTARIES = 13 CHANNELS = O

MCDEL OPTION . . . . . > SELECTION . . . . . >

CONSERVATIVE SUBSTANCE

PHOSPHORUS BALANCE

NITROGEN BALANCE

CHLOROPHYLL-A

SECCHI DEPTH

DISPERSION

PHOSPHORUS CALIBRATION

NITROGEN CALIBRATION

AVAILABILITY FACTORS

MASS-BALANCE TABLES

O NOT CCM4PUTED

1

1

1

1

1

1

1

1

1

2ND ORDER, AVAIL P

2ND ORDER, AVAIL N

P, N, LIGHT, T

VS. CHLA & TURBIDITY

FISCHER-NUMERIC

DECAY RATES

DECAY RATES

USE FOR MODEL 1 ONLY

USE ESTIMATED CONCENTRATIONS

4-62 Chapter4 BATHTUB
l%e lower halfof the screen summarizes the dimensions and selected model

options for the current case. Input values can be listed by selecting Gx.wY

List:

II List Input Values for the Current Case

Keystone Reservoir, Oklahoma

MODEL OPTIONS:

1 CONSERVATIVE SUBSTANCE

2 PHOSPHORUS BALANCE

3 NITROGEN BALANCE

4 CHLOROPHYLL-A

5 SECCHI DEPTH

6 DISPERSION

7 PHOSPHORUS CALIBRATION

8 NITROGEN CALIBRATION

9 ERROR ANALYSIS

10 AVAILABILITY FACTORS

11 MASS-BALANCE TABLES

o

1

1

1

1

1

1

1

1

1

1

NOT CCMPUTED

2ND ORDER, AVAIL P

2ND ORDER, AVAIL N

P, N, LIGHT, T

VS. CHLA & TURBIDITY

FISCHER-NUMERIC

DECAY RATES

DECAY RATES

MODEL & DATA

USE FOR MODEL 1 ONLY

USE ESTIMATED CONCS

ATMOSPHERIC LOADS & AVAILABILITY FACTORS:

ATMOSPHERIC-LOADS AVAILABILITY

VARIABLE KG/Kn2-YR FACTOR

1 CONSERV .00 .: .00

2 TOTAL P 30.00 .50 .33

3 TOTAL N 1000.00 .50 .59

4 ORTHO P 15.00 .50 1.93

5 INORG N 500.00 .50 .79

GLOBAL INPUT VALUES:

PARAMETER MEAN

PERIOD LENGTH YRS .420 .0::

PRECIPITATION M .530 .200

EVAPORATION M .900 .300

INCREASE IN STORAGE M .000 .000

TRIBUTARY DRAINAGE AREAS AND FLOW:

ID TYPE SEG NAME DRAINAGE AREA

KM2

14 7ARKANsAs OUTFLOU 162804.000

1 1 ARKANSAS INFLOU 123625.000

:1 1 HELLROARING 27.700

41 4 CIMARRON 34929.000

4 LAGOON 123.000

:: 1 UNGAUGED-SEG 1 600.000

71 2 UNGAUGED-SEG 2 400.000

81 4 UNGAUGED-SEG 4 2440.000

91 5 UNGAUGED-SEG 5 150.000

1 6 UNGAUGED-SEG 6 400.000

;: 3 1 CLEVELAND STPS .000

12 3 4 CIUARRON STPS .000

13 3 6 MANNFORD STP .000

TRIBUTARY CONCENTRATIONS (PPB): MEAN/CV

ID CONSERV TOTAL P TOTAL N

1 .0/ .00 109.0/ .04 1464.0/ .10

.0/ .00 570.0/ .20 2467.0/ .15

: .0/ .00 72.0/ .22 1639.0/ .06

4 .0/ .00 3U.01 .11 1884.0/ .09

5 .0/ .00 150.0/ .19 1940.0/ .06

6 .0/ .00 72.0/ .30 1639.0/ .30

7 .0/ .00 72.0/ .30 1639.0/ .30

8 .0/ .00 150.0/ .30 1940.0/ .30

9 .0/ .00 150.0/ .30 1940.0/ .30

MEAN FLOU

HM3/YR

10556.000

6770.000

10.000

2572.000

37.000

216.000

143.000

736.000

45.000

120.000

1.000

1.000

1.000

ORTHO P

86.0/ .10

158.0/ .09

12.0/ .09

133.0/ .07

22.0/ .16

12.0/ .30

12.0/ .30

22.0/ .30

22.0/ .30

CV OF MEAN FLOU

.100

.100

.100

.100

.100

.200

.200

.200

.200

.200

.200

.200

.200

INORG N

771.0/ .33

500.0/ .30

268.0/ .06

285.0/ .17

431.0/ .13

268.0/ .30

268.0/ .30

431.0/ .30

431.0/ .30

Chapter4 BATHTUB 4-63
10 .0/ .00 150.0/ .30 1940.0/ .30 22.0/ .30 431.0/ .30

11 .0/ .00 4535.0/ .00 13605.0/ .00 4535.0/ .00 13605.0/ .00

12 .0/ .00 14261.0/ .0038456.0/ .00 14261.0/ .0038456.0/ .00

13 .0/ .00 1135.0/ .00 3400.0/ .00 1135.0/ .00 3400.0/ .00

MCX)EL SEGMENTS & CALIBRATION FACTORS:

----------- CALIBRATION FACTORS . . . . . . -----

SEG WTFLOU GR~P SEGMENT NAME P SED N SED CHL-A SECCHI HOD DISP

1 2 1 ARKANSAS UPPER

Cv :

2 3 1 ARKANSAS MID .

3 7 1 ARKANSAS LOUEiv4 5 1 CIUARRON UPPE:V:

Cv :

5 6 1 CIMARRON MID

6 7 1 CIMARRON LOUE;V:

Cv :

7 0 1 DAM AREA

Cv :

SEGMENT MORPHOMETRY: MEAN/CV

LENGTH AREA

ID LABEL KM KM2

1 ARKANSAS UPPER 15.00 8.4000

2 ARKANSAS MID 15.00 25.2000

3 ARKANSAS LOUER 15.00 25.2000

4 CIMARRON UPPER 15.00 8.4000

5 CIUARRON MID 15.00 12.6000

6 CIMARRON LOUER 15.00 21.0000

7DAM AREA 4.00 8.4000

SEGUENT OBSERVED UATER QUALITY:

1.00 1.00 1.00

.000 .000 .000

1.00 1.00 1.00

.000 .000 .000

1.00 1.00 1.00

.000 .000 .000

1.00 1.00 1.00

.000 .000 .000

1.00 1.00 1.00

.000 .000 .000

1.00 1.00 1.00

.000 .000 .000

1.00 1.00 1.00

.000 .000 .000

ZMEAN

M

1.20

7.17

8.77

2.59

7.17

10.46

13.05

ZMIX

M

1.20/ .12

5.75/ .12

6.37/ .12

2.59/ .12

5.75/ .12

6.89/ .12

7.45/ .12

1.00 1.00

.000 .000

1.00 1.00

.000 .000

1.00 1.00

.000 .000

1.00 1.00

.000 .000

1.00 1.00

.000 .000

1.00 1.00

.000 .000

1.00 1.00

.000 .000

ZHYP

M

.00/ .00

.00/ .00

.00/ .00

.00/ .00

.00/ .00

.00/ .00

.00/ .00

1.000

.000

1.000

.000

1.000

.000

1.000

.000

1.000

.000

1.000

.000

1.000

.000

SEG TURBID CONSER TOTALP TOTALN CHL-A SECCHI ORG-N TP-OP HODV MODV

1 MN:.

2 %

Cv :

3 MN:

4 w .

5 &

Cv :

6 P!N:

Cv :

7 MN:

Cv :

I/u

3.45

.39

2.60

.40

2.43

.31

4.41

2:E -

.25

1.45

.30

1.91

.30

. . .

.ii

.0

.00

.0

.00

. i

.0

.00

. i

.0

● 00

14(X)EL COEFFICIENTS:

COEFFICIENT

DISPERSION FACTOR

P DECAY RATE

N DECAY RATE

CHL-A MCXIEL

SECCHI MCX)EL

ORGANIC N M(DEL

TP-OP HODEL

HOW MODEL

MODV MODEL

BETA lJ12/MG

MINIMUM QS

CHLA FLUSHING TE

CHLOROPHYLL-A CV

MG/M3 MG/H3

367.0 1575.0

.09 .15

.0 .0

.00 .00

149.0 1303.0

.14 .06

234.0 1077.0

.11 .12

130.0 1099.0

.15 .09

99.0 1079.0

.13 .10

145.0 1277.0

.18 .05

MEAN

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

.025

4.000

1.000

.620

.;

.45

.55

.26

.10

.12

.15

.15

.22

.00

.00

.00

.00

MG/M3

62.0

.62

.0

.00

2.8

.48

23.7

.53

7.2

.61

8.7

.44

3.6

.57

M

.2

.19

.0

.00

.;:

. i:

.4

.23

. i:

.5

.29

MG/M3

856.0

.14

.0

.00

523.0

.09

700.0

.06

573.0

.05

508.0

.07

453.0

.02

MG/M3 MG/M3-D MG/M3-D

250.0 .0 .0

.16 .00 .00

.0 .0 .0

.00 .00 .00

48.0 .0 .0

.22 .00 .00

148.0 .0 .0

.24 .00 .00

51.0 .0 .0

.16 .00 .00

37.0 .0 .0

.15 .00 .00

34.0 .0 .0

.50 .00 .00

CASE NOTES:

epa/nes data

4-64

Chapter4 BATHTUB
l’he listing of input values can be used to check and70r document the input

casejile. l’he listing should be checked against original data sources to

identlfi any dda-entry errors.

l%e listing is copied to a temporary diskfile and ajile viewing utility is

loaded. Function keys are identljied at the bottom of the screen. The user can

scroll forward or backward through the output listing by using the keypad

arrows. Xhe ~130meL’ key moves to the top of thejle. The c~33nd~,key moves

to the bottom of the$le. A Help screen related to the current output listing

can be viewed by pressing <~1’1~~.i’%elisting can be saved in a permanent

disk$le by pressing <3?8:’>.Pressing <l%sc>returns to the main menu. A

short summary of segment morphometric features can be viewed by selecting

Casdt-fo?pho:

CASE: Keystone Reservoir, Oklahoma

Segment Area Zmean

km2

1 ARKANSAS UPPER 8.40 1.2:

2 ARKANSAS MID 25.20 7.17

3 ARKANSAS LOUER 25.20 8.77

4 CIMARRON UPPER 8.40 2.59

5 CIMARRON HID 12.60 7.17

6 CIMARRON LOWER 21.00 10.46

7 DAM AREA 8.40 13.05

Total Area = 109.20 km2

Total Volune = 853.15 hti

Mean Depth = 7.81 m

Length

km

15.00

15.00

15.00

15.00

15.00

15.00

4.00

Volwll’

hm3

10.1

180.7

221.0

21.8

90.3

219.7

109.6

Uidth

km

.56

1.68

1.68

.56

.84

1.40

2.10

L/U

26.79

8.93

8.93

26.79

17.86

10.71

1.90

7his procedure summarizes input morphometric data for each segment. Average segment width is calculated as the ratio of surface area to segment length.

Total surface area, volume, and mean depth are also listed. The model can be

executed with a fill error analysis by selecting RunAWodeVAW

7 BATHTUB - VERSION 5.4

Case B410 List Plot Utilities Help Quit

l!ode~ Sensitivity

NoError Inputs Mode 1 ~

Error Analysis - Al 1 Input Variables and Model Parameters

The program jirst chech for invalid input values.

CHECKING INPUT VALUES . . .

INPUTS seem OK...

Chapter 4 BATHTUB 4-65
If input &ta errors are encountered or the mass-balance equations cannot be

solved, error messages are listed here and control returns to the main menu.

Otherwise, the error analysis proceeds:

WIT

ERROR ANALYSIS - SOLUTION AT ITERATION: 1696

TESTING X 1644/ 1696 ITERATIONS = 1

After completing the error analysis, control returns to the main menu. A

‘Model Ekecuted’ message appears in the lower right-hand corner of the

screen. l%is indicates that the execution was successji.d and the List and Plot

routines can be accessed to review results. Output screens and comments for

Listprocedures are given below. Menu screens are not repeated.

EYZ:’:’:’:”S-U::::;’’”;Z2 ‘a’’itsh”rt

Procedure: List / Hydraul

CASE: Keystone Reservoir, Oklahoma

HYDRAULIC AND DISPERSION PARAMETERS:

NET RESIDENCE OVERFLOU

lNFLOU TIME RATE

SEG OUT HM3/YR YRS M/YR

1 2 6989.60 .00144 832.1

2 3 7110.40 .02541 282.2

3 7 7088.20 .03118 281.3

45 3338.60 .00652 397.5

5 6 3372.50 .02679 267.7

6 7 3475.00 .06321 165.5

7 0 10555.80 .01038 1256.6

MEAN ----DISPERSION -----

VELOCITY ESTIMATED NUMERIC

KM/YR KM2/YR KM2/YR

10401.2 279864. 78009.

590.3 31846. 4427.

481.1 21914. 3608.

2301.8 32455. 17264.

560.0 7552. 4200.

237.3 6474. 1780.

385.2 19633. 770.

EXCHANGE

RATE

HM3/YR

9043.

22018.

17981.

1469.

1346.

4582.

0.

l%isoutputformat summarizessegment linkagesandjlows betweenmodel

segments. 7henetinj70w represents sum ofinjlows (external +outjlowfrom

upstream segments +precipitation) minus evaporation. Dispersion and

exchange rates are calculated according to the specljieddispersion model (see

Table 4.2). Numeric dispersion rates aresubtracted@om estimated dispersion

rates before calculating exchange flows. A40delsegmentation shouldbe

designed so that estimated dispersion exceeds numeric dispersion in each segment. Numeric dispersion rates can be reduced by decreasing segment

lengths. The exchange rate represents the dlyusive exchange-between each

segment (SEG) and its downstream segment (OUT).

Procedure: List / Balances / Gross

4-66

CASE: Keystone Reservoir, Oklahoma

GROSS UATER BALANCE:

DRAINAGE AREA ---- FL(NJ (HM3/YR) ---- RUNOF F

ID T LOCATION KM2 MEAN VARIANCE CV M/YR -------- -------- -------- -------- -------- -------- . . ------ -------- -------- ----

1 4 ARKANSAS OUTFLOU 162804.000 10556.000 .111E+07 .100 .065

2 1 ARKANSAS INFLOU 123625.000 6770.000 .458E+06 .100 .055

Chapter4 BATHTUB
3 1 HELLROARING 27.700 10.000 .1OOE+O1 .100 .361

4 1 CIMARRON 34929.000 2572.000 .662E+05 .100 .074

5 1 LAGOON 123.000 37.000 .137E+02 .100 .301

6 1 UNGAUGED-SEG 1 600.000 216.000 .187E+04 .200 .360

7 1 UNGAUGED-SEG 2 400.000 143.000 .818E+03 .200 .357

8 1 UNGAUGED-SEG 4 2440.000 736.000 .217E+05 .200 .302

9 1 UNGAUGED-SEG 5 150.000 45.000 .81OE+O2 .200 .300

10 1 UNGAUGED-SEG 6 400.000 120.000 .576E+03 .200 .300

11 3 CLEVELAND STPS .000 1.000 .400E-01 .200 .000

12 3 CIMARRON STPS .000 1.000 .400E-01 .200 .000

13 3 MANNFORD STP .000 1.000 .400E-01 .200 .000 - - - - - - -- - - - - - - - - - - - - - - - - - - - . . - - - - - - - - - - -- . - - - - - - - - - - - . - - - - - - - - - . - - - - - - - - - . . -

PRECIPITATION 109.200 137.800 .760E+03 .200 1.262

TRIBUTARY INFLOU 325389.400 10649.000 .550E+06 .070 .033

POINT-SWRCE INFLOU .000 3.000 .120E+O0 .115 .000

***TOTAL lMFLW 325498.600 10789.800 .550E+06 .069 .033

GAUGED WTFLOU 162804.000 10556.000 .IIIE+07 .100 .065

ADVECTIVE OUTFLOU 162694.600 -.201 .167E+07 9.990 .000

***ToTAL WTFLW 325498.600 10555.800 .555E+06 .071 .032 ***EvAp~ATI m .000 234.000 .493E+04 .300 .000 . . . - . . - . . -- . . . . . . . -- . . . . . - . . . . . . . . . . . --- . . . . . . . . . . . . - . . . . . . . . . . . - - - - - - --- - - -

GROSS MASS BALANCE BASED UPON ESTIMATED CONCENTRATIONS

C(MIPONENT: TOTAL P

----- LOADING ---- --- VARIANCE --- CONC EXPORT

ID T LOCATION KG/YR %(I) KG/YR**2 %(I) CV MG/M3 KG/KM2 . --- ------- -- -- - - --- . - ----- . - . . . ------- -- --- . . . . . ---- . . - - - - - - -- - - - - - - - - - - - - - - - .

1.4 ARKANSAS WTFLOU 1400865.0 31.4 .132E+12 40.9 .259 132.7 8.6

2 1 ARKANSAS INFLObJ 3337881.0 74.8 .305E+12 94.9 .166 493.0 27.0

3 1 HELLROARING 469.2 .0 .755E+04 .0 .185 46.9 16.9

4 1 CIMARRON 969155.3 21.7 .158E+11 4.9 .130 376.8 27.7

5 1 LAGOON 3402.5 .1 .475E+06 .0 .203 92.0 27.7

6 1 UNGAUGED-SEG 1 10134.7 .2 .134E+08 .0 .361 46.9 16.9

7 1 UNGAUGED-SEG 2 6709.6 .2 .585E+07 .0 .361 46.9 16.8

8 1 UNGAUGED-SEG 4 67682.6 1.5 .596E+09 .2 .361 92.0 27.7

9 1 UNGAUGED-SEG 5 4138.2 .1 .223E+07 .0 .361 92.0 27.6

10 1 UNGAUGED-SEG 6 11035.2 .2 .158E+08 .0 .361 92.0 27.6

11 3 CLEVELAND STPS 10249.1 .2 .420E+07 .0 .200 10249.1 .0

123 CIMARRON STPS 32229.9 .7 .416E+08 .0 .200 32229.9 .0

13 3 MANNFORD STP 2565.1 .1 .263E+06 .0 .200 2565.1 .0 ------- ------- ------ ------- . . . . . . ------- ------ . . . . . . . ------ ------ ------ ------ --

PRECIPITATION 4242.4 .1 .450E+07 .0 .500 30.8 38.8

TRIBUTARY INFLOU 4410608.0 98.9 .322E+12 100.0 .129 414.2 13.6

POINT-SWRCE INFL(.NJ 45044.1 1.0 .460E+08 .0 .151 15014.7 .0

***ToTAL INFLW 4459894.0 100.0 .322E+12 100.0 .127 413.3 13.7

GAUGED WTFLOU 1400865.0 31.4 .132E+12 40.9 .259 132.7 8.6

ADVECTIVE WTFLOU -26.6 .0 .296E+11 9.2 9.999 132.7 .0

***ToTAL WTFLW 1400839.0 31.4 .133E+12 41.2 .260 132.7 4.3

***RETENTI~ 3059056.0 68.6 .275E+12 85.6 .172 .0 .0 ------- --- . ---- ----- ----- .- . . . . -. ------- - - . . . . . . . ---- - . . - . - - - - - - - - - - - - - - - - - - - - .

HYDRAULIC -------------- TOTAL P . . . --- --- . -- - -

OVERFLCW RESIDENCE POOL RESIDENCE TURNOVER RETENTION

RATE TIME CONC TIME RATIO COEF

M/YR YRS MG/M3 YRS -

96.66 .0808 163.6 .0313 13.4246 .6859

l%eoutputformat summarizes thewater andmass balance calculations over

the entire reservoir. Resultsfor the TotalNbalance arenotshown. Results

arereviewedto ensure thatan accurate waterbalance has been established

andthatall drainage areashave been accountedfor before proceedingto

subsequentmodelingsteps. i%eoutput includesamean, variance, andCVfor

each water andmass balance term. In the case ofthe mass balance, loading

means andvariances are also expressed aspercentages ofthetotal injlow

mean andvariance, respectively. Xheseprovideperspectiveson predominant

loadinganderrorsources. Zhevariance distribution canbe usedtoprioritize

Chapter4 BATHTUB 4-67
fiture data collection efiorts by keying on the major sources of error (e.g., by

increasing sampling frequencies).

The tables also include hydrologic summary statistics (surface over~ow rate

and hydraulic residence time) and mass balance statistics (mass residence

time, turnover ratio, and retention coe~cien~. As discussed above, the mass

residence time and turnover ratio are used in selecting an appropriate averaging period for water and mass balance calculations.

In the case of the Keystone phosphorus balance, the turnover ratio is 13.4,

which means that phosphorus stored in the water column was displaced

approximately 13.4 times during the 5-month balance period based upon

observed pool phosphorus concentrations. 7his is a relatively favorable ratio

for mass balance modeling because it indicates that pool nutrient levels are

not likely to reflect loading conditions experienced prior to the mass balance

period. As discussed above, a turnover ratio of 2 or more is desirable for

modeling purposes.

Procedure: List / Balances / Detai led

SEGMENT BALANCE BASED UPON EST I MATED CONCENTRATEIONS

CWPONENT : TOTAL P SEGMENT : 3 ARKANSAS LOUER

--- FLOU --- --- LOAD --- CONC

ID T LOCATION HM3/YR % KG/YR x MG/M3 ------- ------- ------- ------- ------- ------- ------- . . . . . . . ------- ------- -.

------- ------- ------- ------- ------- ------- ------- ------- ------- ------- --

PRECIPITATION 31.80 .4 979.0 .1 30.8

ADVECT IVE I NFLOU 7110.40 99.6 1366361.0 73.5 192.2

NET DIFFUSIVE INFLOU .00 .0 492427.5 26.5 .0 *** ToTAL I MFL~ 7142.20 100.0 1859768.0 100.0 260.4

ADVECT IVE CNJTFLOU 7088.20 99.2 1085383.0 58.4 153.1

***TOTAL WTFLW 7088.20 99.2 1085383.0 58.4 153.1 ***EvApmAT10N 54.00 .8 .0 .0 .0

***Retention .00 .0 774385.1 41.6 .0

-------- -------- -------- -------- -------- . . . ----- -------- . ------- .---.---

RESID. TIME = .031 YRS, OVERFLOU RATE = 281.3 M/YR, DEPTH = 8.8 M

SEGMENT BALANCE BASED UPON ESTIMATED CONCENTRATIONS

COMPONENT: TOTAL N SEGMENT : 3 ARKANSAS LOUER

--- FLOU --- --- LOAD --- CONC

ID T LOCATION HM3/YR % KG/YR % MG/M3 ------- ------- ------- ------- ------ ------- ------ ------- ------ ------ ..----

-------- -------- ------- -------- -------- -------- -------- ------- ------- . . .

PRECIPITATION 31.80 .4 24822.0 .2 780.6

ADVECTIVE INFLW 7110.40 99.6 9592980.0 92.2 1349.1

NET DIFFUSIVE INFLOU .00 .0 791456.0 .0

***TOTAL lMFL~ 7142.20 100.0 10409260.0 10;:t 1457.4

ADVECTIVE OUTFLOU 7088.20 99.2 8937663.0 85.9 1260.9

***ToTAL WTFLW 7088.20 99.2 8937663.0 85.9 1260.9 ***EvApmAT1 m 54.00 .8 .0 .0 .0

***RETEMT1~ .00 .0 1471595.0 14.1 .0 -- ---- ----- --- . ---- . . ---- . . . . . . ------- --- . . . . . ------ . . . . . . . . . - - - - - - -- - - -

RESID. TIME = .031 YRS, OVERFLOU RATE = 281.3 M/YR, DEPTH = 8.8 M

Zhisoutputformat presents detailed water andmass balances bysegment.

Results areshown onlyforS’egment 3. Thesummaryincludesflow, load, and

mean concentrationfor each externalsource, discharge, andcomputedsummary term. The summary terms inch.de internal transfers (attributed toadvection andexchange with neighboring segments) aswell as external inputs,

Chapter4 BATHTUB
outflows, and retention. i%e advective outflow term for each segment is

derivedfiom thejlow balance.

Procedure: List / Balances / Smnary

CASE: Keystone Reservoir, Oklahoma

WATER BALANCE TERMS (HM3/YR):

-------- INFLOW -------- STORAGE --- OUTFLOW --- DOUNSTR

SEG EXTERNAL PRECIP ADVECT INCREASE AOVECT DISCH EXCHANGE EVAP

------- ------- ------- ------ . . . ---- ------- ------- ------- ------- ------ ------ .

1 .700E+04 .106E+O2 .000E+OO .000E+OO .699E+04 .000E+OO .904E+04 .180E+02

2 .143E+03 .318E+02 .699E+04 .000E+OO .711E+04 .000E+OO .220E+05 .540E+02

3 .000E+OO .318E+02 .711E+04 .000E+OO .709E+04 .000E+OO .180E+05 .540E+02

4 .335E+04 .106E+O2 .000E+OO .OOOE+OO .334E+04 .000E+OO .147E+04 .180E+02

5 .450E+02 .159E+02 .334E+04 .000E+OO .337E+04 .000E+OO .135E+04 .270E+02

6 .121E+03 .265E+02 .337E+04 .000E+OO .348E+04 .000E+OO .458E+04 .450E+02

7 .000E+OO .106E+O2 .I06E+05 .000E+OO-.201E+O0 .I06E+05 .000E+OO .180E+02 ------- ------- ------- ------- ------- ------- ------ ------ . . . . . . ------ ------ ---

NET .107E+O5 .138E+03 .000E+OO .000E+OO-.201E+O0 .I06E+05 .000E+OO .234E+03 ------- ---- ---- ----- ----- . . . -. . ------- . . . -. . . ---- - - - - - - - - - - . - . . . . . - - - - - . - - -

MASS BALANCE TERMS (KG/YR) FOR: TOTAL P BASED UPON ESTIMATED CONCS:

--------- INFLOWS -------- STORAGE ---- OUTFLOUS---- NET NET

SEG EXTERNAL ATMOSP ADVECT INCREASE ADVECT DISCH EXCHANGE RETENT

-------- -------- -------- . . ------ ------- . . . . . . . ------- . . . . . . . ------- ------- -

1 .336E+07 .326E+03 .000E+OO .000E+OO .216E+07 .000E+OO-.I06E+07 .144E+06

2 .671E+04 .979E+03 .216E+07 .000E+OO .137E+07 .000E+OO .196E+06 .997E+06

3 .000E+OO .979E+03 .137E+07 .000E+OO .109E+O7 .000E+OO .492E+06 .774E+06

4 .107E+O7 .326E+03 .000E+OO .000E+OO .779E+06 .000E+OO-.117E+06 .177E+06

5 .414E+04 .490E+03 .779E+06 .000E+OO .517E+06 .000E+OO .518E+05 .318E+06

6 .136E+05 .816E+03 .517E+06 .000E+OO .364E+06 .000E+OO .193E+06 .361E+06

7 .000E+OO .326E+03 .145E+07 .000E+OO-.266E+02 .115E+07 .239E+06 .539E+06 ------- ------- ------- ------ ------- ------- ------- ------ ------- -....- ------ --

NET .446E+07 .424E+04 .000E+OO .000E+OO-.266E+02 .115E+07 .000E+OO .331E+07 - - - - -- - - -- - - - . - - - - - - - - - - - - - - - - - - - - - - - - - . . . . . - - - - - . - . . . . . - - - - - - - - - . . - - . - - - - -

MASS BALANCE TERMS (KG/YR) FOR: TOTAL N BASED UPON ESTIMATED CONCS:

--------- INFLOW -------- STORAGE ---- CMJTFLOUS---- NET NET

SEG EXTERNAL ATMOSP ADVECT INCREASE ADVECT DISCH EXCHANGE RETENT . --- ---- --- . ---- . --- . . - ----- . - . . . . . ------- -- . . . . . - - - --- - - -- - - - . - - - - - - -- - - - -

1 .128E+08 .827E+04 .000E+OO .000E+OO .109E+O8 .000E+OO-.186E+07 .102E+O6

2 .169E+06 .248E+05 .109E+O8 .000E+OO .959E+07 .000E+OO-.871E+05 .138E+07

3 .000E+OO .248E+05 .959E+07 .000E+OO .894E+07 .000E+OO .791E+06 .147E+07

4 .464E+07 .827E+04 .000E+OO .000E+OO .431E+07 .000E+OO-.183E+06 .152E+06

5 .668E+05 .124E+05 .431E+07 .000E+OO .394E+07 .000E+OO .611E+05 .516E+06

6 .183E+06 .207E+05 .394E+07 .000E+OO .374E+07 .000E+OO .670E+06 .107E+O7

7 .000E+OO .827E+04 .127E+08 .000E+OO-.240E+03 .155E+08 .603E+06-.216E+07 . --- ------- - ---- . ----- . ------- - . . . . . . . . - ------- - - - - - - . - - . . . . . . - - - - - - - - - - - - -

NET .179E+08 .108E+O6 .000E+OO .000E+OO-.240E+03 .155E+08 .000E+OO .252E+07 . ---- ---- ------- - . ---- .- . . . ------ . - . . . -- - - . -. ---- - - - - - . . - . . - - . . - - - - - - - - - - - -

l%isisa condensedversion of the water andmass balances bysegment. S’ummary terms are presentedin tabIes thatdepict the routing ofwater andnutrientmass through the reservoir segments. Injlowterms include external

watershed loadings, atmospheric loadings, andadvectionfrom upstream segments. Outjlow terms includeadvection todownstream segmentsandspeci-

$edwithdrawals ordischarges. 7hewater balance alsoincludes storage,

evaporation, andgross dlf+siveexchange with downstream segments,

although the latter isnotafactor in thewaterbalance calculation because it

occurs in both directions. The mass balance tables also include storage,

Chapter4 BATHTUB 4-69
retention, and net exchange with adjacent (upstream and downstream)

segments. In the mass balances, the net exchange term isformulated as an

input (i.e., it will be positive or negative), depending upon whether dispersion

causes net transport of mass into or out of the segment, respectively.

Note that the advective outjlowfiom each segment is calculatedfiom the

water balance. If the computed advective outflowfiom any segment (except

those segments that discharge out of the system) is less than zero, the water

and balances are satis+ed by backjlowfiom downstream segments (i.e., the

direction of the advectiveflow at the corresponding segment interface is

reversed). 7his might occur, for example, for a segment in which the evaporation rate exceeds the sum of external in.ow and precipitation. The program

handles this condition by reversing the~ow direction. Solutions to waterbalance and mass-balance equations cannot be obtained lj’the net water

injlow for the entire reservoir (sum of injlows +precipitation - evaporation) is

negative.

In the last (near-dam) segment, the advective outjlow term of the water balance table represents the cumulative water balance error fthe reservoir discharge rate is specljled. In the Keystone example, a residual water balance

error of-O. 2 hm3/year is indicated. Since this is small relative to the gauged

outjlow (10,556 hm3/ year), the impact on the water and nutrient balance calculations is negligible. l%is water balance has been achieved by adjusting

flow rates specl~edfor ungauged drainage areas.

Procedure: List / Compar

CASE: Keystone Reservoir, Oklahoma

T STATISTICS COMPARE OBSERVED AND PREDICTED MEANS

USING THE FOLLOUING ERROR TERMS:

1 = OBSERVED UATER WALITY ERROR ONLY

2 = ERROR TYPICAL OF MODEL DEVELOPMENT DATA SET

3 = OBSERVED AND PREDICTED ERROR

SEGHENT : 1 ARKANSAS UPPER

OBSERVED ESTIMATED T STATISTICS

VARIABLE MEAN CV MEAN CV RAT 10 1 2 3 ------- ------- ------- ------- ------- ------- ------- ------- ------. ------- ---

TOTAL P UG/M3 367.0 .09 308.9 .25 1.19 1.91 .64 .64

TOTAL N HG/M3 1575.0 .15 1554.3 .19 1.01 .09 .06 .05

C. NUTRIENT #tG/M3 113.0 .14 109.4 .20 1.03 .24 .16 .13

CHL-A #!G/M3 62.0 .62 40.1 .36 1.55 .70 1.26 .61

SECCHI M .2 .19 .2 .29 .89 -.61 -.41 -.34

ORGAN I C N MG/M3 856.0 .14 1331.3 .25 .64 -3.15 -1.77 -1.53

TP-ORTHO-P MG/M3 250.0 .16 149.1 .25 1.68 3.23 1.41 1.73 ------- ------- ------- ------- ------- ------- ------- ------- ------- . . . . . . . ---

4-70

etc.. for segments 2-6

Chapter 4 BATHTUB
SEGMENT : 7 DAM AREA

OBSERVED ESTIMATED T STATISTICS

VARIABLE MEAN CV MEAN CV RAT 10 1 2 3

------ ------ ----- ----- ------ ------ ------ ----- . . . . . ------ ----- ----- ----- --

TOTAL P MG/M3 145.0 .18 132.7 .24 1.09 .49 .33 .30

TOTAL N MG/M3 1277.0 .05 1196.9 .17 1.07 1.30 .29 .37

C.NUTRIENT MG/M3 78.8 .10 72.9 .16 1.08 .77 .39 .42

CHL-A MG/M3 3.6 .57 5.5 .38 .65 -.74 -1.23 -.62

SECCH I M .5 .29 .5 .28 1.02 .08 .08 .06

ORGANIC N MG/M3 453.0 .02 426.2 .16 1.06 3.04 .24 .39

TP-ORTHO-P MG/M3 34.0 .50 51.0 .28 .67 -.81 -1.11 -.71 ------- ------- ------- ------ ------- ------ ------- ------ ------ ------- ------ -

SEGMENT : 8AREA-UTD MEAN

OBSERVED ESTIMATED T STATISTICS

VARIABLE HEAN CV MEAN CV RATIO 1 2 3 ------- ------- ------- ------ ------- ------- ------- ------ ------- ------ ------

TOTAL P MG/M3 163.6 .13 169.5 .17 .97 -.28 -.13 -.16

TOTAL N MG/lJ13 1218.4 .09 1255.2 .14 .97 -.33 -.14 -.18

C.NUTRIENT MG/M3 76.1 .11 80.1 .13 .95 -.47 -.25 -.30

CHL-A MG/M3 13.0 .56 9.6 .29 1.35 .53 .87 .47

SECCHI M .4 .28 .4 .16 1.03 .10 .10 .09

ORGANIC N MG/M3 570.8 .08 562.1 .16 1.02 .20 .06 .08

TP-ORTHO-P MG/M3 74.5 .20 71.3 .20 1.04 .21 .12 .15 ------- ------ ------- ------ ------- ------- ------- ------ ------- ------ ------ -

7%isformatcompares observedandpredicted water qualityconditions ineach

modelsegment. Itcanbe usedto testmodel applicability to reservoirs with

adequate water quality monitoring data. Area-weightedmeans across allreservoirsegments are also calculated andcompared. T-statistics compare

observedarui predictedmeans on logarithmic scales using three alternative

measures oferror:

a. l%e~rst testconsiders error inthe observed value only, asspecljied in

InputGroup IO. Iftheabsolute value ofthe T(l)is less than 2.O,the

observedmean is notsignl~cantly dl~ferentfiom thepredictedmean at

the 95-percentcon@ence level, given theprecision in the observed

mean value, which reflects variab ilityin the monitoring data andsamplingprogram design.

b. Zhesecondtest(supplementarytothe third) compares theerrorwith

thestandarderror estimatedfiom the modeldevelopment data setand

is independent ofthe observed andestimatedC Vs.

c. The thirdtestconsiders observedandpredicted CVsfor each case,

variable, andsegment. Iftheabsolute value ofT(3) exceeds2, the

dl~ference between theobservedand predictedmeansis greater than

expected(atthe 95-percent con@ence leve~, givenpotential errorsin

the observedwater qualitydata, model input data, andinherent model

errors.

Since deviationswould be expectedto occur by chance in5percent ofthe tests

applied to reservoirs conforming tothe mode[s, results ofthe T-tests should be

interpretedcautiously. Error terms usedin calculating T(2) and T(3) have

been calibratedfor predictingarea-weighted mean conditions; observed

versuspredicted deviations may begreaterfor station-meaner segment-mean

Chapter4 BATHTUB 4-71
values. In calculating the CVsfor area-weighted mean observed conditions,

the program attributes the major source of error to temporal variance and

assumes that the errors are correlated across stations. Note that comparisons

of area-weighted mean conditions are to be accurate only if sampling stations

are distributed throughout the reservoir. If data sets do not provide adequate

spatial coverage, the observe&predicted comparisons must be based upon

datafiom individual segments with suficient data.

Procedure: List / Diagnos

CASE: Keystone Reservoir, Oklahoma

OBSERVED AND PREDICTED DIAGNOSTIC VARIABLES

RANKED AGAINST CE MODEL DEVELOPMENT DATA SET

SEGMENT : 7 DAM AREA

----- VALUES ----- --- RANKS (%) ----

VARIABLE OBSERVED ESTIMATED OBSERVED ESTIMATED -------- -------- ------- . ------- ------- -------- . . . . . . . ---

TOTAL P MG/M3

TOTAL N MG/M3

C.NUTRIENT MG/M3

CHL-A MG/M3

SECCHI M

ORGANIC N MG/M3

TP-ORTHO-P MG/M3

ANTILOG PC-1

ANTILOG PC-2

(N - 150) / P

INORGANIC N / P

TURBIDITY 1/M

ZMIX * TURBIDITY

ZMIX / SECCHI

CHL-A * SECCHI

CHL-A / TOTAL P

FREQ(CHL-a>lO) %

FREQ(CHL-a>20) %

FREQ(CHL-a>30) %

FREQ(CHL-a>40) %

FREQ(CHL-a>50) %

FREQ(CHL-a>60) %

CARLSON TSI-P

CARLSON TSI-CHLA

CARLSON TSI-SEC

145.00

1277.00

78.83

3.60

.50

453.00

34.00

323.73

1.66

7.77

7.42

1.91

14.23

14.90

1.80

.02

2.51

.11

.01

.00

.00

.00

75.91

43.17

69.99

132.71

1196.90

72.90

5.50

.49

426.24

50.96

387.01

2.21

7.89

9.43

1.91

14.23

15.25

2.69

.04

10.13

.84

.12

.02

.01

.00

74.64

47.32

70.33

89.1

64.8

83.9

10.7

15.5

46.5

55.2

58.4

.5

12.5

8.2

90.3

97.4

97.5

.7

.1

.0

.0

.0

.0

.0

.0

.0

.0

.0

87.1

60.9

81.4

24.4

14.8

41.7

71.2

63.6

2.1

13.0

12.4

90.3

97.4

97.7

3.0

.7

.0

.0

.0

.0

.0

.0

.0

.0

.0 ------- ------- ------- ------ ------- ------- ------ ------ ---

Thisformatlists observed values, estimated values, anderror ratios andranks

them against the modeldevelopment data set. Approximate rankingsare cornputedfio mthegeometric meanandgeometric standarddeviation ofareaweightedmean observed values in the modeldevelopmen tdata setassuming a

log-normal distribution. Ehevariable listinchdesthebasicnet workvariables

plus nine composite variables that are usefulfordiagnosticpurposes. Diagnostic variables are usedto assess the relative importance ofphosphorus,

nitrogen, andlight as controllingfactors, as outlinedin Table 4.6.

4-72

Chapter4 BATHTUB
Procedure: List / Profiles

CASE: Keystone Reservoir, Oklahoma

PREDICTED CONCENTRATIONS:

VARIABLE SEGMENT--> 1 2 3 4 5 6

7 8 -------- -------- -------- ------- -------- -------- ------- -------- . . . ---- -..-.--

TOTAL P MG/M3 308.93 192.16 153.13 233.24 153.42 104.83

132.71 169.46

TOTAL N MG/H3 1554.32 1349.15 1260.92 1291.77 1167.48 1077.22

1196.90 1255.19

C.NUTRIENT MG/N3 109.44 88.66 79.22 88.10 74.21 62.20

72.90 80.07

CHL-A MG/M3 40.11 6.88 5.96 13.60 6.93 6.92

5.50 9.65

SECCH 1 M .22 .36 .39 .21 .40 .62

.49 .41

ORGANIC N MG/M3 1331.32 509.55 475.98 798.97 489.75 423.97

426.24 562.13

TP-ORTHO-P MG/t13 149.06 69.76 64.11 124.57 63.22 42.57

50.96 71.34 ------- --- . ---- - --- - - --- - - - - - - - ------- - - - - - - - - - - -- - - - - - - - - - - - - - - . - - - - - - . - - - -

7hisisa shortsummary ofpredictedconcentrations in each modelsegment.

Procedure: List / Flownet

SEGMENT NETUORK: FLOUS IN

*************** sE~ENT:

PRECIP AND EVAPORATION:

EXTERNAL INFLOU:

EXTERNAL INFLOU:

EXTERNAL INFLOU:

EXTERNAL INFLOU:

DISCHARGE TO SEGMENT:

*************** sE~ENT:

PRECIP AND EVAPORATION:

INFLW FROM SEGMENT:

EXTERNAL INFLOU:

DISCHARGE TO SEGMENT:

*************** sE~ENT:

PRECIP AND EVAPORATION:

INFLOU FROM SEGMENT:

DISCHARGE TO SEGMENT:

*************** sE~E)JT:

PRECIP AND EVAPORATION:

EXTERNAL INFLOU:

EXTERNAL INFLOU:

EXTERNAL INFLOU:

EXTERNAL INFLOU:

DISCHARGE TO SEGMENT:

*************** sE~E)JT:

PRECIP AND EVAPORATION:

INFLOU FROM SEGMENT:

EXTERNAL INFLOU:

DISCHARGE TO SEGMENT:

*************** sE~ENT:

PRECIP AND EVAPORATION:

INFLOU FROM SEGMENT:

EXTERNAL INFLOU:

HM3/YR

1 ARKANSAS UPPER

2 ARKANSAS INFLOW

3 HELLROARING

6 UNGAUGED-SEG 1

11 CLEVELAND STPS

2 ARKANSAS MID

2 ARKANSAS HID

1 ARKANSAS UPPER

7UNGAUGED-SEG 2

3 ARKANSAS LOUER

3 ARKANSAS LOUER

2 ARKANSAS MID

7DAM AREA

4 CIMARRON UPPER

4 CIMARRON

5 LAGOON

8 UNGAUGED-SEG 4

12 CIMARRON STPS

5 CIMARRON MID

5 CIMARRON MID

4 CIMARRON UPPER

9 UNGAUGED-SEG 5

6 CIMARRON LOUER

6 CI!4ARRON LWER

5 CIMARRON MID

10 UNGAUGED-SEG 6

lNFLOU

10.60

6770.00

10.00

216.00

1.00

INFLW

31.80

6989.60

143.00

INFLW

31.80

7110.40

INFLW

10.60

2572.00

37.00

736.00

1.00

INFLOU

15.90

3338.60

45.00

INFLW

26.50

3372.50

120.00

WTFLOU EXCHANGE

18.00

6989.60

OUTFLOU

54.00

7110.40

OUTFLOU

54.00

7088.20

WTFLOU

18.00

9043.10

EXCHANGE

9043.10

22018.01

EXCHANGE

22018.01

17980.92

EXCHANGE

3338.60 1468.88

OUTFLOU EXCHANGE

27.00

1468.88

3372.50 1346.13

WTFLW EXCHANGE

45.00

1346.13

Chapter4 BATHTUB 4-73
EXTERNAL INFLOU: 13 MANNFORD STP

DISCHARGE TO SEGMENT: 7DAM AREA

*************** SE~ENT: 7 DAM AREA

PRECIP AND EVAPORATION:

INFLOU FROM SEGMENT: 3 ARKANSAS LOUER

INFLOU FROM SEGMENT: 6 CIMARRON LOUER

OUTFLOU / UITHDRAUAL: 1 ARKANSAS OUTFLOU

DISCHARGE OUT OF SYSTEM:

1.00

3475.00 4582.44

INFLOU OUTFLOU EXCHANGE

10.60 18.00

7088.20 17980.92

3475.00 4582.44

10556.00

-.20

Z+isformatsummarizes thewater balancefor each segment. Inj70w, out@ow,

andexchange termsare listed. Zhisishelpfilfor checking segmenthributary

linkage against schematic diagrams such as Figure 4.9.

Procedure: List / Table

CASE: Keystone Reservoir, Oklahoma

TOTAL P MG/M3

TOTAL N MG/M3

CHL-A MG/M3

SECCH I M

Segment TOTAL P TOTAL N CHL-A SECCHI

1 ARKANSAS UPPER 308.93 1554.32 40.11 .22

2 ARKANSAS MID 192.16 1349.15 6.88 .36

3 ARKANSAS LOUER 153.13 1260.92 5.96 .39

4 CIMARRON UPPER 233.24 1291.77 13.60 .21

5 CIMARRON MID 153.42 1167.48 6.93 .40

6 CIMARRON LOUER 104.83 1077.22 6.92 .62

7 DAM AREA 132.71 1196.90 5.50 .49

8 AREA-UTD MEAN 169.46 1255.19 9.65 .41

User selects variables to be included from a list of all predicted variables.

Valuesfor TotalP, TotalN, Chla, andS’ecchi preselected in this example.

Procedure: List / Short

Keystone Reservoir, Oklahoma

SEGMENT = 1 ARKANSAS UPPER

CONSERVATIVE SUB= .0 TOTAL P MG/M3=

CHL-A MG/M3= 40.1 SECCHI M=

TP-ORTHO-P UG/M3= 149.1 HOD-V MG/M3-DAY=

C.NUTRIENT MG/M3= 109.4 ANTILOG PC-1

(N - 150) / P = 4.5 ZMIX * TURBIDITY=

CHL-A * SECCHI = 9.0 CHL-A / TOTAL P =

INORGANIC N / P = 1.4 FREQ(CHL-a>lO) %=

FREQ(CHL-a>30) %= 56.3 FREQ(CHL-a>40) %=

FREQ(CHL-a>.60) %= 16.9 CARLSON TSI-P =

CARLSON TSI-SEC = 81.5

SEGMENT = 4 CIMARRON UPPER

CONSERVATIVE SUB= .0 TOTAL P MG/M3=

CHL-A MG/M3= 13.6 SECCHI M=

TP-ORTHO-P MG/M3= 124.6 HOD-V MG/M3-DAY=

C.NUTRIENT MG/M3= 88.1 ANTILOG PC-1 =

(N - 150) /P = 4.9 ZMIX * TURBIDITY=

CHL-A * SECCHI = 2.9 CHL-A/ TOTAL P =

INORGANIC N / P = 4.S FREQ(CHL-a>lO) %=

FREQ(CHL-a>30) %= 5.6 FREQ(CHL-a>40) %=

FREQ(CHL-a>60) %= .3 CARLSON TSI-P =

CARLSON TSI-SEC = 82.4

308.9

.2

.0

3207.1

4.1

.1

97.3

38.0

86.8

233.2

.2

.0

1332.2

11.4

.1

57.4

2.0

82.8

TOTAL N MG/M3=

ORGANIC N MG/M3=

MOD-vMG/M3-DAY=

ANTILOG PC-2 =

ZMIX / SECCHI =

TURBIDITY I/M=

FREQ(CHL-a>20) %=

FREQ(CHL-a>50) %=

CARLSON TSI-CHLA=

TOTAL N MG/M3=

ORGANIC N MG/M3=

MW-V MG/M3-DAY=

ANTILOG PC-2 =

ZMIX / SECCHI =

TURBIDITY I/M=

FREQ(CHL-a>20) %=

FREQ(CHL-a>50) %=

CARLSON TSI-CHLA=

1554.3

1331.3

.0

5.7

5.3

3.4

79.2

25.3

66.8

1291.8

799.0

.0

2.5

12.3

4.4

17.6

.8

56.2

4-74

Chapter4 BATHTUB
SEGMENT z 7 DAM AREA

CONSERVATIVE SUB= .0

CHL-A UG/M3= 5.5

TP-ORTHO-P MG/M3= 51.0

C. NUTRIENT MG/M3= 72.9

(N - 150) / P = 7.9

CHL-A * SECCHI = 2.7

INORGANIC N / P = 9.4

FREQ(CHL-a>30) %= .1

FREQ(CHL-a>60) %= .0

CARLSON TSI-SEC = 70.3

TOTAL P MG/M3=

SECCHI M=

H~-V MG/M3-DAY=

ANTILOG PC-1

ZMIX * TURBIDITY:

CHL-A / TOTAL P =

FREQ(CHL-a>lO) %=

FREQ(CHL-a>40) %=

CARLSON TSI-P =

Procedure: Run / Sensitivity / Total P

PROFILE SENSITIVITY ANALYSIS FOR: TOTAL P

DECAY DISPERSION SEGMENT

FACTOR FACTOR 1 2 3 4

132.7

.5

.0

387.0

14.2

.0

10.1

.0

74.6

5

TOTAL N MG/M3=

ORGANIC N MG/M3=

McK)-v MG/M3-DAY=

ANTILOG PC-2 =

ZMIX / SECCHI =

TURBIDITY l/M=

FREQ(CHL-a>20) %=

FREQ(CHL-a>50) %=

CARLSON TSI-CHLA=

6 7 8

.50 .25 458.0 276.5 202.0 282.5 200.5 125.0 163.0 227.1

.50 1.00 339.2

.50 4.00 245.9

1.00 .25 439.0

1.00 1.00 308.9

1.00 4.00 207.1

2.00 .25 408.6

2.00 1.00 279.3

2.00 4.00 173.8

OBSERVED: 367.0

239.6

211.7

219.6

192.2

167.5

166.1

149.7

129.8

.0

203.2 259.6 193.8 148.8 181.8 213.2

199.5 214.6 188.8 176.8 191.6 200.8

144.6 257.0 157.1 86.3 111.8 180.9

153.1 233.2 153.4 104.8 132.7 169.5

153.8 181.3 148.2 131.4 145.7 157.6

98.0 223.8 115.7 56.4 72.5 139.4

110.7 202.8 115.4 70.1 92.4 131.1

115.2 151.5 113.2 94.0 107.1 121.0

149.0 234.0 130.0 99.0 145.0 163.6

1196.9

426.2

.0

2.2

15.3

1.9

.8

.0

47.3

Zhisprocedure tests the sensitivityanalysis ofpredictedconcentrations to

Iongitudinaldispersion anddecay (sedimentation) rates. These are twomajor

factors controlling theprediction ofspatial gradients inreservoirs. Dispersionrates are variedbyafactor of4, anddecayrates, byafactorof2, in

roughproportion to expected error magnitudesfor nutrient sedimentation

options lor2anddispersion optionl (Walker 1985). Generally, concentrationstendtobe more sensitiveto dispersion in upper-pool segments, where

dispersion accountsfordilution ofmajor injlows. Sensitivity todecayrateis

usuah’ygreater in near-dam segments, as comparedwith upper-pool segments.

Plotprocedures compare observedandpredicted concentrationsin each

modelsegment. Zhe PlotiSomeprocedureis demonstrated below:

Ei::pB ‘U:’’’’”;4 ‘e” ‘“it

SELECT VARIABLES TO BE PLOTTED

Chapter4 BATHTUB 4-75
VARIABLE

CONSERVATIVE SUB

TOTAL P MG/1113

TOTAL N MG/M3

CHL A MG/M3

SECCHI M

ORGANIC N MG/M3

TP-ORTHO-P MG/M3

HOD-V MG/M3-DAY

MCKI-V MG/M3-DAY

C.NUTRIENT MG/M3

ANTILOG PC-1

ANTILOG PC-2

(N - 150) / P

ZUIX * TURBIDITY

ZMIX / SECCHI

CHL A * SECCHI

CHL A / TOTAL P

TURBIDITY 1/M

PRESS <SPACE> TO SELECT(*) OR NO( ), <ENTER>=DONE, <a>= ALL, <n>=NONE

7_hesevariables areidenti~ed in Table 4.6. Zbelist extends below those listed

in thewindow; toseethe remainderofthe list, press ”-”Pglln ‘. For demonstrationpurposes, TotalP, TotalN, Chla, and Secchiare selectedbymoving

the cursor toeach jieldandpressing the+ptce’bar:

SELECT VARIABLES TO BE PLOTTED

VARIABLE

CONSERVATIVE SUB

* TOTAL P MG/M3

* TOTAL N MG/M3

* CHL A MG/M3

* SECCHI M

ORGANIC N MG/M3

TP-ORTHO-P MG/M3

H~-V MG/M3-DAY

Mm-v MG/M3-DAY

C.NUTRIENT MG/M3

ANTILOG PC-1

ANTILOG PC-2

(N - 150) / P

ZMIX * TURBIDITY

ZMIX / SECCHI

CHL A * SECCHI

CHL A / TOTAL P

TURBIDITY 1/M

PRESS <SPACE> TO SELECT(*) OR NO( ), <ENTER>=DONE, <a>= ALL, <n>=NONE

Plotformatis selected@om thefollowingchoices:

SELECT PLOT FORMAT

> OBS, EST VS. SEGMENT

OBSERVED VS. PREDICTED

OBS/PREDICTED RATIOS

ALL

4-76

Chapter4 BATHTUB
l%efirst format is selected for demonstration. i%is compares observed and

predicted concentrations by model segment. Solid symbols are mean values.

Vertical lines are mean &1 standard error. Plots that follow are in the same

order as the selected variable list.

TOTALP N(WI3

HEAN+/- 1 SThNl)f’iRDERROR

40[

N

1

.......................... I........................................................ T

..............................................................................................

I I I I I

1234 s

SEGtlENT

1

...............................................!

I I

7 8 9

TOTALN HG/H3

HEAN +/- 1 STONDRRD ERROR

b

1 I I I I I I I

1234 5678 9

SEGNENT

Chapter 4 BATHTUB 4-77
CHL-A H(YN3

c

H

L

fl

HEM +/- 1 SThNDflRD ERROR

lfq .............. ..................................................................................................................................

~:::::~i..c .........................................rl. .....................................!............................... ................................................. .................................................................................

t

1

1 ................................................!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .? ! T1

l~:~:~F~~::~E~::\,,,,,,,, ..........................................................fi........ ................. .......................................

—

F I ...........................................................................................................................

................................................................................................................................................. 1

1} I I I I 1 i 1 I

81234 678 9

SEGllEN:

■ ESTINATE x OBSERUED

SECCHI H

MEAN +/- 1 STftNDflRD ERROR

s

E

c

c

H

1

,1

.

.’

.,

............................................................!... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...............

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....

. . . . . . . . . . . . . . . . . . . . . ../ . . . . ..[ . . . . . . . . . . . . . . . . . ..[ . . . . . ..!...l..~..

...............................................

k [ ...............................................

-,1 I I I I I I [

01234 5678 9

SEGtlENT

= ESTIIMTE x OBSERUED

Select Quit to end the session.

BATHTUB - VERSION 5.4

List Plot Utilities Help w

4-78

Chapter4 BATHTUB
Input@les should be saved before quitting. Type ‘Y’or ‘y’to end session.

Ty~ any other key to return to menu.

Instructional Cases

The following hypothetical cases illustrate BATHTUB applications to predict among-reservoir or within-reservoir (spatial or temporal) variations in

trophic-state indicators. Each case is described by (a) a basic data sheet

showing the segmentation scheme and essential input data and (b) a listing of

BATHTUB input file (default option and model settings excluded). The following examples are presented:

case Se.gnmtatm. n Scheme

1 Single reservoir, spatially averaged

2 Single reservoir, spatially segmented

3 Reservoir embayment, spatially segmented

4 Single reservoir, spatially averaged, multiple scenario

5 Collection of reservoirs, spatially averaged

These simple cases can be used for training purposes or as templates for creating real applications. An input file for each case is supplied with the program.

The following procedure is suggested:

a.

b.

c.

d.

e.

f .

g.

Select application of interest from listings below.

Review basic data sheet.

Review listing of BATHTUB input values.

Start program, read case data file, and execute model.

List and review model output.

Plot observed and predicted variables.

Edit case data and rerun the model to evaluate sensitivity to loadings or

other input parameters of interest.

Chapter 4 BATHTUB 4-79
Basic data sheet for Case 1

Single reservoir, spatially averaged

c

B

Mass Balance Period: 1 October 1979 - 1 October 1980

Stream Monitoring Data:

Drainage Mean Flow-Ueighted

Area Flow Total P Concentration

W!3DIJLIJ.IL yQ2&CA 380

B 100 ‘ 300 167

c 50 150 167

D 570 1,430 (Not Measured)

Atmospheric total P load = 30 kg/km2-yr

Precipitation rate = 0.7 m/yr

Evaporation rate = 1.0 m/yr

Reservoir total volune = 704 hm3

Reservoir total surface area = 40 km2

Reservoir total length = 30 km

Reservoir surface elevation 1 Ott 1979 = 180.0 m

Reservoir surface elevation 1 Ott 1980 = 179.5 m

Observed pool water quality data: None

Listing of input values for Case 1

Single Reservoir, 1 Segment

ATMOSPHERIC LOADS & AVAILABILITY FACTORS:

ATMOSPHERIC-LOADS AVAILABILITY

VARIABLE KG/KM2-YR Cv FACTOR

1 CONSERV .00 .00 .00

2 TOTAL P 30.00 .50 1.00

3 TOTAL N 1000.00 .50 .59

4 ORTHO P 15.00 .50 .00

5 INORG N 500.00 .50 .79

GLOBAL INPUT VALUES:

PARAMETER MEAN Cv

PERIOD LENGTH YRS 1.000 .000

PRECIPITATION H .000 .200

EVAPORATION M .000 .300

INCREASE IN STORAGE M .000 .000

4-80

Chapter4 BATHTUB
TRIBUTARY DRAINAGE AREAS AND FLWS:

ID TYPE SEG NAME DRAINAGE AREA

KM2

11 1 stream a 380.000

21 1 stream b 100.000

31 1 stream c 50.000

44 1 outflou d 570.000

TRIBUTARY CONCENTRATIONS (PPB): MEAN/CV

ID CONSERV TOTAL P TOTAL N

1 .0/ .00 60.0/ .00 .0/ .00

.0/ .00 167.0/ .00 .0/ .00

: .0/ .00 167.0/ .00 .0/ .00

4 .0/ .00 .0/ .00 .0/ .00

MODEL SEGMENTS & CALIBRATION FACTORS:

MEAN FLOU CV OF MEAN FLOW

HM3/YR

1014.000 .000

300.000 .000

150.000 .000

1430.000 .000

ORTHO P INORG N

.0/ .00 .0/ .00

.0/ .00 .0/ .00

.0/ .00 .0/ .00

.0/ .00 .0/ .00

----------- CALIBRATION FACTORS ----- . . . . . -

SEG OUTFLOU GRWP SEGMENT NAME P SED N SED CHL-A SECCHI DISP

1 0 1 single 1.00 1.00 1.00 1.00 1!: 1.000

Cv: .000 .000 .000 .000 .000 .000

SEGMENT MORPHOMETRY: MEAN/CV

LENGTH AREA ZMEAN ZMIX ZHYP

ID LABEL KM KM2 M M M

1 single 30.00 40.0000 17.60 8.03/ .12 .00/ .00

SEGMENT OBSERVED HATER QUALITY:

SEG TURBID CONSER TOTALP TOTALN CHL-A SECCHI ORG-N TP-OP HODV MODV

l/M . . . MG/M3 MG/M3 MG/M3 M MG/M3 MG/M3 MG/M3-D MG/M3-D

1 MN: .10 .0 .0 .0 .0 .0 .0 .0 .0 .0

Cv : .00 .00 .00 .00 .00 .00 .00 .00 .00 .00

CASE NOTES:

single reservoir

spatially averaged

Basic data sheet for Case2

Single Reservoir, Spatially Segmented

c

B

D

Mass Balance Period: 1 October 1979 - 1 October 1980

Stream Monitoring Data: Same as CASE 1

Chapter4 BATHTUB 4-81
Segment Morphometry:

Surface Area Volune Length ~2 ++

Upper 8

Middle 16 256 10

Lower 16 384 10

Atmospheric total P load = 30 kg/km2-yr

Precipitation rate = 0.7 m/yr

Evaporation rate = 1.0 m/yr

Reservoir surface elevation 1 Ott 1979 = 180.0 m

Reservoir surface elevation 1 Ott 1980 = 179.5 m

Observed pool uater quality data: None

Listing of input values for Case2

1 Reservoir, 3 Segments

ATMOSPHERIC LOADS & AVAILABILITY FACTORS:

ATMOSPHERIC-LOADS AVAILABILITY

VARIABLE KG/KM2-YR Cv FACTOR

1 CONSERV .00 .00 .00

2 TOTAL P 30.00 .00 1.00

3 TOTAL N .00 .00 .00

4 ORTHO P .00 .00 .00

5 lNORGN .00 .00 .00

GLOBAL INPUT VALUES:

PARAHETER MEAN

PERI~ LENGTH YRS 1.000 . Oti

PRECIPITATION M .700 .000

EVAPORATION M 1.000 .000

INCREASE IN STORAGE M -.500 .000

TRIBUTARY DRAINAGE AREAS AND FLOWS:

ID TYPE SEG NAME DRAINAGE AREA MEAN FLOW CV OF MEAN FLOW

KM2 HM3/YR

11 1 Stream A 380.000 1014.000 .000

21 2 Stream B 100.000 300.000 .000

31 3 Stream C 50.000 150.000 .000

44 3 StreamD 570.000 1430.000 .000

TRIBUTARY CONCENTRATIONS (PPB): MEAN/CV

ID CONSERV TOTAL P TOTAL N ORTHO P INORG N

1 .0/ .00 60.0/ .00 .0/ .00 .0/ .00 .0/ .00

2 .0/ .00 167.0/ .00 .0/ .00 .0/ .00 .0/ .00

3 .0/ .00 167.0/ .00 .0/ .00 .0/ .00 .0/ .00

4 .0/ .00 .0/ .00 .0/ .00 .0/ .00 .0/ .00

MODEL SEGMENTS & CALIBRATION FACTORS:

----------- CALIBRATION FACTORS . - . . . --- - - -

SEG WTFLOW GRWP SEGMENT NAME P SED N SED CHL-A SECCHI HOD DISP

1 2 1 Upper Pool 1.00 1.00 1.00 1.00 1.00 1.000

Cv : .000 .000 .000 .000 .000 .000

2 3 1 Mid Pool 1.00 1.00 1.00 1.00 1.00 1.000

Cv : .000 .000 .000 .000 .000 .000

3 0 1 Near Dam 1.00 1.00 1.00 1.00 1.00 1.000

Cv : .000 .000 .000 .000 .000 .000

4-82

SEGUENT MORPHOMETRY: MEAN/CV

LENGTH AREA ZMEAN ZMIX ZHYP

ID LABEL KM KM2 M M M

1 Upper Pool 10.00 8.0000 8.00 6.09/ .12 .00/ .00

2 Hid Pool 10.00 16.0000 16.00 7.87/ .12 .00/ .00

3 Near Dam 10.00 16.0000 24.00 8.35/ .12 .00/ .00

Chapter4 BATHTUB
SEGMENT OBSERVED UATER QUALITY:

SEG TURBID CONSER TOTALP TOTALN

l/pl . . . MG/M3 MG/M3

1 MN: .00 .0 .0 .0

Cv : .00 .00 .00 .00

2 MN: .00 .0 .0 .0

Cv : .00 .00 .00 .00

3 MN: .00 .0 .0 .0

Cv : .00 .00 .00 .00

CHL-A SECCHI

MG/M3 M

.0 .0

.00 .00

.0 .0

.00 .00

.0 .0

.00 .00

CASE NOTES:

single reservoir

3 segments

Basic data sheet for Case3

Reservoir Enhyment, Spatially Segmented

ORG-N

MG/M3

.0

.00

.0

.00

.0

.00

TP-OP HODV MODV

MG/M3 MG/M3-D MG/M3-D

.0 .0 .0

.00 .00 .00

.0 .0 .0

.00 .00 .00

.0 .0 .0

.00 .00 .00

Mass Balance Period: 1 October 1979 - 1 October 1980

Stream Monitoring Data: Same as CASE 1

Segment Morphometry: Same as CASE 2

Estimated diffusive exchange with main reservoir = 2,000 hms/yr

Total P concentration in main reservoir = 15 mg/m3

Atmospheric total p load = 30 kg/km2-yr

Precipitation rate = 0.7m/yr

Evaporation rate = 1.0 m/yr

Reservoir surface elevation 1 Ott 1979 = 180.0 m

Reservoir surface elevation 1 Ott 1980 = 179.5 m

Observed pool water quality data: None

Listing of input values for Case3

Segmented Res. Enbayment

ATMOSPHERIC LOADS & AVAILABILITY FACTORS:

ATMOSPHERIC-LOADS AVAILABILITY

VARIABLE KG/KM2-YR FACTOR

1 CONSERV .00 .W .00

2 TOTAL P 30.00 .00 1.00

3 TOTAL N .00 .00 .00

Chapter4 BATHTUB 4-83
4 ORTHO P .00 .00 .00

5 INORG N .00 .00 .00

GLOBAL INPUT VALUES:

PARAMETER MEAN

PERIOD LENGTH YRS 1.000 .0:

PRECIPITATION M .700 .000

EVAPORATION M 1.000 .000

INCREASE IN STORAGE U -.500 .000

TRIBUTARY DRAINAGE AREAS AND FLOUS:

ID TYPE SEG NAME DRAINAGE AREA MEAN FLOU CV OF MEAN FLOU

HM3/YR

11 1 Stream A 380. z: 1014.000 .000

21 2 StreamB 100.000 300.000 .000

31 3 StreamC 50.000 150.000 .000

44 3 StreamD 570.000 1430.000 .000

56 3 Exchange .000 2000.000 .000

TRIBUTARY CONCENTRATIONS (PPB): MEAN/CV

ID CONSERV TOTAL P TOTAL N ORTHO P INORG N

1 .0/ .00 60.0/ .00 .0/ .00 .0/ .00 .0/ .00

2 .0/ .00 167.0/ .00 .0/ .00 .0/ .00 .0/ .00

3 .0/ .00 167.0/ .00 .0/ .00 .0/ .00 .0/ .00

4 .0/ .00 .0/ .00 .0/ .00 .0/ .00 .0/ .00

5 .0/ .00 15.0/ .00 .0/ .00 .0/ .00 .0/ .00

MODEL SEGMENTS & CALIBRATION FACTORS:

----------- CALIBRATION FACTORS ------ -----

SEG OUTFLOU GRWP SEGMENT NAME P SED N SED CHL-A SECCHI HOD DISP

1 2 1 Upper Pool 1.00 1.00 1.00 1.00 1.00 1.000

Cv : .000 .000 .000 .000 .000 .000

2 3 1 Mid Pool 1.00 1.00 1.00 1.00 1.00 1.000

Cv : .000 .000 .000 .000 .000 .000

3 0 1 Near Dam 1.00 1.00 1.00 1.00 1.00 1.000

Cv : .000 .000 .000 .000 .000 .000

SEGMENT MORPHOMETRY: MEAN/CV

LENGTH AREA ZMEAN ZMIX ZHYP

ID LABEL KM KM2 M M M

1 Upper Pool 10.00 8.0000 8.00 6.09/ .12 .00/ .00

2 Mid Pool 10.00 16.0000 16.00 7.87/ .12 .00/ .00

3 Near Dam 10.00 16.0000 24.00 8.35/ .12 .00/ .00

SEGMENT OBSERVED UATER QUALITY:

SEG TURBID CONSER TOTALP TOTALN

l/#1 . . . MG/M3 MG/M3

1 MN: .00 .0 .0 .0

Cv : .00 .00 .00 .00

2 MN: .00 .0 .0 .0

Cv : .00 .00 .00 .00

3 MN: .00 .0 .0 .0

Cv : .00 .00 .00 .00

CHL-A SECCHI

MG/M3 M

.0 .0

.00 .00

.0 .0

.00 .00

.0 .0

.00 .00

ORG-N

MG/M3

.0

.00

.0

.00

.0

.00

TP-OP HOOV MODV

MG/M3 MG/M3-D MG/M3-D

.0 .0 .0

.00 .00 .00

.0 .0 .0

.00 .00 .00

.0 .0 .0

.00 .00 .00

CASE NOTES:

single reservoir enbayment, spatially segmented

Tributary #5 (TYPE C(X)E=6) is used to specify exchange between last segment and

downstream reservoir area.

Basic data sheet for Case4

Single reservoir, Spatially Averaged, Multiple Load Scenario

Chapter4 BATHTUB
c

A 1980 CONDITIONS

Bc

1

A 1985 CONDITIONS

Bc

A r‘ 1990 CONDITIONS

B

Mass Balance Period: 1 yr

Stream Inflow Data:

Drainage

Area

-+

A

A 380

A 380

B 100

c 50

Mean

Flow

*

1:014

1,014

300

150

Flow-Ueighted

Total P Concentration

- Scena rio

1980 conditions

120 1985 conditions

180 1990 conditions

167 1980, 1985, 1990 conditions

167 1980, 1985, 1990 conditions

Atmospheric total P Load = 30 kg/km2-yr

Precipitation rate = 0.7 m/yr

Evaporation rate = 1.0 m/yr

Reservoir total volune = 704 hm3

Reservoir total surface area = 40 kmz

Reservoir total length = 30 km

Reservoir surface elevations constant

Listing of input values for Case 4

Single Reserv, 3 Scenarios

ATMOSPHERIC LOADS & AVAILABILITY FACTORS:

ATMOSPHERIC-LOADS AVAILABILITY

VARIABLE KG/KM2-YR Cv FACTOR

1 CONSERV .00 .00 .00

2 TOTAL P 30.00 .00 1.00

3 TOTAL N .00 .00 .00

4 ORTHOP .00 .00 .00

5 INORG N .00 .00 .00

GLOBAL INPUT VALUES:

PARAMETER MEAN Cv

PERIOD LENGTH YRS 1.000 .000

PRECIPITATION M .700 .000

Chapter4 BATHTUB 4-85
EVAPORATION M 1.000 .000

INCREASE IN STORAGE M .000 .000

TRIBUTARY DRAINAGE AREAS AND FLWS:

ID TYPE SEG NAME DRAINAGE AREA

KM2

11 1 Stream A 1980 380.000

21 1 Stream B 1980 100.000

31 1 Stream C 1980 50.000

41 2 Stream A 1985 380.000

51 2 StreamB 1985 100.000

61 2 StreamC 1985 50.000

71 3 Stream A 1990 380.000

81 3 StreamB 1990 100.000

91 3 StreamC 1990 50.000

TRIBUTARY CONCENTRATIONS (PPB): MEAN/CV

ID CONSERV TOTAL P TOTAL N

1 .0/ .00 60.0/ .00 .0/ .00

2 .0/ .00 167.0/ .00 .0/ .00

3 .0/ .00 167.0/ .00 .0/ .00

4 .0/ .00 120.0/ .00 .0/ .00

5 .0/ .00 167.0/ .00 .0/ .00

6 .0/ .00 167.0/ .00 .0/ .00

7 .0/ .00 180.0/ .00 .0/ .00

8 .0/ .00 167.0/ .00 .0/ .00

9 .0/ .00 167.0/ .00 .0/ .00

MODEL SEGMENTS & CALIBRATION FACTORS:

MEAN FLOU CV OF MEAN FLOU

HlJ13/YR

1014.000

300.000

150.000

1014.000

300.000

150.000

1014.000

300.000

150.000

ORTHO P

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.000

.000

.000

.000

.000

.000

.000

.000

.000

IN(IRG N

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

.0/ .00

----------- CALIBRATION FACTORS ------ -----

SEG WTFLOU GRWP SEGMENT NAME P SED N SED CHL-A SECCHI HOD DISP

1 0 1 1980 Conditions 1.00 1.00 1.00

Cv : .000 .000 .000

2 0 2 1985 Conditions 1.00 1.00 1.00

Cv : .000 .000 .000

3 0 3 1990 Conditions 1.00 1.00 1.00

Cv : .000 .000 .000

SEGMENT 140RPHOMETRY: MEAN/CV

LENGTH AREA ZMEAN ZMIX

ID LABEL KM2 M M

1 1980 Conditions 30.: 40.0000 17.60 8.03/ .12

2 1985 Conditions 30.00 40.0000 17.60 8.03/ .12

3 1990 Conditions 30.00 40.0000 17.60 8.03/ .12

SEGMENT OBSERVED UATER QUALITY: (none)

CASE NOTES:

single reservoir, spatially averaged

multiple load comparisons

each segment represents a different year

1.00 1.00 1.000

.000 .000 .000

1.00 1.00 1.000

.000 .000 .000

1.00 1.00 1.000

.000 .000 .000

ZHYP

M

.00/ .00

.00/ .00

.00/ .00

Basic data sheet for Case 5

Collection of Reservoirs, Spatially Averaged

4-86

Chapter4 BATHTUB
‘~ “’’’””’R’

‘~ ‘EsERvO’R2

c~ “’’’”0’”3

Mass Balance Period: 1 yr

Reservoir Morphometry:

Surface Area Volume Length

km2 -ADLm1 8

2 16 256 10

3 16 3a4 10

Stream Monitoring Data:

Drainage Mean Flow-Ueighted

Area Flow Total P Concentration

WSQIl+_ *-

A

B 100 ’300 167

c 50 150 167

Atmospheric total P load = 30 kg/km2-yr

Precipitation rate = 0.7 m/yr

Evaporation rate = 1.0 m/yr

Reservoir surface elevations constant

Listing of input values for Case 5

Collection of reservoirs

ATMOSPHERIC LOADS & AVAILABILITY FACTORS:

ATMOSPHERIC-LOADS AVAILABILITY

VARIABLE KG/KM2-YR Cv FACTOR

1 CONSERV .00 .00 .00

2 TOTAL P 30.00 .00 1.00

3 TOTAL N .00 .00 .00

4 ORTHO P .00 .00 .00

5 INORG N .00 .00 .00

Chapter4 BATHTUB 4-87
liLU6AL lNIWI VALUES:

PARAMETER MEAN

AVERAGING PERIOD YRS 1.000 .0%

PRECIPITATION METERS .700 .000

EVAPORATION METERS 1.000 .000

STORAGE INCREASE METERS .000 .000

TRIBUTARY DRAINAGE AREAS AND FLOWS:

ID TYPE SEG NAME DRAINAGE AREA

KM2

11 1 Stream A 380.000

21 2 Stream B 100.000

31 3 Stream C 50.000

TRIBUTARY CONCENTRATIONS (PPB): 14EAN/CV

ID CONSERV TOTAL P TOTAL N

1 .0/ .00 60.0/ .00 .0/ .00

2 .0/ .00 167.0/ .00 .0/ .00

3 .0/ .00 167.0/ .00 .0/ .00

~EL SEGMENTS & CALIBRATION FACTORS:------- . .

MEAN FLOW CV OF MEAN FLOU

HM3/YR

1014.000 .000

300.000 .000

150.000 .000

ORTHO P INORG N

.0/ .00 .0/ .00

.0/ .00 .0/ .00

.0/ .00 .0/ .00

-- CALIBRATION FACTORS --

SEG WTFLOU GROUP SEGMENT NAME P SED N SED CHL-A SECCHI HOD

1 0 1 Reservoir 1

2 0 2 Reservoir 2

3 0 3 Reservoir 3

SEGMENT MORPH@lETRY: MEAN/CV

LENGTH

ID LABEL

1 Reservoir 1 10.:

1.00 1.00 1.00

Cv : .000 .000 .000

1.00 1.00 1.00

Cv : .000 .000 .000

1.00 1.00 1.00

Cv : .000 .000 .000

AREA ZMEAN ZMIX

KM2 M M

8.0000 8.00 6.09/ .12

2 Reservoir 2 10.00 16.0000 16.00 7.87j .12

3 Reservoir 3 10.00 16.0000 24.00 8.35/ .12

SEGMENT OBSERVED UATER QUALITY:

SEG TURBID CONSER TOTALP TOTALN CHL-A SECCHI ORG-N

l/~ . . . MG/M3 MG/M3 MG/M3 M MG/M3

1 MN: .00 .0 .0 .0 .0 .0 .0

Cv : .00 .00 .00 .00 .00 .00 .00

2 MN: .00 .0 .0 .0 .0 .0

Cv : .00 .6: .00 .00 .00 .00 .00

3 MN: .00 .0 .0 .0 .0 .0 .0

Cv : .00 .00 .00 .00 .00 .00 .00

CASE NOTES:

collection of reservoirs

spatially averaged

1.00 1.00

.000 .000

1.00 1.00

.000 .000

1.00 1.00

.000 .000

ZHYP

M

.00/ .00

.00/ .00

.00/ .00

TP-OP HODV

----- -

DISP

1.000

.000

1.000

.000

1.000

.000

MODV

MG/M3 MG/M3-D MG/M3-D

.0 .0 .0

.00 .00 .00

.0 .0 .0

.00 .00 .00

.0 .0 .0

.00 .00 .00

4-88

Chapter4 BATHTUB
References

Bachman, R W. (1980). “Prediction of total nitrogen in lakes and reservoirs.”

Restoration of lakes and inland waters; Proceedings of an international

symposium on inland waters and lake restoration. Portkmd, Maine,

U.S. Environmental Protection Agency, OffIce of Water Regulations and

Standards, EPA-440/5-8 1-010, Washington, DC, 320-324.

Beale, E. M. L. (1962). “Some uses of computers in operational research,”

Industrielle Organization31, 51-52.

Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and u!ecision for civil engineers. McGraw-Hill, New York.

Bodo, B., and Umy, T. B. (1983). “Sampling strategies for mass-discharge

estimation,” Journal of the Engineering Division, American Society of

Civil Engineers 198(4), 812-829.

. (1984). “Errata: Sampling strategies for mass-discharge estimation,” Journal of the Environmental Engineering Division, American ,S’ocie~ of Civil Engineers 11O(4), 867-870.

Burden, R L., Faires, J. D., and Reynolds, A. C. (1981). Numerical analysis.

2d cd., Prindle, Weber, and Schmidt, Publishers, Boston, MA.

Canfield, D. E., and Bachman, R. W. (1981). “Prediction of total phosphorus

concentrations, chlorophyll-~ and Secchi depths in natural and artificial

hikes,” Canadian Journal for Fisheries and Aquatic ,$’ciences38(4),

414-423.

Carlson, R. E. (1977). “Atrophic state index for lakes,” Limnology and

Oceanography 22(2), 361-369.

Chapr~ S. C., and Reckhow, K. H. (1983). Engineering approaches for lake

management; Volume 2: Mechanistic modeling. Butterworth Publishers,

Boston, MA.

References R-1
Cochran, W. G. (1977). Sampling techniques. John Wiley and Sons, New

York.

Ficsher, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H.

(1979). Mixing in inland and coastal waters. Academic Press, New York.

International Joint Commission. (1977). Quality control handbook for pilot

watershed studies. International Reference Group on Great Lakes Pollution for Land Use Activities, Windsor, Ontario, Canada.

Jones, J. R., and Bachman, R. W. (1976), “Prediction of phosphorus and

chlorophyll levels in lakes,” J. Water Pollution Control Federation 48,

2176-2182.

Mosteller, F., and Tukey, J. W. (1978). Data analysis and regression -A

second course in statistics. Addison-Wesley, Reading, MA.

Snedecor, G. W., and Cochran, W. G. (1989). Statistical methods. 8th cd.,

Iowa State Universtiy Press, Ames, IA.

U.S. Army Engineer District, Buffalo. (1975). “Lake Erie wastewater management study: Prelimin~ feasibility report,” Buffalo, NY.

U.S. Environmental Protection Agency. (1975). National Eutrophication

Survey, Working Papers, Environmental Support Laboratory, Las Vegas,

NV.

Verhoff, F. H., Yaksich, S. M., and Melfi, D. A. (1980). “River nutrient and

chemical transport estimation,” Journal of the Environmental Engineering

Division, American Society of Civil Engineers 106(EE3),591 -608.

Vollenweider, R. A. (1976). “Advances in defting critical loading levels for

phosphorus in lake eutrophication,” A4em. Ist. Ital. Idrobiol 33,53-83.

Walker, W. W. (1980). “Analysis of water quality variations in reservoirs:

Implications for monitoring and modelling efforts.” Proceedings of the

symposium on surface water impoundments. Minneapolis, MN., H. G.

Stefan, cd., American Society of Civil Engineers, New York, 472-481.

. (198 1). “Empirical methods for predicting eutrophication in

impoundments; Report 1, Phase I: Data base development,” Technical

Report E-8 1-9, U.S. Army Engineer Waterways Experiment Station,

Vicksburg, MS.

R-2

References
Walker, W. W. (1982). “Empirical methods for predicting eutrophication in

impoundments; Report 2, Phase II: Model testing,” Technical Report

E-8 1-9, U.S. Army Engineer Waterways Experiment Station, Vicksburg,

MS.

. (1983). “Data analysis and model development for the Lake

Morey314 diagnostic study,” prepared for Vermont Agency of Environmental Conservation, Department of Water Resources, Lakes Program,

Montpelier, VT.

. (1984). “Empirical prediction of chlorophyll in reservoirs,”

Lake and reservoir management. U.S. Environmental Protection Agency,

Ofice of Water Regulation and Standards, EPA-440/5/84 -OOl, 292-297.

, (1985). “Empirical methods for predicting eutrophication in

impoundments; Report 3, Phase III: Model refinements,” Technical

Report E-8 1-9, U.S. Army Engineer Waterways Experiment Station,

Vicksburg, MS.

. (1987). “Empirical methods for predicting eutrophication in

impoundments; Report 4, Phase III: Applications manual,” Technical

Report E-8 1-9, U.S. Army Engineer Waterways Experiment Station,

Vicksburg, MS.

Westerdahl, H. E., Ford, W. B., Harris, J., and Lee, C. R. (1981). “Evaluation

of techniques to estimate annual water quality loadings to reservoirs,”

Technical Report E-8 1-1, U.S. Army Engineer Waterways Experiment

Station, Vicksburg, MS.

References R-3
Bibliography

CarlsoU R. E. (1977). Atrophic state index for lakes,” Limnolo~ and

Oceanography 22(2), 361-369.

LaBaugh, J. W., and Winter, T. C. (1981). “Preliminary total phosphorus

budgets of two Colorado reservoirs.” Proceedings of the symposium on

surface water impoundments. Minneapolis, MN, H. G. Stefan, ed.,

American Society of Civil Engineers, New York, 360-370.

Larsen, D. P., and Mercier, H. T. (1976). “Phosphorus retention capacity of

lakes,” L Fish. Res. Bd. Can. 33, 1742-1750.

Omernik, J. M. (1977). ‘Nonpoint source - stream nutrient level relationships:

A nationwide study,” EPA-600/3 -77-l 05, Corvallis Environmental

Research Laboratory, U.S, Environmental Protection Agency.

Organization for Economic Cooperation and Development. (1982). Eutrophication of waters - Monitoring, assessment, and control. Synthesis Report

of the OECD Cooperative Programme on Eutrophication, Paris, OECD

Publications, Washington, DC.

Rast, W., Jones, A., and Lee, G. F. (1983). “Predictive capability of

U.S. OECD phosphorus loading-eutrophication response models,” Journal

of the Water Pollution Control Federation, 55(7), 990-1003.

Reckhow, K. H., Beulac, M. N., and Simpson, J. T. (1980). “Modeling phosphorus loading and lake response under uncertainty: A manual and compilation of export coefhcients,” U.S. Environmental Protection Agency,

Clean Lakes Section.

Reckhow, K. H., and Chapr~ S. C. (1983). Engineering approaches for lake

management; Volume 1: Data analysis and empirical modeling. Butterworth Publishers, Boston, MA.

Sonzogni, W. C., Chapr~ S. C., Armstrong, D. E., and Logan, T. J. (1982).

“Bioavailability of phosphorus inputs to lakes,” Journal of Environmental

Quality 11(4), 555-562.

Bibliography B-1
StaufEer, R E. (1981). “Sampling strategies for estimating the magnitude and

importance of internal phosphorus supplies in lakes,” EPA-600/3 -81-O15,

Environmental Research Laboratory, U.S. Environmental Protection

Agency.

Taylor, W. D., Lambou, V. W., Williams, L. R., and Hem, S. C. (1980).

“Trophic state of lakes and reservoirs,” Technical Report E-80-3,

U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Vollenweider, R A. (1975). “Input-output models with special reference to

the phosphorus loading concept in limnology,” Schweitz. Z. Hydrol. 37,

53-84.

Walker, W. W. (1982a). “An empirical analysis of phosphorus, nitrogen, and

turbidity effects on reservoir chlorophyll-a levels,” Canadian Water

Resources Journal 7(1), 88-107.

. (1982b). “A sensitivity and error analysis framework for lake

eutrophication modeling,” Water Resources Bulletin 18(1), 53-61.

Winter, T. C. (1981). “Uncertainties in estimating the water balance of lakes,”

Water Research Bulletin 17, 82-115.

B-2

Bibliography
Appendix A

Installation

The programs require an IBM-compatible PC with at least a 286 processor,

a math co-processor, and 3 megabytes of disk storage. At least 530 kilobytes

of conventional memory must be available for the programs to run.

Installation is initiated by inserting the distribution diskette in an appropriate floppy drive and entering the following command:

>inst~l C:

Note that drives other than c: maybe substituted and that a parent directo~ can

be established (e.g., c:lmodels). The installation program creates destination

directories for each set of program files and installs files to appropriate directories. For instance, after issuing the command install c:, the following occurs:

FLUX files are installed in directory c:\flux

PROFILE files are installed in directory c:\profile

BATHTUB files are installed in directory c:\bathtub

Assistance in the acquisition and implementation of the software is available by contacting:

Dr. Robert H. Kennedy

Environmental Laboratory

USAE Waterways Experiment Station

3909 Halls Ferry Road

Vicksburg, MS 39180-6199

Phone: (601) 634-3659

Fax: (601) 634-3713

E-mail: webmaster(@limnos. wes.army.mil

Software and update messages are also available on the Internet:

http://limnos.wes. army.roil/software/

Appendix A Installation Al
Appendix B

Conversion Factors

To obtain values expressed in

units of Multiply units expreseed in By

Concentration grams/cubic meter (gm/m3) 1.000 x 103

milligrams/cubic meter (mg/m3) microgramsfliter @g/Q) 1.000

milligramsfliter (mg/Q) 1.000 x 103

parts/billion (ppb) 1.000

parts/million (ppm) 1.000 x 103

pounds/gallon (lb/gal) 1.198 X 108

Flow acre-foot/day (acre-ft/day) 4.502 X 10”1

cubic hectometers/year (hm3/year) cubic feet/second (ft3/s) 8.931 X 10”’

cubic meters/second (m3/s) 3.154 x 10’

million gallons/day (mgd) 1.382

Area acres (acres) 4.047 x 10-3

square kilometers (km*) hectares (ha) 1.000 x 10-2

square feet (ft2) 9.294 X 10-8

square meters (m*) 1.000 x 10-6

square miles 2.590

Depth feet (ft) 3.048 X 10“’

meters (m) inches (in.) 2.540 x 10-2

volume cubic meters (m3) 1.000 x 10-6

cubic hectometers (hm3) acre-foot (acre-ft) 0.1234 X 10-2

Appendix B Conversion Factors BI
REPORT DOCUMENTATION PAGE Form Approved

OMBNO. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data

sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding thta burden estimate or any other

aspect of thks collection of information, including suggestions for reducing this burden, to Washington Headquarters services, Directorate for Information Operations and Reporta,

1216 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington,

DC 20603.

1.A(3ENCY USE ONLY /Leave blank) 3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

~ ‘ins’repoti(up’~

Simplified Procedures for Eutrophication Assessment

and Prediction: User Manual

6. AUTHOR(S)

William W. Walker

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

REPORT NUMBER

1127 Lowell Road

Concord, MA 01742

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORINGIMONITORING

U.S. Army Corps of Engineers AGENCY REPORT NUMBER

Washington, DC 20314-1000;

U.S. Army Engineer Waterways Experiment Station Instruction Report W-96-

3909 Halls Ferry Road, Vicksburg, MS 39180-6199

11. SUPPLEMENTARY NOTES

Available from National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161.

A copy of the FLUX, PROFILE, and BATHTUB software is provided on the enclosed diskette.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

13. ABSTRACT (Maximum 200 words)

Eutrophication has several direct and indirect effects on reservoir water quality and uses. The report documents assessment procedures which have been developed for application to Corps of Engineers reservoirs. Study

phases include problem identification, data gathering, and model implementation. Three computer programs are

designed to assist in the last two phases:

a. FLUX-estimation of tributary nutrient loadings from grab-sample concentration data and continuous

flow records using a variety of calculation methods which permit quantification of potential errors and

evaluation of alternative sampling program designs.

b. PROFILE-display and reduction of pool water quality data, including calculation of hypolimnetic

oxygen depletion rates, characterization of spatial and temporal variability, and robust statistical

summary of mixed-layer concentration data.

c. BATHTUB—implementation of nutrient balance models and eutrophication response models in a

spatially segmented hydraulic network which accounts for advective transport, diffusive transport, and

nutrient sedimentation.

(Continued)

14. SUBJECT TERMS 15. NUMBER OF PAGES

Data analysis Eutrophication Reservoirs 235

Empirical model Nutrient loading Water quality 16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

OF REPORT OF THIS PAGE OF ABSTRACT

UNCLASSIFIED UNCLASSIFIED

..--. —----- -—--- -- NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. 239-18

298-102
13. (Concluded).

Eutrophication-related water quality conditions (expressed in terms of total phosphorus, total nitrogen,

chlorophyll a, transparency, organic nitrogen, particulate phosphorus, and hypolimnectic oxygen depletion rate)

are predicted using empirical relationships which have been calibrated and tested for reservoir applications. Based

upon research using several independent data sets, previous northern-lake-based empirical modeling approaches

have been modified to account for effects of (a) nonlinear nutrient sedimentation kinetics; (b) algae growth limitation by phosphorus, nitrogen, light, and flushing rate; (c) inflow nutrient partitioning (bioavailability of dissolved

versus particulate loadings); (d) seasonal variations in loadings and morphometry; and (e) spatial variations in

nutrients and related trophic state indicators.

To reflect input data limitations and inherent model errors, inputs and outputs can be expressed in probabilistic terms. The segmented model can be applied to single reservoirs (mixed or spatially segmented), partial

reservoirs (embayments, separate tributary arms), networks of reservoirs (hydrological y linked), or collections of

reservoirs (hydrologically independent). The last type of application permits regional comparative assessments of

reservoir conditions, controlling factors, and model performance. This instructional report describes use of PCDOS versions of the software and follows a four-report series describing database development, model testing,

model refinements, and application procedures for earlier versions of these programs.